%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV024+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 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 : n009.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 : Sun Sep 27 08:57:57 AM UTC 2026
% Result : Theorem 18.60s 11.24s
% Output : Refutation 17.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 103
% Syntax : Number of formulae : 272 ( 162 unt; 0 typ; 5 def)
% Number of atoms : 1541 ( 519 equ; 0 cnn)
% Maximal formula atoms : 383 ( 5 avg)
% Number of connectives : 5137 ( 667 ~; 665 |; 409 &;3234 @)
% ( 5 <=>; 157 =>; 0 <=; 0 <~>)
% Maximal formula depth : 70 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 63 ( 60 usr; 40 con; 0-4 aty)
% Number of variables : 394 ( 0 ^; 388 !; 1 ?; 394 :)
% ( 0 !>; 0 ?*; 0 @-; 5 @+)
% Comments :
%------------------------------------------------------------------------------
thf(init_decl,type,
init: $i ).
thf(s_best7_init_decl,type,
s_best7_init: $i ).
thf(s_sworst7_init_decl,type,
s_sworst7_init: $i ).
thf(s_worst7_init_decl,type,
s_worst7_init: $i ).
thf(leq_decl,type,
leq: $i > $i > $o ).
thf(n0_decl,type,
n0: $i ).
thf(s_best7_decl,type,
s_best7: $i ).
thf(s_sworst7_decl,type,
s_sworst7: $i ).
thf(s_worst7_decl,type,
s_worst7: $i ).
thf(pv7_decl,type,
pv7: $i ).
thf(pv8_decl,type,
pv8: $i ).
thf(pv19_decl,type,
pv19: $i ).
thf(pv20_decl,type,
pv20: $i ).
thf(n3_decl,type,
n3: $i ).
thf(minus_decl,type,
minus: $i > $i > $i ).
thf(n410_decl,type,
n410: $i ).
thf(n1_decl,type,
n1: $i ).
thf(n330_decl,type,
n330: $i ).
thf(n2_decl,type,
n2: $i ).
thf(a_select3_decl,type,
a_select3: $i > $i > $i > $i ).
thf(simplex7_init_decl,type,
simplex7_init: $i ).
thf(a_select2_decl,type,
a_select2: $i > $i > $i ).
thf(s_values7_init_decl,type,
s_values7_init: $i ).
thf(s_center7_init_decl,type,
s_center7_init: $i ).
thf(s_try7_init_decl,type,
s_try7_init: $i ).
thf(gt_decl,type,
gt: $i > $i > $o ).
thf(loopcounter_decl,type,
loopcounter: $i ).
thf(pvar1400_init_decl,type,
pvar1400_init: $i ).
thf(pvar1401_init_decl,type,
pvar1401_init: $i ).
thf(pvar1402_init_decl,type,
pvar1402_init: $i ).
thf(plus_decl,type,
plus: $i > $i > $i ).
thf(n4_decl,type,
n4: $i ).
thf(succ_decl,type,
succ: $i > $i ).
thf(n5_decl,type,
n5: $i ).
thf(pred_decl,type,
pred: $i > $i ).
thf(tptp_update2_decl,type,
tptp_update2: $i > $i > $i > $i ).
thf(tptp_minus_1_decl,type,
tptp_minus_1: $i ).
thf(sum_decl,type,
sum: $i > $i > $i > $i ).
thf(tptp_const_array2_decl,type,
tptp_const_array2: $i > $i > $i > $i ).
thf(dim_decl,type,
dim: $i > $i > $i ).
thf(tptp_mmul_decl,type,
tptp_mmul: $i > $i > $i ).
thf(trans_decl,type,
trans: $i > $i ).
thf(tptp_update3_decl,type,
tptp_update3: $i > $i > $i > $i > $i ).
thf(tptp_madd_decl,type,
tptp_madd: $i > $i > $i ).
thf(geq_decl,type,
geq: $i > $i > $o ).
thf(uniform_int_rnd_decl,type,
uniform_int_rnd: $i > $i > $i ).
thf(tptp_msub_decl,type,
tptp_msub: $i > $i > $i ).
thf(tptp_float_0_0_decl,type,
tptp_float_0_0: $i ).
thf(lt_decl,type,
lt: $i > $i > $o ).
thf(tptp_const_array1_decl,type,
tptp_const_array1: $i > $i > $i ).
thf(inv_decl,type,
inv: $i > $i ).
thf(sk1_decl,type,
sk1: $o ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(sk4_decl,type,
sk4: $o ).
thf(sk5_decl,type,
sk5: $i ).
thf(sk6_decl,type,
sk6: $o ).
thf(sk7_decl,type,
sk7: $i ).
thf(sk8_decl,type,
sk8: $o ).
thf(sk9_decl,type,
sk9: $i ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ( ( ( n2 @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ! [B: $i] :
( ( ( n3 @ ( B @ leq ) )
& ( B @ ( n0 @ leq ) ) )
=> ( ( A @ ( B @ ( simplex7_init @ a_select3 ) ) )
= init ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ( ( ( n3 @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( sk2 @ ( A @ ( simplex7_init @ a_select3 ) ) )
= init ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( @+[A: $i] :
~ ( ( ( n3 @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A @ ( s_values7_init @ a_select2 ) )
= init ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( @+[A: $i] :
~ ( ( ( n2 @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A @ ( s_center7_init @ a_select2 ) )
= init ) ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( @+[A: $i] :
~ ( ( ( n1 @ ( n3 @ minus ) @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A @ ( s_try7_init @ a_select2 ) )
= init ) ) ) ) ).
thf(62,axiom,
n0 @ ( n410 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_410_0) ).
thf(479,plain,
n0 @ ( n410 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(76,axiom,
! [A: $i] :
( ( ( n2 @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A = n2 )
| ( A = n1 )
| ( A = n0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',finite_domain_2) ).
thf(578,plain,
! [A: $i] :
( ( ( n2 @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A = n2 )
| ( A = n1 )
| ( A = n0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( A = B )
| ( A @ ( B @ gt ) )
| ( B @ ( A @ gt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',totality) ).
thf(205,plain,
! [A: $i,B: $i] :
( ( A = B )
| ( A @ ( B @ gt ) )
| ( B @ ( A @ gt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(1,conjecture,
( ( ( ( n1 @ ( loopcounter @ gt ) )
=> ( ( pvar1402_init = init )
& ( pvar1401_init = init )
& ( pvar1400_init = init ) ) )
& ! [A: $i] :
( ( ( n1 @ ( n3 @ minus ) @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A @ ( s_try7_init @ a_select2 ) )
= init ) )
& ! [A: $i] :
( ( ( n2 @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A @ ( s_center7_init @ a_select2 ) )
= init ) )
& ! [A: $i] :
( ( ( n3 @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A @ ( s_values7_init @ a_select2 ) )
= init ) )
& ! [A: $i] :
( ( ( n2 @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ! [B: $i] :
( ( ( n3 @ ( B @ leq ) )
& ( B @ ( n0 @ leq ) ) )
=> ( ( A @ ( B @ ( simplex7_init @ a_select3 ) ) )
= init ) ) )
& ( n1 @ ( n330 @ minus ) @ ( pv20 @ leq ) )
& ( n1 @ ( n410 @ minus ) @ ( pv19 @ leq ) )
& ( n1 @ ( n330 @ minus ) @ ( pv8 @ leq ) )
& ( n1 @ ( n410 @ minus ) @ ( pv7 @ leq ) )
& ( n3 @ ( s_worst7 @ leq ) )
& ( n3 @ ( s_sworst7 @ leq ) )
& ( n3 @ ( s_best7 @ leq ) )
& ( pv20 @ ( n0 @ leq ) )
& ( pv19 @ ( n0 @ leq ) )
& ( pv8 @ ( n0 @ leq ) )
& ( pv7 @ ( n0 @ leq ) )
& ( s_worst7 @ ( n0 @ leq ) )
& ( s_sworst7 @ ( n0 @ leq ) )
& ( s_best7 @ ( n0 @ leq ) )
& ( s_worst7_init = init )
& ( s_sworst7_init = init )
& ( s_best7_init = init )
& ( init = init ) )
=> ( ( ( n1 @ ( loopcounter @ gt ) )
=> ( ( pvar1402_init = init )
& ( pvar1401_init = init )
& ( pvar1400_init = init ) ) )
& ! [A: $i] :
( ( ( n1 @ ( n3 @ minus ) @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A @ ( s_try7_init @ a_select2 ) )
= init ) )
& ! [A: $i] :
( ( ( n2 @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A @ ( s_center7_init @ a_select2 ) )
= init ) )
& ! [A: $i] :
( ( ( n3 @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A @ ( s_values7_init @ a_select2 ) )
= init ) )
& ! [A: $i] :
( ( ( n2 @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ! [B: $i] :
( ( ( n3 @ ( B @ leq ) )
& ( B @ ( n0 @ leq ) ) )
=> ( ( A @ ( B @ ( simplex7_init @ a_select3 ) ) )
= init ) ) )
& ( n1 @ ( n330 @ minus ) @ ( pv20 @ leq ) )
& ( n1 @ ( n410 @ minus ) @ ( pv19 @ leq ) )
& ( n1 @ ( n410 @ minus ) @ ( pv7 @ leq ) )
& ( n3 @ ( s_worst7 @ leq ) )
& ( n3 @ ( s_sworst7 @ leq ) )
& ( n3 @ ( s_best7 @ leq ) )
& ( pv20 @ ( n0 @ leq ) )
& ( pv19 @ ( n0 @ leq ) )
& ( pv7 @ ( n0 @ leq ) )
& ( s_worst7 @ ( n0 @ leq ) )
& ( s_sworst7 @ ( n0 @ leq ) )
& ( s_best7 @ ( n0 @ leq ) )
& ( ( n2 @ ( s_try7_init @ a_select2 ) )
= init )
& ( ( n1 @ ( s_try7_init @ a_select2 ) )
= init )
& ( ( n0 @ ( s_try7_init @ a_select2 ) )
= init )
& ( s_worst7_init = init )
& ( s_sworst7_init = init )
& ( s_best7_init = init )
& ( init = init ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gauss_init_0009) ).
thf(2,negated_conjecture,
~ ( ( ( ( n1 @ ( loopcounter @ gt ) )
=> ( ( pvar1402_init = init )
& ( pvar1401_init = init )
& ( pvar1400_init = init ) ) )
& ! [A: $i] :
( ( ( n1 @ ( n3 @ minus ) @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A @ ( s_try7_init @ a_select2 ) )
= init ) )
& ! [A: $i] :
( ( ( n2 @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A @ ( s_center7_init @ a_select2 ) )
= init ) )
& ! [A: $i] :
( ( ( n3 @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A @ ( s_values7_init @ a_select2 ) )
= init ) )
& ! [A: $i] :
( ( ( n2 @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ! [B: $i] :
( ( ( n3 @ ( B @ leq ) )
& ( B @ ( n0 @ leq ) ) )
=> ( ( A @ ( B @ ( simplex7_init @ a_select3 ) ) )
= init ) ) )
& ( n1 @ ( n330 @ minus ) @ ( pv20 @ leq ) )
& ( n1 @ ( n410 @ minus ) @ ( pv19 @ leq ) )
& ( n1 @ ( n330 @ minus ) @ ( pv8 @ leq ) )
& ( n1 @ ( n410 @ minus ) @ ( pv7 @ leq ) )
& ( n3 @ ( s_worst7 @ leq ) )
& ( n3 @ ( s_sworst7 @ leq ) )
& ( n3 @ ( s_best7 @ leq ) )
& ( pv20 @ ( n0 @ leq ) )
& ( pv19 @ ( n0 @ leq ) )
& ( pv8 @ ( n0 @ leq ) )
& ( pv7 @ ( n0 @ leq ) )
& ( s_worst7 @ ( n0 @ leq ) )
& ( s_sworst7 @ ( n0 @ leq ) )
& ( s_best7 @ ( n0 @ leq ) )
& ( s_worst7_init = init )
& ( s_sworst7_init = init )
& ( s_best7_init = init )
& ( init = init ) )
=> ( ( ( n1 @ ( loopcounter @ gt ) )
=> ( ( pvar1402_init = init )
& ( pvar1401_init = init )
& ( pvar1400_init = init ) ) )
& ! [A: $i] :
( ( ( n1 @ ( n3 @ minus ) @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A @ ( s_try7_init @ a_select2 ) )
= init ) )
& ! [A: $i] :
( ( ( n2 @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A @ ( s_center7_init @ a_select2 ) )
= init ) )
& ! [A: $i] :
( ( ( n3 @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A @ ( s_values7_init @ a_select2 ) )
= init ) )
& ! [A: $i] :
( ( ( n2 @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ! [B: $i] :
( ( ( n3 @ ( B @ leq ) )
& ( B @ ( n0 @ leq ) ) )
=> ( ( A @ ( B @ ( simplex7_init @ a_select3 ) ) )
= init ) ) )
& ( n1 @ ( n330 @ minus ) @ ( pv20 @ leq ) )
& ( n1 @ ( n410 @ minus ) @ ( pv19 @ leq ) )
& ( n1 @ ( n410 @ minus ) @ ( pv7 @ leq ) )
& ( n3 @ ( s_worst7 @ leq ) )
& ( n3 @ ( s_sworst7 @ leq ) )
& ( n3 @ ( s_best7 @ leq ) )
& ( pv20 @ ( n0 @ leq ) )
& ( pv19 @ ( n0 @ leq ) )
& ( pv7 @ ( n0 @ leq ) )
& ( s_worst7 @ ( n0 @ leq ) )
& ( s_sworst7 @ ( n0 @ leq ) )
& ( s_best7 @ ( n0 @ leq ) )
& ( ( n2 @ ( s_try7_init @ a_select2 ) )
= init )
& ( ( n1 @ ( s_try7_init @ a_select2 ) )
= init )
& ( ( n0 @ ( s_try7_init @ a_select2 ) )
= init )
& ( s_worst7_init = init )
& ( s_sworst7_init = init )
& ( s_best7_init = init )
& ( init = init ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(100,plain,
~ ( ( ( ( n1 @ ( loopcounter @ gt ) )
=> ( ( pvar1402_init = init )
& ( pvar1401_init = init )
& ( pvar1400_init = init ) ) )
& ! [A: $i] :
( ( ( n1 @ ( n3 @ minus ) @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A @ ( s_try7_init @ a_select2 ) )
= init ) )
& ! [A: $i] :
( ( ( n2 @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A @ ( s_center7_init @ a_select2 ) )
= init ) )
& ! [A: $i] :
( ( ( n3 @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A @ ( s_values7_init @ a_select2 ) )
= init ) )
& ! [A: $i] :
( ( ( n2 @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ! [B: $i] :
( ( ( n3 @ ( B @ leq ) )
& ( B @ ( n0 @ leq ) ) )
=> ( ( A @ ( B @ ( simplex7_init @ a_select3 ) ) )
= init ) ) )
& ( n1 @ ( n330 @ minus ) @ ( pv20 @ leq ) )
& ( n1 @ ( n410 @ minus ) @ ( pv19 @ leq ) )
& ( n1 @ ( n330 @ minus ) @ ( pv8 @ leq ) )
& ( n1 @ ( n410 @ minus ) @ ( pv7 @ leq ) )
& ( n3 @ ( s_worst7 @ leq ) )
& ( n3 @ ( s_sworst7 @ leq ) )
& ( n3 @ ( s_best7 @ leq ) )
& ( pv20 @ ( n0 @ leq ) )
& ( pv19 @ ( n0 @ leq ) )
& ( pv8 @ ( n0 @ leq ) )
& ( pv7 @ ( n0 @ leq ) )
& ( s_worst7 @ ( n0 @ leq ) )
& ( s_sworst7 @ ( n0 @ leq ) )
& ( s_best7 @ ( n0 @ leq ) )
& ( s_worst7_init = init )
& ( s_sworst7_init = init )
& ( s_best7_init = init ) )
=> ( ( ( n1 @ ( loopcounter @ gt ) )
=> ( ( pvar1402_init = init )
& ( pvar1401_init = init )
& ( pvar1400_init = init ) ) )
& ! [A: $i] :
( ( ( n1 @ ( n3 @ minus ) @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A @ ( s_try7_init @ a_select2 ) )
= init ) )
& ! [A: $i] :
( ( ( n2 @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A @ ( s_center7_init @ a_select2 ) )
= init ) )
& ! [A: $i] :
( ( ( n3 @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A @ ( s_values7_init @ a_select2 ) )
= init ) )
& ! [A: $i] :
( ( ( n2 @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ! [B: $i] :
( ( ( n3 @ ( B @ leq ) )
& ( B @ ( n0 @ leq ) ) )
=> ( ( A @ ( B @ ( simplex7_init @ a_select3 ) ) )
= init ) ) )
& ( n1 @ ( n330 @ minus ) @ ( pv20 @ leq ) )
& ( n1 @ ( n410 @ minus ) @ ( pv19 @ leq ) )
& ( n1 @ ( n410 @ minus ) @ ( pv7 @ leq ) )
& ( n3 @ ( s_worst7 @ leq ) )
& ( n3 @ ( s_sworst7 @ leq ) )
& ( n3 @ ( s_best7 @ leq ) )
& ( pv20 @ ( n0 @ leq ) )
& ( pv19 @ ( n0 @ leq ) )
& ( pv7 @ ( n0 @ leq ) )
& ( s_worst7 @ ( n0 @ leq ) )
& ( s_sworst7 @ ( n0 @ leq ) )
& ( s_best7 @ ( n0 @ leq ) )
& ( ( n2 @ ( s_try7_init @ a_select2 ) )
= init )
& ( ( n1 @ ( s_try7_init @ a_select2 ) )
= init )
& ( ( n0 @ ( s_try7_init @ a_select2 ) )
= init )
& ( s_worst7_init = init )
& ( s_sworst7_init = init )
& ( s_best7_init = init ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(101,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( pvar1402_init != init )
| ( pvar1401_init != init )
| ( pvar1400_init != init )
| sk8
| sk6
| sk4
| sk1
| ~ ( n1 @ ( n330 @ minus ) @ ( pv20 @ leq ) )
| ~ ( n1 @ ( n410 @ minus ) @ ( pv19 @ leq ) )
| ~ ( n1 @ ( n410 @ minus ) @ ( pv7 @ leq ) )
| ~ ( n3 @ ( s_worst7 @ leq ) )
| ~ ( n3 @ ( s_sworst7 @ leq ) )
| ~ ( n3 @ ( s_best7 @ leq ) )
| ~ ( pv20 @ ( n0 @ leq ) )
| ~ ( pv19 @ ( n0 @ leq ) )
| ~ ( pv7 @ ( n0 @ leq ) )
| ~ ( s_worst7 @ ( n0 @ leq ) )
| ~ ( s_sworst7 @ ( n0 @ leq ) )
| ~ ( s_best7 @ ( n0 @ leq ) )
| ( ( n2 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( ( n1 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( ( n0 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( s_worst7_init != init )
| ( s_sworst7_init != init )
| ( s_best7_init != init ) )
& ( ( n1 @ ( loopcounter @ gt ) )
| sk8
| sk6
| sk4
| sk1
| ~ ( n1 @ ( n330 @ minus ) @ ( pv20 @ leq ) )
| ~ ( n1 @ ( n410 @ minus ) @ ( pv19 @ leq ) )
| ~ ( n1 @ ( n410 @ minus ) @ ( pv7 @ leq ) )
| ~ ( n3 @ ( s_worst7 @ leq ) )
| ~ ( n3 @ ( s_sworst7 @ leq ) )
| ~ ( n3 @ ( s_best7 @ leq ) )
| ~ ( pv20 @ ( n0 @ leq ) )
| ~ ( pv19 @ ( n0 @ leq ) )
| ~ ( pv7 @ ( n0 @ leq ) )
| ~ ( s_worst7 @ ( n0 @ leq ) )
| ~ ( s_sworst7 @ ( n0 @ leq ) )
| ~ ( s_best7 @ ( n0 @ leq ) )
| ( ( n2 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( ( n1 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( ( n0 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( s_worst7_init != init )
| ( s_sworst7_init != init )
| ( s_best7_init != init ) )
& ( ~ sk8
| ( ( sk9 @ ( s_try7_init @ a_select2 ) )
!= init )
| sk6
| sk4
| sk1
| ~ ( n1 @ ( n330 @ minus ) @ ( pv20 @ leq ) )
| ~ ( n1 @ ( n410 @ minus ) @ ( pv19 @ leq ) )
| ~ ( n1 @ ( n410 @ minus ) @ ( pv7 @ leq ) )
| ~ ( n3 @ ( s_worst7 @ leq ) )
| ~ ( n3 @ ( s_sworst7 @ leq ) )
| ~ ( n3 @ ( s_best7 @ leq ) )
| ~ ( pv20 @ ( n0 @ leq ) )
| ~ ( pv19 @ ( n0 @ leq ) )
| ~ ( pv7 @ ( n0 @ leq ) )
| ~ ( s_worst7 @ ( n0 @ leq ) )
| ~ ( s_sworst7 @ ( n0 @ leq ) )
| ~ ( s_best7 @ ( n0 @ leq ) )
| ( ( n2 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( ( n1 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( ( n0 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( s_worst7_init != init )
| ( s_sworst7_init != init )
| ( s_best7_init != init ) )
& ( ~ sk8
| ( n1 @ ( n3 @ minus ) @ ( sk9 @ leq ) )
| sk6
| sk4
| sk1
| ~ ( n1 @ ( n330 @ minus ) @ ( pv20 @ leq ) )
| ~ ( n1 @ ( n410 @ minus ) @ ( pv19 @ leq ) )
| ~ ( n1 @ ( n410 @ minus ) @ ( pv7 @ leq ) )
| ~ ( n3 @ ( s_worst7 @ leq ) )
| ~ ( n3 @ ( s_sworst7 @ leq ) )
| ~ ( n3 @ ( s_best7 @ leq ) )
| ~ ( pv20 @ ( n0 @ leq ) )
| ~ ( pv19 @ ( n0 @ leq ) )
| ~ ( pv7 @ ( n0 @ leq ) )
| ~ ( s_worst7 @ ( n0 @ leq ) )
| ~ ( s_sworst7 @ ( n0 @ leq ) )
| ~ ( s_best7 @ ( n0 @ leq ) )
| ( ( n2 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( ( n1 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( ( n0 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( s_worst7_init != init )
| ( s_sworst7_init != init )
| ( s_best7_init != init ) )
& ( ~ sk8
| ( sk9 @ ( n0 @ leq ) )
| sk6
| sk4
| sk1
| ~ ( n1 @ ( n330 @ minus ) @ ( pv20 @ leq ) )
| ~ ( n1 @ ( n410 @ minus ) @ ( pv19 @ leq ) )
| ~ ( n1 @ ( n410 @ minus ) @ ( pv7 @ leq ) )
| ~ ( n3 @ ( s_worst7 @ leq ) )
| ~ ( n3 @ ( s_sworst7 @ leq ) )
| ~ ( n3 @ ( s_best7 @ leq ) )
| ~ ( pv20 @ ( n0 @ leq ) )
| ~ ( pv19 @ ( n0 @ leq ) )
| ~ ( pv7 @ ( n0 @ leq ) )
| ~ ( s_worst7 @ ( n0 @ leq ) )
| ~ ( s_sworst7 @ ( n0 @ leq ) )
| ~ ( s_best7 @ ( n0 @ leq ) )
| ( ( n2 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( ( n1 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( ( n0 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( s_worst7_init != init )
| ( s_sworst7_init != init )
| ( s_best7_init != init ) )
& ( ~ sk6
| ( ( sk7 @ ( s_center7_init @ a_select2 ) )
!= init )
| sk4
| sk1
| ~ ( n1 @ ( n330 @ minus ) @ ( pv20 @ leq ) )
| ~ ( n1 @ ( n410 @ minus ) @ ( pv19 @ leq ) )
| ~ ( n1 @ ( n410 @ minus ) @ ( pv7 @ leq ) )
| ~ ( n3 @ ( s_worst7 @ leq ) )
| ~ ( n3 @ ( s_sworst7 @ leq ) )
| ~ ( n3 @ ( s_best7 @ leq ) )
| ~ ( pv20 @ ( n0 @ leq ) )
| ~ ( pv19 @ ( n0 @ leq ) )
| ~ ( pv7 @ ( n0 @ leq ) )
| ~ ( s_worst7 @ ( n0 @ leq ) )
| ~ ( s_sworst7 @ ( n0 @ leq ) )
| ~ ( s_best7 @ ( n0 @ leq ) )
| ( ( n2 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( ( n1 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( ( n0 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( s_worst7_init != init )
| ( s_sworst7_init != init )
| ( s_best7_init != init ) )
& ( ~ sk6
| ( n2 @ ( sk7 @ leq ) )
| sk4
| sk1
| ~ ( n1 @ ( n330 @ minus ) @ ( pv20 @ leq ) )
| ~ ( n1 @ ( n410 @ minus ) @ ( pv19 @ leq ) )
| ~ ( n1 @ ( n410 @ minus ) @ ( pv7 @ leq ) )
| ~ ( n3 @ ( s_worst7 @ leq ) )
| ~ ( n3 @ ( s_sworst7 @ leq ) )
| ~ ( n3 @ ( s_best7 @ leq ) )
| ~ ( pv20 @ ( n0 @ leq ) )
| ~ ( pv19 @ ( n0 @ leq ) )
| ~ ( pv7 @ ( n0 @ leq ) )
| ~ ( s_worst7 @ ( n0 @ leq ) )
| ~ ( s_sworst7 @ ( n0 @ leq ) )
| ~ ( s_best7 @ ( n0 @ leq ) )
| ( ( n2 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( ( n1 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( ( n0 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( s_worst7_init != init )
| ( s_sworst7_init != init )
| ( s_best7_init != init ) )
& ( ~ sk6
| ( sk7 @ ( n0 @ leq ) )
| sk4
| sk1
| ~ ( n1 @ ( n330 @ minus ) @ ( pv20 @ leq ) )
| ~ ( n1 @ ( n410 @ minus ) @ ( pv19 @ leq ) )
| ~ ( n1 @ ( n410 @ minus ) @ ( pv7 @ leq ) )
| ~ ( n3 @ ( s_worst7 @ leq ) )
| ~ ( n3 @ ( s_sworst7 @ leq ) )
| ~ ( n3 @ ( s_best7 @ leq ) )
| ~ ( pv20 @ ( n0 @ leq ) )
| ~ ( pv19 @ ( n0 @ leq ) )
| ~ ( pv7 @ ( n0 @ leq ) )
| ~ ( s_worst7 @ ( n0 @ leq ) )
| ~ ( s_sworst7 @ ( n0 @ leq ) )
| ~ ( s_best7 @ ( n0 @ leq ) )
| ( ( n2 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( ( n1 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( ( n0 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( s_worst7_init != init )
| ( s_sworst7_init != init )
| ( s_best7_init != init ) )
& ( ~ sk4
| ( ( sk5 @ ( s_values7_init @ a_select2 ) )
!= init )
| sk1
| ~ ( n1 @ ( n330 @ minus ) @ ( pv20 @ leq ) )
| ~ ( n1 @ ( n410 @ minus ) @ ( pv19 @ leq ) )
| ~ ( n1 @ ( n410 @ minus ) @ ( pv7 @ leq ) )
| ~ ( n3 @ ( s_worst7 @ leq ) )
| ~ ( n3 @ ( s_sworst7 @ leq ) )
| ~ ( n3 @ ( s_best7 @ leq ) )
| ~ ( pv20 @ ( n0 @ leq ) )
| ~ ( pv19 @ ( n0 @ leq ) )
| ~ ( pv7 @ ( n0 @ leq ) )
| ~ ( s_worst7 @ ( n0 @ leq ) )
| ~ ( s_sworst7 @ ( n0 @ leq ) )
| ~ ( s_best7 @ ( n0 @ leq ) )
| ( ( n2 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( ( n1 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( ( n0 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( s_worst7_init != init )
| ( s_sworst7_init != init )
| ( s_best7_init != init ) )
& ( ~ sk4
| ( n3 @ ( sk5 @ leq ) )
| sk1
| ~ ( n1 @ ( n330 @ minus ) @ ( pv20 @ leq ) )
| ~ ( n1 @ ( n410 @ minus ) @ ( pv19 @ leq ) )
| ~ ( n1 @ ( n410 @ minus ) @ ( pv7 @ leq ) )
| ~ ( n3 @ ( s_worst7 @ leq ) )
| ~ ( n3 @ ( s_sworst7 @ leq ) )
| ~ ( n3 @ ( s_best7 @ leq ) )
| ~ ( pv20 @ ( n0 @ leq ) )
| ~ ( pv19 @ ( n0 @ leq ) )
| ~ ( pv7 @ ( n0 @ leq ) )
| ~ ( s_worst7 @ ( n0 @ leq ) )
| ~ ( s_sworst7 @ ( n0 @ leq ) )
| ~ ( s_best7 @ ( n0 @ leq ) )
| ( ( n2 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( ( n1 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( ( n0 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( s_worst7_init != init )
| ( s_sworst7_init != init )
| ( s_best7_init != init ) )
& ( ~ sk4
| ( sk5 @ ( n0 @ leq ) )
| sk1
| ~ ( n1 @ ( n330 @ minus ) @ ( pv20 @ leq ) )
| ~ ( n1 @ ( n410 @ minus ) @ ( pv19 @ leq ) )
| ~ ( n1 @ ( n410 @ minus ) @ ( pv7 @ leq ) )
| ~ ( n3 @ ( s_worst7 @ leq ) )
| ~ ( n3 @ ( s_sworst7 @ leq ) )
| ~ ( n3 @ ( s_best7 @ leq ) )
| ~ ( pv20 @ ( n0 @ leq ) )
| ~ ( pv19 @ ( n0 @ leq ) )
| ~ ( pv7 @ ( n0 @ leq ) )
| ~ ( s_worst7 @ ( n0 @ leq ) )
| ~ ( s_sworst7 @ ( n0 @ leq ) )
| ~ ( s_best7 @ ( n0 @ leq ) )
| ( ( n2 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( ( n1 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( ( n0 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( s_worst7_init != init )
| ( s_sworst7_init != init )
| ( s_best7_init != init ) )
& ( ~ sk1
| ( ( sk2 @ ( sk3 @ ( simplex7_init @ a_select3 ) ) )
!= init )
| ~ ( n1 @ ( n330 @ minus ) @ ( pv20 @ leq ) )
| ~ ( n1 @ ( n410 @ minus ) @ ( pv19 @ leq ) )
| ~ ( n1 @ ( n410 @ minus ) @ ( pv7 @ leq ) )
| ~ ( n3 @ ( s_worst7 @ leq ) )
| ~ ( n3 @ ( s_sworst7 @ leq ) )
| ~ ( n3 @ ( s_best7 @ leq ) )
| ~ ( pv20 @ ( n0 @ leq ) )
| ~ ( pv19 @ ( n0 @ leq ) )
| ~ ( pv7 @ ( n0 @ leq ) )
| ~ ( s_worst7 @ ( n0 @ leq ) )
| ~ ( s_sworst7 @ ( n0 @ leq ) )
| ~ ( s_best7 @ ( n0 @ leq ) )
| ( ( n2 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( ( n1 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( ( n0 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( s_worst7_init != init )
| ( s_sworst7_init != init )
| ( s_best7_init != init ) )
& ( ~ sk1
| ( n3 @ ( sk3 @ leq ) )
| ~ ( n1 @ ( n330 @ minus ) @ ( pv20 @ leq ) )
| ~ ( n1 @ ( n410 @ minus ) @ ( pv19 @ leq ) )
| ~ ( n1 @ ( n410 @ minus ) @ ( pv7 @ leq ) )
| ~ ( n3 @ ( s_worst7 @ leq ) )
| ~ ( n3 @ ( s_sworst7 @ leq ) )
| ~ ( n3 @ ( s_best7 @ leq ) )
| ~ ( pv20 @ ( n0 @ leq ) )
| ~ ( pv19 @ ( n0 @ leq ) )
| ~ ( pv7 @ ( n0 @ leq ) )
| ~ ( s_worst7 @ ( n0 @ leq ) )
| ~ ( s_sworst7 @ ( n0 @ leq ) )
| ~ ( s_best7 @ ( n0 @ leq ) )
| ( ( n2 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( ( n1 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( ( n0 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( s_worst7_init != init )
| ( s_sworst7_init != init )
| ( s_best7_init != init ) )
& ( ~ sk1
| ( sk3 @ ( n0 @ leq ) )
| ~ ( n1 @ ( n330 @ minus ) @ ( pv20 @ leq ) )
| ~ ( n1 @ ( n410 @ minus ) @ ( pv19 @ leq ) )
| ~ ( n1 @ ( n410 @ minus ) @ ( pv7 @ leq ) )
| ~ ( n3 @ ( s_worst7 @ leq ) )
| ~ ( n3 @ ( s_sworst7 @ leq ) )
| ~ ( n3 @ ( s_best7 @ leq ) )
| ~ ( pv20 @ ( n0 @ leq ) )
| ~ ( pv19 @ ( n0 @ leq ) )
| ~ ( pv7 @ ( n0 @ leq ) )
| ~ ( s_worst7 @ ( n0 @ leq ) )
| ~ ( s_sworst7 @ ( n0 @ leq ) )
| ~ ( s_best7 @ ( n0 @ leq ) )
| ( ( n2 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( ( n1 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( ( n0 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( s_worst7_init != init )
| ( s_sworst7_init != init )
| ( s_best7_init != init ) )
& ( ~ sk1
| ( n2 @ ( sk2 @ leq ) )
| ~ ( n1 @ ( n330 @ minus ) @ ( pv20 @ leq ) )
| ~ ( n1 @ ( n410 @ minus ) @ ( pv19 @ leq ) )
| ~ ( n1 @ ( n410 @ minus ) @ ( pv7 @ leq ) )
| ~ ( n3 @ ( s_worst7 @ leq ) )
| ~ ( n3 @ ( s_sworst7 @ leq ) )
| ~ ( n3 @ ( s_best7 @ leq ) )
| ~ ( pv20 @ ( n0 @ leq ) )
| ~ ( pv19 @ ( n0 @ leq ) )
| ~ ( pv7 @ ( n0 @ leq ) )
| ~ ( s_worst7 @ ( n0 @ leq ) )
| ~ ( s_sworst7 @ ( n0 @ leq ) )
| ~ ( s_best7 @ ( n0 @ leq ) )
| ( ( n2 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( ( n1 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( ( n0 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( s_worst7_init != init )
| ( s_sworst7_init != init )
| ( s_best7_init != init ) )
& ( ~ sk1
| ( sk2 @ ( n0 @ leq ) )
| ~ ( n1 @ ( n330 @ minus ) @ ( pv20 @ leq ) )
| ~ ( n1 @ ( n410 @ minus ) @ ( pv19 @ leq ) )
| ~ ( n1 @ ( n410 @ minus ) @ ( pv7 @ leq ) )
| ~ ( n3 @ ( s_worst7 @ leq ) )
| ~ ( n3 @ ( s_sworst7 @ leq ) )
| ~ ( n3 @ ( s_best7 @ leq ) )
| ~ ( pv20 @ ( n0 @ leq ) )
| ~ ( pv19 @ ( n0 @ leq ) )
| ~ ( pv7 @ ( n0 @ leq ) )
| ~ ( s_worst7 @ ( n0 @ leq ) )
| ~ ( s_sworst7 @ ( n0 @ leq ) )
| ~ ( s_best7 @ ( n0 @ leq ) )
| ( ( n2 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( ( n1 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( ( n0 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( s_worst7_init != init )
| ( s_sworst7_init != init )
| ( s_best7_init != init ) )
& ( ( pvar1402_init = init )
| ~ ( n1 @ ( loopcounter @ gt ) ) )
& ( ( pvar1401_init = init )
| ~ ( n1 @ ( loopcounter @ gt ) ) )
& ( ( pvar1400_init = init )
| ~ ( n1 @ ( loopcounter @ gt ) ) )
& ( ( ( E @ ( s_try7_init @ a_select2 ) )
= init )
| ~ ( n1 @ ( n3 @ minus ) @ ( E @ leq ) )
| ~ ( E @ ( n0 @ leq ) ) )
& ( ( ( D @ ( s_center7_init @ a_select2 ) )
= init )
| ~ ( n2 @ ( D @ leq ) )
| ~ ( D @ ( n0 @ leq ) ) )
& ( ( ( C @ ( s_values7_init @ a_select2 ) )
= init )
| ~ ( n3 @ ( C @ leq ) )
| ~ ( C @ ( n0 @ leq ) ) )
& ( ( ( A @ ( B @ ( simplex7_init @ a_select3 ) ) )
= init )
| ~ ( n3 @ ( B @ leq ) )
| ~ ( B @ ( n0 @ leq ) )
| ~ ( n2 @ ( A @ leq ) )
| ~ ( A @ ( n0 @ leq ) ) )
& ( n1 @ ( n330 @ minus ) @ ( pv20 @ leq ) )
& ( n1 @ ( n410 @ minus ) @ ( pv19 @ leq ) )
& ( n1 @ ( n330 @ minus ) @ ( pv8 @ leq ) )
& ( n1 @ ( n410 @ minus ) @ ( pv7 @ leq ) )
& ( n3 @ ( s_worst7 @ leq ) )
& ( n3 @ ( s_sworst7 @ leq ) )
& ( n3 @ ( s_best7 @ leq ) )
& ( pv20 @ ( n0 @ leq ) )
& ( pv19 @ ( n0 @ leq ) )
& ( pv8 @ ( n0 @ leq ) )
& ( pv7 @ ( n0 @ leq ) )
& ( s_worst7 @ ( n0 @ leq ) )
& ( s_sworst7 @ ( n0 @ leq ) )
& ( s_best7 @ ( n0 @ leq ) )
& ( s_worst7_init = init )
& ( s_sworst7_init = init )
& ( s_best7_init = init ) ),
inference(cnf,[status(esa)],[100]) ).
thf(115,plain,
pv20 @ ( n0 @ leq ),
inference(cnfConj,[status(thm)],[101]) ).
thf(90,axiom,
! [A: $i] :
( ( ( n4 @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A = n4 )
| ( A = n3 )
| ( A = n2 )
| ( A = n1 )
| ( A = n0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',finite_domain_4) ).
thf(614,plain,
! [A: $i] :
( ( ( n4 @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A = n4 )
| ( A = n3 )
| ( A = n2 )
| ( A = n1 )
| ( A = n0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(26,axiom,
n1 @ ( n5 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_5_1) ).
thf(217,plain,
n1 @ ( n5 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(38,axiom,
tptp_minus_1 @ ( n0 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_0_tptp_minus_1) ).
thf(276,plain,
tptp_minus_1 @ ( n0 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(47,axiom,
( ( tptp_minus_1 @ succ )
= n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_tptp_minus_1) ).
thf(385,plain,
( ( tptp_minus_1 @ succ )
= n0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(46,axiom,
n0 @ ( n5 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_5_0) ).
thf(384,plain,
n0 @ ( n5 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(4,axiom,
! [A: $i] :
( ( n5 @ ( A @ plus ) )
= ( A @ succ @ succ @ succ @ succ @ succ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_plus_5_r) ).
thf(174,plain,
! [A: $i] :
( ( n5 @ ( A @ plus ) )
= ( A @ succ @ succ @ succ @ succ @ succ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(35,axiom,
n3 @ ( n5 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_5_3) ).
thf(257,plain,
n3 @ ( n5 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(125,plain,
n3 @ ( s_worst7 @ leq ),
inference(cnfConj,[status(thm)],[101]) ).
thf(15,axiom,
n1 @ ( n3 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_3_1) ).
thf(196,plain,
n1 @ ( n3 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(124,plain,
s_sworst7_init = init,
inference(cnfConj,[status(thm)],[101]) ).
thf(157,plain,
s_sworst7_init = init,
inference(lifteq,[status(thm)],[124]) ).
thf(9,axiom,
n1 @ ( n330 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_330_1) ).
thf(189,plain,
n1 @ ( n330 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(86,axiom,
! [A: $i] :
( ( ( n3 @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A = n3 )
| ( A = n2 )
| ( A = n1 )
| ( A = n0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',finite_domain_3) ).
thf(606,plain,
! [A: $i] :
( ( ( n3 @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A = n3 )
| ( A = n2 )
| ( A = n1 )
| ( A = n0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(42,axiom,
! [A: $i] :
( ( ( n0 @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( A = n0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',finite_domain_0) ).
thf(284,plain,
! [A: $i] :
( ( ( n0 @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( A = n0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(32,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i,F: $i] :
( ( ( D @ ( F @ leq ) )
& ( F @ ( n0 @ leq ) )
& ( D @ ( E @ leq ) )
& ( E @ ( n0 @ leq ) ) )
=> ( ( F @ ( E @ ( B @ a_select3 ) ) )
= ( E @ ( F @ ( B @ a_select3 ) ) ) ) )
=> ! [E: $i,F: $i] :
( ( ( C @ ( F @ leq ) )
& ( F @ ( n0 @ leq ) )
& ( C @ ( E @ leq ) )
& ( E @ ( n0 @ leq ) ) )
=> ( ( F @ ( E @ ( A @ trans @ ( B @ tptp_mmul ) @ ( A @ tptp_mmul ) @ a_select3 ) ) )
= ( E @ ( F @ ( A @ trans @ ( B @ tptp_mmul ) @ ( A @ tptp_mmul ) @ a_select3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',matrix_symm_aba2) ).
thf(228,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i,F: $i] :
( ( ( D @ ( F @ leq ) )
& ( F @ ( n0 @ leq ) )
& ( D @ ( E @ leq ) )
& ( E @ ( n0 @ leq ) ) )
=> ( ( F @ ( E @ ( B @ a_select3 ) ) )
= ( E @ ( F @ ( B @ a_select3 ) ) ) ) )
=> ! [E: $i,F: $i] :
( ( ( C @ ( F @ leq ) )
& ( F @ ( n0 @ leq ) )
& ( C @ ( E @ leq ) )
& ( E @ ( n0 @ leq ) ) )
=> ( ( F @ ( E @ ( A @ trans @ ( B @ tptp_mmul ) @ ( A @ tptp_mmul ) @ a_select3 ) ) )
= ( E @ ( F @ ( A @ trans @ ( B @ tptp_mmul ) @ ( A @ tptp_mmul ) @ a_select3 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(25,axiom,
n5 @ ( n330 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_330_5) ).
thf(216,plain,
n5 @ ( n330 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(61,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( A @ leq ) )
& ( A @ ( B @ leq ) ) )
=> ( ( A @ ( D @ ( C @ ( B @ dim ) @ tptp_const_array1 ) @ a_select2 ) )
= D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',const_array1_select) ).
thf(475,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( A @ leq ) )
& ( A @ ( B @ leq ) ) )
=> ( ( A @ ( D @ ( C @ ( B @ dim ) @ tptp_const_array1 ) @ a_select2 ) )
= D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(106,plain,
s_sworst7 @ ( n0 @ leq ),
inference(cnfConj,[status(thm)],[101]) ).
thf(73,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( A @ minus ) @ leq ) )
=> ( B @ ( n0 @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_minus) ).
thf(574,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( A @ minus ) @ leq ) )
=> ( B @ ( n0 @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(138,plain,
( ~ sk4
| ( ( sk5 @ ( s_values7_init @ a_select2 ) )
!= init )
| sk1
| ~ ( n1 @ ( n330 @ minus ) @ ( pv20 @ leq ) )
| ~ ( n1 @ ( n410 @ minus ) @ ( pv19 @ leq ) )
| ~ ( n1 @ ( n410 @ minus ) @ ( pv7 @ leq ) )
| ~ ( n3 @ ( s_worst7 @ leq ) )
| ~ ( n3 @ ( s_sworst7 @ leq ) )
| ~ ( n3 @ ( s_best7 @ leq ) )
| ~ ( pv20 @ ( n0 @ leq ) )
| ~ ( pv19 @ ( n0 @ leq ) )
| ~ ( pv7 @ ( n0 @ leq ) )
| ~ ( s_worst7 @ ( n0 @ leq ) )
| ~ ( s_sworst7 @ ( n0 @ leq ) )
| ~ ( s_best7 @ ( n0 @ leq ) )
| ( ( n2 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( ( n1 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( ( n0 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( s_worst7_init != init )
| ( s_sworst7_init != init )
| ( s_best7_init != init ) ),
inference(cnfConj,[status(thm)],[101]) ).
thf(142,plain,
( ~ sk4
| sk1
| ~ ( n1 @ ( n330 @ minus ) @ ( pv20 @ leq ) )
| ~ ( n1 @ ( n410 @ minus ) @ ( pv19 @ leq ) )
| ~ ( n1 @ ( n410 @ minus ) @ ( pv7 @ leq ) )
| ~ ( n3 @ ( s_worst7 @ leq ) )
| ~ ( n3 @ ( s_sworst7 @ leq ) )
| ~ ( n3 @ ( s_best7 @ leq ) )
| ~ ( pv20 @ ( n0 @ leq ) )
| ~ ( pv19 @ ( n0 @ leq ) )
| ~ ( pv7 @ ( n0 @ leq ) )
| ~ ( s_worst7 @ ( n0 @ leq ) )
| ~ ( s_sworst7 @ ( n0 @ leq ) )
| ~ ( s_best7 @ ( n0 @ leq ) )
| ( ( sk5 @ ( s_values7_init @ a_select2 ) )
!= init )
| ( ( n2 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( ( n1 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( ( n0 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( s_worst7_init != init )
| ( s_sworst7_init != init )
| ( s_best7_init != init ) ),
inference(lifteq,[status(thm)],[138]) ).
thf(140,plain,
s_worst7_init = init,
inference(cnfConj,[status(thm)],[101]) ).
thf(161,plain,
s_worst7_init = init,
inference(lifteq,[status(thm)],[140]) ).
thf(131,plain,
pv7 @ ( n0 @ leq ),
inference(cnfConj,[status(thm)],[101]) ).
thf(132,plain,
n1 @ ( n410 @ minus ) @ ( pv19 @ leq ),
inference(cnfConj,[status(thm)],[101]) ).
thf(102,plain,
n1 @ ( n330 @ minus ) @ ( pv20 @ leq ),
inference(cnfConj,[status(thm)],[101]) ).
thf(103,plain,
n3 @ ( s_sworst7 @ leq ),
inference(cnfConj,[status(thm)],[101]) ).
thf(104,plain,
n3 @ ( s_best7 @ leq ),
inference(cnfConj,[status(thm)],[101]) ).
thf(108,plain,
s_best7 @ ( n0 @ leq ),
inference(cnfConj,[status(thm)],[101]) ).
thf(109,plain,
pv19 @ ( n0 @ leq ),
inference(cnfConj,[status(thm)],[101]) ).
thf(127,plain,
s_best7_init = init,
inference(cnfConj,[status(thm)],[101]) ).
thf(146,plain,
s_best7_init = init,
inference(lifteq,[status(thm)],[127]) ).
thf(118,plain,
s_worst7 @ ( n0 @ leq ),
inference(cnfConj,[status(thm)],[101]) ).
thf(122,plain,
n1 @ ( n410 @ minus ) @ ( pv7 @ leq ),
inference(cnfConj,[status(thm)],[101]) ).
thf(965,plain,
( ~ sk4
| sk1
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ~ $true
| ( ( sk5 @ ( s_values7_init @ a_select2 ) )
!= init )
| ( ( n2 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( ( n1 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( ( n0 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( init != init )
| ( init != init )
| ( init != init ) ),
inference(rewrite,[status(thm)],[142,161,131,132,102,103,104,106,108,109,146,115,118,122,125,157]) ).
thf(966,plain,
( ~ sk4
| sk1
| ( ( sk5 @ ( s_values7_init @ a_select2 ) )
!= init )
| ( ( n2 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( ( n1 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( ( n0 @ ( s_try7_init @ a_select2 ) )
!= init ) ),
inference(simp,[status(thm)],[965]) ).
thf(10,axiom,
n2 @ ( n3 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_3_2) ).
thf(190,plain,
n2 @ ( n3 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(50,axiom,
! [A: $i] :
~ ( A @ ( A @ gt ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',irreflexivity_gt) ).
thf(394,plain,
! [A: $i] :
~ ( A @ ( A @ gt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(395,plain,
~ ? [A: $i] : ( A @ ( A @ gt ) ),
inference(miniscope,[status(thm)],[394]) ).
thf(396,plain,
! [A: $i] :
~ ( A @ ( A @ gt ) ),
inference(cnf,[status(esa)],[395]) ).
thf(902,plain,
! [A: $i] :
( ( ( n2 @ ( n3 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[190,396]) ).
thf(903,plain,
! [A: $i] :
( ( n2 @ ( n3 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[902]) ).
thf(904,plain,
! [A: $i] :
( ( n2 != A )
| ( n3 != A ) ),
inference(simp,[status(thm)],[903]) ).
thf(905,plain,
n2 != n3,
inference(simp,[status(thm)],[904]) ).
thf(63,axiom,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i,E: $i] :
( ( ( C @ ( E @ leq ) )
& ( E @ ( n0 @ leq ) )
& ( C @ ( D @ leq ) )
& ( D @ ( n0 @ leq ) ) )
=> ( ( E @ ( D @ ( B @ a_select3 ) ) )
= ( D @ ( E @ ( B @ a_select3 ) ) ) ) )
& ! [D: $i,E: $i] :
( ( ( C @ ( E @ leq ) )
& ( E @ ( n0 @ leq ) )
& ( C @ ( D @ leq ) )
& ( D @ ( n0 @ leq ) ) )
=> ( ( E @ ( D @ ( A @ a_select3 ) ) )
= ( D @ ( E @ ( A @ a_select3 ) ) ) ) ) )
=> ! [D: $i,E: $i] :
( ( ( C @ ( E @ leq ) )
& ( E @ ( n0 @ leq ) )
& ( C @ ( D @ leq ) )
& ( D @ ( n0 @ leq ) ) )
=> ( ( E @ ( D @ ( B @ ( A @ tptp_madd ) @ a_select3 ) ) )
= ( D @ ( E @ ( B @ ( A @ tptp_madd ) @ a_select3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',matrix_symm_add) ).
thf(480,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i,E: $i] :
( ( ( C @ ( E @ leq ) )
& ( E @ ( n0 @ leq ) )
& ( C @ ( D @ leq ) )
& ( D @ ( n0 @ leq ) ) )
=> ( ( E @ ( D @ ( B @ a_select3 ) ) )
= ( D @ ( E @ ( B @ a_select3 ) ) ) ) )
& ! [D: $i,E: $i] :
( ( ( C @ ( E @ leq ) )
& ( E @ ( n0 @ leq ) )
& ( C @ ( D @ leq ) )
& ( D @ ( n0 @ leq ) ) )
=> ( ( E @ ( D @ ( A @ a_select3 ) ) )
= ( D @ ( E @ ( A @ a_select3 ) ) ) ) ) )
=> ! [D: $i,E: $i] :
( ( ( C @ ( E @ leq ) )
& ( E @ ( n0 @ leq ) )
& ( C @ ( D @ leq ) )
& ( D @ ( n0 @ leq ) ) )
=> ( ( E @ ( D @ ( B @ ( A @ tptp_madd ) @ a_select3 ) ) )
= ( D @ ( E @ ( B @ ( A @ tptp_madd ) @ a_select3 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(84,axiom,
! [A: $i] :
( ( A @ ( n1 @ plus ) )
= ( A @ succ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_plus_1_l) ).
thf(602,plain,
! [A: $i] :
( ( A @ ( n1 @ plus ) )
= ( A @ succ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(51,axiom,
! [A: $i,B: $i] :
( ( A @ ( n0 @ leq ) )
=> ( A @ ( B @ uniform_int_rnd ) @ ( n0 @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',uniform_int_rand_ranges_lo) ).
thf(397,plain,
! [A: $i,B: $i] :
( ( A @ ( n0 @ leq ) )
=> ( A @ ( B @ uniform_int_rnd ) @ ( n0 @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(40,axiom,
n3 @ ( n410 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_410_3) ).
thf(280,plain,
n3 @ ( n410 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(30,axiom,
! [A: $i] :
( ( A @ ( tptp_minus_1 @ ( n0 @ sum ) ) )
= n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_plus_base) ).
thf(221,plain,
! [A: $i] :
( ( A @ ( tptp_minus_1 @ ( n0 @ sum ) ) )
= n0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(53,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( B @ ( D @ ( C @ ( B @ ( A @ tptp_update3 ) ) ) @ a_select3 ) ) )
= D ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sel3_update_1) ).
thf(452,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( B @ ( D @ ( C @ ( B @ ( A @ tptp_update3 ) ) ) @ a_select3 ) ) )
= D ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( B @ ( A @ tptp_update2 ) ) @ a_select2 ) )
= C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sel2_update_1) ).
thf(201,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( B @ ( A @ tptp_update2 ) ) @ a_select2 ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(45,axiom,
! [A: $i,B: $i] :
( ( ( A != B )
& ( B @ ( A @ leq ) ) )
=> ( A @ ( B @ gt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_gt2) ).
thf(381,plain,
! [A: $i,B: $i] :
( ( ( A != B )
& ( B @ ( A @ leq ) ) )
=> ( A @ ( B @ gt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(29,axiom,
n4 @ ( n330 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_330_4) ).
thf(220,plain,
n4 @ ( n330 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(81,axiom,
n4 @ ( n410 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_410_4) ).
thf(598,plain,
n4 @ ( n410 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(12,axiom,
n0 @ ( n330 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_330_0) ).
thf(192,plain,
n0 @ ( n330 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(97,axiom,
tptp_minus_1 @ ( n410 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_410_tptp_minus_1) ).
thf(630,plain,
tptp_minus_1 @ ( n410 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(16,axiom,
( ( n0 @ succ )
= n1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_1) ).
thf(197,plain,
( ( n0 @ succ )
= n1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(95,axiom,
( ( n0 @ succ @ succ @ succ @ succ @ succ )
= n5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_5) ).
thf(625,plain,
( ( n0 @ succ @ succ @ succ @ succ @ succ )
= n5 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(78,axiom,
! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( ( B @ ( D @ leq ) )
& ( D @ ( n0 @ leq ) )
& ( B @ ( C @ leq ) )
& ( C @ ( n0 @ leq ) ) )
=> ( ( D @ ( C @ ( A @ a_select3 ) ) )
= ( C @ ( D @ ( A @ a_select3 ) ) ) ) )
=> ! [C: $i,D: $i] :
( ( ( B @ ( D @ leq ) )
& ( D @ ( n0 @ leq ) )
& ( B @ ( C @ leq ) )
& ( C @ ( n0 @ leq ) ) )
=> ( ( D @ ( C @ ( A @ inv @ a_select3 ) ) )
= ( C @ ( D @ ( A @ inv @ a_select3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',matrix_symm_inv) ).
thf(583,plain,
! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( ( B @ ( D @ leq ) )
& ( D @ ( n0 @ leq ) )
& ( B @ ( C @ leq ) )
& ( C @ ( n0 @ leq ) ) )
=> ( ( D @ ( C @ ( A @ a_select3 ) ) )
= ( C @ ( D @ ( A @ a_select3 ) ) ) ) )
=> ! [C: $i,D: $i] :
( ( ( B @ ( D @ leq ) )
& ( D @ ( n0 @ leq ) )
& ( B @ ( C @ leq ) )
& ( C @ ( n0 @ leq ) ) )
=> ( ( D @ ( C @ ( A @ inv @ a_select3 ) ) )
= ( C @ ( D @ ( A @ inv @ a_select3 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( F @ ( D @ leq ) )
& ( D @ ( E @ leq ) )
& ( C @ ( A @ leq ) )
& ( A @ ( B @ leq ) ) )
=> ( ( D @ ( A @ ( G @ ( F @ ( E @ dim ) @ ( C @ ( B @ dim ) @ tptp_const_array2 ) ) @ a_select3 ) ) )
= G ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',const_array2_select) ).
thf(224,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( F @ ( D @ leq ) )
& ( D @ ( E @ leq ) )
& ( C @ ( A @ leq ) )
& ( A @ ( B @ leq ) ) )
=> ( ( D @ ( A @ ( G @ ( F @ ( E @ dim ) @ ( C @ ( B @ dim ) @ tptp_const_array2 ) ) @ a_select3 ) ) )
= G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(68,axiom,
( ( n0 @ succ @ succ @ succ )
= n3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_3) ).
thf(554,plain,
( ( n0 @ succ @ succ @ succ )
= n3 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ gt ) )
=> ( B @ ( A @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_gt1) ).
thf(193,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ gt ) )
=> ( B @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(898,plain,
! [A: $i] :
( ( ( n1 @ ( n330 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[189,396]) ).
thf(899,plain,
! [A: $i] :
( ( n1 @ ( n330 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[898]) ).
thf(900,plain,
! [A: $i] :
( ( n1 != A )
| ( n330 != A ) ),
inference(simp,[status(thm)],[899]) ).
thf(901,plain,
n330 != n1,
inference(simp,[status(thm)],[900]) ).
thf(66,axiom,
tptp_minus_1 @ ( n4 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_4_tptp_minus_1) ).
thf(547,plain,
tptp_minus_1 @ ( n4 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(49,axiom,
n2 @ ( n410 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_410_2) ).
thf(393,plain,
n2 @ ( n410 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(980,plain,
! [A: $i] :
( ( ( n0 @ ( n330 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[192,396]) ).
thf(981,plain,
! [A: $i] :
( ( n0 @ ( n330 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[980]) ).
thf(983,plain,
! [A: $i] :
( ( n0 != A )
| ( n330 != A ) ),
inference(simp,[status(thm)],[981]) ).
thf(984,plain,
n330 != n0,
inference(simp,[status(thm)],[983]) ).
thf(71,axiom,
! [A: $i] :
( ( n1 @ ( A @ plus ) )
= ( A @ succ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_plus_1_r) ).
thf(569,plain,
! [A: $i] :
( ( n1 @ ( A @ plus ) )
= ( A @ succ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(85,axiom,
n0 @ ( n4 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_4_0) ).
thf(605,plain,
n0 @ ( n4 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(92,axiom,
! [A: $i] :
( ( n2 @ ( A @ plus ) )
= ( A @ succ @ succ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_plus_2_r) ).
thf(618,plain,
! [A: $i] :
( ( n2 @ ( A @ plus ) )
= ( A @ succ @ succ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(37,axiom,
! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( ( B @ ( D @ leq ) )
& ( D @ ( n0 @ leq ) )
& ( B @ ( C @ leq ) )
& ( C @ ( n0 @ leq ) ) )
=> ( ( D @ ( C @ ( A @ a_select3 ) ) )
= ( C @ ( D @ ( A @ a_select3 ) ) ) ) )
=> ! [C: $i,D: $i] :
( ( ( B @ ( D @ leq ) )
& ( D @ ( n0 @ leq ) )
& ( B @ ( C @ leq ) )
& ( C @ ( n0 @ leq ) ) )
=> ( ( D @ ( C @ ( A @ trans @ a_select3 ) ) )
= ( C @ ( D @ ( A @ trans @ a_select3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',matrix_symm_trans) ).
thf(264,plain,
! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( ( B @ ( D @ leq ) )
& ( D @ ( n0 @ leq ) )
& ( B @ ( C @ leq ) )
& ( C @ ( n0 @ leq ) ) )
=> ( ( D @ ( C @ ( A @ a_select3 ) ) )
= ( C @ ( D @ ( A @ a_select3 ) ) ) ) )
=> ! [C: $i,D: $i] :
( ( ( B @ ( D @ leq ) )
& ( D @ ( n0 @ leq ) )
& ( B @ ( C @ leq ) )
& ( C @ ( n0 @ leq ) ) )
=> ( ( D @ ( C @ ( A @ trans @ a_select3 ) ) )
= ( C @ ( D @ ( A @ trans @ a_select3 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(6,axiom,
! [A: $i] :
( ( A @ pred @ succ )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_pred) ).
thf(180,plain,
! [A: $i] :
( ( A @ pred @ succ )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(44,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ geq ) )
<=> ( A @ ( B @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_geq) ).
thf(375,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ leq ) )
=> ( B @ ( A @ geq ) ) )
& ( ( B @ ( A @ geq ) )
=> ( A @ ( B @ leq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(11,axiom,
n1 @ ( n2 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_2_1) ).
thf(191,plain,
n1 @ ( n2 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(75,axiom,
n330 @ ( n410 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_410_330) ).
thf(577,plain,
n330 @ ( n410 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(41,axiom,
! [A: $i] :
( ( n1 @ ( A @ minus ) )
= ( A @ pred ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pred_minus_1) ).
thf(281,plain,
! [A: $i] :
( ( n1 @ ( A @ minus ) )
= ( A @ pred ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(19,axiom,
tptp_minus_1 @ ( n2 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_2_tptp_minus_1) ).
thf(204,plain,
tptp_minus_1 @ ( n2 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(72,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ leq ) )
=> ( B @ succ @ ( A @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_succ) ).
thf(572,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ leq ) )
=> ( B @ succ @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(88,axiom,
! [A: $i] : ( A @ ( A @ succ @ gt ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_succ) ).
thf(611,plain,
! [A: $i] : ( A @ ( A @ succ @ gt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(141,plain,
( ~ sk1
| ( ( sk2 @ ( sk3 @ ( simplex7_init @ a_select3 ) ) )
!= init )
| ~ ( n1 @ ( n330 @ minus ) @ ( pv20 @ leq ) )
| ~ ( n1 @ ( n410 @ minus ) @ ( pv19 @ leq ) )
| ~ ( n1 @ ( n410 @ minus ) @ ( pv7 @ leq ) )
| ~ ( n3 @ ( s_worst7 @ leq ) )
| ~ ( n3 @ ( s_sworst7 @ leq ) )
| ~ ( n3 @ ( s_best7 @ leq ) )
| ~ ( pv20 @ ( n0 @ leq ) )
| ~ ( pv19 @ ( n0 @ leq ) )
| ~ ( pv7 @ ( n0 @ leq ) )
| ~ ( s_worst7 @ ( n0 @ leq ) )
| ~ ( s_sworst7 @ ( n0 @ leq ) )
| ~ ( s_best7 @ ( n0 @ leq ) )
| ( ( n2 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( ( n1 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( ( n0 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( s_worst7_init != init )
| ( s_sworst7_init != init )
| ( s_best7_init != init ) ),
inference(cnfConj,[status(thm)],[101]) ).
thf(144,plain,
( ~ sk1
| ~ ( n1 @ ( n330 @ minus ) @ ( pv20 @ leq ) )
| ~ ( n1 @ ( n410 @ minus ) @ ( pv19 @ leq ) )
| ~ ( n1 @ ( n410 @ minus ) @ ( pv7 @ leq ) )
| ~ ( n3 @ ( s_worst7 @ leq ) )
| ~ ( n3 @ ( s_sworst7 @ leq ) )
| ~ ( n3 @ ( s_best7 @ leq ) )
| ~ ( pv20 @ ( n0 @ leq ) )
| ~ ( pv19 @ ( n0 @ leq ) )
| ~ ( pv7 @ ( n0 @ leq ) )
| ~ ( s_worst7 @ ( n0 @ leq ) )
| ~ ( s_sworst7 @ ( n0 @ leq ) )
| ~ ( s_best7 @ ( n0 @ leq ) )
| ( ( sk2 @ ( sk3 @ ( simplex7_init @ a_select3 ) ) )
!= init )
| ( ( n2 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( ( n1 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( ( n0 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( s_worst7_init != init )
| ( s_sworst7_init != init )
| ( s_best7_init != init ) ),
inference(lifteq,[status(thm)],[141]) ).
thf(641,plain,
( ~ sk1
| ~ ( n1 @ ( n330 @ minus ) @ ( pv20 @ leq ) )
| ~ ( n1 @ ( n410 @ minus ) @ ( pv19 @ leq ) )
| ~ ( n1 @ ( n410 @ minus ) @ ( pv7 @ leq ) )
| ~ ( n3 @ ( s_worst7 @ leq ) )
| ~ $true
| ~ ( n3 @ ( s_best7 @ leq ) )
| ~ ( pv20 @ ( n0 @ leq ) )
| ~ ( pv19 @ ( n0 @ leq ) )
| ~ ( pv7 @ ( n0 @ leq ) )
| ~ ( s_worst7 @ ( n0 @ leq ) )
| ~ ( s_sworst7 @ ( n0 @ leq ) )
| ~ ( s_best7 @ ( n0 @ leq ) )
| ( ( sk2 @ ( sk3 @ ( simplex7_init @ a_select3 ) ) )
!= init )
| ( ( n2 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( ( n1 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( ( n0 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( init != init )
| ( init != init )
| ( init != init ) ),
inference(rewrite,[status(thm)],[144,161,146,103,157]) ).
thf(642,plain,
( ~ sk1
| ~ ( n1 @ ( n330 @ minus ) @ ( pv20 @ leq ) )
| ~ ( n1 @ ( n410 @ minus ) @ ( pv19 @ leq ) )
| ~ ( n1 @ ( n410 @ minus ) @ ( pv7 @ leq ) )
| ~ ( n3 @ ( s_worst7 @ leq ) )
| ~ ( n3 @ ( s_best7 @ leq ) )
| ~ ( pv20 @ ( n0 @ leq ) )
| ~ ( pv19 @ ( n0 @ leq ) )
| ~ ( pv7 @ ( n0 @ leq ) )
| ~ ( s_worst7 @ ( n0 @ leq ) )
| ~ ( s_sworst7 @ ( n0 @ leq ) )
| ~ ( s_best7 @ ( n0 @ leq ) )
| ( ( sk2 @ ( sk3 @ ( simplex7_init @ a_select3 ) ) )
!= init )
| ( ( n2 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( ( n1 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( ( n0 @ ( s_try7_init @ a_select2 ) )
!= init ) ),
inference(simp,[status(thm)],[641]) ).
thf(678,plain,
( ~ sk1
| ~ ( n1 @ ( n330 @ minus ) @ ( pv20 @ leq ) )
| ~ ( n1 @ ( n410 @ minus ) @ ( pv19 @ leq ) )
| ~ ( n1 @ ( n410 @ minus ) @ ( pv7 @ leq ) )
| ~ ( n3 @ ( s_worst7 @ leq ) )
| ~ $true
| ~ ( pv20 @ ( n0 @ leq ) )
| ~ ( pv19 @ ( n0 @ leq ) )
| ~ ( pv7 @ ( n0 @ leq ) )
| ~ ( s_worst7 @ ( n0 @ leq ) )
| ~ ( s_sworst7 @ ( n0 @ leq ) )
| ~ ( s_best7 @ ( n0 @ leq ) )
| ( ( sk2 @ ( sk3 @ ( simplex7_init @ a_select3 ) ) )
!= init )
| ( ( n2 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( ( n1 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( ( n0 @ ( s_try7_init @ a_select2 ) )
!= init ) ),
inference(rewrite,[status(thm)],[642,104]) ).
thf(679,plain,
( ~ sk1
| ~ ( n1 @ ( n330 @ minus ) @ ( pv20 @ leq ) )
| ~ ( n1 @ ( n410 @ minus ) @ ( pv19 @ leq ) )
| ~ ( n1 @ ( n410 @ minus ) @ ( pv7 @ leq ) )
| ~ ( n3 @ ( s_worst7 @ leq ) )
| ~ ( pv20 @ ( n0 @ leq ) )
| ~ ( pv19 @ ( n0 @ leq ) )
| ~ ( pv7 @ ( n0 @ leq ) )
| ~ ( s_worst7 @ ( n0 @ leq ) )
| ~ ( s_sworst7 @ ( n0 @ leq ) )
| ~ ( s_best7 @ ( n0 @ leq ) )
| ( ( sk2 @ ( sk3 @ ( simplex7_init @ a_select3 ) ) )
!= init )
| ( ( n2 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( ( n1 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( ( n0 @ ( s_try7_init @ a_select2 ) )
!= init ) ),
inference(simp,[status(thm)],[678]) ).
thf(680,plain,
( ~ sk1
| ~ $true
| ~ ( n1 @ ( n410 @ minus ) @ ( pv19 @ leq ) )
| ~ ( n1 @ ( n410 @ minus ) @ ( pv7 @ leq ) )
| ~ ( n3 @ ( s_worst7 @ leq ) )
| ~ $true
| ~ $true
| ~ ( pv7 @ ( n0 @ leq ) )
| ~ $true
| ~ $true
| ~ $true
| ( ( sk2 @ ( sk3 @ ( simplex7_init @ a_select3 ) ) )
!= init )
| ( ( n2 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( ( n1 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( ( n0 @ ( s_try7_init @ a_select2 ) )
!= init ) ),
inference(rewrite,[status(thm)],[679,115,102,118,106,108,109]) ).
thf(681,plain,
( ~ sk1
| ~ ( n1 @ ( n410 @ minus ) @ ( pv19 @ leq ) )
| ~ ( n1 @ ( n410 @ minus ) @ ( pv7 @ leq ) )
| ~ ( n3 @ ( s_worst7 @ leq ) )
| ~ ( pv7 @ ( n0 @ leq ) )
| ( ( sk2 @ ( sk3 @ ( simplex7_init @ a_select3 ) ) )
!= init )
| ( ( n2 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( ( n1 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( ( n0 @ ( s_try7_init @ a_select2 ) )
!= init ) ),
inference(simp,[status(thm)],[680]) ).
thf(724,plain,
( ( ( n3 @ ( s_worst7 @ leq ) )
!= ( n3 @ ( s_best7 @ leq ) ) )
| ~ sk1
| ~ ( n1 @ ( n410 @ minus ) @ ( pv19 @ leq ) )
| ~ ( n1 @ ( n410 @ minus ) @ ( pv7 @ leq ) )
| ~ $true
| ~ ( pv7 @ ( n0 @ leq ) )
| ( ( sk2 @ ( sk3 @ ( simplex7_init @ a_select3 ) ) )
!= init )
| ( ( n2 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( ( n1 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( ( n0 @ ( s_try7_init @ a_select2 ) )
!= init ) ),
inference(paramod_ordered,[status(thm)],[104,681]) ).
thf(725,plain,
( ( ( n3 @ ( s_worst7 @ leq ) )
!= ( n3 @ ( s_best7 @ leq ) ) )
| ~ sk1
| ~ ( n1 @ ( n410 @ minus ) @ ( pv19 @ leq ) )
| ~ ( n1 @ ( n410 @ minus ) @ ( pv7 @ leq ) )
| ~ ( pv7 @ ( n0 @ leq ) )
| ( ( sk2 @ ( sk3 @ ( simplex7_init @ a_select3 ) ) )
!= init )
| ( ( n2 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( ( n1 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( ( n0 @ ( s_try7_init @ a_select2 ) )
!= init ) ),
inference(simp,[status(thm)],[724]) ).
thf(771,plain,
( ( n3 != n3 )
| ( s_worst7 != s_best7 )
| ~ sk1
| ~ ( n1 @ ( n410 @ minus ) @ ( pv19 @ leq ) )
| ~ ( n1 @ ( n410 @ minus ) @ ( pv7 @ leq ) )
| ~ ( pv7 @ ( n0 @ leq ) )
| ( ( sk2 @ ( sk3 @ ( simplex7_init @ a_select3 ) ) )
!= init )
| ( ( n2 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( ( n1 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( ( n0 @ ( s_try7_init @ a_select2 ) )
!= init ) ),
inference(simp,[status(thm)],[725]) ).
thf(790,plain,
( ( s_worst7 != s_best7 )
| ~ sk1
| ~ ( n1 @ ( n410 @ minus ) @ ( pv19 @ leq ) )
| ~ ( n1 @ ( n410 @ minus ) @ ( pv7 @ leq ) )
| ~ ( pv7 @ ( n0 @ leq ) )
| ( ( sk2 @ ( sk3 @ ( simplex7_init @ a_select3 ) ) )
!= init )
| ( ( n2 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( ( n1 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( ( n0 @ ( s_try7_init @ a_select2 ) )
!= init ) ),
inference(simp,[status(thm)],[771]) ).
thf(896,plain,
( ( s_worst7 != s_best7 )
| ~ sk1
| ~ ( n1 @ ( n410 @ minus ) @ ( pv19 @ leq ) )
| ~ ( n1 @ ( n410 @ minus ) @ ( pv7 @ leq ) )
| ~ $true
| ( ( sk2 @ ( sk3 @ ( simplex7_init @ a_select3 ) ) )
!= init )
| ( ( n2 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( ( n1 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( ( n0 @ ( s_try7_init @ a_select2 ) )
!= init ) ),
inference(rewrite,[status(thm)],[790,131]) ).
thf(897,plain,
( ( s_worst7 != s_best7 )
| ~ sk1
| ~ ( n1 @ ( n410 @ minus ) @ ( pv19 @ leq ) )
| ~ ( n1 @ ( n410 @ minus ) @ ( pv7 @ leq ) )
| ( ( sk2 @ ( sk3 @ ( simplex7_init @ a_select3 ) ) )
!= init )
| ( ( n2 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( ( n1 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( ( n0 @ ( s_try7_init @ a_select2 ) )
!= init ) ),
inference(simp,[status(thm)],[896]) ).
thf(906,plain,
( ( s_worst7 != s_best7 )
| ~ sk1
| ~ ( n1 @ ( n410 @ minus ) @ ( pv19 @ leq ) )
| ~ $true
| ( ( sk2 @ ( sk3 @ ( simplex7_init @ a_select3 ) ) )
!= init )
| ( ( n2 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( ( n1 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( ( n0 @ ( s_try7_init @ a_select2 ) )
!= init ) ),
inference(rewrite,[status(thm)],[897,122]) ).
thf(907,plain,
( ( s_worst7 != s_best7 )
| ~ sk1
| ~ ( n1 @ ( n410 @ minus ) @ ( pv19 @ leq ) )
| ( ( sk2 @ ( sk3 @ ( simplex7_init @ a_select3 ) ) )
!= init )
| ( ( n2 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( ( n1 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( ( n0 @ ( s_try7_init @ a_select2 ) )
!= init ) ),
inference(simp,[status(thm)],[906]) ).
thf(922,plain,
( ( ( n1 @ ( n410 @ minus ) @ ( pv19 @ leq ) )
!= ( n1 @ ( n410 @ minus ) @ ( pv7 @ leq ) ) )
| ( s_worst7 != s_best7 )
| ~ sk1
| ~ $true
| ( ( sk2 @ ( sk3 @ ( simplex7_init @ a_select3 ) ) )
!= init )
| ( ( n2 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( ( n1 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( ( n0 @ ( s_try7_init @ a_select2 ) )
!= init ) ),
inference(paramod_ordered,[status(thm)],[122,907]) ).
thf(923,plain,
( ( ( n1 @ ( n410 @ minus ) @ ( pv19 @ leq ) )
!= ( n1 @ ( n410 @ minus ) @ ( pv7 @ leq ) ) )
| ( s_worst7 != s_best7 )
| ~ sk1
| ( ( sk2 @ ( sk3 @ ( simplex7_init @ a_select3 ) ) )
!= init )
| ( ( n2 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( ( n1 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( ( n0 @ ( s_try7_init @ a_select2 ) )
!= init ) ),
inference(simp,[status(thm)],[922]) ).
thf(946,plain,
( ( ( n1 @ ( n410 @ minus ) )
!= ( n1 @ ( n410 @ minus ) ) )
| ( pv19 != pv7 )
| ( s_worst7 != s_best7 )
| ~ sk1
| ( ( sk2 @ ( sk3 @ ( simplex7_init @ a_select3 ) ) )
!= init )
| ( ( n2 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( ( n1 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( ( n0 @ ( s_try7_init @ a_select2 ) )
!= init ) ),
inference(simp,[status(thm)],[923]) ).
thf(947,plain,
( ( pv19 != pv7 )
| ( s_worst7 != s_best7 )
| ~ sk1
| ( ( sk2 @ ( sk3 @ ( simplex7_init @ a_select3 ) ) )
!= init )
| ( ( n2 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( ( n1 @ ( s_try7_init @ a_select2 ) )
!= init )
| ( ( n0 @ ( s_try7_init @ a_select2 ) )
!= init ) ),
inference(simp,[status(thm)],[946]) ).
thf(113,plain,
pv8 @ ( n0 @ leq ),
inference(cnfConj,[status(thm)],[101]) ).
thf(28,axiom,
n3 @ ( n4 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_4_3) ).
thf(219,plain,
n3 @ ( n4 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(21,axiom,
n1 @ ( n4 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_4_1) ).
thf(208,plain,
n1 @ ( n4 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(82,axiom,
n0 @ ( n2 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_2_0) ).
thf(599,plain,
n0 @ ( n2 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(48,axiom,
! [A: $i,B: $i] :
( ( B @ pred @ ( A @ leq ) )
<=> ( A @ ( B @ gt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_gt_pred) ).
thf(387,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ gt ) )
=> ( B @ pred @ ( A @ leq ) ) )
& ( ( B @ pred @ ( A @ leq ) )
=> ( A @ ( B @ gt ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(98,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) )
& ! [E: $i] :
( ( ( B @ ( E @ leq ) )
& ( E @ ( n0 @ leq ) ) )
=> ( ( E @ ( C @ a_select2 ) )
= D ) ) )
=> ( ( A @ ( D @ ( B @ ( C @ tptp_update2 ) ) @ a_select2 ) )
= D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sel2_update_3) ).
thf(631,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) )
& ! [E: $i] :
( ( ( B @ ( E @ leq ) )
& ( E @ ( n0 @ leq ) ) )
=> ( ( E @ ( C @ a_select2 ) )
= D ) ) )
=> ( ( A @ ( D @ ( B @ ( C @ tptp_update2 ) ) @ a_select2 ) )
= D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(65,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i,E: $i] :
( ( ( C @ ( E @ leq ) )
& ( E @ ( n0 @ leq ) )
& ( C @ ( D @ leq ) )
& ( D @ ( n0 @ leq ) ) )
=> ( ( E @ ( D @ ( B @ a_select3 ) ) )
= ( D @ ( E @ ( B @ a_select3 ) ) ) ) )
=> ! [D: $i,E: $i] :
( ( ( C @ ( E @ leq ) )
& ( E @ ( n0 @ leq ) )
& ( C @ ( D @ leq ) )
& ( D @ ( n0 @ leq ) ) )
=> ( ( E @ ( D @ ( A @ trans @ ( B @ tptp_mmul ) @ ( A @ tptp_mmul ) @ a_select3 ) ) )
= ( D @ ( E @ ( A @ trans @ ( B @ tptp_mmul ) @ ( A @ tptp_mmul ) @ a_select3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',matrix_symm_aba1) ).
thf(535,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i,E: $i] :
( ( ( C @ ( E @ leq ) )
& ( E @ ( n0 @ leq ) )
& ( C @ ( D @ leq ) )
& ( D @ ( n0 @ leq ) ) )
=> ( ( E @ ( D @ ( B @ a_select3 ) ) )
= ( D @ ( E @ ( B @ a_select3 ) ) ) ) )
=> ! [D: $i,E: $i] :
( ( ( C @ ( E @ leq ) )
& ( E @ ( n0 @ leq ) )
& ( C @ ( D @ leq ) )
& ( D @ ( n0 @ leq ) ) )
=> ( ( E @ ( D @ ( A @ trans @ ( B @ tptp_mmul ) @ ( A @ tptp_mmul ) @ a_select3 ) ) )
= ( D @ ( E @ ( A @ trans @ ( B @ tptp_mmul ) @ ( A @ tptp_mmul ) @ a_select3 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(87,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ leq ) )
& ( B @ ( A @ leq ) ) )
=> ( C @ ( A @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_leq) ).
thf(609,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ leq ) )
& ( B @ ( A @ leq ) ) )
=> ( C @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(93,axiom,
! [A: $i] :
( ( n3 @ ( A @ plus ) )
= ( A @ succ @ succ @ succ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_plus_3_r) ).
thf(621,plain,
! [A: $i] :
( ( n3 @ ( A @ plus ) )
= ( A @ succ @ succ @ succ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(57,axiom,
n2 @ ( n5 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_5_2) ).
thf(462,plain,
n2 @ ( n5 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(54,axiom,
! [A: $i] :
( tptp_float_0_0
= ( A @ ( tptp_minus_1 @ ( n0 @ sum ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_plus_base_float) ).
thf(455,plain,
! [A: $i] :
( tptp_float_0_0
= ( A @ ( tptp_minus_1 @ ( n0 @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(33,axiom,
! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( ( B @ ( D @ leq ) )
& ( D @ ( n0 @ leq ) )
& ( B @ ( C @ leq ) )
& ( C @ ( n0 @ leq ) ) )
=> ( ( D @ ( C @ ( A @ a_select3 ) ) )
= ( C @ ( D @ ( A @ a_select3 ) ) ) ) )
=> ! [C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ ( E @ leq ) )
& ( E @ ( n0 @ leq ) )
& ( B @ ( D @ leq ) )
& ( D @ ( n0 @ leq ) )
& ( B @ ( C @ leq ) )
& ( C @ ( n0 @ leq ) ) )
=> ( ( D @ ( C @ ( F @ ( E @ ( E @ ( A @ tptp_update3 ) ) ) @ a_select3 ) ) )
= ( C @ ( D @ ( F @ ( E @ ( E @ ( A @ tptp_update3 ) ) ) @ a_select3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',matrix_symm_update_diagonal) ).
thf(241,plain,
! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( ( B @ ( D @ leq ) )
& ( D @ ( n0 @ leq ) )
& ( B @ ( C @ leq ) )
& ( C @ ( n0 @ leq ) ) )
=> ( ( D @ ( C @ ( A @ a_select3 ) ) )
= ( C @ ( D @ ( A @ a_select3 ) ) ) ) )
=> ! [C: $i,D: $i,E: $i,F: $i] :
( ( ( B @ ( E @ leq ) )
& ( E @ ( n0 @ leq ) )
& ( B @ ( D @ leq ) )
& ( D @ ( n0 @ leq ) )
& ( B @ ( C @ leq ) )
& ( C @ ( n0 @ leq ) ) )
=> ( ( D @ ( C @ ( F @ ( E @ ( E @ ( A @ tptp_update3 ) ) ) @ a_select3 ) ) )
= ( C @ ( D @ ( F @ ( E @ ( E @ ( A @ tptp_update3 ) ) ) @ a_select3 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(67,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ leq ) )
<=> ( A @ ( B @ succ @ gt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_succ_gt_equiv) ).
thf(548,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ succ @ gt ) )
=> ( B @ ( A @ leq ) ) )
& ( ( B @ ( A @ leq ) )
=> ( A @ ( B @ succ @ gt ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(22,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ( B @ ( C @ a_select2 ) )
= D )
& ( A != B ) )
=> ( ( B @ ( E @ ( A @ ( C @ tptp_update2 ) ) @ a_select2 ) )
= D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sel2_update_2) ).
thf(209,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ( B @ ( C @ a_select2 ) )
= D )
& ( A != B ) )
=> ( ( B @ ( E @ ( A @ ( C @ tptp_update2 ) ) @ a_select2 ) )
= D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(91,axiom,
tptp_minus_1 @ ( n3 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_3_tptp_minus_1) ).
thf(617,plain,
tptp_minus_1 @ ( n3 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(55,axiom,
n0 @ ( n3 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_3_0) ).
thf(458,plain,
n0 @ ( n3 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(129,plain,
( ( pvar1400_init = init )
| ~ ( n1 @ ( loopcounter @ gt ) ) ),
inference(cnfConj,[status(thm)],[101]) ).
thf(145,plain,
( ~ ( n1 @ ( loopcounter @ gt ) )
| ( pvar1400_init = init ) ),
inference(lifteq,[status(thm)],[129]) ).
thf(17,axiom,
( ( n0 @ succ @ succ @ succ @ succ )
= n4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_4) ).
thf(199,plain,
( ( n0 @ succ @ succ @ succ @ succ )
= n4 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(5,axiom,
! [A: $i] :
( ( A @ succ @ pred )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pred_succ) ).
thf(177,plain,
! [A: $i] :
( ( A @ succ @ pred )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(58,axiom,
n3 @ ( n330 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_330_3) ).
thf(463,plain,
n3 @ ( n330 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(948,plain,
! [A: $i] :
( ( ( n1 @ ( n2 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[191,396]) ).
thf(949,plain,
! [A: $i] :
( ( n1 @ ( n2 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[948]) ).
thf(950,plain,
! [A: $i] :
( ( n1 != A )
| ( n2 != A ) ),
inference(simp,[status(thm)],[949]) ).
thf(951,plain,
n2 != n1,
inference(simp,[status(thm)],[950]) ).
thf(60,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( ( D @ ( C @ ( E @ a_select3 ) ) )
= F )
& ( B = D )
& ( A != C ) )
=> ( ( D @ ( C @ ( G @ ( B @ ( A @ ( E @ tptp_update3 ) ) ) @ a_select3 ) ) )
= F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sel3_update_2) ).
thf(470,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( ( D @ ( C @ ( E @ a_select3 ) ) )
= F )
& ( B = D )
& ( A != C ) )
=> ( ( D @ ( C @ ( G @ ( B @ ( A @ ( E @ tptp_update3 ) ) ) @ a_select3 ) ) )
= F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(74,axiom,
tptp_minus_1 @ ( n1 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_1_tptp_minus_1) ).
thf(576,plain,
tptp_minus_1 @ ( n1 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(89,axiom,
n4 @ ( n5 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_5_4) ).
thf(613,plain,
n4 @ ( n5 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(83,axiom,
! [A: $i] : ( A @ ( A @ leq ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_leq) ).
thf(600,plain,
! [A: $i] : ( A @ ( A @ leq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(79,axiom,
tptp_minus_1 @ ( n5 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_5_tptp_minus_1) ).
thf(595,plain,
tptp_minus_1 @ ( n5 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(96,axiom,
! [A: $i] :
( ( ( n5 @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A = n5 )
| ( A = n4 )
| ( A = n3 )
| ( A = n2 )
| ( A = n1 )
| ( A = n0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',finite_domain_5) ).
thf(627,plain,
! [A: $i] :
( ( ( n5 @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A = n5 )
| ( A = n4 )
| ( A = n3 )
| ( A = n2 )
| ( A = n1 )
| ( A = n0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(69,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( B @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( C @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) )
& ! [G: $i,H: $i] :
( ( ( D @ ( H @ leq ) )
& ( C @ ( G @ leq ) )
& ( H @ ( n0 @ leq ) )
& ( G @ ( n0 @ leq ) ) )
=> ( ( H @ ( G @ ( E @ a_select3 ) ) )
= F ) ) )
=> ( ( B @ ( A @ ( F @ ( D @ ( C @ ( E @ tptp_update3 ) ) ) @ a_select3 ) ) )
= F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sel3_update_3) ).
thf(556,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( B @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( C @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) )
& ! [G: $i,H: $i] :
( ( ( D @ ( H @ leq ) )
& ( C @ ( G @ leq ) )
& ( H @ ( n0 @ leq ) )
& ( G @ ( n0 @ leq ) ) )
=> ( ( H @ ( G @ ( E @ a_select3 ) ) )
= F ) ) )
=> ( ( B @ ( A @ ( F @ ( D @ ( C @ ( E @ tptp_update3 ) ) ) @ a_select3 ) ) )
= F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(77,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ gt ) )
& ( B @ ( A @ gt ) ) )
=> ( C @ ( A @ gt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_gt) ).
thf(581,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ gt ) )
& ( B @ ( A @ gt ) ) )
=> ( C @ ( A @ gt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(27,axiom,
n2 @ ( n330 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_330_2) ).
thf(218,plain,
n2 @ ( n330 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(36,axiom,
! [A: $i,B: $i] :
( ( B @ succ @ ( A @ succ @ leq ) )
<=> ( B @ ( A @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_succ_succ) ).
thf(258,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ leq ) )
=> ( B @ succ @ ( A @ succ @ leq ) ) )
& ( ( B @ succ @ ( A @ succ @ leq ) )
=> ( B @ ( A @ leq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(8,axiom,
! [A: $i] :
( ( A @ ( n4 @ plus ) )
= ( A @ succ @ succ @ succ @ succ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_plus_4_l) ).
thf(186,plain,
! [A: $i] :
( ( A @ ( n4 @ plus ) )
= ( A @ succ @ succ @ succ @ succ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(114,plain,
n1 @ ( n330 @ minus ) @ ( pv8 @ leq ),
inference(cnfConj,[status(thm)],[101]) ).
thf(3,axiom,
! [A: $i] :
( ( n4 @ ( A @ plus ) )
= ( A @ succ @ succ @ succ @ succ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_plus_4_r) ).
thf(171,plain,
! [A: $i] :
( ( n4 @ ( A @ plus ) )
= ( A @ succ @ succ @ succ @ succ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(70,axiom,
n5 @ ( n410 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_410_5) ).
thf(568,plain,
n5 @ ( n410 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(23,axiom,
tptp_minus_1 @ ( n330 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_330_tptp_minus_1) ).
thf(214,plain,
tptp_minus_1 @ ( n330 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(43,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ! [I: $i,J: $i] :
( ( ( G @ ( J @ leq ) )
& ( J @ ( n0 @ leq ) )
& ( G @ ( I @ leq ) )
& ( I @ ( n0 @ leq ) ) )
=> ( ( J @ ( I @ ( F @ a_select3 ) ) )
= ( I @ ( J @ ( F @ a_select3 ) ) ) ) )
& ! [I: $i,J: $i] :
( ( ( G @ ( J @ leq ) )
& ( J @ ( n0 @ leq ) )
& ( G @ ( I @ leq ) )
& ( I @ ( n0 @ leq ) ) )
=> ( ( J @ ( I @ ( A @ a_select3 ) ) )
= ( I @ ( J @ ( A @ a_select3 ) ) ) ) )
& ! [I: $i,J: $i] :
( ( ( H @ ( J @ leq ) )
& ( J @ ( n0 @ leq ) )
& ( H @ ( I @ leq ) )
& ( I @ ( n0 @ leq ) ) )
=> ( ( J @ ( I @ ( D @ a_select3 ) ) )
= ( I @ ( J @ ( D @ a_select3 ) ) ) ) ) )
=> ! [I: $i,J: $i] :
( ( ( G @ ( J @ leq ) )
& ( J @ ( n0 @ leq ) )
& ( G @ ( I @ leq ) )
& ( I @ ( n0 @ leq ) ) )
=> ( ( J @ ( I @ ( B @ trans @ ( E @ trans @ ( F @ tptp_mmul ) @ ( E @ tptp_mmul ) @ ( C @ trans @ ( D @ tptp_mmul ) @ ( C @ tptp_mmul ) @ tptp_madd ) @ tptp_mmul ) @ ( B @ tptp_mmul ) @ ( A @ tptp_madd ) @ a_select3 ) ) )
= ( I @ ( J @ ( B @ trans @ ( E @ trans @ ( F @ tptp_mmul ) @ ( E @ tptp_mmul ) @ ( C @ trans @ ( D @ tptp_mmul ) @ ( C @ tptp_mmul ) @ tptp_madd ) @ tptp_mmul ) @ ( B @ tptp_mmul ) @ ( A @ tptp_madd ) @ a_select3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',matrix_symm_joseph_update) ).
thf(287,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ! [I: $i,J: $i] :
( ( ( G @ ( J @ leq ) )
& ( J @ ( n0 @ leq ) )
& ( G @ ( I @ leq ) )
& ( I @ ( n0 @ leq ) ) )
=> ( ( J @ ( I @ ( F @ a_select3 ) ) )
= ( I @ ( J @ ( F @ a_select3 ) ) ) ) )
& ! [I: $i,J: $i] :
( ( ( G @ ( J @ leq ) )
& ( J @ ( n0 @ leq ) )
& ( G @ ( I @ leq ) )
& ( I @ ( n0 @ leq ) ) )
=> ( ( J @ ( I @ ( A @ a_select3 ) ) )
= ( I @ ( J @ ( A @ a_select3 ) ) ) ) )
& ! [I: $i,J: $i] :
( ( ( H @ ( J @ leq ) )
& ( J @ ( n0 @ leq ) )
& ( H @ ( I @ leq ) )
& ( I @ ( n0 @ leq ) ) )
=> ( ( J @ ( I @ ( D @ a_select3 ) ) )
= ( I @ ( J @ ( D @ a_select3 ) ) ) ) ) )
=> ! [I: $i,J: $i] :
( ( ( G @ ( J @ leq ) )
& ( J @ ( n0 @ leq ) )
& ( G @ ( I @ leq ) )
& ( I @ ( n0 @ leq ) ) )
=> ( ( J @ ( I @ ( B @ trans @ ( E @ trans @ ( F @ tptp_mmul ) @ ( E @ tptp_mmul ) @ ( C @ trans @ ( D @ tptp_mmul ) @ ( C @ tptp_mmul ) @ tptp_madd ) @ tptp_mmul ) @ ( B @ tptp_mmul ) @ ( A @ tptp_madd ) @ a_select3 ) ) )
= ( I @ ( J @ ( B @ trans @ ( E @ trans @ ( F @ tptp_mmul ) @ ( E @ tptp_mmul ) @ ( C @ trans @ ( D @ tptp_mmul ) @ ( C @ tptp_mmul ) @ tptp_madd ) @ tptp_mmul ) @ ( B @ tptp_mmul ) @ ( A @ tptp_madd ) @ a_select3 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(7,axiom,
! [A: $i] :
( ( A @ ( n5 @ plus ) )
= ( A @ succ @ succ @ succ @ succ @ succ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_plus_5_l) ).
thf(183,plain,
! [A: $i] :
( ( A @ ( n5 @ plus ) )
= ( A @ succ @ succ @ succ @ succ @ succ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(14,axiom,
n1 @ ( n410 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_410_1) ).
thf(195,plain,
n1 @ ( n410 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(52,axiom,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i,E: $i] :
( ( ( C @ ( E @ leq ) )
& ( E @ ( n0 @ leq ) )
& ( C @ ( D @ leq ) )
& ( D @ ( n0 @ leq ) ) )
=> ( ( E @ ( D @ ( B @ a_select3 ) ) )
= ( D @ ( E @ ( B @ a_select3 ) ) ) ) )
& ! [D: $i,E: $i] :
( ( ( C @ ( E @ leq ) )
& ( E @ ( n0 @ leq ) )
& ( C @ ( D @ leq ) )
& ( D @ ( n0 @ leq ) ) )
=> ( ( E @ ( D @ ( A @ a_select3 ) ) )
= ( D @ ( E @ ( A @ a_select3 ) ) ) ) ) )
=> ! [D: $i,E: $i] :
( ( ( C @ ( E @ leq ) )
& ( E @ ( n0 @ leq ) )
& ( C @ ( D @ leq ) )
& ( D @ ( n0 @ leq ) ) )
=> ( ( E @ ( D @ ( B @ ( A @ tptp_msub ) @ a_select3 ) ) )
= ( D @ ( E @ ( B @ ( A @ tptp_msub ) @ a_select3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',matrix_symm_sub) ).
thf(400,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i,E: $i] :
( ( ( C @ ( E @ leq ) )
& ( E @ ( n0 @ leq ) )
& ( C @ ( D @ leq ) )
& ( D @ ( n0 @ leq ) ) )
=> ( ( E @ ( D @ ( B @ a_select3 ) ) )
= ( D @ ( E @ ( B @ a_select3 ) ) ) ) )
& ! [D: $i,E: $i] :
( ( ( C @ ( E @ leq ) )
& ( E @ ( n0 @ leq ) )
& ( C @ ( D @ leq ) )
& ( D @ ( n0 @ leq ) ) )
=> ( ( E @ ( D @ ( A @ a_select3 ) ) )
= ( D @ ( E @ ( A @ a_select3 ) ) ) ) ) )
=> ! [D: $i,E: $i] :
( ( ( C @ ( E @ leq ) )
& ( E @ ( n0 @ leq ) )
& ( C @ ( D @ leq ) )
& ( D @ ( n0 @ leq ) ) )
=> ( ( E @ ( D @ ( B @ ( A @ tptp_msub ) @ a_select3 ) ) )
= ( D @ ( E @ ( B @ ( A @ tptp_msub ) @ a_select3 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(64,axiom,
! [A: $i,B: $i] :
( ( A @ ( n0 @ leq ) )
=> ( A @ ( A @ ( B @ uniform_int_rnd ) @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',uniform_int_rand_ranges_hi) ).
thf(532,plain,
! [A: $i,B: $i] :
( ( A @ ( n0 @ leq ) )
=> ( A @ ( A @ ( B @ uniform_int_rnd ) @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(94,axiom,
n0 @ ( n1 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_1_0) ).
thf(624,plain,
n0 @ ( n1 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(59,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ lt ) )
<=> ( A @ ( B @ gt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lt_gt) ).
thf(464,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ gt ) )
=> ( B @ ( A @ lt ) ) )
& ( ( B @ ( A @ lt ) )
=> ( A @ ( B @ gt ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(80,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ succ @ leq ) )
=> ( A @ ( B @ gt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_succ_gt) ).
thf(596,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ succ @ leq ) )
=> ( A @ ( B @ gt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(56,axiom,
! [A: $i] :
( ( ( n1 @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A = n1 )
| ( A = n0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',finite_domain_1) ).
thf(459,plain,
! [A: $i] :
( ( ( n1 @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A = n1 )
| ( A = n0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(987,plain,
! [A: $i] :
( ( ( n1 @ ( n410 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[195,396]) ).
thf(988,plain,
! [A: $i] :
( ( n1 @ ( n410 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[987]) ).
thf(990,plain,
! [A: $i] :
( ( n1 != A )
| ( n410 != A ) ),
inference(simp,[status(thm)],[988]) ).
thf(992,plain,
n1 != n410,
inference(simp,[status(thm)],[990]) ).
thf(39,axiom,
! [A: $i] :
( ( A @ ( n2 @ plus ) )
= ( A @ succ @ succ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_plus_2_l) ).
thf(277,plain,
! [A: $i] :
( ( A @ ( n2 @ plus ) )
= ( A @ succ @ succ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(34,axiom,
! [A: $i] :
( ( A @ ( n3 @ plus ) )
= ( A @ succ @ succ @ succ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_plus_3_l) ).
thf(254,plain,
! [A: $i] :
( ( A @ ( n3 @ plus ) )
= ( A @ succ @ succ @ succ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(24,axiom,
n2 @ ( n4 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_4_2) ).
thf(215,plain,
n2 @ ( n4 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(99,axiom,
( ( n0 @ succ @ succ )
= n2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_2) ).
thf(639,plain,
( ( n0 @ succ @ succ )
= n2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(2307,plain,
$false,
inference(e,[status(thm)],[479,578,205,115,614,217,276,385,384,174,257,125,196,157,189,606,284,228,216,475,106,574,966,905,480,602,397,280,221,132,396,452,201,381,220,102,598,192,630,197,625,583,224,109,554,193,901,547,393,984,569,605,618,264,161,180,375,191,577,118,281,204,572,611,947,113,219,208,599,387,631,535,103,609,621,108,462,455,394,241,548,209,617,458,145,199,177,463,951,470,576,613,600,595,627,556,581,218,104,258,186,114,171,568,214,287,146,190,183,195,400,532,624,464,596,459,992,131,277,254,122,215,639,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV024+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.10 % 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
% 0.17/5.45 % Computer : n009.cluster.edu
% 0.17/5.45 % Model : x86_64 x86_64
% 0.17/5.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/5.45 % Memory : 8046.5625MB
% 0.17/5.45 % OS : Linux 6.8.0-71-generic
% 0.17/5.45 % CPULimit : 300
% 0.17/5.45 % WCLimit : 300
% 0.17/5.45 % DateTime : Sat Sep 26 13:05:50 UTC 2026
% 0.17/5.45 % CPUTime :
% 0.17/5.45 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
% 0.97/6.19 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.52/6.59 % [INFO] Parsing done (394ms).
% 1.81/6.61 % [INFO] Running in sequential loop mode.
% 2.43/7.12 % [INFO] eprover registered as external prover.
% 2.43/7.13 % [INFO] Scanning for conjecture ...
% 2.97/7.43 % [INFO] Found a conjecture (or negated_conjecture) and 99 axioms. Running axiom selection ...
% 3.28/7.64 % [INFO] Axiom selection finished. Selected 97 axioms (removed 2 axioms).
% 3.62/7.84 % [INFO] Problem is first-order (TPTP FOF).
% 3.62/7.88 % [INFO] Type checking passed.
% 3.62/7.88 % [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 ...
% 18.60/11.23 % External prover 'e' found a proof!
% 18.60/11.23 % [INFO] Killing All external provers ...
% 18.60/11.23 % Time passed: 5574ms (effective reasoning time: 4614ms)
% 18.60/11.23 % 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)>
% 18.60/11.24 % Axioms used in derivation (97): sel3_update_2, gt_2_tptp_minus_1, gt_0_tptp_minus_1, gt_3_1, sel2_update_2, succ_plus_5_l, lt_gt, gt_5_tptp_minus_1, succ_plus_3_r, gt_4_3, transitivity_gt, matrix_symm_inv, matrix_symm_trans, finite_domain_1, gt_5_0, const_array2_select, gt_410_1, gt_330_tptp_minus_1, gt_410_4, sel3_update_3, leq_geq, gt_1_0, leq_gt2, gt_5_4, succ_plus_1_l, gt_3_2, matrix_symm_add, leq_succ_gt, finite_domain_5, pred_minus_1, gt_330_5, successor_3, gt_3_tptp_minus_1, matrix_symm_update_diagonal, sel2_update_1, gt_410_5, gt_4_2, matrix_symm_sub, gt_5_3, gt_330_4, successor_4, gt_succ, succ_plus_4_l, reflexivity_leq, successor_2, gt_410_tptp_minus_1, leq_gt1, gt_1_tptp_minus_1, gt_410_2, finite_domain_2, matrix_symm_aba1, finite_domain_4, gt_410_3, gt_330_0, matrix_symm_aba2, succ_tptp_minus_1, succ_plus_5_r, gt_410_330, leq_succ_succ, sum_plus_base_float, succ_plus_2_l, gt_4_1, gt_2_0, gt_5_2, gt_330_3, const_array1_select, leq_gt_pred, matrix_symm_joseph_update, succ_pred, totality, transitivity_leq, finite_domain_3, uniform_int_rand_ranges_lo, sel3_update_1, successor_1, sum_plus_base, irreflexivity_gt, successor_5, gt_3_0, sel2_update_3, pred_succ, succ_plus_1_r, succ_plus_3_l, gt_330_1, gt_4_tptp_minus_1, succ_plus_4_r, gt_410_0, gt_4_0, succ_plus_2_r, leq_succ_gt_equiv, gt_5_1, uniform_int_rand_ranges_hi, gt_2_1, finite_domain_0, leq_succ, gt_330_2, leq_minus
% 18.60/11.24 % No. of inferences in proof: 267
% 18.60/11.24 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 5574 ms resp. 4614 ms w/o parsing
% 17.63/11.32 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 17.63/11.32 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------