%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU451+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n002.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 08:39:02 AM UTC 2026
% Result : Theorem 8.67s 4.56s
% Output : Refutation 9.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 41
% Syntax : Number of formulae : 84 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 213 ( 17 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 693 ( 26 ~; 2 |; 80 &; 538 @)
% ( 2 <=>; 45 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 21 usr; 2 con; 0-6 aty)
% Number of variables : 190 ( 0 ^; 172 !; 18 ?; 190 :)
% Comments :
%------------------------------------------------------------------------------
thf(m2_relset_1_decl,type,
m2_relset_1: $i > $i > $i > $o ).
thf(k9_relset_2_decl,type,
k9_relset_2: $i > $i > $i > $i > $i > $i ).
thf(k6_partfun1_decl,type,
k6_partfun1: $i > $i ).
thf(v1_xboole_0_decl,type,
v1_xboole_0: $i > $o ).
thf(k1_xboole_0_decl,type,
k1_xboole_0: $i ).
thf(m1_subset_1_decl,type,
m1_subset_1: $i > $i > $o ).
thf(r2_hidden_decl,type,
r2_hidden: $i > $i > $o ).
thf(v1_relat_1_decl,type,
v1_relat_1: $i > $o ).
thf(k5_relat_1_decl,type,
k5_relat_1: $i > $i > $i ).
thf(v3_relat_2_decl,type,
v3_relat_2: $i > $o ).
thf(v8_relat_2_decl,type,
v8_relat_2: $i > $o ).
thf(v1_relat_2_decl,type,
v1_relat_2: $i > $o ).
thf(k6_relat_1_decl,type,
k6_relat_1: $i > $i ).
thf(v1_funct_1_decl,type,
v1_funct_1: $i > $o ).
thf(v4_relat_2_decl,type,
v4_relat_2: $i > $o ).
thf(r1_tarski_decl,type,
r1_tarski: $i > $i > $o ).
thf(k1_zfmisc_1_decl,type,
k1_zfmisc_1: $i > $i ).
thf(k2_zfmisc_1_decl,type,
k2_zfmisc_1: $i > $i > $i ).
thf(m1_relset_1_decl,type,
m1_relset_1: $i > $i > $i > $o ).
thf(v1_partfun1_decl,type,
v1_partfun1: $i > $i > $i > $o ).
thf(k7_relset_1_decl,type,
k7_relset_1: $i > $i > $i > $i > $i > $i > $i ).
thf(29,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ( A @ v1_relat_1 ) )
=> ( B @ ( A @ k5_relat_1 ) @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_relat_1) ).
thf(138,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ( A @ v1_relat_1 ) )
=> ( B @ ( A @ k5_relat_1 ) @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(24,axiom,
! [A: $i] :
~ ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(120,plain,
! [A: $i] :
~ ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(110,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(41,axiom,
! [A: $i] :
( ( A @ ( A @ ( A @ k6_partfun1 @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k6_partfun1 @ v1_partfun1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_partfun1) ).
thf(179,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ k6_partfun1 @ m2_relset_1 ) ) )
& ( A @ ( A @ ( A @ k6_partfun1 @ v1_partfun1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(10,axiom,
! [A: $i] :
( ( ( A @ v8_relat_2 )
& ( A @ v3_relat_2 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v1_relat_2 )
& ( A @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_partfun1) ).
thf(70,plain,
! [A: $i] :
( ( ( A @ v8_relat_2 )
& ( A @ v3_relat_2 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v1_relat_2 )
& ( A @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(5,axiom,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( A != B )
& ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
thf(53,plain,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( A != B )
& ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(15,axiom,
( ( k1_xboole_0 @ v1_relat_1 )
& ( k1_xboole_0 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
thf(96,plain,
( ( k1_xboole_0 @ v1_relat_1 )
& ( k1_xboole_0 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(26,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m1_relset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_relset_1) ).
thf(128,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m1_relset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(34,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( B @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
& ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) )
=> ( C @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ k9_relset_2 ) ) ) ) @ m2_relset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k9_relset_2) ).
thf(159,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( B @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
& ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) )
=> ( C @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ k9_relset_2 ) ) ) ) @ m2_relset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(40,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( C @ ( F @ m1_relset_1 ) ) )
& ( B @ ( A @ ( E @ m1_relset_1 ) ) ) )
=> ( D @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k7_relset_1 ) ) ) ) ) @ m2_relset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_relset_1) ).
thf(177,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( C @ ( F @ m1_relset_1 ) ) )
& ( B @ ( A @ ( E @ m1_relset_1 ) ) ) )
=> ( D @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k7_relset_1 ) ) ) ) ) @ m2_relset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( ( C @ ( A @ k6_partfun1 @ ( B @ ( A @ ( A @ k9_relset_2 ) ) ) ) )
= ( B @ k6_partfun1 @ ( C @ ( B @ ( B @ ( A @ k9_relset_2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_relset_2) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( ( C @ ( A @ k6_partfun1 @ ( B @ ( A @ ( A @ k9_relset_2 ) ) ) ) )
= ( B @ k6_partfun1 @ ( C @ ( B @ ( B @ ( A @ k9_relset_2 ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(43,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( ( C @ ( A @ k6_partfun1 @ ( B @ ( A @ ( A @ k9_relset_2 ) ) ) ) )
= ( B @ k6_partfun1 @ ( C @ ( B @ ( B @ ( A @ k9_relset_2 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(17,axiom,
! [A: $i] :
? [B: $i] :
( ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(104,plain,
! [A: $i] :
? [B: $i] :
( ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(21,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(114,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ m1_subset_1 ) )
=> ( ( B @ ( A @ r2_hidden ) )
| ( B @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(51,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ m1_subset_1 ) )
=> ( ( B @ ( A @ r2_hidden ) )
| ( B @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(14,axiom,
! [A: $i,B: $i] : ( A @ ( A @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(94,plain,
! [A: $i] : ( A @ ( A @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(36,axiom,
! [A: $i] :
( ( A @ k6_partfun1 )
= ( A @ k6_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_partfun1) ).
thf(163,plain,
! [A: $i] :
( ( A @ k6_partfun1 )
= ( A @ k6_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(16,axiom,
? [A: $i] :
( ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
thf(100,plain,
? [A: $i] :
( ( A @ v1_relat_1 )
& ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(39,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( B @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
& ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ k9_relset_2 ) ) ) ) )
= ( E @ ( D @ k5_relat_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k9_relset_2) ).
thf(174,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( B @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
& ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) ) )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ k9_relset_2 ) ) ) ) )
= ( E @ ( D @ k5_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(42,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( ( ( B @ k6_partfun1 @ ( C @ ( B @ ( B @ ( B @ ( A @ k7_relset_1 ) ) ) ) ) )
= C )
& ( ( C @ ( A @ k6_partfun1 @ ( B @ ( A @ ( A @ ( A @ k7_relset_1 ) ) ) ) ) )
= C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_funct_2) ).
thf(185,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( ( ( B @ k6_partfun1 @ ( C @ ( B @ ( B @ ( B @ ( A @ k7_relset_1 ) ) ) ) ) )
= C )
& ( ( C @ ( A @ k6_partfun1 @ ( B @ ( A @ ( A @ ( A @ k7_relset_1 ) ) ) ) ) )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(32,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( C @ ( F @ m1_relset_1 ) ) )
& ( B @ ( A @ ( E @ m1_relset_1 ) ) ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k7_relset_1 ) ) ) ) ) )
= ( F @ ( E @ k5_relat_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k7_relset_1) ).
thf(152,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( C @ ( F @ m1_relset_1 ) ) )
& ( B @ ( A @ ( E @ m1_relset_1 ) ) ) )
=> ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ k7_relset_1 ) ) ) ) ) )
= ( F @ ( E @ k5_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(57,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( B @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) )
<=> ( B @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
thf(132,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ r1_tarski ) )
=> ( B @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) ) )
& ( ( B @ k1_zfmisc_1 @ ( A @ m1_subset_1 ) )
=> ( B @ ( A @ r1_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( B @ ( A @ k2_zfmisc_1 ) @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_subset_1) ).
thf(116,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ~ ( B @ ( A @ k2_zfmisc_1 ) @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(11,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
thf(74,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(37,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
<=> ( B @ ( A @ ( C @ m1_relset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
thf(166,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( B @ ( A @ ( C @ m2_relset_1 ) ) ) )
& ( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( B @ ( A @ ( C @ m1_relset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(35,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m2_relset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_relset_1) ).
thf(161,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m2_relset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ v1_xboole_0 )
& ( C @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
thf(149,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ v1_xboole_0 )
& ( C @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ( A @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k5_relat_1 ) @ v1_relat_1 )
& ( B @ ( A @ k5_relat_1 ) @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc9_relat_1) ).
thf(59,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ( A @ v1_xboole_0 ) )
=> ( ( B @ ( A @ k5_relat_1 ) @ v1_relat_1 )
& ( B @ ( A @ k5_relat_1 ) @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(23,axiom,
! [A: $i] : ( A @ k6_relat_1 @ v1_relat_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_relat_1) ).
thf(118,plain,
! [A: $i] : ( A @ k6_relat_1 @ v1_relat_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(38,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).
thf(172,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m2_relset_1 ) ) )
=> ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(12,axiom,
? [A: $i] :
( ( A @ v1_relat_1 )
& ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
thf(76,plain,
? [A: $i] :
( ( A @ v1_relat_1 )
& ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(30,axiom,
! [A: $i] :
? [B: $i] :
( ( A @ ( A @ ( B @ v1_partfun1 ) ) )
& ( B @ v8_relat_2 )
& ( B @ v4_relat_2 )
& ( B @ v3_relat_2 )
& ( B @ v1_relat_2 )
& ( B @ v1_relat_1 )
& ( A @ ( A @ ( B @ m1_relset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_partfun1) ).
thf(140,plain,
! [A: $i] :
? [B: $i] :
( ( A @ ( A @ ( B @ v1_partfun1 ) ) )
& ( B @ v8_relat_2 )
& ( B @ v4_relat_2 )
& ( B @ v3_relat_2 )
& ( B @ v1_relat_2 )
& ( B @ v1_relat_1 )
& ( A @ ( A @ ( B @ m1_relset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ( A @ v1_xboole_0 ) )
=> ( ( A @ ( B @ k5_relat_1 ) @ v1_relat_1 )
& ( A @ ( B @ k5_relat_1 ) @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc10_relat_1) ).
thf(66,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_relat_1 )
& ( A @ v1_xboole_0 ) )
=> ( ( A @ ( B @ k5_relat_1 ) @ v1_relat_1 )
& ( A @ ( B @ k5_relat_1 ) @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(33,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ~ ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(155,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ~ ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( C @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).
thf(108,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ k2_zfmisc_1 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ( C @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(27,axiom,
! [A: $i,B: $i] : ( B @ ( A @ k2_zfmisc_1 ) @ v1_relat_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_sysrel) ).
thf(130,plain,
! [A: $i,B: $i] : ( B @ ( A @ k2_zfmisc_1 ) @ v1_relat_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(13,axiom,
! [A: $i] :
( ( A @ k6_relat_1 @ v8_relat_2 )
& ( A @ k6_relat_1 @ v4_relat_2 )
& ( A @ k6_relat_1 @ v3_relat_2 )
& ( A @ k6_relat_1 @ v1_relat_2 )
& ( A @ k6_relat_1 @ v1_funct_1 )
& ( A @ k6_relat_1 @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_partfun1) ).
thf(80,plain,
! [A: $i] :
( ( A @ k6_relat_1 @ v8_relat_2 )
& ( A @ k6_relat_1 @ v4_relat_2 )
& ( A @ k6_relat_1 @ v3_relat_2 )
& ( A @ k6_relat_1 @ v1_relat_2 )
& ( A @ k6_relat_1 @ v1_funct_1 )
& ( A @ k6_relat_1 @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( B @ ( A @ r2_hidden ) ) )
=> ( C @ ( A @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
thf(112,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
& ( B @ ( A @ r2_hidden ) ) )
=> ( C @ ( A @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(25,axiom,
! [A: $i,B: $i] :
? [C: $i] :
( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_partfun1) ).
thf(123,plain,
! [A: $i,B: $i] :
? [C: $i] :
( ( C @ v1_funct_1 )
& ( C @ v1_relat_1 )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(3,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(48,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(8,axiom,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(63,plain,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(197,plain,
$false,
inference(e,[status(thm)],[138,120,110,179,70,53,96,128,159,177,43,104,114,51,94,163,100,174,185,152,57,132,116,74,166,161,149,59,118,172,76,140,66,155,108,130,80,112,123,48,63]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU451+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.13 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.24/0.50 % Computer : n002.cluster.edu
% 0.24/0.50 % Model : x86_64 x86_64
% 0.24/0.50 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.24/0.50 % Memory : 8046.5625MB
% 0.24/0.50 % OS : Linux 6.8.0-71-generic
% 0.24/0.50 % CPULimit : 300
% 0.24/0.50 % WCLimit : 300
% 0.24/0.50 % DateTime : Sat Sep 26 10:04:50 UTC 2026
% 0.24/0.51 % CPUTime :
% 0.24/0.51 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.57/1.43 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.08/1.78 % [INFO] Parsing done (343ms).
% 2.48/1.81 % [INFO] Running in sequential loop mode.
% 3.45/2.45 % [INFO] eprover registered as external prover.
% 3.45/2.46 % [INFO] Scanning for conjecture ...
% 3.85/2.65 % [INFO] Found a conjecture (or negated_conjecture) and 47 axioms. Running axiom selection ...
% 4.03/2.79 % [INFO] Axiom selection finished. Selected 40 axioms (removed 7 axioms).
% 4.50/2.90 % [INFO] Problem is first-order (TPTP FOF).
% 4.50/2.92 % [INFO] Type checking passed.
% 4.50/2.93 % [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 ...
% 8.67/4.55 % External prover 'e' found a proof!
% 8.67/4.55 % [INFO] Killing All external provers ...
% 8.67/4.55 % Time passed: 3822ms (effective reasoning time: 2737ms)
% 8.67/4.55 % 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)>
% 8.67/4.56 % Axioms used in derivation (40): fc2_partfun1, fc9_relat_1, existence_m1_relset_1, dt_k6_relat_1, redefinition_k7_relset_1, t8_boole, fc1_sysrel, antisymmetry_r2_hidden, t23_funct_2, redefinition_m2_relset_1, fc4_relat_1, t1_subset, dt_k7_relset_1, fc4_subset_1, rc2_partfun1, dt_k6_partfun1, dt_m2_relset_1, cc1_relat_1, t6_boole, rc2_subset_1, rc3_partfun1, t5_subset, dt_k9_relset_2, t4_subset, cc1_partfun1, t7_boole, fc1_subset_1, redefinition_k6_partfun1, fc10_relat_1, rc1_subset_1, t3_subset, cc1_relset_1, existence_m1_subset_1, rc2_relat_1, existence_m2_relset_1, rc1_relat_1, dt_k5_relat_1, reflexivity_r1_tarski, redefinition_k9_relset_2, t2_subset
% 8.67/4.56 % No. of inferences in proof: 84
% 8.67/4.56 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3822 ms resp. 2737 ms w/o parsing
% 9.35/4.70 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 9.35/4.70 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------