%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ALG218+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 : n015.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 06:46:20 AM UTC 2026
% Result : Theorem 8.23s 8.69s
% Output : Refutation 9.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 71
% Syntax : Number of formulae : 144 ( 33 unt; 0 typ; 0 def)
% Number of atoms : 824 ( 43 equ; 0 cnn)
% Maximal formula atoms : 25 ( 5 avg)
% Number of connectives : 2211 ( 124 ~; 2 |; 537 &;1407 @)
% ( 7 <=>; 134 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 50 ( 48 usr; 2 con; 0-5 aty)
% Number of variables : 294 ( 0 ^; 244 !; 50 ?; 294 :)
% 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(v7_group_1_decl,type,
v7_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(v10_vectsp_1_decl,type,
v10_vectsp_1: $i > $o ).
thf(v2_vectsp_2_decl,type,
v2_vectsp_2: $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(k1_zfmisc_1_decl,type,
k1_zfmisc_1: $i > $i ).
thf(u1_struct_0_decl,type,
u1_struct_0: $i > $i ).
thf(k1_rmod_5_decl,type,
k1_rmod_5: $i > $i > $i > $i ).
thf(k1_rmod_2_decl,type,
k1_rmod_2: $i > $i > $i ).
thf(k1_xboole_0_decl,type,
k1_xboole_0: $i ).
thf(k7_rlvect_2_decl,type,
k7_rlvect_2: $i > $i > $i ).
thf(k1_rlvect_1_decl,type,
k1_rlvect_1: $i > $i ).
thf(l1_group_1_decl,type,
l1_group_1: $i > $o ).
thf(m2_relset_1_decl,type,
m2_relset_1: $i > $i > $i > $o ).
thf(m1_relset_1_decl,type,
m1_relset_1: $i > $i > $i > $o ).
thf(v1_xboole_0_decl,type,
v1_xboole_0: $i > $o ).
thf(k2_zfmisc_1_decl,type,
k2_zfmisc_1: $i > $i > $i ).
thf(l1_vectsp_1_decl,type,
l1_vectsp_1: $i > $o ).
thf(r2_hidden_decl,type,
r2_hidden: $i > $i > $o ).
thf(l1_struct_0_decl,type,
l1_struct_0: $i > $o ).
thf(l2_vectsp_1_decl,type,
l2_vectsp_1: $i > $o ).
thf(r1_tarski_decl,type,
r1_tarski: $i > $i > $o ).
thf(l2_struct_0_decl,type,
l2_struct_0: $i > $o ).
thf(l1_rlvect_1_decl,type,
l1_rlvect_1: $i > $o ).
thf(k1_tarski_decl,type,
k1_tarski: $i > $i ).
thf(v1_finset_1_decl,type,
v1_finset_1: $i > $o ).
thf(v3_vectsp_2_decl,type,
v3_vectsp_2: $i > $i > $o ).
thf(m1_rmod_2_decl,type,
m1_rmod_2: $i > $i > $i > $o ).
thf(r1_rlvect_1_decl,type,
r1_rlvect_1: $i > $i > $o ).
thf(v1_relat_1_decl,type,
v1_relat_1: $i > $o ).
thf(v1_funct_1_decl,type,
v1_funct_1: $i > $o ).
thf(v1_funct_2_decl,type,
v1_funct_2: $i > $i > $i > $o ).
thf(g1_vectsp_2_decl,type,
g1_vectsp_2: $i > $i > $i > $i > $i > $i ).
thf(u1_rlvect_1_decl,type,
u1_rlvect_1: $i > $i ).
thf(u2_struct_0_decl,type,
u2_struct_0: $i > $i ).
thf(u1_vectsp_2_decl,type,
u1_vectsp_2: $i > $i > $i ).
thf(v2_group_1_decl,type,
v2_group_1: $i > $o ).
thf(60,axiom,
! [A: $i] :
( ( A @ l2_struct_0 )
=> ( A @ u1_struct_0 @ ( A @ u2_struct_0 @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u2_struct_0) ).
thf(340,plain,
! [A: $i] :
( ( A @ l2_struct_0 )
=> ( A @ u1_struct_0 @ ( A @ u2_struct_0 @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(5,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(110,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)],[5]) ).
thf(57,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B @ ( A @ u1_struct_0 @ ( B @ k2_zfmisc_1 ) @ ( E @ m1_relset_1 ) ) )
& ( B @ ( A @ u1_struct_0 @ ( B @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ( B @ ( D @ m1_subset_1 ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( A @ l1_struct_0 ) )
=> ! [F: $i,G: $i,H: $i,I: $i,J: $i] :
( ( ( E @ ( D @ ( C @ ( B @ ( A @ g1_vectsp_2 ) ) ) ) )
= ( J @ ( I @ ( H @ ( G @ ( F @ g1_vectsp_2 ) ) ) ) ) )
=> ( ( E = J )
& ( D = I )
& ( C = H )
& ( B = G )
& ( A = F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',free_g1_vectsp_2) ).
thf(321,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B @ ( A @ u1_struct_0 @ ( B @ k2_zfmisc_1 ) @ ( E @ m1_relset_1 ) ) )
& ( B @ ( A @ u1_struct_0 @ ( B @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ( B @ ( D @ m1_subset_1 ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( A @ l1_struct_0 ) )
=> ! [F: $i,G: $i,H: $i,I: $i,J: $i] :
( ( ( E @ ( D @ ( C @ ( B @ ( A @ g1_vectsp_2 ) ) ) ) )
= ( J @ ( I @ ( H @ ( G @ ( F @ g1_vectsp_2 ) ) ) ) ) )
=> ( ( E = J )
& ( D = I )
& ( C = H )
& ( B = G )
& ( A = F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(66,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k7_rlvect_2 ) )
= ( B @ k1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k7_rlvect_2) ).
thf(361,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( B @ ( A @ k7_rlvect_2 ) )
= ( B @ k1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(69,axiom,
! [A: $i] :
( ( A @ l1_vectsp_1 )
=> ( ( ( A @ v6_vectsp_1 )
& ( A @ v7_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v8_vectsp_1 )
& ( A @ v6_vectsp_1 )
& ( A @ v2_group_1 )
& ~ ( A @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_vectsp_2) ).
thf(371,plain,
! [A: $i] :
( ( A @ l1_vectsp_1 )
=> ( ( ( A @ v6_vectsp_1 )
& ( A @ v7_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v8_vectsp_1 )
& ( A @ v6_vectsp_1 )
& ( A @ v2_group_1 )
& ~ ( A @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(20,axiom,
! [A: $i] :
~ ( A @ k1_tarski @ v1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_subset_1) ).
thf(166,plain,
! [A: $i] :
~ ( A @ k1_tarski @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(55,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(310,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)],[55]) ).
thf(7,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(114,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m2_relset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(45,axiom,
? [A: $i] :
( ~ ( A @ v3_struct_0 )
& ( A @ l1_struct_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_struct_0) ).
thf(277,plain,
? [A: $i] :
( ~ ( A @ v3_struct_0 )
& ( A @ l1_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(16,axiom,
? [A: $i] : ( A @ l2_struct_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l2_struct_0) ).
thf(138,plain,
? [A: $i] : ( A @ l2_struct_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(58,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(333,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)],[58]) ).
thf(63,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(352,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)],[63]) ).
thf(54,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ m1_subset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(308,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(43,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B @ ( A @ u1_struct_0 @ ( B @ k2_zfmisc_1 ) @ ( E @ m1_relset_1 ) ) )
& ( B @ ( A @ u1_struct_0 @ ( B @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ( B @ ( D @ m1_subset_1 ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ( A @ l1_struct_0 ) )
=> ( ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ g1_vectsp_2 ) ) ) ) @ v3_vectsp_2 ) )
& ~ ( E @ ( D @ ( C @ ( B @ ( A @ g1_vectsp_2 ) ) ) ) @ v3_struct_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_vectsp_2) ).
thf(269,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B @ ( A @ u1_struct_0 @ ( B @ k2_zfmisc_1 ) @ ( E @ m1_relset_1 ) ) )
& ( B @ ( A @ u1_struct_0 @ ( B @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ( B @ ( D @ m1_subset_1 ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ~ ( B @ v1_xboole_0 )
& ( A @ l1_struct_0 ) )
=> ( ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ g1_vectsp_2 ) ) ) ) @ v3_vectsp_2 ) )
& ~ ( E @ ( D @ ( C @ ( B @ ( A @ g1_vectsp_2 ) ) ) ) @ v3_struct_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(10,axiom,
? [A: $i] : ( A @ v1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(120,plain,
? [A: $i] : ( A @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(40,axiom,
! [A: $i] :
~ ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(247,plain,
! [A: $i] :
~ ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(23,axiom,
? [A: $i] : ( A @ l1_vectsp_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_vectsp_1) ).
thf(185,plain,
? [A: $i] : ( A @ l1_vectsp_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(48,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(288,plain,
! [A: $i] :
( ( A @ l1_struct_0 )
=> ? [B: $i] : ( A @ ( B @ l1_vectsp_2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(25,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(189,plain,
! [A: $i] :
( ( A @ l2_vectsp_1 )
=> ( ( A @ l2_struct_0 )
& ( A @ l1_vectsp_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(47,axiom,
? [A: $i] :
( ~ ( A @ v3_struct_0 )
& ( A @ l2_struct_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_struct_0) ).
thf(284,plain,
? [A: $i] :
( ~ ( A @ v3_struct_0 )
& ( A @ l2_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(56,axiom,
! [A: $i,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 )
& ( 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 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_rmod_2 ) ) )
=> ( ( A @ ( C @ l1_vectsp_2 ) )
& ( A @ ( C @ v5_vectsp_2 ) )
& ( C @ v6_rlvect_1 )
& ( C @ v5_rlvect_1 )
& ( C @ v4_rlvect_1 )
& ( C @ v3_rlvect_1 )
& ~ ( C @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_rmod_2) ).
thf(312,plain,
! [A: $i,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 )
& ( 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 ) )
=> ! [C: $i] :
( ( B @ ( A @ ( C @ m1_rmod_2 ) ) )
=> ( ( A @ ( C @ l1_vectsp_2 ) )
& ( A @ ( C @ v5_vectsp_2 ) )
& ( C @ v6_rlvect_1 )
& ( C @ v5_rlvect_1 )
& ( C @ v4_rlvect_1 )
& ( C @ v3_rlvect_1 )
& ~ ( C @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(116,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(39,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(243,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)],[39]) ).
thf(3,axiom,
? [A: $i] : ( A @ l1_group_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_group_1) ).
thf(102,plain,
? [A: $i] : ( A @ l1_group_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(33,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(220,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(68,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ l1_vectsp_2 ) )
& ( A @ l1_struct_0 ) )
=> ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k2_zfmisc_1 ) @ ( B @ ( A @ u1_vectsp_2 ) @ m2_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k2_zfmisc_1 ) @ ( B @ ( A @ u1_vectsp_2 ) @ v1_funct_2 ) ) )
& ( B @ ( A @ u1_vectsp_2 ) @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u1_vectsp_2) ).
thf(366,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ l1_vectsp_2 ) )
& ( A @ l1_struct_0 ) )
=> ( ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k2_zfmisc_1 ) @ ( B @ ( A @ u1_vectsp_2 ) @ m2_relset_1 ) ) )
& ( B @ u1_struct_0 @ ( A @ u1_struct_0 @ ( B @ u1_struct_0 @ k2_zfmisc_1 ) @ ( B @ ( A @ u1_vectsp_2 ) @ v1_funct_2 ) ) )
& ( B @ ( A @ u1_vectsp_2 ) @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(52,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(302,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)],[52]) ).
thf(42,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 @ v3_vectsp_2 ) )
& ( B @ v6_rlvect_1 )
& ( B @ v5_rlvect_1 )
& ( B @ v4_rlvect_1 )
& ( B @ v3_rlvect_1 )
& ~ ( B @ v3_struct_0 )
& ( A @ ( B @ l1_vectsp_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc13_vectsp_2) ).
thf(260,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 @ v3_vectsp_2 ) )
& ( B @ v6_rlvect_1 )
& ( B @ v5_rlvect_1 )
& ( B @ v4_rlvect_1 )
& ( B @ v3_rlvect_1 )
& ~ ( B @ v3_struct_0 )
& ( A @ ( B @ l1_vectsp_2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(65,axiom,
! [A: $i] :
( ( A @ l1_rlvect_1 )
=> ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u1_rlvect_1 @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u1_rlvect_1 @ v1_funct_2 ) ) )
& ( A @ u1_rlvect_1 @ v1_funct_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_u1_rlvect_1) ).
thf(356,plain,
! [A: $i] :
( ( A @ l1_rlvect_1 )
=> ( ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u1_rlvect_1 @ m2_relset_1 ) ) )
& ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ ( A @ u1_struct_0 @ k2_zfmisc_1 ) @ ( A @ u1_rlvect_1 @ v1_funct_2 ) ) )
& ( A @ u1_rlvect_1 @ v1_funct_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( A @ ( B @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
thf(169,plain,
! [A: $i,B: $i] :
( ( ( ( A @ ( B @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( A @ ( B @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(12,axiom,
! [A: $i] :
( ( A @ l1_group_1 )
=> ( A @ l1_struct_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_group_1) ).
thf(124,plain,
! [A: $i] :
( ( A @ l1_group_1 )
=> ( A @ l1_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(26,axiom,
! [A: $i] :
( ( A @ l2_struct_0 )
=> ( A @ l1_struct_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l2_struct_0) ).
thf(193,plain,
! [A: $i] :
( ( A @ l2_struct_0 )
=> ( A @ l1_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(1,conjecture,
! [A: $i] :
( ( ( A @ l3_vectsp_1 )
& ( A @ v2_vectsp_2 )
& ~ ( A @ v10_vectsp_1 )
& ( A @ v8_vectsp_1 )
& ( A @ v7_vectsp_1 )
& ( A @ v6_vectsp_1 )
& ( A @ v7_group_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 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ~ ( ( C
!= ( B @ k1_rlvect_1 @ ( B @ k7_rlvect_2 ) ) )
& ( C != k1_xboole_0 )
& ( ( C @ ( B @ ( A @ k1_rmod_5 ) ) )
= ( B @ ( A @ k1_rmod_2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_rmod_5) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ( A @ l3_vectsp_1 )
& ( A @ v2_vectsp_2 )
& ~ ( A @ v10_vectsp_1 )
& ( A @ v8_vectsp_1 )
& ( A @ v7_vectsp_1 )
& ( A @ v6_vectsp_1 )
& ( A @ v7_group_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 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ~ ( ( C
!= ( B @ k1_rlvect_1 @ ( B @ k7_rlvect_2 ) ) )
& ( C != k1_xboole_0 )
& ( ( C @ ( B @ ( A @ k1_rmod_5 ) ) )
= ( B @ ( A @ k1_rmod_2 ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(73,plain,
~ ! [A: $i] :
( ( ( A @ l3_vectsp_1 )
& ( A @ v2_vectsp_2 )
& ~ ( A @ v10_vectsp_1 )
& ( A @ v8_vectsp_1 )
& ( A @ v7_vectsp_1 )
& ( A @ v6_vectsp_1 )
& ( A @ v7_group_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 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ~ ( ( C
!= ( B @ k1_rlvect_1 @ ( B @ k7_rlvect_2 ) ) )
& ( C != k1_xboole_0 )
& ( ( C @ ( B @ ( A @ k1_rmod_5 ) ) )
= ( B @ ( A @ k1_rmod_2 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(30,axiom,
! [A: $i] :
( ( A @ l1_struct_0 )
=> ? [B: $i] :
( ( A @ ( B @ v3_vectsp_2 ) )
& ( A @ ( B @ l1_vectsp_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc8_vectsp_2) ).
thf(205,plain,
! [A: $i] :
( ( A @ l1_struct_0 )
=> ? [B: $i] :
( ( A @ ( B @ v3_vectsp_2 ) )
& ( A @ ( B @ l1_vectsp_2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(14,axiom,
! [A: $i,B: $i] : ( A @ ( A @ r1_tarski ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(128,plain,
! [A: $i] : ( A @ ( A @ r1_tarski ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(36,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(237,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)],[36]) ).
thf(9,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(118,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ m1_relset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(46,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ l1_vectsp_2 ) )
& ( A @ l1_struct_0 ) )
=> ( ( A @ ( B @ v3_vectsp_2 ) )
=> ( B
= ( B @ ( A @ u1_vectsp_2 ) @ ( B @ u2_struct_0 @ ( B @ u1_rlvect_1 @ ( B @ u1_struct_0 @ ( A @ g1_vectsp_2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',abstractness_v3_vectsp_2) ).
thf(281,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ l1_vectsp_2 ) )
& ( A @ l1_struct_0 ) )
=> ( ( A @ ( B @ v3_vectsp_2 ) )
=> ( B
= ( B @ ( A @ u1_vectsp_2 ) @ ( B @ u2_struct_0 @ ( B @ u1_rlvect_1 @ ( B @ u1_struct_0 @ ( A @ g1_vectsp_2 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(72,axiom,
! [A: $i,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 )
& ( 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 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m1_rmod_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_rmod_2) ).
thf(382,plain,
! [A: $i,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 )
& ( 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 ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ m1_rmod_2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(22,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(181,plain,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( A != B )
& ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(24,axiom,
! [A: $i] :
( ( A @ l1_rlvect_1 )
=> ( A @ l2_struct_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_rlvect_1) ).
thf(187,plain,
! [A: $i] :
( ( A @ l1_rlvect_1 )
=> ( A @ l2_struct_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(70,axiom,
k1_xboole_0 @ v1_xboole_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(377,plain,
k1_xboole_0 @ v1_xboole_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(17,axiom,
? [A: $i] :
~ ( A @ v1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(140,plain,
? [A: $i] :
~ ( A @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(32,axiom,
! [A: $i,B: $i] :
( ( ( B @ l3_vectsp_1 )
& ( B @ v8_vectsp_1 )
& ( B @ v7_vectsp_1 )
& ( B @ v6_vectsp_1 )
& ( B @ v4_group_1 )
& ( B @ v6_rlvect_1 )
& ( B @ v5_rlvect_1 )
& ( B @ v4_rlvect_1 )
& ( B @ v3_rlvect_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ ( C @ l1_vectsp_2 ) )
& ( B @ ( C @ v5_vectsp_2 ) )
& ( C @ v6_rlvect_1 )
& ( C @ v5_rlvect_1 )
& ( C @ v4_rlvect_1 )
& ( C @ v3_rlvect_1 )
& ~ ( C @ v3_struct_0 ) )
=> ( ( A @ ( C @ ( B @ k1_rmod_2 ) @ r1_rlvect_1 ) )
<=> ( A
= ( C @ k1_rlvect_1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_rmod_2) ).
thf(213,plain,
! [A: $i,B: $i] :
( ( ( B @ l3_vectsp_1 )
& ( B @ v8_vectsp_1 )
& ( B @ v7_vectsp_1 )
& ( B @ v6_vectsp_1 )
& ( B @ v4_group_1 )
& ( B @ v6_rlvect_1 )
& ( B @ v5_rlvect_1 )
& ( B @ v4_rlvect_1 )
& ( B @ v3_rlvect_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ ( C @ l1_vectsp_2 ) )
& ( B @ ( C @ v5_vectsp_2 ) )
& ( C @ v6_rlvect_1 )
& ( C @ v5_rlvect_1 )
& ( C @ v4_rlvect_1 )
& ( C @ v3_rlvect_1 )
& ~ ( C @ v3_struct_0 ) )
=> ( ( ( A
= ( C @ k1_rlvect_1 ) )
=> ( A @ ( C @ ( B @ k1_rmod_2 ) @ r1_rlvect_1 ) ) )
& ( ( A @ ( C @ ( B @ k1_rmod_2 ) @ r1_rlvect_1 ) )
=> ( A
= ( C @ k1_rlvect_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(28,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(198,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)],[28]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r1_tarski ) )
<=> ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( B @ ( C @ r2_hidden ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
thf(130,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( B @ ( C @ r2_hidden ) ) )
=> ( B @ ( A @ r1_tarski ) ) )
& ( ( B @ ( A @ r1_tarski ) )
=> ! [C: $i] :
( ( A @ ( C @ r2_hidden ) )
=> ( B @ ( C @ r2_hidden ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(34,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(223,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)],[34]) ).
thf(53,axiom,
? [A: $i] : ( A @ l3_vectsp_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l3_vectsp_1) ).
thf(306,plain,
? [A: $i] : ( A @ l3_vectsp_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(38,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(241,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)],[38]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( 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 )
& ( A @ l3_vectsp_1 )
& ( A @ v2_vectsp_2 )
& ~ ( A @ v10_vectsp_1 )
& ( A @ v8_vectsp_1 )
& ( A @ v7_vectsp_1 )
& ( A @ v6_vectsp_1 )
& ( A @ v7_group_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 @ ( A @ ( C @ ( B @ ( A @ k1_rmod_5 ) ) @ m1_rmod_2 ) ) )
& ( A @ ( C @ ( B @ ( A @ k1_rmod_5 ) ) @ v3_vectsp_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_rmod_5) ).
thf(209,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ u1_struct_0 @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( 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 )
& ( A @ l3_vectsp_1 )
& ( A @ v2_vectsp_2 )
& ~ ( A @ v10_vectsp_1 )
& ( A @ v8_vectsp_1 )
& ( A @ v7_vectsp_1 )
& ( A @ v6_vectsp_1 )
& ( A @ v7_group_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 @ ( A @ ( C @ ( B @ ( A @ k1_rmod_5 ) ) @ m1_rmod_2 ) ) )
& ( A @ ( C @ ( B @ ( A @ k1_rmod_5 ) ) @ v3_vectsp_2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(6,axiom,
! [A: $i] :
( ( A @ l1_vectsp_1 )
=> ( A @ l1_group_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_vectsp_1) ).
thf(112,plain,
! [A: $i] :
( ( A @ l1_vectsp_1 )
=> ( A @ l1_group_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(61,axiom,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ ( A @ k7_rlvect_2 ) @ m1_subset_1 ) )
& ( B @ ( A @ k7_rlvect_2 ) @ v1_finset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_rlvect_2) ).
thf(342,plain,
! [A: $i,B: $i] :
( ( ( A @ u1_struct_0 @ ( B @ m1_subset_1 ) )
& ( A @ l1_struct_0 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ u1_struct_0 @ k1_zfmisc_1 @ ( B @ ( A @ k7_rlvect_2 ) @ m1_subset_1 ) )
& ( B @ ( A @ k7_rlvect_2 ) @ v1_finset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( B
= ( A @ k1_tarski ) )
<=> ! [C: $i] :
( ( B @ ( C @ r2_hidden ) )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
thf(145,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( ( C = A )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ( C = A ) ) )
=> ( B
= ( A @ k1_tarski ) ) )
& ( ( B
= ( A @ k1_tarski ) )
=> ! [C: $i] :
( ( ( C = A )
=> ( B @ ( C @ r2_hidden ) ) )
& ( ( B @ ( C @ r2_hidden ) )
=> ( C = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(59,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(336,plain,
! [A: $i] :
( ( A @ l3_vectsp_1 )
=> ( ( A @ l2_vectsp_1 )
& ( A @ l1_rlvect_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(18,axiom,
? [A: $i] : ( A @ l1_rlvect_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_rlvect_1) ).
thf(143,plain,
? [A: $i] : ( A @ l1_rlvect_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(41,axiom,
! [A: $i,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 )
& ( 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 ) )
=> ? [C: $i] :
( ( A @ ( C @ v5_vectsp_2 ) )
& ( A @ ( C @ v3_vectsp_2 ) )
& ( C @ v6_rlvect_1 )
& ( C @ v5_rlvect_1 )
& ( C @ v4_rlvect_1 )
& ( C @ v3_rlvect_1 )
& ~ ( C @ v3_struct_0 )
& ( B @ ( A @ ( C @ m1_rmod_2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_rmod_2) ).
thf(250,plain,
! [A: $i,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 )
& ( 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 ) )
=> ? [C: $i] :
( ( A @ ( C @ v5_vectsp_2 ) )
& ( A @ ( C @ v3_vectsp_2 ) )
& ( C @ v6_rlvect_1 )
& ( C @ v5_rlvect_1 )
& ( C @ v4_rlvect_1 )
& ( C @ v3_rlvect_1 )
& ~ ( C @ v3_struct_0 )
& ( B @ ( A @ ( C @ m1_rmod_2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(29,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(203,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(4,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(104,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)],[4]) ).
thf(62,axiom,
! [A: $i] :
( ( A @ l1_vectsp_1 )
=> ( ( ( A @ v8_vectsp_1 )
& ( A @ v7_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v8_vectsp_1 )
& ( A @ v6_vectsp_1 )
& ( A @ v2_group_1 )
& ~ ( A @ v3_struct_0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_vectsp_2) ).
thf(346,plain,
! [A: $i] :
( ( A @ l1_vectsp_1 )
=> ( ( ( A @ v8_vectsp_1 )
& ( A @ v7_group_1 )
& ~ ( A @ v3_struct_0 ) )
=> ( ( A @ v8_vectsp_1 )
& ( A @ v6_vectsp_1 )
& ( A @ v2_group_1 )
& ~ ( A @ v3_struct_0 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(49,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B @ ( A @ u1_struct_0 @ ( B @ k2_zfmisc_1 ) @ ( E @ m1_relset_1 ) ) )
& ( B @ ( A @ u1_struct_0 @ ( B @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ( B @ ( D @ m1_subset_1 ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( A @ l1_struct_0 ) )
=> ( ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ g1_vectsp_2 ) ) ) ) @ l1_vectsp_2 ) )
& ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ g1_vectsp_2 ) ) ) ) @ v3_vectsp_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_g1_vectsp_2) ).
thf(290,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( B @ ( A @ u1_struct_0 @ ( B @ k2_zfmisc_1 ) @ ( E @ m1_relset_1 ) ) )
& ( B @ ( A @ u1_struct_0 @ ( B @ k2_zfmisc_1 ) @ ( E @ v1_funct_2 ) ) )
& ( E @ v1_funct_1 )
& ( B @ ( D @ m1_subset_1 ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ m1_relset_1 ) ) )
& ( B @ ( B @ ( B @ k2_zfmisc_1 ) @ ( C @ v1_funct_2 ) ) )
& ( C @ v1_funct_1 )
& ( A @ l1_struct_0 ) )
=> ( ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ g1_vectsp_2 ) ) ) ) @ l1_vectsp_2 ) )
& ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ g1_vectsp_2 ) ) ) ) @ v3_vectsp_2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(71,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(378,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)],[71]) ).
thf(51,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(300,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)],[51]) ).
thf(44,axiom,
! [A: $i,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 )
& ( 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 @ ( A @ ( B @ ( A @ k1_rmod_2 ) @ m1_rmod_2 ) ) )
& ( A @ ( B @ ( A @ k1_rmod_2 ) @ v3_vectsp_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_rmod_2) ).
thf(273,plain,
! [A: $i,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 )
& ( 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 @ ( A @ ( B @ ( A @ k1_rmod_2 ) @ m1_rmod_2 ) ) )
& ( A @ ( B @ ( A @ k1_rmod_2 ) @ v3_vectsp_2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(37,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(239,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)],[37]) ).
thf(27,axiom,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(195,plain,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(50,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(294,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)],[50]) ).
thf(13,axiom,
? [A: $i] : ( A @ l2_vectsp_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l2_vectsp_1) ).
thf(126,plain,
? [A: $i] : ( A @ l2_vectsp_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(35,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 @ v5_vectsp_2 ) )
& ( A @ ( B @ v3_vectsp_2 ) )
& ( B @ v6_rlvect_1 )
& ( B @ v5_rlvect_1 )
& ( B @ v4_rlvect_1 )
& ( B @ v3_rlvect_1 )
& ~ ( B @ v3_struct_0 )
& ( A @ ( B @ l1_vectsp_2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc16_vectsp_2) ).
thf(227,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 @ v5_vectsp_2 ) )
& ( A @ ( B @ v3_vectsp_2 ) )
& ( B @ v6_rlvect_1 )
& ( B @ v5_rlvect_1 )
& ( B @ v4_rlvect_1 )
& ( B @ v3_rlvect_1 )
& ~ ( B @ v3_struct_0 )
& ( A @ ( B @ l1_vectsp_2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(11,axiom,
? [A: $i] : ( A @ l1_struct_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(122,plain,
? [A: $i] : ( A @ l1_struct_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(64,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(354,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)],[64]) ).
thf(67,axiom,
! [A: $i,B: $i] :
( ( ( B @ l3_vectsp_1 )
& ( B @ v2_vectsp_2 )
& ~ ( B @ v10_vectsp_1 )
& ( B @ v8_vectsp_1 )
& ( B @ v7_vectsp_1 )
& ( B @ v6_vectsp_1 )
& ( B @ v7_group_1 )
& ( B @ v4_group_1 )
& ( B @ v6_rlvect_1 )
& ( B @ v5_rlvect_1 )
& ( B @ v4_rlvect_1 )
& ( B @ v3_rlvect_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ ( C @ l1_vectsp_2 ) )
& ( B @ ( C @ v5_vectsp_2 ) )
& ( C @ v6_rlvect_1 )
& ( C @ v5_rlvect_1 )
& ( C @ v4_rlvect_1 )
& ( C @ v3_rlvect_1 )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( C @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( A @ r2_hidden ) )
=> ( A @ ( D @ ( C @ ( B @ k1_rmod_5 ) ) @ r1_rlvect_1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_rmod_5) ).
thf(364,plain,
! [A: $i,B: $i] :
( ( ( B @ l3_vectsp_1 )
& ( B @ v2_vectsp_2 )
& ~ ( B @ v10_vectsp_1 )
& ( B @ v8_vectsp_1 )
& ( B @ v7_vectsp_1 )
& ( B @ v6_vectsp_1 )
& ( B @ v7_group_1 )
& ( B @ v4_group_1 )
& ( B @ v6_rlvect_1 )
& ( B @ v5_rlvect_1 )
& ( B @ v4_rlvect_1 )
& ( B @ v3_rlvect_1 )
& ~ ( B @ v3_struct_0 ) )
=> ! [C: $i] :
( ( ( B @ ( C @ l1_vectsp_2 ) )
& ( B @ ( C @ v5_vectsp_2 ) )
& ( C @ v6_rlvect_1 )
& ( C @ v5_rlvect_1 )
& ( C @ v4_rlvect_1 )
& ( C @ v3_rlvect_1 )
& ~ ( C @ v3_struct_0 ) )
=> ! [D: $i] :
( ( C @ u1_struct_0 @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( A @ r2_hidden ) )
=> ( A @ ( D @ ( C @ ( B @ k1_rmod_5 ) ) @ r1_rlvect_1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(387,plain,
$false,
inference(e,[status(thm)],[340,110,321,361,371,166,310,114,277,138,333,352,308,269,120,247,185,288,189,284,312,116,243,102,220,366,302,260,356,169,124,193,73,205,128,237,118,281,382,181,187,377,140,213,198,130,223,306,241,209,112,342,145,336,143,250,203,104,346,290,378,300,273,239,195,294,126,227,122,354,364]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG218+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.07 % 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
% 0.15/5.41 % Computer : n015.cluster.edu
% 0.15/5.41 % Model : x86_64 x86_64
% 0.15/5.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/5.41 % Memory : 8046.5625MB
% 0.15/5.41 % OS : Linux 6.8.0-71-generic
% 0.15/5.41 % CPULimit : 300
% 0.15/5.41 % WCLimit : 300
% 0.15/5.41 % DateTime : Sat Sep 26 21:33:06 UTC 2026
% 0.15/5.41 % CPUTime :
% 0.15/5.41 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
% 0.18/6.01 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.39/6.28 % [INFO] Parsing done (272ms).
% 1.39/6.29 % [INFO] Running in sequential loop mode.
% 2.33/6.69 % [INFO] eprover registered as external prover.
% 2.33/6.70 % [INFO] Scanning for conjecture ...
% 2.72/6.85 % [INFO] Found a conjecture (or negated_conjecture) and 78 axioms. Running axiom selection ...
% 2.91/6.98 % [INFO] Axiom selection finished. Selected 70 axioms (removed 8 axioms).
% 3.35/7.15 % [INFO] Problem is first-order (TPTP FOF).
% 3.59/7.17 % [INFO] Type checking passed.
% 3.59/7.17 % [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 ...
% 8.23/8.68 % External prover 'e' found a proof!
% 8.23/8.68 % [INFO] Killing All external provers ...
% 8.23/8.68 % Time passed: 3121ms (effective reasoning time: 2381ms)
% 8.23/8.68 % 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)>
% 8.23/8.68 % Axioms used in derivation (70): d1_tarski, dt_k7_rlvect_2, dt_u2_struct_0, dt_u1_vectsp_2, dt_l1_vectsp_2, t4_subset, cc2_vectsp_2, rc1_subset_1, dt_k1_rlvect_1, t46_rmod_2, dt_k1_rmod_5, rc8_vectsp_2, redefinition_m2_relset_1, redefinition_k7_rlvect_2, rc13_vectsp_2, dt_k1_rmod_2, fc1_xboole_0, t1_subset, rc2_rlvect_2, rc1_rmod_2, fc4_subset_1, dt_l2_vectsp_1, dt_m2_relset_1, dt_m1_rmod_2, abstractness_v3_vectsp_2, dt_l1_rlvect_1, dt_l1_group_1, t6_boole, rc2_subset_1, existence_l2_struct_0, t5_subset, dt_g1_vectsp_2, existence_m1_relset_1, fc2_subset_1, t7_boole, cc3_vectsp_2, rc3_struct_0, fc1_subset_1, dt_l3_vectsp_1, t3_subset, cc1_relset_1, fc1_vectsp_2, existence_l1_vectsp_2, existence_m1_subset_1, rc16_vectsp_2, existence_m2_relset_1, existence_l1_vectsp_1, d3_tarski, fc1_struct_0, dt_l1_vectsp_1, rc9_vectsp_2, reflexivity_r1_tarski, dt_u1_rlvect_1, dt_l2_struct_0, existence_m1_rmod_2, existence_l3_vectsp_1, t8_boole, rc1_xboole_0, rc5_struct_0, t2_subset, free_g1_vectsp_2, d10_xboole_0, existence_l1_group_1, existence_l1_struct_0, t10_rmod_5, rc4_struct_0, rc2_xboole_0, existence_l1_rlvect_1, existence_l2_vectsp_1, antisymmetry_r2_hidden
% 8.23/8.68 % No. of inferences in proof: 144
% 8.23/8.69 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3121 ms resp. 2381 ms w/o parsing
% 9.23/8.81 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 9.23/8.81 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------