%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GRP632+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 : n001.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 07:21:28 AM UTC 2026
% Result : Theorem 16.01s 10.22s
% Output : Refutation 16.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 72
% Syntax : Number of formulae : 146 ( 25 unt; 0 typ; 0 def)
% Number of atoms : 543 ( 30 equ; 0 cnn)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 1699 ( 69 ~; 2 |; 274 &;1233 @)
% ( 3 <=>; 118 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 40 ( 38 usr; 2 con; 0-6 aty)
% Number of variables : 307 ( 0 ^; 263 !; 44 ?; 307 :)
% Comments :
%------------------------------------------------------------------------------
thf(v3_struct_0_decl,type,
v3_struct_0: $i > $o ).
thf(v1_group_1_decl,type,
v1_group_1: $i > $o ).
thf(v3_group_1_decl,type,
v3_group_1: $i > $o ).
thf(v4_group_1_decl,type,
v4_group_1: $i > $o ).
thf(l1_group_1_decl,type,
l1_group_1: $i > $o ).
thf(m2_fraenkel_decl,type,
m2_fraenkel: $i > $i > $i > $i > $o ).
thf(u1_struct_0_decl,type,
u1_struct_0: $i > $i ).
thf(k4_autgroup_decl,type,
k4_autgroup: $i > $i ).
thf(k7_funct_2_decl,type,
k7_funct_2: $i > $i > $i > $i > $i > $i ).
thf(k6_autgroup_decl,type,
k6_autgroup: $i > $i > $i ).
thf(k2_group_1_decl,type,
k2_group_1: $i > $i ).
thf(v1_relat_1_decl,type,
v1_relat_1: $i > $o ).
thf(k6_relat_1_decl,type,
k6_relat_1: $i > $i ).
thf(r2_hidden_decl,type,
r2_hidden: $i > $i > $o ).
thf(v1_funct_1_decl,type,
v1_funct_1: $i > $o ).
thf(v2_funct_1_decl,type,
v2_funct_1: $i > $o ).
thf(r1_tarski_decl,type,
r1_tarski: $i > $i > $o ).
thf(v1_xboole_0_decl,type,
v1_xboole_0: $i > $o ).
thf(v1_funct_2_decl,type,
v1_funct_2: $i > $i > $i > $o ).
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(g1_group_1_decl,type,
g1_group_1: $i > $i > $i ).
thf(m1_subset_1_decl,type,
m1_subset_1: $i > $i > $o ).
thf(k1_zfmisc_1_decl,type,
k1_zfmisc_1: $i > $i ).
thf(m2_relset_1_decl,type,
m2_relset_1: $i > $i > $i > $o ).
thf(l1_struct_0_decl,type,
l1_struct_0: $i > $o ).
thf(v1_partfun1_decl,type,
v1_partfun1: $i > $i > $i > $o ).
thf(m1_fraenkel_decl,type,
m1_fraenkel: $i > $i > $i > $o ).
thf(v1_fraenkel_decl,type,
v1_fraenkel: $i > $o ).
thf(k7_relset_1_decl,type,
k7_relset_1: $i > $i > $i > $i > $i > $i > $i ).
thf(k6_partfun1_decl,type,
k6_partfun1: $i > $i ).
thf(v3_funct_2_decl,type,
v3_funct_2: $i > $i > $i > $o ).
thf(v2_funct_2_decl,type,
v2_funct_2: $i > $i > $i > $o ).
thf(k5_relat_1_decl,type,
k5_relat_1: $i > $i > $i ).
thf(k1_xboole_0_decl,type,
k1_xboole_0: $i ).
thf(v1_relat_2_decl,type,
v1_relat_2: $i > $o ).
thf(v2_group_1_decl,type,
v2_group_1: $i > $o ).
thf(u1_group_1_decl,type,
u1_group_1: $i > $i ).
thf(57,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( B @ ( A @ g1_group_1 ) @ l1_group_1 )
& ( B @ ( A @ g1_group_1 ) @ v1_group_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_g1_group_1) ).
thf(288,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( B @ ( A @ g1_group_1 ) @ l1_group_1 )
& ( B @ ( A @ g1_group_1 ) @ v1_group_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(28,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(169,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)],[28]) ).
thf(71,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( A @ k2_group_1 @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_group_1) ).
thf(343,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( A @ k2_group_1 @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(54,axiom,
? [A: $i] :
( ( A @ v1_group_1 )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_group_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_group_1) ).
thf(279,plain,
? [A: $i] :
( ( A @ v1_group_1 )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_group_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(56,axiom,
? [A: $i] : ( A @ l1_group_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_group_1) ).
thf(286,plain,
? [A: $i] : ( A @ l1_group_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(33,axiom,
? [A: $i] :
~ ( A @ v1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(194,plain,
? [A: $i] :
~ ( A @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(16,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(127,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)],[16]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i,D: $i] :
( ( ( B @ ( A @ g1_group_1 ) )
= ( D @ ( C @ g1_group_1 ) ) )
=> ( ( B = D )
& ( A = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',free_g1_group_1) ).
thf(107,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 ) )
=> ! [C: $i,D: $i] :
( ( ( B @ ( A @ g1_group_1 ) )
= ( D @ ( C @ g1_group_1 ) ) )
=> ( ( B = D )
& ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(18,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(138,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m1_relset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(8,axiom,
? [A: $i] :
( ( A @ v1_xboole_0 )
& ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_partfun1) ).
thf(101,plain,
? [A: $i] :
( ( A @ v1_xboole_0 )
& ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(73,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( B @ ( E @ m1_relset_1 ) ) )
& ( C @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ( B @ ( A @ ( D @ m1_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( C @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ k7_funct_2 ) ) ) ) @ m2_relset_1 ) ) )
& ( C @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ k7_funct_2 ) ) ) ) @ v1_funct_2 ) ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ k7_funct_2 ) ) ) ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_funct_2) ).
thf(347,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( B @ ( E @ m1_relset_1 ) ) )
& ( C @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ( B @ ( A @ ( D @ m1_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( C @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ k7_funct_2 ) ) ) ) @ m2_relset_1 ) ) )
& ( C @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ k7_funct_2 ) ) ) ) @ v1_funct_2 ) ) )
& ( E @ ( D @ ( C @ ( B @ ( A @ k7_funct_2 ) ) ) ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(5,axiom,
? [A: $i] :
( ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_funct_1) ).
thf(88,plain,
? [A: $i] :
( ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(11,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(115,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)],[11]) ).
thf(63,axiom,
? [A: $i] :
( ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ( A @ v2_group_1 )
& ( A @ v1_group_1 )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_group_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_group_1) ).
thf(308,plain,
? [A: $i] :
( ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ( A @ v2_group_1 )
& ( A @ v1_group_1 )
& ~ ( A @ v3_struct_0 )
& ( A @ l1_group_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(20,axiom,
? [A: $i] : ( A @ l1_struct_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(142,plain,
? [A: $i] : ( A @ l1_struct_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(70,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( B @ ( E @ m1_relset_1 ) ) )
& ( C @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ( B @ ( A @ ( D @ m1_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ k7_funct_2 ) ) ) ) )
= ( E @ ( D @ k5_relat_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k7_funct_2) ).
thf(340,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( C @ ( B @ ( E @ m1_relset_1 ) ) )
& ( C @ ( B @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ( B @ ( A @ ( D @ m1_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 ) )
=> ( ( E @ ( D @ ( C @ ( B @ ( A @ k7_funct_2 ) ) ) ) )
= ( E @ ( D @ k5_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( ( ( B @ ( A @ ( C @ v3_funct_2 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v2_funct_2 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v2_funct_1 )
& ( C @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_funct_2) ).
thf(184,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( ( ( B @ ( A @ ( C @ v3_funct_2 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v2_funct_2 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v2_funct_1 )
& ( C @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(15,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_funct_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(125,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(24,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(157,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(6,axiom,
! [A: $i] :
( ( A @ k6_relat_1 @ v1_funct_1 )
& ( A @ k6_relat_1 @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_funct_1) ).
thf(93,plain,
! [A: $i] :
( ( A @ k6_relat_1 @ v1_funct_1 )
& ( A @ k6_relat_1 @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(55,axiom,
! [A: $i] :
( ( A @ l1_group_1 )
=> ( A @ l1_struct_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_group_1) ).
thf(284,plain,
! [A: $i] :
( ( A @ l1_group_1 )
=> ( A @ l1_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(66,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( B @ ( A @ g1_group_1 ) @ v1_group_1 )
& ~ ( B @ ( A @ g1_group_1 ) @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_group_1) ).
thf(325,plain,
! [A: $i,B: $i] :
( ( ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ m1_relset_1 ) ) )
& ( A @ ( A @ ( A @ k2_zfmisc_1 ) @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_funct_1 )
& ~ ( A @ v1_xboole_0 ) )
=> ( ( B @ ( A @ g1_group_1 ) @ v1_group_1 )
& ~ ( B @ ( A @ g1_group_1 ) @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(64,axiom,
! [A: $i] :
( ( A @ l1_group_1 )
=> ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u1_group_1 @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u1_group_1 @ v1_funct_2 ) ) )
& ( A @ u1_group_1 @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u1_group_1) ).
thf(316,plain,
! [A: $i] :
( ( A @ l1_group_1 )
=> ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u1_group_1 @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u1_group_1 @ v1_funct_2 ) ) )
& ( A @ u1_group_1 @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(65,axiom,
! [A: $i] :
( ( A @ l1_group_1 )
=> ( ( ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v2_group_1 )
& ~ ( A @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_group_1) ).
thf(321,plain,
! [A: $i] :
( ( A @ l1_group_1 )
=> ( ( ( A @ v3_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v2_group_1 )
& ~ ( A @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(39,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(211,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(44,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(238,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)],[44]) ).
thf(14,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(121,plain,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( A != B )
& ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(3,axiom,
! [A: $i] : ( A @ k6_relat_1 @ v1_relat_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_relat_1) ).
thf(84,plain,
! [A: $i] : ( A @ k6_relat_1 @ v1_relat_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(17,axiom,
! [A: $i,B: $i] :
? [C: $i] :
( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_2) ).
thf(132,plain,
! [A: $i,B: $i] :
? [C: $i] :
( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 )
& ( B @ ( A @ ( C @ m1_relset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(1,conjecture,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ( A @ v1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ k4_autgroup @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ m2_fraenkel ) ) ) )
=> ( ( ( A @ k2_group_1 @ ( A @ k6_autgroup ) @ ( B @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k7_funct_2 ) ) ) ) )
= B )
& ( ( B @ ( A @ k2_group_1 @ ( A @ k6_autgroup ) @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k7_funct_2 ) ) ) ) )
= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_autgroup) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ( A @ v1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ k4_autgroup @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ m2_fraenkel ) ) ) )
=> ( ( ( A @ k2_group_1 @ ( A @ k6_autgroup ) @ ( B @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k7_funct_2 ) ) ) ) )
= B )
& ( ( B @ ( A @ k2_group_1 @ ( A @ k6_autgroup ) @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k7_funct_2 ) ) ) ) )
= B ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(74,plain,
~ ! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ( A @ v1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( A @ k4_autgroup @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ m2_fraenkel ) ) ) )
=> ( ( ( A @ k2_group_1 @ ( A @ k6_autgroup ) @ ( B @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k7_funct_2 ) ) ) ) )
= B )
& ( ( B @ ( A @ k2_group_1 @ ( A @ k6_autgroup ) @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k7_funct_2 ) ) ) ) )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(58,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ( A @ v1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k2_group_1 @ ( A @ k6_autgroup ) )
= ( A @ u1_struct_0 @ k6_partfun1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_autgroup) ).
thf(292,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ( A @ v1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ k2_group_1 @ ( A @ k6_autgroup ) )
= ( A @ u1_struct_0 @ k6_partfun1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(12,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(117,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)],[12]) ).
thf(41,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(220,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m2_relset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(60,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ( A @ v1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ k4_autgroup @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ ( A @ k6_autgroup ) @ m2_fraenkel ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_autgroup) ).
thf(297,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ( A @ v1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ k4_autgroup @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ ( A @ k6_autgroup ) @ m2_fraenkel ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(53,axiom,
! [A: $i] :
( ( ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ~ ( B @ v1_xboole_0 )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc5_struct_0) ).
thf(275,plain,
! [A: $i] :
( ( ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ~ ( B @ v1_xboole_0 )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(43,axiom,
! [A: $i] :
? [B: $i] :
( ( A @ ( A @ ( B @ v3_funct_2 ) ) )
& ( A @ ( A @ ( B @ v2_funct_2 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v2_funct_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 )
& ( A @ ( A @ ( B @ m1_relset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_2) ).
thf(229,plain,
! [A: $i] :
? [B: $i] :
( ( A @ ( A @ ( B @ v3_funct_2 ) ) )
& ( A @ ( A @ ( B @ v2_funct_2 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v2_funct_1 )
& ( B @ v1_funct_1 )
& ( B @ v1_relat_1 )
& ( A @ ( A @ ( B @ m1_relset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(48,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(252,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)],[48]) ).
thf(34,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(197,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)],[34]) ).
thf(67,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m1_fraenkel ) ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [D: $i] :
( ( C @ ( B @ ( A @ ( D @ m2_fraenkel ) ) ) )
<=> ( C @ ( D @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_fraenkel) ).
thf(329,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m1_fraenkel ) ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [D: $i] :
( ( ( C @ ( D @ m1_subset_1 ) )
=> ( C @ ( B @ ( A @ ( D @ m2_fraenkel ) ) ) ) )
& ( ( C @ ( B @ ( A @ ( D @ m2_fraenkel ) ) ) )
=> ( C @ ( D @ m1_subset_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(21,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(144,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)],[21]) ).
thf(68,axiom,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ( A @ v1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ k4_autgroup @ m1_fraenkel ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_autgroup) ).
thf(335,plain,
! [A: $i] :
( ( ( A @ l1_group_1 )
& ( A @ v4_group_1 )
& ( A @ v3_group_1 )
& ( A @ v1_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ k4_autgroup @ m1_fraenkel ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(86,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(25,axiom,
! [A: $i] :
( ( A @ v1_fraenkel )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_fraenkel) ).
thf(159,plain,
! [A: $i] :
( ( A @ v1_fraenkel )
=> ! [B: $i] :
( ( A @ ( B @ m1_subset_1 ) )
=> ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ( ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( B @ ( A @ ( C @ v1_partfun1 ) ) )
& ~ ( C @ v1_xboole_0 )
& ( C @ v1_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc6_funct_2) ).
thf(172,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ v1_xboole_0 )
& ~ ( A @ v1_xboole_0 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( B @ ( A @ ( C @ v1_partfun1 ) ) )
& ~ ( C @ v1_xboole_0 )
& ( C @ v1_funct_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(10,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(113,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(46,axiom,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_xboole_0 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_funct_1) ).
thf(245,plain,
! [A: $i] :
( ( ( A @ v1_funct_1 )
& ( A @ v1_xboole_0 )
& ( A @ v1_relat_1 ) )
=> ( ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(52,axiom,
? [A: $i] :
( ( A @ v1_group_1 )
& ( A @ l1_group_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_group_1) ).
thf(271,plain,
? [A: $i] :
( ( A @ v1_group_1 )
& ( A @ l1_group_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(38,axiom,
! [A: $i] :
( ( A @ k6_partfun1 )
= ( A @ k6_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_partfun1) ).
thf(208,plain,
! [A: $i] :
( ( A @ k6_partfun1 )
= ( A @ k6_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(72,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m1_fraenkel ) ) )
& ~ ( B @ v1_xboole_0 ) )
=> ? [D: $i] : ( C @ ( B @ ( A @ ( D @ m2_fraenkel ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_fraenkel) ).
thf(345,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m1_fraenkel ) ) )
& ~ ( B @ v1_xboole_0 ) )
=> ? [D: $i] : ( C @ ( B @ ( A @ ( D @ m2_fraenkel ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(19,axiom,
? [A: $i] : ( A @ v1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(140,plain,
? [A: $i] : ( A @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(45,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( ( ( B @ ( A @ ( C @ v2_funct_2 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v2_funct_1 )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v3_funct_2 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_funct_2) ).
thf(240,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( ( ( B @ ( A @ ( C @ v2_funct_2 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v2_funct_1 )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v3_funct_2 ) ) )
& ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(23,axiom,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m1_fraenkel ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_fraenkel) ).
thf(155,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m1_fraenkel ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(61,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m1_fraenkel ) ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [D: $i] :
( ( C @ ( B @ ( A @ ( D @ m2_fraenkel ) ) ) )
=> ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_fraenkel) ).
thf(299,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( C @ m1_fraenkel ) ) )
& ~ ( B @ v1_xboole_0 ) )
=> ! [D: $i] :
( ( C @ ( B @ ( A @ ( D @ m2_fraenkel ) ) ) )
=> ( ( B @ ( A @ ( D @ m2_relset_1 ) ) )
& ( B @ ( A @ ( D @ v1_funct_2 ) ) )
& ( D @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(51,axiom,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( B @ ( A @ k5_relat_1 ) @ v1_funct_1 )
& ( B @ ( A @ k5_relat_1 ) @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_funct_1) ).
thf(267,plain,
! [A: $i,B: $i] :
( ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) )
=> ( ( B @ ( A @ k5_relat_1 ) @ v1_funct_1 )
& ( B @ ( A @ k5_relat_1 ) @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(27,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(167,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)],[27]) ).
thf(59,axiom,
! [A: $i] :
( ( ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ~ ( A @ u1_struct_0 @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_struct_0) ).
thf(295,plain,
! [A: $i] :
( ( ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ~ ( A @ u1_struct_0 @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( B @ ( A @ ( C @ v1_partfun1 ) ) )
& ( C @ v1_funct_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc5_funct_2) ).
thf(150,plain,
! [A: $i,B: $i] :
( ~ ( B @ v1_xboole_0 )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( B @ ( A @ ( C @ v1_partfun1 ) ) )
& ( C @ v1_funct_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(47,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(250,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)],[47]) ).
thf(7,axiom,
! [A: $i,B: $i] : ( A @ ( A @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(99,plain,
! [A: $i] : ( A @ ( A @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(36,axiom,
? [A: $i] :
( ( A @ v1_fraenkel )
& ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_fraenkel) ).
thf(203,plain,
? [A: $i] :
( ( A @ v1_fraenkel )
& ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(62,axiom,
? [A: $i] :
( ~ ( A @ v3_struct_0 )
& ( A @ l1_struct_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_struct_0) ).
thf(304,plain,
? [A: $i] :
( ~ ( A @ v3_struct_0 )
& ( A @ l1_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(49,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( ( ( B @ ( A @ ( C @ v1_partfun1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_2) ).
thf(258,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m1_relset_1 ) ) )
=> ( ( ( B @ ( A @ ( C @ v1_partfun1 ) ) )
& ( C @ v1_funct_1 ) )
=> ( ( B @ ( A @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(13,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(119,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)],[13]) ).
thf(37,axiom,
k1_xboole_0 @ v1_xboole_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(207,plain,
k1_xboole_0 @ v1_xboole_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(40,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(214,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)],[40]) ).
thf(50,axiom,
? [A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_xboole_0 )
& ( A @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).
thf(262,plain,
? [A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_xboole_0 )
& ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(32,axiom,
? [A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(190,plain,
? [A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(30,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(178,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)],[30]) ).
thf(26,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m1_fraenkel ) ) )
=> ( ( C @ v1_fraenkel )
& ~ ( C @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_fraenkel) ).
thf(163,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ m1_fraenkel ) ) )
=> ( ( C @ v1_fraenkel )
& ~ ( C @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(35,axiom,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(200,plain,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(69,axiom,
! [A: $i] :
( ( A @ l1_group_1 )
=> ( ( A @ v1_group_1 )
=> ( A
= ( A @ u1_group_1 @ ( A @ u1_struct_0 @ g1_group_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',abstractness_v1_group_1) ).
thf(337,plain,
! [A: $i] :
( ( A @ l1_group_1 )
=> ( ( A @ v1_group_1 )
=> ( A
= ( A @ u1_group_1 @ ( A @ u1_struct_0 @ g1_group_1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(42,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ m1_relset_1 ) ) )
=> ( ( ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_relat_2 )
& ( A @ ( A @ ( B @ v1_partfun1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( A @ ( B @ v3_funct_2 ) ) )
& ( A @ ( A @ ( B @ v2_funct_2 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v2_funct_1 )
& ( B @ v1_funct_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc4_funct_2) ).
thf(222,plain,
! [A: $i,B: $i] :
( ( A @ ( A @ ( B @ m1_relset_1 ) ) )
=> ( ( ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v1_relat_2 )
& ( A @ ( A @ ( B @ v1_partfun1 ) ) )
& ( B @ v1_funct_1 ) )
=> ( ( A @ ( A @ ( B @ v3_funct_2 ) ) )
& ( A @ ( A @ ( B @ v2_funct_2 ) ) )
& ( A @ ( A @ ( B @ v1_funct_2 ) ) )
& ( B @ v2_funct_1 )
& ( B @ v1_funct_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(424,plain,
$false,
inference(e,[status(thm)],[288,169,343,279,286,194,127,107,138,101,347,88,115,308,142,340,184,125,157,93,284,325,316,321,211,238,121,84,132,74,292,117,220,297,275,229,252,197,329,144,335,86,159,172,113,245,271,208,345,140,240,155,299,267,167,295,150,250,99,203,304,258,119,207,214,262,190,178,163,200,337,222]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP632+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.09 % 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
% 0.20/5.47 % Computer : n001.cluster.edu
% 0.20/5.47 % Model : x86_64 x86_64
% 0.20/5.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/5.47 % Memory : 8046.5625MB
% 0.20/5.47 % OS : Linux 6.8.0-71-generic
% 0.20/5.47 % CPULimit : 300
% 0.20/5.47 % WCLimit : 300
% 0.20/5.47 % DateTime : Fri Sep 25 15:17:32 UTC 2026
% 0.20/5.47 % CPUTime :
% 0.20/5.48 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
% 0.25/6.04 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.96/6.32 % [INFO] Parsing done (275ms).
% 1.96/6.33 % [INFO] Running in sequential loop mode.
% 3.11/6.87 % [INFO] eprover registered as external prover.
% 3.11/6.89 % [INFO] Scanning for conjecture ...
% 3.62/7.08 % [INFO] Found a conjecture (or negated_conjecture) and 81 axioms. Running axiom selection ...
% 3.92/7.25 % [INFO] Axiom selection finished. Selected 71 axioms (removed 10 axioms).
% 4.42/7.42 % [INFO] Problem is first-order (TPTP FOF).
% 4.42/7.45 % [INFO] Type checking passed.
% 4.42/7.46 % [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 ...
% 16.01/10.21 % External prover 'e' found a proof!
% 16.01/10.21 % [INFO] Killing All external provers ...
% 16.01/10.22 % Time passed: 4530ms (effective reasoning time: 3881ms)
% 16.01/10.22 % 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)>
% 16.01/10.22 % Axioms used in derivation (71): free_g1_group_1, cc4_funct_2, dt_k7_relset_1, t5_subset, dt_m2_fraenkel, dt_m1_fraenkel, existence_m2_relset_1, dt_k6_relat_1, redefinition_k7_relset_1, rc2_xboole_0, t23_funct_2, rc3_group_1, redefinition_m2_relset_1, fc1_xboole_0, t1_subset, redefinition_k7_funct_2, rc2_partfun1, rc3_funct_1, cc1_fraenkel, fc1_funct_1, rc1_fraenkel, dt_k6_partfun1, dt_m2_relset_1, dt_u1_group_1, dt_k7_funct_2, existence_m2_fraenkel, rc1_funct_1, dt_l1_group_1, cc2_funct_2, t6_boole, dt_k6_autgroup, existence_m1_relset_1, cc3_funct_2, fc2_funct_1, t4_subset, cc1_funct_2, dt_k4_autgroup, t7_boole, cc1_funct_1, rc3_struct_0, redefinition_k6_partfun1, cc1_group_1, rc2_funct_1, redefinition_m2_fraenkel, rc1_funct_2, cc2_funct_1, t3_subset, cc1_relset_1, existence_m1_subset_1, fc1_struct_0, cc6_funct_2, dt_k5_relat_1, reflexivity_r1_tarski, t8_boole, rc1_xboole_0, existence_m1_fraenkel, rc5_struct_0, t2_subset, fc1_group_1, dt_k2_group_1, existence_l1_group_1, rc1_group_1, existence_l1_struct_0, rc2_group_1, rc1_partfun1, cc5_funct_2, t24_autgroup, antisymmetry_r2_hidden, rc2_funct_2, dt_g1_group_1, abstractness_v1_group_1
% 16.01/10.22 % No. of inferences in proof: 146
% 16.01/10.22 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4530 ms resp. 3881 ms w/o parsing
% 16.07/10.37 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 16.07/10.38 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------