%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP004+2 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:35:24 AM UTC 2026
% Result : Theorem 9.03s 3.20s
% Output : Refutation 9.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 27
% Syntax : Number of formulae : 56 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 190 ( 18 equ; 0 cnn)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 768 ( 8 ~; 0 |; 14 &; 626 @)
% ( 8 <=>; 112 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 19 usr; 6 con; 0-2 aty)
% Number of variables : 100 ( 0 ^; 100 !; 0 ?; 100 :)
% Comments :
%------------------------------------------------------------------------------
thf(ne_decl,type,
ne: $i > $o ).
thf(mem_decl,type,
mem: $i > $i > $o ).
thf(arr_decl,type,
arr: $i > $i > $i ).
thf(bool_decl,type,
bool: $i ).
thf(p_decl,type,
p: $i > $o ).
thf(ap_decl,type,
ap: $i > $i > $i ).
thf(c_2Epred__set_2ESUBSET_decl,type,
c_2Epred__set_2ESUBSET: $i > $i ).
thf(c_2Epred__set_2EREST_decl,type,
c_2Epred__set_2EREST: $i > $i ).
thf(c_2Ebool_2E_21_decl,type,
c_2Ebool_2E_21: $i > $i ).
thf(c_2Emin_2E_3D_decl,type,
c_2Emin_2E_3D: $i > $i ).
thf(k_decl,type,
k: $i > $i > $i ).
thf(c_2Emin_2E_3D_3D_3E_decl,type,
c_2Emin_2E_3D_3D_3E: $i ).
thf(c_2Ebool_2E_7E_decl,type,
c_2Ebool_2E_7E: $i ).
thf(c_2Epred__set_2EDELETE_decl,type,
c_2Epred__set_2EDELETE: $i > $i ).
thf(c_2Epred__set_2ECHOICE_decl,type,
c_2Epred__set_2ECHOICE: $i > $i ).
thf(c_2Ebool_2E_2F_5C_decl,type,
c_2Ebool_2E_2F_5C: $i ).
thf(c_2Ebool_2EIN_decl,type,
c_2Ebool_2EIN: $i > $i ).
thf(ind_decl,type,
ind: $i ).
thf(i_decl,type,
i: $i > $i ).
thf(22,axiom,
ind @ ne,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ind_ne) ).
thf(101,plain,
ind @ ne,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(10,axiom,
! [A: $i] :
( ( bool @ ( A @ mem ) )
=> ! [B: $i] :
( ( bool @ ( B @ mem ) )
=> ( ( ( A @ p )
<=> ( B @ p ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',boolext) ).
thf(56,plain,
! [A: $i] :
( ( bool @ ( A @ mem ) )
=> ! [B: $i] :
( ( bool @ ( B @ mem ) )
=> ( ( ( ( B @ p )
=> ( A @ p ) )
& ( ( A @ p )
=> ( B @ p ) ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(28,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ arr ) @ ( C @ mem ) )
=> ! [D: $i] :
( ( B @ ( A @ arr ) @ ( D @ mem ) )
=> ( ! [E: $i] :
( ( A @ ( E @ mem ) )
=> ( ( E @ ( C @ ap ) )
= ( E @ ( D @ ap ) ) ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcext) ).
thf(116,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ arr ) @ ( C @ mem ) )
=> ! [D: $i] :
( ( B @ ( A @ arr ) @ ( D @ mem ) )
=> ( ! [E: $i] :
( ( A @ ( E @ mem ) )
=> ( ( E @ ( C @ ap ) )
= ( E @ ( D @ ap ) ) ) )
=> ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(23,axiom,
! [A: $i] :
( ( A @ ne )
=> ( bool @ ( A @ arr ) @ ( A @ arr ) @ ( A @ c_2Emin_2E_3D @ mem ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Emin_2E_3D) ).
thf(102,plain,
! [A: $i] :
( ( A @ ne )
=> ( bool @ ( A @ arr ) @ ( A @ arr ) @ ( A @ c_2Emin_2E_3D @ mem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(12,axiom,
! [A: $i] :
( ( A @ ne )
=> ( bool @ ( bool @ ( A @ arr ) @ arr ) @ ( A @ c_2Ebool_2E_21 @ mem ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ebool_2E_21) ).
thf(70,plain,
! [A: $i] :
( ( A @ ne )
=> ( bool @ ( bool @ ( A @ arr ) @ arr ) @ ( A @ c_2Ebool_2E_21 @ mem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(18,axiom,
bool @ ( bool @ arr ) @ ( c_2Ebool_2E_7E @ mem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ebool_2E_7E) ).
thf(92,plain,
bool @ ( bool @ arr ) @ ( c_2Ebool_2E_7E @ mem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ arr ) @ ( C @ mem ) )
=> ! [D: $i] :
( ( A @ ( D @ mem ) )
=> ( B @ ( D @ ( C @ ap ) @ mem ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_tp) ).
thf(53,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ arr ) @ ( C @ mem ) )
=> ! [D: $i] :
( ( A @ ( D @ mem ) )
=> ( B @ ( D @ ( C @ ap ) @ mem ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(3,axiom,
! [A: $i] :
( ( A @ ne )
=> ! [B: $i] :
( ( bool @ ( A @ arr ) @ ( B @ mem ) )
=> ( ( B @ ( A @ c_2Ebool_2E_21 @ ap ) @ p )
<=> ! [C: $i] :
( ( A @ ( C @ mem ) )
=> ( C @ ( B @ ap ) @ p ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_all_p) ).
thf(34,plain,
! [A: $i] :
( ( A @ ne )
=> ! [B: $i] :
( ( bool @ ( A @ arr ) @ ( B @ mem ) )
=> ( ( ! [C: $i] :
( ( A @ ( C @ mem ) )
=> ( C @ ( B @ ap ) @ p ) )
=> ( B @ ( A @ c_2Ebool_2E_21 @ ap ) @ p ) )
& ( ( B @ ( A @ c_2Ebool_2E_21 @ ap ) @ p )
=> ! [C: $i] :
( ( A @ ( C @ mem ) )
=> ( C @ ( B @ ap ) @ p ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(6,axiom,
! [A: $i] :
( ( A @ ne )
=> ( bool @ ( A @ arr ) @ ( bool @ ( A @ arr ) @ arr ) @ ( A @ c_2Epred__set_2EREST @ mem ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Epred__set_2EREST) ).
thf(49,plain,
! [A: $i] :
( ( A @ ne )
=> ( bool @ ( A @ arr ) @ ( bool @ ( A @ arr ) @ arr ) @ ( A @ c_2Epred__set_2EREST @ mem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(4,axiom,
! [A: $i] :
( ( A @ ne )
=> ! [B: $i] :
( ( A @ ( B @ mem ) )
=> ! [C: $i] :
( ( A @ ( C @ mem ) )
=> ( ( C @ ( B @ ( A @ c_2Emin_2E_3D @ ap ) @ ap ) @ p )
<=> ( B = C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_eq_p) ).
thf(39,plain,
! [A: $i] :
( ( A @ ne )
=> ! [B: $i] :
( ( A @ ( B @ mem ) )
=> ! [C: $i] :
( ( A @ ( C @ mem ) )
=> ( ( ( B = C )
=> ( C @ ( B @ ( A @ c_2Emin_2E_3D @ ap ) @ ap ) @ p ) )
& ( ( C @ ( B @ ( A @ c_2Emin_2E_3D @ ap ) @ ap ) @ p )
=> ( B = C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(11,axiom,
! [A: $i] :
( ( bool @ ( A @ mem ) )
=> ( ( A @ ( c_2Ebool_2E_7E @ ap ) @ p )
<=> ~ ( A @ p ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_neg_p) ).
thf(66,plain,
! [A: $i] :
( ( bool @ ( A @ mem ) )
=> ( ( ~ ( A @ p )
=> ( A @ ( c_2Ebool_2E_7E @ ap ) @ p ) )
& ( ( A @ ( c_2Ebool_2E_7E @ ap ) @ p )
=> ~ ( A @ p ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(21,axiom,
! [A: $i] :
( ( A @ ne )
=> ! [B: $i] :
( ( bool @ ( A @ arr ) @ ( B @ mem ) )
=> ! [C: $i] :
( ( bool @ ( A @ arr ) @ ( C @ mem ) )
=> ( ( C @ ( B @ ( A @ c_2Epred__set_2ESUBSET @ ap ) @ ap ) @ p )
<=> ! [D: $i] :
( ( A @ ( D @ mem ) )
=> ( ( B @ ( D @ ( A @ c_2Ebool_2EIN @ ap ) @ ap ) @ p )
=> ( C @ ( D @ ( A @ c_2Ebool_2EIN @ ap ) @ ap ) @ p ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_thm_2Epred__set_2ESUBSET__DEF) ).
thf(95,plain,
! [A: $i] :
( ( A @ ne )
=> ! [B: $i] :
( ( bool @ ( A @ arr ) @ ( B @ mem ) )
=> ! [C: $i] :
( ( bool @ ( A @ arr ) @ ( C @ mem ) )
=> ( ( ! [D: $i] :
( ( A @ ( D @ mem ) )
=> ( ( B @ ( D @ ( A @ c_2Ebool_2EIN @ ap ) @ ap ) @ p )
=> ( C @ ( D @ ( A @ c_2Ebool_2EIN @ ap ) @ ap ) @ p ) ) )
=> ( C @ ( B @ ( A @ c_2Epred__set_2ESUBSET @ ap ) @ ap ) @ p ) )
& ( ( C @ ( B @ ( A @ c_2Epred__set_2ESUBSET @ ap ) @ ap ) @ p )
=> ! [D: $i] :
( ( A @ ( D @ mem ) )
=> ( ( B @ ( D @ ( A @ c_2Ebool_2EIN @ ap ) @ ap ) @ p )
=> ( C @ ( D @ ( A @ c_2Ebool_2EIN @ ap ) @ ap ) @ p ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(13,axiom,
! [A: $i] :
( ( A @ ne )
=> ! [B: $i] :
( ( bool @ ( A @ arr ) @ ( B @ mem ) )
=> ( ( B @ ( A @ c_2Epred__set_2EREST @ ap ) )
= ( B @ ( A @ c_2Epred__set_2ECHOICE @ ap ) @ ( B @ ( A @ c_2Epred__set_2EDELETE @ ap ) @ ap ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_thm_2Epred__set_2EREST__DEF) ).
thf(72,plain,
! [A: $i] :
( ( A @ ne )
=> ! [B: $i] :
( ( bool @ ( A @ arr ) @ ( B @ mem ) )
=> ( ( B @ ( A @ c_2Epred__set_2EREST @ ap ) )
= ( B @ ( A @ c_2Epred__set_2ECHOICE @ ap ) @ ( B @ ( A @ c_2Epred__set_2EDELETE @ ap ) @ ap ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(24,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ mem ) )
=> ( ( B @ ( A @ i @ ap ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ibeta) ).
thf(104,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ mem ) )
=> ( ( B @ ( A @ i @ ap ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(7,axiom,
! [A: $i] :
( ( A @ ne )
=> ! [B: $i] :
( ( B @ ne )
=> ( B @ ( A @ arr ) @ ne ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arr_ne) ).
thf(51,plain,
! [A: $i] :
( ( A @ ne )
=> ! [B: $i] :
( ( B @ ne )
=> ( B @ ( A @ arr ) @ ne ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(17,axiom,
! [A: $i] :
( ( A @ ne )
=> ( bool @ ( bool @ ( A @ arr ) @ arr ) @ ( bool @ ( A @ arr ) @ arr ) @ ( A @ c_2Epred__set_2ESUBSET @ mem ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Epred__set_2ESUBSET) ).
thf(90,plain,
! [A: $i] :
( ( A @ ne )
=> ( bool @ ( bool @ ( A @ arr ) @ arr ) @ ( bool @ ( A @ arr ) @ arr ) @ ( A @ c_2Epred__set_2ESUBSET @ mem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ mem ) )
=> ( ( C @ ( B @ ( A @ k ) @ ap ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kbeta) ).
thf(46,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ mem ) )
=> ( ( C @ ( B @ ( A @ k ) @ ap ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(19,axiom,
bool @ ne,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bool_ne) ).
thf(93,plain,
bool @ ne,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(1,conjecture,
! [A: $i] :
( ( A @ ne )
=> ! [B: $i] :
( ( bool @ ( A @ arr ) @ ( B @ mem ) )
=> ( B @ ( B @ ( A @ c_2Epred__set_2EREST @ ap ) @ ( A @ c_2Epred__set_2ESUBSET @ ap ) @ ap ) @ p ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Epred__set_2EREST__SUBSET) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( A @ ne )
=> ! [B: $i] :
( ( bool @ ( A @ arr ) @ ( B @ mem ) )
=> ( B @ ( B @ ( A @ c_2Epred__set_2EREST @ ap ) @ ( A @ c_2Epred__set_2ESUBSET @ ap ) @ ap ) @ p ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(29,plain,
~ ! [A: $i] :
( ( A @ ne )
=> ! [B: $i] :
( ( bool @ ( A @ arr ) @ ( B @ mem ) )
=> ( B @ ( B @ ( A @ c_2Epred__set_2EREST @ ap ) @ ( A @ c_2Epred__set_2ESUBSET @ ap ) @ ap ) @ p ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(26,axiom,
! [A: $i] :
( ( bool @ ( A @ mem ) )
=> ! [B: $i] :
( ( bool @ ( B @ mem ) )
=> ( ( B @ ( A @ ( c_2Emin_2E_3D_3D_3E @ ap ) @ ap ) @ p )
<=> ( ( A @ p )
=> ( B @ p ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_imp_p) ).
thf(109,plain,
! [A: $i] :
( ( bool @ ( A @ mem ) )
=> ! [B: $i] :
( ( bool @ ( B @ mem ) )
=> ( ( ( ( A @ p )
=> ( B @ p ) )
=> ( B @ ( A @ ( c_2Emin_2E_3D_3D_3E @ ap ) @ ap ) @ p ) )
& ( ( B @ ( A @ ( c_2Emin_2E_3D_3D_3E @ ap ) @ ap ) @ p )
=> ( ( A @ p )
=> ( B @ p ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(15,axiom,
! [A: $i] :
( ( bool @ ( A @ mem ) )
=> ! [B: $i] :
( ( bool @ ( B @ mem ) )
=> ( ( B @ ( A @ ( c_2Ebool_2E_2F_5C @ ap ) @ ap ) @ p )
<=> ( ( B @ p )
& ( A @ p ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_and_p) ).
thf(77,plain,
! [A: $i] :
( ( bool @ ( A @ mem ) )
=> ! [B: $i] :
( ( bool @ ( B @ mem ) )
=> ( ( ( ( B @ p )
& ( A @ p ) )
=> ( B @ ( A @ ( c_2Ebool_2E_2F_5C @ ap ) @ ap ) @ p ) )
& ( ( B @ ( A @ ( c_2Ebool_2E_2F_5C @ ap ) @ ap ) @ p )
=> ( ( B @ p )
& ( A @ p ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(9,axiom,
bool @ ( bool @ arr ) @ ( bool @ arr ) @ ( c_2Emin_2E_3D_3D_3E @ mem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Emin_2E_3D_3D_3E) ).
thf(55,plain,
bool @ ( bool @ arr ) @ ( bool @ arr ) @ ( c_2Emin_2E_3D_3D_3E @ mem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(27,axiom,
! [A: $i] :
( ( A @ ne )
=> ( A @ ( bool @ ( A @ arr ) @ arr ) @ ( A @ c_2Epred__set_2ECHOICE @ mem ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Epred__set_2ECHOICE) ).
thf(114,plain,
! [A: $i] :
( ( A @ ne )
=> ( A @ ( bool @ ( A @ arr ) @ arr ) @ ( A @ c_2Epred__set_2ECHOICE @ mem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(14,axiom,
! [A: $i] :
( ( A @ ne )
=> ( bool @ ( A @ arr ) @ ( A @ arr ) @ ( bool @ ( A @ arr ) @ arr ) @ ( A @ c_2Epred__set_2EDELETE @ mem ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Epred__set_2EDELETE) ).
thf(75,plain,
! [A: $i] :
( ( A @ ne )
=> ( bool @ ( A @ arr ) @ ( A @ arr ) @ ( bool @ ( A @ arr ) @ arr ) @ ( A @ c_2Epred__set_2EDELETE @ mem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(16,axiom,
! [A: $i] :
( ( A @ ne )
=> ! [B: $i] :
( ( bool @ ( A @ arr ) @ ( B @ mem ) )
=> ! [C: $i] :
( ( A @ ( C @ mem ) )
=> ! [D: $i] :
( ( A @ ( D @ mem ) )
=> ( ( D @ ( B @ ( A @ c_2Epred__set_2EDELETE @ ap ) @ ap ) @ ( C @ ( A @ c_2Ebool_2EIN @ ap ) @ ap ) @ p )
<=> ( ( C != D )
& ( B @ ( C @ ( A @ c_2Ebool_2EIN @ ap ) @ ap ) @ p ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Epred__set_2EIN__DELETE) ).
thf(82,plain,
! [A: $i] :
( ( A @ ne )
=> ! [B: $i] :
( ( bool @ ( A @ arr ) @ ( B @ mem ) )
=> ! [C: $i] :
( ( A @ ( C @ mem ) )
=> ! [D: $i] :
( ( A @ ( D @ mem ) )
=> ( ( ( ( C != D )
& ( B @ ( C @ ( A @ c_2Ebool_2EIN @ ap ) @ ap ) @ p ) )
=> ( D @ ( B @ ( A @ c_2Epred__set_2EDELETE @ ap ) @ ap ) @ ( C @ ( A @ c_2Ebool_2EIN @ ap ) @ ap ) @ p ) )
& ( ( D @ ( B @ ( A @ c_2Epred__set_2EDELETE @ ap ) @ ap ) @ ( C @ ( A @ c_2Ebool_2EIN @ ap ) @ ap ) @ p )
=> ( ( C != D )
& ( B @ ( C @ ( A @ c_2Ebool_2EIN @ ap ) @ ap ) @ p ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(25,axiom,
! [A: $i] :
( ( A @ ne )
=> ( bool @ ( bool @ ( A @ arr ) @ arr ) @ ( A @ arr ) @ ( A @ c_2Ebool_2EIN @ mem ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ebool_2EIN) ).
thf(107,plain,
! [A: $i] :
( ( A @ ne )
=> ( bool @ ( bool @ ( A @ arr ) @ arr ) @ ( A @ arr ) @ ( A @ c_2Ebool_2EIN @ mem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(20,axiom,
bool @ ( bool @ arr ) @ ( bool @ arr ) @ ( c_2Ebool_2E_2F_5C @ mem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ebool_2E_2F_5C) ).
thf(94,plain,
bool @ ( bool @ arr ) @ ( bool @ arr ) @ ( c_2Ebool_2E_2F_5C @ mem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(653,plain,
$false,
inference(e,[status(thm)],[101,56,116,102,70,92,53,34,49,39,66,95,72,104,51,90,46,93,29,109,77,55,114,75,82,107,94]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP004+2 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.06 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.10/0.37 % Computer : n003.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 25 17:04:24 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.64/0.69 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.96/0.81 % [INFO] Parsing done (123ms).
% 0.96/0.82 % [INFO] Running in sequential loop mode.
% 1.65/1.18 % [INFO] eprover registered as external prover.
% 1.65/1.19 % [INFO] Scanning for conjecture ...
% 1.96/1.30 % [INFO] Found a conjecture (or negated_conjecture) and 26 axioms. Running axiom selection ...
% 1.96/1.39 % [INFO] Axiom selection finished. Selected 26 axioms (removed 0 axioms).
% 2.18/1.45 % [INFO] Problem is first-order (TPTP FOF).
% 2.18/1.46 % [INFO] Type checking passed.
% 2.18/1.47 % [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 ...
% 8.73/3.20 % External prover 'e' found a proof!
% 8.73/3.20 % [INFO] Killing All external provers ...
% 9.03/3.20 % Time passed: 2731ms (effective reasoning time: 2372ms)
% 9.03/3.20 % 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)>
% 9.03/3.20 % Axioms used in derivation (26): conj_thm_2Epred__set_2EIN__DELETE, ibeta, kbeta, funcext, mem_c_2Epred__set_2EDELETE, mem_c_2Ebool_2E_21, ax_and_p, mem_c_2Emin_2E_3D, mem_c_2Ebool_2E_7E, arr_ne, ax_all_p, mem_c_2Epred__set_2EREST, ap_tp, mem_c_2Epred__set_2ESUBSET, boolext, mem_c_2Epred__set_2ECHOICE, ax_thm_2Epred__set_2EREST__DEF, ax_neg_p, mem_c_2Ebool_2E_2F_5C, ax_imp_p, ax_eq_p, ax_thm_2Epred__set_2ESUBSET__DEF, mem_c_2Ebool_2EIN, ind_ne, mem_c_2Emin_2E_3D_3D_3E, bool_ne
% 9.03/3.20 % No. of inferences in proof: 56
% 9.03/3.20 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2731 ms resp. 2372 ms w/o parsing
% 9.03/3.24 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 9.03/3.24 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------