%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ALG224+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 06:46:22 AM UTC 2026
% Result : Theorem 56.27s 11.22s
% Output : Refutation 56.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 38
% Syntax : Number of formulae : 78 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 242 ( 4 equ; 0 cnn)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 674 ( 40 ~; 2 |; 95 &; 470 @)
% ( 2 <=>; 65 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 15 usr; 2 con; 0-4 aty)
% Number of variables : 156 ( 0 ^; 126 !; 30 ?; 156 :)
% Comments :
%------------------------------------------------------------------------------
thf(m1_pboole_decl,type,
m1_pboole: $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(k1_closure2_decl,type,
k1_closure2: $i > $i > $i ).
thf(r2_closure3_decl,type,
r2_closure3: $i > $i > $i > $i > $o ).
thf(v1_xboole_0_decl,type,
v1_xboole_0: $i > $o ).
thf(v1_fraenkel_decl,type,
v1_fraenkel: $i > $o ).
thf(k1_xboole_0_decl,type,
k1_xboole_0: $i ).
thf(v1_funct_1_decl,type,
v1_funct_1: $i > $o ).
thf(v1_relat_1_decl,type,
v1_relat_1: $i > $o ).
thf(v2_funct_1_decl,type,
v2_funct_1: $i > $o ).
thf(v1_finset_1_decl,type,
v1_finset_1: $i > $o ).
thf(r2_hidden_decl,type,
r2_hidden: $i > $i > $o ).
thf(r1_tarski_decl,type,
r1_tarski: $i > $i > $o ).
thf(v1_pralg_2_decl,type,
v1_pralg_2: $i > $o ).
thf(23,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_pboole) ).
thf(120,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( ( B @ v1_funct_1 )
& ( B @ v1_relat_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(31,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(153,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_subset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(33,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(160,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)],[33]) ).
thf(8,axiom,
? [A: $i] :
( ( A @ v1_finset_1 )
& ~ ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_finset_1) ).
thf(65,plain,
? [A: $i] :
( ( A @ v1_finset_1 )
& ~ ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(29,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(141,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)],[29]) ).
thf(35,axiom,
! [A: $i] :
( ( A @ v1_finset_1 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B @ v1_finset_1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_finset_1) ).
thf(166,plain,
! [A: $i] :
( ( A @ v1_finset_1 )
=> ! [B: $i] :
( ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) )
=> ( B @ v1_finset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(30,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( B @ ( A @ k1_closure2 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( A @ k1_closure2 ) @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( D @ ( C @ ( B @ ( A @ r2_closure3 ) ) ) )
<=> ! [E: $i] :
~ ( ! [F: $i] :
~ ( ( E @ ( F @ r1_tarski ) )
& ( D @ ( F @ r2_hidden ) ) )
& ( C @ ( E @ r2_hidden ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_closure3) ).
thf(145,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( B @ ( A @ k1_closure2 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( A @ k1_closure2 ) @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ( ( ! [E: $i] :
~ ( ! [F: $i] :
~ ( ( E @ ( F @ r1_tarski ) )
& ( D @ ( F @ r2_hidden ) ) )
& ( C @ ( E @ r2_hidden ) ) )
=> ( D @ ( C @ ( B @ ( A @ r2_closure3 ) ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ r2_closure3 ) ) ) )
=> ! [E: $i] :
~ ( ! [F: $i] :
~ ( ( E @ ( F @ r1_tarski ) )
& ( D @ ( F @ r2_hidden ) ) )
& ( C @ ( E @ r2_hidden ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(38,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_pboole ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_pboole) ).
thf(177,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ m1_pboole ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(10,axiom,
k1_xboole_0 @ v1_xboole_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(72,plain,
k1_xboole_0 @ v1_xboole_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(15,axiom,
? [A: $i] : ( A @ v1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(87,plain,
? [A: $i] : ( A @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(25,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(126,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)],[25]) ).
thf(9,axiom,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( B @ ( A @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(69,plain,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( B @ ( A @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
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(138,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(34,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(164,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)],[34]) ).
thf(39,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ? [C: $i] :
( ( C @ v1_pralg_2 )
& ( C @ v1_fraenkel )
& ~ ( C @ v1_xboole_0 )
& ( B @ ( A @ k1_closure2 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_closure2) ).
thf(179,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ? [C: $i] :
( ( C @ v1_pralg_2 )
& ( C @ v1_fraenkel )
& ~ ( C @ v1_xboole_0 )
& ( B @ ( A @ k1_closure2 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(16,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)],[16]) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( ( B @ ( A @ k1_closure2 ) @ v1_pralg_2 )
& ( B @ ( A @ k1_closure2 ) @ v1_fraenkel )
& ~ ( B @ ( A @ k1_closure2 ) @ v1_xboole_0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_closure2) ).
thf(133,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ( ( B @ ( A @ k1_closure2 ) @ v1_pralg_2 )
& ( B @ ( A @ k1_closure2 ) @ v1_fraenkel )
& ~ ( B @ ( A @ k1_closure2 ) @ v1_xboole_0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r2_hidden ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(85,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ~ ( A @ ( B @ r2_hidden ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(7,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(60,plain,
? [A: $i] :
( ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(22,axiom,
! [A: $i] :
~ ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(117,plain,
! [A: $i] :
~ ( A @ k1_zfmisc_1 @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
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(124,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ r2_hidden ) )
=> ( B @ ( A @ m1_subset_1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(18,axiom,
? [A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).
thf(96,plain,
? [A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(11,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_finset_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_finset_1) ).
thf(73,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_finset_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(26,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ( B @ v1_finset_1 )
& ~ ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_finset_1) ).
thf(128,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ( B @ v1_finset_1 )
& ~ ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(5,axiom,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( A != B )
& ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
thf(54,plain,
! [A: $i,B: $i] :
~ ( ( B @ v1_xboole_0 )
& ( A != B )
& ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(3,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_fraenkel ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_closure2) ).
thf(49,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_fraenkel ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(20,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(103,plain,
? [A: $i] :
( ( A @ v1_funct_1 )
& ( A @ v1_xboole_0 )
& ( A @ v1_relat_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(17,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(91,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)],[17]) ).
thf(32,axiom,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ( B @ v1_finset_1 )
& ~ ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_finset_1) ).
thf(155,plain,
! [A: $i] :
( ~ ( A @ v1_xboole_0 )
=> ? [B: $i] :
( ( B @ v1_finset_1 )
& ~ ( B @ v1_xboole_0 )
& ( A @ k1_zfmisc_1 @ ( B @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ? [C: $i] :
( ( C @ v1_fraenkel )
& ( C @ v1_finset_1 )
& ( C @ v2_funct_1 )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 )
& ( C @ v1_xboole_0 )
& ( B @ ( A @ k1_closure2 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_closure2) ).
thf(108,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ? [C: $i] :
( ( C @ v1_fraenkel )
& ( C @ v1_finset_1 )
& ( C @ v2_funct_1 )
& ( C @ v1_funct_1 )
& ( C @ v1_relat_1 )
& ( C @ v1_xboole_0 )
& ( B @ ( A @ k1_closure2 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( B @ ( A @ k1_closure2 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( A @ k1_closure2 ) @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ ( A @ k1_closure2 ) @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ( ( ( E @ ( D @ ( B @ ( A @ r2_closure3 ) ) ) )
& ( D @ ( C @ ( B @ ( A @ r2_closure3 ) ) ) ) )
=> ( E @ ( C @ ( B @ ( A @ r2_closure3 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_closure3) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( B @ ( A @ k1_closure2 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( A @ k1_closure2 ) @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ ( A @ k1_closure2 ) @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ( ( ( E @ ( D @ ( B @ ( A @ r2_closure3 ) ) ) )
& ( D @ ( C @ ( B @ ( A @ r2_closure3 ) ) ) ) )
=> ( E @ ( C @ ( B @ ( A @ r2_closure3 ) ) ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(40,plain,
~ ! [A: $i,B: $i] :
( ( A @ ( B @ m1_pboole ) )
=> ! [C: $i] :
( ( B @ ( A @ k1_closure2 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
=> ! [D: $i] :
( ( B @ ( A @ k1_closure2 ) @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
=> ! [E: $i] :
( ( B @ ( A @ k1_closure2 ) @ k1_zfmisc_1 @ ( E @ m1_subset_1 ) )
=> ( ( ( E @ ( D @ ( B @ ( A @ r2_closure3 ) ) ) )
& ( D @ ( C @ ( B @ ( A @ r2_closure3 ) ) ) ) )
=> ( E @ ( C @ ( B @ ( A @ r2_closure3 ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(37,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(171,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)],[37]) ).
thf(12,axiom,
? [A: $i] :
( ( A @ v1_fraenkel )
& ( A @ v1_finset_1 )
& ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 )
& ( A @ v1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_closure2) ).
thf(75,plain,
? [A: $i] :
( ( A @ v1_fraenkel )
& ( A @ v1_finset_1 )
& ( A @ v2_funct_1 )
& ( A @ v1_funct_1 )
& ( A @ v1_relat_1 )
& ( A @ v1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(6,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_funct_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
thf(58,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A @ v1_funct_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(36,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ k1_closure2 ) @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( B @ ( A @ k1_closure2 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ( C @ ( C @ ( B @ ( A @ r2_closure3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r2_closure3) ).
thf(168,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( A @ k1_closure2 ) @ k1_zfmisc_1 @ ( D @ m1_subset_1 ) )
& ( B @ ( A @ k1_closure2 ) @ k1_zfmisc_1 @ ( C @ m1_subset_1 ) )
& ( A @ ( B @ m1_pboole ) ) )
=> ( C @ ( C @ ( B @ ( A @ r2_closure3 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(4,axiom,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(51,plain,
! [A: $i] :
( ( A @ v1_xboole_0 )
=> ( A = k1_xboole_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( C @ ( A @ r1_tarski ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).
thf(83,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ r1_tarski ) )
& ( B @ ( A @ r1_tarski ) ) )
=> ( C @ ( A @ r1_tarski ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(19,axiom,
? [A: $i] :
~ ( A @ v1_xboole_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(100,plain,
? [A: $i] :
~ ( A @ v1_xboole_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(26172,plain,
$false,
inference(e,[status(thm)],[120,153,160,65,141,166,145,177,72,87,126,69,138,164,179,89,133,85,60,117,124,96,73,128,54,49,103,91,155,108,40,171,75,58,168,51,83,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG224+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
% 0.14/0.40 % Computer : n002.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Sat Sep 26 21:36:37 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 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
% 0.88/0.97 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.29/1.18 % [INFO] Parsing done (208ms).
% 1.29/1.19 % [INFO] Running in sequential loop mode.
% 2.01/1.58 % [INFO] eprover registered as external prover.
% 2.01/1.59 % [INFO] Scanning for conjecture ...
% 2.42/1.71 % [INFO] Found a conjecture (or negated_conjecture) and 41 axioms. Running axiom selection ...
% 2.42/1.79 % [INFO] Axiom selection finished. Selected 37 axioms (removed 4 axioms).
% 2.63/1.85 % [INFO] Problem is first-order (TPTP FOF).
% 2.63/1.86 % [INFO] Type checking passed.
% 2.63/1.87 % [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 ...
% 56.27/11.21 % External prover 'e' found a proof!
% 56.27/11.21 % [INFO] Killing All external provers ...
% 56.27/11.21 % Time passed: 10668ms (effective reasoning time: 10014ms)
% 56.27/11.21 % 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)>
% 56.27/11.22 % Axioms used in derivation (37): cc2_finset_1, rc1_funct_1, rc3_finset_1, antisymmetry_r2_hidden, rc4_finset_1, fc2_closure2, fc1_xboole_0, t1_subset, rc3_funct_1, rc2_closure2, t6_boole, rc2_subset_1, t1_xboole_1, t5_subset, t4_subset, cc1_closure2, t7_boole, cc1_funct_1, fc1_subset_1, rc2_funct_1, rc1_subset_1, dt_m1_pboole, existence_m1_pboole, cc2_funct_1, t3_subset, existence_m1_subset_1, reflexivity_r2_closure3, reflexivity_r1_tarski, rc1_finset_1, cc1_finset_1, t8_boole, rc1_xboole_0, t2_subset, rc1_closure2, rc3_closure2, d2_closure3, rc2_xboole_0
% 56.27/11.22 % No. of inferences in proof: 78
% 56.27/11.22 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 10668 ms resp. 10014 ms w/o parsing
% 56.27/11.30 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 56.27/11.30 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------