%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP108^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:06:47 AM UTC 2026
% Result : Theorem 182.00s 111.32s
% Output : Refutation 184.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 249
% Syntax : Number of formulae : 871 ( 358 unt; 0 typ; 4 def)
% Number of atoms : 2709 (1528 equ; 3 cnn)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 31307 (1070 ~; 795 |; 19 &;28920 @)
% ( 0 <=>; 503 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Number of types : 6 ( 5 usr)
% Number of type conns : 54 ( 54 >; 0 *; 0 +; 0 <<)
% Number of symbols : 48 ( 44 usr; 19 con; 0-3 aty)
% Number of variables : 1404 ( 163 ^;1225 !; 12 ?;1404 :)
% ( 0 !>; 0 ?*; 0 @-; 4 @+)
% Comments :
%------------------------------------------------------------------------------
thf(partia1833973666xt_a_b_type,type,
partia1833973666xt_a_b: $tType ).
thf(product_prod_a_a_type,type,
product_prod_a_a: $tType ).
thf(set_a_type,type,
set_a: $tType ).
thf(int_type,type,
int: $tType ).
thf(a_type,type,
a: $tType ).
thf(a_l_coset_a_b_decl,type,
a_l_coset_a_b: partia1833973666xt_a_b > a > set_a > set_a ).
thf(additi2104487374up_a_b_decl,type,
additi2104487374up_a_b: set_a > partia1833973666xt_a_b > $o ).
thf(set_add_a_b_decl,type,
set_add_a_b: partia1833973666xt_a_b > set_a > set_a > set_a ).
thf(partia1066395285xt_a_b_decl,type,
partia1066395285xt_a_b: partia1833973666xt_a_b > set_a ).
thf(mult_a_ring_ext_a_b_decl,type,
mult_a_ring_ext_a_b: partia1833973666xt_a_b > a > a > a ).
thf(minus_minus_int_decl,type,
minus_minus_int: int > int > int ).
thf(minus_minus_set_a_decl,type,
minus_minus_set_a: set_a > set_a > set_a ).
thf(plus_plus_int_decl,type,
plus_plus_int: int > int > int ).
thf(uminus_uminus_int_decl,type,
uminus_uminus_int: int > int ).
thf(uminus_uminus_set_a_decl,type,
uminus_uminus_set_a: set_a > set_a ).
thf(locali1648887798ac_a_b_decl,type,
locali1648887798ac_a_b: partia1833973666xt_a_b > set_a > $o ).
thf(locali807230110ng_a_b_decl,type,
locali807230110ng_a_b: partia1833973666xt_a_b > set_a > $o ).
thf(locali880295127ng_a_b_decl,type,
locali880295127ng_a_b: partia1833973666xt_a_b > set_a > $o ).
thf(locali425460998xt_a_b_decl,type,
locali425460998xt_a_b: partia1833973666xt_a_b > set_a > $o ).
thf(bot_bot_set_a_decl,type,
bot_bot_set_a: set_a ).
thf(ord_less_eq_int_decl,type,
ord_less_eq_int: int > int > $o ).
thf(ord_less_eq_set_a_decl,type,
ord_less_eq_set_a: set_a > set_a > $o ).
thf(product_fst_a_a_decl,type,
product_fst_a_a: product_prod_a_a > a ).
thf(product_snd_a_a_decl,type,
product_snd_a_a: product_prod_a_a > a ).
thf(a_inv_a_b_decl,type,
a_inv_a_b: partia1833973666xt_a_b > a > a ).
thf(a_minus_a_b_decl,type,
a_minus_a_b: partia1833973666xt_a_b > a > a > a ).
thf(add_pow_a_b_int_decl,type,
add_pow_a_b_int: partia1833973666xt_a_b > int > a > a ).
thf(add_a_b_decl,type,
add_a_b: partia1833973666xt_a_b > a > a > a ).
thf(zero_a_b_decl,type,
zero_a_b: partia1833973666xt_a_b > a ).
thf(semiring_a_b_decl,type,
semiring_a_b: partia1833973666xt_a_b > $o ).
thf(collect_a_decl,type,
collect_a: ( a > $o ) > set_a ).
thf(member_a_decl,type,
member_a: a > set_a > $o ).
thf(r_decl,type,
r: partia1833973666xt_a_b ).
thf(s_decl,type,
s: set_a ).
thf(r2_decl,type,
r2: a ).
thf(r3_decl,type,
r3: a ).
thf(s2_decl,type,
s2: a ).
thf(s3_decl,type,
s3: a ).
thf(t_decl,type,
t: a ).
thf(t2_decl,type,
t2: a ).
thf(x_decl,type,
x: product_prod_a_a ).
thf(y_decl,type,
y: product_prod_a_a ).
thf(sk1_decl,type,
sk1: ( a > $o ) > ( a > $o ) > a ).
thf(sk2_decl,type,
sk2: set_a > a ).
thf(sk6_decl,type,
sk6: a ).
thf(sk15_decl,type,
sk15: a ).
thf(sk22_decl,type,
sk22: a ).
thf(sk23_decl,type,
sk23: a ).
thf(sk24_decl,type,
sk24: a ).
thf(sk1_def,definition,
( sk1
= ( ^ [A: a > $o,B: a > $o] :
@+[C: a] :
( ( B @ C )
!= ( A @ C ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( ^ [A: set_a] :
@+[B: a] : ( member_a @ B @ A ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( @+[A: a] :
~ ( ( member_a @ A @ s )
=> ( ( mult_a_ring_ext_a_b @ r @ A @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) )
!= ( zero_a_b @ r ) ) ) ) ) ).
thf(sk15_def,definition,
( sk15
= ( @+[A: a] :
~ ( ( member_a @ A @ s )
=> ( ( mult_a_ring_ext_a_b @ r @ A @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) )
!= ( zero_a_b @ r ) ) ) ) ) ).
thf(183,axiom,
! [A: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( member_a @ ( a_inv_a_b @ r @ A ) @ ( partia1066395285xt_a_b @ r ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_add_Oinv__closed) ).
thf(809,plain,
! [A: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( member_a @ ( a_inv_a_b @ r @ A ) @ ( partia1066395285xt_a_b @ r ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(126,axiom,
! [A: a,B: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( mult_a_ring_ext_a_b @ r @ A @ ( a_inv_a_b @ r @ B ) )
= ( a_inv_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_r__minus) ).
thf(629,plain,
! [A: a,B: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( mult_a_ring_ext_a_b @ r @ A @ ( a_inv_a_b @ r @ B ) )
= ( a_inv_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(19,axiom,
! [A: a,B: a > $o] :
( ( member_a @ A @ ( collect_a @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_mem__Collect__eq) ).
thf(295,plain,
! [A: a,B: a > $o] :
( ( member_a @ A @ ( collect_a @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(296,plain,
! [B: a > $o,A: a] :
( ( member_a @ A @ ( collect_a @ B ) )
= ( B @ A ) ),
inference(cnf,[status(esa)],[295]) ).
thf(297,plain,
! [B: a > $o,A: a] :
( ( member_a @ A @ ( collect_a @ B ) )
= ( B @ A ) ),
inference(lifteq,[status(thm)],[296]) ).
thf(223,axiom,
member_a @ t2 @ s,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_f4) ).
thf(910,plain,
member_a @ t2 @ s,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(9131,plain,
! [B: a > $o,A: a] :
( ( member_a @ A @ ( collect_a @ B ) )
| ( ( B @ A )
!= ( member_a @ t2 @ s ) ) ),
inference(paramod_ordered,[status(thm)],[297,910]) ).
thf(9273,plain,
( member_a @ t2
@ ( collect_a
@ ^ [A: a] : ( member_a @ A @ s ) ) ),
inference(pre_uni,[status(thm)],[9131:[bind(A,$thf( t2 )),bind(B,$thf( ^ [C: a] : ( member_a @ C @ s ) ))]]) ).
thf(81,axiom,
! [A: int,B: int,C: int] :
( ( ( minus_minus_int @ A @ B )
= C )
= ( A
= ( plus_plus_int @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_diff__eq__eq) ).
thf(479,plain,
! [A: int,B: int,C: int] :
( ( ( minus_minus_int @ A @ B )
= C )
= ( A
= ( plus_plus_int @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(38,axiom,
! [A: set_a] :
( ! [B: a] :
~ ( member_a @ B @ A )
=> ( A = bot_bot_set_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_equals0I) ).
thf(347,plain,
! [A: set_a] :
( ! [B: a] :
~ ( member_a @ B @ A )
=> ( A = bot_bot_set_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(9698,plain,
! [B: a > $o,A: a] :
( ( member_a @ A @ ( collect_a @ B ) )
| ( ( member_a @ t2
@ ( collect_a
@ ^ [C: a] : ( member_a @ C @ s ) ) )
!= ( B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9273,297]) ).
thf(9738,plain,
( member_a @ t2
@ ( collect_a
@ ^ [A: a] :
( member_a @ A
@ ( collect_a
@ ^ [B: a] : ( member_a @ B @ s ) ) ) ) ),
inference(pre_uni,[status(thm)],[9698:[bind(A,$thf( t2 )),bind(B,$thf( ^ [C: a] : ( member_a @ C @ ( collect_a @ ^ [D: a] : ( member_a @ D @ s ) ) ) ))]]) ).
thf(48,axiom,
! [A: a] :
~ ( member_a @ A @ bot_bot_set_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_emptyE) ).
thf(381,plain,
! [A: a] :
~ ( member_a @ A @ bot_bot_set_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(382,plain,
~ ? [A: a] : ( member_a @ A @ bot_bot_set_a ),
inference(miniscope,[status(thm)],[381]) ).
thf(383,plain,
! [A: a] :
~ ( member_a @ A @ bot_bot_set_a ),
inference(cnf,[status(esa)],[382]) ).
thf(14362,plain,
! [A: a] :
( ~ $true
| ( ( member_a @ t2
@ ( collect_a
@ ^ [B: a] :
( member_a @ B
@ ( collect_a
@ ^ [C: a] : ( member_a @ C @ s ) ) ) ) )
!= ( member_a @ A @ bot_bot_set_a ) ) ),
inference(paramod_ordered,[status(thm)],[9738,383]) ).
thf(14363,plain,
! [A: a] :
( ( member_a @ t2
@ ( collect_a
@ ^ [B: a] :
( member_a @ B
@ ( collect_a
@ ^ [C: a] : ( member_a @ C @ s ) ) ) ) )
!= ( member_a @ A @ bot_bot_set_a ) ),
inference(simp,[status(thm)],[14362]) ).
thf(14386,plain,
! [A: a] :
( ( t2 != A )
| ( ( collect_a
@ ^ [B: a] :
( member_a @ B
@ ( collect_a
@ ^ [C: a] : ( member_a @ C @ s ) ) ) )
!= bot_bot_set_a ) ),
inference(simp,[status(thm)],[14363]) ).
thf(14404,plain,
( ( collect_a
@ ^ [A: a] :
( member_a @ A
@ ( collect_a
@ ^ [B: a] : ( member_a @ B @ s ) ) ) )
!= bot_bot_set_a ),
inference(simp,[status(thm)],[14386]) ).
thf(216,axiom,
! [A: set_a,B: a,C: a] :
( ( ord_less_eq_set_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ C @ ( partia1066395285xt_a_b @ r ) )
=> ( ( a_l_coset_a_b @ r @ B @ ( a_l_coset_a_b @ r @ C @ A ) )
= ( a_l_coset_a_b @ r @ ( add_a_b @ r @ B @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_a__lcos__m__assoc) ).
thf(893,plain,
! [A: set_a,B: a,C: a] :
( ( ord_less_eq_set_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ C @ ( partia1066395285xt_a_b @ r ) )
=> ( ( a_l_coset_a_b @ r @ B @ ( a_l_coset_a_b @ r @ C @ A ) )
= ( a_l_coset_a_b @ r @ ( add_a_b @ r @ B @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(167,axiom,
member_a @ ( product_snd_a_a @ y ) @ ( partia1066395285xt_a_b @ r ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_f21) ).
thf(769,plain,
member_a @ ( product_snd_a_a @ y ) @ ( partia1066395285xt_a_b @ r ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(9181,plain,
! [B: a > $o,A: a] :
( ( member_a @ A @ ( collect_a @ B ) )
| ( ( B @ A )
!= ( member_a @ ( product_snd_a_a @ y ) @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[297,769]) ).
thf(9411,plain,
( member_a @ ( product_snd_a_a @ y )
@ ( collect_a
@ ^ [A: a] : ( member_a @ A @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(pre_uni,[status(thm)],[9181:[bind(A,$thf( product_snd_a_a @ y )),bind(B,$thf( ^ [C: a] : ( member_a @ C @ ( partia1066395285xt_a_b @ r ) ) ))]]) ).
thf(3,axiom,
! [A: int,B: int,C: int,D: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_eq_int @ C @ D )
=> ( ord_less_eq_int @ ( minus_minus_int @ A @ D ) @ ( minus_minus_int @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_diff__mono) ).
thf(249,plain,
! [A: int,B: int,C: int,D: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_eq_int @ C @ D )
=> ( ord_less_eq_int @ ( minus_minus_int @ A @ D ) @ ( minus_minus_int @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(33,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( plus_plus_int @ ( minus_minus_int @ B @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_le__add__diff__inverse2) ).
thf(333,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( plus_plus_int @ ( minus_minus_int @ B @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(125,axiom,
member_a @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( partia1066395285xt_a_b @ r ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_f41) ).
thf(628,plain,
member_a @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( partia1066395285xt_a_b @ r ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(145,axiom,
! [A: a,B: a,C: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ C @ ( partia1066395285xt_a_b @ r ) )
=> ( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ A @ B ) @ C )
= ( mult_a_ring_ext_a_b @ r @ A @ ( mult_a_ring_ext_a_b @ r @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_m__assoc) ).
thf(683,plain,
! [A: a,B: a,C: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ C @ ( partia1066395285xt_a_b @ r ) )
=> ( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ A @ B ) @ C )
= ( mult_a_ring_ext_a_b @ r @ A @ ( mult_a_ring_ext_a_b @ r @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(158,axiom,
! [A: product_prod_a_a,B: product_prod_a_a] :
( ( ( ( product_fst_a_a @ A )
= ( product_fst_a_a @ B ) )
& ( ( product_snd_a_a @ A )
= ( product_snd_a_a @ B ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_prod_Oexpand) ).
thf(730,plain,
! [A: product_prod_a_a,B: product_prod_a_a] :
( ( ( ( product_fst_a_a @ A )
= ( product_fst_a_a @ B ) )
& ( ( product_snd_a_a @ A )
= ( product_snd_a_a @ B ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(210,axiom,
member_a @ t @ ( partia1066395285xt_a_b @ r ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_f18) ).
thf(878,plain,
member_a @ t @ ( partia1066395285xt_a_b @ r ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(206,axiom,
member_a @ s3 @ ( partia1066395285xt_a_b @ r ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_f20) ).
thf(867,plain,
member_a @ s3 @ ( partia1066395285xt_a_b @ r ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(104,axiom,
! [A: a,B: a,C: a] :
( ( ( add_a_b @ r @ A @ B )
= ( zero_a_b @ r ) )
=> ( ( ( add_a_b @ r @ B @ C )
= ( zero_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ C @ ( partia1066395285xt_a_b @ r ) )
=> ( A = C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_local_Ominus__unique) ).
thf(561,plain,
! [A: a,B: a,C: a] :
( ( ( add_a_b @ r @ A @ B )
= ( zero_a_b @ r ) )
=> ( ( ( add_a_b @ r @ B @ C )
= ( zero_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ C @ ( partia1066395285xt_a_b @ r ) )
=> ( A = C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(562,plain,
! [A: a,B: a] :
( ( ( add_a_b @ r @ A @ B )
= ( zero_a_b @ r ) )
=> ! [C: a] :
( ( ( add_a_b @ r @ B @ C )
= ( zero_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ C @ ( partia1066395285xt_a_b @ r ) )
=> ( A = C ) ) ) ) ) ),
inference(miniscope,[status(thm)],[561]) ).
thf(563,plain,
! [C: a,B: a,A: a] :
( ( ( add_a_b @ r @ A @ B )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ B @ C )
!= ( zero_a_b @ r ) )
| ~ ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
| ~ ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
| ~ ( member_a @ C @ ( partia1066395285xt_a_b @ r ) )
| ( A = C ) ),
inference(cnf,[status(esa)],[562]) ).
thf(564,plain,
! [C: a,B: a,A: a] :
( ( ( add_a_b @ r @ A @ B )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ B @ C )
!= ( zero_a_b @ r ) )
| ( A = C )
| ~ ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
| ~ ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
| ~ ( member_a @ C @ ( partia1066395285xt_a_b @ r ) ) ),
inference(lifteq,[status(thm)],[563]) ).
thf(1,conjecture,
( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(247,plain,
( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(248,plain,
( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) ) ),
inference(lifteq,[status(thm)],[247]) ).
thf(1182,plain,
! [C: a,B: a,A: a] :
( ( ( add_a_b @ r @ A @ B )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ B @ C )
!= ( zero_a_b @ r ) )
| ~ ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
| ~ ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
| ~ ( member_a @ C @ ( partia1066395285xt_a_b @ r ) )
| ( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ A )
!= ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) ) )
| ( C
!= ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[564,248]) ).
thf(1183,plain,
! [B: a,A: a] :
( ( ( add_a_b @ r @ A @ B )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ B @ ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( zero_a_b @ r ) )
| ~ ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
| ~ ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
| ~ ( member_a @ ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) @ ( partia1066395285xt_a_b @ r ) )
| ( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ A )
!= ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[1182:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ))]]) ).
thf(1306,plain,
! [B: a,A: a] :
( ( ( add_a_b @ r @ A @ B )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ B @ ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( zero_a_b @ r ) )
| ~ $true
| ~ ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
| ~ ( member_a @ ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) @ ( partia1066395285xt_a_b @ r ) )
| ( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ A )
!= ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) ) )
| ( ( member_a @ t @ ( partia1066395285xt_a_b @ r ) )
!= ( member_a @ B @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[878,1183]) ).
thf(1307,plain,
! [B: a,A: a] :
( ( ( add_a_b @ r @ A @ B )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ B @ ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( zero_a_b @ r ) )
| ~ ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
| ~ ( member_a @ ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) @ ( partia1066395285xt_a_b @ r ) )
| ( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ A )
!= ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) ) )
| ( ( member_a @ t @ ( partia1066395285xt_a_b @ r ) )
!= ( member_a @ B @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(simp,[status(thm)],[1306]) ).
thf(1308,plain,
! [A: a] :
( ( ( add_a_b @ r @ A @ t )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ t @ ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( zero_a_b @ r ) )
| ~ ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
| ~ ( member_a @ ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) @ ( partia1066395285xt_a_b @ r ) )
| ( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ A )
!= ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[1307:[bind(A,$thf( A )),bind(B,$thf( t ))]]) ).
thf(1610,plain,
! [A: a] :
( ( ( add_a_b @ r @ A @ t )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ t @ ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( zero_a_b @ r ) )
| ~ $true
| ~ ( member_a @ ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) @ ( partia1066395285xt_a_b @ r ) )
| ( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ A )
!= ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) ) )
| ( ( member_a @ t @ ( partia1066395285xt_a_b @ r ) )
!= ( member_a @ A @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[878,1308]) ).
thf(1611,plain,
! [A: a] :
( ( ( add_a_b @ r @ A @ t )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ t @ ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( zero_a_b @ r ) )
| ~ ( member_a @ ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) @ ( partia1066395285xt_a_b @ r ) )
| ( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ A )
!= ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) ) )
| ( ( member_a @ t @ ( partia1066395285xt_a_b @ r ) )
!= ( member_a @ A @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(simp,[status(thm)],[1610]) ).
thf(1612,plain,
( ( ( add_a_b @ r @ t @ t )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ t @ ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( zero_a_b @ r ) )
| ~ ( member_a @ ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) ) ),
inference(pattern_uni,[status(thm)],[1611:[bind(A,$thf( t ))]]) ).
thf(2113,plain,
( ( ( add_a_b @ r @ t @ t )
!= ( zero_a_b @ r ) )
| ~ ( member_a @ ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ t @ ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( add_a_b @ r @ t @ t ) )
| ( ( zero_a_b @ r )
!= ( zero_a_b @ r ) ) ),
inference(eqfactor_ordered,[status(thm)],[1612]) ).
thf(2121,plain,
( ( ( add_a_b @ r @ t @ t )
!= ( zero_a_b @ r ) )
| ~ ( member_a @ ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( r != r )
| ( t != t )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t ) ),
inference(simp,[status(thm)],[2113]) ).
thf(2128,plain,
( ( ( add_a_b @ r @ t @ t )
!= ( zero_a_b @ r ) )
| ~ ( member_a @ ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t ) ),
inference(simp,[status(thm)],[2121]) ).
thf(2268,plain,
( ( ( add_a_b @ r @ t @ t )
!= ( zero_a_b @ r ) )
| ~ $true
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( member_a @ ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) @ ( partia1066395285xt_a_b @ r ) )
!= ( member_a @ t @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[878,2128]) ).
thf(2269,plain,
( ( ( add_a_b @ r @ t @ t )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( member_a @ ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) @ ( partia1066395285xt_a_b @ r ) )
!= ( member_a @ t @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(simp,[status(thm)],[2268]) ).
thf(2490,plain,
( ( ( add_a_b @ r @ t @ t )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( partia1066395285xt_a_b @ r )
!= ( partia1066395285xt_a_b @ r ) ) ),
inference(simp,[status(thm)],[2269]) ).
thf(2510,plain,
( ( ( add_a_b @ r @ t @ t )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t ) ),
inference(simp,[status(thm)],[2490]) ).
thf(2514,plain,
! [C: a,B: a,A: a] :
( ( ( add_a_b @ r @ A @ B )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ B @ C )
!= ( zero_a_b @ r ) )
| ~ ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
| ~ ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
| ~ ( member_a @ C @ ( partia1066395285xt_a_b @ r ) )
| ( C
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( A
!= ( add_a_b @ r @ t @ t ) ) ),
inference(paramod_ordered,[status(thm)],[564,2510]) ).
thf(2515,plain,
! [B: a,A: a] :
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ A )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ A @ B )
!= ( zero_a_b @ r ) )
| ~ ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
| ~ ( member_a @ ( add_a_b @ r @ t @ t ) @ ( partia1066395285xt_a_b @ r ) )
| ~ ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
| ( B
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t ) ),
inference(pattern_uni,[status(thm)],[2514:[bind(A,$thf( add_a_b @ r @ t @ t )),bind(B,$thf( B )),bind(C,$thf( C ))]]) ).
thf(2651,plain,
! [A: a] :
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ A )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ A @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ~ ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
| ~ ( member_a @ ( add_a_b @ r @ t @ t ) @ ( partia1066395285xt_a_b @ r ) )
| ~ ( member_a @ ( zero_a_b @ r ) @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t ) ),
inference(simp,[status(thm)],[2515]) ).
thf(163,axiom,
member_a @ ( zero_a_b @ r ) @ ( partia1066395285xt_a_b @ r ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_zero__closed) ).
thf(758,plain,
member_a @ ( zero_a_b @ r ) @ ( partia1066395285xt_a_b @ r ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(2695,plain,
! [A: a] :
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ A )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ A @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ~ ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
| ~ ( member_a @ ( add_a_b @ r @ t @ t ) @ ( partia1066395285xt_a_b @ r ) )
| ~ $true
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t ) ),
inference(rewrite,[status(thm)],[2651,758]) ).
thf(2696,plain,
! [A: a] :
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ A )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ A @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ~ ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
| ~ ( member_a @ ( add_a_b @ r @ t @ t ) @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t ) ),
inference(simp,[status(thm)],[2695]) ).
thf(2711,plain,
! [A: a] :
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ A )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ A @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ~ $true
| ~ ( member_a @ ( add_a_b @ r @ t @ t ) @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( member_a @ s3 @ ( partia1066395285xt_a_b @ r ) )
!= ( member_a @ A @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[867,2696]) ).
thf(2712,plain,
! [A: a] :
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ A )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ A @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ~ ( member_a @ ( add_a_b @ r @ t @ t ) @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( member_a @ s3 @ ( partia1066395285xt_a_b @ r ) )
!= ( member_a @ A @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(simp,[status(thm)],[2711]) ).
thf(2713,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ s3 )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ s3 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ~ ( member_a @ ( add_a_b @ r @ t @ t ) @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t ) ),
inference(pattern_uni,[status(thm)],[2712:[bind(A,$thf( s3 ))]]) ).
thf(6650,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ s3 )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ s3 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ~ $true
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( member_a @ ( add_a_b @ r @ t @ t ) @ ( partia1066395285xt_a_b @ r ) )
!= ( member_a @ t @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[878,2713]) ).
thf(6651,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ s3 )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ s3 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( member_a @ ( add_a_b @ r @ t @ t ) @ ( partia1066395285xt_a_b @ r ) )
!= ( member_a @ t @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(simp,[status(thm)],[6650]) ).
thf(6863,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ s3 )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ s3 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( add_a_b @ r @ t @ t )
!= t )
| ( ( partia1066395285xt_a_b @ r )
!= ( partia1066395285xt_a_b @ r ) ) ),
inference(simp,[status(thm)],[6651]) ).
thf(6883,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ s3 )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ s3 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( add_a_b @ r @ t @ t )
!= t ) ),
inference(simp,[status(thm)],[6863]) ).
thf(240,axiom,
semiring_a_b @ r,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_local_Osemiring__axioms) ).
thf(959,plain,
semiring_a_b @ r,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(9189,plain,
! [B: a > $o,A: a] :
( ( member_a @ A @ ( collect_a @ B ) )
| ( ( semiring_a_b @ r )
!= ( B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[959,297]) ).
thf(9420,plain,
! [A: a] :
( member_a @ A
@ ( collect_a
@ ^ [B: a] : ( semiring_a_b @ r ) ) ),
inference(pre_uni,[status(thm)],[9189:[bind(A,$thf( A )),bind(B,$thf( ^ [C: a] : ( semiring_a_b @ r ) ))]]) ).
thf(18101,plain,
! [A: a] :
( member_a @ A
@ ( collect_a
@ ^ [B: a] : $true ) ),
inference(rewrite,[status(thm)],[9420,959]) ).
thf(14,axiom,
! [A: set_a] :
( ( collect_a
@ ^ [B: a] : ( member_a @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_Collect__mem__eq) ).
thf(281,plain,
! [A: set_a] :
( ( collect_a
@ ^ [B: a] : ( member_a @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(282,plain,
! [A: set_a] :
( ( collect_a
@ ^ [B: a] : ( member_a @ B @ A ) )
= A ),
inference(cnf,[status(esa)],[281]) ).
thf(283,plain,
! [A: set_a] :
( ( collect_a
@ ^ [B: a] : ( member_a @ B @ A ) )
= A ),
inference(lifteq,[status(thm)],[282]) ).
thf(191,axiom,
member_a @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ s,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_f8) ).
thf(833,plain,
member_a @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ s,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(98,axiom,
! [A: set_a] :
( ( minus_minus_set_a @ A @ A )
= bot_bot_set_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_Diff__cancel) ).
thf(539,plain,
! [A: set_a] :
( ( minus_minus_set_a @ A @ A )
= bot_bot_set_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(540,plain,
! [A: set_a] :
( ( minus_minus_set_a @ A @ A )
= bot_bot_set_a ),
inference(cnf,[status(esa)],[539]) ).
thf(541,plain,
! [A: set_a] :
( ( minus_minus_set_a @ A @ A )
= bot_bot_set_a ),
inference(lifteq,[status(thm)],[540]) ).
thf(5518,plain,
! [B: set_a,A: set_a] :
( ( ( collect_a
@ ^ [C: a] : ( member_a @ C @ A ) )
= bot_bot_set_a )
| ( A
!= ( minus_minus_set_a @ B @ B ) ) ),
inference(paramod_ordered,[status(thm)],[283,541]) ).
thf(5519,plain,
! [A: set_a] :
( ( collect_a
@ ^ [B: a] : ( member_a @ B @ ( minus_minus_set_a @ A @ A ) ) )
= bot_bot_set_a ),
inference(pattern_uni,[status(thm)],[5518:[bind(A,$thf( minus_minus_set_a @ D @ D )),bind(B,$thf( D ))]]) ).
thf(5520,plain,
! [A: set_a] :
( ( collect_a
@ ^ [B: a] : ( member_a @ B @ ( minus_minus_set_a @ A @ A ) ) )
= bot_bot_set_a ),
inference(simp,[status(thm)],[5519]) ).
thf(46,axiom,
! [A: a > $o] :
( ( ( collect_a @ A )
= bot_bot_set_a )
= ( ! [B: a] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_Collect__empty__eq) ).
thf(375,plain,
! [A: a > $o] :
( ( ( collect_a @ A )
= bot_bot_set_a )
= ( ! [B: a] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(376,plain,
! [A: a > $o] :
( ( ( collect_a @ A )
= bot_bot_set_a )
= ( ! [B: a] :
~ ( A @ B ) ) ),
inference(cnf,[status(esa)],[375]) ).
thf(377,plain,
! [A: a > $o] :
( ( ( collect_a @ A )
= bot_bot_set_a )
= ( ! [B: a] :
~ ( A @ B ) ) ),
inference(lifteq,[status(thm)],[376]) ).
thf(6500,plain,
! [B: a > $o,A: set_a] :
( ( ( bot_bot_set_a = bot_bot_set_a )
= ( ! [C: a] :
~ ( B @ C ) ) )
| ( ( collect_a
@ ^ [C: a] : ( member_a @ C @ ( minus_minus_set_a @ A @ A ) ) )
!= ( collect_a @ B ) ) ),
inference(paramod_ordered,[status(thm)],[5520,377]) ).
thf(6501,plain,
! [B: a > $o,A: set_a] :
( ! [C: a] :
~ ( B @ C )
| ( ( collect_a
@ ^ [C: a] : ( member_a @ C @ ( minus_minus_set_a @ A @ A ) ) )
!= ( collect_a @ B ) ) ),
inference(simp,[status(thm)],[6500]) ).
thf(6502,plain,
! [A: set_a,B: a] :
~ ( member_a @ B @ ( minus_minus_set_a @ A @ A ) ),
inference(pattern_uni,[status(thm)],[6501:[bind(A,$thf( A )),bind(B,$thf( ^ [C: a] : ( member_a @ C @ ( minus_minus_set_a @ A @ A ) ) ))]]) ).
thf(6511,plain,
! [B: a,A: set_a] :
~ ( member_a @ B @ ( minus_minus_set_a @ A @ A ) ),
inference(cnf,[status(esa)],[6502]) ).
thf(6555,plain,
! [B: a,A: set_a] :
( ~ $true
| ( ( member_a @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ s )
!= ( member_a @ B @ ( minus_minus_set_a @ A @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[833,6511]) ).
thf(6556,plain,
! [B: a,A: set_a] :
( ( member_a @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ s )
!= ( member_a @ B @ ( minus_minus_set_a @ A @ A ) ) ),
inference(simp,[status(thm)],[6555]) ).
thf(6566,plain,
! [B: a,A: set_a] :
( ( ( mult_a_ring_ext_a_b @ r @ t2 @ t )
!= B )
| ( ( minus_minus_set_a @ A @ A )
!= s ) ),
inference(simp,[status(thm)],[6556]) ).
thf(6591,plain,
! [A: set_a] :
( ( minus_minus_set_a @ A @ A )
!= s ),
inference(simp,[status(thm)],[6566]) ).
thf(6617,plain,
! [B: set_a,A: set_a] :
( ( ( collect_a
@ ^ [C: a] : ( member_a @ C @ A ) )
!= s )
| ( A
!= ( minus_minus_set_a @ B @ B ) ) ),
inference(paramod_ordered,[status(thm)],[283,6591]) ).
thf(6618,plain,
! [A: set_a] :
( ( collect_a
@ ^ [B: a] : ( member_a @ B @ ( minus_minus_set_a @ A @ A ) ) )
!= s ),
inference(pattern_uni,[status(thm)],[6617:[bind(A,$thf( minus_minus_set_a @ D @ D )),bind(B,$thf( D ))]]) ).
thf(6619,plain,
! [A: set_a] :
( ( collect_a
@ ^ [B: a] : ( member_a @ B @ ( minus_minus_set_a @ A @ A ) ) )
!= s ),
inference(simp,[status(thm)],[6618]) ).
thf(161,axiom,
! [A: a,B: a] :
( ( member_a @ A @ s )
=> ( ( member_a @ B @ s )
=> ( member_a @ ( mult_a_ring_ext_a_b @ r @ A @ B ) @ s ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_m__closed) ).
thf(741,plain,
! [A: a,B: a] :
( ( member_a @ A @ s )
=> ( ( member_a @ B @ s )
=> ( member_a @ ( mult_a_ring_ext_a_b @ r @ A @ B ) @ s ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(204,axiom,
( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) )
= ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_f34) ).
thf(861,plain,
( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) )
= ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(58,axiom,
( plus_plus_int
= ( ^ [A: int,B: int] : ( plus_plus_int @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_add_Ocommute) ).
thf(408,plain,
( plus_plus_int
= ( ^ [A: int,B: int] : ( plus_plus_int @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(409,plain,
( plus_plus_int
= ( ^ [A: int,B: int] : ( plus_plus_int @ B @ A ) ) ),
inference(lifteq,[status(thm)],[408]) ).
thf(977,plain,
! [A: int] :
( ( plus_plus_int @ A )
= ( ^ [B: int] : ( plus_plus_int @ B @ A ) ) ),
inference(func_ext,[status(esa)],[409]) ).
thf(94,axiom,
! [A: set_a,B: set_a,C: a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_subsetD) ).
thf(523,plain,
! [A: set_a,B: set_a,C: a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(109,axiom,
member_a @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( partia1066395285xt_a_b @ r ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_f15) ).
thf(582,plain,
member_a @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( partia1066395285xt_a_b @ r ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(136,axiom,
! [A: a,B: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( add_a_b @ r @ A @ ( add_a_b @ r @ ( a_inv_a_b @ r @ A ) @ B ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_r__neg2) ).
thf(655,plain,
! [A: a,B: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( add_a_b @ r @ A @ ( add_a_b @ r @ ( a_inv_a_b @ r @ A ) @ B ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(120,axiom,
( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) )
= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ t2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_f23) ).
thf(614,plain,
( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) )
= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ t2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(10,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
= ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_minus__le__iff) ).
thf(269,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
= ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(41,axiom,
! [A: set_a] :
( ( minus_minus_set_a @ bot_bot_set_a @ A )
= bot_bot_set_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_empty__Diff) ).
thf(357,plain,
! [A: set_a] :
( ( minus_minus_set_a @ bot_bot_set_a @ A )
= bot_bot_set_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(358,plain,
! [A: set_a] :
( ( minus_minus_set_a @ bot_bot_set_a @ A )
= bot_bot_set_a ),
inference(cnf,[status(esa)],[357]) ).
thf(359,plain,
! [A: set_a] :
( ( minus_minus_set_a @ bot_bot_set_a @ A )
= bot_bot_set_a ),
inference(lifteq,[status(thm)],[358]) ).
thf(4754,plain,
! [B: set_a,A: set_a] :
( ( ( collect_a
@ ^ [C: a] : ( member_a @ C @ A ) )
= bot_bot_set_a )
| ( A
!= ( minus_minus_set_a @ bot_bot_set_a @ B ) ) ),
inference(paramod_ordered,[status(thm)],[283,359]) ).
thf(4755,plain,
! [A: set_a] :
( ( collect_a
@ ^ [B: a] : ( member_a @ B @ ( minus_minus_set_a @ bot_bot_set_a @ A ) ) )
= bot_bot_set_a ),
inference(pattern_uni,[status(thm)],[4754:[bind(A,$thf( minus_minus_set_a @ bot_bot_set_a @ D )),bind(B,$thf( D ))]]) ).
thf(4771,plain,
! [A: set_a] :
( ( collect_a
@ ^ [B: a] : ( member_a @ B @ ( minus_minus_set_a @ bot_bot_set_a @ A ) ) )
= bot_bot_set_a ),
inference(simp,[status(thm)],[4755]) ).
thf(4772,plain,
( ( collect_a
@ ^ [A: a] : ( member_a @ A @ bot_bot_set_a ) )
= bot_bot_set_a ),
inference(rewrite,[status(thm)],[4771,359]) ).
thf(14422,plain,
( ( bot_bot_set_a != bot_bot_set_a )
| ( ( collect_a
@ ^ [A: a] :
( member_a @ A
@ ( collect_a
@ ^ [B: a] : ( member_a @ B @ s ) ) ) )
!= ( collect_a
@ ^ [A: a] : ( member_a @ A @ bot_bot_set_a ) ) ) ),
inference(paramod_ordered,[status(thm)],[4772,14404]) ).
thf(14423,plain,
( ( collect_a
@ ^ [A: a] :
( member_a @ A
@ ( collect_a
@ ^ [B: a] : ( member_a @ B @ s ) ) ) )
!= ( collect_a
@ ^ [A: a] : ( member_a @ A @ bot_bot_set_a ) ) ),
inference(simp,[status(thm)],[14422]) ).
thf(14435,plain,
( ( ^ [A: a] :
( member_a @ A
@ ( collect_a
@ ^ [B: a] : ( member_a @ B @ s ) ) ) )
!= ( ^ [A: a] : ( member_a @ A @ bot_bot_set_a ) ) ),
inference(simp,[status(thm)],[14423]) ).
thf(14441,plain,
( ( ^ [A: a] :
( member_a @ A
@ ( collect_a
@ ^ [B: a] : ( member_a @ B @ s ) ) ) )
!= ( ^ [A: a] : $false ) ),
inference(rewrite,[status(thm)],[14435,383]) ).
thf(49,axiom,
! [A: set_a] : ( ord_less_eq_set_a @ bot_bot_set_a @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_empty__subsetI) ).
thf(384,plain,
! [A: set_a] : ( ord_less_eq_set_a @ bot_bot_set_a @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(218,axiom,
member_a @ t2 @ ( partia1066395285xt_a_b @ r ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_f17) ).
thf(901,plain,
member_a @ t2 @ ( partia1066395285xt_a_b @ r ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(139,axiom,
member_a @ s2 @ ( partia1066395285xt_a_b @ r ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_f19) ).
thf(668,plain,
member_a @ s2 @ ( partia1066395285xt_a_b @ r ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(2739,plain,
! [A: a] :
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ A )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ A @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ~ $true
| ~ ( member_a @ ( add_a_b @ r @ t @ t ) @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( member_a @ s2 @ ( partia1066395285xt_a_b @ r ) )
!= ( member_a @ A @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[668,2696]) ).
thf(2740,plain,
! [A: a] :
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ A )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ A @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ~ ( member_a @ ( add_a_b @ r @ t @ t ) @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( member_a @ s2 @ ( partia1066395285xt_a_b @ r ) )
!= ( member_a @ A @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(simp,[status(thm)],[2739]) ).
thf(2741,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ s2 )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ s2 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ~ ( member_a @ ( add_a_b @ r @ t @ t ) @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t ) ),
inference(pattern_uni,[status(thm)],[2740:[bind(A,$thf( s2 ))]]) ).
thf(14580,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ s2 )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ s2 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ~ $true
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( member_a @ ( add_a_b @ r @ t @ t ) @ ( partia1066395285xt_a_b @ r ) )
!= ( member_a @ t2 @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[901,2741]) ).
thf(14581,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ s2 )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ s2 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( member_a @ ( add_a_b @ r @ t @ t ) @ ( partia1066395285xt_a_b @ r ) )
!= ( member_a @ t2 @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(simp,[status(thm)],[14580]) ).
thf(14817,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ s2 )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ s2 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( add_a_b @ r @ t @ t )
!= t2 )
| ( ( partia1066395285xt_a_b @ r )
!= ( partia1066395285xt_a_b @ r ) ) ),
inference(simp,[status(thm)],[14581]) ).
thf(14856,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ s2 )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ s2 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( add_a_b @ r @ t @ t )
!= t2 ) ),
inference(simp,[status(thm)],[14817]) ).
thf(185,axiom,
! [A: a,B: a,C: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ C @ ( partia1066395285xt_a_b @ r ) )
=> ( ( ( add_a_b @ r @ B @ A )
= ( add_a_b @ r @ C @ A ) )
= ( B = C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_local_Oadd_Oright__cancel) ).
thf(814,plain,
! [A: a,B: a,C: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ C @ ( partia1066395285xt_a_b @ r ) )
=> ( ( ( add_a_b @ r @ B @ A )
= ( add_a_b @ r @ C @ A ) )
= ( B = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(231,axiom,
! [A: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( ( a_inv_a_b @ r @ A )
= ( zero_a_b @ r ) )
= ( A
= ( zero_a_b @ r ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_add_Oinv__eq__1__iff) ).
thf(930,plain,
! [A: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( ( a_inv_a_b @ r @ A )
= ( zero_a_b @ r ) )
= ( A
= ( zero_a_b @ r ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(152,axiom,
! [A: a,B: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( add_a_b @ r @ A @ B )
= ( add_a_b @ r @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_add_Om__comm) ).
thf(709,plain,
! [A: a,B: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( add_a_b @ r @ A @ B )
= ( add_a_b @ r @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(196,axiom,
member_a @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) ) @ ( partia1066395285xt_a_b @ r ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_f39) ).
thf(841,plain,
member_a @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) ) @ ( partia1066395285xt_a_b @ r ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(246,axiom,
! [A: a,B: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( a_inv_a_b @ r @ ( add_a_b @ r @ A @ B ) )
= ( add_a_b @ r @ ( a_inv_a_b @ r @ A ) @ ( a_inv_a_b @ r @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_local_Ominus__add) ).
thf(973,plain,
! [A: a,B: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( a_inv_a_b @ r @ ( add_a_b @ r @ A @ B ) )
= ( add_a_b @ r @ ( a_inv_a_b @ r @ A ) @ ( a_inv_a_b @ r @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(16,axiom,
! [A: a > $o,B: a > $o] :
( ! [C: a] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect_a @ A )
= ( collect_a @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_Collect__cong) ).
thf(286,plain,
! [A: a > $o,B: a > $o] :
( ! [C: a] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect_a @ A )
= ( collect_a @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(287,plain,
! [B: a > $o,A: a > $o] :
( ( ( A @ ( sk1 @ B @ A ) )
!= ( B @ ( sk1 @ B @ A ) ) )
| ( ( collect_a @ A )
= ( collect_a @ B ) ) ),
inference(cnf,[status(esa)],[286]) ).
thf(288,plain,
! [B: a > $o,A: a > $o] :
( ( ( A @ ( sk1 @ B @ A ) )
!= ( B @ ( sk1 @ B @ A ) ) )
| ( ( collect_a @ A )
= ( collect_a @ B ) ) ),
inference(lifteq,[status(thm)],[287]) ).
thf(21,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_add__left__mono) ).
thf(301,plain,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(190,axiom,
! [A: a,B: a,C: a] :
( ( ( add_a_b @ r @ A @ B )
= C )
=> ( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ C @ ( partia1066395285xt_a_b @ r ) )
=> ( ( add_a_b @ r @ ( a_inv_a_b @ r @ A ) @ C )
= B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_a__transpose__inv) ).
thf(829,plain,
! [A: a,B: a,C: a] :
( ( ( add_a_b @ r @ A @ B )
= C )
=> ( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ C @ ( partia1066395285xt_a_b @ r ) )
=> ( ( add_a_b @ r @ ( a_inv_a_b @ r @ A ) @ C )
= B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(56,axiom,
! [A: a > $o] :
( ( bot_bot_set_a
= ( collect_a @ A ) )
= ( ! [B: a] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_empty__Collect__eq) ).
thf(402,plain,
! [A: a > $o] :
( ( bot_bot_set_a
= ( collect_a @ A ) )
= ( ! [B: a] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(403,plain,
! [A: a > $o] :
( ( bot_bot_set_a
= ( collect_a @ A ) )
= ( ! [B: a] :
~ ( A @ B ) ) ),
inference(cnf,[status(esa)],[402]) ).
thf(404,plain,
! [A: a > $o] :
( ( bot_bot_set_a
= ( collect_a @ A ) )
= ( ! [B: a] :
~ ( A @ B ) ) ),
inference(lifteq,[status(thm)],[403]) ).
thf(27,axiom,
! [A: int,B: int,C: int] :
( ( A
= ( minus_minus_int @ B @ C ) )
= ( ( plus_plus_int @ A @ C )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_eq__diff__eq) ).
thf(318,plain,
! [A: int,B: int,C: int] :
( ( A
= ( minus_minus_int @ B @ C ) )
= ( ( plus_plus_int @ A @ C )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(319,plain,
! [C: int,B: int,A: int] :
( ( A
= ( minus_minus_int @ B @ C ) )
= ( ( plus_plus_int @ A @ C )
= B ) ),
inference(cnf,[status(esa)],[318]) ).
thf(320,plain,
! [C: int,B: int,A: int] :
( ( A
= ( minus_minus_int @ B @ C ) )
= ( ( plus_plus_int @ A @ C )
= B ) ),
inference(lifteq,[status(thm)],[319]) ).
thf(105,axiom,
! [A: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( add_a_b @ r @ A @ ( a_inv_a_b @ r @ A ) )
= ( zero_a_b @ r ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_r__neg) ).
thf(565,plain,
! [A: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( add_a_b @ r @ A @ ( a_inv_a_b @ r @ A ) )
= ( zero_a_b @ r ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(51,axiom,
! [A: int,B: int,C: int] :
( ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C )
= ( minus_minus_int @ A @ ( plus_plus_int @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_diff__diff__add) ).
thf(389,plain,
! [A: int,B: int,C: int] :
( ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C )
= ( minus_minus_int @ A @ ( plus_plus_int @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(156,axiom,
( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) )
= ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_f25) ).
thf(724,plain,
( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) )
= ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(2697,plain,
! [A: a] :
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ A )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ A @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ~ $true
| ~ ( member_a @ ( add_a_b @ r @ t @ t ) @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( member_a @ t @ ( partia1066395285xt_a_b @ r ) )
!= ( member_a @ A @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[878,2696]) ).
thf(2698,plain,
! [A: a] :
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ A )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ A @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ~ ( member_a @ ( add_a_b @ r @ t @ t ) @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( member_a @ t @ ( partia1066395285xt_a_b @ r ) )
!= ( member_a @ A @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(simp,[status(thm)],[2697]) ).
thf(2699,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ t )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ t @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ~ ( member_a @ ( add_a_b @ r @ t @ t ) @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t ) ),
inference(pattern_uni,[status(thm)],[2698:[bind(A,$thf( t ))]]) ).
thf(3006,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ t )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ t @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ~ $true
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( member_a @ ( add_a_b @ r @ t @ t ) @ ( partia1066395285xt_a_b @ r ) )
!= ( member_a @ t @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[878,2699]) ).
thf(3007,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ t )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ t @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( member_a @ ( add_a_b @ r @ t @ t ) @ ( partia1066395285xt_a_b @ r ) )
!= ( member_a @ t @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(simp,[status(thm)],[3006]) ).
thf(3196,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ t )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ t @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( add_a_b @ r @ t @ t )
!= t )
| ( ( partia1066395285xt_a_b @ r )
!= ( partia1066395285xt_a_b @ r ) ) ),
inference(simp,[status(thm)],[3007]) ).
thf(3221,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ t )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ t @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( add_a_b @ r @ t @ t )
!= t ) ),
inference(simp,[status(thm)],[3196]) ).
thf(6672,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ s3 )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ s3 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ~ $true
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( member_a @ ( add_a_b @ r @ t @ t ) @ ( partia1066395285xt_a_b @ r ) )
!= ( member_a @ ( product_snd_a_a @ y ) @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[769,2713]) ).
thf(6673,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ s3 )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ s3 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( member_a @ ( add_a_b @ r @ t @ t ) @ ( partia1066395285xt_a_b @ r ) )
!= ( member_a @ ( product_snd_a_a @ y ) @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(simp,[status(thm)],[6672]) ).
thf(6873,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ s3 )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ s3 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( add_a_b @ r @ t @ t )
!= ( product_snd_a_a @ y ) )
| ( ( partia1066395285xt_a_b @ r )
!= ( partia1066395285xt_a_b @ r ) ) ),
inference(simp,[status(thm)],[6673]) ).
thf(6892,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ s3 )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ s3 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( add_a_b @ r @ t @ t )
!= ( product_snd_a_a @ y ) ) ),
inference(simp,[status(thm)],[6873]) ).
thf(175,axiom,
! [A: a,B: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( a_inv_a_b @ r @ ( add_a_b @ r @ A @ B ) )
= ( add_a_b @ r @ ( a_inv_a_b @ r @ B ) @ ( a_inv_a_b @ r @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_add_Oinv__mult__group) ).
thf(785,plain,
! [A: a,B: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( a_inv_a_b @ r @ ( add_a_b @ r @ A @ B ) )
= ( add_a_b @ r @ ( a_inv_a_b @ r @ B ) @ ( a_inv_a_b @ r @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(6682,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ s3 )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ s3 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ~ $true
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( member_a @ ( add_a_b @ r @ t @ t ) @ ( partia1066395285xt_a_b @ r ) )
!= ( member_a @ s3 @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[867,2713]) ).
thf(6683,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ s3 )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ s3 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( member_a @ ( add_a_b @ r @ t @ t ) @ ( partia1066395285xt_a_b @ r ) )
!= ( member_a @ s3 @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(simp,[status(thm)],[6682]) ).
thf(6857,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ s3 )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ s3 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( add_a_b @ r @ t @ t )
!= s3 )
| ( ( partia1066395285xt_a_b @ r )
!= ( partia1066395285xt_a_b @ r ) ) ),
inference(simp,[status(thm)],[6683]) ).
thf(6878,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ s3 )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ s3 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( add_a_b @ r @ t @ t )
!= s3 ) ),
inference(simp,[status(thm)],[6857]) ).
thf(348,plain,
! [A: set_a] :
( ~ ? [B: a] : ( member_a @ B @ A )
=> ( A = bot_bot_set_a ) ),
inference(miniscope,[status(thm)],[347]) ).
thf(349,plain,
! [A: set_a] :
( ( member_a @ ( sk2 @ A ) @ A )
| ( A = bot_bot_set_a ) ),
inference(cnf,[status(esa)],[348]) ).
thf(350,plain,
! [A: set_a] :
( ( A = bot_bot_set_a )
| ( member_a @ ( sk2 @ A ) @ A ) ),
inference(lifteq,[status(thm)],[349]) ).
thf(106,axiom,
~ ! [A: a] :
( ( member_a @ A @ s )
=> ( ( mult_a_ring_ext_a_b @ r @ A @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) )
!= ( zero_a_b @ r ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062t_H_O_A_092_060lbrakk_062t_H_A_092_060in_062_AS_059_At_H_A_092_060otimes_062_A_Isnd_Ay_H_A_092_060otimes_062_Ar_H_A_092_060ominus_062_As_H_A_092_060otimes_062_Afst_Ay_H_J_A_061_A_092_060zero_062_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062) ).
thf(568,plain,
~ ! [A: a] :
( ( member_a @ A @ s )
=> ( ( mult_a_ring_ext_a_b @ r @ A @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) )
!= ( zero_a_b @ r ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(569,plain,
~ ! [A: a] :
( ( member_a @ A @ s )
=> ( ( mult_a_ring_ext_a_b @ r @ A @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) )
!= ( zero_a_b @ r ) ) ),
inference(polarity_switch,[status(thm)],[568]) ).
thf(570,plain,
( ( member_a @ sk6 @ s )
& ( ( mult_a_ring_ext_a_b @ r @ sk6 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) )
= ( zero_a_b @ r ) ) ),
inference(cnf,[status(esa)],[569]) ).
thf(571,plain,
member_a @ sk6 @ s,
inference(cnfConj,[status(thm)],[570]) ).
thf(993,plain,
! [A: a] :
( ~ $true
| ( ( member_a @ sk6 @ s )
!= ( member_a @ A @ bot_bot_set_a ) ) ),
inference(paramod_ordered,[status(thm)],[571,383]) ).
thf(994,plain,
! [A: a] :
( ( member_a @ sk6 @ s )
!= ( member_a @ A @ bot_bot_set_a ) ),
inference(simp,[status(thm)],[993]) ).
thf(995,plain,
! [A: a] :
( ( sk6 != A )
| ( s != bot_bot_set_a ) ),
inference(simp,[status(thm)],[994]) ).
thf(996,plain,
s != bot_bot_set_a,
inference(simp,[status(thm)],[995]) ).
thf(16687,plain,
! [A: set_a] :
( ( member_a @ ( sk2 @ A ) @ A )
| ( bot_bot_set_a != bot_bot_set_a )
| ( A != s ) ),
inference(paramod_ordered,[status(thm)],[350,996]) ).
thf(16688,plain,
! [A: set_a] :
( ( member_a @ ( sk2 @ A ) @ A )
| ( A != s ) ),
inference(simp,[status(thm)],[16687]) ).
thf(16689,plain,
member_a @ ( sk2 @ s ) @ s,
inference(pattern_uni,[status(thm)],[16688:[bind(A,$thf( s ))]]) ).
thf(238,axiom,
~ ! [A: a] :
( ( member_a @ A @ s )
=> ( ( mult_a_ring_ext_a_b @ r @ A @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) )
!= ( zero_a_b @ r ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062t_O_A_092_060lbrakk_062t_A_092_060in_062_AS_059_At_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Ar_A_092_060ominus_062_As_A_092_060otimes_062_Afst_Ax_H_J_A_061_A_092_060zero_062_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062) ).
thf(949,plain,
~ ! [A: a] :
( ( member_a @ A @ s )
=> ( ( mult_a_ring_ext_a_b @ r @ A @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) )
!= ( zero_a_b @ r ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(99,axiom,
! [A: int,B: int] :
( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_diff__add__cancel) ).
thf(542,plain,
! [A: int,B: int] :
( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(122,axiom,
member_a @ t @ s,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_f6) ).
thf(619,plain,
member_a @ t @ s,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(193,axiom,
member_a @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( partia1066395285xt_a_b @ r ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23__092_060open_062snd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060in_062_Acarrier_AR_092_060close_062) ).
thf(838,plain,
member_a @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( partia1066395285xt_a_b @ r ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(181,axiom,
! [A: partia1833973666xt_a_b,B: a,C: a,D: a] :
( ( semiring_a_b @ A )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ A ) )
=> ( ( member_a @ C @ ( partia1066395285xt_a_b @ A ) )
=> ( ( member_a @ D @ ( partia1066395285xt_a_b @ A ) )
=> ( ( add_a_b @ A @ B @ ( add_a_b @ A @ C @ D ) )
= ( add_a_b @ A @ C @ ( add_a_b @ A @ B @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_semiring_Osemiring__simprules_I12_J) ).
thf(802,plain,
! [A: partia1833973666xt_a_b,B: a,C: a,D: a] :
( ( semiring_a_b @ A )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ A ) )
=> ( ( member_a @ C @ ( partia1066395285xt_a_b @ A ) )
=> ( ( member_a @ D @ ( partia1066395285xt_a_b @ A ) )
=> ( ( add_a_b @ A @ B @ ( add_a_b @ A @ C @ D ) )
= ( add_a_b @ A @ C @ ( add_a_b @ A @ B @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(37,axiom,
! [A: int,B: int,C: int] :
( ( minus_minus_int @ A @ ( minus_minus_int @ B @ C ) )
= ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_diff__diff__eq2) ).
thf(344,plain,
! [A: int,B: int,C: int] :
( ( minus_minus_int @ A @ ( minus_minus_int @ B @ C ) )
= ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(232,axiom,
( ( (=) @ product_prod_a_a )
= ( ^ [A: product_prod_a_a,B: product_prod_a_a] :
( ( ( product_fst_a_a @ A )
= ( product_fst_a_a @ B ) )
& ( ( product_snd_a_a @ A )
= ( product_snd_a_a @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_prod__eq__iff) ).
thf(933,plain,
( ( (=) @ product_prod_a_a )
= ( ^ [A: product_prod_a_a,B: product_prod_a_a] :
( ( ( product_fst_a_a @ A )
= ( product_fst_a_a @ B ) )
& ( ( product_snd_a_a @ A )
= ( product_snd_a_a @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(934,plain,
( ( ^ [A: product_prod_a_a,B: product_prod_a_a] :
( ( ( product_fst_a_a @ A )
= ( product_fst_a_a @ B ) )
& ( ( product_snd_a_a @ A )
= ( product_snd_a_a @ B ) ) ) )
= ( (=) @ product_prod_a_a ) ),
inference(lifteq,[status(thm)],[933]) ).
thf(219,axiom,
member_a @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) @ ( partia1066395285xt_a_b @ r ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_f28) ).
thf(902,plain,
member_a @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) @ ( partia1066395285xt_a_b @ r ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(61,axiom,
! [A: set_a] :
( ( ? [B: a] : ( member_a @ B @ A ) )
= ( A != bot_bot_set_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_ex__in__conv) ).
thf(416,plain,
! [A: set_a] :
( ( ? [B: a] : ( member_a @ B @ A ) )
= ( A != bot_bot_set_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(17,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_diff__right__mono) ).
thf(289,plain,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(7,axiom,
! [A: int,B: int,C: int,D: int] :
( ( ( A = B )
& ( ord_less_eq_int @ C @ D ) )
=> ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_add__mono__thms__linordered__semiring_I2_J) ).
thf(261,plain,
! [A: int,B: int,C: int,D: int] :
( ( ( A = B )
& ( ord_less_eq_int @ C @ D ) )
=> ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(14614,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ s2 )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ s2 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ~ $true
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( member_a @ ( add_a_b @ r @ t @ t ) @ ( partia1066395285xt_a_b @ r ) )
!= ( member_a @ s3 @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[867,2741]) ).
thf(14615,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ s2 )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ s2 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( member_a @ ( add_a_b @ r @ t @ t ) @ ( partia1066395285xt_a_b @ r ) )
!= ( member_a @ s3 @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(simp,[status(thm)],[14614]) ).
thf(14833,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ s2 )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ s2 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( add_a_b @ r @ t @ t )
!= s3 )
| ( ( partia1066395285xt_a_b @ r )
!= ( partia1066395285xt_a_b @ r ) ) ),
inference(simp,[status(thm)],[14615]) ).
thf(14864,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ s2 )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ s2 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( add_a_b @ r @ t @ t )
!= s3 ) ),
inference(simp,[status(thm)],[14833]) ).
thf(201,axiom,
! [A: a,B: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( ( add_a_b @ r @ A @ B )
= ( zero_a_b @ r ) )
=> ( A
= ( a_inv_a_b @ r @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_sum__zero__eq__neg) ).
thf(853,plain,
! [A: a,B: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( ( add_a_b @ r @ A @ B )
= ( zero_a_b @ r ) )
=> ( A
= ( a_inv_a_b @ r @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(245,axiom,
! [A: partia1833973666xt_a_b,B: a,C: a,D: a] :
( ( semiring_a_b @ A )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ A ) )
=> ( ( member_a @ C @ ( partia1066395285xt_a_b @ A ) )
=> ( ( member_a @ D @ ( partia1066395285xt_a_b @ A ) )
=> ( ( mult_a_ring_ext_a_b @ A @ ( add_a_b @ A @ B @ C ) @ D )
= ( add_a_b @ A @ ( mult_a_ring_ext_a_b @ A @ B @ D ) @ ( mult_a_ring_ext_a_b @ A @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_semiring_Ol__distr) ).
thf(969,plain,
! [A: partia1833973666xt_a_b,B: a,C: a,D: a] :
( ( semiring_a_b @ A )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ A ) )
=> ( ( member_a @ C @ ( partia1066395285xt_a_b @ A ) )
=> ( ( member_a @ D @ ( partia1066395285xt_a_b @ A ) )
=> ( ( mult_a_ring_ext_a_b @ A @ ( add_a_b @ A @ B @ C ) @ D )
= ( add_a_b @ A @ ( mult_a_ring_ext_a_b @ A @ B @ D ) @ ( mult_a_ring_ext_a_b @ A @ C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(5318,plain,
( ( ( add_a_b @ r @ t @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( add_a_b @ r @ t @ t )
!= t )
| ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ t )
!= ( add_a_b @ r @ t @ ( zero_a_b @ r ) ) )
| ( ( zero_a_b @ r )
!= ( zero_a_b @ r ) ) ),
inference(eqfactor_ordered,[status(thm)],[3221]) ).
thf(5320,plain,
( ( ( add_a_b @ r @ t @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( add_a_b @ r @ t @ t )
!= t )
| ( r != r )
| ( ( add_a_b @ r @ t @ t )
!= t )
| ( ( zero_a_b @ r )
!= t ) ),
inference(simp,[status(thm)],[5318]) ).
thf(5323,plain,
( ( ( add_a_b @ r @ t @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( add_a_b @ r @ t @ t )
!= t )
| ( ( zero_a_b @ r )
!= t ) ),
inference(simp,[status(thm)],[5320]) ).
thf(5479,plain,
( ( ( add_a_b @ r @ t @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ t @ t )
!= t )
| ( ( zero_a_b @ r )
!= t )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= ( add_a_b @ r @ t @ t ) )
| ( t != t ) ),
inference(eqfactor_ordered,[status(thm)],[5323]) ).
thf(5480,plain,
( ( ( add_a_b @ r @ t @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ t @ t )
!= t )
| ( ( zero_a_b @ r )
!= t )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= ( add_a_b @ r @ t @ t ) ) ),
inference(simp,[status(thm)],[5479]) ).
thf(15,axiom,
! [A: int,B: int,C: int,D: int] :
( ( ( ord_less_eq_int @ A @ B )
& ( ord_less_eq_int @ C @ D ) )
=> ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_add__mono__thms__linordered__semiring_I1_J) ).
thf(284,plain,
! [A: int,B: int,C: int,D: int] :
( ( ( ord_less_eq_int @ A @ B )
& ( ord_less_eq_int @ C @ D ) )
=> ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(168,axiom,
! [A: a > a > $o,B: product_prod_a_a] :
( ( A @ ( product_snd_a_a @ B ) @ ( product_fst_a_a @ B ) )
=> ~ ! [C: a,D: a] :
~ ( A @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_exE__realizer_H) ).
thf(770,plain,
! [A: a > a > $o,B: product_prod_a_a] :
( ( A @ ( product_snd_a_a @ B ) @ ( product_fst_a_a @ B ) )
=> ~ ! [C: a,D: a] :
~ ( A @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(228,axiom,
( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) )
= ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_f35) ).
thf(924,plain,
( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) )
= ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(6521,plain,
! [B: a,A: set_a] :
( ~ $true
| ( ( member_a @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( partia1066395285xt_a_b @ r ) )
!= ( member_a @ B @ ( minus_minus_set_a @ A @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[838,6511]) ).
thf(6522,plain,
! [B: a,A: set_a] :
( ( member_a @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( partia1066395285xt_a_b @ r ) )
!= ( member_a @ B @ ( minus_minus_set_a @ A @ A ) ) ),
inference(simp,[status(thm)],[6521]) ).
thf(6565,plain,
! [B: a,A: set_a] :
( ( ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) )
!= B )
| ( ( minus_minus_set_a @ A @ A )
!= ( partia1066395285xt_a_b @ r ) ) ),
inference(simp,[status(thm)],[6522]) ).
thf(6590,plain,
! [A: set_a] :
( ( minus_minus_set_a @ A @ A )
!= ( partia1066395285xt_a_b @ r ) ),
inference(simp,[status(thm)],[6565]) ).
thf(7142,plain,
! [B: set_a,A: set_a] :
( ( ( collect_a
@ ^ [C: a] : ( member_a @ C @ A ) )
!= ( partia1066395285xt_a_b @ r ) )
| ( A
!= ( minus_minus_set_a @ B @ B ) ) ),
inference(paramod_ordered,[status(thm)],[283,6590]) ).
thf(7143,plain,
! [A: set_a] :
( ( collect_a
@ ^ [B: a] : ( member_a @ B @ ( minus_minus_set_a @ A @ A ) ) )
!= ( partia1066395285xt_a_b @ r ) ),
inference(pattern_uni,[status(thm)],[7142:[bind(A,$thf( minus_minus_set_a @ D @ D )),bind(B,$thf( D ))]]) ).
thf(7144,plain,
! [A: set_a] :
( ( collect_a
@ ^ [B: a] : ( member_a @ B @ ( minus_minus_set_a @ A @ A ) ) )
!= ( partia1066395285xt_a_b @ r ) ),
inference(simp,[status(thm)],[7143]) ).
thf(176,axiom,
( ( a_inv_a_b @ r @ ( zero_a_b @ r ) )
= ( zero_a_b @ r ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_local_Ominus__zero) ).
thf(789,plain,
( ( a_inv_a_b @ r @ ( zero_a_b @ r ) )
= ( zero_a_b @ r ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(107,axiom,
! [A: partia1833973666xt_a_b,B: a,C: a,D: a] :
( ( semiring_a_b @ A )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ A ) )
=> ( ( member_a @ C @ ( partia1066395285xt_a_b @ A ) )
=> ( ( member_a @ D @ ( partia1066395285xt_a_b @ A ) )
=> ( ( mult_a_ring_ext_a_b @ A @ ( mult_a_ring_ext_a_b @ A @ B @ C ) @ D )
= ( mult_a_ring_ext_a_b @ A @ B @ ( mult_a_ring_ext_a_b @ A @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_semiring_Osemiring__simprules_I8_J) ).
thf(574,plain,
! [A: partia1833973666xt_a_b,B: a,C: a,D: a] :
( ( semiring_a_b @ A )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ A ) )
=> ( ( member_a @ C @ ( partia1066395285xt_a_b @ A ) )
=> ( ( member_a @ D @ ( partia1066395285xt_a_b @ A ) )
=> ( ( mult_a_ring_ext_a_b @ A @ ( mult_a_ring_ext_a_b @ A @ B @ C ) @ D )
= ( mult_a_ring_ext_a_b @ A @ B @ ( mult_a_ring_ext_a_b @ A @ C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(182,axiom,
! [A: set_a] :
( ( ord_less_eq_set_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( a_l_coset_a_b @ r @ ( zero_a_b @ r ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_a__lcos__mult__one) ).
thf(806,plain,
! [A: set_a] :
( ( ord_less_eq_set_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( a_l_coset_a_b @ r @ ( zero_a_b @ r ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(39,axiom,
! [A: int,B: int,C: int] :
( ( minus_minus_int @ A @ ( plus_plus_int @ B @ C ) )
= ( minus_minus_int @ ( minus_minus_int @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_diff__add__eq__diff__diff__swap) ).
thf(351,plain,
! [A: int,B: int,C: int] :
( ( minus_minus_int @ A @ ( plus_plus_int @ B @ C ) )
= ( minus_minus_int @ ( minus_minus_int @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(352,plain,
! [C: int,B: int,A: int] :
( ( minus_minus_int @ A @ ( plus_plus_int @ B @ C ) )
= ( minus_minus_int @ ( minus_minus_int @ A @ C ) @ B ) ),
inference(cnf,[status(esa)],[351]) ).
thf(353,plain,
! [C: int,B: int,A: int] :
( ( minus_minus_int @ A @ ( plus_plus_int @ B @ C ) )
= ( minus_minus_int @ ( minus_minus_int @ A @ C ) @ B ) ),
inference(lifteq,[status(thm)],[352]) ).
thf(8248,plain,
! [B: set_a,A: set_a] :
( ( ( collect_a
@ ^ [C: a] : ( member_a @ C @ A ) )
!= s )
| ( A
!= ( collect_a
@ ^ [C: a] : ( member_a @ C @ ( minus_minus_set_a @ B @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[283,6619]) ).
thf(8249,plain,
! [A: set_a] :
( ( collect_a
@ ^ [B: a] :
( member_a @ B
@ ( collect_a
@ ^ [C: a] : ( member_a @ C @ ( minus_minus_set_a @ A @ A ) ) ) ) )
!= s ),
inference(pattern_uni,[status(thm)],[8248:[bind(A,$thf( collect_a @ ^ [C: a] : ( member_a @ C @ ( minus_minus_set_a @ B @ B ) ) )),bind(B,$thf( B ))]]) ).
thf(8254,plain,
! [A: set_a] :
( ( collect_a
@ ^ [B: a] :
( member_a @ B
@ ( collect_a
@ ^ [C: a] : ( member_a @ C @ ( minus_minus_set_a @ A @ A ) ) ) ) )
!= s ),
inference(simp,[status(thm)],[8249]) ).
thf(8853,plain,
! [B: set_a,A: set_a] :
( ( ( collect_a
@ ^ [C: a] :
( member_a @ C
@ ( collect_a
@ ^ [D: a] : ( member_a @ D @ bot_bot_set_a ) ) ) )
!= s )
| ( ( minus_minus_set_a @ A @ A )
!= ( minus_minus_set_a @ B @ B ) ) ),
inference(paramod_ordered,[status(thm)],[541,8254]) ).
thf(8854,plain,
( ( collect_a
@ ^ [A: a] :
( member_a @ A
@ ( collect_a
@ ^ [B: a] : ( member_a @ B @ bot_bot_set_a ) ) ) )
!= s ),
inference(pattern_uni,[status(thm)],[8853:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(9781,plain,
( ( collect_a
@ ^ [A: a] : ( member_a @ A @ bot_bot_set_a ) )
!= s ),
inference(rewrite,[status(thm)],[8854,4772]) ).
thf(9716,plain,
! [A: a] :
( ~ $true
| ( ( member_a @ t2
@ ( collect_a
@ ^ [B: a] : ( member_a @ B @ s ) ) )
!= ( member_a @ A @ bot_bot_set_a ) ) ),
inference(paramod_ordered,[status(thm)],[9273,383]) ).
thf(9717,plain,
! [A: a] :
( ( member_a @ t2
@ ( collect_a
@ ^ [B: a] : ( member_a @ B @ s ) ) )
!= ( member_a @ A @ bot_bot_set_a ) ),
inference(simp,[status(thm)],[9716]) ).
thf(9746,plain,
! [A: a] :
( ( t2 != A )
| ( ( collect_a
@ ^ [B: a] : ( member_a @ B @ s ) )
!= bot_bot_set_a ) ),
inference(simp,[status(thm)],[9717]) ).
thf(9757,plain,
( ( collect_a
@ ^ [A: a] : ( member_a @ A @ s ) )
!= bot_bot_set_a ),
inference(simp,[status(thm)],[9746]) ).
thf(9767,plain,
( ( bot_bot_set_a != bot_bot_set_a )
| ( ( collect_a
@ ^ [A: a] : ( member_a @ A @ s ) )
!= ( collect_a
@ ^ [A: a] : ( member_a @ A @ bot_bot_set_a ) ) ) ),
inference(paramod_ordered,[status(thm)],[4772,9757]) ).
thf(9768,plain,
( ( collect_a
@ ^ [A: a] : ( member_a @ A @ s ) )
!= ( collect_a
@ ^ [A: a] : ( member_a @ A @ bot_bot_set_a ) ) ),
inference(simp,[status(thm)],[9767]) ).
thf(9775,plain,
( ( ^ [A: a] : ( member_a @ A @ s ) )
!= ( ^ [A: a] : ( member_a @ A @ bot_bot_set_a ) ) ),
inference(simp,[status(thm)],[9768]) ).
thf(9778,plain,
( ( ^ [A: a] : ( member_a @ A @ s ) )
!= ( ^ [A: a] : $false ) ),
inference(rewrite,[status(thm)],[9775,383]) ).
thf(9779,plain,
member_a @ sk22 @ s,
inference(func_ext,[status(esa)],[9778]) ).
thf(222,axiom,
! [A: a,B: a,C: a] :
( ( A = B )
=> ( ( add_a_b @ r @ C @ A )
= ( add_a_b @ r @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_right__add__eq) ).
thf(905,plain,
! [A: a,B: a,C: a] :
( ( A = B )
=> ( ( add_a_b @ r @ C @ A )
= ( add_a_b @ r @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(14596,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ s2 )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ s2 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ~ $true
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( member_a @ ( add_a_b @ r @ t @ t ) @ ( partia1066395285xt_a_b @ r ) )
!= ( member_a @ s2 @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[668,2741]) ).
thf(14597,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ s2 )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ s2 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( member_a @ ( add_a_b @ r @ t @ t ) @ ( partia1066395285xt_a_b @ r ) )
!= ( member_a @ s2 @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(simp,[status(thm)],[14596]) ).
thf(14806,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ s2 )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ s2 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( add_a_b @ r @ t @ t )
!= s2 )
| ( ( partia1066395285xt_a_b @ r )
!= ( partia1066395285xt_a_b @ r ) ) ),
inference(simp,[status(thm)],[14597]) ).
thf(14847,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ s2 )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ s2 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( add_a_b @ r @ t @ t )
!= s2 ) ),
inference(simp,[status(thm)],[14806]) ).
thf(28,axiom,
! [A: int] :
( ( uminus_uminus_int @ ( uminus_uminus_int @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_add_Oinverse__inverse) ).
thf(321,plain,
! [A: int] :
( ( uminus_uminus_int @ ( uminus_uminus_int @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(83,axiom,
! [A: int,B: int] :
( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( plus_plus_int @ A @ B ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_minus__add__cancel) ).
thf(485,plain,
! [A: int,B: int] :
( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( plus_plus_int @ A @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(192,axiom,
! [A: partia1833973666xt_a_b,B: a] :
( ( semiring_a_b @ A )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ A ) )
=> ( ( mult_a_ring_ext_a_b @ A @ ( zero_a_b @ A ) @ B )
= ( zero_a_b @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_semiring_Ol__null) ).
thf(834,plain,
! [A: partia1833973666xt_a_b,B: a] :
( ( semiring_a_b @ A )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ A ) )
=> ( ( mult_a_ring_ext_a_b @ A @ ( zero_a_b @ A ) @ B )
= ( zero_a_b @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(116,axiom,
member_a @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) @ ( partia1066395285xt_a_b @ r ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_f14) ).
thf(602,plain,
member_a @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) @ ( partia1066395285xt_a_b @ r ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(146,axiom,
! [A: a,B: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( ( add_a_b @ r @ A @ B )
= A )
= ( B
= ( zero_a_b @ r ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_add_Ol__cancel__one) ).
thf(687,plain,
! [A: a,B: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( ( add_a_b @ r @ A @ B )
= A )
= ( B
= ( zero_a_b @ r ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(13,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ B ) )
= ( ord_less_eq_int @ B @ ( uminus_uminus_int @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_le__minus__iff) ).
thf(278,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ B ) )
= ( ord_less_eq_int @ B @ ( uminus_uminus_int @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(279,plain,
! [B: int,A: int] :
( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ B ) )
= ( ord_less_eq_int @ B @ ( uminus_uminus_int @ A ) ) ),
inference(cnf,[status(esa)],[278]) ).
thf(280,plain,
! [B: int,A: int] :
( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ B ) )
= ( ord_less_eq_int @ B @ ( uminus_uminus_int @ A ) ) ),
inference(lifteq,[status(thm)],[279]) ).
thf(128,axiom,
member_a @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( partia1066395285xt_a_b @ r ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_f13) ).
thf(634,plain,
member_a @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( partia1066395285xt_a_b @ r ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(73,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ ( minus_minus_int @ A @ B ) @ C )
= ( ord_less_eq_int @ A @ ( plus_plus_int @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_diff__le__eq) ).
thf(453,plain,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ ( minus_minus_int @ A @ B ) @ C )
= ( ord_less_eq_int @ A @ ( plus_plus_int @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(9236,plain,
! [B: a > $o,A: a] :
( ( member_a @ A @ ( collect_a @ B ) )
| ( ( B @ A )
!= ( member_a @ s3 @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[297,867]) ).
thf(9341,plain,
( member_a @ s3
@ ( collect_a
@ ^ [A: a] : ( member_a @ A @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(pre_uni,[status(thm)],[9236:[bind(A,$thf( s3 )),bind(B,$thf( ^ [C: a] : ( member_a @ C @ ( partia1066395285xt_a_b @ r ) ) ))]]) ).
thf(9209,plain,
! [B: a > $o,A: a] :
( ( member_a @ A @ ( collect_a @ B ) )
| ( ( member_a @ sk6 @ s )
!= ( B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[571,297]) ).
thf(9347,plain,
( member_a @ sk6
@ ( collect_a
@ ^ [A: a] : ( member_a @ A @ s ) ) ),
inference(pre_uni,[status(thm)],[9209:[bind(A,$thf( sk6 )),bind(B,$thf( ^ [C: a] : ( member_a @ C @ s ) ))]]) ).
thf(34,axiom,
! [A: set_a,B: set_a,C: a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_in__mono) ).
thf(336,plain,
! [A: set_a,B: set_a,C: a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(337,plain,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ! [C: a] :
( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ),
inference(miniscope,[status(thm)],[336]) ).
thf(338,plain,
! [C: a,B: set_a,A: set_a] :
( ~ ( ord_less_eq_set_a @ A @ B )
| ~ ( member_a @ C @ A )
| ( member_a @ C @ B ) ),
inference(cnf,[status(esa)],[337]) ).
thf(32,axiom,
! [A: set_a,B: set_a] :
( ( ( minus_minus_set_a @ A @ B )
= bot_bot_set_a )
= ( ord_less_eq_set_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_Diff__eq__empty__iff) ).
thf(330,plain,
! [A: set_a,B: set_a] :
( ( ( minus_minus_set_a @ A @ B )
= bot_bot_set_a )
= ( ord_less_eq_set_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(331,plain,
! [B: set_a,A: set_a] :
( ( ( minus_minus_set_a @ A @ B )
= bot_bot_set_a )
= ( ord_less_eq_set_a @ A @ B ) ),
inference(cnf,[status(esa)],[330]) ).
thf(332,plain,
! [B: set_a,A: set_a] :
( ( ord_less_eq_set_a @ A @ B )
= ( ( minus_minus_set_a @ A @ B )
= bot_bot_set_a ) ),
inference(lifteq,[status(thm)],[331]) ).
thf(15040,plain,
! [C: a,B: set_a,A: set_a] :
( ( ( minus_minus_set_a @ A @ B )
!= bot_bot_set_a )
| ~ ( member_a @ C @ A )
| ( member_a @ C @ B ) ),
inference(rewrite,[status(thm)],[338,332]) ).
thf(15041,plain,
! [C: a,B: set_a,A: set_a] :
( ( ( minus_minus_set_a @ A @ B )
!= bot_bot_set_a )
| ~ ( member_a @ C @ A )
| ( member_a @ C @ B ) ),
inference(lifteq,[status(thm)],[15040]) ).
thf(90,axiom,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ A @ ( minus_minus_int @ B @ C ) )
= ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_add__diff__eq) ).
thf(507,plain,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ A @ ( minus_minus_int @ B @ C ) )
= ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(25,axiom,
! [A: int,B: int] :
( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
= ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_minus__add__distrib) ).
thf(312,plain,
! [A: int,B: int] :
( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
= ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(8,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_le__imp__neg__le) ).
thf(265,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(199,axiom,
( ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_f33) ).
thf(849,plain,
( ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(23,axiom,
! [A: int,B: int,C: int,D: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_eq_int @ C @ D )
=> ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_add__mono) ).
thf(307,plain,
! [A: int,B: int,C: int,D: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_eq_int @ C @ D )
=> ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(18,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ A @ C ) )
= ( ord_less_eq_int @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_add__le__cancel__left) ).
thf(292,plain,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ A @ C ) )
= ( ord_less_eq_int @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(92,axiom,
! [A: set_a,B: set_a] :
( ( A = B )
=> ~ ( ( ord_less_eq_set_a @ A @ B )
=> ~ ( ord_less_eq_set_a @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_equalityE) ).
thf(512,plain,
! [A: set_a,B: set_a] :
( ( A = B )
=> ~ ( ( ord_less_eq_set_a @ A @ B )
=> ~ ( ord_less_eq_set_a @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(36,axiom,
( ord_less_eq_set_a
= ( ^ [A: set_a,B: set_a] :
! [C: a] :
( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_subset__eq) ).
thf(342,plain,
( ord_less_eq_set_a
= ( ^ [A: set_a,B: set_a] :
! [C: a] :
( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(343,plain,
( ord_less_eq_set_a
= ( ^ [A: set_a,B: set_a] :
! [C: a] :
( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ) ),
inference(lifteq,[status(thm)],[342]) ).
thf(13814,plain,
( ( ^ [A: set_a,B: set_a] :
( ( minus_minus_set_a @ A @ B )
= bot_bot_set_a ) )
= ( ^ [A: set_a,B: set_a] :
! [C: a] :
( ( member_a @ C @ A )
=> ( member_a @ C @ B ) ) ) ),
inference(rewrite,[status(thm)],[343,332]) ).
thf(143,axiom,
( ( member_a @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( partia1066395285xt_a_b @ r ) )
=> ( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) )
= ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21__092_060open_062_092_060lbrakk_062snd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_Ar_J_A_092_060ominus_062_As_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ay_H_A_092_060otimes_062_Afst_Ax_H_J_A_092_060in_062_Acarrier_AR_059_Asnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_A_092_060otimes_062_Ar_H_J_A_092_060ominus_062_As_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Afst_Ay_H_J_A_092_060in_062_Acarrier_AR_059_At_A_092_060otimes_062_At_H_A_092_060in_062_Acarrier_AR_092_060rbrakk_062_A_092_060Longrightarrow_062_At_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_Ar_J_A_092_060ominus_062_As_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ay_H_A_092_060otimes_062_Afst_Ax_H_J_A_092_060oplus_062_A_Isnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_A_092_060otimes_062_Ar_H_J_A_092_060ominus_062_As_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Afst_Ay_H_J_J_J_A_061_At_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_Ar_J_A_092_060ominus_062_As_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ay_H_A_092_060otimes_062_Afst_Ax_H_J_J_A_092_060oplus_062_At_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_A_092_060otimes_062_Ar_H_J_A_092_060ominus_062_As_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Afst_Ay_H_J_J_092_060close_062) ).
thf(678,plain,
( ( member_a @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( partia1066395285xt_a_b @ r ) )
=> ( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) )
= ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(131,axiom,
member_a @ ( product_fst_a_a @ x ) @ ( partia1066395285xt_a_b @ r ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_f22) ).
thf(641,plain,
member_a @ ( product_fst_a_a @ x ) @ ( partia1066395285xt_a_b @ r ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(9159,plain,
! [B: a > $o,A: a] :
( ( member_a @ A @ ( collect_a @ B ) )
| ( ( B @ A )
!= ( member_a @ ( product_fst_a_a @ x ) @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[297,641]) ).
thf(9308,plain,
( member_a @ ( product_fst_a_a @ x )
@ ( collect_a
@ ^ [A: a] : ( member_a @ A @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(pre_uni,[status(thm)],[9159:[bind(A,$thf( product_fst_a_a @ x )),bind(B,$thf( ^ [C: a] : ( member_a @ C @ ( partia1066395285xt_a_b @ r ) ) ))]]) ).
thf(17080,plain,
! [B: a > $o,A: a] :
( ( member_a @ A @ ( collect_a @ B ) )
| ( ( member_a @ ( sk2 @ s ) @ s )
!= ( B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[16689,297]) ).
thf(17125,plain,
( member_a @ ( sk2 @ s )
@ ( collect_a
@ ^ [A: a] : ( member_a @ A @ s ) ) ),
inference(pre_uni,[status(thm)],[17080:[bind(A,$thf( sk2 @ s )),bind(B,$thf( ^ [C: a] : ( member_a @ C @ s ) ))]]) ).
thf(2724,plain,
! [A: a] :
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ A )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ A @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ~ $true
| ~ ( member_a @ ( add_a_b @ r @ t @ t ) @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( member_a @ t2 @ ( partia1066395285xt_a_b @ r ) )
!= ( member_a @ A @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[901,2696]) ).
thf(2725,plain,
! [A: a] :
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ A )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ A @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ~ ( member_a @ ( add_a_b @ r @ t @ t ) @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( member_a @ t2 @ ( partia1066395285xt_a_b @ r ) )
!= ( member_a @ A @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(simp,[status(thm)],[2724]) ).
thf(2726,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ t2 )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ t2 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ~ ( member_a @ ( add_a_b @ r @ t @ t ) @ ( partia1066395285xt_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t ) ),
inference(pattern_uni,[status(thm)],[2725:[bind(A,$thf( t2 ))]]) ).
thf(9869,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ t2 )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ t2 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ~ $true
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( member_a @ ( add_a_b @ r @ t @ t ) @ ( partia1066395285xt_a_b @ r ) )
!= ( member_a @ t @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[878,2726]) ).
thf(9870,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ t2 )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ t2 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( member_a @ ( add_a_b @ r @ t @ t ) @ ( partia1066395285xt_a_b @ r ) )
!= ( member_a @ t @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(simp,[status(thm)],[9869]) ).
thf(10109,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ t2 )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ t2 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( add_a_b @ r @ t @ t )
!= t )
| ( ( partia1066395285xt_a_b @ r )
!= ( partia1066395285xt_a_b @ r ) ) ),
inference(simp,[status(thm)],[9870]) ).
thf(10139,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ t2 )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ t2 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( add_a_b @ r @ t @ t )
!= t ) ),
inference(simp,[status(thm)],[10109]) ).
thf(97,axiom,
! [A: int,B: int,C: int,D: int] :
( ( A
= ( plus_plus_int @ B @ C ) )
=> ( ( minus_minus_int @ D @ A )
= ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( minus_minus_int @ D @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_group__cancel_Osub2) ).
thf(534,plain,
! [A: int,B: int,C: int,D: int] :
( ( A
= ( plus_plus_int @ B @ C ) )
=> ( ( minus_minus_int @ D @ A )
= ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( minus_minus_int @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(6674,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ s3 )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ s3 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ~ $true
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( member_a @ ( add_a_b @ r @ t @ t ) @ ( partia1066395285xt_a_b @ r ) )
!= ( member_a @ s2 @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[668,2713]) ).
thf(6675,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ s3 )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ s3 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( member_a @ ( add_a_b @ r @ t @ t ) @ ( partia1066395285xt_a_b @ r ) )
!= ( member_a @ s2 @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(simp,[status(thm)],[6674]) ).
thf(6864,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ s3 )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ s3 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( add_a_b @ r @ t @ t )
!= s2 )
| ( ( partia1066395285xt_a_b @ r )
!= ( partia1066395285xt_a_b @ r ) ) ),
inference(simp,[status(thm)],[6675]) ).
thf(6884,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ s3 )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ s3 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( add_a_b @ r @ t @ t )
!= s2 ) ),
inference(simp,[status(thm)],[6864]) ).
thf(179,axiom,
! [A: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( mult_a_ring_ext_a_b @ r @ ( zero_a_b @ r ) @ A )
= ( zero_a_b @ r ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_l__null) ).
thf(798,plain,
! [A: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( mult_a_ring_ext_a_b @ r @ ( zero_a_b @ r ) @ A )
= ( zero_a_b @ r ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(5481,plain,
( ( ( add_a_b @ r @ t @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ t @ t )
!= t )
| ( ( zero_a_b @ r )
!= t )
| ( r != r )
| ( ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) )
!= t )
| ( ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) )
!= t ) ),
inference(simp,[status(thm)],[5479]) ).
thf(5487,plain,
( ( ( add_a_b @ r @ t @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ t @ t )
!= t )
| ( ( zero_a_b @ r )
!= t )
| ( ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) )
!= t )
| ( ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) )
!= t ) ),
inference(simp,[status(thm)],[5481]) ).
thf(44,axiom,
! [A: int,B: int,C: int,D: int] :
( ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ C )
=> ( ( ord_less_eq_int @ C @ ( plus_plus_int @ D @ B ) )
=> ( ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ C )
=> ( ( ord_less_eq_int @ C @ ( plus_plus_int @ D @ B ) )
=> ( ord_less_eq_int @ ( minus_minus_int @ C @ B ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_add__le__add__imp__diff__le) ).
thf(366,plain,
! [A: int,B: int,C: int,D: int] :
( ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ C )
=> ( ( ord_less_eq_int @ C @ ( plus_plus_int @ D @ B ) )
=> ( ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ C )
=> ( ( ord_less_eq_int @ C @ ( plus_plus_int @ D @ B ) )
=> ( ord_less_eq_int @ ( minus_minus_int @ C @ B ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(9889,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ t2 )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ t2 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ~ $true
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( member_a @ ( add_a_b @ r @ t @ t ) @ ( partia1066395285xt_a_b @ r ) )
!= ( member_a @ t2 @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[901,2726]) ).
thf(9890,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ t2 )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ t2 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( member_a @ ( add_a_b @ r @ t @ t ) @ ( partia1066395285xt_a_b @ r ) )
!= ( member_a @ t2 @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(simp,[status(thm)],[9889]) ).
thf(10102,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ t2 )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ t2 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( add_a_b @ r @ t @ t )
!= t2 )
| ( ( partia1066395285xt_a_b @ r )
!= ( partia1066395285xt_a_b @ r ) ) ),
inference(simp,[status(thm)],[9890]) ).
thf(10133,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ t2 )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ t2 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( add_a_b @ r @ t @ t )
!= t2 ) ),
inference(simp,[status(thm)],[10102]) ).
thf(9230,plain,
! [C: a,B: a > $o,A: a] :
( ~ ( member_a @ A @ ( collect_a @ B ) )
| ( ( B @ A )
!= ( member_a @ C @ bot_bot_set_a ) ) ),
inference(paramod_ordered,[status(thm)],[297,383]) ).
thf(9320,plain,
! [B: a > a,A: a] :
~ ( member_a @ A
@ ( collect_a
@ ^ [C: a] : ( member_a @ ( B @ C ) @ bot_bot_set_a ) ) ),
inference(pre_uni,[status(thm)],[9230:[bind(A,$thf( A )),bind(B,$thf( ^ [E: a] : ( member_a @ ( D @ E ) @ bot_bot_set_a ) )),bind(C,$thf( D @ A ))]]) ).
thf(9563,plain,
! [B: a > a,A: a] :
~ ( member_a @ A
@ ( collect_a
@ ^ [C: a] : ( member_a @ ( B @ C ) @ bot_bot_set_a ) ) ),
inference(simp,[status(thm)],[9320]) ).
thf(10567,plain,
! [A: a] :
~ ( member_a @ A
@ ( collect_a
@ ^ [B: a] : $false ) ),
inference(rewrite,[status(thm)],[9563,383]) ).
thf(10580,plain,
! [A: a] :
( ~ $true
| ( ( member_a @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( partia1066395285xt_a_b @ r ) )
!= ( member_a @ A
@ ( collect_a
@ ^ [B: a] : $false ) ) ) ),
inference(paramod_ordered,[status(thm)],[838,10567]) ).
thf(10581,plain,
! [A: a] :
( ( member_a @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( partia1066395285xt_a_b @ r ) )
!= ( member_a @ A
@ ( collect_a
@ ^ [B: a] : $false ) ) ),
inference(simp,[status(thm)],[10580]) ).
thf(10637,plain,
! [A: a] :
( ( ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) )
!= A )
| ( ( collect_a
@ ^ [B: a] : $false )
!= ( partia1066395285xt_a_b @ r ) ) ),
inference(simp,[status(thm)],[10581]) ).
thf(10670,plain,
( ( collect_a
@ ^ [A: a] : $false )
!= ( partia1066395285xt_a_b @ r ) ),
inference(simp,[status(thm)],[10637]) ).
thf(11610,plain,
! [A: set_a] :
( ( A
!= ( partia1066395285xt_a_b @ r ) )
| ( ( collect_a
@ ^ [B: a] : ( member_a @ B @ A ) )
!= ( collect_a
@ ^ [B: a] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[283,10670]) ).
thf(11616,plain,
( ( ^ [A: a] : ( member_a @ A @ ( partia1066395285xt_a_b @ r ) ) )
!= ( ^ [A: a] : $false ) ),
inference(simp,[status(thm)],[11610]) ).
thf(12469,plain,
member_a @ sk23 @ ( partia1066395285xt_a_b @ r ),
inference(func_ext,[status(esa)],[11616]) ).
thf(12487,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ t2 )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ t2 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ~ $true
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( member_a @ ( add_a_b @ r @ t @ t ) @ ( partia1066395285xt_a_b @ r ) )
!= ( member_a @ sk23 @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[12469,2726]) ).
thf(12488,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ t2 )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ t2 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( member_a @ ( add_a_b @ r @ t @ t ) @ ( partia1066395285xt_a_b @ r ) )
!= ( member_a @ sk23 @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(simp,[status(thm)],[12487]) ).
thf(12527,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ t2 )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ t2 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( add_a_b @ r @ t @ t )
!= sk23 )
| ( ( partia1066395285xt_a_b @ r )
!= ( partia1066395285xt_a_b @ r ) ) ),
inference(simp,[status(thm)],[12488]) ).
thf(12542,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ t2 )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ t2 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( add_a_b @ r @ t @ t )
!= sk23 ) ),
inference(simp,[status(thm)],[12527]) ).
thf(171,axiom,
( ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) )
= ( zero_a_b @ r ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_f7) ).
thf(778,plain,
( ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) )
= ( zero_a_b @ r ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(950,plain,
~ ! [A: a] :
( ( member_a @ A @ s )
=> ( ( mult_a_ring_ext_a_b @ r @ A @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) )
!= ( zero_a_b @ r ) ) ),
inference(polarity_switch,[status(thm)],[949]) ).
thf(951,plain,
( ( member_a @ sk15 @ s )
& ( ( mult_a_ring_ext_a_b @ r @ sk15 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) )
= ( zero_a_b @ r ) ) ),
inference(cnf,[status(esa)],[950]) ).
thf(952,plain,
member_a @ sk15 @ s,
inference(cnfConj,[status(thm)],[951]) ).
thf(115,axiom,
! [A: partia1833973666xt_a_b,B: a,C: a,D: a] :
( ( semiring_a_b @ A )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ A ) )
=> ( ( member_a @ C @ ( partia1066395285xt_a_b @ A ) )
=> ( ( member_a @ D @ ( partia1066395285xt_a_b @ A ) )
=> ( ( mult_a_ring_ext_a_b @ A @ D @ ( add_a_b @ A @ B @ C ) )
= ( add_a_b @ A @ ( mult_a_ring_ext_a_b @ A @ D @ B ) @ ( mult_a_ring_ext_a_b @ A @ D @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_semiring_Or__distr) ).
thf(598,plain,
! [A: partia1833973666xt_a_b,B: a,C: a,D: a] :
( ( semiring_a_b @ A )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ A ) )
=> ( ( member_a @ C @ ( partia1066395285xt_a_b @ A ) )
=> ( ( member_a @ D @ ( partia1066395285xt_a_b @ A ) )
=> ( ( mult_a_ring_ext_a_b @ A @ D @ ( add_a_b @ A @ B @ C ) )
= ( add_a_b @ A @ ( mult_a_ring_ext_a_b @ A @ D @ B ) @ ( mult_a_ring_ext_a_b @ A @ D @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(52,axiom,
! [A: int,B: int] :
( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_add__diff__cancel) ).
thf(392,plain,
! [A: int,B: int] :
( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(64,axiom,
! [A: int,B: int] :
( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_add__diff__cancel__right_H) ).
thf(424,plain,
! [A: int,B: int] :
( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(12,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ord_less_eq_int @ ( minus_minus_int @ C @ B ) @ ( minus_minus_int @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_diff__left__mono) ).
thf(275,plain,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ord_less_eq_int @ ( minus_minus_int @ C @ B ) @ ( minus_minus_int @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(3022,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ t )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ t @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ~ $true
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( member_a @ ( add_a_b @ r @ t @ t ) @ ( partia1066395285xt_a_b @ r ) )
!= ( member_a @ s2 @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[668,2699]) ).
thf(3023,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ t )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ t @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( member_a @ ( add_a_b @ r @ t @ t ) @ ( partia1066395285xt_a_b @ r ) )
!= ( member_a @ s2 @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(simp,[status(thm)],[3022]) ).
thf(3202,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ t )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ t @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( add_a_b @ r @ t @ t )
!= s2 )
| ( ( partia1066395285xt_a_b @ r )
!= ( partia1066395285xt_a_b @ r ) ) ),
inference(simp,[status(thm)],[3023]) ).
thf(3207,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ t )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ t @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( add_a_b @ r @ t @ t )
!= s2 ) ),
inference(simp,[status(thm)],[3202]) ).
thf(6634,plain,
! [B: a > $o,A: set_a] :
( ( ( bot_bot_set_a = A )
= ( ! [C: a] :
~ ( B @ C ) ) )
| ( ( collect_a
@ ^ [C: a] : ( member_a @ C @ A ) )
!= ( collect_a @ B ) ) ),
inference(paramod_ordered,[status(thm)],[283,404]) ).
thf(6635,plain,
! [A: set_a] :
( ( bot_bot_set_a = A )
= ( ! [B: a] :
~ ( member_a @ B @ A ) ) ),
inference(pattern_uni,[status(thm)],[6634:[bind(A,$thf( A )),bind(B,$thf( ^ [C: a] : ( member_a @ C @ A ) ))]]) ).
thf(78,axiom,
! [A: int,B: int,C: int] :
( ( A
= ( plus_plus_int @ B @ C ) )
=> ( ( uminus_uminus_int @ A )
= ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_group__cancel_Oneg1) ).
thf(467,plain,
! [A: int,B: int,C: int] :
( ( A
= ( plus_plus_int @ B @ C ) )
=> ( ( uminus_uminus_int @ A )
= ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(4,axiom,
! [A: int,B: int,C: int,D: int] :
( ( ( ord_less_eq_int @ A @ B )
& ( C = D ) )
=> ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_add__mono__thms__linordered__semiring_I3_J) ).
thf(252,plain,
! [A: int,B: int,C: int,D: int] :
( ( ( ord_less_eq_int @ A @ B )
& ( C = D ) )
=> ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(211,axiom,
! [A: partia1833973666xt_a_b,B: a,C: a] :
( ( semiring_a_b @ A )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ A ) )
=> ( ( member_a @ C @ ( partia1066395285xt_a_b @ A ) )
=> ( ( add_a_b @ A @ B @ C )
= ( add_a_b @ A @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_semiring_Osemiring__simprules_I7_J) ).
thf(879,plain,
! [A: partia1833973666xt_a_b,B: a,C: a] :
( ( semiring_a_b @ A )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ A ) )
=> ( ( member_a @ C @ ( partia1066395285xt_a_b @ A ) )
=> ( ( add_a_b @ A @ B @ C )
= ( add_a_b @ A @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(67,axiom,
! [A: int,B: int] :
( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B )
= ( minus_minus_int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_uminus__add__conv__diff) ).
thf(435,plain,
! [A: int,B: int] :
( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B )
= ( minus_minus_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(31,axiom,
! [A: partia1833973666xt_a_b,B: set_a] :
( ( locali425460998xt_a_b @ A @ B )
=> ( locali425460998xt_a_b @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_Localization__Mirabelle__afvchqjmgj_Osubmonoid_Ois__submonoid) ).
thf(329,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(9081,plain,
! [B: a > $o,A: a] :
( ( member_a @ A @ ( collect_a @ B ) )
| ( ( member_a @ t @ ( partia1066395285xt_a_b @ r ) )
!= ( B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[878,297]) ).
thf(9391,plain,
( member_a @ t
@ ( collect_a
@ ^ [A: a] : ( member_a @ A @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(pre_uni,[status(thm)],[9081:[bind(A,$thf( t )),bind(B,$thf( ^ [C: a] : ( member_a @ C @ ( partia1066395285xt_a_b @ r ) ) ))]]) ).
thf(110,axiom,
! [A: set_a,B: set_a] :
( ( additi2104487374up_a_b @ A @ r )
=> ( ( additi2104487374up_a_b @ B @ r )
=> ( additi2104487374up_a_b @ ( set_add_a_b @ r @ A @ B ) @ r ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_add__additive__subgroups) ).
thf(583,plain,
! [A: set_a,B: set_a] :
( ( additi2104487374up_a_b @ A @ r )
=> ( ( additi2104487374up_a_b @ B @ r )
=> ( additi2104487374up_a_b @ ( set_add_a_b @ r @ A @ B ) @ r ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(76,axiom,
! [A: set_a] :
( ( ! [B: a] :
~ ( member_a @ B @ A ) )
= ( A = bot_bot_set_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_all__not__in__conv) ).
thf(461,plain,
! [A: set_a] :
( ( ! [B: a] :
~ ( member_a @ B @ A ) )
= ( A = bot_bot_set_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(85,axiom,
! [A: int,B: int] :
( ( ( uminus_uminus_int @ A )
= B )
= ( ( uminus_uminus_int @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_minus__equation__iff) ).
thf(493,plain,
! [A: int,B: int] :
( ( ( uminus_uminus_int @ A )
= B )
= ( ( uminus_uminus_int @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(29,axiom,
! [A: int,B: int] :
( ( plus_plus_int @ A @ ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_add__minus__cancel) ).
thf(324,plain,
! [A: int,B: int] :
( ( plus_plus_int @ A @ ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(285,plain,
! [D: int,C: int,B: int,A: int] :
( ~ ( ord_less_eq_int @ A @ B )
| ~ ( ord_less_eq_int @ C @ D )
| ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ),
inference(cnf,[status(esa)],[284]) ).
thf(74,axiom,
! [A: partia1833973666xt_a_b,B: set_a] :
( ( locali1648887798ac_a_b @ A @ B )
=> ( locali807230110ng_a_b @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_eq__obj__rng__of__frac_Oaxioms_I2_J) ).
thf(456,plain,
! [A: partia1833973666xt_a_b,B: set_a] :
( ( locali1648887798ac_a_b @ A @ B )
=> ( locali807230110ng_a_b @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(197,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( ord_less_eq_set_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ord_less_eq_set_a @ ( set_add_a_b @ r @ A @ B ) @ ( partia1066395285xt_a_b @ r ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_set__add__closed) ).
thf(842,plain,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( ord_less_eq_set_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ord_less_eq_set_a @ ( set_add_a_b @ r @ A @ B ) @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(108,axiom,
! [A: a,B: int,C: int] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( add_pow_a_b_int @ r @ ( minus_minus_int @ B @ C ) @ A )
= ( add_a_b @ r @ ( add_pow_a_b_int @ r @ B @ A ) @ ( a_inv_a_b @ r @ ( add_pow_a_b_int @ r @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_add_Oint__pow__diff) ).
thf(578,plain,
! [A: a,B: int,C: int] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( add_pow_a_b_int @ r @ ( minus_minus_int @ B @ C ) @ A )
= ( add_a_b @ r @ ( add_pow_a_b_int @ r @ B @ A ) @ ( a_inv_a_b @ r @ ( add_pow_a_b_int @ r @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(134,axiom,
! [A: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( a_inv_a_b @ r @ ( a_inv_a_b @ r @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_local_Ominus__minus) ).
thf(650,plain,
! [A: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( a_inv_a_b @ r @ ( a_inv_a_b @ r @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(3016,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ t )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ t @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ~ $true
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( member_a @ ( add_a_b @ r @ t @ t ) @ ( partia1066395285xt_a_b @ r ) )
!= ( member_a @ t2 @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[901,2699]) ).
thf(3017,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ t )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ t @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( member_a @ ( add_a_b @ r @ t @ t ) @ ( partia1066395285xt_a_b @ r ) )
!= ( member_a @ t2 @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(simp,[status(thm)],[3016]) ).
thf(3191,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ t )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ t @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( add_a_b @ r @ t @ t )
!= t2 )
| ( ( partia1066395285xt_a_b @ r )
!= ( partia1066395285xt_a_b @ r ) ) ),
inference(simp,[status(thm)],[3017]) ).
thf(3218,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ t )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ t @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( add_a_b @ r @ t @ t )
!= t2 ) ),
inference(simp,[status(thm)],[3191]) ).
thf(40,axiom,
! [A: int,B: int,C: int] :
( ( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ C @ B ) )
= ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_group__add__class_Oadd_Oright__cancel) ).
thf(354,plain,
! [A: int,B: int,C: int] :
( ( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ C @ B ) )
= ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(355,plain,
! [C: int,B: int,A: int] :
( ( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ C @ B ) )
= ( A = C ) ),
inference(cnf,[status(esa)],[354]) ).
thf(356,plain,
! [C: int,B: int,A: int] :
( ( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ C @ B ) )
= ( A = C ) ),
inference(lifteq,[status(thm)],[355]) ).
thf(174,axiom,
( ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
= ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ t ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_f26) ).
thf(783,plain,
( ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
= ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ t ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(202,axiom,
! [A: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( add_a_b @ r @ ( zero_a_b @ r ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_l__zero) ).
thf(857,plain,
! [A: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( add_a_b @ r @ ( zero_a_b @ r ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(12517,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ t )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ t @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ~ $true
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( member_a @ ( add_a_b @ r @ t @ t ) @ ( partia1066395285xt_a_b @ r ) )
!= ( member_a @ sk23 @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[12469,2699]) ).
thf(12518,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ t )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ t @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( member_a @ ( add_a_b @ r @ t @ t ) @ ( partia1066395285xt_a_b @ r ) )
!= ( member_a @ sk23 @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(simp,[status(thm)],[12517]) ).
thf(12521,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ t )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ t @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( add_a_b @ r @ t @ t )
!= sk23 )
| ( ( partia1066395285xt_a_b @ r )
!= ( partia1066395285xt_a_b @ r ) ) ),
inference(simp,[status(thm)],[12518]) ).
thf(12538,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ t )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ t @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( add_a_b @ r @ t @ t )
!= sk23 ) ),
inference(simp,[status(thm)],[12521]) ).
thf(26,axiom,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) )
= ( plus_plus_int @ B @ ( plus_plus_int @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_add_Oleft__commute) ).
thf(315,plain,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) )
= ( plus_plus_int @ B @ ( plus_plus_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(316,plain,
! [C: int,B: int,A: int] :
( ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) )
= ( plus_plus_int @ B @ ( plus_plus_int @ A @ C ) ) ),
inference(cnf,[status(esa)],[315]) ).
thf(317,plain,
! [C: int,B: int,A: int] :
( ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) )
= ( plus_plus_int @ B @ ( plus_plus_int @ A @ C ) ) ),
inference(lifteq,[status(thm)],[316]) ).
thf(3028,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ t )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ t @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ~ $true
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( member_a @ ( add_a_b @ r @ t @ t ) @ ( partia1066395285xt_a_b @ r ) )
!= ( member_a @ s3 @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[867,2699]) ).
thf(3029,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ t )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ t @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( member_a @ ( add_a_b @ r @ t @ t ) @ ( partia1066395285xt_a_b @ r ) )
!= ( member_a @ s3 @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(simp,[status(thm)],[3028]) ).
thf(3200,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ t )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ t @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( add_a_b @ r @ t @ t )
!= s3 )
| ( ( partia1066395285xt_a_b @ r )
!= ( partia1066395285xt_a_b @ r ) ) ),
inference(simp,[status(thm)],[3029]) ).
thf(3205,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ t )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ t @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( add_a_b @ r @ t @ t )
!= s3 ) ),
inference(simp,[status(thm)],[3200]) ).
thf(87,axiom,
! [A: int,B: int,C: int] :
( ( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_add__left__cancel) ).
thf(499,plain,
! [A: int,B: int,C: int] :
( ( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ A @ C ) )
= ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(213,axiom,
! [A: a,B: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( member_a @ ( a_minus_a_b @ r @ A @ B ) @ ( partia1066395285xt_a_b @ r ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_minus__closed) ).
thf(884,plain,
! [A: a,B: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( member_a @ ( a_minus_a_b @ r @ A @ B ) @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(84,axiom,
! [A: int,B: int,C: int,D: int] :
( ( A
= ( plus_plus_int @ B @ C ) )
=> ( ( plus_plus_int @ D @ A )
= ( plus_plus_int @ B @ ( plus_plus_int @ D @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_group__cancel_Oadd2) ).
thf(488,plain,
! [A: int,B: int,C: int,D: int] :
( ( A
= ( plus_plus_int @ B @ C ) )
=> ( ( plus_plus_int @ D @ A )
= ( plus_plus_int @ B @ ( plus_plus_int @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(35,axiom,
! [A: set_a] :
( ( minus_minus_set_a @ A @ bot_bot_set_a )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_Diff__empty) ).
thf(339,plain,
! [A: set_a] :
( ( minus_minus_set_a @ A @ bot_bot_set_a )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(140,axiom,
! [A: a,B: a,C: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ C @ ( partia1066395285xt_a_b @ r ) )
=> ( ( mult_a_ring_ext_a_b @ r @ ( add_a_b @ r @ A @ B ) @ C )
= ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ A @ C ) @ ( mult_a_ring_ext_a_b @ r @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_l__distr) ).
thf(669,plain,
! [A: a,B: a,C: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ C @ ( partia1066395285xt_a_b @ r ) )
=> ( ( mult_a_ring_ext_a_b @ r @ ( add_a_b @ r @ A @ B ) @ C )
= ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ A @ C ) @ ( mult_a_ring_ext_a_b @ r @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(132,axiom,
( a_minus_a_b
= ( ^ [A: partia1833973666xt_a_b,B: a,C: a] : ( add_a_b @ A @ B @ ( a_inv_a_b @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_a__minus__def) ).
thf(642,plain,
( a_minus_a_b
= ( ^ [A: partia1833973666xt_a_b,B: a,C: a] : ( add_a_b @ A @ B @ ( a_inv_a_b @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(95,axiom,
! [A: int,B: int,C: int] :
( ( ( plus_plus_int @ A @ B )
= C )
=> ( A
= ( minus_minus_int @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_add__implies__diff) ).
thf(526,plain,
! [A: int,B: int,C: int] :
( ( ( plus_plus_int @ A @ B )
= C )
=> ( A
= ( minus_minus_int @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(130,axiom,
! [A: a,B: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( A
= ( add_a_b @ r @ A @ B ) )
= ( B
= ( zero_a_b @ r ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_add_Ol__cancel__one_H) ).
thf(637,plain,
! [A: a,B: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( A
= ( add_a_b @ r @ A @ B ) )
= ( B
= ( zero_a_b @ r ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(30,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ C )
=> ( ord_less_eq_int @ A @ ( minus_minus_int @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_add__le__imp__le__diff) ).
thf(327,plain,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ C )
=> ( ord_less_eq_int @ A @ ( minus_minus_int @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(328,plain,
! [C: int,B: int,A: int] :
( ~ ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ C )
| ( ord_less_eq_int @ A @ ( minus_minus_int @ C @ B ) ) ),
inference(cnf,[status(esa)],[327]) ).
thf(79,axiom,
! [A: int,B: int] :
( ( minus_minus_int @ ( uminus_uminus_int @ A ) @ B )
= ( minus_minus_int @ ( uminus_uminus_int @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_minus__diff__commute) ).
thf(471,plain,
! [A: int,B: int] :
( ( minus_minus_int @ ( uminus_uminus_int @ A ) @ B )
= ( minus_minus_int @ ( uminus_uminus_int @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(5,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ C @ B ) )
= ( ord_less_eq_int @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_add__le__cancel__right) ).
thf(256,plain,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ C @ B ) )
= ( ord_less_eq_int @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(14442,plain,
( member_a @ sk24
@ ( collect_a
@ ^ [A: a] : ( member_a @ A @ s ) ) ),
inference(func_ext,[status(esa)],[14441]) ).
thf(14472,plain,
! [B: a > $o,A: a] :
( ( B @ A )
| ( ( member_a @ sk24
@ ( collect_a
@ ^ [C: a] : ( member_a @ C @ s ) ) )
!= ( member_a @ A @ ( collect_a @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[14442,297]) ).
thf(14473,plain,
member_a @ sk24 @ s,
inference(pattern_uni,[status(thm)],[14472:[bind(A,$thf( sk24 )),bind(B,$thf( ^ [C: a] : ( member_a @ C @ s ) ))]]) ).
thf(224,axiom,
! [A: partia1833973666xt_a_b,B: a,C: a,D: a] :
( ( semiring_a_b @ A )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ A ) )
=> ( ( member_a @ C @ ( partia1066395285xt_a_b @ A ) )
=> ( ( member_a @ D @ ( partia1066395285xt_a_b @ A ) )
=> ( ( add_a_b @ A @ ( add_a_b @ A @ B @ C ) @ D )
= ( add_a_b @ A @ B @ ( add_a_b @ A @ C @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_semiring_Osemiring__simprules_I5_J) ).
thf(911,plain,
! [A: partia1833973666xt_a_b,B: a,C: a,D: a] :
( ( semiring_a_b @ A )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ A ) )
=> ( ( member_a @ C @ ( partia1066395285xt_a_b @ A ) )
=> ( ( member_a @ D @ ( partia1066395285xt_a_b @ A ) )
=> ( ( add_a_b @ A @ ( add_a_b @ A @ B @ C ) @ D )
= ( add_a_b @ A @ B @ ( add_a_b @ A @ C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(9899,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ t2 )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ t2 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ~ $true
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( member_a @ ( add_a_b @ r @ t @ t ) @ ( partia1066395285xt_a_b @ r ) )
!= ( member_a @ ( product_snd_a_a @ y ) @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[769,2726]) ).
thf(9900,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ t2 )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ t2 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( member_a @ ( add_a_b @ r @ t @ t ) @ ( partia1066395285xt_a_b @ r ) )
!= ( member_a @ ( product_snd_a_a @ y ) @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(simp,[status(thm)],[9899]) ).
thf(10087,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ t2 )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ t2 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( add_a_b @ r @ t @ t )
!= ( product_snd_a_a @ y ) )
| ( ( partia1066395285xt_a_b @ r )
!= ( partia1066395285xt_a_b @ r ) ) ),
inference(simp,[status(thm)],[9900]) ).
thf(10122,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ t2 )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ t2 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( add_a_b @ r @ t @ t )
!= ( product_snd_a_a @ y ) ) ),
inference(simp,[status(thm)],[10087]) ).
thf(266,plain,
! [B: int,A: int] :
( ~ ( ord_less_eq_int @ A @ B )
| ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ),
inference(cnf,[status(esa)],[265]) ).
thf(166,axiom,
! [A: a,B: a,C: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ C @ ( partia1066395285xt_a_b @ r ) )
=> ( ( mult_a_ring_ext_a_b @ r @ A @ ( mult_a_ring_ext_a_b @ r @ B @ C ) )
= ( mult_a_ring_ext_a_b @ r @ B @ ( mult_a_ring_ext_a_b @ r @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_m__lcomm) ).
thf(765,plain,
! [A: a,B: a,C: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ C @ ( partia1066395285xt_a_b @ r ) )
=> ( ( mult_a_ring_ext_a_b @ r @ A @ ( mult_a_ring_ext_a_b @ r @ B @ C ) )
= ( mult_a_ring_ext_a_b @ r @ B @ ( mult_a_ring_ext_a_b @ r @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(54,axiom,
! [A: partia1833973666xt_a_b] :
( ( semiring_a_b @ A )
=> ( member_a @ ( zero_a_b @ A ) @ ( partia1066395285xt_a_b @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_semiring_Osemiring__simprules_I2_J) ).
thf(398,plain,
! [A: partia1833973666xt_a_b] :
( ( semiring_a_b @ A )
=> ( member_a @ ( zero_a_b @ A ) @ ( partia1066395285xt_a_b @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(96,axiom,
! [A: int,B: int,C: int,D: int] :
( ( ( A = B )
& ( C = D ) )
=> ( ( plus_plus_int @ A @ C )
= ( plus_plus_int @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_add__mono__thms__linordered__semiring_I4_J) ).
thf(530,plain,
! [A: int,B: int,C: int,D: int] :
( ( ( A = B )
& ( C = D ) )
=> ( ( plus_plus_int @ A @ C )
= ( plus_plus_int @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(229,axiom,
member_a @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( partia1066395285xt_a_b @ r ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_f27) ).
thf(926,plain,
member_a @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( partia1066395285xt_a_b @ r ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(127,axiom,
member_a @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( partia1066395285xt_a_b @ r ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_f9) ).
thf(633,plain,
member_a @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( partia1066395285xt_a_b @ r ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(42,axiom,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
= ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(360,plain,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
= ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(169,axiom,
! [A: a,B: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( member_a @ ( mult_a_ring_ext_a_b @ r @ A @ B ) @ ( partia1066395285xt_a_b @ r ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_semiring__simprules_I3_J) ).
thf(773,plain,
! [A: a,B: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( member_a @ ( mult_a_ring_ext_a_b @ r @ A @ B ) @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(111,axiom,
! [A: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( add_a_b @ r @ ( a_inv_a_b @ r @ A ) @ A )
= ( zero_a_b @ r ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_l__neg) ).
thf(586,plain,
! [A: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( add_a_b @ r @ ( a_inv_a_b @ r @ A ) @ A )
= ( zero_a_b @ r ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(20,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
= ( ord_less_eq_int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_neg__le__iff__le) ).
thf(298,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
= ( ord_less_eq_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(66,axiom,
! [A: int,B: int,C: int] :
( ( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ C @ B ) )
=> ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_add__right__imp__eq) ).
thf(430,plain,
! [A: int,B: int,C: int] :
( ( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ C @ B ) )
=> ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(462,plain,
! [A: set_a] :
( ( ! [B: a] :
~ ( member_a @ B @ A ) )
= ( A = bot_bot_set_a ) ),
inference(cnf,[status(esa)],[461]) ).
thf(463,plain,
! [A: set_a] :
( ( ! [B: a] :
~ ( member_a @ B @ A ) )
= ( A = bot_bot_set_a ) ),
inference(lifteq,[status(thm)],[462]) ).
thf(8448,plain,
! [B: set_a,A: set_a] :
( ( ( bot_bot_set_a = A )
= ( B = bot_bot_set_a ) )
| ( ( ! [C: a] :
~ ( member_a @ C @ A ) )
!= ( ! [C: a] :
~ ( member_a @ C @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[6635,463]) ).
thf(8449,plain,
! [A: set_a] :
( ( bot_bot_set_a = A )
= ( A = bot_bot_set_a ) ),
inference(pattern_uni,[status(thm)],[8448:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(417,plain,
! [A: set_a] :
( ( ? [B: a] : ( member_a @ B @ A ) )
= ( A != bot_bot_set_a ) ),
inference(cnf,[status(esa)],[416]) ).
thf(418,plain,
! [A: set_a] :
( ( ? [B: a] : ( member_a @ B @ A ) )
= ( A != bot_bot_set_a ) ),
inference(lifteq,[status(thm)],[417]) ).
thf(8530,plain,
! [B: set_a,A: set_a] :
( ( ( bot_bot_set_a != A )
= ( ? [C: a] : ( member_a @ C @ B ) ) )
| ( ( A = bot_bot_set_a )
!= ( B = bot_bot_set_a ) ) ),
inference(paramod_ordered,[status(thm)],[8449,418]) ).
thf(8531,plain,
! [A: set_a] :
( ( bot_bot_set_a != A )
= ( ? [B: a] : ( member_a @ B @ A ) ) ),
inference(pattern_uni,[status(thm)],[8530:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(159,axiom,
! [A: a,B: a,C: int] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( mult_a_ring_ext_a_b @ r @ ( add_pow_a_b_int @ r @ C @ A ) @ B )
= ( add_pow_a_b_int @ r @ C @ ( mult_a_ring_ext_a_b @ r @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_add__pow__ldistr__int) ).
thf(733,plain,
! [A: a,B: a,C: int] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( mult_a_ring_ext_a_b @ r @ ( add_pow_a_b_int @ r @ C @ A ) @ B )
= ( add_pow_a_b_int @ r @ C @ ( mult_a_ring_ext_a_b @ r @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(187,axiom,
! [A: a,B: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( A
= ( add_a_b @ r @ B @ A ) )
= ( B
= ( zero_a_b @ r ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_add_Or__cancel__one_H) ).
thf(819,plain,
! [A: a,B: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( A
= ( add_a_b @ r @ B @ A ) )
= ( B
= ( zero_a_b @ r ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(221,axiom,
locali807230110ng_a_b @ r @ s,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_mult__submonoid__of__crng__axioms) ).
thf(904,plain,
locali807230110ng_a_b @ r @ s,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(6662,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ s3 )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ s3 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ~ $true
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( member_a @ ( add_a_b @ r @ t @ t ) @ ( partia1066395285xt_a_b @ r ) )
!= ( member_a @ t2 @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[901,2713]) ).
thf(6663,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ s3 )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ s3 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( member_a @ ( add_a_b @ r @ t @ t ) @ ( partia1066395285xt_a_b @ r ) )
!= ( member_a @ t2 @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(simp,[status(thm)],[6662]) ).
thf(6861,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ s3 )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ s3 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( add_a_b @ r @ t @ t )
!= t2 )
| ( ( partia1066395285xt_a_b @ r )
!= ( partia1066395285xt_a_b @ r ) ) ),
inference(simp,[status(thm)],[6663]) ).
thf(6881,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ s3 )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ s3 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( add_a_b @ r @ t @ t )
!= t2 ) ),
inference(simp,[status(thm)],[6861]) ).
thf(290,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
=> ! [C: int] : ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ C ) ) ),
inference(miniscope,[status(thm)],[289]) ).
thf(291,plain,
! [C: int,B: int,A: int] :
( ~ ( ord_less_eq_int @ A @ B )
| ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ C ) ) ),
inference(cnf,[status(esa)],[290]) ).
thf(100,axiom,
! [A: int,B: int,C: int] :
( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ A @ C ) )
= ( minus_minus_int @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_add__diff__cancel__left) ).
thf(545,plain,
! [A: int,B: int,C: int] :
( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ A @ C ) )
= ( minus_minus_int @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(6,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ A @ C ) )
=> ( ord_less_eq_int @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_add__le__imp__le__left) ).
thf(259,plain,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ A @ C ) )
=> ( ord_less_eq_int @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(60,axiom,
! [A: int,B: int,C: int] :
( ( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ A @ C ) )
= ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_add_Oleft__cancel) ).
thf(413,plain,
! [A: int,B: int,C: int] :
( ( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ A @ C ) )
= ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(9187,plain,
! [B: a > $o,A: a] :
( ( member_a @ A @ ( collect_a @ B ) )
| ( ( member_a @ s2 @ ( partia1066395285xt_a_b @ r ) )
!= ( B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[668,297]) ).
thf(9339,plain,
( member_a @ s2
@ ( collect_a
@ ^ [A: a] : ( member_a @ A @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(pre_uni,[status(thm)],[9187:[bind(A,$thf( s2 )),bind(B,$thf( ^ [C: a] : ( member_a @ C @ ( partia1066395285xt_a_b @ r ) ) ))]]) ).
thf(9895,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ t2 )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ t2 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ~ $true
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( member_a @ ( add_a_b @ r @ t @ t ) @ ( partia1066395285xt_a_b @ r ) )
!= ( member_a @ ( product_fst_a_a @ x ) @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[641,2726]) ).
thf(9896,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ t2 )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ t2 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( member_a @ ( add_a_b @ r @ t @ t ) @ ( partia1066395285xt_a_b @ r ) )
!= ( member_a @ ( product_fst_a_a @ x ) @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(simp,[status(thm)],[9895]) ).
thf(10094,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ t2 )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ t2 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( add_a_b @ r @ t @ t )
!= ( product_fst_a_a @ x ) )
| ( ( partia1066395285xt_a_b @ r )
!= ( partia1066395285xt_a_b @ r ) ) ),
inference(simp,[status(thm)],[9896]) ).
thf(10127,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ t2 )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ t2 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( add_a_b @ r @ t @ t )
!= ( product_fst_a_a @ x ) ) ),
inference(simp,[status(thm)],[10094]) ).
thf(70,axiom,
! [A: partia1833973666xt_a_b,B: set_a] :
( ( locali807230110ng_a_b @ A @ B )
=> ( locali880295127ng_a_b @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_mult__submonoid__of__crng_Oaxioms_I2_J) ).
thf(445,plain,
! [A: partia1833973666xt_a_b,B: set_a] :
( ( locali807230110ng_a_b @ A @ B )
=> ( locali880295127ng_a_b @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(16513,plain,
! [B: a,A: set_a] :
( ( A = bot_bot_set_a )
| ~ $true
| ( ( member_a @ ( sk2 @ A ) @ A )
!= ( member_a @ B
@ ( collect_a
@ ^ [C: a] : $false ) ) ) ),
inference(paramod_ordered,[status(thm)],[350,10567]) ).
thf(16514,plain,
! [B: a,A: set_a] :
( ( A = bot_bot_set_a )
| ( ( member_a @ ( sk2 @ A ) @ A )
!= ( member_a @ B
@ ( collect_a
@ ^ [C: a] : $false ) ) ) ),
inference(simp,[status(thm)],[16513]) ).
thf(16515,plain,
( ( collect_a
@ ^ [A: a] : $false )
= bot_bot_set_a ),
inference(pattern_uni,[status(thm)],[16514:[bind(A,$thf( collect_a @ ^ [C: a] : $false )),bind(B,$thf( sk2 @ ( collect_a @ ^ [C: a] : $false ) ))]]) ).
thf(119,axiom,
( ( partia1066395285xt_a_b @ r )
!= bot_bot_set_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_carrier__not__empty) ).
thf(611,plain,
( ( partia1066395285xt_a_b @ r )
!= bot_bot_set_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(153,axiom,
! [A: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( add_a_b @ r @ A @ ( zero_a_b @ r ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_r__zero) ).
thf(713,plain,
! [A: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( add_a_b @ r @ A @ ( zero_a_b @ r ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(334,plain,
! [B: int,A: int] :
( ~ ( ord_less_eq_int @ A @ B )
| ( ( plus_plus_int @ ( minus_minus_int @ B @ A ) @ A )
= B ) ),
inference(cnf,[status(esa)],[333]) ).
thf(335,plain,
! [B: int,A: int] :
( ( ( plus_plus_int @ ( minus_minus_int @ B @ A ) @ A )
= B )
| ~ ( ord_less_eq_int @ A @ B ) ),
inference(lifteq,[status(thm)],[334]) ).
thf(226,axiom,
! [A: a,B: a] :
( ( a_minus_a_b @ r @ A @ B )
= ( add_a_b @ r @ A @ ( a_inv_a_b @ r @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_minus__eq) ).
thf(919,plain,
! [A: a,B: a] :
( ( a_minus_a_b @ r @ A @ B )
= ( add_a_b @ r @ A @ ( a_inv_a_b @ r @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(150,axiom,
! [A: a,B: a] :
( ( ( add_a_b @ r @ A @ B )
= ( zero_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( a_inv_a_b @ r @ B )
= A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_minus__equality) ).
thf(704,plain,
! [A: a,B: a] :
( ( ( add_a_b @ r @ A @ B )
= ( zero_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( a_inv_a_b @ r @ B )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(237,axiom,
( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
= ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_f31) ).
thf(947,plain,
( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
= ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(3020,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ t )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ t @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ~ $true
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( member_a @ ( add_a_b @ r @ t @ t ) @ ( partia1066395285xt_a_b @ r ) )
!= ( member_a @ ( product_snd_a_a @ y ) @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[769,2699]) ).
thf(3021,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ t )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ t @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( member_a @ ( add_a_b @ r @ t @ t ) @ ( partia1066395285xt_a_b @ r ) )
!= ( member_a @ ( product_snd_a_a @ y ) @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(simp,[status(thm)],[3020]) ).
thf(3199,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ t )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ t @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( add_a_b @ r @ t @ t )
!= ( product_snd_a_a @ y ) )
| ( ( partia1066395285xt_a_b @ r )
!= ( partia1066395285xt_a_b @ r ) ) ),
inference(simp,[status(thm)],[3021]) ).
thf(3223,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ t )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ t @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( add_a_b @ r @ t @ t )
!= ( product_snd_a_a @ y ) ) ),
inference(simp,[status(thm)],[3199]) ).
thf(144,axiom,
( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) )
= ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ t2 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ t2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_f12) ).
thf(681,plain,
( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) )
= ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ t2 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ t2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(62,axiom,
! [A: int,B: int] :
( ( uminus_uminus_int @ ( minus_minus_int @ A @ B ) )
= ( minus_minus_int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_minus__diff__eq) ).
thf(419,plain,
! [A: int,B: int] :
( ( uminus_uminus_int @ ( minus_minus_int @ A @ B ) )
= ( minus_minus_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(121,axiom,
! [A: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( mult_a_ring_ext_a_b @ r @ A @ ( zero_a_b @ r ) )
= ( zero_a_b @ r ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_r__null) ).
thf(616,plain,
! [A: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( mult_a_ring_ext_a_b @ r @ A @ ( zero_a_b @ r ) )
= ( zero_a_b @ r ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(270,plain,
! [B: int,A: int] :
( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
= ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ A ) ),
inference(cnf,[status(esa)],[269]) ).
thf(271,plain,
! [B: int,A: int] :
( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
= ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ A ) ),
inference(lifteq,[status(thm)],[270]) ).
thf(24,axiom,
( minus_minus_int
= ( ^ [A: int,B: int] : ( plus_plus_int @ A @ ( uminus_uminus_int @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_ab__group__add__class_Oab__diff__conv__add__uminus) ).
thf(310,plain,
( minus_minus_int
= ( ^ [A: int,B: int] : ( plus_plus_int @ A @ ( uminus_uminus_int @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(311,plain,
( ( ^ [A: int,B: int] : ( plus_plus_int @ A @ ( uminus_uminus_int @ B ) ) )
= minus_minus_int ),
inference(lifteq,[status(thm)],[310]) ).
thf(979,plain,
! [A: int] :
( ( ^ [B: int] : ( plus_plus_int @ A @ ( uminus_uminus_int @ B ) ) )
= ( minus_minus_int @ A ) ),
inference(func_ext,[status(esa)],[311]) ).
thf(12473,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ s3 )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ s3 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ~ $true
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( member_a @ ( add_a_b @ r @ t @ t ) @ ( partia1066395285xt_a_b @ r ) )
!= ( member_a @ sk23 @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[12469,2713]) ).
thf(12474,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ s3 )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ s3 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( member_a @ ( add_a_b @ r @ t @ t ) @ ( partia1066395285xt_a_b @ r ) )
!= ( member_a @ sk23 @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(simp,[status(thm)],[12473]) ).
thf(12520,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ s3 )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ s3 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( add_a_b @ r @ t @ t )
!= sk23 )
| ( ( partia1066395285xt_a_b @ r )
!= ( partia1066395285xt_a_b @ r ) ) ),
inference(simp,[status(thm)],[12474]) ).
thf(12537,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ s3 )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ s3 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( add_a_b @ r @ t @ t )
!= sk23 ) ),
inference(simp,[status(thm)],[12520]) ).
thf(160,axiom,
! [A: partia1833973666xt_a_b,B: a] :
( ( semiring_a_b @ A )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ A ) )
=> ( ( add_a_b @ A @ B @ ( zero_a_b @ A ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_semiring_Osemiring__simprules_I11_J) ).
thf(737,plain,
! [A: partia1833973666xt_a_b,B: a] :
( ( semiring_a_b @ A )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ A ) )
=> ( ( add_a_b @ A @ B @ ( zero_a_b @ A ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(205,axiom,
! [A: a,B: a,C: int] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( add_pow_a_b_int @ r @ C @ ( add_a_b @ r @ A @ B ) )
= ( add_a_b @ r @ ( add_pow_a_b_int @ r @ C @ A ) @ ( add_pow_a_b_int @ r @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_add_Oint__pow__distrib) ).
thf(863,plain,
! [A: a,B: a,C: int] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( add_pow_a_b_int @ r @ C @ ( add_a_b @ r @ A @ B ) )
= ( add_a_b @ r @ ( add_pow_a_b_int @ r @ C @ A ) @ ( add_pow_a_b_int @ r @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(9123,plain,
! [B: a > $o,A: a] :
( ( member_a @ A @ ( collect_a @ B ) )
| ( ( B @ A )
!= ( member_a @ sk15 @ s ) ) ),
inference(paramod_ordered,[status(thm)],[297,952]) ).
thf(9311,plain,
( member_a @ sk15
@ ( collect_a
@ ^ [A: a] : ( member_a @ A @ s ) ) ),
inference(pre_uni,[status(thm)],[9123:[bind(A,$thf( sk15 )),bind(B,$thf( ^ [C: a] : ( member_a @ C @ s ) ))]]) ).
thf(10418,plain,
! [B: a > $o,A: a] :
( ( member_a @ A @ ( collect_a @ B ) )
| ( ( B @ A )
!= ( member_a @ sk15
@ ( collect_a
@ ^ [C: a] : ( member_a @ C @ s ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[297,9311]) ).
thf(10457,plain,
( member_a @ sk15
@ ( collect_a
@ ^ [A: a] :
( member_a @ A
@ ( collect_a
@ ^ [B: a] : ( member_a @ B @ s ) ) ) ) ),
inference(pre_uni,[status(thm)],[10418:[bind(A,$thf( sk15 )),bind(B,$thf( ^ [C: a] : ( member_a @ C @ ( collect_a @ ^ [D: a] : ( member_a @ D @ s ) ) ) ))]]) ).
thf(215,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( ord_less_eq_set_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ord_less_eq_set_a @ ( set_add_a_b @ r @ A @ B ) @ ( partia1066395285xt_a_b @ r ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_setadd__subset__G) ).
thf(890,plain,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( ord_less_eq_set_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ord_less_eq_set_a @ ( set_add_a_b @ r @ A @ B ) @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(322,plain,
! [A: int] :
( ( uminus_uminus_int @ ( uminus_uminus_int @ A ) )
= A ),
inference(cnf,[status(esa)],[321]) ).
thf(323,plain,
! [A: int] :
( ( uminus_uminus_int @ ( uminus_uminus_int @ A ) )
= A ),
inference(lifteq,[status(thm)],[322]) ).
thf(114,axiom,
! [A: a,B: int] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( add_pow_a_b_int @ r @ ( uminus_uminus_int @ B ) @ A )
= ( a_inv_a_b @ r @ ( add_pow_a_b_int @ r @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_add_Oint__pow__neg) ).
thf(594,plain,
! [A: a,B: int] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( add_pow_a_b_int @ r @ ( uminus_uminus_int @ B ) @ A )
= ( a_inv_a_b @ r @ ( add_pow_a_b_int @ r @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(157,axiom,
! [A: a,B: a,C: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ C @ ( partia1066395285xt_a_b @ r ) )
=> ( ( add_a_b @ r @ ( add_a_b @ r @ A @ B ) @ C )
= ( add_a_b @ r @ A @ ( add_a_b @ r @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_add_Om__assoc) ).
thf(726,plain,
! [A: a,B: a,C: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ C @ ( partia1066395285xt_a_b @ r ) )
=> ( ( add_a_b @ r @ ( add_a_b @ r @ A @ B ) @ C )
= ( add_a_b @ r @ A @ ( add_a_b @ r @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(93,axiom,
! [A: int,B: int] :
( ( minus_minus_int @ A @ ( uminus_uminus_int @ B ) )
= ( plus_plus_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_diff__minus__eq__add) ).
thf(520,plain,
! [A: int,B: int] :
( ( minus_minus_int @ A @ ( uminus_uminus_int @ B ) )
= ( plus_plus_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(250,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
=> ! [C: int,D: int] :
( ( ord_less_eq_int @ C @ D )
=> ( ord_less_eq_int @ ( minus_minus_int @ A @ D ) @ ( minus_minus_int @ B @ C ) ) ) ),
inference(miniscope,[status(thm)],[249]) ).
thf(251,plain,
! [D: int,C: int,B: int,A: int] :
( ~ ( ord_less_eq_int @ A @ B )
| ~ ( ord_less_eq_int @ C @ D )
| ( ord_less_eq_int @ ( minus_minus_int @ A @ D ) @ ( minus_minus_int @ B @ C ) ) ),
inference(cnf,[status(esa)],[250]) ).
thf(242,axiom,
! [A: partia1833973666xt_a_b,B: a,C: a] :
( ( semiring_a_b @ A )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ A ) )
=> ( ( member_a @ C @ ( partia1066395285xt_a_b @ A ) )
=> ( member_a @ ( add_a_b @ A @ B @ C ) @ ( partia1066395285xt_a_b @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_semiring_Osemiring__simprules_I1_J) ).
thf(964,plain,
! [A: partia1833973666xt_a_b,B: a,C: a] :
( ( semiring_a_b @ A )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ A ) )
=> ( ( member_a @ C @ ( partia1066395285xt_a_b @ A ) )
=> ( member_a @ ( add_a_b @ A @ B @ C ) @ ( partia1066395285xt_a_b @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(225,axiom,
! [A: partia1833973666xt_a_b,B: a] :
( ( semiring_a_b @ A )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ A ) )
=> ( ( add_a_b @ A @ ( zero_a_b @ A ) @ B )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_semiring_Osemiring__simprules_I6_J) ).
thf(915,plain,
! [A: partia1833973666xt_a_b,B: a] :
( ( semiring_a_b @ A )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ A ) )
=> ( ( add_a_b @ A @ ( zero_a_b @ A ) @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(236,axiom,
! [A: a,B: a,C: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ C @ ( partia1066395285xt_a_b @ r ) )
=> ( ( A
= ( add_a_b @ r @ ( a_inv_a_b @ r @ B ) @ C ) )
= ( C
= ( add_a_b @ r @ B @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_add_Oinv__solve__left) ).
thf(943,plain,
! [A: a,B: a,C: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ C @ ( partia1066395285xt_a_b @ r ) )
=> ( ( A
= ( add_a_b @ r @ ( a_inv_a_b @ r @ B ) @ C ) )
= ( C
= ( add_a_b @ r @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(184,axiom,
! [A: partia1833973666xt_a_b,B: a,C: a] :
( ( semiring_a_b @ A )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ A ) )
=> ( ( member_a @ C @ ( partia1066395285xt_a_b @ A ) )
=> ( member_a @ ( mult_a_ring_ext_a_b @ A @ B @ C ) @ ( partia1066395285xt_a_b @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_semiring_Osemiring__simprules_I3_J) ).
thf(811,plain,
! [A: partia1833973666xt_a_b,B: a,C: a] :
( ( semiring_a_b @ A )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ A ) )
=> ( ( member_a @ C @ ( partia1066395285xt_a_b @ A ) )
=> ( member_a @ ( mult_a_ring_ext_a_b @ A @ B @ C ) @ ( partia1066395285xt_a_b @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(189,axiom,
( ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) )
= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_f32) ).
thf(827,plain,
( ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) )
= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(172,axiom,
member_a @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) ) @ ( partia1066395285xt_a_b @ r ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_f37) ).
thf(780,plain,
member_a @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) ) @ ( partia1066395285xt_a_b @ r ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(212,axiom,
ord_less_eq_set_a @ s @ ( partia1066395285xt_a_b @ r ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_subset) ).
thf(883,plain,
ord_less_eq_set_a @ s @ ( partia1066395285xt_a_b @ r ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(22,axiom,
! [A: int,B: int,C: int,D: int] :
( ( ( minus_minus_int @ A @ B )
= ( minus_minus_int @ C @ D ) )
=> ( ( ord_less_eq_int @ A @ B )
= ( ord_less_eq_int @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_diff__eq__diff__less__eq) ).
thf(304,plain,
! [A: int,B: int,C: int,D: int] :
( ( ( minus_minus_int @ A @ B )
= ( minus_minus_int @ C @ D ) )
=> ( ( ord_less_eq_int @ A @ B )
= ( ord_less_eq_int @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(305,plain,
! [D: int,C: int,B: int,A: int] :
( ( ( minus_minus_int @ A @ B )
!= ( minus_minus_int @ C @ D ) )
| ( ( ord_less_eq_int @ A @ B )
= ( ord_less_eq_int @ C @ D ) ) ),
inference(cnf,[status(esa)],[304]) ).
thf(306,plain,
! [D: int,C: int,B: int,A: int] :
( ( ( minus_minus_int @ A @ B )
!= ( minus_minus_int @ C @ D ) )
| ( ( ord_less_eq_int @ A @ B )
= ( ord_less_eq_int @ C @ D ) ) ),
inference(lifteq,[status(thm)],[305]) ).
thf(227,axiom,
( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) )
= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_f29) ).
thf(922,plain,
( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) )
= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(207,axiom,
! [A: a,B: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( mult_a_ring_ext_a_b @ r @ ( a_inv_a_b @ r @ A ) @ B )
= ( a_inv_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_l__minus) ).
thf(868,plain,
! [A: a,B: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( mult_a_ring_ext_a_b @ r @ ( a_inv_a_b @ r @ A ) @ B )
= ( a_inv_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(9,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ C @ B ) )
=> ( ord_less_eq_int @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_add__le__imp__le__right) ).
thf(267,plain,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ C @ B ) )
=> ( ord_less_eq_int @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(200,axiom,
( ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) )
= ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ t2 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ t2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39__092_060open_062t_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_Ar_J_J_A_092_060ominus_062_At_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Is_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ay_H_A_092_060otimes_062_Afst_Ax_H_J_J_A_061_At_H_A_092_060otimes_062_As_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_At_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Ar_J_A_092_060ominus_062_At_H_A_092_060otimes_062_As_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_At_A_092_060otimes_062_A_Is_A_092_060otimes_062_Afst_Ax_H_J_092_060close_062) ).
thf(851,plain,
( ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) )
= ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ t2 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ t2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(89,axiom,
! [A: partia1833973666xt_a_b,B: set_a] :
( ( locali425460998xt_a_b @ A @ B )
=> ( ord_less_eq_set_a @ B @ ( partia1066395285xt_a_b @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_Localization__Mirabelle__afvchqjmgj_Osubmonoid_Osubset) ).
thf(505,plain,
! [A: partia1833973666xt_a_b,B: set_a] :
( ( locali425460998xt_a_b @ A @ B )
=> ( ord_less_eq_set_a @ B @ ( partia1066395285xt_a_b @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(68,axiom,
! [A: int,B: int] :
( ( ( uminus_uminus_int @ A )
= ( uminus_uminus_int @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_neg__equal__iff__equal) ).
thf(438,plain,
! [A: int,B: int] :
( ( ( uminus_uminus_int @ A )
= ( uminus_uminus_int @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(14550,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ s2 )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ s2 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ~ $true
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( member_a @ ( add_a_b @ r @ t @ t ) @ ( partia1066395285xt_a_b @ r ) )
!= ( member_a @ t @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[878,2741]) ).
thf(14551,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ s2 )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ s2 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( member_a @ ( add_a_b @ r @ t @ t ) @ ( partia1066395285xt_a_b @ r ) )
!= ( member_a @ t @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(simp,[status(thm)],[14550]) ).
thf(14832,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ s2 )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ s2 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( add_a_b @ r @ t @ t )
!= t )
| ( ( partia1066395285xt_a_b @ r )
!= ( partia1066395285xt_a_b @ r ) ) ),
inference(simp,[status(thm)],[14551]) ).
thf(14862,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ s2 )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ s2 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( add_a_b @ r @ t @ t )
!= t ) ),
inference(simp,[status(thm)],[14832]) ).
thf(135,axiom,
( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) )
= ( a_minus_a_b @ r @ ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52__092_060open_062t_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_Ar_J_A_092_060ominus_062_As_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ay_H_A_092_060otimes_062_Afst_Ax_H_J_J_A_092_060oplus_062_At_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_A_092_060otimes_062_Ar_H_J_A_092_060ominus_062_As_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Afst_Ay_H_J_J_A_061_At_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_Ar_J_J_A_092_060ominus_062_At_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Is_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ay_H_A_092_060otimes_062_Afst_Ax_H_J_J_A_092_060oplus_062_At_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_A_092_060otimes_062_Ar_H_J_J_A_092_060ominus_062_At_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Is_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Afst_Ay_H_J_J_092_060close_062) ).
thf(653,plain,
( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) )
= ( a_minus_a_b @ r @ ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(141,axiom,
! [A: int] :
( ( add_pow_a_b_int @ r @ A @ ( zero_a_b @ r ) )
= ( zero_a_b @ r ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_add_Oint__pow__one) ).
thf(673,plain,
! [A: int] :
( ( add_pow_a_b_int @ r @ A @ ( zero_a_b @ r ) )
= ( zero_a_b @ r ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(674,plain,
! [A: int] :
( ( add_pow_a_b_int @ r @ A @ ( zero_a_b @ r ) )
= ( zero_a_b @ r ) ),
inference(cnf,[status(esa)],[673]) ).
thf(675,plain,
! [A: int] :
( ( add_pow_a_b_int @ r @ A @ ( zero_a_b @ r ) )
= ( zero_a_b @ r ) ),
inference(lifteq,[status(thm)],[674]) ).
thf(112,axiom,
! [A: partia1833973666xt_a_b,B: set_a,C: a,D: a] :
( ( locali425460998xt_a_b @ A @ B )
=> ( ( member_a @ C @ B )
=> ( ( member_a @ D @ B )
=> ( member_a @ ( mult_a_ring_ext_a_b @ A @ C @ D ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_Localization__Mirabelle__afvchqjmgj_Osubmonoid_Om__closed) ).
thf(589,plain,
! [A: partia1833973666xt_a_b,B: set_a,C: a,D: a] :
( ( locali425460998xt_a_b @ A @ B )
=> ( ( member_a @ C @ B )
=> ( ( member_a @ D @ B )
=> ( member_a @ ( mult_a_ring_ext_a_b @ A @ C @ D ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(101,axiom,
! [A: int,B: int,C: int] :
( ( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ A @ C ) )
=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_add__left__imp__eq) ).
thf(548,plain,
! [A: int,B: int,C: int] :
( ( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ A @ C ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(230,axiom,
! [A: a,B: a] :
( ( ( add_a_b @ r @ A @ B )
= ( zero_a_b @ r ) )
=> ( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( add_a_b @ r @ B @ A )
= ( zero_a_b @ r ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_add_Oinv__comm) ).
thf(927,plain,
! [A: a,B: a] :
( ( ( add_a_b @ r @ A @ B )
= ( zero_a_b @ r ) )
=> ( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( add_a_b @ r @ B @ A )
= ( zero_a_b @ r ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(9909,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ t2 )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ t2 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ~ $true
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( member_a @ ( add_a_b @ r @ t @ t ) @ ( partia1066395285xt_a_b @ r ) )
!= ( member_a @ s3 @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[867,2726]) ).
thf(9910,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ t2 )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ t2 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( member_a @ ( add_a_b @ r @ t @ t ) @ ( partia1066395285xt_a_b @ r ) )
!= ( member_a @ s3 @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(simp,[status(thm)],[9909]) ).
thf(10100,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ t2 )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ t2 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( add_a_b @ r @ t @ t )
!= s3 )
| ( ( partia1066395285xt_a_b @ r )
!= ( partia1066395285xt_a_b @ r ) ) ),
inference(simp,[status(thm)],[9910]) ).
thf(10132,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ t2 )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ t2 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( add_a_b @ r @ t @ t )
!= s3 ) ),
inference(simp,[status(thm)],[10100]) ).
thf(234,axiom,
member_a @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) @ ( partia1066395285xt_a_b @ r ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_f38) ).
thf(939,plain,
member_a @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) @ ( partia1066395285xt_a_b @ r ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(102,axiom,
! [A: set_a] :
( ( ord_less_eq_set_a @ A @ bot_bot_set_a )
= ( A = bot_bot_set_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_subset__empty) ).
thf(553,plain,
! [A: set_a] :
( ( ord_less_eq_set_a @ A @ bot_bot_set_a )
= ( A = bot_bot_set_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(7061,plain,
( ( ( add_a_b @ r @ s3 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( add_a_b @ r @ t @ t )
!= s3 )
| ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ s3 )
!= ( add_a_b @ r @ s3 @ ( zero_a_b @ r ) ) )
| ( ( zero_a_b @ r )
!= ( zero_a_b @ r ) ) ),
inference(eqfactor_ordered,[status(thm)],[6878]) ).
thf(7063,plain,
( ( ( add_a_b @ r @ s3 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( add_a_b @ r @ t @ t )
!= s3 )
| ( r != r )
| ( ( add_a_b @ r @ t @ t )
!= s3 )
| ( ( zero_a_b @ r )
!= s3 ) ),
inference(simp,[status(thm)],[7061]) ).
thf(7070,plain,
( ( ( add_a_b @ r @ s3 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( add_a_b @ r @ t @ t )
!= s3 )
| ( ( zero_a_b @ r )
!= s3 ) ),
inference(simp,[status(thm)],[7063]) ).
thf(178,axiom,
! [A: set_a,B: a] :
( ( ord_less_eq_set_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ord_less_eq_set_a @ ( a_l_coset_a_b @ r @ B @ A ) @ ( partia1066395285xt_a_b @ r ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_a__l__coset__subset__G) ).
thf(795,plain,
! [A: set_a,B: a] :
( ( ord_less_eq_set_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ord_less_eq_set_a @ ( a_l_coset_a_b @ r @ B @ A ) @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(3010,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ t )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ t @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ~ $true
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( member_a @ ( add_a_b @ r @ t @ t ) @ ( partia1066395285xt_a_b @ r ) )
!= ( member_a @ ( product_fst_a_a @ x ) @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[641,2699]) ).
thf(3011,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ t )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ t @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( member_a @ ( add_a_b @ r @ t @ t ) @ ( partia1066395285xt_a_b @ r ) )
!= ( member_a @ ( product_fst_a_a @ x ) @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(simp,[status(thm)],[3010]) ).
thf(3201,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ t )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ t @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( add_a_b @ r @ t @ t )
!= ( product_fst_a_a @ x ) )
| ( ( partia1066395285xt_a_b @ r )
!= ( partia1066395285xt_a_b @ r ) ) ),
inference(simp,[status(thm)],[3011]) ).
thf(3206,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ t )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ t @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( add_a_b @ r @ t @ t )
!= ( product_fst_a_a @ x ) ) ),
inference(simp,[status(thm)],[3201]) ).
thf(244,axiom,
locali1648887798ac_a_b @ r @ s,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_eq__obj__rng__of__frac__axioms) ).
thf(968,plain,
locali1648887798ac_a_b @ r @ s,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(75,axiom,
! [A: int,B: int] :
( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
= ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_add_Oinverse__distrib__swap) ).
thf(458,plain,
! [A: int,B: int] :
( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
= ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(188,axiom,
! [A: a,B: a,C: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ C @ ( partia1066395285xt_a_b @ r ) )
=> ( ( ( add_a_b @ r @ B @ ( a_inv_a_b @ r @ C ) )
= A )
= ( B
= ( add_a_b @ r @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_add_Oinv__solve__right_H) ).
thf(823,plain,
! [A: a,B: a,C: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ C @ ( partia1066395285xt_a_b @ r ) )
=> ( ( ( add_a_b @ r @ B @ ( a_inv_a_b @ r @ C ) )
= A )
= ( B
= ( add_a_b @ r @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(170,axiom,
( ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) )
= ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30__092_060open_062t_H_A_092_060otimes_062_A_Isnd_Ay_H_A_092_060otimes_062_Ar_H_A_092_060ominus_062_As_H_A_092_060otimes_062_Afst_Ay_H_J_A_061_At_H_A_092_060otimes_062_A_Isnd_Ay_H_A_092_060otimes_062_Ar_H_J_A_092_060ominus_062_At_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_Afst_Ay_H_J_092_060close_062) ).
thf(776,plain,
( ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) )
= ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(208,axiom,
! [A: partia1833973666xt_a_b,B: a] :
( ( semiring_a_b @ A )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ A ) )
=> ( ( mult_a_ring_ext_a_b @ A @ B @ ( zero_a_b @ A ) )
= ( zero_a_b @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_semiring_Or__null) ).
thf(872,plain,
! [A: partia1833973666xt_a_b,B: a] :
( ( semiring_a_b @ A )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ A ) )
=> ( ( mult_a_ring_ext_a_b @ A @ B @ ( zero_a_b @ A ) )
= ( zero_a_b @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(151,axiom,
( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) ) )
= ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50__092_060open_062t_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_Ar_A_092_060oplus_062_As_A_092_060otimes_062_Ar_H_J_J_A_061_At_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_J_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_Ar_J_A_092_060oplus_062_At_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_J_A_092_060otimes_062_A_Is_A_092_060otimes_062_Ar_H_J_092_060close_062) ).
thf(707,plain,
( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) ) )
= ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(214,axiom,
! [A: product_prod_a_a,B: product_prod_a_a] :
( ( ( product_fst_a_a @ A )
= ( product_fst_a_a @ B ) )
=> ( ( ( product_snd_a_a @ A )
= ( product_snd_a_a @ B ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_prod__eqI) ).
thf(887,plain,
! [A: product_prod_a_a,B: product_prod_a_a] :
( ( ( product_fst_a_a @ A )
= ( product_fst_a_a @ B ) )
=> ( ( ( product_snd_a_a @ A )
= ( product_snd_a_a @ B ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(12600,plain,
! [A: a] :
( ~ $true
| ( ( member_a @ s2
@ ( collect_a
@ ^ [B: a] : ( member_a @ B @ ( partia1066395285xt_a_b @ r ) ) ) )
!= ( member_a @ A @ bot_bot_set_a ) ) ),
inference(paramod_ordered,[status(thm)],[9339,383]) ).
thf(12601,plain,
! [A: a] :
( ( member_a @ s2
@ ( collect_a
@ ^ [B: a] : ( member_a @ B @ ( partia1066395285xt_a_b @ r ) ) ) )
!= ( member_a @ A @ bot_bot_set_a ) ),
inference(simp,[status(thm)],[12600]) ).
thf(12635,plain,
! [A: a] :
( ( s2 != A )
| ( ( collect_a
@ ^ [B: a] : ( member_a @ B @ ( partia1066395285xt_a_b @ r ) ) )
!= bot_bot_set_a ) ),
inference(simp,[status(thm)],[12601]) ).
thf(12648,plain,
( ( collect_a
@ ^ [A: a] : ( member_a @ A @ ( partia1066395285xt_a_b @ r ) ) )
!= bot_bot_set_a ),
inference(simp,[status(thm)],[12635]) ).
thf(10500,plain,
! [B: a > $o,A: a] :
( ( member_a @ A @ ( collect_a @ B ) )
| ( ( B @ A )
!= ( member_a @ sk6
@ ( collect_a
@ ^ [C: a] : ( member_a @ C @ s ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[297,9347]) ).
thf(10540,plain,
( member_a @ sk6
@ ( collect_a
@ ^ [A: a] :
( member_a @ A
@ ( collect_a
@ ^ [B: a] : ( member_a @ B @ s ) ) ) ) ),
inference(pre_uni,[status(thm)],[10500:[bind(A,$thf( sk6 )),bind(B,$thf( ^ [C: a] : ( member_a @ C @ ( collect_a @ ^ [D: a] : ( member_a @ D @ s ) ) ) ))]]) ).
thf(9901,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ t2 )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ t2 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ~ $true
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( member_a @ ( add_a_b @ r @ t @ t ) @ ( partia1066395285xt_a_b @ r ) )
!= ( member_a @ s2 @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[668,2726]) ).
thf(9902,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ t2 )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ t2 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( member_a @ ( add_a_b @ r @ t @ t ) @ ( partia1066395285xt_a_b @ r ) )
!= ( member_a @ s2 @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(simp,[status(thm)],[9901]) ).
thf(10090,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ t2 )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ t2 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( add_a_b @ r @ t @ t )
!= s2 )
| ( ( partia1066395285xt_a_b @ r )
!= ( partia1066395285xt_a_b @ r ) ) ),
inference(simp,[status(thm)],[9902]) ).
thf(10123,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ t2 )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ t2 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( add_a_b @ r @ t @ t )
!= s2 ) ),
inference(simp,[status(thm)],[10090]) ).
thf(177,axiom,
! [A: a,B: a,C: int] :
( ( ( add_a_b @ r @ A @ B )
= ( add_a_b @ r @ B @ A ) )
=> ( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( add_pow_a_b_int @ r @ C @ ( add_a_b @ r @ A @ B ) )
= ( add_a_b @ r @ ( add_pow_a_b_int @ r @ C @ A ) @ ( add_pow_a_b_int @ r @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_add_Oint__pow__mult__distrib) ).
thf(791,plain,
! [A: a,B: a,C: int] :
( ( ( add_a_b @ r @ A @ B )
= ( add_a_b @ r @ B @ A ) )
=> ( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( add_pow_a_b_int @ r @ C @ ( add_a_b @ r @ A @ B ) )
= ( add_a_b @ r @ ( add_pow_a_b_int @ r @ C @ A ) @ ( add_pow_a_b_int @ r @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(69,axiom,
! [A: set_a,B: set_a] :
( ! [C: a] :
( ( member_a @ C @ A )
=> ( member_a @ C @ B ) )
=> ( ord_less_eq_set_a @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_subsetI) ).
thf(441,plain,
! [A: set_a,B: set_a] :
( ! [C: a] :
( ( member_a @ C @ A )
=> ( member_a @ C @ B ) )
=> ( ord_less_eq_set_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(45,axiom,
! [A: int,B: int,C: int,D: int] :
( ( A
= ( plus_plus_int @ B @ C ) )
=> ( ( plus_plus_int @ A @ D )
= ( plus_plus_int @ B @ ( plus_plus_int @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_group__cancel_Oadd1) ).
thf(370,plain,
! [A: int,B: int,C: int,D: int] :
( ( A
= ( plus_plus_int @ B @ C ) )
=> ( ( plus_plus_int @ A @ D )
= ( plus_plus_int @ B @ ( plus_plus_int @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(88,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ A @ ( minus_minus_int @ B @ C ) )
= ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_le__diff__eq) ).
thf(502,plain,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ A @ ( minus_minus_int @ B @ C ) )
= ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(195,axiom,
member_a @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( partia1066395285xt_a_b @ r ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_f10) ).
thf(840,plain,
member_a @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( partia1066395285xt_a_b @ r ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(643,plain,
( ( ^ [A: partia1833973666xt_a_b,B: a,C: a] : ( add_a_b @ A @ B @ ( a_inv_a_b @ A @ C ) ) )
= a_minus_a_b ),
inference(lifteq,[status(thm)],[642]) ).
thf(12486,plain,
! [B: a > $o,A: a] :
( ( member_a @ A @ ( collect_a @ B ) )
| ( ( B @ A )
!= ( member_a @ sk23 @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[297,12469]) ).
thf(12523,plain,
( member_a @ sk23
@ ( collect_a
@ ^ [A: a] : ( member_a @ A @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(pre_uni,[status(thm)],[12486:[bind(A,$thf( sk23 )),bind(B,$thf( ^ [C: a] : ( member_a @ C @ ( partia1066395285xt_a_b @ r ) ) ))]]) ).
thf(162,axiom,
! [A: set_a] :
( ( ord_less_eq_set_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( A != bot_bot_set_a )
=> ( ! [B: a] :
( ( member_a @ B @ A )
=> ( member_a @ ( a_inv_a_b @ r @ B ) @ A ) )
=> ( ! [B: a] :
( ( member_a @ B @ A )
=> ! [C: a] :
( ( member_a @ C @ A )
=> ( member_a @ ( add_a_b @ r @ B @ C ) @ A ) ) )
=> ( member_a @ ( zero_a_b @ r ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_add_Oone__in__subset) ).
thf(744,plain,
! [A: set_a] :
( ( ord_less_eq_set_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( A != bot_bot_set_a )
=> ( ! [B: a] :
( ( member_a @ B @ A )
=> ( member_a @ ( a_inv_a_b @ r @ B ) @ A ) )
=> ( ! [B: a] :
( ( member_a @ B @ A )
=> ! [C: a] :
( ( member_a @ C @ A )
=> ( member_a @ ( add_a_b @ r @ B @ C ) @ A ) ) )
=> ( member_a @ ( zero_a_b @ r ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(612,plain,
( ( partia1066395285xt_a_b @ r )
!= bot_bot_set_a ),
inference(polarity_switch,[status(thm)],[611]) ).
thf(613,plain,
( ( partia1066395285xt_a_b @ r )
!= bot_bot_set_a ),
inference(lifteq,[status(thm)],[612]) ).
thf(50,axiom,
! [A: int,B: int,C: int] :
( ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C )
= ( minus_minus_int @ ( minus_minus_int @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_diff__right__commute) ).
thf(386,plain,
! [A: int,B: int,C: int] :
( ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C )
= ( minus_minus_int @ ( minus_minus_int @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(313,plain,
! [B: int,A: int] :
( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
= ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) ) ),
inference(cnf,[status(esa)],[312]) ).
thf(314,plain,
! [B: int,A: int] :
( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
= ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) ) ),
inference(lifteq,[status(thm)],[313]) ).
thf(209,axiom,
( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
= ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_f40) ).
thf(876,plain,
( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
= ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(72,axiom,
! [A: int,B: int,C: int] :
( ( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ C @ B ) )
= ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_add__right__cancel) ).
thf(450,plain,
! [A: int,B: int,C: int] :
( ( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ C @ B ) )
= ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(82,axiom,
! [A: int,B: int] :
( ( A
= ( uminus_uminus_int @ B ) )
= ( B
= ( uminus_uminus_int @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_equation__minus__iff) ).
thf(482,plain,
! [A: int,B: int] :
( ( A
= ( uminus_uminus_int @ B ) )
= ( B
= ( uminus_uminus_int @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(220,axiom,
member_a @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) @ ( partia1066395285xt_a_b @ r ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_f42) ).
thf(903,plain,
member_a @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) @ ( partia1066395285xt_a_b @ r ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(164,axiom,
! [A: a,B: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( a_inv_a_b @ r @ ( add_a_b @ r @ A @ B ) )
= ( a_minus_a_b @ r @ ( a_inv_a_b @ r @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_inv__add) ).
thf(759,plain,
! [A: a,B: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( a_inv_a_b @ r @ ( add_a_b @ r @ A @ B ) )
= ( a_minus_a_b @ r @ ( a_inv_a_b @ r @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(9091,plain,
! [B: a > $o,A: a] :
( ( member_a @ A @ ( collect_a @ B ) )
| ( ( B @ A )
!= ( member_a @ t @ s ) ) ),
inference(paramod_ordered,[status(thm)],[297,619]) ).
thf(9282,plain,
( member_a @ t
@ ( collect_a
@ ^ [A: a] : ( member_a @ A @ s ) ) ),
inference(pre_uni,[status(thm)],[9091:[bind(A,$thf( t )),bind(B,$thf( ^ [C: a] : ( member_a @ C @ s ) ))]]) ).
thf(10333,plain,
! [B: a > $o,A: a] :
( ( member_a @ A @ ( collect_a @ B ) )
| ( ( member_a @ t
@ ( collect_a
@ ^ [C: a] : ( member_a @ C @ s ) ) )
!= ( B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9282,297]) ).
thf(10376,plain,
( member_a @ t
@ ( collect_a
@ ^ [A: a] :
( member_a @ A
@ ( collect_a
@ ^ [B: a] : ( member_a @ B @ s ) ) ) ) ),
inference(pre_uni,[status(thm)],[10333:[bind(A,$thf( t )),bind(B,$thf( ^ [C: a] : ( member_a @ C @ ( collect_a @ ^ [D: a] : ( member_a @ D @ s ) ) ) ))]]) ).
thf(6668,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ s3 )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ s3 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ~ $true
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( member_a @ ( add_a_b @ r @ t @ t ) @ ( partia1066395285xt_a_b @ r ) )
!= ( member_a @ ( product_fst_a_a @ x ) @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[641,2713]) ).
thf(6669,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ s3 )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ s3 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( member_a @ ( add_a_b @ r @ t @ t ) @ ( partia1066395285xt_a_b @ r ) )
!= ( member_a @ ( product_fst_a_a @ x ) @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(simp,[status(thm)],[6668]) ).
thf(6862,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ s3 )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ s3 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( add_a_b @ r @ t @ t )
!= ( product_fst_a_a @ x ) )
| ( ( partia1066395285xt_a_b @ r )
!= ( partia1066395285xt_a_b @ r ) ) ),
inference(simp,[status(thm)],[6669]) ).
thf(6882,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ s3 )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ s3 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( add_a_b @ r @ t @ t )
!= ( product_fst_a_a @ x ) ) ),
inference(simp,[status(thm)],[6862]) ).
thf(9805,plain,
! [B: a > $o,A: a] :
( ( member_a @ A @ ( collect_a @ B ) )
| ( ( member_a @ sk22 @ s )
!= ( B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9779,297]) ).
thf(9834,plain,
( member_a @ sk22
@ ( collect_a
@ ^ [A: a] : ( member_a @ A @ s ) ) ),
inference(pre_uni,[status(thm)],[9805:[bind(A,$thf( sk22 )),bind(B,$thf( ^ [C: a] : ( member_a @ C @ s ) ))]]) ).
thf(198,axiom,
! [A: a,B: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( add_a_b @ r @ ( a_inv_a_b @ r @ A ) @ ( add_a_b @ r @ A @ B ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_r__neg1) ).
thf(845,plain,
! [A: a,B: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( add_a_b @ r @ ( a_inv_a_b @ r @ A ) @ ( add_a_b @ r @ A @ B ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(43,axiom,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
= ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_add_Oassoc) ).
thf(363,plain,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
= ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(103,axiom,
! [A: set_a,B: a] :
( ( A = bot_bot_set_a )
=> ~ ( member_a @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_equals0D) ).
thf(556,plain,
! [A: set_a,B: a] :
( ( A = bot_bot_set_a )
=> ~ ( member_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(149,axiom,
! [A: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ? [B: a] :
( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
& ( ( add_a_b @ r @ A @ B )
= ( zero_a_b @ r ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_add_Or__inv__ex) ).
thf(699,plain,
! [A: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ? [B: a] :
( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
& ( ( add_a_b @ r @ A @ B )
= ( zero_a_b @ r ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(257,plain,
! [C: int,B: int,A: int] :
( ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ C @ B ) )
= ( ord_less_eq_int @ A @ C ) ),
inference(cnf,[status(esa)],[256]) ).
thf(258,plain,
! [C: int,B: int,A: int] :
( ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ C @ B ) )
= ( ord_less_eq_int @ A @ C ) ),
inference(lifteq,[status(thm)],[257]) ).
thf(173,axiom,
( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) ) @ ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) )
= ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_f36) ).
thf(781,plain,
( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) ) @ ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) )
= ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(14584,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ s2 )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ s2 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ~ $true
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( member_a @ ( add_a_b @ r @ t @ t ) @ ( partia1066395285xt_a_b @ r ) )
!= ( member_a @ sk23 @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[12469,2741]) ).
thf(14585,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ s2 )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ s2 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( member_a @ ( add_a_b @ r @ t @ t ) @ ( partia1066395285xt_a_b @ r ) )
!= ( member_a @ sk23 @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(simp,[status(thm)],[14584]) ).
thf(14800,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ s2 )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ s2 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( add_a_b @ r @ t @ t )
!= sk23 )
| ( ( partia1066395285xt_a_b @ r )
!= ( partia1066395285xt_a_b @ r ) ) ),
inference(simp,[status(thm)],[14585]) ).
thf(14845,plain,
( ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ s2 )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ s2 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( add_a_b @ r @ t @ t )
!= sk23 ) ),
inference(simp,[status(thm)],[14800]) ).
thf(11777,plain,
( ( ( add_a_b @ r @ t2 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( add_a_b @ r @ t @ t )
!= t2 )
| ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ t2 )
!= ( add_a_b @ r @ t2 @ ( zero_a_b @ r ) ) )
| ( ( zero_a_b @ r )
!= ( zero_a_b @ r ) ) ),
inference(eqfactor_ordered,[status(thm)],[10133]) ).
thf(11779,plain,
( ( ( add_a_b @ r @ t2 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( add_a_b @ r @ t @ t )
!= t2 )
| ( r != r )
| ( ( add_a_b @ r @ t @ t )
!= t2 )
| ( ( zero_a_b @ r )
!= t2 ) ),
inference(simp,[status(thm)],[11777]) ).
thf(11780,plain,
( ( ( add_a_b @ r @ t2 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( add_a_b @ r @ t @ t )
!= t2 )
| ( ( zero_a_b @ r )
!= t2 ) ),
inference(simp,[status(thm)],[11779]) ).
thf(47,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ ( uminus_uminus_set_a @ A ) @ ( uminus_uminus_set_a @ B ) )
= ( ord_less_eq_set_a @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_Compl__subset__Compl__iff) ).
thf(378,plain,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ ( uminus_uminus_set_a @ A ) @ ( uminus_uminus_set_a @ B ) )
= ( ord_less_eq_set_a @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(91,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ord_less_eq_set_a @ ( uminus_uminus_set_a @ B ) @ ( uminus_uminus_set_a @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_Compl__anti__mono) ).
thf(510,plain,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ord_less_eq_set_a @ ( uminus_uminus_set_a @ B ) @ ( uminus_uminus_set_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(11962,plain,
! [B: a > $o,A: a] :
( ( member_a @ A @ ( collect_a @ B ) )
| ( ( member_a @ sk22
@ ( collect_a
@ ^ [C: a] : ( member_a @ C @ s ) ) )
!= ( B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9834,297]) ).
thf(11999,plain,
( member_a @ sk22
@ ( collect_a
@ ^ [A: a] :
( member_a @ A
@ ( collect_a
@ ^ [B: a] : ( member_a @ B @ s ) ) ) ) ),
inference(pre_uni,[status(thm)],[11962:[bind(A,$thf( sk22 )),bind(B,$thf( ^ [C: a] : ( member_a @ C @ ( collect_a @ ^ [D: a] : ( member_a @ D @ s ) ) ) ))]]) ).
thf(16737,plain,
! [A: set_a] :
( ( member_a @ ( sk2 @ A ) @ A )
| ( bot_bot_set_a != bot_bot_set_a )
| ( A
!= ( partia1066395285xt_a_b @ r ) ) ),
inference(paramod_ordered,[status(thm)],[350,613]) ).
thf(16738,plain,
! [A: set_a] :
( ( member_a @ ( sk2 @ A ) @ A )
| ( A
!= ( partia1066395285xt_a_b @ r ) ) ),
inference(simp,[status(thm)],[16737]) ).
thf(16739,plain,
member_a @ ( sk2 @ ( partia1066395285xt_a_b @ r ) ) @ ( partia1066395285xt_a_b @ r ),
inference(pattern_uni,[status(thm)],[16738:[bind(A,$thf( partia1066395285xt_a_b @ r ))]]) ).
thf(345,plain,
! [C: int,B: int,A: int] :
( ( minus_minus_int @ A @ ( minus_minus_int @ B @ C ) )
= ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ B ) ),
inference(cnf,[status(esa)],[344]) ).
thf(346,plain,
! [C: int,B: int,A: int] :
( ( minus_minus_int @ A @ ( minus_minus_int @ B @ C ) )
= ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ B ) ),
inference(lifteq,[status(thm)],[345]) ).
thf(154,axiom,
! [A: a,B: a,C: a,D: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ C @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ D @ ( partia1066395285xt_a_b @ r ) )
=> ( ( a_minus_a_b @ r @ ( add_a_b @ r @ ( a_minus_a_b @ r @ A @ C ) @ B ) @ D )
= ( a_minus_a_b @ r @ ( a_minus_a_b @ r @ ( add_a_b @ r @ A @ B ) @ C ) @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_four__elem__comm) ).
thf(716,plain,
! [A: a,B: a,C: a,D: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ C @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ D @ ( partia1066395285xt_a_b @ r ) )
=> ( ( a_minus_a_b @ r @ ( add_a_b @ r @ ( a_minus_a_b @ r @ A @ C ) @ B ) @ D )
= ( a_minus_a_b @ r @ ( a_minus_a_b @ r @ ( add_a_b @ r @ A @ B ) @ C ) @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(165,axiom,
( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) )
= ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_f30) ).
thf(763,plain,
( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) )
= ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(11,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_add__right__mono) ).
thf(272,plain,
! [A: int,B: int,C: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(9175,plain,
! [B: a > $o,A: a] :
( ( member_a @ A @ ( collect_a @ B ) )
| ( ( member_a @ ( zero_a_b @ r ) @ ( partia1066395285xt_a_b @ r ) )
!= ( B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[758,297]) ).
thf(9350,plain,
( member_a @ ( zero_a_b @ r )
@ ( collect_a
@ ^ [A: a] : ( member_a @ A @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(pre_uni,[status(thm)],[9175:[bind(A,$thf( zero_a_b @ r )),bind(B,$thf( ^ [C: a] : ( member_a @ C @ ( partia1066395285xt_a_b @ r ) ) ))]]) ).
thf(299,plain,
! [B: int,A: int] :
( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
= ( ord_less_eq_int @ B @ A ) ),
inference(cnf,[status(esa)],[298]) ).
thf(300,plain,
! [B: int,A: int] :
( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
= ( ord_less_eq_int @ B @ A ) ),
inference(lifteq,[status(thm)],[299]) ).
thf(123,axiom,
! [A: a,B: int,C: int] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( add_pow_a_b_int @ r @ ( plus_plus_int @ B @ C ) @ A )
= ( add_a_b @ r @ ( add_pow_a_b_int @ r @ B @ A ) @ ( add_pow_a_b_int @ r @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_add_Oint__pow__mult) ).
thf(620,plain,
! [A: a,B: int,C: int] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( add_pow_a_b_int @ r @ ( plus_plus_int @ B @ C ) @ A )
= ( add_a_b @ r @ ( add_pow_a_b_int @ r @ B @ A ) @ ( add_pow_a_b_int @ r @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(71,axiom,
! [A: a] :
~ ( member_a @ A @ bot_bot_set_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_empty__iff) ).
thf(447,plain,
! [A: a] :
~ ( member_a @ A @ bot_bot_set_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(186,axiom,
member_a @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) @ ( partia1066395285xt_a_b @ r ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_f16) ).
thf(818,plain,
member_a @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) @ ( partia1066395285xt_a_b @ r ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(57,axiom,
! [A: int,B: int,C: int,D: int] :
( ( ( minus_minus_int @ A @ B )
= ( minus_minus_int @ C @ D ) )
=> ( ( A = B )
= ( C = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_diff__eq__diff__eq) ).
thf(405,plain,
! [A: int,B: int,C: int,D: int] :
( ( ( minus_minus_int @ A @ B )
= ( minus_minus_int @ C @ D ) )
=> ( ( A = B )
= ( C = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(117,axiom,
! [A: a,B: a,C: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ C @ ( partia1066395285xt_a_b @ r ) )
=> ( ( A
= ( add_a_b @ r @ B @ ( a_inv_a_b @ r @ C ) ) )
= ( B
= ( add_a_b @ r @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_add_Oinv__solve__right) ).
thf(603,plain,
! [A: a,B: a,C: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ C @ ( partia1066395285xt_a_b @ r ) )
=> ( ( A
= ( add_a_b @ r @ B @ ( a_inv_a_b @ r @ C ) ) )
= ( B
= ( add_a_b @ r @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(59,axiom,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ C )
= ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_diff__add__eq) ).
thf(410,plain,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ C )
= ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(243,axiom,
member_a @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) @ ( partia1066395285xt_a_b @ r ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_f11) ).
thf(967,plain,
member_a @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) @ ( partia1066395285xt_a_b @ r ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(63,axiom,
( minus_minus_int
= ( ^ [A: int,B: int] : ( plus_plus_int @ A @ ( uminus_uminus_int @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_diff__conv__add__uminus) ).
thf(422,plain,
( minus_minus_int
= ( ^ [A: int,B: int] : ( plus_plus_int @ A @ ( uminus_uminus_int @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(790,plain,
( ( a_inv_a_b @ r @ ( zero_a_b @ r ) )
= ( zero_a_b @ r ) ),
inference(lifteq,[status(thm)],[789]) ).
thf(325,plain,
! [B: int,A: int] :
( ( plus_plus_int @ A @ ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B ) )
= B ),
inference(cnf,[status(esa)],[324]) ).
thf(326,plain,
! [B: int,A: int] :
( ( plus_plus_int @ A @ ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B ) )
= B ),
inference(lifteq,[status(thm)],[325]) ).
thf(340,plain,
! [A: set_a] :
( ( minus_minus_set_a @ A @ bot_bot_set_a )
= A ),
inference(cnf,[status(esa)],[339]) ).
thf(341,plain,
! [A: set_a] :
( ( minus_minus_set_a @ A @ bot_bot_set_a )
= A ),
inference(lifteq,[status(thm)],[340]) ).
thf(138,axiom,
! [A: a,B: a,C: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ C @ ( partia1066395285xt_a_b @ r ) )
=> ( ( mult_a_ring_ext_a_b @ r @ C @ ( add_a_b @ r @ A @ B ) )
= ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ C @ A ) @ ( mult_a_ring_ext_a_b @ r @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_r__distr) ).
thf(664,plain,
! [A: a,B: a,C: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ C @ ( partia1066395285xt_a_b @ r ) )
=> ( ( mult_a_ring_ext_a_b @ r @ C @ ( add_a_b @ r @ A @ B ) )
= ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ C @ A ) @ ( mult_a_ring_ext_a_b @ r @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(55,axiom,
! [A: partia1833973666xt_a_b,B: set_a] :
( ( locali880295127ng_a_b @ A @ B )
=> ( locali425460998xt_a_b @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_mult__submonoid__of__rng_Oaxioms_I2_J) ).
thf(400,plain,
! [A: partia1833973666xt_a_b,B: set_a] :
( ( locali880295127ng_a_b @ A @ B )
=> ( locali425460998xt_a_b @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(148,axiom,
! [A: a,B: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( member_a @ ( add_a_b @ r @ A @ B ) @ ( partia1066395285xt_a_b @ r ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_add_Om__closed) ).
thf(696,plain,
! [A: a,B: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( member_a @ ( add_a_b @ r @ A @ B ) @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(155,axiom,
! [A: a,B: a,C: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ C @ ( partia1066395285xt_a_b @ r ) )
=> ( ( add_a_b @ r @ A @ ( add_a_b @ r @ B @ C ) )
= ( add_a_b @ r @ B @ ( add_a_b @ r @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_add_Om__lcomm) ).
thf(720,plain,
! [A: a,B: a,C: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ C @ ( partia1066395285xt_a_b @ r ) )
=> ( ( add_a_b @ r @ A @ ( add_a_b @ r @ B @ C ) )
= ( add_a_b @ r @ B @ ( add_a_b @ r @ A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(239,axiom,
! [A: a,B: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( mult_a_ring_ext_a_b @ r @ A @ B )
= ( mult_a_ring_ext_a_b @ r @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_m__comm) ).
thf(955,plain,
! [A: a,B: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( mult_a_ring_ext_a_b @ r @ A @ B )
= ( mult_a_ring_ext_a_b @ r @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(293,plain,
! [C: int,B: int,A: int] :
( ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ A @ C ) )
= ( ord_less_eq_int @ B @ C ) ),
inference(cnf,[status(esa)],[292]) ).
thf(294,plain,
! [C: int,B: int,A: int] :
( ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ A @ C ) )
= ( ord_less_eq_int @ B @ C ) ),
inference(lifteq,[status(thm)],[293]) ).
thf(180,axiom,
locali880295127ng_a_b @ r @ s,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_mult__submonoid__of__rng__axioms) ).
thf(801,plain,
locali880295127ng_a_b @ r @ s,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(217,axiom,
! [A: a,B: a,C: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ C @ ( partia1066395285xt_a_b @ r ) )
=> ( ( a_minus_a_b @ r @ ( a_minus_a_b @ r @ C @ A ) @ B )
= ( a_minus_a_b @ r @ C @ ( add_a_b @ r @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_right__inv__add) ).
thf(897,plain,
! [A: a,B: a,C: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ C @ ( partia1066395285xt_a_b @ r ) )
=> ( ( a_minus_a_b @ r @ ( a_minus_a_b @ r @ C @ A ) @ B )
= ( a_minus_a_b @ r @ C @ ( add_a_b @ r @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(80,axiom,
! [A: int,B: int,C: int,D: int] :
( ( A
= ( plus_plus_int @ B @ C ) )
=> ( ( minus_minus_int @ A @ D )
= ( plus_plus_int @ B @ ( minus_minus_int @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_group__cancel_Osub1) ).
thf(474,plain,
! [A: int,B: int,C: int,D: int] :
( ( A
= ( plus_plus_int @ B @ C ) )
=> ( ( minus_minus_int @ A @ D )
= ( plus_plus_int @ B @ ( minus_minus_int @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(241,axiom,
! [A: a,B: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( ( add_a_b @ r @ B @ A )
= A )
= ( B
= ( zero_a_b @ r ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_add_Or__cancel__one) ).
thf(960,plain,
! [A: a,B: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( ( add_a_b @ r @ B @ A )
= A )
= ( B
= ( zero_a_b @ r ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(129,axiom,
( ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) )
= ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29__092_060open_062t_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Ar_A_092_060ominus_062_As_A_092_060otimes_062_Afst_Ax_H_J_A_061_At_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Ar_J_A_092_060ominus_062_At_A_092_060otimes_062_A_Is_A_092_060otimes_062_Afst_Ax_H_J_092_060close_062) ).
thf(635,plain,
( ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) )
= ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(77,axiom,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( plus_plus_int @ A @ ( minus_minus_int @ B @ A ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_le__add__diff__inverse) ).
thf(464,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
=> ( ( plus_plus_int @ A @ ( minus_minus_int @ B @ A ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(14477,plain,
! [B: a > $o,A: a] :
( ( member_a @ A @ ( collect_a @ B ) )
| ( ( B @ A )
!= ( member_a @ sk24
@ ( collect_a
@ ^ [C: a] : ( member_a @ C @ s ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[297,14442]) ).
thf(14514,plain,
( member_a @ sk24
@ ( collect_a
@ ^ [A: a] :
( member_a @ A
@ ( collect_a
@ ^ [B: a] : ( member_a @ B @ s ) ) ) ) ),
inference(pre_uni,[status(thm)],[14477:[bind(A,$thf( sk24 )),bind(B,$thf( ^ [C: a] : ( member_a @ C @ ( collect_a @ ^ [D: a] : ( member_a @ D @ s ) ) ) ))]]) ).
thf(65,axiom,
! [A: int,B: int] :
( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ A )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_add__diff__cancel__left_H) ).
thf(427,plain,
! [A: int,B: int] :
( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(203,axiom,
member_a @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( partia1066395285xt_a_b @ r ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34__092_060open_062t_A_092_060otimes_062_As_A_092_060otimes_062_Asnd_Ax_H_A_092_060in_062_Acarrier_AR_092_060close_062) ).
thf(860,plain,
member_a @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( partia1066395285xt_a_b @ r ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(133,axiom,
! [A: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ! [B: a] :
( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( add_a_b @ r @ A @ B )
= B ) )
=> ( A
= ( zero_a_b @ r ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_add_Oone__unique) ).
thf(644,plain,
! [A: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ! [B: a] :
( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( add_a_b @ r @ A @ B )
= B ) )
=> ( A
= ( zero_a_b @ r ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(13816,plain,
( ( minus_minus_set_a @ s @ ( partia1066395285xt_a_b @ r ) )
= bot_bot_set_a ),
inference(rewrite,[status(thm)],[883,332]) ).
thf(13824,plain,
( ( minus_minus_set_a @ s @ ( partia1066395285xt_a_b @ r ) )
= bot_bot_set_a ),
inference(lifteq,[status(thm)],[13816]) ).
thf(118,axiom,
! [A: a,B: int] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( add_pow_a_b_int @ r @ B @ ( a_inv_a_b @ r @ A ) )
= ( a_inv_a_b @ r @ ( add_pow_a_b_int @ r @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_add_Oint__pow__inv) ).
thf(607,plain,
! [A: a,B: int] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( add_pow_a_b_int @ r @ B @ ( a_inv_a_b @ r @ A ) )
= ( a_inv_a_b @ r @ ( add_pow_a_b_int @ r @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(53,axiom,
! [A: int,B: int,C: int] :
( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ C @ B ) )
= ( minus_minus_int @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_add__diff__cancel__right) ).
thf(395,plain,
! [A: int,B: int,C: int] :
( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ C @ B ) )
= ( minus_minus_int @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(124,axiom,
! [A: a,B: a,C: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ C @ ( partia1066395285xt_a_b @ r ) )
=> ( ( ( add_a_b @ r @ ( a_inv_a_b @ r @ B ) @ C )
= A )
= ( C
= ( add_a_b @ r @ B @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_add_Oinv__solve__left_H) ).
thf(624,plain,
! [A: a,B: a,C: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ C @ ( partia1066395285xt_a_b @ r ) )
=> ( ( ( add_a_b @ r @ ( a_inv_a_b @ r @ B ) @ C )
= A )
= ( C
= ( add_a_b @ r @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(194,axiom,
locali425460998xt_a_b @ r @ s,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_submonoid__axioms) ).
thf(839,plain,
locali425460998xt_a_b @ r @ s,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(276,plain,
! [A: int,B: int] :
( ( ord_less_eq_int @ A @ B )
=> ! [C: int] : ( ord_less_eq_int @ ( minus_minus_int @ C @ B ) @ ( minus_minus_int @ C @ A ) ) ),
inference(miniscope,[status(thm)],[275]) ).
thf(277,plain,
! [C: int,B: int,A: int] :
( ~ ( ord_less_eq_int @ A @ B )
| ( ord_less_eq_int @ ( minus_minus_int @ C @ B ) @ ( minus_minus_int @ C @ A ) ) ),
inference(cnf,[status(esa)],[276]) ).
thf(147,axiom,
! [A: a,B: a,C: a] :
( ( A = B )
=> ( ( a_minus_a_b @ r @ C @ A )
= ( a_minus_a_b @ r @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_local_Oright__minus__eq) ).
thf(691,plain,
! [A: a,B: a,C: a] :
( ( A = B )
=> ( ( a_minus_a_b @ r @ C @ A )
= ( a_minus_a_b @ r @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(235,axiom,
! [A: a,B: int] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( member_a @ ( add_pow_a_b_int @ r @ B @ A ) @ ( partia1066395285xt_a_b @ r ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_add_Oint__pow__closed) ).
thf(940,plain,
! [A: a,B: int] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( member_a @ ( add_pow_a_b_int @ r @ B @ A ) @ ( partia1066395285xt_a_b @ r ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(233,axiom,
! [A: a,B: a,C: int] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( mult_a_ring_ext_a_b @ r @ A @ ( add_pow_a_b_int @ r @ C @ B ) )
= ( add_pow_a_b_int @ r @ C @ ( mult_a_ring_ext_a_b @ r @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_add__pow__rdistr__int) ).
thf(935,plain,
! [A: a,B: a,C: int] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
=> ( ( mult_a_ring_ext_a_b @ r @ A @ ( add_pow_a_b_int @ r @ C @ B ) )
= ( add_pow_a_b_int @ r @ C @ ( mult_a_ring_ext_a_b @ r @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(15849,plain,
( ( ( add_a_b @ r @ s2 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( add_a_b @ r @ t @ t )
!= s2 )
| ( ( add_a_b @ r @ ( add_a_b @ r @ t @ t ) @ s2 )
!= ( add_a_b @ r @ s2 @ ( zero_a_b @ r ) ) )
| ( ( zero_a_b @ r )
!= ( zero_a_b @ r ) ) ),
inference(eqfactor_ordered,[status(thm)],[14847]) ).
thf(15851,plain,
( ( ( add_a_b @ r @ s2 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( add_a_b @ r @ t @ t )
!= s2 )
| ( r != r )
| ( ( add_a_b @ r @ t @ t )
!= s2 )
| ( ( zero_a_b @ r )
!= s2 ) ),
inference(simp,[status(thm)],[15849]) ).
thf(15855,plain,
( ( ( add_a_b @ r @ s2 @ ( zero_a_b @ r ) )
!= ( zero_a_b @ r ) )
| ( ( add_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ s2 ) @ ( product_snd_a_a @ x ) ) @ ( mult_a_ring_ext_a_b @ r @ t @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ ( product_fst_a_a @ y ) ) ) ) ) )
!= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ t ) )
| ( ( add_a_b @ r @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ y ) @ ( product_fst_a_a @ x ) ) ) ) @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ r3 ) ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_fst_a_a @ y ) ) ) ) )
!= t )
| ( ( add_a_b @ r @ t @ t )
!= s2 )
| ( ( zero_a_b @ r )
!= s2 ) ),
inference(simp,[status(thm)],[15851]) ).
thf(137,axiom,
! [A: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ? [B: a] :
( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
& ( ( add_a_b @ r @ B @ A )
= ( zero_a_b @ r ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_add_Ol__inv__ex) ).
thf(659,plain,
! [A: a] :
( ( member_a @ A @ ( partia1066395285xt_a_b @ r ) )
=> ? [B: a] :
( ( member_a @ B @ ( partia1066395285xt_a_b @ r ) )
& ( ( add_a_b @ r @ B @ A )
= ( zero_a_b @ r ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(142,axiom,
( ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) )
= ( zero_a_b @ r ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_f5) ).
thf(676,plain,
( ( mult_a_ring_ext_a_b @ r @ t2 @ ( a_minus_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ ( product_fst_a_a @ x ) ) ) )
= ( zero_a_b @ r ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(113,axiom,
( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) )
= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ t2 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_f24) ).
thf(592,plain,
( ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t2 @ t ) @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ ( product_snd_a_a @ y ) ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ r2 ) ) )
= ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ ( mult_a_ring_ext_a_b @ r @ t @ s3 ) @ ( product_snd_a_a @ y ) ) @ t2 ) @ ( mult_a_ring_ext_a_b @ r @ ( product_snd_a_a @ x ) @ r2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(86,axiom,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_subset__antisym) ).
thf(496,plain,
! [A: set_a,B: set_a] :
( ( ord_less_eq_set_a @ A @ B )
=> ( ( ord_less_eq_set_a @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(9137,plain,
! [B: a > $o,A: a] :
( ( member_a @ A @ ( collect_a @ B ) )
| ( ( B @ A )
!= ( member_a @ t2 @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(paramod_ordered,[status(thm)],[297,901]) ).
thf(9399,plain,
( member_a @ t2
@ ( collect_a
@ ^ [A: a] : ( member_a @ A @ ( partia1066395285xt_a_b @ r ) ) ) ),
inference(pre_uni,[status(thm)],[9137:[bind(A,$thf( t2 )),bind(B,$thf( ^ [C: a] : ( member_a @ C @ ( partia1066395285xt_a_b @ r ) ) ))]]) ).
thf(18406,plain,
$false,
inference(e,[status(thm)],[809,629,9273,479,347,14404,893,9411,249,333,628,683,730,6883,18101,6619,741,247,861,408,977,523,582,878,655,614,269,14441,384,14856,814,930,709,841,973,288,301,829,404,320,565,389,724,3221,6892,785,6878,16689,949,542,619,838,802,344,934,357,902,416,289,261,14864,2713,853,969,5323,5480,284,770,924,7144,789,574,806,353,9781,1183,9779,905,14847,321,485,834,602,6591,687,280,634,453,9341,9347,15041,507,312,9738,265,849,307,292,248,512,13814,678,9308,17125,10139,381,534,6884,798,5487,366,10133,12542,778,952,598,561,392,297,424,275,3207,6635,910,467,252,879,435,329,9391,583,461,493,2741,324,285,456,842,578,650,3218,2726,356,783,857,12538,317,3205,499,884,488,339,933,669,901,642,526,637,1612,328,471,256,4772,14473,911,10122,266,12469,541,765,398,530,926,633,360,773,586,298,430,8531,375,733,819,904,402,6881,286,291,281,545,259,413,9339,10127,445,16515,611,713,335,919,704,947,350,641,3223,681,5520,419,8254,616,271,2510,979,377,996,12537,737,318,863,10457,890,758,323,594,726,520,251,964,915,769,943,668,330,811,9757,959,827,780,883,306,922,278,868,267,851,505,438,14862,653,675,589,548,927,10132,939,342,553,7070,795,3206,968,458,823,776,872,707,887,12648,327,409,310,10540,295,10123,673,791,441,370,502,840,463,359,643,12523,744,336,613,386,8449,314,571,6511,876,450,539,2696,482,903,759,10376,6882,9834,845,363,556,699,304,258,351,418,781,14845,11780,568,378,510,11999,16739,1308,14442,383,346,716,763,272,9350,9311,300,620,447,315,818,405,867,603,833,410,967,422,790,564,326,341,9778,664,400,696,720,955,283,294,801,897,474,6590,9282,960,635,464,332,14514,427,860,644,2699,11616,13824,607,395,624,839,277,691,940,935,15855,659,676,592,496,9399,354]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP108^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.10/0.21 % Computer : n006.cluster.edu
% 0.10/0.21 % Model : x86_64 x86_64
% 0.10/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.21 % Memory : 8046.5625MB
% 0.10/0.21 % OS : Linux 6.8.0-71-generic
% 0.10/0.21 % CPULimit : 300
% 0.10/0.21 % WCLimit : 300
% 0.10/0.21 % DateTime : Tue Sep 29 19:54:09 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.90/0.80 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.34/1.23 % [INFO] Parsing done (427ms).
% 2.34/1.24 % [INFO] Running in sequential loop mode.
% 3.58/1.63 % [INFO] eprover registered as external prover.
% 3.58/1.64 % [INFO] Scanning for conjecture ...
% 4.08/1.82 % [INFO] Found a conjecture (or negated_conjecture) and 244 axioms. Running axiom selection ...
% 4.37/2.01 % [INFO] Axiom selection finished. Selected 244 axioms (removed 0 axioms).
% 5.51/2.22 % [INFO] Problem is higher-order (TPTP THF).
% 5.51/2.24 % [INFO] Type checking passed.
% 5.51/2.25 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 182.00/111.31 % External prover 'e' found a proof!
% 182.00/111.31 % [INFO] Killing All external provers ...
% 182.00/111.31 % Time passed: 110965ms (effective reasoning time: 110061ms)
% 182.00/111.31 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 182.00/111.32 % Axioms used in derivation (244): fact_161_minus__add__distrib, fact_13_f42, fact_197_diff__add__eq__diff__diff__swap, fact_128_eq__obj__rng__of__frac_Oaxioms_I2_J, fact_234_empty__Diff, fact_168_add_Ocommute, fact_191_diff__mono, fact_99_m__closed, fact_156_add__diff__cancel__right, fact_4_m__assoc, fact_148_add__right__cancel, fact_229_Compl__subset__Compl__iff, fact_0_f18, fact_208_add__le__imp__le__diff, fact_206_minus__diff__commute, fact_159_diff__add__cancel, fact_78_r__neg2, fact_108_add_Oinv__eq__1__iff, fact_115_semiring_Osemiring__simprules_I6_J, fact_25_f11, fact_75_add_Oinv__comm, fact_31_f16, fact_36_f34, fact_65_f8, fact_192_le__imp__neg__le, fact_112_submonoid__axioms, fact_145_uminus__add__conv__diff, fact_55_f39, fact_106_add_Ol__cancel__one_H, fact_194_le__minus__iff, fact_110_mult__submonoid__of__crng__axioms, fact_29__092_060open_062t_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Ar_A_092_060ominus_062_As_A_092_060otimes_062_Afst_Ax_H_J_A_061_At_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Ar_J_A_092_060ominus_062_At_A_092_060otimes_062_A_Is_A_092_060otimes_062_Afst_Ax_H_J_092_060close_062, fact_136_semiring_Osemiring__simprules_I1_J, fact_185_add__mono__thms__linordered__semiring_I1_J, fact_214_add_Oone__in__subset, fact_59_minus__closed, fact_203_group__cancel_Osub1, fact_217_carrier__not__empty, fact_162_minus__add__cancel, fact_222_Diff__eq__empty__iff, fact_144_diff__minus__eq__add, fact_153_add__le__cancel__left, fact_167_add_Oleft__commute, fact_183_add__left__mono, fact_9_add_Om__lcomm, fact_66_local_Osemiring__axioms, fact_176_diff__right__commute, fact_218_a__l__coset__subset__G, fact_97_add_Oinv__closed, fact_68_prod__eqI, fact_88_sum__zero__eq__neg, fact_123_add_Oint__pow__closed, fact_63_f4, fact_72_add_Or__inv__ex, fact_237_equals0D, fact_53_f31, fact_142_subset, fact_171_add_Oassoc, fact_42_f32, fact_157_add__diff__cancel__left_H, fact_8_add_Om__comm, fact_243_subset__eq, fact_182_add__right__mono, fact_57_f5, fact_11_f19, fact_10_f20, fact_121_add_Oint__pow__distrib, fact_212_diff__conv__add__uminus, fact_98_local_Ominus__zero, fact_169_group__add__class_Oadd_Oright__cancel, fact_41_f25, fact_173_group__cancel_Oadd1, fact_179_equation__minus__iff, fact_158_add__diff__cancel__left, fact_205_group__cancel_Oneg1, fact_184_add__mono, fact_216_a__lcos__m__assoc, fact_238_equals0I, fact_143_Localization__Mirabelle__afvchqjmgj_Osubmonoid_Osubset, fact_33_f9, fact_193_minus__le__iff, fact_122_add_Oint__pow__mult__distrib, fact_92_inv__add, fact_50__092_060open_062t_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_Ar_A_092_060oplus_062_As_A_092_060otimes_062_Ar_H_J_J_A_061_At_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_J_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_Ar_J_A_092_060oplus_062_At_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_J_A_092_060otimes_062_A_Is_A_092_060otimes_062_Ar_H_J_092_060close_062, fact_46_Collect__mem__eq, fact_16_four__elem__comm, fact_71_local_Ominus__unique, fact_119_add__pow__ldistr__int, fact_189_diff__right__mono, fact_125_Localization__Mirabelle__afvchqjmgj_Osubmonoid_Ois__submonoid, fact_154_neg__le__iff__le, fact_2_right__add__eq, fact_138_semiring_Ol__distr, fact_18_f21, fact_114_semiring_Osemiring__simprules_I11_J, fact_105_add_Or__cancel__one, fact_141_add_Oint__pow__mult, fact_64_f6, fact_95_zero__closed, fact_198_diff__add__eq, fact_224_all__not__in__conv, fact_22_f15, fact_211_ab__group__add__class_Oab__diff__conv__add__uminus, fact_137_semiring_Osemiring__simprules_I2_J, fact_96_local_Ominus__minus, fact_77_l__minus, fact_113_add_Oint__pow__inv, fact_232_empty__subsetI, fact_102_r__zero, fact_6_m__lcomm, fact_69_exE__realizer_H, fact_70_prod_Oexpand, fact_21__092_060open_062_092_060lbrakk_062snd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_Ar_J_A_092_060ominus_062_As_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ay_H_A_092_060otimes_062_Afst_Ax_H_J_A_092_060in_062_Acarrier_AR_059_Asnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_A_092_060otimes_062_Ar_H_J_A_092_060ominus_062_As_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Afst_Ay_H_J_A_092_060in_062_Acarrier_AR_059_At_A_092_060otimes_062_At_H_A_092_060in_062_Acarrier_AR_092_060rbrakk_062_A_092_060Longrightarrow_062_At_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_Ar_J_A_092_060ominus_062_As_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ay_H_A_092_060otimes_062_Afst_Ax_H_J_A_092_060oplus_062_A_Isnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_A_092_060otimes_062_Ar_H_J_A_092_060ominus_062_As_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Afst_Ay_H_J_J_J_A_061_At_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_Ar_J_A_092_060ominus_062_As_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ay_H_A_092_060otimes_062_Afst_Ax_H_J_J_A_092_060oplus_062_At_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_A_092_060otimes_062_Ar_H_J_A_092_060ominus_062_As_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Afst_Ay_H_J_J_092_060close_062, fact_103_l__zero, fact_202_diff__eq__eq, fact_172_group__cancel_Oadd2, fact_213_group__cancel_Osub2, fact_20_f22, fact_170_add_Oleft__cancel, fact_35_f23, fact_132_semiring_Osemiring__simprules_I3_J, fact_146_le__add__diff__inverse, fact_81_add_Oinv__solve__right_H, fact_236_emptyE, fact_199_diff__diff__eq2, fact_225_Collect__empty__eq, fact_12_f41, fact_45_mem__Collect__eq, fact_210_diff__le__eq, fact_74_add_Ol__inv__ex, fact_67_minus__eq, fact_150_neg__equal__iff__equal, fact_34__092_060open_062t_A_092_060otimes_062_As_A_092_060otimes_062_Asnd_Ax_H_A_092_060in_062_Acarrier_AR_092_060close_062, fact_135_semiring_Osemiring__simprules_I5_J, fact_204_add_Oinverse__distrib__swap, fact_241_subsetD, fact_131_semiring_Osemiring__simprules_I8_J, fact_54_f37, fact_134_semiring_Osemiring__simprules_I7_J, fact_80_local_Ominus__add, fact_91_l__neg, fact_140_add_Oint__pow__neg, fact_60_add_Om__closed, fact_130_a__minus__def, fact_226_empty__Collect__eq, fact_82_add_Oinv__solve__right, fact_133_semiring_Osemiring__simprules_I12_J, fact_240_in__mono, fact_5_m__comm, fact_3_local_Oright__minus__eq, fact_58_f7, fact_151_add_Oinverse__inverse, fact_7_add_Om__assoc, fact_164_minus__diff__eq, fact_227_subsetI, fact_17_right__inv__add, fact_94__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062t_H_O_A_092_060lbrakk_062t_H_A_092_060in_062_AS_059_At_H_A_092_060otimes_062_A_Isnd_Ay_H_A_092_060otimes_062_Ar_H_A_092_060ominus_062_As_H_A_092_060otimes_062_Afst_Ay_H_J_A_061_A_092_060zero_062_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, fact_221_add__additive__subgroups, fact_174_add__mono__thms__linordered__semiring_I4_J, fact_111_prod__eq__iff, fact_49_f33, fact_47_Collect__cong, fact_124_add_Oint__pow__one, fact_220_set__add__closed, fact_101_l__null, fact_149_add__left__cancel, fact_233_Diff__empty, fact_239_ex__in__conv, fact_155_add__diff__cancel__right_H, fact_30__092_060open_062t_H_A_092_060otimes_062_A_Isnd_Ay_H_A_092_060otimes_062_Ar_H_A_092_060ominus_062_As_H_A_092_060otimes_062_Afst_Ay_H_J_A_061_At_H_A_092_060otimes_062_A_Isnd_Ay_H_A_092_060otimes_062_Ar_H_J_A_092_060ominus_062_At_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_Afst_Ay_H_J_092_060close_062, fact_230_Compl__anti__mono, fact_61_local_Oadd_Oright__cancel, fact_1_f17, fact_27_f27, fact_223_empty__iff, fact_235_Diff__cancel, fact_39__092_060open_062t_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_Ar_J_J_A_092_060ominus_062_At_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Is_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ay_H_A_092_060otimes_062_Afst_Ax_H_J_J_A_061_At_H_A_092_060otimes_062_As_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_At_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Ar_J_A_092_060ominus_062_At_H_A_092_060otimes_062_As_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_At_A_092_060otimes_062_A_Is_A_092_060otimes_062_Afst_Ax_H_J_092_060close_062, fact_19_f40, fact_175_ab__semigroup__add__class_Oadd__ac_I1_J, fact_73_add_Oone__unique, fact_32_f24, fact_23__092_060open_062snd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060in_062_Acarrier_AR_092_060close_062, fact_14_l__distr, fact_152_add__le__cancel__right, fact_231_subset__empty, fact_209_le__diff__eq, fact_104_add_Or__cancel__one_H, fact_190_diff__left__mono, fact_166_add__left__imp__eq, fact_126_mult__submonoid__of__crng_Oaxioms_I2_J, fact_40_f12, fact_83_add_Oinv__solve__left_H, fact_86_a__transpose__inv, fact_79_r__neg1, fact_187_add__mono__thms__linordered__semiring_I3_J, fact_28_f35, fact_196_diff__diff__add, fact_15_r__distr, fact_76_r__minus, fact_100_r__null, fact_56_f38, fact_107_add_Ol__cancel__one, fact_160_add__diff__cancel, fact_38_f13, fact_181_add__le__imp__le__left, fact_24_f28, fact_62_semiring__simprules_I3_J, fact_48_f30, fact_52__092_060open_062t_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_Ar_J_A_092_060ominus_062_As_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ay_H_A_092_060otimes_062_Afst_Ax_H_J_J_A_092_060oplus_062_At_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_A_092_060otimes_062_Ar_H_J_A_092_060ominus_062_As_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Afst_Ay_H_J_J_A_061_At_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_Ar_J_J_A_092_060ominus_062_At_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Is_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ay_H_A_092_060otimes_062_Afst_Ax_H_J_J_A_092_060oplus_062_At_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_A_092_060otimes_062_Ar_H_J_J_A_092_060ominus_062_At_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Is_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Afst_Ay_H_J_J_092_060close_062, fact_242_equalityE, fact_177_diff__eq__diff__eq, fact_219_setadd__subset__G, fact_120_add__pow__rdistr__int, fact_163_add__minus__cancel, fact_207_add__le__add__imp__diff__le, fact_87_eq__obj__rng__of__frac__axioms, fact_228_subset__antisym, fact_195_add__implies__diff, fact_165_add__right__imp__eq, fact_186_add__mono__thms__linordered__semiring_I2_J, fact_118_semiring_Or__distr, fact_37_f36, fact_44_f29, fact_188_diff__eq__diff__less__eq, fact_116_semiring_Ol__null, fact_84_add_Oinv__solve__left, fact_129_Localization__Mirabelle__afvchqjmgj_Osubmonoid_Om__closed, fact_147_le__add__diff__inverse2, fact_89_r__neg, fact_93__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062t_O_A_092_060lbrakk_062t_A_092_060in_062_AS_059_At_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Ar_A_092_060ominus_062_As_A_092_060otimes_062_Afst_Ax_H_J_A_061_A_092_060zero_062_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, fact_139_add_Oint__pow__diff, fact_117_semiring_Or__null, fact_43_f26, fact_90_minus__equality, fact_26_f10, fact_180_add__le__imp__le__right, fact_178_minus__equation__iff, fact_109_mult__submonoid__of__rng__axioms, fact_85_add_Oinv__mult__group, fact_215_a__lcos__mult__one, fact_200_add__diff__eq, fact_201_eq__diff__eq, fact_51_f14, fact_127_mult__submonoid__of__rng_Oaxioms_I2_J
% 182.00/111.32 % No. of inferences in proof: 867
% 182.00/111.32 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 110965 ms resp. 110061 ms w/o parsing
% 184.08/111.80 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 184.08/111.80 % [INFO] Killing All external provers ...
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