%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ALG216+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 : n026.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 06:46:19 AM UTC 2026
% Result : Theorem 5.11s 13.09s
% Output : Refutation 5.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 47
% Syntax : Number of formulae : 96 ( 31 unt; 0 typ; 0 def)
% Number of atoms : 314 ( 19 equ; 0 cnn)
% Maximal formula atoms : 23 ( 3 avg)
% Number of connectives : 826 ( 71 ~; 4 |; 141 &; 537 @)
% ( 1 <=>; 72 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 33 ( 31 usr; 2 con; 0-3 aty)
% Number of variables : 158 ( 0 ^; 122 !; 36 ?; 158 :)
% Comments :
%------------------------------------------------------------------------------
thf(v3_struct_0_decl,type,
v3_struct_0: $i > $o ).
thf(v3_rlvect_1_decl,type,
v3_rlvect_1: $i > $o ).
thf(v4_rlvect_1_decl,type,
v4_rlvect_1: $i > $o ).
thf(v5_rlvect_1_decl,type,
v5_rlvect_1: $i > $o ).
thf(v6_rlvect_1_decl,type,
v6_rlvect_1: $i > $o ).
thf(v4_group_1_decl,type,
v4_group_1: $i > $o ).
thf(v6_vectsp_1_decl,type,
v6_vectsp_1: $i > $o ).
thf(v7_vectsp_1_decl,type,
v7_vectsp_1: $i > $o ).
thf(v8_vectsp_1_decl,type,
v8_vectsp_1: $i > $o ).
thf(l3_vectsp_1_decl,type,
l3_vectsp_1: $i > $o ).
thf(v5_vectsp_2_decl,type,
v5_vectsp_2: $i > $i > $o ).
thf(l1_vectsp_2_decl,type,
l1_vectsp_2: $i > $i > $o ).
thf(m1_subset_1_decl,type,
m1_subset_1: $i > $i > $o ).
thf(u1_struct_0_decl,type,
u1_struct_0: $i > $i ).
thf(k1_rlvect_1_decl,type,
k1_rlvect_1: $i > $i ).
thf(k2_group_1_decl,type,
k2_group_1: $i > $i ).
thf(v1_rmod_5_decl,type,
v1_rmod_5: $i > $i > $i > $o ).
thf(k8_rlvect_2_decl,type,
k8_rlvect_2: $i > $i > $i > $i ).
thf(l1_vectsp_1_decl,type,
l1_vectsp_1: $i > $o ).
thf(k2_tarski_decl,type,
k2_tarski: $i > $i > $i ).
thf(v1_xboole_0_decl,type,
v1_xboole_0: $i > $o ).
thf(k1_xboole_0_decl,type,
k1_xboole_0: $i ).
thf(l1_struct_0_decl,type,
l1_struct_0: $i > $o ).
thf(l1_group_1_decl,type,
l1_group_1: $i > $o ).
thf(l2_vectsp_1_decl,type,
l2_vectsp_1: $i > $o ).
thf(r1_tarski_decl,type,
r1_tarski: $i > $i > $o ).
thf(l1_rlvect_1_decl,type,
l1_rlvect_1: $i > $o ).
thf(r2_hidden_decl,type,
r2_hidden: $i > $i > $o ).
thf(k1_zfmisc_1_decl,type,
k1_zfmisc_1: $i > $i ).
thf(l2_struct_0_decl,type,
l2_struct_0: $i > $o ).
thf(v1_finset_1_decl,type,
v1_finset_1: $i > $o ).
thf(21,axiom,
! [A: $i] :
( ( A @ l1_rlvect_1 )
=> ( A @ l2_struct_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_rlvect_1) ).
thf(115,plain,
! [A: $i] :
( ( A @ l1_rlvect_1 )
=> ( A @ l2_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(30,axiom,
! [A: $i] :
( ( A @ l1_struct_0 )
=> ? [B: $i] : ( A @ ( B @ l1_vectsp_2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_vectsp_2) ).
thf(142,plain,
! [A: $i] :
( ( A @ l1_struct_0 )
=> ? [B: $i] : ( A @ ( B @ l1_vectsp_2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(28,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(134,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)],[28]) ).
thf(46,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(191,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)],[46]) ).
thf(32,axiom,
! [A: $i] :
( ( A @ l1_struct_0 )
=> ! [B: $i] :
( ( A @ ( B @ l1_vectsp_2 ) )
=> ( B @ l1_rlvect_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_vectsp_2) ).
thf(150,plain,
! [A: $i] :
( ( A @ l1_struct_0 )
=> ! [B: $i] :
( ( A @ ( B @ l1_vectsp_2 ) )
=> ( B @ l1_rlvect_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(17,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(104,plain,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( A != B )
& ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(7,axiom,
! [A: $i] :
( ( A @ l1_group_1 )
=> ( A @ l1_struct_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_group_1) ).
thf(82,plain,
! [A: $i] :
( ( A @ l1_group_1 )
=> ( A @ l1_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(43,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k8_rlvect_2 ) ) )
= ( C @ ( B @ k2_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k8_rlvect_2) ).
thf(183,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k8_rlvect_2 ) ) )
= ( C @ ( B @ k2_tarski ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(12,axiom,
? [A: $i] : ( A @ l1_rlvect_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_rlvect_1) ).
thf(94,plain,
? [A: $i] : ( A @ l1_rlvect_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(29,axiom,
? [A: $i] :
( ~ ( A @ v3_struct_0 )
& ( A @ l2_struct_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_struct_0) ).
thf(138,plain,
? [A: $i] :
( ~ ( A @ v3_struct_0 )
& ( A @ l2_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(15,axiom,
k1_xboole_0 @ v1_xboole_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(101,plain,
k1_xboole_0 @ v1_xboole_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(19,axiom,
! [A: $i] :
~ ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(110,plain,
! [A: $i] :
~ ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(25,axiom,
! [A: $i] :
( ( ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( B @ v1_finset_1 )
& ~ ( B @ v1_xboole_0 )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_rlvect_2) ).
thf(125,plain,
! [A: $i] :
( ( ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ? [B: $i] :
( ( B @ v1_finset_1 )
& ~ ( B @ v1_xboole_0 )
& ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(45,axiom,
! [A: $i] :
( ( A @ l2_struct_0 )
=> ( A @ u1_struct_0 @ ( A @ k1_rlvect_1 @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_rlvect_1) ).
thf(189,plain,
! [A: $i] :
( ( A @ l2_struct_0 )
=> ( A @ u1_struct_0 @ ( A @ k1_rlvect_1 @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(33,axiom,
! [A: $i] :
( ( A @ l1_struct_0 )
=> ? [B: $i] :
( ~ ( B @ v3_struct_0 )
& ( A @ ( B @ l1_vectsp_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc9_vectsp_2) ).
thf(152,plain,
! [A: $i] :
( ( A @ l1_struct_0 )
=> ? [B: $i] :
( ~ ( B @ v3_struct_0 )
& ( A @ ( B @ l1_vectsp_2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(42,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k8_rlvect_2 ) ) @ m1_subset_1 ) )
& ( C @ ( B @ ( A @ k8_rlvect_2 ) ) @ v1_finset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_rlvect_2) ).
thf(179,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ ( B @ ( A @ k8_rlvect_2 ) ) @ m1_subset_1 ) )
& ( C @ ( B @ ( A @ k8_rlvect_2 ) ) @ v1_finset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(23,axiom,
! [A: $i] :
( ( A @ l2_struct_0 )
=> ( A @ l1_struct_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l2_struct_0) ).
thf(121,plain,
! [A: $i] :
( ( A @ l2_struct_0 )
=> ( A @ l1_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(8,axiom,
? [A: $i] : ( A @ l2_vectsp_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l2_vectsp_1) ).
thf(84,plain,
? [A: $i] : ( A @ l2_vectsp_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(27,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(132,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)],[27]) ).
thf(10,axiom,
! [A: $i,B: $i] : ( A @ ( A @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(89,plain,
! [A: $i] : ( A @ ( A @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_tarski ) )
= ( A @ ( B @ k2_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(74,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ k2_tarski ) )
= ( A @ ( B @ k2_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(22,axiom,
! [A: $i] :
( ( A @ l2_vectsp_1 )
=> ( ( A @ l2_struct_0 )
& ( A @ l1_vectsp_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l2_vectsp_1) ).
thf(117,plain,
! [A: $i] :
( ( A @ l2_vectsp_1 )
=> ( ( A @ l2_struct_0 )
& ( A @ l1_vectsp_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(48,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(201,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)],[48]) ).
thf(16,axiom,
! [A: $i] :
( ( A @ l1_vectsp_1 )
=> ( A @ l1_group_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_vectsp_1) ).
thf(102,plain,
! [A: $i] :
( ( A @ l1_vectsp_1 )
=> ( A @ l1_group_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(36,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(160,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)],[36]) ).
thf(38,axiom,
! [A: $i] :
( ( A @ l3_vectsp_1 )
=> ( ( A @ l2_vectsp_1 )
& ( A @ l1_rlvect_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l3_vectsp_1) ).
thf(165,plain,
! [A: $i] :
( ( A @ l3_vectsp_1 )
=> ( ( A @ l2_vectsp_1 )
& ( A @ l1_rlvect_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(34,axiom,
? [A: $i] : ( A @ l3_vectsp_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l3_vectsp_1) ).
thf(156,plain,
? [A: $i] : ( A @ l3_vectsp_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(39,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(169,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)],[39]) ).
thf(5,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(77,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(47,axiom,
! [A: $i] :
( ( ( A @ l3_vectsp_1 )
& ( A @ v8_vectsp_1 )
& ( A @ v7_vectsp_1 )
& ( A @ v6_vectsp_1 )
& ( A @ v4_group_1 )
& ( A @ v6_rlvect_1 )
& ( A @ v5_rlvect_1 )
& ( A @ v4_rlvect_1 )
& ( A @ v3_rlvect_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ l1_vectsp_2 ) )
& ( A @ ( B @ v5_vectsp_2 ) )
& ( B @ v6_rlvect_1 )
& ( B @ v5_rlvect_1 )
& ( B @ v4_rlvect_1 )
& ( B @ v3_rlvect_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( D @ ( C @ ( B @ k8_rlvect_2 ) ) @ v1_rmod_5 ) ) )
=> ( ( ( D
!= ( B @ k1_rlvect_1 ) )
& ( C
!= ( B @ k1_rlvect_1 ) ) )
| ( ( A @ k1_rlvect_1 )
= ( A @ k2_group_1 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_rmod_5) ).
thf(193,plain,
! [A: $i] :
( ( ( A @ l3_vectsp_1 )
& ( A @ v8_vectsp_1 )
& ( A @ v7_vectsp_1 )
& ( A @ v6_vectsp_1 )
& ( A @ v4_group_1 )
& ( A @ v6_rlvect_1 )
& ( A @ v5_rlvect_1 )
& ( A @ v4_rlvect_1 )
& ( A @ v3_rlvect_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ l1_vectsp_2 ) )
& ( A @ ( B @ v5_vectsp_2 ) )
& ( B @ v6_rlvect_1 )
& ( B @ v5_rlvect_1 )
& ( B @ v4_rlvect_1 )
& ( B @ v3_rlvect_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ u1_struct_0 @ ( D @ m1_subset_1 ) )
=> ( ( B @ ( A @ ( D @ ( C @ ( B @ k8_rlvect_2 ) ) @ v1_rmod_5 ) ) )
=> ( ( ( D
!= ( B @ k1_rlvect_1 ) )
& ( C
!= ( B @ k1_rlvect_1 ) ) )
| ( ( A @ k1_rlvect_1 )
= ( A @ k2_group_1 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(13,axiom,
? [A: $i] : ( A @ l1_group_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_group_1) ).
thf(96,plain,
? [A: $i] : ( A @ l1_group_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(31,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)],[31]) ).
thf(1,conjecture,
! [A: $i] :
( ( ( A @ l3_vectsp_1 )
& ( A @ v8_vectsp_1 )
& ( A @ v7_vectsp_1 )
& ( A @ v6_vectsp_1 )
& ( A @ v4_group_1 )
& ( A @ v6_rlvect_1 )
& ( A @ v5_rlvect_1 )
& ( A @ v4_rlvect_1 )
& ( A @ v3_rlvect_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ l1_vectsp_2 ) )
& ( A @ ( B @ v5_vectsp_2 ) )
& ( B @ v6_rlvect_1 )
& ( B @ v5_rlvect_1 )
& ( B @ v4_rlvect_1 )
& ( B @ v3_rlvect_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ k1_rlvect_1 )
!= ( A @ k2_group_1 ) )
=> ( ~ ( B @ ( A @ ( C @ ( B @ k1_rlvect_1 @ ( B @ k8_rlvect_2 ) ) @ v1_rmod_5 ) ) )
& ~ ( B @ ( A @ ( B @ k1_rlvect_1 @ ( C @ ( B @ k8_rlvect_2 ) ) @ v1_rmod_5 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_rmod_5) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ( A @ l3_vectsp_1 )
& ( A @ v8_vectsp_1 )
& ( A @ v7_vectsp_1 )
& ( A @ v6_vectsp_1 )
& ( A @ v4_group_1 )
& ( A @ v6_rlvect_1 )
& ( A @ v5_rlvect_1 )
& ( A @ v4_rlvect_1 )
& ( A @ v3_rlvect_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ l1_vectsp_2 ) )
& ( A @ ( B @ v5_vectsp_2 ) )
& ( B @ v6_rlvect_1 )
& ( B @ v5_rlvect_1 )
& ( B @ v4_rlvect_1 )
& ( B @ v3_rlvect_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ k1_rlvect_1 )
!= ( A @ k2_group_1 ) )
=> ( ~ ( B @ ( A @ ( C @ ( B @ k1_rlvect_1 @ ( B @ k8_rlvect_2 ) ) @ v1_rmod_5 ) ) )
& ~ ( B @ ( A @ ( B @ k1_rlvect_1 @ ( C @ ( B @ k8_rlvect_2 ) ) @ v1_rmod_5 ) ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(49,plain,
~ ! [A: $i] :
( ( ( A @ l3_vectsp_1 )
& ( A @ v8_vectsp_1 )
& ( A @ v7_vectsp_1 )
& ( A @ v6_vectsp_1 )
& ( A @ v4_group_1 )
& ( A @ v6_rlvect_1 )
& ( A @ v5_rlvect_1 )
& ( A @ v4_rlvect_1 )
& ( A @ v3_rlvect_1 )
& ~ ( A @ v3_struct_0 ) )
=> ! [B: $i] :
( ( ( A @ ( B @ l1_vectsp_2 ) )
& ( A @ ( B @ v5_vectsp_2 ) )
& ( B @ v6_rlvect_1 )
& ( B @ v5_rlvect_1 )
& ( B @ v4_rlvect_1 )
& ( B @ v3_rlvect_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( B @ u1_struct_0 @ ( C @ m1_subset_1 ) )
=> ( ( ( A @ k1_rlvect_1 )
!= ( A @ k2_group_1 ) )
=> ( ~ ( B @ ( A @ ( C @ ( B @ k1_rlvect_1 @ ( B @ k8_rlvect_2 ) ) @ v1_rmod_5 ) ) )
& ~ ( B @ ( A @ ( B @ k1_rlvect_1 @ ( C @ ( B @ k8_rlvect_2 ) ) @ v1_rmod_5 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(9,axiom,
! [A: $i,B: $i] :
~ ( B @ ( A @ k2_tarski ) @ v1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_subset_1) ).
thf(86,plain,
! [A: $i,B: $i] :
~ ( B @ ( A @ k2_tarski ) @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(20,axiom,
? [A: $i] : ( A @ v1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(113,plain,
? [A: $i] : ( A @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(14,axiom,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(98,plain,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(11,axiom,
? [A: $i] :
~ ( A @ v1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(91,plain,
? [A: $i] :
~ ( A @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(108,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(26,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(130,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(6,axiom,
? [A: $i] : ( A @ l1_struct_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(80,plain,
? [A: $i] : ( A @ l1_struct_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(37,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(162,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)],[37]) ).
thf(24,axiom,
? [A: $i] : ( A @ l2_struct_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l2_struct_0) ).
thf(123,plain,
? [A: $i] : ( A @ l2_struct_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(3,axiom,
? [A: $i] : ( A @ l1_vectsp_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_vectsp_1) ).
thf(72,plain,
? [A: $i] : ( A @ l1_vectsp_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(41,axiom,
? [A: $i] :
( ~ ( A @ v3_struct_0 )
& ( A @ l1_struct_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_struct_0) ).
thf(175,plain,
? [A: $i] :
( ~ ( A @ v3_struct_0 )
& ( A @ l1_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(35,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(158,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(44,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k8_rlvect_2 ) ) )
= ( B @ ( C @ ( A @ k8_rlvect_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k8_rlvect_2) ).
thf(186,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ u1_struct_0 @ ( C @ m1_subset_1 ) )
& ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( C @ ( B @ ( A @ k8_rlvect_2 ) ) )
= ( B @ ( C @ ( A @ k8_rlvect_2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(40,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(171,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)],[40]) ).
thf(205,plain,
$false,
inference(e,[status(thm)],[115,142,134,191,150,104,82,183,94,138,101,110,125,189,152,179,121,84,132,89,74,117,201,102,160,165,156,169,77,193,96,144,49,86,113,98,91,108,130,80,162,123,72,175,158,186,171]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG216+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.08 % 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
% 0.15/10.63 % Computer : n026.cluster.edu
% 0.15/10.63 % Model : x86_64 x86_64
% 0.15/10.63 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/10.63 % Memory : 8046.5625MB
% 0.15/10.63 % OS : Linux 6.8.0-71-generic
% 0.15/10.63 % CPULimit : 300
% 0.15/10.63 % WCLimit : 300
% 0.15/10.63 % DateTime : Sat Sep 26 21:31:23 UTC 2026
% 0.15/10.63 % CPUTime :
% 0.15/10.63 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
% 0.96/11.22 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.30/11.43 % [INFO] Parsing done (216ms).
% 1.30/11.45 % [INFO] Running in sequential loop mode.
% 1.95/11.85 % [INFO] eprover registered as external prover.
% 1.95/11.86 % [INFO] Scanning for conjecture ...
% 2.14/11.98 % [INFO] Found a conjecture (or negated_conjecture) and 52 axioms. Running axiom selection ...
% 2.39/12.08 % [INFO] Axiom selection finished. Selected 46 axioms (removed 6 axioms).
% 2.60/12.15 % [INFO] Problem is first-order (TPTP FOF).
% 2.60/12.15 % [INFO] Type checking passed.
% 2.60/12.16 % [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 ...
% 5.11/13.09 % External prover 'e' found a proof!
% 5.11/13.09 % [INFO] Killing All external provers ...
% 5.11/13.09 % Time passed: 2314ms (effective reasoning time: 1635ms)
% 5.11/13.09 % 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)>
% 5.11/13.09 % Axioms used in derivation (46): commutativity_k8_rlvect_2, dt_l1_vectsp_2, t4_subset, dt_k8_rlvect_2, dt_k1_rlvect_1, existence_l1_vectsp_1, dt_l2_struct_0, existence_l1_struct_0, fc1_xboole_0, t1_subset, redefinition_k8_rlvect_2, rc2_rlvect_2, dt_l2_vectsp_1, dt_l1_rlvect_1, dt_l1_group_1, t6_boole, rc2_subset_1, existence_l2_struct_0, fc3_subset_1, t5_subset, t7_boole, rc3_struct_0, fc1_subset_1, rc1_subset_1, t5_rmod_5, dt_l3_vectsp_1, t3_subset, existence_l1_vectsp_2, existence_m1_subset_1, commutativity_k2_tarski, fc1_struct_0, dt_l1_vectsp_1, rc9_vectsp_2, reflexivity_r1_tarski, existence_l3_vectsp_1, t8_boole, rc1_xboole_0, rc5_struct_0, t2_subset, dt_k2_group_1, existence_l1_group_1, rc4_struct_0, rc2_xboole_0, existence_l1_rlvect_1, existence_l2_vectsp_1, antisymmetry_r2_hidden
% 5.11/13.09 % No. of inferences in proof: 96
% 5.11/13.09 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2314 ms resp. 1635 ms w/o parsing
% 5.47/13.18 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.47/13.19 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------