%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV114+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 : n018.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 08:58:10 AM UTC 2026
% Result : Theorem 87.80s 24.41s
% Output : Refutation 89.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 113
% Syntax : Number of formulae : 940 ( 359 unt; 0 typ; 13 def)
% Number of atoms : 3699 (1154 equ; 0 cnn)
% Maximal formula atoms : 212 ( 3 avg)
% Number of connectives : 11112 (1587 ~;1723 |; 381 &;7251 @)
% ( 5 <=>; 165 =>; 0 <=; 0 <~>)
% Maximal formula depth : 54 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 55 ( 52 usr; 27 con; 0-4 aty)
% Number of variables : 1146 ( 14 ^;1117 !; 2 ?;1146 :)
% ( 0 !>; 0 ?*; 0 @-; 13 @+)
% Comments :
%------------------------------------------------------------------------------
thf(leq_decl,type,
leq: $i > $i > $o ).
thf(n0_decl,type,
n0: $i ).
thf(pv5_decl,type,
pv5: $i ).
thf(minus_decl,type,
minus: $i > $i > $i ).
thf(n999_decl,type,
n999: $i ).
thf(n1_decl,type,
n1: $i ).
thf(n6_decl,type,
n6: $i ).
thf(a_select3_decl,type,
a_select3: $i > $i > $i > $i ).
thf(q_ds1_filter_decl,type,
q_ds1_filter: $i ).
thf(n3_decl,type,
n3: $i ).
thf(r_ds1_filter_decl,type,
r_ds1_filter: $i ).
thf(pminus_ds1_filter_decl,type,
pminus_ds1_filter: $i ).
thf(id_ds1_filter_decl,type,
id_ds1_filter: $i ).
thf(a_select2_decl,type,
a_select2: $i > $i > $i ).
thf(tptp_update2_decl,type,
tptp_update2: $i > $i > $i > $i ).
thf(gt_decl,type,
gt: $i > $i > $o ).
thf(n2_decl,type,
n2: $i ).
thf(tptp_minus_1_decl,type,
tptp_minus_1: $i ).
thf(n5_decl,type,
n5: $i ).
thf(plus_decl,type,
plus: $i > $i > $i ).
thf(n4_decl,type,
n4: $i ).
thf(succ_decl,type,
succ: $i > $i ).
thf(pred_decl,type,
pred: $i > $i ).
thf(lt_decl,type,
lt: $i > $i > $o ).
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(tptp_msub_decl,type,
tptp_msub: $i > $i > $i ).
thf(tptp_float_0_0_decl,type,
tptp_float_0_0: $i ).
thf(tptp_const_array1_decl,type,
tptp_const_array1: $i > $i > $i ).
thf(uniform_int_rnd_decl,type,
uniform_int_rnd: $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: $i ).
thf(sk7_decl,type,
sk7: $i ).
thf(sk8_decl,type,
sk8: $i ).
thf(sk9_decl,type,
sk9: $i ).
thf(sk10_decl,type,
sk10: $i ).
thf(sk11_decl,type,
sk11: $i > $i > $i > $i > $i ).
thf(sk12_decl,type,
sk12: $i > $i > $i > $i ).
thf(sk13_decl,type,
sk13: $i > $i > $i > $i ).
thf(sk14_decl,type,
sk14: $i > $i > $i ).
thf(sk15_decl,type,
sk15: $i > $i > $i ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( n1 @ ( n6 @ minus ) @ ( B @ leq ) )
& ( n1 @ ( n6 @ minus ) @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( q_ds1_filter @ a_select3 ) ) )
= ( A @ ( B @ ( q_ds1_filter @ a_select3 ) ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ( ( ( n1 @ ( n6 @ minus ) @ ( A @ leq ) )
& ( n1 @ ( n6 @ minus ) @ ( sk2 @ leq ) )
& ( A @ ( n0 @ leq ) )
& ( sk2 @ ( n0 @ leq ) ) )
=> ( ( A @ ( sk2 @ ( q_ds1_filter @ a_select3 ) ) )
= ( sk2 @ ( A @ ( q_ds1_filter @ a_select3 ) ) ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( n1 @ ( n3 @ minus ) @ ( B @ leq ) )
& ( n1 @ ( n3 @ minus ) @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( r_ds1_filter @ a_select3 ) ) )
= ( A @ ( B @ ( r_ds1_filter @ a_select3 ) ) ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( @+[A: $i] :
~ ( ( ( n1 @ ( n3 @ minus ) @ ( A @ leq ) )
& ( n1 @ ( n3 @ minus ) @ ( sk5 @ leq ) )
& ( A @ ( n0 @ leq ) )
& ( sk5 @ ( n0 @ leq ) ) )
=> ( ( A @ ( sk5 @ ( r_ds1_filter @ a_select3 ) ) )
= ( sk5 @ ( A @ ( r_ds1_filter @ a_select3 ) ) ) ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( n1 @ ( n6 @ minus ) @ ( B @ leq ) )
& ( n1 @ ( n6 @ minus ) @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( pminus_ds1_filter @ a_select3 ) ) )
= ( A @ ( B @ ( pminus_ds1_filter @ a_select3 ) ) ) ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( @+[A: $i] :
~ ( ( ( n1 @ ( n6 @ minus ) @ ( A @ leq ) )
& ( n1 @ ( n6 @ minus ) @ ( sk7 @ leq ) )
& ( A @ ( n0 @ leq ) )
& ( sk7 @ ( n0 @ leq ) ) )
=> ( ( A @ ( sk7 @ ( pminus_ds1_filter @ a_select3 ) ) )
= ( sk7 @ ( A @ ( pminus_ds1_filter @ a_select3 ) ) ) ) ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( @+[A: $i] :
~ ( ( ( n1 @ ( n0 @ minus ) @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ! [B: $i] :
( ( ( n1 @ ( n6 @ minus ) @ ( B @ leq ) )
& ( B @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( id_ds1_filter @ a_select3 ) ) )
= ( A @ ( B @ ( id_ds1_filter @ a_select3 ) ) ) ) ) ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( @+[A: $i] :
~ ( ( ( n1 @ ( n6 @ minus ) @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A @ ( sk9 @ ( id_ds1_filter @ a_select3 ) ) )
= ( sk9 @ ( A @ ( id_ds1_filter @ a_select3 ) ) ) ) ) ) ) ).
thf(sk11_def,definition,
( sk11
= ( ^ [A: $i,B: $i,C: $i,D: $i] :
@+[E: $i] :
~ ( ( ( C @ ( E @ leq ) )
& ( E @ ( n0 @ leq ) ) )
=> ( ( E @ ( B @ a_select2 ) )
= A ) ) ) ) ).
thf(sk12_def,definition,
( sk12
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ! [E: $i] :
( ( ( A @ ( E @ leq ) )
& ( E @ ( n0 @ leq ) )
& ( A @ ( D @ leq ) )
& ( D @ ( n0 @ leq ) ) )
=> ( ( E @ ( D @ ( B @ a_select3 ) ) )
= ( D @ ( E @ ( B @ a_select3 ) ) ) ) ) ) ) ).
thf(sk13_def,definition,
( sk13
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ( ( ( A @ ( D @ leq ) )
& ( D @ ( n0 @ leq ) )
& ( A @ ( C @ ( B @ ( A @ sk12 ) ) @ leq ) )
& ( C @ ( B @ ( A @ sk12 ) ) @ ( n0 @ leq ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ sk12 ) ) @ ( B @ a_select3 ) ) )
= ( C @ ( B @ ( A @ sk12 ) ) @ ( D @ ( B @ a_select3 ) ) ) ) ) ) ) ).
thf(sk14_def,definition,
( sk14
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ! [D: $i] :
( ( ( A @ ( D @ leq ) )
& ( D @ ( n0 @ leq ) )
& ( A @ ( C @ leq ) )
& ( C @ ( n0 @ leq ) ) )
=> ( ( D @ ( C @ ( B @ a_select3 ) ) )
= ( C @ ( D @ ( B @ a_select3 ) ) ) ) ) ) ) ).
thf(sk15_def,definition,
( sk15
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( ( A @ ( C @ leq ) )
& ( C @ ( n0 @ leq ) )
& ( A @ ( B @ ( A @ sk14 ) @ leq ) )
& ( B @ ( A @ sk14 ) @ ( n0 @ leq ) ) )
=> ( ( C @ ( B @ ( A @ sk14 ) @ ( B @ a_select3 ) ) )
= ( B @ ( A @ sk14 ) @ ( C @ ( B @ a_select3 ) ) ) ) ) ) ) ).
thf(7,axiom,
n2 @ ( n5 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_5_2) ).
thf(172,plain,
n2 @ ( n5 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(17,axiom,
! [A: $i] :
~ ( A @ ( A @ gt ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',irreflexivity_gt) ).
thf(195,plain,
! [A: $i] :
~ ( A @ ( A @ gt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(196,plain,
~ ? [A: $i] : ( A @ ( A @ gt ) ),
inference(miniscope,[status(thm)],[195]) ).
thf(197,plain,
! [A: $i] :
~ ( A @ ( A @ gt ) ),
inference(cnf,[status(esa)],[196]) ).
thf(637,plain,
! [A: $i] :
( ( ( n2 @ ( n5 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[172,197]) ).
thf(638,plain,
! [A: $i] :
( ( n2 @ ( n5 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[637]) ).
thf(642,plain,
! [A: $i] :
( ( n2 != A )
| ( n5 != A ) ),
inference(simp,[status(thm)],[638]) ).
thf(645,plain,
n5 != n2,
inference(simp,[status(thm)],[642]) ).
thf(9,axiom,
! [A: $i] :
( ( n5 @ ( A @ plus ) )
= ( A @ succ @ succ @ succ @ succ @ succ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_plus_5_r) ).
thf(176,plain,
! [A: $i] :
( ( n5 @ ( A @ plus ) )
= ( A @ succ @ succ @ succ @ succ @ succ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(177,plain,
! [A: $i] :
( ( n5 @ ( A @ plus ) )
= ( A @ succ @ succ @ succ @ succ @ succ ) ),
inference(cnf,[status(esa)],[176]) ).
thf(178,plain,
! [A: $i] :
( ( n5 @ ( A @ plus ) )
= ( A @ succ @ succ @ succ @ succ @ succ ) ),
inference(lifteq,[status(thm)],[177]) ).
thf(22,axiom,
! [A: $i] :
( ( A @ ( n4 @ plus ) )
= ( A @ succ @ succ @ succ @ succ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_plus_4_l) ).
thf(208,plain,
! [A: $i] :
( ( A @ ( n4 @ plus ) )
= ( A @ succ @ succ @ succ @ succ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(209,plain,
! [A: $i] :
( ( A @ ( n4 @ plus ) )
= ( A @ succ @ succ @ succ @ succ ) ),
inference(cnf,[status(esa)],[208]) ).
thf(210,plain,
! [A: $i] :
( ( A @ ( n4 @ plus ) )
= ( A @ succ @ succ @ succ @ succ ) ),
inference(lifteq,[status(thm)],[209]) ).
thf(11915,plain,
! [B: $i,A: $i] :
( ( ( n5 @ ( A @ plus ) )
!= ( B @ ( n4 @ plus ) ) )
| ( ( A @ succ @ succ @ succ @ succ @ succ )
= ( B @ succ @ succ @ succ @ succ ) ) ),
inference(paramod_ordered,[status(thm)],[178,210]) ).
thf(11916,plain,
( ( n4 @ succ @ succ @ succ @ succ @ succ )
= ( n5 @ succ @ succ @ succ @ succ ) ),
inference(pattern_uni,[status(thm)],[11915:[bind(A,$thf( n4 )),bind(B,$thf( n5 ))]]) ).
thf(30,axiom,
( ( n0 @ succ @ succ @ succ @ succ )
= n4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_4) ).
thf(222,plain,
( ( n0 @ succ @ succ @ succ @ succ )
= n4 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(223,plain,
( ( n0 @ succ @ succ @ succ @ succ )
= n4 ),
inference(lifteq,[status(thm)],[222]) ).
thf(29,axiom,
( ( n0 @ succ )
= n1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_1) ).
thf(220,plain,
( ( n0 @ succ )
= n1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(221,plain,
( ( n0 @ succ )
= n1 ),
inference(lifteq,[status(thm)],[220]) ).
thf(3508,plain,
( ( n1 @ succ @ succ @ succ )
= n4 ),
inference(rewrite,[status(thm)],[223,221]) ).
thf(95,axiom,
( ( n0 @ succ @ succ @ succ @ succ @ succ )
= n5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_5) ).
thf(621,plain,
( ( n0 @ succ @ succ @ succ @ succ @ succ )
= n5 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(622,plain,
( ( n0 @ succ @ succ @ succ @ succ @ succ )
= n5 ),
inference(lifteq,[status(thm)],[621]) ).
thf(3858,plain,
( ( n1 @ succ @ succ @ succ @ succ )
= n5 ),
inference(rewrite,[status(thm)],[622,221]) ).
thf(3871,plain,
( ( ( n1 @ succ @ succ @ succ )
!= ( n1 @ succ @ succ @ succ ) )
| ( ( n4 @ succ )
= n5 ) ),
inference(paramod_ordered,[status(thm)],[3508,3858]) ).
thf(3872,plain,
( ( n4 @ succ )
= n5 ),
inference(pattern_uni,[status(thm)],[3871:[]]) ).
thf(70,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)],[70]) ).
thf(555,plain,
( ( n0 @ succ @ succ @ succ )
= n3 ),
inference(lifteq,[status(thm)],[554]) ).
thf(3469,plain,
( ( n1 @ succ @ succ )
= n3 ),
inference(rewrite,[status(thm)],[555,221]) ).
thf(3527,plain,
( ( ( n1 @ succ @ succ )
!= ( n1 @ succ @ succ ) )
| ( ( n3 @ succ )
= n4 ) ),
inference(paramod_ordered,[status(thm)],[3469,3508]) ).
thf(3528,plain,
( ( n3 @ succ )
= n4 ),
inference(pattern_uni,[status(thm)],[3527:[]]) ).
thf(15,axiom,
! [A: $i] :
( ( A @ ( n2 @ plus ) )
= ( A @ succ @ succ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_plus_2_l) ).
thf(189,plain,
! [A: $i] :
( ( A @ ( n2 @ plus ) )
= ( A @ succ @ succ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(190,plain,
! [A: $i] :
( ( A @ ( n2 @ plus ) )
= ( A @ succ @ succ ) ),
inference(cnf,[status(esa)],[189]) ).
thf(191,plain,
! [A: $i] :
( ( A @ ( n2 @ plus ) )
= ( A @ succ @ succ ) ),
inference(lifteq,[status(thm)],[190]) ).
thf(11907,plain,
! [B: $i,A: $i] :
( ( ( n5 @ ( A @ plus ) )
!= ( B @ ( n2 @ plus ) ) )
| ( ( A @ succ @ succ @ succ @ succ @ succ )
= ( B @ succ @ succ ) ) ),
inference(paramod_ordered,[status(thm)],[178,191]) ).
thf(11908,plain,
( ( n2 @ succ @ succ @ succ @ succ @ succ )
= ( n5 @ succ @ succ ) ),
inference(pattern_uni,[status(thm)],[11907:[bind(A,$thf( n2 )),bind(B,$thf( n5 ))]]) ).
thf(86,axiom,
( ( n0 @ succ @ succ @ succ @ succ @ succ @ succ )
= n6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_6) ).
thf(604,plain,
( ( n0 @ succ @ succ @ succ @ succ @ succ @ succ )
= n6 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(605,plain,
( ( n0 @ succ @ succ @ succ @ succ @ succ @ succ )
= n6 ),
inference(lifteq,[status(thm)],[604]) ).
thf(4123,plain,
( ( n1 @ succ @ succ @ succ @ succ @ succ )
= n6 ),
inference(rewrite,[status(thm)],[605,221]) ).
thf(4131,plain,
( ( ( n1 @ succ @ succ @ succ @ succ )
!= ( n1 @ succ @ succ @ succ @ succ ) )
| ( ( n5 @ succ )
= n6 ) ),
inference(paramod_ordered,[status(thm)],[3858,4123]) ).
thf(4132,plain,
( ( n5 @ succ )
= n6 ),
inference(pattern_uni,[status(thm)],[4131:[]]) ).
thf(84,axiom,
( ( n0 @ succ @ succ )
= n2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_2) ).
thf(601,plain,
( ( n0 @ succ @ succ )
= n2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(602,plain,
( ( n0 @ succ @ succ )
= n2 ),
inference(lifteq,[status(thm)],[601]) ).
thf(3315,plain,
( ( n1 @ succ )
= n2 ),
inference(rewrite,[status(thm)],[602,221]) ).
thf(3478,plain,
( ( ( n1 @ succ )
!= ( n1 @ succ ) )
| ( ( n2 @ succ )
= n3 ) ),
inference(paramod_ordered,[status(thm)],[3315,3469]) ).
thf(3479,plain,
( ( n2 @ succ )
= n3 ),
inference(pattern_uni,[status(thm)],[3478:[]]) ).
thf(11939,plain,
( ( n3 @ succ @ succ @ succ @ succ )
= ( n6 @ succ ) ),
inference(rewrite,[status(thm)],[11908,4132,3479]) ).
thf(12035,plain,
( ( ( n3 @ succ )
!= ( n3 @ succ ) )
| ( ( n4 @ succ @ succ @ succ )
= ( n6 @ succ ) ) ),
inference(paramod_ordered,[status(thm)],[3528,11939]) ).
thf(12036,plain,
( ( n4 @ succ @ succ @ succ )
= ( n6 @ succ ) ),
inference(pattern_uni,[status(thm)],[12035:[]]) ).
thf(12789,plain,
( ( n5 @ succ @ succ )
= ( n6 @ succ ) ),
inference(rewrite,[status(thm)],[12036,3872]) ).
thf(15702,plain,
( ( n5 @ succ @ succ @ succ @ succ )
= ( n6 @ succ @ succ @ succ ) ),
inference(rewrite,[status(thm)],[11916,3872,12789]) ).
thf(10,axiom,
! [A: $i] : ( A @ ( A @ succ @ gt ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_succ) ).
thf(179,plain,
! [A: $i] : ( A @ ( A @ succ @ gt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(180,plain,
! [A: $i] : ( A @ ( A @ succ @ gt ) ),
inference(cnf,[status(esa)],[179]) ).
thf(4983,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ succ @ gt ) )
!= ( B @ ( B @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[180,197]) ).
thf(4984,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ succ @ gt ) )
!= ( B @ ( B @ gt ) ) ),
inference(simp,[status(thm)],[4983]) ).
thf(5005,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( ( A @ succ )
!= B ) ),
inference(simp,[status(thm)],[4984]) ).
thf(5006,plain,
! [A: $i] :
( ( A @ succ )
!= A ),
inference(simp,[status(thm)],[5005]) ).
thf(15769,plain,
! [A: $i] :
( ( ( n5 @ succ @ succ @ succ @ succ )
!= ( A @ succ ) )
| ( ( n6 @ succ @ succ @ succ )
!= A ) ),
inference(paramod_ordered,[status(thm)],[15702,5006]) ).
thf(15770,plain,
( ( n5 @ succ @ succ @ succ )
!= ( n6 @ succ @ succ @ succ ) ),
inference(pattern_uni,[status(thm)],[15769:[bind(A,$thf( n5 @ succ @ succ @ succ ))]]) ).
thf(16012,plain,
( ( n6 @ succ @ succ @ succ )
!= ( n6 @ succ @ succ ) ),
inference(rewrite,[status(thm)],[15770,12789]) ).
thf(16013,plain,
( ( n6 @ succ @ succ )
!= ( n6 @ succ ) ),
inference(simp,[status(thm)],[16012]) ).
thf(47,axiom,
n3 @ ( n5 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_5_3) ).
thf(280,plain,
n3 @ ( n5 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ lt ) )
<=> ( A @ ( B @ gt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lt_gt) ).
thf(198,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)],[18]) ).
thf(199,plain,
( ! [A: $i,B: $i] :
( ( A @ ( B @ gt ) )
=> ( B @ ( A @ lt ) ) )
& ! [A: $i,B: $i] :
( ( B @ ( A @ lt ) )
=> ( A @ ( B @ gt ) ) ) ),
inference(miniscope,[status(thm)],[198]) ).
thf(200,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ lt ) )
| ~ ( C @ ( D @ gt ) ) )
& ( ( A @ ( B @ gt ) )
| ~ ( B @ ( A @ lt ) ) ) ),
inference(cnf,[status(esa)],[199]) ).
thf(202,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ lt ) )
| ~ ( A @ ( B @ gt ) ) ),
inference(cnfConj,[status(thm)],[200]) ).
thf(203,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ lt ) )
| ~ ( A @ ( B @ gt ) ) ),
inference(simp,[status(thm)],[202]) ).
thf(16806,plain,
! [B: $i,A: $i] :
( ( ( n3 @ ( n5 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[280,203]) ).
thf(16807,plain,
! [B: $i,A: $i] :
( ( ( n3 @ ( n5 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[16806]) ).
thf(16808,plain,
n5 @ ( n3 @ lt ),
inference(pattern_uni,[status(thm)],[16807:[bind(A,$thf( n3 )),bind(B,$thf( n5 ))]]) ).
thf(62,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(468,plain,
! [A: $i] :
( tptp_float_0_0
= ( A @ ( tptp_minus_1 @ ( n0 @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(1,conjecture,
( ( ! [A: $i,B: $i] :
( ( ( n1 @ ( n6 @ minus ) @ ( B @ leq ) )
& ( n1 @ ( n6 @ minus ) @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( pminus_ds1_filter @ a_select3 ) ) )
= ( A @ ( B @ ( pminus_ds1_filter @ a_select3 ) ) ) ) )
& ! [A: $i,B: $i] :
( ( ( n1 @ ( n3 @ minus ) @ ( B @ leq ) )
& ( n1 @ ( n3 @ minus ) @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( r_ds1_filter @ a_select3 ) ) )
= ( A @ ( B @ ( r_ds1_filter @ a_select3 ) ) ) ) )
& ! [A: $i,B: $i] :
( ( ( n1 @ ( n6 @ minus ) @ ( B @ leq ) )
& ( n1 @ ( n6 @ minus ) @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( q_ds1_filter @ a_select3 ) ) )
= ( A @ ( B @ ( q_ds1_filter @ a_select3 ) ) ) ) )
& ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
& ( pv5 @ ( n0 @ leq ) ) )
=> ( ! [A: $i] :
( ( ( n1 @ ( n0 @ minus ) @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ! [B: $i] :
( ( ( n1 @ ( n6 @ minus ) @ ( B @ leq ) )
& ( B @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( id_ds1_filter @ a_select3 ) ) )
= ( A @ ( B @ ( id_ds1_filter @ a_select3 ) ) ) ) ) )
& ! [A: $i,B: $i] :
( ( ( n1 @ ( n6 @ minus ) @ ( B @ leq ) )
& ( n1 @ ( n6 @ minus ) @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( pminus_ds1_filter @ a_select3 ) ) )
= ( A @ ( B @ ( pminus_ds1_filter @ a_select3 ) ) ) ) )
& ! [A: $i,B: $i] :
( ( ( n1 @ ( n3 @ minus ) @ ( B @ leq ) )
& ( n1 @ ( n3 @ minus ) @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( r_ds1_filter @ a_select3 ) ) )
= ( A @ ( B @ ( r_ds1_filter @ a_select3 ) ) ) ) )
& ! [A: $i,B: $i] :
( ( ( n1 @ ( n6 @ minus ) @ ( B @ leq ) )
& ( n1 @ ( n6 @ minus ) @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( q_ds1_filter @ a_select3 ) ) )
= ( A @ ( B @ ( q_ds1_filter @ a_select3 ) ) ) ) )
& ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
& ( pv5 @ ( n0 @ leq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quaternion_ds1_symm_0007) ).
thf(2,negated_conjecture,
~ ( ( ! [A: $i,B: $i] :
( ( ( n1 @ ( n6 @ minus ) @ ( B @ leq ) )
& ( n1 @ ( n6 @ minus ) @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( pminus_ds1_filter @ a_select3 ) ) )
= ( A @ ( B @ ( pminus_ds1_filter @ a_select3 ) ) ) ) )
& ! [A: $i,B: $i] :
( ( ( n1 @ ( n3 @ minus ) @ ( B @ leq ) )
& ( n1 @ ( n3 @ minus ) @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( r_ds1_filter @ a_select3 ) ) )
= ( A @ ( B @ ( r_ds1_filter @ a_select3 ) ) ) ) )
& ! [A: $i,B: $i] :
( ( ( n1 @ ( n6 @ minus ) @ ( B @ leq ) )
& ( n1 @ ( n6 @ minus ) @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( q_ds1_filter @ a_select3 ) ) )
= ( A @ ( B @ ( q_ds1_filter @ a_select3 ) ) ) ) )
& ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
& ( pv5 @ ( n0 @ leq ) ) )
=> ( ! [A: $i] :
( ( ( n1 @ ( n0 @ minus ) @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ! [B: $i] :
( ( ( n1 @ ( n6 @ minus ) @ ( B @ leq ) )
& ( B @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( id_ds1_filter @ a_select3 ) ) )
= ( A @ ( B @ ( id_ds1_filter @ a_select3 ) ) ) ) ) )
& ! [A: $i,B: $i] :
( ( ( n1 @ ( n6 @ minus ) @ ( B @ leq ) )
& ( n1 @ ( n6 @ minus ) @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( pminus_ds1_filter @ a_select3 ) ) )
= ( A @ ( B @ ( pminus_ds1_filter @ a_select3 ) ) ) ) )
& ! [A: $i,B: $i] :
( ( ( n1 @ ( n3 @ minus ) @ ( B @ leq ) )
& ( n1 @ ( n3 @ minus ) @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( r_ds1_filter @ a_select3 ) ) )
= ( A @ ( B @ ( r_ds1_filter @ a_select3 ) ) ) ) )
& ! [A: $i,B: $i] :
( ( ( n1 @ ( n6 @ minus ) @ ( B @ leq ) )
& ( n1 @ ( n6 @ minus ) @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( q_ds1_filter @ a_select3 ) ) )
= ( A @ ( B @ ( q_ds1_filter @ a_select3 ) ) ) ) )
& ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
& ( pv5 @ ( n0 @ leq ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(102,plain,
~ ( ( ! [A: $i,B: $i] :
( ( ( n1 @ ( n6 @ minus ) @ ( B @ leq ) )
& ( n1 @ ( n6 @ minus ) @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( pminus_ds1_filter @ a_select3 ) ) )
= ( A @ ( B @ ( pminus_ds1_filter @ a_select3 ) ) ) ) )
& ! [A: $i,B: $i] :
( ( ( n1 @ ( n3 @ minus ) @ ( B @ leq ) )
& ( n1 @ ( n3 @ minus ) @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( r_ds1_filter @ a_select3 ) ) )
= ( A @ ( B @ ( r_ds1_filter @ a_select3 ) ) ) ) )
& ! [A: $i,B: $i] :
( ( ( n1 @ ( n6 @ minus ) @ ( B @ leq ) )
& ( n1 @ ( n6 @ minus ) @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( q_ds1_filter @ a_select3 ) ) )
= ( A @ ( B @ ( q_ds1_filter @ a_select3 ) ) ) ) )
& ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
& ( pv5 @ ( n0 @ leq ) ) )
=> ( ! [A: $i] :
( ( ( n1 @ ( n0 @ minus ) @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ! [B: $i] :
( ( ( n1 @ ( n6 @ minus ) @ ( B @ leq ) )
& ( B @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( id_ds1_filter @ a_select3 ) ) )
= ( A @ ( B @ ( id_ds1_filter @ a_select3 ) ) ) ) ) )
& ! [A: $i,B: $i] :
( ( ( n1 @ ( n6 @ minus ) @ ( B @ leq ) )
& ( n1 @ ( n6 @ minus ) @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( pminus_ds1_filter @ a_select3 ) ) )
= ( A @ ( B @ ( pminus_ds1_filter @ a_select3 ) ) ) ) )
& ! [A: $i,B: $i] :
( ( ( n1 @ ( n3 @ minus ) @ ( B @ leq ) )
& ( n1 @ ( n3 @ minus ) @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( r_ds1_filter @ a_select3 ) ) )
= ( A @ ( B @ ( r_ds1_filter @ a_select3 ) ) ) ) )
& ! [A: $i,B: $i] :
( ( ( n1 @ ( n6 @ minus ) @ ( B @ leq ) )
& ( n1 @ ( n6 @ minus ) @ ( A @ leq ) )
& ( B @ ( n0 @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( B @ ( A @ ( q_ds1_filter @ a_select3 ) ) )
= ( A @ ( B @ ( q_ds1_filter @ a_select3 ) ) ) ) )
& ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
& ( pv5 @ ( n0 @ leq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(103,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( ( sk10 @ ( sk9 @ ( id_ds1_filter @ a_select3 ) ) )
!= ( sk9 @ ( sk10 @ ( id_ds1_filter @ a_select3 ) ) ) )
| ( ( sk8 @ ( sk7 @ ( pminus_ds1_filter @ a_select3 ) ) )
!= ( sk7 @ ( sk8 @ ( pminus_ds1_filter @ a_select3 ) ) ) )
| sk4
| sk1
| ~ ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
| ~ ( pv5 @ ( n0 @ leq ) ) )
& ( ( n1 @ ( n6 @ minus ) @ ( sk10 @ leq ) )
| ( ( sk8 @ ( sk7 @ ( pminus_ds1_filter @ a_select3 ) ) )
!= ( sk7 @ ( sk8 @ ( pminus_ds1_filter @ a_select3 ) ) ) )
| sk4
| sk1
| ~ ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
| ~ ( pv5 @ ( n0 @ leq ) ) )
& ( ( sk10 @ ( n0 @ leq ) )
| ( ( sk8 @ ( sk7 @ ( pminus_ds1_filter @ a_select3 ) ) )
!= ( sk7 @ ( sk8 @ ( pminus_ds1_filter @ a_select3 ) ) ) )
| sk4
| sk1
| ~ ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
| ~ ( pv5 @ ( n0 @ leq ) ) )
& ( ( n1 @ ( n0 @ minus ) @ ( sk9 @ leq ) )
| ( ( sk8 @ ( sk7 @ ( pminus_ds1_filter @ a_select3 ) ) )
!= ( sk7 @ ( sk8 @ ( pminus_ds1_filter @ a_select3 ) ) ) )
| sk4
| sk1
| ~ ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
| ~ ( pv5 @ ( n0 @ leq ) ) )
& ( ( sk9 @ ( n0 @ leq ) )
| ( ( sk8 @ ( sk7 @ ( pminus_ds1_filter @ a_select3 ) ) )
!= ( sk7 @ ( sk8 @ ( pminus_ds1_filter @ a_select3 ) ) ) )
| sk4
| sk1
| ~ ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
| ~ ( pv5 @ ( n0 @ leq ) ) )
& ( ( ( sk10 @ ( sk9 @ ( id_ds1_filter @ a_select3 ) ) )
!= ( sk9 @ ( sk10 @ ( id_ds1_filter @ a_select3 ) ) ) )
| ( n1 @ ( n6 @ minus ) @ ( sk8 @ leq ) )
| sk4
| sk1
| ~ ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
| ~ ( pv5 @ ( n0 @ leq ) ) )
& ( ( n1 @ ( n6 @ minus ) @ ( sk10 @ leq ) )
| ( n1 @ ( n6 @ minus ) @ ( sk8 @ leq ) )
| sk4
| sk1
| ~ ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
| ~ ( pv5 @ ( n0 @ leq ) ) )
& ( ( sk10 @ ( n0 @ leq ) )
| ( n1 @ ( n6 @ minus ) @ ( sk8 @ leq ) )
| sk4
| sk1
| ~ ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
| ~ ( pv5 @ ( n0 @ leq ) ) )
& ( ( n1 @ ( n0 @ minus ) @ ( sk9 @ leq ) )
| ( n1 @ ( n6 @ minus ) @ ( sk8 @ leq ) )
| sk4
| sk1
| ~ ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
| ~ ( pv5 @ ( n0 @ leq ) ) )
& ( ( sk9 @ ( n0 @ leq ) )
| ( n1 @ ( n6 @ minus ) @ ( sk8 @ leq ) )
| sk4
| sk1
| ~ ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
| ~ ( pv5 @ ( n0 @ leq ) ) )
& ( ( ( sk10 @ ( sk9 @ ( id_ds1_filter @ a_select3 ) ) )
!= ( sk9 @ ( sk10 @ ( id_ds1_filter @ a_select3 ) ) ) )
| ( n1 @ ( n6 @ minus ) @ ( sk7 @ leq ) )
| sk4
| sk1
| ~ ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
| ~ ( pv5 @ ( n0 @ leq ) ) )
& ( ( n1 @ ( n6 @ minus ) @ ( sk10 @ leq ) )
| ( n1 @ ( n6 @ minus ) @ ( sk7 @ leq ) )
| sk4
| sk1
| ~ ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
| ~ ( pv5 @ ( n0 @ leq ) ) )
& ( ( sk10 @ ( n0 @ leq ) )
| ( n1 @ ( n6 @ minus ) @ ( sk7 @ leq ) )
| sk4
| sk1
| ~ ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
| ~ ( pv5 @ ( n0 @ leq ) ) )
& ( ( n1 @ ( n0 @ minus ) @ ( sk9 @ leq ) )
| ( n1 @ ( n6 @ minus ) @ ( sk7 @ leq ) )
| sk4
| sk1
| ~ ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
| ~ ( pv5 @ ( n0 @ leq ) ) )
& ( ( sk9 @ ( n0 @ leq ) )
| ( n1 @ ( n6 @ minus ) @ ( sk7 @ leq ) )
| sk4
| sk1
| ~ ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
| ~ ( pv5 @ ( n0 @ leq ) ) )
& ( ( ( sk10 @ ( sk9 @ ( id_ds1_filter @ a_select3 ) ) )
!= ( sk9 @ ( sk10 @ ( id_ds1_filter @ a_select3 ) ) ) )
| ( sk8 @ ( n0 @ leq ) )
| sk4
| sk1
| ~ ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
| ~ ( pv5 @ ( n0 @ leq ) ) )
& ( ( n1 @ ( n6 @ minus ) @ ( sk10 @ leq ) )
| ( sk8 @ ( n0 @ leq ) )
| sk4
| sk1
| ~ ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
| ~ ( pv5 @ ( n0 @ leq ) ) )
& ( ( sk10 @ ( n0 @ leq ) )
| ( sk8 @ ( n0 @ leq ) )
| sk4
| sk1
| ~ ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
| ~ ( pv5 @ ( n0 @ leq ) ) )
& ( ( n1 @ ( n0 @ minus ) @ ( sk9 @ leq ) )
| ( sk8 @ ( n0 @ leq ) )
| sk4
| sk1
| ~ ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
| ~ ( pv5 @ ( n0 @ leq ) ) )
& ( ( sk9 @ ( n0 @ leq ) )
| ( sk8 @ ( n0 @ leq ) )
| sk4
| sk1
| ~ ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
| ~ ( pv5 @ ( n0 @ leq ) ) )
& ( ( ( sk10 @ ( sk9 @ ( id_ds1_filter @ a_select3 ) ) )
!= ( sk9 @ ( sk10 @ ( id_ds1_filter @ a_select3 ) ) ) )
| ( sk7 @ ( n0 @ leq ) )
| sk4
| sk1
| ~ ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
| ~ ( pv5 @ ( n0 @ leq ) ) )
& ( ( n1 @ ( n6 @ minus ) @ ( sk10 @ leq ) )
| ( sk7 @ ( n0 @ leq ) )
| sk4
| sk1
| ~ ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
| ~ ( pv5 @ ( n0 @ leq ) ) )
& ( ( sk10 @ ( n0 @ leq ) )
| ( sk7 @ ( n0 @ leq ) )
| sk4
| sk1
| ~ ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
| ~ ( pv5 @ ( n0 @ leq ) ) )
& ( ( n1 @ ( n0 @ minus ) @ ( sk9 @ leq ) )
| ( sk7 @ ( n0 @ leq ) )
| sk4
| sk1
| ~ ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
| ~ ( pv5 @ ( n0 @ leq ) ) )
& ( ( sk9 @ ( n0 @ leq ) )
| ( sk7 @ ( n0 @ leq ) )
| sk4
| sk1
| ~ ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
| ~ ( pv5 @ ( n0 @ leq ) ) )
& ( ~ sk4
| ( ( sk6 @ ( sk5 @ ( r_ds1_filter @ a_select3 ) ) )
!= ( sk5 @ ( sk6 @ ( r_ds1_filter @ a_select3 ) ) ) )
| sk1
| ~ ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
| ~ ( pv5 @ ( n0 @ leq ) ) )
& ( ~ sk4
| ( n1 @ ( n3 @ minus ) @ ( sk6 @ leq ) )
| sk1
| ~ ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
| ~ ( pv5 @ ( n0 @ leq ) ) )
& ( ~ sk4
| ( n1 @ ( n3 @ minus ) @ ( sk5 @ leq ) )
| sk1
| ~ ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
| ~ ( pv5 @ ( n0 @ leq ) ) )
& ( ~ sk4
| ( sk6 @ ( n0 @ leq ) )
| sk1
| ~ ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
| ~ ( pv5 @ ( n0 @ leq ) ) )
& ( ~ sk4
| ( sk5 @ ( n0 @ leq ) )
| sk1
| ~ ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
| ~ ( pv5 @ ( n0 @ leq ) ) )
& ( ~ sk1
| ( ( sk3 @ ( sk2 @ ( q_ds1_filter @ a_select3 ) ) )
!= ( sk2 @ ( sk3 @ ( q_ds1_filter @ a_select3 ) ) ) )
| ~ ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
| ~ ( pv5 @ ( n0 @ leq ) ) )
& ( ~ sk1
| ( n1 @ ( n6 @ minus ) @ ( sk3 @ leq ) )
| ~ ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
| ~ ( pv5 @ ( n0 @ leq ) ) )
& ( ~ sk1
| ( n1 @ ( n6 @ minus ) @ ( sk2 @ leq ) )
| ~ ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
| ~ ( pv5 @ ( n0 @ leq ) ) )
& ( ~ sk1
| ( sk3 @ ( n0 @ leq ) )
| ~ ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
| ~ ( pv5 @ ( n0 @ leq ) ) )
& ( ~ sk1
| ( sk2 @ ( n0 @ leq ) )
| ~ ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
| ~ ( pv5 @ ( n0 @ leq ) ) )
& ( ( ( F @ ( E @ ( pminus_ds1_filter @ a_select3 ) ) )
= ( E @ ( F @ ( pminus_ds1_filter @ a_select3 ) ) ) )
| ~ ( n1 @ ( n6 @ minus ) @ ( F @ leq ) )
| ~ ( n1 @ ( n6 @ minus ) @ ( E @ leq ) )
| ~ ( F @ ( n0 @ leq ) )
| ~ ( E @ ( n0 @ leq ) ) )
& ( ( ( D @ ( C @ ( r_ds1_filter @ a_select3 ) ) )
= ( C @ ( D @ ( r_ds1_filter @ a_select3 ) ) ) )
| ~ ( n1 @ ( n3 @ minus ) @ ( D @ leq ) )
| ~ ( n1 @ ( n3 @ minus ) @ ( C @ leq ) )
| ~ ( D @ ( n0 @ leq ) )
| ~ ( C @ ( n0 @ leq ) ) )
& ( ( ( B @ ( A @ ( q_ds1_filter @ a_select3 ) ) )
= ( A @ ( B @ ( q_ds1_filter @ a_select3 ) ) ) )
| ~ ( n1 @ ( n6 @ minus ) @ ( B @ leq ) )
| ~ ( n1 @ ( n6 @ minus ) @ ( A @ leq ) )
| ~ ( B @ ( n0 @ leq ) )
| ~ ( A @ ( n0 @ leq ) ) )
& ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
& ( pv5 @ ( n0 @ leq ) ) ),
inference(cnf,[status(esa)],[102]) ).
thf(129,plain,
( ~ sk1
| ( ( sk3 @ ( sk2 @ ( q_ds1_filter @ a_select3 ) ) )
!= ( sk2 @ ( sk3 @ ( q_ds1_filter @ a_select3 ) ) ) )
| ~ ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
| ~ ( pv5 @ ( n0 @ leq ) ) ),
inference(cnfConj,[status(thm)],[103]) ).
thf(147,plain,
( ~ sk1
| ~ ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
| ~ ( pv5 @ ( n0 @ leq ) )
| ( ( sk2 @ ( sk3 @ ( q_ds1_filter @ a_select3 ) ) )
!= ( sk3 @ ( sk2 @ ( q_ds1_filter @ a_select3 ) ) ) ) ),
inference(lifteq,[status(thm)],[129]) ).
thf(128,plain,
pv5 @ ( n0 @ leq ),
inference(cnfConj,[status(thm)],[103]) ).
thf(107,plain,
n1 @ ( n999 @ minus ) @ ( pv5 @ leq ),
inference(cnfConj,[status(thm)],[103]) ).
thf(663,plain,
( ~ sk1
| ~ $true
| ~ $true
| ( ( sk2 @ ( sk3 @ ( q_ds1_filter @ a_select3 ) ) )
!= ( sk3 @ ( sk2 @ ( q_ds1_filter @ a_select3 ) ) ) ) ),
inference(rewrite,[status(thm)],[147,128,107]) ).
thf(664,plain,
( ~ sk1
| ( ( sk2 @ ( sk3 @ ( q_ds1_filter @ a_select3 ) ) )
!= ( sk3 @ ( sk2 @ ( q_ds1_filter @ a_select3 ) ) ) ) ),
inference(simp,[status(thm)],[663]) ).
thf(665,plain,
( ~ sk1
| ( sk3 != sk2 )
| ( sk3 != sk2 )
| ( q_ds1_filter != q_ds1_filter ) ),
inference(simp,[status(thm)],[664]) ).
thf(666,plain,
( ~ sk1
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[665]) ).
thf(66,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(481,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)],[66]) ).
thf(99,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(628,plain,
! [A: $i,B: $i] :
( ( A @ ( n0 @ leq ) )
=> ( A @ ( B @ uniform_int_rnd ) @ ( n0 @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(42,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(246,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)],[42]) ).
thf(247,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F @ ( D @ leq ) )
& ( D @ ( E @ leq ) )
& ( C @ ( A @ leq ) )
& ( A @ ( B @ leq ) ) )
=> ! [G: $i] :
( ( D @ ( A @ ( G @ ( F @ ( E @ dim ) @ ( C @ ( B @ dim ) @ tptp_const_array2 ) ) @ a_select3 ) ) )
= G ) ),
inference(miniscope,[status(thm)],[246]) ).
thf(248,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( G @ ( F @ ( E @ dim ) @ ( C @ ( B @ dim ) @ tptp_const_array2 ) ) @ a_select3 ) ) )
= G )
| ~ ( F @ ( D @ leq ) )
| ~ ( D @ ( E @ leq ) )
| ~ ( C @ ( A @ leq ) )
| ~ ( A @ ( B @ leq ) ) ),
inference(cnf,[status(esa)],[247]) ).
thf(249,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $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(lifteq,[status(thm)],[248]) ).
thf(14,axiom,
! [A: $i] :
( ( A @ pred @ succ )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_pred) ).
thf(186,plain,
! [A: $i] :
( ( A @ pred @ succ )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(187,plain,
! [A: $i] :
( ( A @ pred @ succ )
= A ),
inference(cnf,[status(esa)],[186]) ).
thf(188,plain,
! [A: $i] :
( ( A @ pred @ succ )
= A ),
inference(lifteq,[status(thm)],[187]) ).
thf(7591,plain,
! [B: $i,A: $i] :
( ( ( A @ pred @ succ )
!= ( B @ succ ) )
| ( B @ ( A @ gt ) ) ),
inference(paramod_ordered,[status(thm)],[188,180]) ).
thf(7592,plain,
! [A: $i] : ( A @ pred @ ( A @ gt ) ),
inference(pattern_uni,[status(thm)],[7591:[bind(A,$thf( C )),bind(B,$thf( C @ pred ))]]) ).
thf(7660,plain,
! [A: $i] : ( A @ pred @ ( A @ gt ) ),
inference(simp,[status(thm)],[7592]) ).
thf(106,plain,
( ( ( sk10 @ ( sk9 @ ( id_ds1_filter @ a_select3 ) ) )
!= ( sk9 @ ( sk10 @ ( id_ds1_filter @ a_select3 ) ) ) )
| ( sk8 @ ( n0 @ leq ) )
| sk4
| sk1
| ~ ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
| ~ ( pv5 @ ( n0 @ leq ) ) ),
inference(cnfConj,[status(thm)],[103]) ).
thf(152,plain,
( ( sk8 @ ( n0 @ leq ) )
| sk4
| sk1
| ~ ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
| ~ ( pv5 @ ( n0 @ leq ) )
| ( ( sk9 @ ( sk10 @ ( id_ds1_filter @ a_select3 ) ) )
!= ( sk10 @ ( sk9 @ ( id_ds1_filter @ a_select3 ) ) ) ) ),
inference(lifteq,[status(thm)],[106]) ).
thf(51,axiom,
! [A: $i] :
( ( n1 @ ( A @ minus ) )
= ( A @ pred ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pred_minus_1) ).
thf(300,plain,
! [A: $i] :
( ( n1 @ ( A @ minus ) )
= ( A @ pred ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(301,plain,
! [A: $i] :
( ( n1 @ ( A @ minus ) )
= ( A @ pred ) ),
inference(cnf,[status(esa)],[300]) ).
thf(302,plain,
! [A: $i] :
( ( n1 @ ( A @ minus ) )
= ( A @ pred ) ),
inference(lifteq,[status(thm)],[301]) ).
thf(9019,plain,
( ( sk8 @ ( n0 @ leq ) )
| sk4
| sk1
| ~ ( n999 @ pred @ ( pv5 @ leq ) )
| ~ $true
| ( ( sk9 @ ( sk10 @ ( id_ds1_filter @ a_select3 ) ) )
!= ( sk10 @ ( sk9 @ ( id_ds1_filter @ a_select3 ) ) ) ) ),
inference(rewrite,[status(thm)],[152,128,302]) ).
thf(9020,plain,
( ( sk8 @ ( n0 @ leq ) )
| sk4
| sk1
| ~ ( n999 @ pred @ ( pv5 @ leq ) )
| ( ( sk9 @ ( sk10 @ ( id_ds1_filter @ a_select3 ) ) )
!= ( sk10 @ ( sk9 @ ( id_ds1_filter @ a_select3 ) ) ) ) ),
inference(simp,[status(thm)],[9019]) ).
thf(25,axiom,
n1 @ ( n2 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_2_1) ).
thf(215,plain,
n1 @ ( n2 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(680,plain,
! [A: $i] :
( ( ( n1 @ ( n2 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[215,197]) ).
thf(681,plain,
! [A: $i] :
( ( n1 @ ( n2 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[680]) ).
thf(682,plain,
! [A: $i] :
( ( n1 != A )
| ( n2 != A ) ),
inference(simp,[status(thm)],[681]) ).
thf(683,plain,
n2 != n1,
inference(simp,[status(thm)],[682]) ).
thf(35,axiom,
n1 @ ( n6 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_6_1) ).
thf(237,plain,
n1 @ ( n6 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ gt ) )
=> ( B @ ( A @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_gt1) ).
thf(216,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ gt ) )
=> ( B @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(217,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ leq ) )
| ~ ( A @ ( B @ gt ) ) ),
inference(cnf,[status(esa)],[216]) ).
thf(17435,plain,
! [B: $i,A: $i] :
( ( ( n1 @ ( n6 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[237,217]) ).
thf(17436,plain,
! [B: $i,A: $i] :
( ( ( n1 @ ( n6 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ leq ) ) ),
inference(simp,[status(thm)],[17435]) ).
thf(17437,plain,
n6 @ ( n1 @ leq ),
inference(pattern_uni,[status(thm)],[17436:[bind(A,$thf( n1 )),bind(B,$thf( n6 ))]]) ).
thf(119,plain,
( ~ sk4
| ( n1 @ ( n3 @ minus ) @ ( sk5 @ leq ) )
| sk1
| ~ ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
| ~ ( pv5 @ ( n0 @ leq ) ) ),
inference(cnfConj,[status(thm)],[103]) ).
thf(2173,plain,
( ~ sk4
| ( n1 @ ( n3 @ minus ) @ ( sk5 @ leq ) )
| sk1
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[119,128,107]) ).
thf(2174,plain,
( ~ sk4
| ( n1 @ ( n3 @ minus ) @ ( sk5 @ leq ) )
| sk1 ),
inference(simp,[status(thm)],[2173]) ).
thf(8101,plain,
( ~ sk4
| ( n3 @ pred @ ( sk5 @ leq ) )
| sk1 ),
inference(rewrite,[status(thm)],[2174,302]) ).
thf(13,axiom,
! [A: $i] :
( ( A @ succ @ pred )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pred_succ) ).
thf(183,plain,
! [A: $i] :
( ( A @ succ @ pred )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(184,plain,
! [A: $i] :
( ( A @ succ @ pred )
= A ),
inference(cnf,[status(esa)],[183]) ).
thf(185,plain,
! [A: $i] :
( ( A @ succ @ pred )
= A ),
inference(lifteq,[status(thm)],[184]) ).
thf(5441,plain,
! [A: $i] :
( ( ( n2 @ succ )
!= ( A @ succ ) )
| ( ( n3 @ pred )
= A ) ),
inference(paramod_ordered,[status(thm)],[3479,185]) ).
thf(5442,plain,
( ( n3 @ pred )
= n2 ),
inference(pattern_uni,[status(thm)],[5441:[bind(A,$thf( n2 ))]]) ).
thf(9918,plain,
( ~ sk4
| ( n2 @ ( sk5 @ leq ) )
| sk1 ),
inference(rewrite,[status(thm)],[8101,5442]) ).
thf(80,axiom,
! [A: $i] : ( A @ ( A @ leq ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_leq) ).
thf(594,plain,
! [A: $i] : ( A @ ( A @ leq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(595,plain,
! [A: $i] : ( A @ ( A @ leq ) ),
inference(cnf,[status(esa)],[594]) ).
thf(125,plain,
( ~ sk1
| ( sk3 @ ( n0 @ leq ) )
| ~ ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
| ~ ( pv5 @ ( n0 @ leq ) ) ),
inference(cnfConj,[status(thm)],[103]) ).
thf(651,plain,
( ~ sk1
| ( sk3 @ ( n0 @ leq ) )
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[125,128,107]) ).
thf(652,plain,
( ~ sk1
| ( sk3 @ ( n0 @ leq ) ) ),
inference(simp,[status(thm)],[651]) ).
thf(134,plain,
( ~ sk1
| ( sk2 @ ( n0 @ leq ) )
| ~ ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
| ~ ( pv5 @ ( n0 @ leq ) ) ),
inference(cnfConj,[status(thm)],[103]) ).
thf(990,plain,
( ~ sk1
| ( sk2 @ ( n0 @ leq ) )
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[134,128,107]) ).
thf(991,plain,
( ~ sk1
| ( sk2 @ ( n0 @ leq ) ) ),
inference(simp,[status(thm)],[990]) ).
thf(137,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( r_ds1_filter @ a_select3 ) ) )
= ( A @ ( B @ ( r_ds1_filter @ a_select3 ) ) ) )
| ~ ( n1 @ ( n3 @ minus ) @ ( B @ leq ) )
| ~ ( n1 @ ( n3 @ minus ) @ ( A @ leq ) )
| ~ ( B @ ( n0 @ leq ) )
| ~ ( A @ ( n0 @ leq ) ) ),
inference(cnfConj,[status(thm)],[103]) ).
thf(145,plain,
! [B: $i,A: $i] :
( ~ ( n1 @ ( n3 @ minus ) @ ( B @ leq ) )
| ~ ( n1 @ ( n3 @ minus ) @ ( A @ leq ) )
| ~ ( B @ ( n0 @ leq ) )
| ~ ( A @ ( n0 @ leq ) )
| ( ( B @ ( A @ ( r_ds1_filter @ a_select3 ) ) )
= ( A @ ( B @ ( r_ds1_filter @ a_select3 ) ) ) ) ),
inference(lifteq,[status(thm)],[137]) ).
thf(146,plain,
! [B: $i,A: $i] :
( ~ ( n1 @ ( n3 @ minus ) @ ( B @ leq ) )
| ~ ( n1 @ ( n3 @ minus ) @ ( A @ leq ) )
| ~ ( B @ ( n0 @ leq ) )
| ~ ( A @ ( n0 @ leq ) )
| ( ( B @ ( A @ ( r_ds1_filter @ a_select3 ) ) )
= ( A @ ( B @ ( r_ds1_filter @ a_select3 ) ) ) ) ),
inference(simp,[status(thm)],[145]) ).
thf(6418,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( r_ds1_filter @ a_select3 ) ) )
!= ( sk2 @ ( sk3 @ ( q_ds1_filter @ a_select3 ) ) ) )
| ~ sk1
| ( ( B @ ( A @ ( r_ds1_filter @ a_select3 ) ) )
!= ( sk3 @ ( sk2 @ ( q_ds1_filter @ a_select3 ) ) ) )
| ~ ( n1 @ ( n3 @ minus ) @ ( B @ leq ) )
| ~ ( n1 @ ( n3 @ minus ) @ ( A @ leq ) )
| ~ ( B @ ( n0 @ leq ) )
| ~ ( A @ ( n0 @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[146,664]) ).
thf(6507,plain,
! [B: $i,A: $i] :
( ( A != sk2 )
| ( B != sk3 )
| ( r_ds1_filter != q_ds1_filter )
| ~ sk1
| ( B != sk3 )
| ( A != sk2 )
| ( r_ds1_filter != q_ds1_filter )
| ~ ( n1 @ ( n3 @ minus ) @ ( B @ leq ) )
| ~ ( n1 @ ( n3 @ minus ) @ ( A @ leq ) )
| ~ ( B @ ( n0 @ leq ) )
| ~ ( A @ ( n0 @ leq ) ) ),
inference(simp,[status(thm)],[6418]) ).
thf(6715,plain,
( ~ sk1
| ( r_ds1_filter != q_ds1_filter )
| ~ ( n1 @ ( n3 @ minus ) @ ( sk3 @ leq ) )
| ~ ( n1 @ ( n3 @ minus ) @ ( sk2 @ leq ) )
| ~ ( sk3 @ ( n0 @ leq ) )
| ~ ( sk2 @ ( n0 @ leq ) ) ),
inference(simp,[status(thm)],[6507]) ).
thf(7098,plain,
( ( ( sk2 @ ( n0 @ leq ) )
!= ( sk2 @ ( n0 @ leq ) ) )
| ~ sk1
| ( r_ds1_filter != q_ds1_filter )
| ~ ( n1 @ ( n3 @ minus ) @ ( sk3 @ leq ) )
| ~ ( n1 @ ( n3 @ minus ) @ ( sk2 @ leq ) )
| ~ ( sk3 @ ( n0 @ leq ) )
| ~ $true
| ~ sk1 ),
inference(paramod_ordered,[status(thm)],[991,6715]) ).
thf(7099,plain,
( ( ( sk2 @ ( n0 @ leq ) )
!= ( sk2 @ ( n0 @ leq ) ) )
| ( r_ds1_filter != q_ds1_filter )
| ~ ( n1 @ ( n3 @ minus ) @ ( sk3 @ leq ) )
| ~ ( n1 @ ( n3 @ minus ) @ ( sk2 @ leq ) )
| ~ ( sk3 @ ( n0 @ leq ) )
| ~ sk1 ),
inference(simp,[status(thm)],[7098]) ).
thf(7100,plain,
( ( r_ds1_filter != q_ds1_filter )
| ~ ( n1 @ ( n3 @ minus ) @ ( sk3 @ leq ) )
| ~ ( n1 @ ( n3 @ minus ) @ ( sk2 @ leq ) )
| ~ ( sk3 @ ( n0 @ leq ) )
| ~ sk1 ),
inference(pattern_uni,[status(thm)],[7099:[]]) ).
thf(7394,plain,
( ( ( sk3 @ ( n0 @ leq ) )
!= ( sk3 @ ( n0 @ leq ) ) )
| ( r_ds1_filter != q_ds1_filter )
| ~ ( n1 @ ( n3 @ minus ) @ ( sk3 @ leq ) )
| ~ ( n1 @ ( n3 @ minus ) @ ( sk2 @ leq ) )
| ~ $true
| ~ sk1
| ~ sk1 ),
inference(paramod_ordered,[status(thm)],[652,7100]) ).
thf(7395,plain,
( ( ( sk3 @ ( n0 @ leq ) )
!= ( sk3 @ ( n0 @ leq ) ) )
| ( r_ds1_filter != q_ds1_filter )
| ~ ( n1 @ ( n3 @ minus ) @ ( sk3 @ leq ) )
| ~ ( n1 @ ( n3 @ minus ) @ ( sk2 @ leq ) )
| ~ sk1 ),
inference(simp,[status(thm)],[7394]) ).
thf(7396,plain,
( ( r_ds1_filter != q_ds1_filter )
| ~ ( n1 @ ( n3 @ minus ) @ ( sk3 @ leq ) )
| ~ ( n1 @ ( n3 @ minus ) @ ( sk2 @ leq ) )
| ~ sk1 ),
inference(pattern_uni,[status(thm)],[7395:[]]) ).
thf(8067,plain,
( ( r_ds1_filter != q_ds1_filter )
| ~ ( n3 @ pred @ ( sk3 @ leq ) )
| ~ ( n3 @ pred @ ( sk2 @ leq ) )
| ~ sk1 ),
inference(rewrite,[status(thm)],[7396,302]) ).
thf(8202,plain,
( ( r_ds1_filter != q_ds1_filter )
| ~ ( n2 @ ( sk3 @ leq ) )
| ~ ( n2 @ ( sk2 @ leq ) )
| ~ sk1 ),
inference(rewrite,[status(thm)],[8067,5442]) ).
thf(8251,plain,
! [A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( n2 @ ( sk2 @ leq ) ) )
| ( r_ds1_filter != q_ds1_filter )
| ~ ( n2 @ ( sk3 @ leq ) )
| ~ $true
| ~ sk1 ),
inference(paramod_ordered,[status(thm)],[595,8202]) ).
thf(8252,plain,
! [A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( n2 @ ( sk2 @ leq ) ) )
| ( r_ds1_filter != q_ds1_filter )
| ~ ( n2 @ ( sk3 @ leq ) )
| ~ sk1 ),
inference(simp,[status(thm)],[8251]) ).
thf(8265,plain,
! [A: $i] :
( ( A != n2 )
| ( A != sk2 )
| ( r_ds1_filter != q_ds1_filter )
| ~ ( n2 @ ( sk3 @ leq ) )
| ~ sk1 ),
inference(simp,[status(thm)],[8252]) ).
thf(8276,plain,
( ( sk2 != n2 )
| ( r_ds1_filter != q_ds1_filter )
| ~ ( n2 @ ( sk3 @ leq ) )
| ~ sk1 ),
inference(simp,[status(thm)],[8265]) ).
thf(8303,plain,
! [A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( n2 @ ( sk3 @ leq ) ) )
| ( sk2 != n2 )
| ( r_ds1_filter != q_ds1_filter )
| ~ $true
| ~ sk1 ),
inference(paramod_ordered,[status(thm)],[595,8276]) ).
thf(8304,plain,
! [A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( n2 @ ( sk3 @ leq ) ) )
| ( sk2 != n2 )
| ( r_ds1_filter != q_ds1_filter )
| ~ sk1 ),
inference(simp,[status(thm)],[8303]) ).
thf(8312,plain,
! [A: $i] :
( ( A != n2 )
| ( A != sk3 )
| ( sk2 != n2 )
| ( r_ds1_filter != q_ds1_filter )
| ~ sk1 ),
inference(simp,[status(thm)],[8304]) ).
thf(8315,plain,
( ( sk3 != n2 )
| ( sk2 != n2 )
| ( r_ds1_filter != q_ds1_filter )
| ~ sk1 ),
inference(simp,[status(thm)],[8312]) ).
thf(28,axiom,
n1 @ ( n3 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_3_1) ).
thf(219,plain,
n1 @ ( n3 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(16860,plain,
! [B: $i,A: $i] :
( ( ( n1 @ ( n3 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[219,203]) ).
thf(16861,plain,
! [B: $i,A: $i] :
( ( ( n1 @ ( n3 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[16860]) ).
thf(16862,plain,
n3 @ ( n1 @ lt ),
inference(pattern_uni,[status(thm)],[16861:[bind(A,$thf( n1 )),bind(B,$thf( n3 ))]]) ).
thf(36,axiom,
tptp_minus_1 @ ( n999 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_999_tptp_minus_1) ).
thf(238,plain,
tptp_minus_1 @ ( n999 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(17405,plain,
! [B: $i,A: $i] :
( ( ( tptp_minus_1 @ ( n999 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[238,217]) ).
thf(17406,plain,
! [B: $i,A: $i] :
( ( ( tptp_minus_1 @ ( n999 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ leq ) ) ),
inference(simp,[status(thm)],[17405]) ).
thf(17407,plain,
n999 @ ( tptp_minus_1 @ leq ),
inference(pattern_uni,[status(thm)],[17406:[bind(A,$thf( tptp_minus_1 )),bind(B,$thf( n999 ))]]) ).
thf(24,axiom,
n2 @ ( n3 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_3_2) ).
thf(214,plain,
n2 @ ( n3 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(16896,plain,
! [B: $i,A: $i] :
( ( ( n2 @ ( n3 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[214,203]) ).
thf(16897,plain,
! [B: $i,A: $i] :
( ( ( n2 @ ( n3 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[16896]) ).
thf(16898,plain,
n3 @ ( n2 @ lt ),
inference(pattern_uni,[status(thm)],[16897:[bind(A,$thf( n2 )),bind(B,$thf( n3 ))]]) ).
thf(5443,plain,
! [A: $i] :
( ( ( n3 @ succ )
!= ( A @ succ ) )
| ( ( n4 @ pred )
= A ) ),
inference(paramod_ordered,[status(thm)],[3528,185]) ).
thf(5444,plain,
( ( n4 @ pred )
= n3 ),
inference(pattern_uni,[status(thm)],[5443:[bind(A,$thf( n3 ))]]) ).
thf(45,axiom,
n0 @ ( n999 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_999_0) ).
thf(276,plain,
n0 @ ( n999 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(139,plain,
( ( sk9 @ ( n0 @ leq ) )
| ( sk8 @ ( n0 @ leq ) )
| sk4
| sk1
| ~ ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
| ~ ( pv5 @ ( n0 @ leq ) ) ),
inference(cnfConj,[status(thm)],[103]) ).
thf(4812,plain,
( ( sk9 @ ( n0 @ leq ) )
| ( sk8 @ ( n0 @ leq ) )
| sk4
| sk1
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[139,128,107]) ).
thf(4813,plain,
( ( sk9 @ ( n0 @ leq ) )
| ( sk8 @ ( n0 @ leq ) )
| sk4
| sk1 ),
inference(simp,[status(thm)],[4812]) ).
thf(4883,plain,
( ~ $true
| ( ( sk9 @ ( n0 @ leq ) )
!= ( sk8 @ ( n0 @ leq ) ) )
| ( sk8 @ ( n0 @ leq ) )
| sk4
| sk1 ),
inference(eqfactor_ordered,[status(thm)],[4813]) ).
thf(4884,plain,
( ( ( sk9 @ ( n0 @ leq ) )
!= ( sk8 @ ( n0 @ leq ) ) )
| ( sk8 @ ( n0 @ leq ) )
| sk4
| sk1 ),
inference(simp,[status(thm)],[4883]) ).
thf(142,plain,
( ( ( sk10 @ ( sk9 @ ( id_ds1_filter @ a_select3 ) ) )
!= ( sk9 @ ( sk10 @ ( id_ds1_filter @ a_select3 ) ) ) )
| ( ( sk8 @ ( sk7 @ ( pminus_ds1_filter @ a_select3 ) ) )
!= ( sk7 @ ( sk8 @ ( pminus_ds1_filter @ a_select3 ) ) ) )
| sk4
| sk1
| ~ ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
| ~ ( pv5 @ ( n0 @ leq ) ) ),
inference(cnfConj,[status(thm)],[103]) ).
thf(144,plain,
( sk4
| sk1
| ~ ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
| ~ ( pv5 @ ( n0 @ leq ) )
| ( ( sk9 @ ( sk10 @ ( id_ds1_filter @ a_select3 ) ) )
!= ( sk10 @ ( sk9 @ ( id_ds1_filter @ a_select3 ) ) ) )
| ( ( sk7 @ ( sk8 @ ( pminus_ds1_filter @ a_select3 ) ) )
!= ( sk8 @ ( sk7 @ ( pminus_ds1_filter @ a_select3 ) ) ) ) ),
inference(lifteq,[status(thm)],[142]) ).
thf(5673,plain,
( sk4
| sk1
| ~ $true
| ~ $true
| ( ( sk9 @ ( sk10 @ ( id_ds1_filter @ a_select3 ) ) )
!= ( sk10 @ ( sk9 @ ( id_ds1_filter @ a_select3 ) ) ) )
| ( ( sk7 @ ( sk8 @ ( pminus_ds1_filter @ a_select3 ) ) )
!= ( sk8 @ ( sk7 @ ( pminus_ds1_filter @ a_select3 ) ) ) ) ),
inference(rewrite,[status(thm)],[144,128,107]) ).
thf(5674,plain,
( sk4
| sk1
| ( ( sk9 @ ( sk10 @ ( id_ds1_filter @ a_select3 ) ) )
!= ( sk10 @ ( sk9 @ ( id_ds1_filter @ a_select3 ) ) ) )
| ( ( sk7 @ ( sk8 @ ( pminus_ds1_filter @ a_select3 ) ) )
!= ( sk8 @ ( sk7 @ ( pminus_ds1_filter @ a_select3 ) ) ) ) ),
inference(simp,[status(thm)],[5673]) ).
thf(21,axiom,
tptp_minus_1 @ ( n5 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_5_tptp_minus_1) ).
thf(207,plain,
tptp_minus_1 @ ( n5 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(667,plain,
! [A: $i] :
( ( ( tptp_minus_1 @ ( n5 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[207,197]) ).
thf(668,plain,
! [A: $i] :
( ( tptp_minus_1 @ ( n5 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[667]) ).
thf(669,plain,
! [A: $i] :
( ( tptp_minus_1 != A )
| ( n5 != A ) ),
inference(simp,[status(thm)],[668]) ).
thf(670,plain,
n5 != tptp_minus_1,
inference(simp,[status(thm)],[669]) ).
thf(115,plain,
( ~ sk4
| ( n1 @ ( n3 @ minus ) @ ( sk6 @ leq ) )
| sk1
| ~ ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
| ~ ( pv5 @ ( n0 @ leq ) ) ),
inference(cnfConj,[status(thm)],[103]) ).
thf(2018,plain,
( ~ sk4
| ( n1 @ ( n3 @ minus ) @ ( sk6 @ leq ) )
| sk1
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[115,128,107]) ).
thf(2019,plain,
( ~ sk4
| ( n1 @ ( n3 @ minus ) @ ( sk6 @ leq ) )
| sk1 ),
inference(simp,[status(thm)],[2018]) ).
thf(8102,plain,
( ~ sk4
| ( n3 @ pred @ ( sk6 @ leq ) )
| sk1 ),
inference(rewrite,[status(thm)],[2019,302]) ).
thf(10181,plain,
( ~ sk4
| ( n2 @ ( sk6 @ leq ) )
| sk1 ),
inference(rewrite,[status(thm)],[8102,5442]) ).
thf(67,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(533,plain,
! [A: $i,B: $i] :
( ( A @ ( n0 @ leq ) )
=> ( A @ ( A @ ( B @ uniform_int_rnd ) @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(31,axiom,
tptp_minus_1 @ ( n6 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_6_tptp_minus_1) ).
thf(224,plain,
tptp_minus_1 @ ( n6 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(16815,plain,
! [B: $i,A: $i] :
( ( ( tptp_minus_1 @ ( n6 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[224,203]) ).
thf(16816,plain,
! [B: $i,A: $i] :
( ( ( tptp_minus_1 @ ( n6 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[16815]) ).
thf(16817,plain,
n6 @ ( tptp_minus_1 @ lt ),
inference(pattern_uni,[status(thm)],[16816:[bind(A,$thf( tptp_minus_1 )),bind(B,$thf( n6 ))]]) ).
thf(64,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(472,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)],[64]) ).
thf(57,axiom,
n3 @ ( n6 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_6_3) ).
thf(404,plain,
n3 @ ( n6 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(8104,plain,
n999 @ pred @ ( pv5 @ leq ),
inference(rewrite,[status(thm)],[107,302]) ).
thf(8110,plain,
! [A: $i] :
( ( ( A @ succ @ pred )
!= ( n999 @ pred ) )
| ( A @ ( pv5 @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[185,8104]) ).
thf(8168,plain,
! [A: $i] :
( ( ( A @ succ )
!= n999 )
| ( A @ ( pv5 @ leq ) ) ),
inference(simp,[status(thm)],[8110]) ).
thf(12820,plain,
! [A: $i] :
( ( ( n5 @ succ @ succ )
!= ( A @ succ ) )
| ( ( n6 @ succ )
!= n999 )
| ( A @ ( pv5 @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[12789,8168]) ).
thf(12821,plain,
( ( ( n6 @ succ )
!= n999 )
| ( n5 @ succ @ ( pv5 @ leq ) ) ),
inference(pattern_uni,[status(thm)],[12820:[bind(A,$thf( n5 @ succ ))]]) ).
thf(16348,plain,
( ( ( n6 @ succ )
!= n999 )
| ( n6 @ ( pv5 @ leq ) ) ),
inference(rewrite,[status(thm)],[12821,4132]) ).
thf(16373,plain,
! [A: $i] :
( ( ( A @ pred @ succ )
!= ( n6 @ succ ) )
| ( A != n999 )
| ( n6 @ ( pv5 @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[188,16348]) ).
thf(16472,plain,
( ( ( n999 @ pred )
!= n6 )
| ( n6 @ ( pv5 @ leq ) ) ),
inference(simp,[status(thm)],[16373]) ).
thf(116,plain,
( ~ sk4
| ( ( sk6 @ ( sk5 @ ( r_ds1_filter @ a_select3 ) ) )
!= ( sk5 @ ( sk6 @ ( r_ds1_filter @ a_select3 ) ) ) )
| sk1
| ~ ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
| ~ ( pv5 @ ( n0 @ leq ) ) ),
inference(cnfConj,[status(thm)],[103]) ).
thf(154,plain,
( ~ sk4
| sk1
| ~ ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
| ~ ( pv5 @ ( n0 @ leq ) )
| ( ( sk5 @ ( sk6 @ ( r_ds1_filter @ a_select3 ) ) )
!= ( sk6 @ ( sk5 @ ( r_ds1_filter @ a_select3 ) ) ) ) ),
inference(lifteq,[status(thm)],[116]) ).
thf(10014,plain,
( ~ sk4
| sk1
| ~ ( n999 @ pred @ ( pv5 @ leq ) )
| ~ $true
| ( ( sk5 @ ( sk6 @ ( r_ds1_filter @ a_select3 ) ) )
!= ( sk6 @ ( sk5 @ ( r_ds1_filter @ a_select3 ) ) ) ) ),
inference(rewrite,[status(thm)],[154,128,302]) ).
thf(10015,plain,
( ~ sk4
| sk1
| ~ ( n999 @ pred @ ( pv5 @ leq ) )
| ( ( sk5 @ ( sk6 @ ( r_ds1_filter @ a_select3 ) ) )
!= ( sk6 @ ( sk5 @ ( r_ds1_filter @ a_select3 ) ) ) ) ),
inference(simp,[status(thm)],[10014]) ).
thf(16603,plain,
( ( ( n999 @ pred @ ( pv5 @ leq ) )
!= ( n6 @ ( pv5 @ leq ) ) )
| ~ sk4
| sk1
| ~ $true
| ( ( sk5 @ ( sk6 @ ( r_ds1_filter @ a_select3 ) ) )
!= ( sk6 @ ( sk5 @ ( r_ds1_filter @ a_select3 ) ) ) )
| ( ( n999 @ pred )
!= n6 ) ),
inference(paramod_ordered,[status(thm)],[16472,10015]) ).
thf(16604,plain,
( ( ( n999 @ pred @ ( pv5 @ leq ) )
!= ( n6 @ ( pv5 @ leq ) ) )
| ~ sk4
| sk1
| ( ( sk5 @ ( sk6 @ ( r_ds1_filter @ a_select3 ) ) )
!= ( sk6 @ ( sk5 @ ( r_ds1_filter @ a_select3 ) ) ) )
| ( ( n999 @ pred )
!= n6 ) ),
inference(simp,[status(thm)],[16603]) ).
thf(16696,plain,
( ( ( n999 @ pred )
!= n6 )
| ( pv5 != pv5 )
| ~ sk4
| ( sk6 != sk5 )
| ( sk6 != sk5 )
| ( r_ds1_filter != r_ds1_filter )
| ( ( n999 @ pred )
!= n6 )
| sk1 ),
inference(simp,[status(thm)],[16604]) ).
thf(16752,plain,
( ~ sk4
| ( sk6 != sk5 )
| ( ( n999 @ pred )
!= n6 )
| sk1 ),
inference(simp,[status(thm)],[16696]) ).
thf(38,axiom,
n6 @ ( n999 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_999_6) ).
thf(240,plain,
n6 @ ( n999 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(16866,plain,
! [B: $i,A: $i] :
( ( ( n6 @ ( n999 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[240,203]) ).
thf(16867,plain,
! [B: $i,A: $i] :
( ( ( n6 @ ( n999 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[16866]) ).
thf(16868,plain,
n999 @ ( n6 @ lt ),
inference(pattern_uni,[status(thm)],[16867:[bind(A,$thf( n6 )),bind(B,$thf( n999 ))]]) ).
thf(50,axiom,
tptp_minus_1 @ ( n0 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_0_tptp_minus_1) ).
thf(299,plain,
tptp_minus_1 @ ( n0 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(16875,plain,
! [B: $i,A: $i] :
( ( ( tptp_minus_1 @ ( n0 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[299,203]) ).
thf(16876,plain,
! [B: $i,A: $i] :
( ( ( tptp_minus_1 @ ( n0 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[16875]) ).
thf(16877,plain,
n0 @ ( tptp_minus_1 @ lt ),
inference(pattern_uni,[status(thm)],[16876:[bind(A,$thf( tptp_minus_1 )),bind(B,$thf( n0 ))]]) ).
thf(40,axiom,
n1 @ ( n999 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_999_1) ).
thf(242,plain,
n1 @ ( n999 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(2079,plain,
! [A: $i] :
( ( ( n1 @ ( n999 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[242,197]) ).
thf(2080,plain,
! [A: $i] :
( ( n1 @ ( n999 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[2079]) ).
thf(2081,plain,
! [A: $i] :
( ( n1 != A )
| ( n999 != A ) ),
inference(simp,[status(thm)],[2080]) ).
thf(2082,plain,
n1 != n999,
inference(simp,[status(thm)],[2081]) ).
thf(56,axiom,
n0 @ ( n5 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_5_0) ).
thf(403,plain,
n0 @ ( n5 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(17426,plain,
! [B: $i,A: $i] :
( ( ( n0 @ ( n5 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[403,217]) ).
thf(17427,plain,
! [B: $i,A: $i] :
( ( ( n0 @ ( n5 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ leq ) ) ),
inference(simp,[status(thm)],[17426]) ).
thf(17428,plain,
n5 @ ( n0 @ leq ),
inference(pattern_uni,[status(thm)],[17427:[bind(A,$thf( n0 )),bind(B,$thf( n5 ))]]) ).
thf(5683,plain,
( ( ( sk10 @ ( sk9 @ ( id_ds1_filter @ a_select3 ) ) )
!= ( sk7 @ ( sk8 @ ( pminus_ds1_filter @ a_select3 ) ) ) )
| ( ( sk9 @ ( sk10 @ ( id_ds1_filter @ a_select3 ) ) )
!= ( sk8 @ ( sk7 @ ( pminus_ds1_filter @ a_select3 ) ) ) )
| sk4
| sk1
| ( ( sk7 @ ( sk8 @ ( pminus_ds1_filter @ a_select3 ) ) )
!= ( sk8 @ ( sk7 @ ( pminus_ds1_filter @ a_select3 ) ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[5674]) ).
thf(5690,plain,
( ( sk10 != sk7 )
| ( sk9 != sk8 )
| ( id_ds1_filter != pminus_ds1_filter )
| ( sk9 != sk8 )
| ( sk10 != sk7 )
| ( id_ds1_filter != pminus_ds1_filter )
| ( sk8 != sk7 )
| ( sk8 != sk7 )
| ( pminus_ds1_filter != pminus_ds1_filter )
| sk4
| sk1 ),
inference(simp,[status(thm)],[5683]) ).
thf(5765,plain,
( ( sk9 != sk8 )
| ( sk10 != sk7 )
| ( id_ds1_filter != pminus_ds1_filter )
| ( sk8 != sk7 )
| sk4
| sk1 ),
inference(simp,[status(thm)],[5690]) ).
thf(72,axiom,
! [A: $i] :
( ( n1 @ ( A @ plus ) )
= ( A @ succ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_plus_1_r) ).
thf(568,plain,
! [A: $i] :
( ( n1 @ ( A @ plus ) )
= ( A @ succ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(569,plain,
! [A: $i] :
( ( n1 @ ( A @ plus ) )
= ( A @ succ ) ),
inference(cnf,[status(esa)],[568]) ).
thf(570,plain,
! [A: $i] :
( ( n1 @ ( A @ plus ) )
= ( A @ succ ) ),
inference(lifteq,[status(thm)],[569]) ).
thf(5676,plain,
( ( sk10 != sk9 )
| ( sk10 != sk9 )
| ( id_ds1_filter != id_ds1_filter )
| ( ( sk7 @ ( sk8 @ ( pminus_ds1_filter @ a_select3 ) ) )
!= ( sk8 @ ( sk7 @ ( pminus_ds1_filter @ a_select3 ) ) ) )
| sk4
| sk1 ),
inference(simp,[status(thm)],[5674]) ).
thf(5759,plain,
( ( sk10 != sk9 )
| ( ( sk7 @ ( sk8 @ ( pminus_ds1_filter @ a_select3 ) ) )
!= ( sk8 @ ( sk7 @ ( pminus_ds1_filter @ a_select3 ) ) ) )
| sk4
| sk1 ),
inference(simp,[status(thm)],[5676]) ).
thf(93,axiom,
n0 @ ( n1 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_1_0) ).
thf(619,plain,
n0 @ ( n1 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(16917,plain,
! [B: $i,A: $i] :
( ( ( n1 @ ( n2 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[215,203]) ).
thf(16918,plain,
! [B: $i,A: $i] :
( ( ( n1 @ ( n2 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[16917]) ).
thf(16919,plain,
n2 @ ( n1 @ lt ),
inference(pattern_uni,[status(thm)],[16918:[bind(A,$thf( n1 )),bind(B,$thf( n2 ))]]) ).
thf(19,axiom,
tptp_minus_1 @ ( n4 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_4_tptp_minus_1) ).
thf(204,plain,
tptp_minus_1 @ ( n4 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(17447,plain,
! [B: $i,A: $i] :
( ( ( tptp_minus_1 @ ( n4 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[204,217]) ).
thf(17448,plain,
! [B: $i,A: $i] :
( ( ( tptp_minus_1 @ ( n4 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ leq ) ) ),
inference(simp,[status(thm)],[17447]) ).
thf(17449,plain,
n4 @ ( tptp_minus_1 @ leq ),
inference(pattern_uni,[status(thm)],[17448:[bind(A,$thf( tptp_minus_1 )),bind(B,$thf( n4 ))]]) ).
thf(10060,plain,
! [A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( n999 @ pred @ ( pv5 @ leq ) ) )
| ~ sk4
| sk1
| ~ $true
| ( ( sk5 @ ( sk6 @ ( r_ds1_filter @ a_select3 ) ) )
!= ( sk6 @ ( sk5 @ ( r_ds1_filter @ a_select3 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[595,10015]) ).
thf(10061,plain,
! [A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( n999 @ pred @ ( pv5 @ leq ) ) )
| ~ sk4
| sk1
| ( ( sk5 @ ( sk6 @ ( r_ds1_filter @ a_select3 ) ) )
!= ( sk6 @ ( sk5 @ ( r_ds1_filter @ a_select3 ) ) ) ) ),
inference(simp,[status(thm)],[10060]) ).
thf(10070,plain,
! [A: $i] :
( ( A
!= ( n999 @ pred ) )
| ( A != pv5 )
| ~ sk4
| ( sk6 != sk5 )
| ( sk6 != sk5 )
| ( r_ds1_filter != r_ds1_filter )
| sk1 ),
inference(simp,[status(thm)],[10061]) ).
thf(10142,plain,
( ( ( n999 @ pred )
!= pv5 )
| ~ sk4
| ( sk6 != sk5 )
| sk1 ),
inference(simp,[status(thm)],[10070]) ).
thf(141,plain,
( ( sk10 @ ( n0 @ leq ) )
| ( sk7 @ ( n0 @ leq ) )
| sk4
| sk1
| ~ ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
| ~ ( pv5 @ ( n0 @ leq ) ) ),
inference(cnfConj,[status(thm)],[103]) ).
thf(5337,plain,
( ( sk10 @ ( n0 @ leq ) )
| ( sk7 @ ( n0 @ leq ) )
| sk4
| sk1
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[141,128,107]) ).
thf(5338,plain,
( ( sk10 @ ( n0 @ leq ) )
| ( sk7 @ ( n0 @ leq ) )
| sk4
| sk1 ),
inference(simp,[status(thm)],[5337]) ).
thf(11,axiom,
n4 @ ( n5 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_5_4) ).
thf(181,plain,
n4 @ ( n5 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(16851,plain,
! [B: $i,A: $i] :
( ( ( n4 @ ( n5 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[181,203]) ).
thf(16852,plain,
! [B: $i,A: $i] :
( ( ( n4 @ ( n5 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[16851]) ).
thf(16853,plain,
n5 @ ( n4 @ lt ),
inference(pattern_uni,[status(thm)],[16852:[bind(A,$thf( n4 )),bind(B,$thf( n5 ))]]) ).
thf(87,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)],[87]) ).
thf(2400,plain,
! [A: $i] :
( ( ( n0 @ ( n5 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[403,197]) ).
thf(2401,plain,
! [A: $i] :
( ( n0 @ ( n5 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[2400]) ).
thf(2402,plain,
! [A: $i] :
( ( n0 != A )
| ( n5 != A ) ),
inference(simp,[status(thm)],[2401]) ).
thf(2403,plain,
n5 != n0,
inference(simp,[status(thm)],[2402]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( A = B )
| ( A @ ( B @ gt ) )
| ( B @ ( A @ gt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',totality) ).
thf(164,plain,
! [A: $i,B: $i] :
( ( A = B )
| ( A @ ( B @ gt ) )
| ( B @ ( A @ gt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(10627,plain,
! [A: $i] :
( ( ( A @ succ @ pred )
!= ( n999 @ pred ) )
| ( A != pv5 )
| ~ sk4
| ( sk6 != sk5 )
| sk1 ),
inference(paramod_ordered,[status(thm)],[185,10142]) ).
thf(10641,plain,
( ( ( pv5 @ succ )
!= n999 )
| ~ sk4
| ( sk6 != sk5 )
| sk1 ),
inference(simp,[status(thm)],[10627]) ).
thf(44,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(263,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)],[44]) ).
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,E: $i] :
( ( ( B @ ( E @ leq ) )
& ( E @ ( n0 @ leq ) )
& ( B @ ( D @ leq ) )
& ( D @ ( n0 @ leq ) )
& ( B @ ( C @ leq ) )
& ( C @ ( n0 @ leq ) ) )
=> ! [F: $i] :
( ( D @ ( C @ ( F @ ( E @ ( E @ ( A @ tptp_update3 ) ) ) @ a_select3 ) ) )
= ( C @ ( D @ ( F @ ( E @ ( E @ ( A @ tptp_update3 ) ) ) @ a_select3 ) ) ) ) ) ),
inference(miniscope,[status(thm)],[263]) ).
thf(265,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( ( D @ ( C @ ( F @ ( E @ ( E @ ( A @ tptp_update3 ) ) ) @ a_select3 ) ) )
= ( C @ ( D @ ( F @ ( E @ ( E @ ( A @ tptp_update3 ) ) ) @ a_select3 ) ) ) )
| ~ ( B @ ( E @ leq ) )
| ~ ( E @ ( n0 @ leq ) )
| ~ ( B @ ( D @ leq ) )
| ~ ( D @ ( n0 @ leq ) )
| ~ ( B @ ( C @ leq ) )
| ~ ( C @ ( n0 @ leq ) )
| ( ( A @ ( B @ sk15 ) @ ( A @ ( B @ sk14 ) @ ( A @ a_select3 ) ) )
!= ( A @ ( B @ sk14 ) @ ( A @ ( B @ sk15 ) @ ( A @ a_select3 ) ) ) ) )
& ( ( ( D @ ( C @ ( F @ ( E @ ( E @ ( A @ tptp_update3 ) ) ) @ a_select3 ) ) )
= ( C @ ( D @ ( F @ ( E @ ( E @ ( A @ tptp_update3 ) ) ) @ a_select3 ) ) ) )
| ~ ( B @ ( E @ leq ) )
| ~ ( E @ ( n0 @ leq ) )
| ~ ( B @ ( D @ leq ) )
| ~ ( D @ ( n0 @ leq ) )
| ~ ( B @ ( C @ leq ) )
| ~ ( C @ ( n0 @ leq ) )
| ( B @ ( A @ ( B @ sk15 ) @ leq ) ) )
& ( ( ( D @ ( C @ ( F @ ( E @ ( E @ ( A @ tptp_update3 ) ) ) @ a_select3 ) ) )
= ( C @ ( D @ ( F @ ( E @ ( E @ ( A @ tptp_update3 ) ) ) @ a_select3 ) ) ) )
| ~ ( B @ ( E @ leq ) )
| ~ ( E @ ( n0 @ leq ) )
| ~ ( B @ ( D @ leq ) )
| ~ ( D @ ( n0 @ leq ) )
| ~ ( B @ ( C @ leq ) )
| ~ ( C @ ( n0 @ leq ) )
| ( A @ ( B @ sk15 ) @ ( n0 @ leq ) ) )
& ( ( ( D @ ( C @ ( F @ ( E @ ( E @ ( A @ tptp_update3 ) ) ) @ a_select3 ) ) )
= ( C @ ( D @ ( F @ ( E @ ( E @ ( A @ tptp_update3 ) ) ) @ a_select3 ) ) ) )
| ~ ( B @ ( E @ leq ) )
| ~ ( E @ ( n0 @ leq ) )
| ~ ( B @ ( D @ leq ) )
| ~ ( D @ ( n0 @ leq ) )
| ~ ( B @ ( C @ leq ) )
| ~ ( C @ ( n0 @ leq ) )
| ( B @ ( A @ ( B @ sk14 ) @ leq ) ) )
& ( ( ( D @ ( C @ ( F @ ( E @ ( E @ ( A @ tptp_update3 ) ) ) @ a_select3 ) ) )
= ( C @ ( D @ ( F @ ( E @ ( E @ ( A @ tptp_update3 ) ) ) @ a_select3 ) ) ) )
| ~ ( B @ ( E @ leq ) )
| ~ ( E @ ( n0 @ leq ) )
| ~ ( B @ ( D @ leq ) )
| ~ ( D @ ( n0 @ leq ) )
| ~ ( B @ ( C @ leq ) )
| ~ ( C @ ( n0 @ leq ) )
| ( A @ ( B @ sk14 ) @ ( n0 @ leq ) ) ) ),
inference(cnf,[status(esa)],[264]) ).
thf(268,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( F @ ( E @ ( E @ ( A @ tptp_update3 ) ) ) @ a_select3 ) ) )
= ( C @ ( D @ ( F @ ( E @ ( E @ ( A @ tptp_update3 ) ) ) @ a_select3 ) ) ) )
| ~ ( B @ ( E @ leq ) )
| ~ ( E @ ( n0 @ leq ) )
| ~ ( B @ ( D @ leq ) )
| ~ ( D @ ( n0 @ leq ) )
| ~ ( B @ ( C @ leq ) )
| ~ ( C @ ( n0 @ leq ) )
| ( ( A @ ( B @ sk15 ) @ ( A @ ( B @ sk14 ) @ ( A @ a_select3 ) ) )
!= ( A @ ( B @ sk14 ) @ ( A @ ( B @ sk15 ) @ ( A @ a_select3 ) ) ) ) ),
inference(cnfConj,[status(thm)],[265]) ).
thf(275,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $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 ) ) ) )
| ( ( A @ ( B @ sk14 ) @ ( A @ ( B @ sk15 ) @ ( A @ a_select3 ) ) )
!= ( A @ ( B @ sk15 ) @ ( A @ ( B @ sk14 ) @ ( A @ a_select3 ) ) ) ) ),
inference(lifteq,[status(thm)],[268]) ).
thf(800,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( F @ ( E @ ( E @ ( A @ tptp_update3 ) ) ) @ a_select3 ) ) )
!= ( sk2 @ ( sk3 @ ( q_ds1_filter @ a_select3 ) ) ) )
| ~ sk1
| ( ( C @ ( D @ ( F @ ( E @ ( E @ ( A @ tptp_update3 ) ) ) @ a_select3 ) ) )
!= ( sk3 @ ( sk2 @ ( q_ds1_filter @ a_select3 ) ) ) )
| ~ ( B @ ( E @ leq ) )
| ~ ( E @ ( n0 @ leq ) )
| ~ ( B @ ( D @ leq ) )
| ~ ( D @ ( n0 @ leq ) )
| ~ ( B @ ( C @ leq ) )
| ~ ( C @ ( n0 @ leq ) )
| ( ( A @ ( B @ sk14 ) @ ( A @ ( B @ sk15 ) @ ( A @ a_select3 ) ) )
!= ( A @ ( B @ sk15 ) @ ( A @ ( B @ sk14 ) @ ( A @ a_select3 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[275,664]) ).
thf(872,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D != sk2 )
| ( C != sk3 )
| ( ( F @ ( E @ ( E @ ( A @ tptp_update3 ) ) ) )
!= q_ds1_filter )
| ~ sk1
| ( C != sk3 )
| ( D != sk2 )
| ( ( F @ ( E @ ( E @ ( A @ tptp_update3 ) ) ) )
!= q_ds1_filter )
| ~ ( B @ ( E @ leq ) )
| ~ ( E @ ( n0 @ leq ) )
| ~ ( B @ ( D @ leq ) )
| ~ ( D @ ( n0 @ leq ) )
| ~ ( B @ ( C @ leq ) )
| ~ ( C @ ( n0 @ leq ) )
| ( ( A @ ( B @ sk15 ) )
!= ( A @ ( B @ sk14 ) ) )
| ( ( A @ ( B @ sk15 ) )
!= ( A @ ( B @ sk14 ) ) )
| ( A != A ) ),
inference(simp,[status(thm)],[800]) ).
thf(950,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ sk1
| ( ( D @ ( C @ ( C @ ( A @ tptp_update3 ) ) ) )
!= q_ds1_filter )
| ~ ( B @ ( C @ leq ) )
| ~ ( C @ ( n0 @ leq ) )
| ~ ( B @ ( sk2 @ leq ) )
| ~ ( sk2 @ ( n0 @ leq ) )
| ~ ( B @ ( sk3 @ leq ) )
| ~ ( sk3 @ ( n0 @ leq ) )
| ( ( A @ ( B @ sk15 ) )
!= ( A @ ( B @ sk14 ) ) ) ),
inference(simp,[status(thm)],[872]) ).
thf(1168,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( pv5 @ ( n0 @ leq ) )
!= ( B @ ( C @ leq ) ) )
| ~ sk1
| ( ( D @ ( C @ ( C @ ( A @ tptp_update3 ) ) ) )
!= q_ds1_filter )
| ~ $true
| ~ ( C @ ( n0 @ leq ) )
| ~ ( B @ ( sk2 @ leq ) )
| ~ ( sk2 @ ( n0 @ leq ) )
| ~ ( B @ ( sk3 @ leq ) )
| ~ ( sk3 @ ( n0 @ leq ) )
| ( ( A @ ( B @ sk15 ) )
!= ( A @ ( B @ sk14 ) ) ) ),
inference(paramod_ordered,[status(thm)],[128,950]) ).
thf(1169,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( pv5 @ ( n0 @ leq ) )
!= ( B @ ( C @ leq ) ) )
| ~ sk1
| ( ( D @ ( C @ ( C @ ( A @ tptp_update3 ) ) ) )
!= q_ds1_filter )
| ~ ( C @ ( n0 @ leq ) )
| ~ ( B @ ( sk2 @ leq ) )
| ~ ( sk2 @ ( n0 @ leq ) )
| ~ ( B @ ( sk3 @ leq ) )
| ~ ( sk3 @ ( n0 @ leq ) )
| ( ( A @ ( B @ sk15 ) )
!= ( A @ ( B @ sk14 ) ) ) ),
inference(simp,[status(thm)],[1168]) ).
thf(1170,plain,
! [B: $i,A: $i] :
( ~ sk1
| ( ( B @ ( n0 @ ( n0 @ ( A @ tptp_update3 ) ) ) )
!= q_ds1_filter )
| ~ ( n0 @ ( n0 @ leq ) )
| ~ ( pv5 @ ( sk2 @ leq ) )
| ~ ( sk2 @ ( n0 @ leq ) )
| ~ ( pv5 @ ( sk3 @ leq ) )
| ~ ( sk3 @ ( n0 @ leq ) )
| ( ( A @ ( pv5 @ sk15 ) )
!= ( A @ ( pv5 @ sk14 ) ) ) ),
inference(pattern_uni,[status(thm)],[1169:[bind(A,$thf( A )),bind(B,$thf( pv5 )),bind(C,$thf( n0 ))]]) ).
thf(1256,plain,
! [B: $i,A: $i] :
( ~ sk1
| ( ( B @ ( n0 @ ( n0 @ ( A @ tptp_update3 ) ) ) )
!= q_ds1_filter )
| ~ ( n0 @ ( n0 @ leq ) )
| ~ ( pv5 @ ( sk2 @ leq ) )
| ~ ( sk2 @ ( n0 @ leq ) )
| ~ ( pv5 @ ( sk3 @ leq ) )
| ~ ( sk3 @ ( n0 @ leq ) )
| ( ( A @ ( pv5 @ sk15 ) )
!= ( A @ ( pv5 @ sk14 ) ) ) ),
inference(simp,[status(thm)],[1170]) ).
thf(1297,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( n0 @ leq ) )
!= ( sk2 @ ( n0 @ leq ) ) )
| ~ sk1
| ( ( B @ ( n0 @ ( n0 @ ( A @ tptp_update3 ) ) ) )
!= q_ds1_filter )
| ~ ( n0 @ ( n0 @ leq ) )
| ~ ( pv5 @ ( sk2 @ leq ) )
| ~ $true
| ~ ( pv5 @ ( sk3 @ leq ) )
| ~ ( sk3 @ ( n0 @ leq ) )
| ( ( A @ ( pv5 @ sk15 ) )
!= ( A @ ( pv5 @ sk14 ) ) )
| ~ sk1 ),
inference(paramod_ordered,[status(thm)],[991,1256]) ).
thf(1298,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( n0 @ leq ) )
!= ( sk2 @ ( n0 @ leq ) ) )
| ( ( B @ ( n0 @ ( n0 @ ( A @ tptp_update3 ) ) ) )
!= q_ds1_filter )
| ~ ( n0 @ ( n0 @ leq ) )
| ~ ( pv5 @ ( sk2 @ leq ) )
| ~ ( pv5 @ ( sk3 @ leq ) )
| ~ ( sk3 @ ( n0 @ leq ) )
| ( ( A @ ( pv5 @ sk15 ) )
!= ( A @ ( pv5 @ sk14 ) ) )
| ~ sk1 ),
inference(simp,[status(thm)],[1297]) ).
thf(1299,plain,
! [B: $i,A: $i] :
( ( ( B @ ( n0 @ ( n0 @ ( A @ tptp_update3 ) ) ) )
!= q_ds1_filter )
| ~ ( n0 @ ( n0 @ leq ) )
| ~ ( pv5 @ ( sk2 @ leq ) )
| ~ ( pv5 @ ( sk3 @ leq ) )
| ~ ( sk3 @ ( n0 @ leq ) )
| ( ( A @ ( pv5 @ sk15 ) )
!= ( A @ ( pv5 @ sk14 ) ) )
| ~ sk1 ),
inference(pattern_uni,[status(thm)],[1298:[]]) ).
thf(1556,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( n0 @ leq ) )
!= ( sk3 @ ( n0 @ leq ) ) )
| ( ( B @ ( n0 @ ( n0 @ ( A @ tptp_update3 ) ) ) )
!= q_ds1_filter )
| ~ ( n0 @ ( n0 @ leq ) )
| ~ ( pv5 @ ( sk2 @ leq ) )
| ~ ( pv5 @ ( sk3 @ leq ) )
| ~ $true
| ( ( A @ ( pv5 @ sk15 ) )
!= ( A @ ( pv5 @ sk14 ) ) )
| ~ sk1
| ~ sk1 ),
inference(paramod_ordered,[status(thm)],[652,1299]) ).
thf(1557,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( n0 @ leq ) )
!= ( sk3 @ ( n0 @ leq ) ) )
| ( ( B @ ( n0 @ ( n0 @ ( A @ tptp_update3 ) ) ) )
!= q_ds1_filter )
| ~ ( n0 @ ( n0 @ leq ) )
| ~ ( pv5 @ ( sk2 @ leq ) )
| ~ ( pv5 @ ( sk3 @ leq ) )
| ( ( A @ ( pv5 @ sk15 ) )
!= ( A @ ( pv5 @ sk14 ) ) )
| ~ sk1 ),
inference(simp,[status(thm)],[1556]) ).
thf(1558,plain,
! [B: $i,A: $i] :
( ( ( B @ ( n0 @ ( n0 @ ( A @ tptp_update3 ) ) ) )
!= q_ds1_filter )
| ~ ( n0 @ ( n0 @ leq ) )
| ~ ( pv5 @ ( sk2 @ leq ) )
| ~ ( pv5 @ ( sk3 @ leq ) )
| ( ( A @ ( pv5 @ sk15 ) )
!= ( A @ ( pv5 @ sk14 ) ) )
| ~ sk1 ),
inference(pattern_uni,[status(thm)],[1557:[]]) ).
thf(1839,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( n0 @ leq ) )
!= ( n0 @ ( n0 @ leq ) ) )
| ( ( B @ ( n0 @ ( n0 @ ( A @ tptp_update3 ) ) ) )
!= q_ds1_filter )
| ~ $true
| ~ ( pv5 @ ( sk2 @ leq ) )
| ~ ( pv5 @ ( sk3 @ leq ) )
| ( ( A @ ( pv5 @ sk15 ) )
!= ( A @ ( pv5 @ sk14 ) ) )
| ~ sk1
| ~ sk1 ),
inference(paramod_ordered,[status(thm)],[991,1558]) ).
thf(1840,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( n0 @ leq ) )
!= ( n0 @ ( n0 @ leq ) ) )
| ( ( B @ ( n0 @ ( n0 @ ( A @ tptp_update3 ) ) ) )
!= q_ds1_filter )
| ~ ( pv5 @ ( sk2 @ leq ) )
| ~ ( pv5 @ ( sk3 @ leq ) )
| ( ( A @ ( pv5 @ sk15 ) )
!= ( A @ ( pv5 @ sk14 ) ) )
| ~ sk1 ),
inference(simp,[status(thm)],[1839]) ).
thf(1913,plain,
! [B: $i,A: $i] :
( ( sk2 != n0 )
| ( n0 != n0 )
| ( ( B @ ( n0 @ ( n0 @ ( A @ tptp_update3 ) ) ) )
!= q_ds1_filter )
| ~ ( pv5 @ ( sk2 @ leq ) )
| ~ ( pv5 @ ( sk3 @ leq ) )
| ( ( A @ ( pv5 @ sk15 ) )
!= ( A @ ( pv5 @ sk14 ) ) )
| ~ sk1 ),
inference(simp,[status(thm)],[1840]) ).
thf(1934,plain,
! [B: $i,A: $i] :
( ( sk2 != n0 )
| ( ( B @ ( n0 @ ( n0 @ ( A @ tptp_update3 ) ) ) )
!= q_ds1_filter )
| ~ ( pv5 @ ( sk2 @ leq ) )
| ~ ( pv5 @ ( sk3 @ leq ) )
| ( ( A @ ( pv5 @ sk15 ) )
!= ( A @ ( pv5 @ sk14 ) ) )
| ~ sk1 ),
inference(simp,[status(thm)],[1913]) ).
thf(4662,plain,
! [B: $i,A: $i] :
( ( ( pv5 @ ( sk2 @ leq ) )
!= ( pv5 @ ( n0 @ leq ) ) )
| ( sk2 != n0 )
| ( ( B @ ( n0 @ ( n0 @ ( A @ tptp_update3 ) ) ) )
!= q_ds1_filter )
| ~ $true
| ~ ( pv5 @ ( sk3 @ leq ) )
| ( ( A @ ( pv5 @ sk15 ) )
!= ( A @ ( pv5 @ sk14 ) ) )
| ~ sk1 ),
inference(paramod_ordered,[status(thm)],[128,1934]) ).
thf(4663,plain,
! [B: $i,A: $i] :
( ( ( pv5 @ ( sk2 @ leq ) )
!= ( pv5 @ ( n0 @ leq ) ) )
| ( sk2 != n0 )
| ( ( B @ ( n0 @ ( n0 @ ( A @ tptp_update3 ) ) ) )
!= q_ds1_filter )
| ~ ( pv5 @ ( sk3 @ leq ) )
| ( ( A @ ( pv5 @ sk15 ) )
!= ( A @ ( pv5 @ sk14 ) ) )
| ~ sk1 ),
inference(simp,[status(thm)],[4662]) ).
thf(4732,plain,
! [B: $i,A: $i] :
( ( pv5 != pv5 )
| ( sk2 != n0 )
| ( sk2 != n0 )
| ( ( B @ ( n0 @ ( n0 @ ( A @ tptp_update3 ) ) ) )
!= q_ds1_filter )
| ~ ( pv5 @ ( sk3 @ leq ) )
| ( ( A @ ( pv5 @ sk15 ) )
!= ( A @ ( pv5 @ sk14 ) ) )
| ~ sk1 ),
inference(simp,[status(thm)],[4663]) ).
thf(4744,plain,
! [B: $i,A: $i] :
( ( sk2 != n0 )
| ( ( B @ ( n0 @ ( n0 @ ( A @ tptp_update3 ) ) ) )
!= q_ds1_filter )
| ~ ( pv5 @ ( sk3 @ leq ) )
| ( ( A @ ( pv5 @ sk15 ) )
!= ( A @ ( pv5 @ sk14 ) ) )
| ~ sk1 ),
inference(simp,[status(thm)],[4732]) ).
thf(5501,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( pv5 @ ( sk3 @ leq ) ) )
| ( sk2 != n0 )
| ( ( C @ ( n0 @ ( n0 @ ( B @ tptp_update3 ) ) ) )
!= q_ds1_filter )
| ~ $true
| ( ( B @ ( pv5 @ sk15 ) )
!= ( B @ ( pv5 @ sk14 ) ) )
| ~ sk1 ),
inference(paramod_ordered,[status(thm)],[595,4744]) ).
thf(5502,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( pv5 @ ( sk3 @ leq ) ) )
| ( sk2 != n0 )
| ( ( C @ ( n0 @ ( n0 @ ( B @ tptp_update3 ) ) ) )
!= q_ds1_filter )
| ( ( B @ ( pv5 @ sk15 ) )
!= ( B @ ( pv5 @ sk14 ) ) )
| ~ sk1 ),
inference(simp,[status(thm)],[5501]) ).
thf(5519,plain,
! [C: $i,B: $i,A: $i] :
( ( A != pv5 )
| ( A != sk3 )
| ( sk2 != n0 )
| ( ( C @ ( n0 @ ( n0 @ ( B @ tptp_update3 ) ) ) )
!= q_ds1_filter )
| ( ( B @ ( pv5 @ sk15 ) )
!= ( B @ ( pv5 @ sk14 ) ) )
| ~ sk1 ),
inference(simp,[status(thm)],[5502]) ).
thf(5526,plain,
! [B: $i,A: $i] :
( ( sk3 != pv5 )
| ( sk2 != n0 )
| ( ( B @ ( n0 @ ( n0 @ ( A @ tptp_update3 ) ) ) )
!= q_ds1_filter )
| ( ( A @ ( pv5 @ sk15 ) )
!= ( A @ ( pv5 @ sk14 ) ) )
| ~ sk1 ),
inference(simp,[status(thm)],[5519]) ).
thf(78,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ succ @ leq ) )
=> ( A @ ( B @ gt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_succ_gt) ).
thf(591,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ succ @ leq ) )
=> ( A @ ( B @ gt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(17396,plain,
! [B: $i,A: $i] :
( ( ( n0 @ ( n999 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[276,217]) ).
thf(17397,plain,
! [B: $i,A: $i] :
( ( ( n0 @ ( n999 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ leq ) ) ),
inference(simp,[status(thm)],[17396]) ).
thf(17398,plain,
n999 @ ( n0 @ leq ),
inference(pattern_uni,[status(thm)],[17397:[bind(A,$thf( n0 )),bind(B,$thf( n999 ))]]) ).
thf(117,plain,
( ~ sk1
| ( n1 @ ( n6 @ minus ) @ ( sk2 @ leq ) )
| ~ ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
| ~ ( pv5 @ ( n0 @ leq ) ) ),
inference(cnfConj,[status(thm)],[103]) ).
thf(1693,plain,
( ~ sk1
| ( n1 @ ( n6 @ minus ) @ ( sk2 @ leq ) )
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[117,128,107]) ).
thf(1694,plain,
( ~ sk1
| ( n1 @ ( n6 @ minus ) @ ( sk2 @ leq ) ) ),
inference(simp,[status(thm)],[1693]) ).
thf(8095,plain,
( ~ sk1
| ( n6 @ pred @ ( sk2 @ leq ) ) ),
inference(rewrite,[status(thm)],[1694,302]) ).
thf(5437,plain,
! [A: $i] :
( ( ( n5 @ succ )
!= ( A @ succ ) )
| ( ( n6 @ pred )
= A ) ),
inference(paramod_ordered,[status(thm)],[4132,185]) ).
thf(5438,plain,
( ( n6 @ pred )
= n5 ),
inference(pattern_uni,[status(thm)],[5437:[bind(A,$thf( n5 ))]]) ).
thf(8479,plain,
( ~ sk1
| ( n5 @ ( sk2 @ leq ) ) ),
inference(rewrite,[status(thm)],[8095,5438]) ).
thf(8,axiom,
! [A: $i] :
( ( n4 @ ( A @ plus ) )
= ( A @ succ @ succ @ succ @ succ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_plus_4_r) ).
thf(173,plain,
! [A: $i] :
( ( n4 @ ( A @ plus ) )
= ( A @ succ @ succ @ succ @ succ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(174,plain,
! [A: $i] :
( ( n4 @ ( A @ plus ) )
= ( A @ succ @ succ @ succ @ succ ) ),
inference(cnf,[status(esa)],[173]) ).
thf(175,plain,
! [A: $i] :
( ( n4 @ ( A @ plus ) )
= ( A @ succ @ succ @ succ @ succ ) ),
inference(lifteq,[status(thm)],[174]) ).
thf(9757,plain,
! [B: $i,A: $i] :
( ( ( n4 @ ( A @ plus ) )
!= ( B @ ( n2 @ plus ) ) )
| ( ( A @ succ @ succ @ succ @ succ )
= ( B @ succ @ succ ) ) ),
inference(paramod_ordered,[status(thm)],[175,191]) ).
thf(9758,plain,
( ( n2 @ succ @ succ @ succ @ succ )
= ( n4 @ succ @ succ ) ),
inference(pattern_uni,[status(thm)],[9757:[bind(A,$thf( n2 )),bind(B,$thf( n4 ))]]) ).
thf(9779,plain,
( ( n3 @ succ @ succ @ succ )
= ( n5 @ succ ) ),
inference(rewrite,[status(thm)],[9758,3872,3479]) ).
thf(3072,plain,
! [A: $i] :
( ( ( n0 @ ( n1 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[619,197]) ).
thf(3073,plain,
! [A: $i] :
( ( n0 @ ( n1 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[3072]) ).
thf(3074,plain,
! [A: $i] :
( ( n0 != A )
| ( n1 != A ) ),
inference(simp,[status(thm)],[3073]) ).
thf(3075,plain,
n1 != n0,
inference(simp,[status(thm)],[3074]) ).
thf(17408,plain,
! [B: $i,A: $i] :
( ( ( n3 @ ( n5 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[280,217]) ).
thf(17409,plain,
! [B: $i,A: $i] :
( ( ( n3 @ ( n5 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ leq ) ) ),
inference(simp,[status(thm)],[17408]) ).
thf(17410,plain,
n5 @ ( n3 @ leq ),
inference(pattern_uni,[status(thm)],[17409:[bind(A,$thf( n3 )),bind(B,$thf( n5 ))]]) ).
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(623,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(23,axiom,
! [A: $i] :
( ( n2 @ ( A @ plus ) )
= ( A @ succ @ succ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_plus_2_r) ).
thf(211,plain,
! [A: $i] :
( ( n2 @ ( A @ plus ) )
= ( A @ succ @ succ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(4,axiom,
tptp_minus_1 @ ( n2 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_2_tptp_minus_1) ).
thf(163,plain,
tptp_minus_1 @ ( n2 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(639,plain,
! [A: $i] :
( ( ( tptp_minus_1 @ ( n2 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[163,197]) ).
thf(640,plain,
! [A: $i] :
( ( tptp_minus_1 @ ( n2 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[639]) ).
thf(643,plain,
! [A: $i] :
( ( tptp_minus_1 != A )
| ( n2 != A ) ),
inference(simp,[status(thm)],[640]) ).
thf(646,plain,
tptp_minus_1 != n2,
inference(simp,[status(thm)],[643]) ).
thf(1825,plain,
! [A: $i] :
( ( ( n6 @ ( n999 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[240,197]) ).
thf(1826,plain,
! [A: $i] :
( ( n6 @ ( n999 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[1825]) ).
thf(1827,plain,
! [A: $i] :
( ( n6 != A )
| ( n999 != A ) ),
inference(simp,[status(thm)],[1826]) ).
thf(1828,plain,
n6 != n999,
inference(simp,[status(thm)],[1827]) ).
thf(37,axiom,
n1 @ ( n5 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_5_1) ).
thf(239,plain,
n1 @ ( n5 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(16905,plain,
! [B: $i,A: $i] :
( ( ( n1 @ ( n5 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[239,203]) ).
thf(16906,plain,
! [B: $i,A: $i] :
( ( ( n1 @ ( n5 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[16905]) ).
thf(16907,plain,
n5 @ ( n1 @ lt ),
inference(pattern_uni,[status(thm)],[16906:[bind(A,$thf( n1 )),bind(B,$thf( n5 ))]]) ).
thf(16824,plain,
! [B: $i,A: $i] :
( ( ( n0 @ ( n5 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[403,203]) ).
thf(16825,plain,
! [B: $i,A: $i] :
( ( ( n0 @ ( n5 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[16824]) ).
thf(16826,plain,
n5 @ ( n0 @ lt ),
inference(pattern_uni,[status(thm)],[16825:[bind(A,$thf( n0 )),bind(B,$thf( n5 ))]]) ).
thf(79,axiom,
n0 @ ( n2 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_2_0) ).
thf(593,plain,
n0 @ ( n2 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(17423,plain,
! [B: $i,A: $i] :
( ( ( n0 @ ( n2 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[593,217]) ).
thf(17424,plain,
! [B: $i,A: $i] :
( ( ( n0 @ ( n2 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ leq ) ) ),
inference(simp,[status(thm)],[17423]) ).
thf(17425,plain,
n2 @ ( n0 @ leq ),
inference(pattern_uni,[status(thm)],[17424:[bind(A,$thf( n0 )),bind(B,$thf( n2 ))]]) ).
thf(101,axiom,
n3 @ ( n999 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_999_3) ).
thf(634,plain,
n3 @ ( n999 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(82,axiom,
n0 @ ( n4 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_4_0) ).
thf(599,plain,
n0 @ ( n4 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(17468,plain,
! [B: $i,A: $i] :
( ( ( n0 @ ( n4 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[599,217]) ).
thf(17469,plain,
! [B: $i,A: $i] :
( ( ( n0 @ ( n4 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ leq ) ) ),
inference(simp,[status(thm)],[17468]) ).
thf(17470,plain,
n4 @ ( n0 @ leq ),
inference(pattern_uni,[status(thm)],[17469:[bind(A,$thf( n0 )),bind(B,$thf( n4 ))]]) ).
thf(20,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(205,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ gt ) )
& ( B @ ( A @ gt ) ) )
=> ( C @ ( A @ gt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(206,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ gt ) )
| ~ ( C @ ( B @ gt ) )
| ~ ( B @ ( A @ gt ) ) ),
inference(cnf,[status(esa)],[205]) ).
thf(3883,plain,
( ( ( n1 @ succ )
!= ( n1 @ succ ) )
| ( ( n2 @ succ @ succ @ succ )
= n5 ) ),
inference(paramod_ordered,[status(thm)],[3315,3858]) ).
thf(3884,plain,
( ( n2 @ succ @ succ @ succ )
= n5 ),
inference(pattern_uni,[status(thm)],[3883:[]]) ).
thf(3986,plain,
( ( n3 @ succ @ succ )
= n5 ),
inference(rewrite,[status(thm)],[3884,3479]) ).
thf(41,axiom,
! [A: $i] :
( ( A @ ( tptp_minus_1 @ ( n0 @ sum ) ) )
= n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_plus_base) ).
thf(243,plain,
! [A: $i] :
( ( A @ ( tptp_minus_1 @ ( n0 @ sum ) ) )
= n0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(1402,plain,
! [A: $i] :
( ( ( tptp_minus_1 @ ( n6 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[224,197]) ).
thf(1403,plain,
! [A: $i] :
( ( tptp_minus_1 @ ( n6 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[1402]) ).
thf(1404,plain,
! [A: $i] :
( ( tptp_minus_1 != A )
| ( n6 != A ) ),
inference(simp,[status(thm)],[1403]) ).
thf(1405,plain,
tptp_minus_1 != n6,
inference(simp,[status(thm)],[1404]) ).
thf(33,axiom,
! [A: $i] :
( ( ( n6 @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A = n6 )
| ( A = n5 )
| ( A = n4 )
| ( A = n3 )
| ( A = n2 )
| ( A = n1 )
| ( A = n0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',finite_domain_6) ).
thf(233,plain,
! [A: $i] :
( ( ( n6 @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A = n6 )
| ( A = n5 )
| ( A = n4 )
| ( A = n3 )
| ( A = n2 )
| ( A = n1 )
| ( A = n0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(469,plain,
! [A: $i] :
( tptp_float_0_0
= ( A @ ( tptp_minus_1 @ ( n0 @ sum ) ) ) ),
inference(cnf,[status(esa)],[468]) ).
thf(470,plain,
! [A: $i] :
( ( A @ ( tptp_minus_1 @ ( n0 @ sum ) ) )
= tptp_float_0_0 ),
inference(lifteq,[status(thm)],[469]) ).
thf(244,plain,
! [A: $i] :
( ( A @ ( tptp_minus_1 @ ( n0 @ sum ) ) )
= n0 ),
inference(cnf,[status(esa)],[243]) ).
thf(245,plain,
! [A: $i] :
( ( A @ ( tptp_minus_1 @ ( n0 @ sum ) ) )
= n0 ),
inference(lifteq,[status(thm)],[244]) ).
thf(4893,plain,
tptp_float_0_0 = n0,
inference(rewrite,[status(thm)],[470,245]) ).
thf(4885,plain,
( ( sk9 != sk8 )
| ( n0 != n0 )
| ( sk8 @ ( n0 @ leq ) )
| sk4
| sk1 ),
inference(simp,[status(thm)],[4883]) ).
thf(4888,plain,
( ( sk9 != sk8 )
| ( sk8 @ ( n0 @ leq ) )
| sk4
| sk1 ),
inference(simp,[status(thm)],[4885]) ).
thf(201,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ gt ) )
| ~ ( B @ ( A @ lt ) ) ),
inference(cnfConj,[status(thm)],[200]) ).
thf(63,axiom,
n0 @ ( n3 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_3_0) ).
thf(471,plain,
n0 @ ( n3 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(16827,plain,
! [B: $i,A: $i] :
( ( ( n0 @ ( n3 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[471,203]) ).
thf(16828,plain,
! [B: $i,A: $i] :
( ( ( n0 @ ( n3 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[16827]) ).
thf(16829,plain,
n3 @ ( n0 @ lt ),
inference(pattern_uni,[status(thm)],[16828:[bind(A,$thf( n0 )),bind(B,$thf( n3 ))]]) ).
thf(114,plain,
( ( sk9 @ ( n0 @ leq ) )
| ( sk7 @ ( n0 @ leq ) )
| sk4
| sk1
| ~ ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
| ~ ( pv5 @ ( n0 @ leq ) ) ),
inference(cnfConj,[status(thm)],[103]) ).
thf(1767,plain,
( ( sk9 @ ( n0 @ leq ) )
| ( sk7 @ ( n0 @ leq ) )
| sk4
| sk1
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[114,128,107]) ).
thf(1768,plain,
( ( sk9 @ ( n0 @ leq ) )
| ( sk7 @ ( n0 @ leq ) )
| sk4
| sk1 ),
inference(simp,[status(thm)],[1767]) ).
thf(83,axiom,
n2 @ ( n999 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_999_2) ).
thf(600,plain,
n2 @ ( n999 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(2702,plain,
! [A: $i] :
( ( ( n2 @ ( n999 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[600,197]) ).
thf(2703,plain,
! [A: $i] :
( ( n2 @ ( n999 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[2702]) ).
thf(2704,plain,
! [A: $i] :
( ( n2 != A )
| ( n999 != A ) ),
inference(simp,[status(thm)],[2703]) ).
thf(2705,plain,
n2 != n999,
inference(simp,[status(thm)],[2704]) ).
thf(43,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(250,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)],[43]) ).
thf(251,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 ) ) ) ) )
=> ! [C: $i,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(miniscope,[status(thm)],[250]) ).
thf(252,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( ( F @ ( E @ ( A @ trans @ ( B @ tptp_mmul ) @ ( A @ tptp_mmul ) @ a_select3 ) ) )
= ( E @ ( F @ ( A @ trans @ ( B @ tptp_mmul ) @ ( A @ tptp_mmul ) @ a_select3 ) ) ) )
| ~ ( D @ ( F @ leq ) )
| ~ ( F @ ( n0 @ leq ) )
| ~ ( D @ ( E @ leq ) )
| ~ ( E @ ( n0 @ leq ) )
| ( ( A @ ( B @ ( C @ sk13 ) ) @ ( A @ ( B @ ( C @ sk12 ) ) @ ( B @ a_select3 ) ) )
!= ( A @ ( B @ ( C @ sk12 ) ) @ ( A @ ( B @ ( C @ sk13 ) ) @ ( B @ a_select3 ) ) ) ) )
& ( ( ( F @ ( E @ ( A @ trans @ ( B @ tptp_mmul ) @ ( A @ tptp_mmul ) @ a_select3 ) ) )
= ( E @ ( F @ ( A @ trans @ ( B @ tptp_mmul ) @ ( A @ tptp_mmul ) @ a_select3 ) ) ) )
| ~ ( D @ ( F @ leq ) )
| ~ ( F @ ( n0 @ leq ) )
| ~ ( D @ ( E @ leq ) )
| ~ ( E @ ( n0 @ leq ) )
| ( C @ ( A @ ( B @ ( C @ sk13 ) ) @ 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 ) ) ) )
| ~ ( D @ ( F @ leq ) )
| ~ ( F @ ( n0 @ leq ) )
| ~ ( D @ ( E @ leq ) )
| ~ ( E @ ( n0 @ leq ) )
| ( A @ ( B @ ( C @ sk13 ) ) @ ( 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 ) ) ) )
| ~ ( D @ ( F @ leq ) )
| ~ ( F @ ( n0 @ leq ) )
| ~ ( D @ ( E @ leq ) )
| ~ ( E @ ( n0 @ leq ) )
| ( C @ ( A @ ( B @ ( C @ sk12 ) ) @ 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 ) ) ) )
| ~ ( D @ ( F @ leq ) )
| ~ ( F @ ( n0 @ leq ) )
| ~ ( D @ ( E @ leq ) )
| ~ ( E @ ( n0 @ leq ) )
| ( A @ ( B @ ( C @ sk12 ) ) @ ( n0 @ leq ) ) ) ),
inference(cnf,[status(esa)],[251]) ).
thf(256,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F @ ( E @ ( A @ trans @ ( B @ tptp_mmul ) @ ( A @ tptp_mmul ) @ a_select3 ) ) )
= ( E @ ( F @ ( A @ trans @ ( B @ tptp_mmul ) @ ( A @ tptp_mmul ) @ a_select3 ) ) ) )
| ~ ( D @ ( F @ leq ) )
| ~ ( F @ ( n0 @ leq ) )
| ~ ( D @ ( E @ leq ) )
| ~ ( E @ ( n0 @ leq ) )
| ( A @ ( B @ ( C @ sk13 ) ) @ ( n0 @ leq ) ) ),
inference(cnfConj,[status(thm)],[252]) ).
thf(260,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( F @ leq ) )
| ~ ( F @ ( n0 @ leq ) )
| ~ ( D @ ( E @ leq ) )
| ~ ( E @ ( n0 @ leq ) )
| ( A @ ( B @ ( C @ sk13 ) ) @ ( 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(lifteq,[status(thm)],[256]) ).
thf(5682,plain,
( ( ( sk10 @ ( sk9 @ ( id_ds1_filter @ a_select3 ) ) )
!= ( sk8 @ ( sk7 @ ( pminus_ds1_filter @ a_select3 ) ) ) )
| ( ( sk9 @ ( sk10 @ ( id_ds1_filter @ a_select3 ) ) )
!= ( sk7 @ ( sk8 @ ( pminus_ds1_filter @ a_select3 ) ) ) )
| sk4
| sk1
| ( ( sk7 @ ( sk8 @ ( pminus_ds1_filter @ a_select3 ) ) )
!= ( sk8 @ ( sk7 @ ( pminus_ds1_filter @ a_select3 ) ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[5674]) ).
thf(5742,plain,
( ( sk10 != sk8 )
| ( sk9 != sk7 )
| ( id_ds1_filter != pminus_ds1_filter )
| ( sk9 != sk7 )
| ( sk10 != sk8 )
| ( id_ds1_filter != pminus_ds1_filter )
| ( sk8 != sk7 )
| ( sk8 != sk7 )
| ( pminus_ds1_filter != pminus_ds1_filter )
| sk4
| sk1 ),
inference(simp,[status(thm)],[5682]) ).
thf(5815,plain,
( ( sk9 != sk7 )
| ( sk10 != sk8 )
| ( id_ds1_filter != pminus_ds1_filter )
| ( sk8 != sk7 )
| sk4
| sk1 ),
inference(simp,[status(thm)],[5742]) ).
thf(17465,plain,
! [B: $i,A: $i] :
( ( ( n1 @ ( n3 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[219,217]) ).
thf(17466,plain,
! [B: $i,A: $i] :
( ( ( n1 @ ( n3 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ leq ) ) ),
inference(simp,[status(thm)],[17465]) ).
thf(17467,plain,
n3 @ ( n1 @ leq ),
inference(pattern_uni,[status(thm)],[17466:[bind(A,$thf( n1 )),bind(B,$thf( n3 ))]]) ).
thf(81,axiom,
! [A: $i] :
( ( A @ ( n1 @ plus ) )
= ( A @ succ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_plus_1_l) ).
thf(596,plain,
! [A: $i] :
( ( A @ ( n1 @ plus ) )
= ( A @ succ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(597,plain,
! [A: $i] :
( ( A @ ( n1 @ plus ) )
= ( A @ succ ) ),
inference(cnf,[status(esa)],[596]) ).
thf(598,plain,
! [A: $i] :
( ( A @ ( n1 @ plus ) )
= ( A @ succ ) ),
inference(lifteq,[status(thm)],[597]) ).
thf(3,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(160,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( B @ ( A @ tptp_update2 ) ) @ a_select2 ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(16,axiom,
! [A: $i] :
( ( A @ ( n5 @ plus ) )
= ( A @ succ @ succ @ succ @ succ @ succ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_plus_5_l) ).
thf(192,plain,
! [A: $i] :
( ( A @ ( n5 @ plus ) )
= ( A @ succ @ succ @ succ @ succ @ succ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(59,axiom,
! [A: $i,B: $i] :
( ( B @ pred @ ( A @ leq ) )
<=> ( A @ ( B @ gt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_gt_pred) ).
thf(407,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)],[59]) ).
thf(16863,plain,
! [B: $i,A: $i] :
( ( ( n0 @ ( n4 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[599,203]) ).
thf(16864,plain,
! [B: $i,A: $i] :
( ( ( n0 @ ( n4 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[16863]) ).
thf(16865,plain,
n4 @ ( n0 @ lt ),
inference(pattern_uni,[status(thm)],[16864:[bind(A,$thf( n0 )),bind(B,$thf( n4 ))]]) ).
thf(1821,plain,
! [A: $i] :
( ( ( n1 @ ( n5 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[239,197]) ).
thf(1822,plain,
! [A: $i] :
( ( n1 @ ( n5 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[1821]) ).
thf(1823,plain,
! [A: $i] :
( ( n1 != A )
| ( n5 != A ) ),
inference(simp,[status(thm)],[1822]) ).
thf(1824,plain,
n5 != n1,
inference(simp,[status(thm)],[1823]) ).
thf(104,plain,
( ( ( sk10 @ ( sk9 @ ( id_ds1_filter @ a_select3 ) ) )
!= ( sk9 @ ( sk10 @ ( id_ds1_filter @ a_select3 ) ) ) )
| ( sk7 @ ( n0 @ leq ) )
| sk4
| sk1
| ~ ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
| ~ ( pv5 @ ( n0 @ leq ) ) ),
inference(cnfConj,[status(thm)],[103]) ).
thf(149,plain,
( ( sk7 @ ( n0 @ leq ) )
| sk4
| sk1
| ~ ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
| ~ ( pv5 @ ( n0 @ leq ) )
| ( ( sk9 @ ( sk10 @ ( id_ds1_filter @ a_select3 ) ) )
!= ( sk10 @ ( sk9 @ ( id_ds1_filter @ a_select3 ) ) ) ) ),
inference(lifteq,[status(thm)],[104]) ).
thf(8018,plain,
( ( sk7 @ ( n0 @ leq ) )
| sk4
| sk1
| ~ $true
| ~ $true
| ( ( sk9 @ ( sk10 @ ( id_ds1_filter @ a_select3 ) ) )
!= ( sk10 @ ( sk9 @ ( id_ds1_filter @ a_select3 ) ) ) ) ),
inference(rewrite,[status(thm)],[149,128,107]) ).
thf(8019,plain,
( ( sk7 @ ( n0 @ leq ) )
| sk4
| sk1
| ( ( sk9 @ ( sk10 @ ( id_ds1_filter @ a_select3 ) ) )
!= ( sk10 @ ( sk9 @ ( id_ds1_filter @ a_select3 ) ) ) ) ),
inference(simp,[status(thm)],[8018]) ).
thf(8020,plain,
( ( sk10 != sk9 )
| ( sk10 != sk9 )
| ( id_ds1_filter != id_ds1_filter )
| ( sk7 @ ( n0 @ leq ) )
| sk4
| sk1 ),
inference(simp,[status(thm)],[8019]) ).
thf(8058,plain,
( ( sk10 != sk9 )
| ( sk7 @ ( n0 @ leq ) )
| sk4
| sk1 ),
inference(simp,[status(thm)],[8020]) ).
thf(3311,plain,
! [A: $i] :
( ( ( n3 @ ( n999 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[634,197]) ).
thf(3312,plain,
! [A: $i] :
( ( n3 @ ( n999 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[3311]) ).
thf(3313,plain,
! [A: $i] :
( ( n3 != A )
| ( n999 != A ) ),
inference(simp,[status(thm)],[3312]) ).
thf(3314,plain,
n3 != n999,
inference(simp,[status(thm)],[3313]) ).
thf(16914,plain,
! [B: $i,A: $i] :
( ( ( tptp_minus_1 @ ( n2 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[163,203]) ).
thf(16915,plain,
! [B: $i,A: $i] :
( ( ( tptp_minus_1 @ ( n2 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[16914]) ).
thf(16916,plain,
n2 @ ( tptp_minus_1 @ lt ),
inference(pattern_uni,[status(thm)],[16915:[bind(A,$thf( tptp_minus_1 )),bind(B,$thf( n2 ))]]) ).
thf(105,plain,
( ( n1 @ ( n6 @ minus ) @ ( sk10 @ leq ) )
| ( n1 @ ( n6 @ minus ) @ ( sk7 @ leq ) )
| sk4
| sk1
| ~ ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
| ~ ( pv5 @ ( n0 @ leq ) ) ),
inference(cnfConj,[status(thm)],[103]) ).
thf(653,plain,
( ( n1 @ ( n6 @ minus ) @ ( sk10 @ leq ) )
| ( n1 @ ( n6 @ minus ) @ ( sk7 @ leq ) )
| sk4
| sk1
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[105,128,107]) ).
thf(654,plain,
( ( n1 @ ( n6 @ minus ) @ ( sk10 @ leq ) )
| ( n1 @ ( n6 @ minus ) @ ( sk7 @ leq ) )
| sk4
| sk1 ),
inference(simp,[status(thm)],[653]) ).
thf(655,plain,
( ~ $true
| ( ( n1 @ ( n6 @ minus ) @ ( sk10 @ leq ) )
!= ( n1 @ ( n6 @ minus ) @ ( sk7 @ leq ) ) )
| ( n1 @ ( n6 @ minus ) @ ( sk7 @ leq ) )
| sk4
| sk1 ),
inference(eqfactor_ordered,[status(thm)],[654]) ).
thf(657,plain,
( ( ( n1 @ ( n6 @ minus ) )
!= ( n1 @ ( n6 @ minus ) ) )
| ( sk10 != sk7 )
| ( n1 @ ( n6 @ minus ) @ ( sk7 @ leq ) )
| sk4
| sk1 ),
inference(simp,[status(thm)],[655]) ).
thf(658,plain,
( ( sk10 != sk7 )
| ( n1 @ ( n6 @ minus ) @ ( sk7 @ leq ) )
| sk4
| sk1 ),
inference(simp,[status(thm)],[657]) ).
thf(8096,plain,
( ( sk10 != sk7 )
| ( n6 @ pred @ ( sk7 @ leq ) )
| sk4
| sk1 ),
inference(rewrite,[status(thm)],[658,302]) ).
thf(11532,plain,
( ( sk10 != sk7 )
| ( n5 @ ( sk7 @ leq ) )
| sk4
| sk1 ),
inference(rewrite,[status(thm)],[8096,5438]) ).
thf(133,plain,
( ~ sk4
| ( sk5 @ ( n0 @ leq ) )
| sk1
| ~ ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
| ~ ( pv5 @ ( n0 @ leq ) ) ),
inference(cnfConj,[status(thm)],[103]) ).
thf(1406,plain,
( ~ sk4
| ( sk5 @ ( n0 @ leq ) )
| sk1
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[133,128,107]) ).
thf(1407,plain,
( ~ sk4
| ( sk5 @ ( n0 @ leq ) )
| sk1 ),
inference(simp,[status(thm)],[1406]) ).
thf(12,axiom,
n2 @ ( n4 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_4_2) ).
thf(182,plain,
n2 @ ( n4 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(647,plain,
! [A: $i] :
( ( ( n2 @ ( n4 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[182,197]) ).
thf(648,plain,
! [A: $i] :
( ( n2 @ ( n4 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[647]) ).
thf(649,plain,
! [A: $i] :
( ( n2 != A )
| ( n4 != A ) ),
inference(simp,[status(thm)],[648]) ).
thf(650,plain,
n4 != n2,
inference(simp,[status(thm)],[649]) ).
thf(91,axiom,
tptp_minus_1 @ ( n3 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_3_tptp_minus_1) ).
thf(615,plain,
tptp_minus_1 @ ( n3 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(89,axiom,
n0 @ ( n6 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_6_0) ).
thf(611,plain,
n0 @ ( n6 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(16848,plain,
! [B: $i,A: $i] :
( ( ( n0 @ ( n6 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[611,203]) ).
thf(16849,plain,
! [B: $i,A: $i] :
( ( ( n0 @ ( n6 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[16848]) ).
thf(16850,plain,
n6 @ ( n0 @ lt ),
inference(pattern_uni,[status(thm)],[16849:[bind(A,$thf( n0 )),bind(B,$thf( n6 ))]]) ).
thf(120,plain,
( ( n1 @ ( n0 @ minus ) @ ( sk9 @ leq ) )
| ( ( sk8 @ ( sk7 @ ( pminus_ds1_filter @ a_select3 ) ) )
!= ( sk7 @ ( sk8 @ ( pminus_ds1_filter @ a_select3 ) ) ) )
| sk4
| sk1
| ~ ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
| ~ ( pv5 @ ( n0 @ leq ) ) ),
inference(cnfConj,[status(thm)],[103]) ).
thf(150,plain,
( ( n1 @ ( n0 @ minus ) @ ( sk9 @ leq ) )
| sk4
| sk1
| ~ ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
| ~ ( pv5 @ ( n0 @ leq ) )
| ( ( sk7 @ ( sk8 @ ( pminus_ds1_filter @ a_select3 ) ) )
!= ( sk8 @ ( sk7 @ ( pminus_ds1_filter @ a_select3 ) ) ) ) ),
inference(lifteq,[status(thm)],[120]) ).
thf(8566,plain,
( ( n0 @ pred @ ( sk9 @ leq ) )
| sk4
| sk1
| ~ ( n999 @ pred @ ( pv5 @ leq ) )
| ~ $true
| ( ( sk7 @ ( sk8 @ ( pminus_ds1_filter @ a_select3 ) ) )
!= ( sk8 @ ( sk7 @ ( pminus_ds1_filter @ a_select3 ) ) ) ) ),
inference(rewrite,[status(thm)],[150,128,302]) ).
thf(8567,plain,
( ( n0 @ pred @ ( sk9 @ leq ) )
| sk4
| sk1
| ~ ( n999 @ pred @ ( pv5 @ leq ) )
| ( ( sk7 @ ( sk8 @ ( pminus_ds1_filter @ a_select3 ) ) )
!= ( sk8 @ ( sk7 @ ( pminus_ds1_filter @ a_select3 ) ) ) ) ),
inference(simp,[status(thm)],[8566]) ).
thf(27,axiom,
n2 @ ( n6 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_6_2) ).
thf(218,plain,
n2 @ ( n6 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(986,plain,
! [A: $i] :
( ( ( n2 @ ( n6 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[218,197]) ).
thf(987,plain,
! [A: $i] :
( ( n2 @ ( n6 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[986]) ).
thf(988,plain,
! [A: $i] :
( ( n2 != A )
| ( n6 != A ) ),
inference(simp,[status(thm)],[987]) ).
thf(989,plain,
n2 != n6,
inference(simp,[status(thm)],[988]) ).
thf(8305,plain,
( ( ( n2 @ ( sk3 @ leq ) )
!= ( sk2 @ ( n0 @ leq ) ) )
| ( sk2 != n2 )
| ( r_ds1_filter != q_ds1_filter )
| ~ $true
| ~ sk1
| ~ sk1 ),
inference(paramod_ordered,[status(thm)],[991,8276]) ).
thf(8306,plain,
( ( ( n2 @ ( sk3 @ leq ) )
!= ( sk2 @ ( n0 @ leq ) ) )
| ( sk2 != n2 )
| ( r_ds1_filter != q_ds1_filter )
| ~ sk1 ),
inference(simp,[status(thm)],[8305]) ).
thf(8309,plain,
( ( sk2 != n2 )
| ( sk3 != n0 )
| ( sk2 != n2 )
| ( r_ds1_filter != q_ds1_filter )
| ~ sk1 ),
inference(simp,[status(thm)],[8306]) ).
thf(8314,plain,
( ( sk3 != n0 )
| ( sk2 != n2 )
| ( r_ds1_filter != q_ds1_filter )
| ~ sk1 ),
inference(simp,[status(thm)],[8309]) ).
thf(16908,plain,
! [B: $i,A: $i] :
( ( ( n1 @ ( n999 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[242,203]) ).
thf(16909,plain,
! [B: $i,A: $i] :
( ( ( n1 @ ( n999 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[16908]) ).
thf(16910,plain,
n999 @ ( n1 @ lt ),
inference(pattern_uni,[status(thm)],[16909:[bind(A,$thf( n1 )),bind(B,$thf( n999 ))]]) ).
thf(112,plain,
( ~ sk4
| ( sk6 @ ( n0 @ leq ) )
| sk1
| ~ ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
| ~ ( pv5 @ ( n0 @ leq ) ) ),
inference(cnfConj,[status(thm)],[103]) ).
thf(1016,plain,
( ~ sk4
| ( sk6 @ ( n0 @ leq ) )
| sk1
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[112,128,107]) ).
thf(1017,plain,
( ~ sk4
| ( sk6 @ ( n0 @ leq ) )
| sk1 ),
inference(simp,[status(thm)],[1016]) ).
thf(124,plain,
( ( sk10 @ ( n0 @ leq ) )
| ( sk8 @ ( n0 @ leq ) )
| sk4
| sk1
| ~ ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
| ~ ( pv5 @ ( n0 @ leq ) ) ),
inference(cnfConj,[status(thm)],[103]) ).
thf(2636,plain,
( ( sk10 @ ( n0 @ leq ) )
| ( sk8 @ ( n0 @ leq ) )
| sk4
| sk1
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[124,128,107]) ).
thf(2637,plain,
( ( sk10 @ ( n0 @ leq ) )
| ( sk8 @ ( n0 @ leq ) )
| sk4
| sk1 ),
inference(simp,[status(thm)],[2636]) ).
thf(2684,plain,
( ~ $true
| ( ( sk10 @ ( n0 @ leq ) )
!= ( sk8 @ ( n0 @ leq ) ) )
| ( sk8 @ ( n0 @ leq ) )
| sk4
| sk1 ),
inference(eqfactor_ordered,[status(thm)],[2637]) ).
thf(2685,plain,
( ( ( sk10 @ ( n0 @ leq ) )
!= ( sk8 @ ( n0 @ leq ) ) )
| ( sk8 @ ( n0 @ leq ) )
| sk4
| sk1 ),
inference(simp,[status(thm)],[2684]) ).
thf(2686,plain,
( ( sk10 != sk8 )
| ( n0 != n0 )
| ( sk8 @ ( n0 @ leq ) )
| sk4
| sk1 ),
inference(simp,[status(thm)],[2684]) ).
thf(2692,plain,
( ( sk10 != sk8 )
| ( sk8 @ ( n0 @ leq ) )
| sk4
| sk1 ),
inference(simp,[status(thm)],[2686]) ).
thf(16803,plain,
! [B: $i,A: $i] :
( ( ( tptp_minus_1 @ ( n999 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[238,203]) ).
thf(16804,plain,
! [B: $i,A: $i] :
( ( ( tptp_minus_1 @ ( n999 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[16803]) ).
thf(16805,plain,
n999 @ ( tptp_minus_1 @ lt ),
inference(pattern_uni,[status(thm)],[16804:[bind(A,$thf( tptp_minus_1 )),bind(B,$thf( n999 ))]]) ).
thf(85,axiom,
n5 @ ( n999 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_999_5) ).
thf(603,plain,
n5 @ ( n999 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(2874,plain,
! [A: $i] :
( ( ( n5 @ ( n999 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[603,197]) ).
thf(2875,plain,
! [A: $i] :
( ( n5 @ ( n999 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[2874]) ).
thf(2876,plain,
! [A: $i] :
( ( n5 != A )
| ( n999 != A ) ),
inference(simp,[status(thm)],[2875]) ).
thf(2877,plain,
n5 != n999,
inference(simp,[status(thm)],[2876]) ).
thf(16845,plain,
! [B: $i,A: $i] :
( ( ( tptp_minus_1 @ ( n4 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[204,203]) ).
thf(16846,plain,
! [B: $i,A: $i] :
( ( ( tptp_minus_1 @ ( n4 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[16845]) ).
thf(16847,plain,
n4 @ ( tptp_minus_1 @ lt ),
inference(pattern_uni,[status(thm)],[16846:[bind(A,$thf( tptp_minus_1 )),bind(B,$thf( n4 ))]]) ).
thf(32,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(225,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)],[32]) ).
thf(2169,plain,
! [A: $i] :
( ( ( n3 @ ( n5 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[280,197]) ).
thf(2170,plain,
! [A: $i] :
( ( n3 @ ( n5 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[2169]) ).
thf(2171,plain,
! [A: $i] :
( ( n3 != A )
| ( n5 != A ) ),
inference(simp,[status(thm)],[2170]) ).
thf(2172,plain,
n5 != n3,
inference(simp,[status(thm)],[2171]) ).
thf(676,plain,
! [A: $i] :
( ( ( n2 @ ( n3 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[214,197]) ).
thf(677,plain,
! [A: $i] :
( ( n2 @ ( n3 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[676]) ).
thf(678,plain,
! [A: $i] :
( ( n2 != A )
| ( n3 != A ) ),
inference(simp,[status(thm)],[677]) ).
thf(679,plain,
n2 != n3,
inference(simp,[status(thm)],[678]) ).
thf(98,axiom,
n5 @ ( n6 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_6_5) ).
thf(627,plain,
n5 @ ( n6 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(16887,plain,
! [B: $i,A: $i] :
( ( ( n5 @ ( n6 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[627,203]) ).
thf(16888,plain,
! [B: $i,A: $i] :
( ( ( n5 @ ( n6 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[16887]) ).
thf(16889,plain,
n6 @ ( n5 @ lt ),
inference(pattern_uni,[status(thm)],[16888:[bind(A,$thf( n5 )),bind(B,$thf( n6 ))]]) ).
thf(1536,plain,
! [A: $i] :
( ( ( n1 @ ( n6 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[237,197]) ).
thf(1537,plain,
! [A: $i] :
( ( n1 @ ( n6 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[1536]) ).
thf(1538,plain,
! [A: $i] :
( ( n1 != A )
| ( n6 != A ) ),
inference(simp,[status(thm)],[1537]) ).
thf(1539,plain,
n6 != n1,
inference(simp,[status(thm)],[1538]) ).
thf(143,plain,
( ( ( sk10 @ ( sk9 @ ( id_ds1_filter @ a_select3 ) ) )
!= ( sk9 @ ( sk10 @ ( id_ds1_filter @ a_select3 ) ) ) )
| ( n1 @ ( n6 @ minus ) @ ( sk7 @ leq ) )
| sk4
| sk1
| ~ ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
| ~ ( pv5 @ ( n0 @ leq ) ) ),
inference(cnfConj,[status(thm)],[103]) ).
thf(148,plain,
( ( n1 @ ( n6 @ minus ) @ ( sk7 @ leq ) )
| sk4
| sk1
| ~ ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
| ~ ( pv5 @ ( n0 @ leq ) )
| ( ( sk9 @ ( sk10 @ ( id_ds1_filter @ a_select3 ) ) )
!= ( sk10 @ ( sk9 @ ( id_ds1_filter @ a_select3 ) ) ) ) ),
inference(lifteq,[status(thm)],[143]) ).
thf(7507,plain,
( ( n1 @ ( n6 @ minus ) @ ( sk7 @ leq ) )
| sk4
| sk1
| ~ $true
| ~ $true
| ( ( sk9 @ ( sk10 @ ( id_ds1_filter @ a_select3 ) ) )
!= ( sk10 @ ( sk9 @ ( id_ds1_filter @ a_select3 ) ) ) ) ),
inference(rewrite,[status(thm)],[148,128,107]) ).
thf(7508,plain,
( ( n1 @ ( n6 @ minus ) @ ( sk7 @ leq ) )
| sk4
| sk1
| ( ( sk9 @ ( sk10 @ ( id_ds1_filter @ a_select3 ) ) )
!= ( sk10 @ ( sk9 @ ( id_ds1_filter @ a_select3 ) ) ) ) ),
inference(simp,[status(thm)],[7507]) ).
thf(7509,plain,
( ( sk10 != sk9 )
| ( sk10 != sk9 )
| ( id_ds1_filter != id_ds1_filter )
| ( n1 @ ( n6 @ minus ) @ ( sk7 @ leq ) )
| sk4
| sk1 ),
inference(simp,[status(thm)],[7508]) ).
thf(7548,plain,
( ( sk10 != sk9 )
| ( n1 @ ( n6 @ minus ) @ ( sk7 @ leq ) )
| sk4
| sk1 ),
inference(simp,[status(thm)],[7509]) ).
thf(8105,plain,
( ( sk10 != sk9 )
| ( n6 @ pred @ ( sk7 @ leq ) )
| sk4
| sk1 ),
inference(rewrite,[status(thm)],[7548,302]) ).
thf(12191,plain,
( ( sk10 != sk9 )
| ( n5 @ ( sk7 @ leq ) )
| sk4
| sk1 ),
inference(rewrite,[status(thm)],[8105,5438]) ).
thf(8253,plain,
! [A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( n2 @ ( sk3 @ leq ) ) )
| ( r_ds1_filter != q_ds1_filter )
| ~ $true
| ~ ( n2 @ ( sk2 @ leq ) )
| ~ sk1 ),
inference(paramod_ordered,[status(thm)],[595,8202]) ).
thf(8254,plain,
! [A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( n2 @ ( sk3 @ leq ) ) )
| ( r_ds1_filter != q_ds1_filter )
| ~ ( n2 @ ( sk2 @ leq ) )
| ~ sk1 ),
inference(simp,[status(thm)],[8253]) ).
thf(8269,plain,
! [A: $i] :
( ( A != n2 )
| ( A != sk3 )
| ( r_ds1_filter != q_ds1_filter )
| ~ ( n2 @ ( sk2 @ leq ) )
| ~ sk1 ),
inference(simp,[status(thm)],[8254]) ).
thf(8277,plain,
( ( sk3 != n2 )
| ( r_ds1_filter != q_ds1_filter )
| ~ ( n2 @ ( sk2 @ leq ) )
| ~ sk1 ),
inference(simp,[status(thm)],[8269]) ).
thf(8972,plain,
( ( ( n2 @ ( sk2 @ leq ) )
!= ( sk3 @ ( n0 @ leq ) ) )
| ( sk3 != n2 )
| ( r_ds1_filter != q_ds1_filter )
| ~ $true
| ~ sk1
| ~ sk1 ),
inference(paramod_ordered,[status(thm)],[652,8277]) ).
thf(8973,plain,
( ( ( n2 @ ( sk2 @ leq ) )
!= ( sk3 @ ( n0 @ leq ) ) )
| ( sk3 != n2 )
| ( r_ds1_filter != q_ds1_filter )
| ~ sk1 ),
inference(simp,[status(thm)],[8972]) ).
thf(9013,plain,
( ( sk3 != n2 )
| ( sk2 != n0 )
| ( sk3 != n2 )
| ( r_ds1_filter != q_ds1_filter )
| ~ sk1 ),
inference(simp,[status(thm)],[8973]) ).
thf(9017,plain,
( ( sk2 != n0 )
| ( sk3 != n2 )
| ( r_ds1_filter != q_ds1_filter )
| ~ sk1 ),
inference(simp,[status(thm)],[9013]) ).
thf(2694,plain,
! [A: $i] :
( ( ( n0 @ ( n2 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[593,197]) ).
thf(2695,plain,
! [A: $i] :
( ( n0 @ ( n2 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[2694]) ).
thf(2696,plain,
! [A: $i] :
( ( n0 != A )
| ( n2 != A ) ),
inference(simp,[status(thm)],[2695]) ).
thf(2697,plain,
n2 != n0,
inference(simp,[status(thm)],[2696]) ).
thf(11998,plain,
! [A: $i] :
( ( ( n3 @ succ @ succ @ succ @ succ )
!= ( A @ succ ) )
| ( A @ ( n6 @ succ @ gt ) ) ),
inference(paramod_ordered,[status(thm)],[11939,180]) ).
thf(11999,plain,
n3 @ succ @ succ @ succ @ ( n6 @ succ @ gt ),
inference(pattern_uni,[status(thm)],[11998:[bind(A,$thf( n3 @ succ @ succ @ succ ))]]) ).
thf(15587,plain,
n5 @ succ @ ( n6 @ succ @ gt ),
inference(rewrite,[status(thm)],[11999,9779]) ).
thf(97,axiom,
n1 @ ( n4 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_4_1) ).
thf(626,plain,
n1 @ ( n4 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(3080,plain,
! [A: $i] :
( ( ( n1 @ ( n4 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[626,197]) ).
thf(3081,plain,
! [A: $i] :
( ( n1 @ ( n4 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[3080]) ).
thf(3082,plain,
! [A: $i] :
( ( n1 != A )
| ( n4 != A ) ),
inference(simp,[status(thm)],[3081]) ).
thf(3083,plain,
n4 != n1,
inference(simp,[status(thm)],[3082]) ).
thf(17417,plain,
! [B: $i,A: $i] :
( ( ( tptp_minus_1 @ ( n6 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[224,217]) ).
thf(17418,plain,
! [B: $i,A: $i] :
( ( ( tptp_minus_1 @ ( n6 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ leq ) ) ),
inference(simp,[status(thm)],[17417]) ).
thf(17419,plain,
n6 @ ( tptp_minus_1 @ leq ),
inference(pattern_uni,[status(thm)],[17418:[bind(A,$thf( tptp_minus_1 )),bind(B,$thf( n6 ))]]) ).
thf(1083,plain,
! [A: $i] :
( ( ( n1 @ ( n3 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[219,197]) ).
thf(1084,plain,
! [A: $i] :
( ( n1 @ ( n3 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[1083]) ).
thf(1085,plain,
! [A: $i] :
( ( n1 != A )
| ( n3 != A ) ),
inference(simp,[status(thm)],[1084]) ).
thf(1086,plain,
n3 != n1,
inference(simp,[status(thm)],[1085]) ).
thf(5433,plain,
! [A: $i] :
( ( ( n1 @ succ )
!= ( A @ succ ) )
| ( ( n2 @ pred )
= A ) ),
inference(paramod_ordered,[status(thm)],[3315,185]) ).
thf(5434,plain,
( ( n2 @ pred )
= n1 ),
inference(pattern_uni,[status(thm)],[5433:[bind(A,$thf( n1 ))]]) ).
thf(16884,plain,
! [B: $i,A: $i] :
( ( ( n2 @ ( n999 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[600,203]) ).
thf(16885,plain,
! [B: $i,A: $i] :
( ( ( n2 @ ( n999 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[16884]) ).
thf(16886,plain,
n999 @ ( n2 @ lt ),
inference(pattern_uni,[status(thm)],[16885:[bind(A,$thf( n2 )),bind(B,$thf( n999 ))]]) ).
thf(659,plain,
! [A: $i] :
( ( ( tptp_minus_1 @ ( n4 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[204,197]) ).
thf(660,plain,
! [A: $i] :
( ( tptp_minus_1 @ ( n4 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[659]) ).
thf(661,plain,
! [A: $i] :
( ( tptp_minus_1 != A )
| ( n4 != A ) ),
inference(simp,[status(thm)],[660]) ).
thf(662,plain,
n4 != tptp_minus_1,
inference(simp,[status(thm)],[661]) ).
thf(75,axiom,
tptp_minus_1 @ ( n1 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_1_tptp_minus_1) ).
thf(575,plain,
tptp_minus_1 @ ( n1 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(16911,plain,
! [B: $i,A: $i] :
( ( ( tptp_minus_1 @ ( n1 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[575,203]) ).
thf(16912,plain,
! [B: $i,A: $i] :
( ( ( tptp_minus_1 @ ( n1 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[16911]) ).
thf(16913,plain,
n1 @ ( tptp_minus_1 @ lt ),
inference(pattern_uni,[status(thm)],[16912:[bind(A,$thf( tptp_minus_1 )),bind(B,$thf( n1 ))]]) ).
thf(92,axiom,
! [A: $i] :
( ( n3 @ ( A @ plus ) )
= ( A @ succ @ succ @ succ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_plus_3_r) ).
thf(616,plain,
! [A: $i] :
( ( n3 @ ( A @ plus ) )
= ( A @ succ @ succ @ succ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(617,plain,
! [A: $i] :
( ( n3 @ ( A @ plus ) )
= ( A @ succ @ succ @ succ ) ),
inference(cnf,[status(esa)],[616]) ).
thf(618,plain,
! [A: $i] :
( ( n3 @ ( A @ plus ) )
= ( A @ succ @ succ @ succ ) ),
inference(lifteq,[status(thm)],[617]) ).
thf(165,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( A @ ( B @ gt ) )
| ( B @ ( A @ gt ) ) ),
inference(cnf,[status(esa)],[164]) ).
thf(166,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ gt ) )
| ( B @ ( A @ gt ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[165]) ).
thf(94,axiom,
n4 @ ( n6 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_6_4) ).
thf(620,plain,
n4 @ ( n6 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(3076,plain,
! [A: $i] :
( ( ( n4 @ ( n6 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[620,197]) ).
thf(3077,plain,
! [A: $i] :
( ( n4 @ ( n6 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[3076]) ).
thf(3078,plain,
! [A: $i] :
( ( n4 != A )
| ( n6 != A ) ),
inference(simp,[status(thm)],[3077]) ).
thf(3079,plain,
n4 != n6,
inference(simp,[status(thm)],[3078]) ).
thf(46,axiom,
! [A: $i] :
( ( A @ ( n3 @ plus ) )
= ( A @ succ @ succ @ succ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_plus_3_l) ).
thf(277,plain,
! [A: $i] :
( ( A @ ( n3 @ plus ) )
= ( A @ succ @ succ @ succ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(278,plain,
! [A: $i] :
( ( A @ ( n3 @ plus ) )
= ( A @ succ @ succ @ succ ) ),
inference(cnf,[status(esa)],[277]) ).
thf(279,plain,
! [A: $i] :
( ( A @ ( n3 @ plus ) )
= ( A @ succ @ succ @ succ ) ),
inference(lifteq,[status(thm)],[278]) ).
thf(74,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( A @ minus ) @ leq ) )
=> ( B @ ( n0 @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_minus) ).
thf(573,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( A @ minus ) @ leq ) )
=> ( B @ ( n0 @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(5675,plain,
( ( ( sk9 @ ( sk10 @ ( id_ds1_filter @ a_select3 ) ) )
!= ( sk10 @ ( sk9 @ ( id_ds1_filter @ a_select3 ) ) ) )
| ( sk8 != sk7 )
| ( sk8 != sk7 )
| ( pminus_ds1_filter != pminus_ds1_filter )
| sk4
| sk1 ),
inference(simp,[status(thm)],[5674]) ).
thf(5758,plain,
( ( ( sk9 @ ( sk10 @ ( id_ds1_filter @ a_select3 ) ) )
!= ( sk10 @ ( sk9 @ ( id_ds1_filter @ a_select3 ) ) ) )
| ( sk8 != sk7 )
| sk4
| sk1 ),
inference(simp,[status(thm)],[5675]) ).
thf(77,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(579,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)],[77]) ).
thf(34,axiom,
n4 @ ( n999 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_999_4) ).
thf(236,plain,
n4 @ ( n999 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(1532,plain,
! [A: $i] :
( ( ( n4 @ ( n999 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[236,197]) ).
thf(1533,plain,
! [A: $i] :
( ( n4 @ ( n999 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[1532]) ).
thf(1534,plain,
! [A: $i] :
( ( n4 != A )
| ( n999 != A ) ),
inference(simp,[status(thm)],[1533]) ).
thf(1535,plain,
n4 != n999,
inference(simp,[status(thm)],[1534]) ).
thf(17420,plain,
! [B: $i,A: $i] :
( ( ( tptp_minus_1 @ ( n3 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[615,217]) ).
thf(17421,plain,
! [B: $i,A: $i] :
( ( ( tptp_minus_1 @ ( n3 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ leq ) ) ),
inference(simp,[status(thm)],[17420]) ).
thf(17422,plain,
n3 @ ( tptp_minus_1 @ leq ),
inference(pattern_uni,[status(thm)],[17421:[bind(A,$thf( tptp_minus_1 )),bind(B,$thf( n3 ))]]) ).
thf(253,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F @ ( E @ ( A @ trans @ ( B @ tptp_mmul ) @ ( A @ tptp_mmul ) @ a_select3 ) ) )
= ( E @ ( F @ ( A @ trans @ ( B @ tptp_mmul ) @ ( A @ tptp_mmul ) @ a_select3 ) ) ) )
| ~ ( D @ ( F @ leq ) )
| ~ ( F @ ( n0 @ leq ) )
| ~ ( D @ ( E @ leq ) )
| ~ ( E @ ( n0 @ leq ) )
| ( C @ ( A @ ( B @ ( C @ sk12 ) ) @ leq ) ) ),
inference(cnfConj,[status(thm)],[252]) ).
thf(259,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( F @ leq ) )
| ~ ( F @ ( n0 @ leq ) )
| ~ ( D @ ( E @ leq ) )
| ~ ( E @ ( n0 @ leq ) )
| ( C @ ( A @ ( B @ ( C @ sk12 ) ) @ 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(lifteq,[status(thm)],[253]) ).
thf(60,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(413,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)],[60]) ).
thf(12990,plain,
! [B: $i,A: $i] :
( ( A != sk3 )
| ~ sk1
| ( B != sk2 )
| ( A @ ( B @ gt ) )
| ( B @ ( A @ gt ) ) ),
inference(paramod_ordered,[status(thm)],[166,666]) ).
thf(12991,plain,
! [A: $i] :
( ~ sk1
| ( A != sk2 )
| ( sk3 @ ( A @ gt ) )
| ( A @ ( sk3 @ gt ) ) ),
inference(pattern_uni,[status(thm)],[12990:[bind(A,$thf( sk3 ))]]) ).
thf(15100,plain,
( ~ sk1
| ( sk3 @ ( sk2 @ gt ) )
| ( sk2 @ ( sk3 @ gt ) ) ),
inference(simp,[status(thm)],[12991]) ).
thf(132,plain,
( ( n1 @ ( n6 @ minus ) @ ( sk10 @ leq ) )
| ( n1 @ ( n6 @ minus ) @ ( sk8 @ leq ) )
| sk4
| sk1
| ~ ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
| ~ ( pv5 @ ( n0 @ leq ) ) ),
inference(cnfConj,[status(thm)],[103]) ).
thf(3230,plain,
( ( n1 @ ( n6 @ minus ) @ ( sk10 @ leq ) )
| ( n1 @ ( n6 @ minus ) @ ( sk8 @ leq ) )
| sk4
| sk1
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[132,128,107]) ).
thf(3231,plain,
( ( n1 @ ( n6 @ minus ) @ ( sk10 @ leq ) )
| ( n1 @ ( n6 @ minus ) @ ( sk8 @ leq ) )
| sk4
| sk1 ),
inference(simp,[status(thm)],[3230]) ).
thf(3282,plain,
( ~ $true
| ( ( n1 @ ( n6 @ minus ) @ ( sk10 @ leq ) )
!= ( n1 @ ( n6 @ minus ) @ ( sk8 @ leq ) ) )
| ( n1 @ ( n6 @ minus ) @ ( sk8 @ leq ) )
| sk4
| sk1 ),
inference(eqfactor_ordered,[status(thm)],[3231]) ).
thf(3290,plain,
( ( ( n1 @ ( n6 @ minus ) )
!= ( n1 @ ( n6 @ minus ) ) )
| ( sk10 != sk8 )
| ( n1 @ ( n6 @ minus ) @ ( sk8 @ leq ) )
| sk4
| sk1 ),
inference(simp,[status(thm)],[3282]) ).
thf(3303,plain,
( ( sk10 != sk8 )
| ( n1 @ ( n6 @ minus ) @ ( sk8 @ leq ) )
| sk4
| sk1 ),
inference(simp,[status(thm)],[3290]) ).
thf(8078,plain,
( ( sk10 != sk8 )
| ( n6 @ pred @ ( sk8 @ leq ) )
| sk4
| sk1 ),
inference(rewrite,[status(thm)],[3303,302]) ).
thf(11396,plain,
( ( sk10 != sk8 )
| ( n5 @ ( sk8 @ leq ) )
| sk4
| sk1 ),
inference(rewrite,[status(thm)],[8078,5438]) ).
thf(48,axiom,
! [A: $i,B: $i] :
( ( B @ succ @ ( A @ succ @ leq ) )
<=> ( B @ ( A @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_succ_succ) ).
thf(281,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)],[48]) ).
thf(16794,plain,
! [B: $i,A: $i] :
( ( ( n0 @ ( n999 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[276,203]) ).
thf(16795,plain,
! [B: $i,A: $i] :
( ( ( n0 @ ( n999 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[16794]) ).
thf(16796,plain,
n999 @ ( n0 @ lt ),
inference(pattern_uni,[status(thm)],[16795:[bind(A,$thf( n0 )),bind(B,$thf( n999 ))]]) ).
thf(17456,plain,
! [B: $i,A: $i] :
( ( ( n4 @ ( n5 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[181,217]) ).
thf(17457,plain,
! [B: $i,A: $i] :
( ( ( n4 @ ( n5 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ leq ) ) ),
inference(simp,[status(thm)],[17456]) ).
thf(17458,plain,
n5 @ ( n4 @ leq ),
inference(pattern_uni,[status(thm)],[17457:[bind(A,$thf( n4 )),bind(B,$thf( n5 ))]]) ).
thf(16821,plain,
! [B: $i,A: $i] :
( ( ( n0 @ ( n2 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[593,203]) ).
thf(16822,plain,
! [B: $i,A: $i] :
( ( ( n0 @ ( n2 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[16821]) ).
thf(16823,plain,
n2 @ ( n0 @ lt ),
inference(pattern_uni,[status(thm)],[16822:[bind(A,$thf( n0 )),bind(B,$thf( n2 ))]]) ).
thf(121,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( q_ds1_filter @ a_select3 ) ) )
= ( A @ ( B @ ( q_ds1_filter @ a_select3 ) ) ) )
| ~ ( n1 @ ( n6 @ minus ) @ ( B @ leq ) )
| ~ ( n1 @ ( n6 @ minus ) @ ( A @ leq ) )
| ~ ( B @ ( n0 @ leq ) )
| ~ ( A @ ( n0 @ leq ) ) ),
inference(cnfConj,[status(thm)],[103]) ).
thf(153,plain,
! [B: $i,A: $i] :
( ~ ( n1 @ ( n6 @ minus ) @ ( B @ leq ) )
| ~ ( n1 @ ( n6 @ minus ) @ ( A @ leq ) )
| ~ ( B @ ( n0 @ leq ) )
| ~ ( A @ ( n0 @ leq ) )
| ( ( B @ ( A @ ( q_ds1_filter @ a_select3 ) ) )
= ( A @ ( B @ ( q_ds1_filter @ a_select3 ) ) ) ) ),
inference(lifteq,[status(thm)],[121]) ).
thf(9224,plain,
! [B: $i,A: $i] :
( ~ ( n6 @ pred @ ( B @ leq ) )
| ~ ( n6 @ pred @ ( A @ leq ) )
| ~ ( B @ ( n0 @ leq ) )
| ~ ( A @ ( n0 @ leq ) )
| ( ( B @ ( A @ ( q_ds1_filter @ a_select3 ) ) )
= ( A @ ( B @ ( q_ds1_filter @ a_select3 ) ) ) ) ),
inference(rewrite,[status(thm)],[153,302]) ).
thf(1865,plain,
! [B: $i,A: $i] :
( ( ( pv5 @ ( sk3 @ leq ) )
!= ( pv5 @ ( n0 @ leq ) ) )
| ( ( B @ ( n0 @ ( n0 @ ( A @ tptp_update3 ) ) ) )
!= q_ds1_filter )
| ~ ( n0 @ ( n0 @ leq ) )
| ~ ( pv5 @ ( sk2 @ leq ) )
| ~ $true
| ( ( A @ ( pv5 @ sk15 ) )
!= ( A @ ( pv5 @ sk14 ) ) )
| ~ sk1 ),
inference(paramod_ordered,[status(thm)],[128,1558]) ).
thf(1866,plain,
! [B: $i,A: $i] :
( ( ( pv5 @ ( sk3 @ leq ) )
!= ( pv5 @ ( n0 @ leq ) ) )
| ( ( B @ ( n0 @ ( n0 @ ( A @ tptp_update3 ) ) ) )
!= q_ds1_filter )
| ~ ( n0 @ ( n0 @ leq ) )
| ~ ( pv5 @ ( sk2 @ leq ) )
| ( ( A @ ( pv5 @ sk15 ) )
!= ( A @ ( pv5 @ sk14 ) ) )
| ~ sk1 ),
inference(simp,[status(thm)],[1865]) ).
thf(1928,plain,
! [B: $i,A: $i] :
( ( pv5 != pv5 )
| ( sk3 != n0 )
| ( ( B @ ( n0 @ ( n0 @ ( A @ tptp_update3 ) ) ) )
!= q_ds1_filter )
| ~ ( n0 @ ( n0 @ leq ) )
| ~ ( pv5 @ ( sk2 @ leq ) )
| ( ( A @ ( pv5 @ sk15 ) )
!= ( A @ ( pv5 @ sk14 ) ) )
| ~ sk1 ),
inference(simp,[status(thm)],[1866]) ).
thf(1932,plain,
! [B: $i,A: $i] :
( ( sk3 != n0 )
| ( ( B @ ( n0 @ ( n0 @ ( A @ tptp_update3 ) ) ) )
!= q_ds1_filter )
| ~ ( n0 @ ( n0 @ leq ) )
| ~ ( pv5 @ ( sk2 @ leq ) )
| ( ( A @ ( pv5 @ sk15 ) )
!= ( A @ ( pv5 @ sk14 ) ) )
| ~ sk1 ),
inference(simp,[status(thm)],[1928]) ).
thf(2137,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( n0 @ leq ) )
!= ( n0 @ ( n0 @ leq ) ) )
| ( sk3 != n0 )
| ( ( B @ ( n0 @ ( n0 @ ( A @ tptp_update3 ) ) ) )
!= q_ds1_filter )
| ~ $true
| ~ ( pv5 @ ( sk2 @ leq ) )
| ( ( A @ ( pv5 @ sk15 ) )
!= ( A @ ( pv5 @ sk14 ) ) )
| ~ sk1
| ~ sk1 ),
inference(paramod_ordered,[status(thm)],[652,1932]) ).
thf(2138,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( n0 @ leq ) )
!= ( n0 @ ( n0 @ leq ) ) )
| ( sk3 != n0 )
| ( ( B @ ( n0 @ ( n0 @ ( A @ tptp_update3 ) ) ) )
!= q_ds1_filter )
| ~ ( pv5 @ ( sk2 @ leq ) )
| ( ( A @ ( pv5 @ sk15 ) )
!= ( A @ ( pv5 @ sk14 ) ) )
| ~ sk1 ),
inference(simp,[status(thm)],[2137]) ).
thf(2158,plain,
! [B: $i,A: $i] :
( ( sk3 != n0 )
| ( n0 != n0 )
| ( sk3 != n0 )
| ( ( B @ ( n0 @ ( n0 @ ( A @ tptp_update3 ) ) ) )
!= q_ds1_filter )
| ~ ( pv5 @ ( sk2 @ leq ) )
| ( ( A @ ( pv5 @ sk15 ) )
!= ( A @ ( pv5 @ sk14 ) ) )
| ~ sk1 ),
inference(simp,[status(thm)],[2138]) ).
thf(2166,plain,
! [B: $i,A: $i] :
( ( sk3 != n0 )
| ( ( B @ ( n0 @ ( n0 @ ( A @ tptp_update3 ) ) ) )
!= q_ds1_filter )
| ~ ( pv5 @ ( sk2 @ leq ) )
| ( ( A @ ( pv5 @ sk15 ) )
!= ( A @ ( pv5 @ sk14 ) ) )
| ~ sk1 ),
inference(simp,[status(thm)],[2158]) ).
thf(17399,plain,
! [B: $i,A: $i] :
( ( ( n3 @ ( n6 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[404,217]) ).
thf(17400,plain,
! [B: $i,A: $i] :
( ( ( n3 @ ( n6 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ leq ) ) ),
inference(simp,[status(thm)],[17399]) ).
thf(17401,plain,
n6 @ ( n3 @ leq ),
inference(pattern_uni,[status(thm)],[17400:[bind(A,$thf( n3 )),bind(B,$thf( n6 ))]]) ).
thf(108,plain,
( ( ( sk10 @ ( sk9 @ ( id_ds1_filter @ a_select3 ) ) )
!= ( sk9 @ ( sk10 @ ( id_ds1_filter @ a_select3 ) ) ) )
| ( n1 @ ( n6 @ minus ) @ ( sk8 @ leq ) )
| sk4
| sk1
| ~ ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
| ~ ( pv5 @ ( n0 @ leq ) ) ),
inference(cnfConj,[status(thm)],[103]) ).
thf(155,plain,
( ( n1 @ ( n6 @ minus ) @ ( sk8 @ leq ) )
| sk4
| sk1
| ~ ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
| ~ ( pv5 @ ( n0 @ leq ) )
| ( ( sk9 @ ( sk10 @ ( id_ds1_filter @ a_select3 ) ) )
!= ( sk10 @ ( sk9 @ ( id_ds1_filter @ a_select3 ) ) ) ) ),
inference(lifteq,[status(thm)],[108]) ).
thf(10384,plain,
( ( n6 @ pred @ ( sk8 @ leq ) )
| sk4
| sk1
| ~ ( n999 @ pred @ ( pv5 @ leq ) )
| ~ $true
| ( ( sk9 @ ( sk10 @ ( id_ds1_filter @ a_select3 ) ) )
!= ( sk10 @ ( sk9 @ ( id_ds1_filter @ a_select3 ) ) ) ) ),
inference(rewrite,[status(thm)],[155,128,302]) ).
thf(10385,plain,
( ( n6 @ pred @ ( sk8 @ leq ) )
| sk4
| sk1
| ~ ( n999 @ pred @ ( pv5 @ leq ) )
| ( ( sk9 @ ( sk10 @ ( id_ds1_filter @ a_select3 ) ) )
!= ( sk10 @ ( sk9 @ ( id_ds1_filter @ a_select3 ) ) ) ) ),
inference(simp,[status(thm)],[10384]) ).
thf(226,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( ( A @ ( D @ ( B @ ( C @ tptp_update2 ) ) @ a_select2 ) )
= D )
| ~ ( B @ ( A @ leq ) )
| ~ ( A @ ( n0 @ leq ) )
| ( ( A @ ( B @ ( C @ ( D @ sk11 ) ) ) @ ( C @ a_select2 ) )
!= D ) )
& ( ( ( A @ ( D @ ( B @ ( C @ tptp_update2 ) ) @ a_select2 ) )
= D )
| ~ ( B @ ( A @ leq ) )
| ~ ( A @ ( n0 @ leq ) )
| ( B @ ( A @ ( B @ ( C @ ( D @ sk11 ) ) ) @ leq ) ) )
& ( ( ( A @ ( D @ ( B @ ( C @ tptp_update2 ) ) @ a_select2 ) )
= D )
| ~ ( B @ ( A @ leq ) )
| ~ ( A @ ( n0 @ leq ) )
| ( A @ ( B @ ( C @ ( D @ sk11 ) ) ) @ ( n0 @ leq ) ) ) ),
inference(cnf,[status(esa)],[225]) ).
thf(227,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( B @ ( C @ tptp_update2 ) ) @ a_select2 ) )
= D )
| ~ ( B @ ( A @ leq ) )
| ~ ( A @ ( n0 @ leq ) )
| ( A @ ( B @ ( C @ ( D @ sk11 ) ) ) @ ( n0 @ leq ) ) ),
inference(cnfConj,[status(thm)],[226]) ).
thf(230,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ leq ) )
| ~ ( A @ ( n0 @ leq ) )
| ( A @ ( B @ ( C @ ( D @ sk11 ) ) ) @ ( n0 @ leq ) )
| ( ( A @ ( D @ ( B @ ( C @ tptp_update2 ) ) @ a_select2 ) )
= D ) ),
inference(lifteq,[status(thm)],[227]) ).
thf(5406,plain,
( ~ $true
| ( ( sk10 @ ( n0 @ leq ) )
!= ( sk7 @ ( n0 @ leq ) ) )
| ( sk7 @ ( n0 @ leq ) )
| sk4
| sk1 ),
inference(eqfactor_ordered,[status(thm)],[5338]) ).
thf(5407,plain,
( ( ( sk10 @ ( n0 @ leq ) )
!= ( sk7 @ ( n0 @ leq ) ) )
| ( sk7 @ ( n0 @ leq ) )
| sk4
| sk1 ),
inference(simp,[status(thm)],[5406]) ).
thf(17459,plain,
! [B: $i,A: $i] :
( ( ( n4 @ ( n999 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[236,217]) ).
thf(17460,plain,
! [B: $i,A: $i] :
( ( ( n4 @ ( n999 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ leq ) ) ),
inference(simp,[status(thm)],[17459]) ).
thf(17461,plain,
n999 @ ( n4 @ leq ),
inference(pattern_uni,[status(thm)],[17460:[bind(A,$thf( n4 )),bind(B,$thf( n999 ))]]) ).
thf(58,axiom,
( ( tptp_minus_1 @ succ )
= n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_tptp_minus_1) ).
thf(405,plain,
( ( tptp_minus_1 @ succ )
= n0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(406,plain,
( ( tptp_minus_1 @ succ )
= n0 ),
inference(lifteq,[status(thm)],[405]) ).
thf(16881,plain,
! [B: $i,A: $i] :
( ( ( n2 @ ( n4 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[182,203]) ).
thf(16882,plain,
! [B: $i,A: $i] :
( ( ( n2 @ ( n4 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[16881]) ).
thf(16883,plain,
n4 @ ( n2 @ lt ),
inference(pattern_uni,[status(thm)],[16882:[bind(A,$thf( n2 )),bind(B,$thf( n4 ))]]) ).
thf(52,axiom,
! [A: $i] :
( ( ( n0 @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( A = n0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',finite_domain_0) ).
thf(303,plain,
! [A: $i] :
( ( ( n0 @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( A = n0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(1664,plain,
! [A: $i] :
( ( ( tptp_minus_1 @ ( n999 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[238,197]) ).
thf(1665,plain,
! [A: $i] :
( ( tptp_minus_1 @ ( n999 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[1664]) ).
thf(1666,plain,
! [A: $i] :
( ( tptp_minus_1 != A )
| ( n999 != A ) ),
inference(simp,[status(thm)],[1665]) ).
thf(1667,plain,
tptp_minus_1 != n999,
inference(simp,[status(thm)],[1666]) ).
thf(65,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(477,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)],[65]) ).
thf(123,plain,
( ( sk10 @ ( n0 @ leq ) )
| ( ( sk8 @ ( sk7 @ ( pminus_ds1_filter @ a_select3 ) ) )
!= ( sk7 @ ( sk8 @ ( pminus_ds1_filter @ a_select3 ) ) ) )
| sk4
| sk1
| ~ ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
| ~ ( pv5 @ ( n0 @ leq ) ) ),
inference(cnfConj,[status(thm)],[103]) ).
thf(158,plain,
( ( sk10 @ ( n0 @ leq ) )
| sk4
| sk1
| ~ ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
| ~ ( pv5 @ ( n0 @ leq ) )
| ( ( sk7 @ ( sk8 @ ( pminus_ds1_filter @ a_select3 ) ) )
!= ( sk8 @ ( sk7 @ ( pminus_ds1_filter @ a_select3 ) ) ) ) ),
inference(lifteq,[status(thm)],[123]) ).
thf(11668,plain,
( ( sk10 @ ( n0 @ leq ) )
| sk4
| sk1
| ~ ( n999 @ pred @ ( pv5 @ leq ) )
| ~ $true
| ( ( sk7 @ ( sk8 @ ( pminus_ds1_filter @ a_select3 ) ) )
!= ( sk8 @ ( sk7 @ ( pminus_ds1_filter @ a_select3 ) ) ) ) ),
inference(rewrite,[status(thm)],[158,128,302]) ).
thf(11669,plain,
( ( sk10 @ ( n0 @ leq ) )
| sk4
| sk1
| ~ ( n999 @ pred @ ( pv5 @ leq ) )
| ( ( sk7 @ ( sk8 @ ( pminus_ds1_filter @ a_select3 ) ) )
!= ( sk8 @ ( sk7 @ ( pminus_ds1_filter @ a_select3 ) ) ) ) ),
inference(simp,[status(thm)],[11668]) ).
thf(100,axiom,
! [A: $i] :
( ( ( n1 @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A = n1 )
| ( A = n0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',finite_domain_1) ).
thf(631,plain,
! [A: $i] :
( ( ( n1 @ ( A @ leq ) )
& ( A @ ( n0 @ leq ) ) )
=> ( ( A = n1 )
| ( A = n0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(88,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)],[88]) ).
thf(212,plain,
! [A: $i] :
( ( n2 @ ( A @ plus ) )
= ( A @ succ @ succ ) ),
inference(cnf,[status(esa)],[211]) ).
thf(213,plain,
! [A: $i] :
( ( n2 @ ( A @ plus ) )
= ( A @ succ @ succ ) ),
inference(lifteq,[status(thm)],[212]) ).
thf(5408,plain,
( ( sk10 != sk7 )
| ( n0 != n0 )
| ( sk7 @ ( n0 @ leq ) )
| sk4
| sk1 ),
inference(simp,[status(thm)],[5406]) ).
thf(5410,plain,
( ( sk10 != sk7 )
| ( sk7 @ ( n0 @ leq ) )
| sk4
| sk1 ),
inference(simp,[status(thm)],[5408]) ).
thf(16997,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk3 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) )
| ~ $true
| ~ sk1
| ( sk3 @ ( sk2 @ gt ) ) ),
inference(paramod_ordered,[status(thm)],[15100,203]) ).
thf(16998,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk3 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) )
| ~ sk1
| ( sk3 @ ( sk2 @ gt ) ) ),
inference(simp,[status(thm)],[16997]) ).
thf(16999,plain,
( ( sk3 @ ( sk2 @ lt ) )
| ~ sk1
| ( sk3 @ ( sk2 @ gt ) ) ),
inference(pattern_uni,[status(thm)],[16998:[bind(A,$thf( sk2 )),bind(B,$thf( sk3 ))]]) ).
thf(16797,plain,
! [B: $i,A: $i] :
( ( ( n3 @ ( n6 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[404,203]) ).
thf(16798,plain,
! [B: $i,A: $i] :
( ( ( n3 @ ( n6 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[16797]) ).
thf(16799,plain,
n6 @ ( n3 @ lt ),
inference(pattern_uni,[status(thm)],[16798:[bind(A,$thf( n3 )),bind(B,$thf( n6 ))]]) ).
thf(16800,plain,
! [B: $i,A: $i] :
( ( ( n0 @ ( n1 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[619,203]) ).
thf(16801,plain,
! [B: $i,A: $i] :
( ( ( n0 @ ( n1 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[16800]) ).
thf(16802,plain,
n1 @ ( n0 @ lt ),
inference(pattern_uni,[status(thm)],[16801:[bind(A,$thf( n0 )),bind(B,$thf( n1 ))]]) ).
thf(16902,plain,
! [B: $i,A: $i] :
( ( ( n5 @ ( n999 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[603,203]) ).
thf(16903,plain,
! [B: $i,A: $i] :
( ( ( n5 @ ( n999 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[16902]) ).
thf(16904,plain,
n999 @ ( n5 @ lt ),
inference(pattern_uni,[status(thm)],[16903:[bind(A,$thf( n5 )),bind(B,$thf( n999 ))]]) ).
thf(11989,plain,
! [A: $i] :
( ( ( n3 @ succ @ succ @ succ @ succ )
!= ( A @ succ ) )
| ( ( n6 @ succ )
!= A ) ),
inference(paramod_ordered,[status(thm)],[11939,5006]) ).
thf(11990,plain,
( ( n3 @ succ @ succ @ succ )
!= ( n6 @ succ ) ),
inference(pattern_uni,[status(thm)],[11989:[bind(A,$thf( n3 @ succ @ succ @ succ ))]]) ).
thf(12120,plain,
( ( n5 @ succ )
!= ( n6 @ succ ) ),
inference(rewrite,[status(thm)],[11990,9779]) ).
thf(12134,plain,
( ( ( n5 @ succ )
!= ( n5 @ succ ) )
| ( ( n6 @ succ )
!= n6 ) ),
inference(paramod_ordered,[status(thm)],[4132,12120]) ).
thf(12135,plain,
( ( n6 @ succ )
!= n6 ),
inference(pattern_uni,[status(thm)],[12134:[]]) ).
thf(2083,plain,
! [A: $i] :
( ( ( n0 @ ( n999 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[276,197]) ).
thf(2084,plain,
! [A: $i] :
( ( n0 @ ( n999 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[2083]) ).
thf(2085,plain,
! [A: $i] :
( ( n0 != A )
| ( n999 != A ) ),
inference(simp,[status(thm)],[2084]) ).
thf(2086,plain,
n999 != n0,
inference(simp,[status(thm)],[2085]) ).
thf(2589,plain,
! [A: $i] :
( ( ( tptp_minus_1 @ ( n1 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[575,197]) ).
thf(2590,plain,
! [A: $i] :
( ( tptp_minus_1 @ ( n1 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[2589]) ).
thf(2591,plain,
! [A: $i] :
( ( tptp_minus_1 != A )
| ( n1 != A ) ),
inference(simp,[status(thm)],[2590]) ).
thf(2592,plain,
tptp_minus_1 != n1,
inference(simp,[status(thm)],[2591]) ).
thf(39,axiom,
n3 @ ( n4 @ gt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_4_3) ).
thf(241,plain,
n3 @ ( n4 @ gt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(6,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(167,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)],[6]) ).
thf(54,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ geq ) )
<=> ( A @ ( B @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_geq) ).
thf(394,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)],[54]) ).
thf(53,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(306,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)],[53]) ).
thf(3307,plain,
! [A: $i] :
( ( ( n5 @ ( n6 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[627,197]) ).
thf(3308,plain,
! [A: $i] :
( ( n5 @ ( n6 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[3307]) ).
thf(3309,plain,
! [A: $i] :
( ( n5 != A )
| ( n6 != A ) ),
inference(simp,[status(thm)],[3308]) ).
thf(3310,plain,
n5 != n6,
inference(simp,[status(thm)],[3309]) ).
thf(17411,plain,
! [B: $i,A: $i] :
( ( ( n3 @ ( n999 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[634,217]) ).
thf(17412,plain,
! [B: $i,A: $i] :
( ( ( n3 @ ( n999 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ leq ) ) ),
inference(simp,[status(thm)],[17411]) ).
thf(17413,plain,
n999 @ ( n3 @ leq ),
inference(pattern_uni,[status(thm)],[17412:[bind(A,$thf( n3 )),bind(B,$thf( n999 ))]]) ).
thf(5423,plain,
! [A: $i] :
( ( ( n0 @ succ )
!= ( A @ succ ) )
| ( ( n1 @ pred )
= A ) ),
inference(paramod_ordered,[status(thm)],[221,185]) ).
thf(5424,plain,
( ( n1 @ pred )
= n0 ),
inference(pattern_uni,[status(thm)],[5423:[bind(A,$thf( n0 ))]]) ).
thf(161,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( B @ ( A @ tptp_update2 ) ) @ a_select2 ) )
= C ),
inference(cnf,[status(esa)],[160]) ).
thf(162,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( B @ ( A @ tptp_update2 ) ) @ a_select2 ) )
= C ),
inference(lifteq,[status(thm)],[161]) ).
thf(69,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)],[69]) ).
thf(2420,plain,
! [B: $i,A: $i] :
( ( ( pv5 @ ( sk2 @ leq ) )
!= ( pv5 @ ( n0 @ leq ) ) )
| ( sk3 != n0 )
| ( ( B @ ( n0 @ ( n0 @ ( A @ tptp_update3 ) ) ) )
!= q_ds1_filter )
| ~ $true
| ( ( A @ ( pv5 @ sk15 ) )
!= ( A @ ( pv5 @ sk14 ) ) )
| ~ sk1 ),
inference(paramod_ordered,[status(thm)],[128,2166]) ).
thf(2421,plain,
! [B: $i,A: $i] :
( ( ( pv5 @ ( sk2 @ leq ) )
!= ( pv5 @ ( n0 @ leq ) ) )
| ( sk3 != n0 )
| ( ( B @ ( n0 @ ( n0 @ ( A @ tptp_update3 ) ) ) )
!= q_ds1_filter )
| ( ( A @ ( pv5 @ sk15 ) )
!= ( A @ ( pv5 @ sk14 ) ) )
| ~ sk1 ),
inference(simp,[status(thm)],[2420]) ).
thf(2447,plain,
! [B: $i,A: $i] :
( ( pv5 != pv5 )
| ( sk2 != n0 )
| ( sk3 != n0 )
| ( ( B @ ( n0 @ ( n0 @ ( A @ tptp_update3 ) ) ) )
!= q_ds1_filter )
| ( ( A @ ( pv5 @ sk15 ) )
!= ( A @ ( pv5 @ sk14 ) ) )
| ~ sk1 ),
inference(simp,[status(thm)],[2421]) ).
thf(2449,plain,
! [B: $i,A: $i] :
( ( sk2 != n0 )
| ( sk3 != n0 )
| ( ( B @ ( n0 @ ( n0 @ ( A @ tptp_update3 ) ) ) )
!= q_ds1_filter )
| ( ( A @ ( pv5 @ sk15 ) )
!= ( A @ ( pv5 @ sk14 ) ) )
| ~ sk1 ),
inference(simp,[status(thm)],[2447]) ).
thf(193,plain,
! [A: $i] :
( ( A @ ( n5 @ plus ) )
= ( A @ succ @ succ @ succ @ succ @ succ ) ),
inference(cnf,[status(esa)],[192]) ).
thf(194,plain,
! [A: $i] :
( ( A @ ( n5 @ plus ) )
= ( A @ succ @ succ @ succ @ succ @ succ ) ),
inference(lifteq,[status(thm)],[193]) ).
thf(130,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( pminus_ds1_filter @ a_select3 ) ) )
= ( A @ ( B @ ( pminus_ds1_filter @ a_select3 ) ) ) )
| ~ ( n1 @ ( n6 @ minus ) @ ( B @ leq ) )
| ~ ( n1 @ ( n6 @ minus ) @ ( A @ leq ) )
| ~ ( B @ ( n0 @ leq ) )
| ~ ( A @ ( n0 @ leq ) ) ),
inference(cnfConj,[status(thm)],[103]) ).
thf(156,plain,
! [B: $i,A: $i] :
( ~ ( n1 @ ( n6 @ minus ) @ ( B @ leq ) )
| ~ ( n1 @ ( n6 @ minus ) @ ( A @ leq ) )
| ~ ( B @ ( n0 @ leq ) )
| ~ ( A @ ( n0 @ leq ) )
| ( ( B @ ( A @ ( pminus_ds1_filter @ a_select3 ) ) )
= ( A @ ( B @ ( pminus_ds1_filter @ a_select3 ) ) ) ) ),
inference(lifteq,[status(thm)],[130]) ).
thf(157,plain,
! [B: $i,A: $i] :
( ~ ( n1 @ ( n6 @ minus ) @ ( B @ leq ) )
| ~ ( n1 @ ( n6 @ minus ) @ ( A @ leq ) )
| ~ ( B @ ( n0 @ leq ) )
| ~ ( A @ ( n0 @ leq ) )
| ( ( B @ ( A @ ( pminus_ds1_filter @ a_select3 ) ) )
= ( A @ ( B @ ( pminus_ds1_filter @ a_select3 ) ) ) ) ),
inference(simp,[status(thm)],[156]) ).
thf(10672,plain,
! [B: $i,A: $i] :
( ~ ( n6 @ pred @ ( B @ leq ) )
| ~ ( n6 @ pred @ ( A @ leq ) )
| ~ ( B @ ( n0 @ leq ) )
| ~ ( A @ ( n0 @ leq ) )
| ( ( B @ ( A @ ( pminus_ds1_filter @ a_select3 ) ) )
= ( A @ ( B @ ( pminus_ds1_filter @ a_select3 ) ) ) ) ),
inference(rewrite,[status(thm)],[157,302]) ).
thf(2585,plain,
! [A: $i] :
( ( ( n0 @ ( n3 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[471,197]) ).
thf(2586,plain,
! [A: $i] :
( ( n0 @ ( n3 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[2585]) ).
thf(2587,plain,
! [A: $i] :
( ( n0 != A )
| ( n3 != A ) ),
inference(simp,[status(thm)],[2586]) ).
thf(2588,plain,
n3 != n0,
inference(simp,[status(thm)],[2587]) ).
thf(1938,plain,
! [A: $i] :
( ( ( n3 @ ( n4 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[241,197]) ).
thf(1939,plain,
! [A: $i] :
( ( n3 @ ( n4 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[1938]) ).
thf(1940,plain,
! [A: $i] :
( ( n3 != A )
| ( n4 != A ) ),
inference(simp,[status(thm)],[1939]) ).
thf(1941,plain,
n4 != n3,
inference(simp,[status(thm)],[1940]) ).
thf(110,plain,
( ( sk9 @ ( n0 @ leq ) )
| ( ( sk8 @ ( sk7 @ ( pminus_ds1_filter @ a_select3 ) ) )
!= ( sk7 @ ( sk8 @ ( pminus_ds1_filter @ a_select3 ) ) ) )
| sk4
| sk1
| ~ ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
| ~ ( pv5 @ ( n0 @ leq ) ) ),
inference(cnfConj,[status(thm)],[103]) ).
thf(151,plain,
( ( sk9 @ ( n0 @ leq ) )
| sk4
| sk1
| ~ ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
| ~ ( pv5 @ ( n0 @ leq ) )
| ( ( sk7 @ ( sk8 @ ( pminus_ds1_filter @ a_select3 ) ) )
!= ( sk8 @ ( sk7 @ ( pminus_ds1_filter @ a_select3 ) ) ) ) ),
inference(lifteq,[status(thm)],[110]) ).
thf(8771,plain,
( ( sk9 @ ( n0 @ leq ) )
| sk4
| sk1
| ~ ( n999 @ pred @ ( pv5 @ leq ) )
| ~ $true
| ( ( sk7 @ ( sk8 @ ( pminus_ds1_filter @ a_select3 ) ) )
!= ( sk8 @ ( sk7 @ ( pminus_ds1_filter @ a_select3 ) ) ) ) ),
inference(rewrite,[status(thm)],[151,128,302]) ).
thf(8772,plain,
( ( sk9 @ ( n0 @ leq ) )
| sk4
| sk1
| ~ ( n999 @ pred @ ( pv5 @ leq ) )
| ( ( sk7 @ ( sk8 @ ( pminus_ds1_filter @ a_select3 ) ) )
!= ( sk8 @ ( sk7 @ ( pminus_ds1_filter @ a_select3 ) ) ) ) ),
inference(simp,[status(thm)],[8771]) ).
thf(4919,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( pv5 @ ( sk2 @ leq ) ) )
| ( sk3 != n0 )
| ( ( C @ ( n0 @ ( n0 @ ( B @ tptp_update3 ) ) ) )
!= q_ds1_filter )
| ~ $true
| ( ( B @ ( pv5 @ sk15 ) )
!= ( B @ ( pv5 @ sk14 ) ) )
| ~ sk1 ),
inference(paramod_ordered,[status(thm)],[595,2166]) ).
thf(4920,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ leq ) )
!= ( pv5 @ ( sk2 @ leq ) ) )
| ( sk3 != n0 )
| ( ( C @ ( n0 @ ( n0 @ ( B @ tptp_update3 ) ) ) )
!= q_ds1_filter )
| ( ( B @ ( pv5 @ sk15 ) )
!= ( B @ ( pv5 @ sk14 ) ) )
| ~ sk1 ),
inference(simp,[status(thm)],[4919]) ).
thf(4953,plain,
! [C: $i,B: $i,A: $i] :
( ( A != pv5 )
| ( A != sk2 )
| ( sk3 != n0 )
| ( ( C @ ( n0 @ ( n0 @ ( B @ tptp_update3 ) ) ) )
!= q_ds1_filter )
| ( ( B @ ( pv5 @ sk15 ) )
!= ( B @ ( pv5 @ sk14 ) ) )
| ~ sk1 ),
inference(simp,[status(thm)],[4920]) ).
thf(4971,plain,
! [B: $i,A: $i] :
( ( sk2 != pv5 )
| ( sk3 != n0 )
| ( ( B @ ( n0 @ ( n0 @ ( A @ tptp_update3 ) ) ) )
!= q_ds1_filter )
| ( ( A @ ( pv5 @ sk15 ) )
!= ( A @ ( pv5 @ sk14 ) ) )
| ~ sk1 ),
inference(simp,[status(thm)],[4953]) ).
thf(12840,plain,
! [A: $i] :
( ( ( n5 @ succ @ succ )
!= ( A @ succ ) )
| ( A @ ( n6 @ succ @ gt ) ) ),
inference(paramod_ordered,[status(thm)],[12789,180]) ).
thf(12841,plain,
n5 @ succ @ ( n6 @ succ @ gt ),
inference(pattern_uni,[status(thm)],[12840:[bind(A,$thf( n5 @ succ ))]]) ).
thf(12937,plain,
n6 @ ( n6 @ succ @ gt ),
inference(rewrite,[status(thm)],[12841,4132]) ).
thf(17453,plain,
! [B: $i,A: $i] :
( ( ( n0 @ ( n6 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[611,217]) ).
thf(17454,plain,
! [B: $i,A: $i] :
( ( ( n0 @ ( n6 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ leq ) ) ),
inference(simp,[status(thm)],[17453]) ).
thf(17455,plain,
n6 @ ( n0 @ leq ),
inference(pattern_uni,[status(thm)],[17454:[bind(A,$thf( n0 )),bind(B,$thf( n6 ))]]) ).
thf(118,plain,
( ( n1 @ ( n6 @ minus ) @ ( sk10 @ leq ) )
| ( sk8 @ ( n0 @ leq ) )
| sk4
| sk1
| ~ ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
| ~ ( pv5 @ ( n0 @ leq ) ) ),
inference(cnfConj,[status(thm)],[103]) ).
thf(2327,plain,
( ( n1 @ ( n6 @ minus ) @ ( sk10 @ leq ) )
| ( sk8 @ ( n0 @ leq ) )
| sk4
| sk1
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[118,128,107]) ).
thf(2328,plain,
( ( n1 @ ( n6 @ minus ) @ ( sk10 @ leq ) )
| ( sk8 @ ( n0 @ leq ) )
| sk4
| sk1 ),
inference(simp,[status(thm)],[2327]) ).
thf(8072,plain,
( ( n6 @ pred @ ( sk10 @ leq ) )
| ( sk8 @ ( n0 @ leq ) )
| sk4
| sk1 ),
inference(rewrite,[status(thm)],[2328,302]) ).
thf(11257,plain,
( ( n5 @ ( sk10 @ leq ) )
| ( sk8 @ ( n0 @ leq ) )
| sk4
| sk1 ),
inference(rewrite,[status(thm)],[8072,5438]) ).
thf(2698,plain,
! [A: $i] :
( ( ( n0 @ ( n4 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[599,197]) ).
thf(2699,plain,
! [A: $i] :
( ( n0 @ ( n4 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[2698]) ).
thf(2700,plain,
! [A: $i] :
( ( n0 != A )
| ( n4 != A ) ),
inference(simp,[status(thm)],[2699]) ).
thf(2701,plain,
n4 != n0,
inference(simp,[status(thm)],[2700]) ).
thf(16809,plain,
! [B: $i,A: $i] :
( ( ( n3 @ ( n999 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[634,203]) ).
thf(16810,plain,
! [B: $i,A: $i] :
( ( ( n3 @ ( n999 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[16809]) ).
thf(16811,plain,
n999 @ ( n3 @ lt ),
inference(pattern_uni,[status(thm)],[16810:[bind(A,$thf( n3 )),bind(B,$thf( n999 ))]]) ).
thf(12125,plain,
( ( ( n3 @ succ @ succ @ succ @ succ )
!= ( n5 @ succ ) )
| ( ( n6 @ succ )
!= ( n6 @ succ ) ) ),
inference(paramod_ordered,[status(thm)],[11939,12120]) ).
thf(12126,plain,
( ( n3 @ succ @ succ @ succ @ succ )
!= ( n5 @ succ ) ),
inference(simp,[status(thm)],[12125]) ).
thf(12141,plain,
( ( n3 @ succ @ succ @ succ )
!= n5 ),
inference(simp,[status(thm)],[12126]) ).
thf(12752,plain,
( ( n5 @ succ )
!= n5 ),
inference(rewrite,[status(thm)],[12141,9779]) ).
thf(16890,plain,
! [B: $i,A: $i] :
( ( ( n2 @ ( n6 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[218,203]) ).
thf(16891,plain,
! [B: $i,A: $i] :
( ( ( n2 @ ( n6 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[16890]) ).
thf(16892,plain,
n6 @ ( n2 @ lt ),
inference(pattern_uni,[status(thm)],[16891:[bind(A,$thf( n2 )),bind(B,$thf( n6 ))]]) ).
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(576,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(113,plain,
( ~ sk1
| ( n1 @ ( n6 @ minus ) @ ( sk3 @ leq ) )
| ~ ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
| ~ ( pv5 @ ( n0 @ leq ) ) ),
inference(cnfConj,[status(thm)],[103]) ).
thf(1456,plain,
( ~ sk1
| ( n1 @ ( n6 @ minus ) @ ( sk3 @ leq ) )
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[113,128,107]) ).
thf(1457,plain,
( ~ sk1
| ( n1 @ ( n6 @ minus ) @ ( sk3 @ leq ) ) ),
inference(simp,[status(thm)],[1456]) ).
thf(8081,plain,
( ~ sk1
| ( n6 @ pred @ ( sk3 @ leq ) ) ),
inference(rewrite,[status(thm)],[1457,302]) ).
thf(8391,plain,
( ~ sk1
| ( n5 @ ( sk3 @ leq ) ) ),
inference(rewrite,[status(thm)],[8081,5438]) ).
thf(16893,plain,
! [B: $i,A: $i] :
( ( ( tptp_minus_1 @ ( n5 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[207,203]) ).
thf(16894,plain,
! [B: $i,A: $i] :
( ( ( tptp_minus_1 @ ( n5 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[16893]) ).
thf(16895,plain,
n5 @ ( tptp_minus_1 @ lt ),
inference(pattern_uni,[status(thm)],[16894:[bind(A,$thf( tptp_minus_1 )),bind(B,$thf( n5 ))]]) ).
thf(126,plain,
( ( n1 @ ( n6 @ minus ) @ ( sk10 @ leq ) )
| ( ( sk8 @ ( sk7 @ ( pminus_ds1_filter @ a_select3 ) ) )
!= ( sk7 @ ( sk8 @ ( pminus_ds1_filter @ a_select3 ) ) ) )
| sk4
| sk1
| ~ ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
| ~ ( pv5 @ ( n0 @ leq ) ) ),
inference(cnfConj,[status(thm)],[103]) ).
thf(159,plain,
( ( n1 @ ( n6 @ minus ) @ ( sk10 @ leq ) )
| sk4
| sk1
| ~ ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
| ~ ( pv5 @ ( n0 @ leq ) )
| ( ( sk7 @ ( sk8 @ ( pminus_ds1_filter @ a_select3 ) ) )
!= ( sk8 @ ( sk7 @ ( pminus_ds1_filter @ a_select3 ) ) ) ) ),
inference(lifteq,[status(thm)],[126]) ).
thf(12511,plain,
( ( n6 @ pred @ ( sk10 @ leq ) )
| sk4
| sk1
| ~ ( n999 @ pred @ ( pv5 @ leq ) )
| ~ $true
| ( ( sk7 @ ( sk8 @ ( pminus_ds1_filter @ a_select3 ) ) )
!= ( sk8 @ ( sk7 @ ( pminus_ds1_filter @ a_select3 ) ) ) ) ),
inference(rewrite,[status(thm)],[159,128,302]) ).
thf(12512,plain,
( ( n6 @ pred @ ( sk10 @ leq ) )
| sk4
| sk1
| ~ ( n999 @ pred @ ( pv5 @ leq ) )
| ( ( sk7 @ ( sk8 @ ( pminus_ds1_filter @ a_select3 ) ) )
!= ( sk8 @ ( sk7 @ ( pminus_ds1_filter @ a_select3 ) ) ) ) ),
inference(simp,[status(thm)],[12511]) ).
thf(73,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ leq ) )
=> ( B @ succ @ ( A @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_succ) ).
thf(571,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ leq ) )
=> ( B @ succ @ ( A @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
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(612,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(17450,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk3 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ leq ) )
| ~ $true
| ~ sk1
| ( sk3 @ ( sk2 @ gt ) ) ),
inference(paramod_ordered,[status(thm)],[15100,217]) ).
thf(17451,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk3 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ leq ) )
| ~ sk1
| ( sk3 @ ( sk2 @ gt ) ) ),
inference(simp,[status(thm)],[17450]) ).
thf(17452,plain,
( ( sk3 @ ( sk2 @ leq ) )
| ~ sk1
| ( sk3 @ ( sk2 @ gt ) ) ),
inference(pattern_uni,[status(thm)],[17451:[bind(A,$thf( sk2 )),bind(B,$thf( sk3 ))]]) ).
thf(122,plain,
( ( n1 @ ( n0 @ minus ) @ ( sk9 @ leq ) )
| ( sk7 @ ( n0 @ leq ) )
| sk4
| sk1
| ~ ( n1 @ ( n999 @ minus ) @ ( pv5 @ leq ) )
| ~ ( pv5 @ ( n0 @ leq ) ) ),
inference(cnfConj,[status(thm)],[103]) ).
thf(2515,plain,
( ( n1 @ ( n0 @ minus ) @ ( sk9 @ leq ) )
| ( sk7 @ ( n0 @ leq ) )
| sk4
| sk1
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[122,128,107]) ).
thf(2516,plain,
( ( n1 @ ( n0 @ minus ) @ ( sk9 @ leq ) )
| ( sk7 @ ( n0 @ leq ) )
| sk4
| sk1 ),
inference(simp,[status(thm)],[2515]) ).
thf(8071,plain,
( ( n0 @ pred @ ( sk9 @ leq ) )
| ( sk7 @ ( n0 @ leq ) )
| sk4
| sk1 ),
inference(rewrite,[status(thm)],[2516,302]) ).
thf(5429,plain,
! [A: $i] :
( ( ( tptp_minus_1 @ succ )
!= ( A @ succ ) )
| ( ( n0 @ pred )
= A ) ),
inference(paramod_ordered,[status(thm)],[406,185]) ).
thf(5430,plain,
( ( n0 @ pred )
= tptp_minus_1 ),
inference(pattern_uni,[status(thm)],[5429:[bind(A,$thf( tptp_minus_1 ))]]) ).
thf(8316,plain,
( ( tptp_minus_1 @ ( sk9 @ leq ) )
| ( sk7 @ ( n0 @ leq ) )
| sk4
| sk1 ),
inference(rewrite,[status(thm)],[8071,5430]) ).
thf(7583,plain,
! [B: $i,A: $i] :
( ( ( A @ pred @ succ )
!= ( B @ succ ) )
| ( A != B ) ),
inference(paramod_ordered,[status(thm)],[188,5006]) ).
thf(7584,plain,
! [A: $i] :
( ( A @ pred )
!= A ),
inference(pattern_uni,[status(thm)],[7583:[bind(A,$thf( C )),bind(B,$thf( C @ pred ))]]) ).
thf(7659,plain,
! [A: $i] :
( ( A @ pred )
!= A ),
inference(simp,[status(thm)],[7584]) ).
thf(71,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)],[71]) ).
thf(2882,plain,
! [A: $i] :
( ( ( tptp_minus_1 @ ( n3 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[615,197]) ).
thf(2883,plain,
! [A: $i] :
( ( tptp_minus_1 @ ( n3 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[2882]) ).
thf(2884,plain,
! [A: $i] :
( ( tptp_minus_1 != A )
| ( n3 != A ) ),
inference(simp,[status(thm)],[2883]) ).
thf(2885,plain,
tptp_minus_1 != n3,
inference(simp,[status(thm)],[2884]) ).
thf(61,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(465,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)],[61]) ).
thf(228,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( B @ ( C @ tptp_update2 ) ) @ a_select2 ) )
= D )
| ~ ( B @ ( A @ leq ) )
| ~ ( A @ ( n0 @ leq ) )
| ( B @ ( A @ ( B @ ( C @ ( D @ sk11 ) ) ) @ leq ) ) ),
inference(cnfConj,[status(thm)],[226]) ).
thf(231,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ leq ) )
| ~ ( A @ ( n0 @ leq ) )
| ( B @ ( A @ ( B @ ( C @ ( D @ sk11 ) ) ) @ leq ) )
| ( ( A @ ( D @ ( B @ ( C @ tptp_update2 ) ) @ a_select2 ) )
= D ) ),
inference(lifteq,[status(thm)],[228]) ).
thf(16818,plain,
! [B: $i,A: $i] :
( ( ( tptp_minus_1 @ ( n3 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[615,203]) ).
thf(16819,plain,
! [B: $i,A: $i] :
( ( ( tptp_minus_1 @ ( n3 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[16818]) ).
thf(16820,plain,
n3 @ ( tptp_minus_1 @ lt ),
inference(pattern_uni,[status(thm)],[16819:[bind(A,$thf( tptp_minus_1 )),bind(B,$thf( n3 ))]]) ).
thf(168,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( B @ ( C @ a_select2 ) )
= D )
& ( A != B ) )
=> ! [E: $i] :
( ( B @ ( E @ ( A @ ( C @ tptp_update2 ) ) @ a_select2 ) )
= D ) ),
inference(miniscope,[status(thm)],[167]) ).
thf(169,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( E @ ( A @ ( C @ tptp_update2 ) ) @ a_select2 ) )
= D )
| ( ( B @ ( C @ a_select2 ) )
!= D )
| ( A = B ) ),
inference(cnf,[status(esa)],[168]) ).
thf(170,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( E @ ( A @ ( C @ tptp_update2 ) ) @ a_select2 ) )
= D )
| ( ( B @ ( C @ a_select2 ) )
!= D )
| ( A = B ) ),
inference(lifteq,[status(thm)],[169]) ).
thf(171,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( D @ ( A @ ( C @ tptp_update2 ) ) @ a_select2 ) )
= ( B @ ( C @ a_select2 ) ) )
| ( A = B ) ),
inference(simp,[status(thm)],[170]) ).
thf(257,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F @ ( E @ ( A @ trans @ ( B @ tptp_mmul ) @ ( A @ tptp_mmul ) @ a_select3 ) ) )
= ( E @ ( F @ ( A @ trans @ ( B @ tptp_mmul ) @ ( A @ tptp_mmul ) @ a_select3 ) ) ) )
| ~ ( D @ ( F @ leq ) )
| ~ ( F @ ( n0 @ leq ) )
| ~ ( D @ ( E @ leq ) )
| ~ ( E @ ( n0 @ leq ) )
| ( A @ ( B @ ( C @ sk12 ) ) @ ( n0 @ leq ) ) ),
inference(cnfConj,[status(thm)],[252]) ).
thf(258,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( F @ leq ) )
| ~ ( F @ ( n0 @ leq ) )
| ~ ( D @ ( E @ leq ) )
| ~ ( E @ ( n0 @ leq ) )
| ( A @ ( B @ ( C @ sk12 ) ) @ ( 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(lifteq,[status(thm)],[257]) ).
thf(17462,plain,
! [B: $i,A: $i] :
( ( ( n2 @ ( n5 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[172,217]) ).
thf(17463,plain,
! [B: $i,A: $i] :
( ( ( n2 @ ( n5 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ leq ) ) ),
inference(simp,[status(thm)],[17462]) ).
thf(17464,plain,
n5 @ ( n2 @ leq ),
inference(pattern_uni,[status(thm)],[17463:[bind(A,$thf( n2 )),bind(B,$thf( n5 ))]]) ).
thf(16833,plain,
! [B: $i,A: $i] :
( ( ( n1 @ ( n6 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[237,203]) ).
thf(16834,plain,
! [B: $i,A: $i] :
( ( ( n1 @ ( n6 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[16833]) ).
thf(16835,plain,
n6 @ ( n1 @ lt ),
inference(pattern_uni,[status(thm)],[16834:[bind(A,$thf( n1 )),bind(B,$thf( n6 ))]]) ).
thf(2396,plain,
! [A: $i] :
( ( ( tptp_minus_1 @ ( n0 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[299,197]) ).
thf(2397,plain,
! [A: $i] :
( ( tptp_minus_1 @ ( n0 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[2396]) ).
thf(2398,plain,
! [A: $i] :
( ( tptp_minus_1 != A )
| ( n0 != A ) ),
inference(simp,[status(thm)],[2397]) ).
thf(2399,plain,
tptp_minus_1 != n0,
inference(simp,[status(thm)],[2398]) ).
thf(68,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(536,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)],[68]) ).
thf(234,plain,
! [A: $i] :
( ( A = n6 )
| ( A = n5 )
| ( A = n4 )
| ( A = n3 )
| ( A = n2 )
| ( A = n1 )
| ( A = n0 )
| ~ ( n6 @ ( A @ leq ) )
| ~ ( A @ ( n0 @ leq ) ) ),
inference(cnf,[status(esa)],[233]) ).
thf(235,plain,
! [A: $i] :
( ~ ( n6 @ ( A @ leq ) )
| ~ ( A @ ( n0 @ leq ) )
| ( A = n6 )
| ( A = n5 )
| ( A = n4 )
| ( A = n3 )
| ( A = n2 )
| ( A = n1 )
| ( A = n0 ) ),
inference(lifteq,[status(thm)],[234]) ).
thf(49,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(287,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)],[49]) ).
thf(16869,plain,
! [B: $i,A: $i] :
( ( ( n1 @ ( n4 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[626,203]) ).
thf(16870,plain,
! [B: $i,A: $i] :
( ( ( n1 @ ( n4 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[16869]) ).
thf(16871,plain,
n4 @ ( n1 @ lt ),
inference(pattern_uni,[status(thm)],[16870:[bind(A,$thf( n1 )),bind(B,$thf( n4 ))]]) ).
thf(17429,plain,
! [B: $i,A: $i] :
( ( ( n0 @ ( n3 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[471,217]) ).
thf(17430,plain,
! [B: $i,A: $i] :
( ( ( n0 @ ( n3 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ leq ) ) ),
inference(simp,[status(thm)],[17429]) ).
thf(17431,plain,
n3 @ ( n0 @ leq ),
inference(pattern_uni,[status(thm)],[17430:[bind(A,$thf( n0 )),bind(B,$thf( n3 ))]]) ).
thf(5677,plain,
( ( sk10 != sk9 )
| ( sk10 != sk9 )
| ( id_ds1_filter != id_ds1_filter )
| ( sk8 != sk7 )
| ( sk8 != sk7 )
| ( pminus_ds1_filter != pminus_ds1_filter )
| sk4
| sk1 ),
inference(simp,[status(thm)],[5674]) ).
thf(5760,plain,
( ( sk10 != sk9 )
| ( sk8 != sk7 )
| sk4
| sk1 ),
inference(simp,[status(thm)],[5677]) ).
thf(16872,plain,
! [B: $i,A: $i] :
( ( ( n3 @ ( n4 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[241,203]) ).
thf(16873,plain,
! [B: $i,A: $i] :
( ( ( n3 @ ( n4 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[16872]) ).
thf(16874,plain,
n4 @ ( n3 @ lt ),
inference(pattern_uni,[status(thm)],[16873:[bind(A,$thf( n3 )),bind(B,$thf( n4 ))]]) ).
thf(1811,plain,
( ~ $true
| ( ( sk9 @ ( n0 @ leq ) )
!= ( sk7 @ ( n0 @ leq ) ) )
| ( sk7 @ ( n0 @ leq ) )
| sk4
| sk1 ),
inference(eqfactor_ordered,[status(thm)],[1768]) ).
thf(1813,plain,
( ( sk9 != sk7 )
| ( n0 != n0 )
| ( sk7 @ ( n0 @ leq ) )
| sk4
| sk1 ),
inference(simp,[status(thm)],[1811]) ).
thf(1816,plain,
( ( sk9 != sk7 )
| ( sk7 @ ( n0 @ leq ) )
| sk4
| sk1 ),
inference(simp,[status(thm)],[1813]) ).
thf(4894,plain,
! [B: $i,A: $i] :
( ( ( B @ ( n0 @ ( n0 @ ( A @ tptp_update3 ) ) ) )
!= q_ds1_filter )
| ~ $true
| ~ ( pv5 @ ( sk2 @ leq ) )
| ~ ( pv5 @ ( sk3 @ leq ) )
| ( ( A @ ( pv5 @ sk15 ) )
!= ( A @ ( pv5 @ sk14 ) ) )
| ~ sk1 ),
inference(rewrite,[status(thm)],[1558,595]) ).
thf(4895,plain,
! [B: $i,A: $i] :
( ( ( B @ ( n0 @ ( n0 @ ( A @ tptp_update3 ) ) ) )
!= q_ds1_filter )
| ~ ( pv5 @ ( sk2 @ leq ) )
| ~ ( pv5 @ ( sk3 @ leq ) )
| ( ( A @ ( pv5 @ sk15 ) )
!= ( A @ ( pv5 @ sk14 ) ) )
| ~ sk1 ),
inference(simp,[status(thm)],[4894]) ).
thf(16899,plain,
! [B: $i,A: $i] :
( ( ( n4 @ ( n6 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[620,203]) ).
thf(16900,plain,
! [B: $i,A: $i] :
( ( ( n4 @ ( n6 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[16899]) ).
thf(16901,plain,
n6 @ ( n4 @ lt ),
inference(pattern_uni,[status(thm)],[16900:[bind(A,$thf( n4 )),bind(B,$thf( n6 ))]]) ).
thf(55,axiom,
! [A: $i,B: $i] :
( ( ( A != B )
& ( B @ ( A @ leq ) ) )
=> ( A @ ( B @ gt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_gt2) ).
thf(400,plain,
! [A: $i,B: $i] :
( ( ( A != B )
& ( B @ ( A @ leq ) ) )
=> ( A @ ( B @ gt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(16857,plain,
! [B: $i,A: $i] :
( ( ( n2 @ ( n5 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[172,203]) ).
thf(16858,plain,
! [B: $i,A: $i] :
( ( ( n2 @ ( n5 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[16857]) ).
thf(16859,plain,
n5 @ ( n2 @ lt ),
inference(pattern_uni,[status(thm)],[16858:[bind(A,$thf( n2 )),bind(B,$thf( n5 ))]]) ).
thf(635,plain,
! [A: $i] :
( ( ( n4 @ ( n5 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[181,197]) ).
thf(636,plain,
! [A: $i] :
( ( n4 @ ( n5 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[635]) ).
thf(641,plain,
! [A: $i] :
( ( n4 != A )
| ( n5 != A ) ),
inference(simp,[status(thm)],[636]) ).
thf(644,plain,
n4 != n5,
inference(simp,[status(thm)],[641]) ).
thf(16854,plain,
! [B: $i,A: $i] :
( ( ( n4 @ ( n999 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[236,203]) ).
thf(16855,plain,
! [B: $i,A: $i] :
( ( ( n4 @ ( n999 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ lt ) ) ),
inference(simp,[status(thm)],[16854]) ).
thf(16856,plain,
n999 @ ( n4 @ lt ),
inference(pattern_uni,[status(thm)],[16855:[bind(A,$thf( n4 )),bind(B,$thf( n999 ))]]) ).
thf(2878,plain,
! [A: $i] :
( ( ( n0 @ ( n6 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[611,197]) ).
thf(2879,plain,
! [A: $i] :
( ( n0 @ ( n6 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[2878]) ).
thf(2880,plain,
! [A: $i] :
( ( n0 != A )
| ( n6 != A ) ),
inference(simp,[status(thm)],[2879]) ).
thf(2881,plain,
n6 != n0,
inference(simp,[status(thm)],[2880]) ).
thf(5435,plain,
! [A: $i] :
( ( ( n4 @ succ )
!= ( A @ succ ) )
| ( ( n5 @ pred )
= A ) ),
inference(paramod_ordered,[status(thm)],[3872,185]) ).
thf(5436,plain,
( ( n5 @ pred )
= n4 ),
inference(pattern_uni,[status(thm)],[5435:[bind(A,$thf( n4 ))]]) ).
thf(17402,plain,
! [B: $i,A: $i] :
( ( ( n0 @ ( n1 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[619,217]) ).
thf(17403,plain,
! [B: $i,A: $i] :
( ( ( n0 @ ( n1 @ gt ) )
!= ( A @ ( B @ gt ) ) )
| ( B @ ( A @ leq ) ) ),
inference(simp,[status(thm)],[17402]) ).
thf(17404,plain,
n1 @ ( n0 @ leq ),
inference(pattern_uni,[status(thm)],[17403:[bind(A,$thf( n0 )),bind(B,$thf( n1 ))]]) ).
thf(2450,plain,
! [A: $i] :
( ( ( n3 @ ( n6 @ gt ) )
!= ( A @ ( A @ gt ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[404,197]) ).
thf(2451,plain,
! [A: $i] :
( ( n3 @ ( n6 @ gt ) )
!= ( A @ ( A @ gt ) ) ),
inference(simp,[status(thm)],[2450]) ).
thf(2452,plain,
! [A: $i] :
( ( n3 != A )
| ( n6 != A ) ),
inference(simp,[status(thm)],[2451]) ).
thf(2453,plain,
n3 != n6,
inference(simp,[status(thm)],[2452]) ).
thf(1812,plain,
( ( ( sk9 @ ( n0 @ leq ) )
!= ( sk7 @ ( n0 @ leq ) ) )
| ( sk7 @ ( n0 @ leq ) )
| sk4
| sk1 ),
inference(simp,[status(thm)],[1811]) ).
thf(229,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( B @ ( C @ tptp_update2 ) ) @ a_select2 ) )
= D )
| ~ ( B @ ( A @ leq ) )
| ~ ( A @ ( n0 @ leq ) )
| ( ( A @ ( B @ ( C @ ( D @ sk11 ) ) ) @ ( C @ a_select2 ) )
!= D ) ),
inference(cnfConj,[status(thm)],[226]) ).
thf(232,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ leq ) )
| ~ ( A @ ( n0 @ leq ) )
| ( ( A @ ( D @ ( B @ ( C @ tptp_update2 ) ) @ a_select2 ) )
= D )
| ( ( A @ ( B @ ( C @ ( D @ sk11 ) ) ) @ ( C @ a_select2 ) )
!= D ) ),
inference(lifteq,[status(thm)],[229]) ).
thf(39305,plain,
$false,
inference(e,[status(thm)],[645,16013,16808,468,666,481,628,249,7660,9020,683,3858,17437,9918,8315,16862,12789,17407,16898,5444,217,276,4884,5674,670,10181,533,16817,472,404,16752,185,16868,16877,2082,17428,5765,570,5759,619,16919,17449,10142,5338,16853,606,2403,189,216,164,10641,5526,591,238,17398,8479,9779,3075,179,17410,623,211,646,1828,16907,16826,17425,280,634,221,17470,206,11939,3986,243,1405,233,4893,4888,201,5438,220,102,16829,1768,2705,8168,302,260,5815,17467,598,160,192,407,16865,1824,275,8058,197,3314,16916,11532,1407,8104,224,16472,650,615,188,16850,593,8567,989,15702,4123,8314,16910,1017,2685,5006,403,2692,471,16805,2877,16847,225,554,10015,16348,4744,2172,679,16889,1539,12191,173,9017,2697,15587,3083,17419,1086,205,5434,16886,3508,662,128,237,16913,618,166,3079,279,573,180,16012,5758,601,176,191,579,1535,17422,259,413,15100,11396,281,204,16796,611,17458,16823,181,8202,9224,2166,236,604,17401,172,219,2637,10385,230,245,5407,17461,208,599,8276,406,16883,616,303,1667,477,11669,631,609,594,213,621,626,198,5410,240,16999,16799,16802,16904,5442,12135,2086,2592,241,167,394,306,3310,299,17413,12120,5424,162,4813,548,2449,194,10672,2588,1941,263,8772,3315,4971,3872,12937,182,17455,11257,2701,16811,12752,16892,576,4132,8391,16895,12512,600,175,571,595,612,991,17452,8316,7659,627,556,2885,203,218,250,465,231,16820,652,186,171,258,17464,16835,568,2399,207,536,235,246,214,287,300,620,16871,950,17431,5430,405,183,603,3469,5760,16874,210,1816,4895,8019,195,3479,239,242,664,16901,8277,400,575,16859,596,644,163,178,277,16856,3528,2881,5436,215,17404,2453,1812,222,232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV114+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.07 % 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
% 0.13/0.38 % Computer : n018.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Sat Sep 26 13:16:06 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.39 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
% 0.90/1.10 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.48/1.45 % [INFO] Parsing done (343ms).
% 1.48/1.47 % [INFO] Running in sequential loop mode.
% 2.58/2.06 % [INFO] eprover registered as external prover.
% 2.58/2.07 % [INFO] Scanning for conjecture ...
% 2.81/2.29 % [INFO] Found a conjecture (or negated_conjecture) and 101 axioms. Running axiom selection ...
% 3.14/2.48 % [INFO] Axiom selection finished. Selected 99 axioms (removed 2 axioms).
% 3.46/2.69 % [INFO] Problem is first-order (TPTP FOF).
% 3.62/2.71 % [INFO] Type checking passed.
% 3.62/2.72 % [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 ...
% 87.37/24.39 % External prover 'e' found a proof!
% 87.37/24.40 % [INFO] Killing All external provers ...
% 87.80/24.40 % Time passed: 23867ms (effective reasoning time: 22917ms)
% 87.80/24.40 % 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)>
% 87.80/24.40 % Axioms used in derivation (99): gt_6_0, gt_999_6, gt_0_tptp_minus_1, leq_minus, gt_999_1, sel3_update_2, gt_6_1, sel2_update_2, succ_plus_5_l, lt_gt, gt_5_tptp_minus_1, succ_plus_3_r, gt_4_3, transitivity_gt, gt_6_4, matrix_symm_inv, matrix_symm_trans, finite_domain_1, gt_5_0, const_array2_select, finite_domain_6, gt_2_tptp_minus_1, gt_6_tptp_minus_1, sel3_update_3, leq_geq, gt_999_5, gt_1_0, leq_gt2, gt_5_4, gt_999_0, succ_plus_1_l, gt_3_2, matrix_symm_add, leq_succ_gt, finite_domain_5, pred_minus_1, gt_6_5, successor_3, gt_3_tptp_minus_1, matrix_symm_update_diagonal, sel2_update_1, gt_4_2, matrix_symm_sub, gt_5_3, gt_999_2, successor_4, gt_succ, succ_plus_4_l, reflexivity_leq, successor_2, leq_gt1, gt_1_tptp_minus_1, finite_domain_2, matrix_symm_aba1, finite_domain_4, matrix_symm_aba2, succ_tptp_minus_1, succ_plus_5_r, leq_succ_succ, sum_plus_base_float, succ_plus_2_l, gt_999_3, gt_3_1, gt_4_1, gt_2_0, gt_5_2, gt_999_tptp_minus_1, const_array1_select, leq_gt_pred, matrix_symm_joseph_update, succ_pred, totality, successor_6, transitivity_leq, finite_domain_3, uniform_int_rand_ranges_lo, gt_6_3, sel3_update_1, successor_1, sum_plus_base, irreflexivity_gt, successor_5, gt_3_0, sel2_update_3, pred_succ, gt_999_4, succ_plus_1_r, succ_plus_3_l, gt_4_tptp_minus_1, succ_plus_4_r, gt_4_0, succ_plus_2_r, gt_6_2, leq_succ_gt_equiv, gt_5_1, uniform_int_rand_ranges_hi, gt_2_1, finite_domain_0, leq_succ
% 87.80/24.40 % No. of inferences in proof: 927
% 87.80/24.41 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 23867 ms resp. 22917 ms w/o parsing
% 89.61/24.83 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 89.61/24.84 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------