%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU162+1 : TPTP v9.3.1. Released v3.3.0.
% 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 08:37:50 AM UTC 2026
% Result : Theorem 10.60s 9.74s
% Output : Refutation 11.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 9
% Syntax : Number of formulae : 67 ( 14 unt; 0 typ; 4 def)
% Number of atoms : 188 ( 62 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 551 ( 87 ~; 59 |; 11 &; 375 @)
% ( 3 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 94 ( 0 ^; 88 !; 2 ?; 94 :)
% ( 0 !>; 0 ?*; 0 @-; 4 @+)
% Comments :
%------------------------------------------------------------------------------
thf(set_difference_decl,type,
set_difference: $i > $i > $i ).
thf(singleton_decl,type,
singleton: $i > $i ).
thf(in_decl,type,
in: $i > $i > $o ).
thf(disjoint_decl,type,
disjoint: $i > $i > $o ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(sk4_decl,type,
sk4: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( B @ singleton @ ( A @ set_difference ) )
= A )
=> ~ ( A @ ( B @ in ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ( ( ( A @ singleton @ ( sk1 @ set_difference ) )
= sk1 )
=> ~ ( sk1 @ ( A @ in ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ! [B: $i] :
( ~ ( A @ ( B @ in ) )
=> ( ( B @ singleton @ ( A @ set_difference ) )
= A ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i] :
~ ( ~ ( sk3 @ ( A @ in ) )
=> ( ( A @ singleton @ ( sk3 @ set_difference ) )
= sk3 ) ) ) ) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ in ) )
=> ( B @ ( A @ singleton @ disjoint ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l28_zfmisc_1) ).
thf(27,plain,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ in ) )
=> ( B @ ( A @ singleton @ disjoint ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(28,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ singleton @ disjoint ) )
| ( B @ ( A @ in ) ) ),
inference(cnf,[status(esa)],[27]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ disjoint ) )
=> ( A @ ( B @ disjoint ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
thf(29,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ disjoint ) )
=> ( A @ ( B @ disjoint ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(30,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ disjoint ) )
| ~ ( B @ ( A @ disjoint ) ) ),
inference(cnf,[status(esa)],[29]) ).
thf(92,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ singleton @ disjoint ) )
!= ( D @ ( C @ disjoint ) ) )
| ( C @ ( D @ disjoint ) )
| ~ $true
| ( B @ ( A @ in ) ) ),
inference(paramod_ordered,[status(thm)],[28,30]) ).
thf(93,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ singleton @ disjoint ) )
!= ( D @ ( C @ disjoint ) ) )
| ( C @ ( D @ disjoint ) )
| ( B @ ( A @ in ) ) ),
inference(simp,[status(thm)],[92]) ).
thf(94,plain,
! [B: $i,A: $i] :
( ( B @ singleton @ ( A @ disjoint ) )
| ( A @ ( B @ in ) ) ),
inference(pattern_uni,[status(thm)],[93:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ singleton )),bind(D,$thf( B ))]]) ).
thf(99,plain,
! [B: $i,A: $i] :
( ( B @ singleton @ ( A @ disjoint ) )
| ( A @ ( B @ in ) ) ),
inference(simp,[status(thm)],[94]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ disjoint ) )
<=> ( ( B @ ( A @ set_difference ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_xboole_1) ).
thf(31,plain,
! [A: $i,B: $i] :
( ( ( ( B @ ( A @ set_difference ) )
= A )
=> ( B @ ( A @ disjoint ) ) )
& ( ( B @ ( A @ disjoint ) )
=> ( ( B @ ( A @ set_difference ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(32,plain,
( ! [A: $i,B: $i] :
( ( ( B @ ( A @ set_difference ) )
= A )
=> ( B @ ( A @ disjoint ) ) )
& ! [A: $i,B: $i] :
( ( B @ ( A @ disjoint ) )
=> ( ( B @ ( A @ set_difference ) )
= A ) ) ),
inference(miniscope,[status(thm)],[31]) ).
thf(33,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ disjoint ) )
| ( ( D @ ( C @ set_difference ) )
!= C ) )
& ( ( ( B @ ( A @ set_difference ) )
= A )
| ~ ( B @ ( A @ disjoint ) ) ) ),
inference(cnf,[status(esa)],[32]) ).
thf(34,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ set_difference ) )
= A )
| ~ ( B @ ( A @ disjoint ) ) ),
inference(cnfConj,[status(thm)],[33]) ).
thf(36,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ disjoint ) )
| ( ( B @ ( A @ set_difference ) )
= A ) ),
inference(lifteq,[status(thm)],[34]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( ( B @ singleton @ ( A @ set_difference ) )
= A )
<=> ~ ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_zfmisc_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( ( B @ singleton @ ( A @ set_difference ) )
= A )
<=> ~ ( A @ ( B @ in ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(10,plain,
~ ! [A: $i,B: $i] :
( ( ~ ( A @ ( B @ in ) )
=> ( ( B @ singleton @ ( A @ set_difference ) )
= A ) )
& ( ( ( B @ singleton @ ( A @ set_difference ) )
= A )
=> ~ ( A @ ( B @ in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(11,plain,
~ ( ! [A: $i,B: $i] :
( ~ ( A @ ( B @ in ) )
=> ( ( B @ singleton @ ( A @ set_difference ) )
= A ) )
& ! [A: $i,B: $i] :
( ( ( B @ singleton @ ( A @ set_difference ) )
= A )
=> ~ ( A @ ( B @ in ) ) ) ),
inference(miniscope,[status(thm)],[10]) ).
thf(12,plain,
( ( ( ( sk4 @ singleton @ ( sk3 @ set_difference ) )
!= sk3 )
| ( sk1 @ ( sk2 @ in ) ) )
& ( ~ ( sk3 @ ( sk4 @ in ) )
| ( sk1 @ ( sk2 @ in ) ) )
& ( ( ( sk4 @ singleton @ ( sk3 @ set_difference ) )
!= sk3 )
| ( ( sk2 @ singleton @ ( sk1 @ set_difference ) )
= sk1 ) )
& ( ~ ( sk3 @ ( sk4 @ in ) )
| ( ( sk2 @ singleton @ ( sk1 @ set_difference ) )
= sk1 ) ) ),
inference(cnf,[status(esa)],[11]) ).
thf(14,plain,
( ( ( sk4 @ singleton @ ( sk3 @ set_difference ) )
!= sk3 )
| ( ( sk2 @ singleton @ ( sk1 @ set_difference ) )
= sk1 ) ),
inference(cnfConj,[status(thm)],[12]) ).
thf(18,plain,
( ( ( sk4 @ singleton @ ( sk3 @ set_difference ) )
!= sk3 )
| ( ( sk2 @ singleton @ ( sk1 @ set_difference ) )
= sk1 ) ),
inference(lifteq,[status(thm)],[14]) ).
thf(35,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ disjoint ) )
| ( ( B @ ( A @ set_difference ) )
!= A ) ),
inference(cnfConj,[status(thm)],[33]) ).
thf(37,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ disjoint ) )
| ( ( B @ ( A @ set_difference ) )
!= A ) ),
inference(lifteq,[status(thm)],[35]) ).
thf(38,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ disjoint ) )
| ( ( B @ ( A @ set_difference ) )
!= A ) ),
inference(simp,[status(thm)],[37]) ).
thf(16,plain,
( ( ( sk4 @ singleton @ ( sk3 @ set_difference ) )
!= sk3 )
| ( sk1 @ ( sk2 @ in ) ) ),
inference(cnfConj,[status(thm)],[12]) ).
thf(19,plain,
( ( sk1 @ ( sk2 @ in ) )
| ( ( sk4 @ singleton @ ( sk3 @ set_difference ) )
!= sk3 ) ),
inference(lifteq,[status(thm)],[16]) ).
thf(159,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ set_difference ) )
!= ( sk4 @ singleton @ ( sk3 @ set_difference ) ) )
| ( sk1 @ ( sk2 @ in ) )
| ( A != sk3 )
| ~ ( B @ ( A @ disjoint ) ) ),
inference(paramod_ordered,[status(thm)],[36,19]) ).
thf(160,plain,
( ( sk1 @ ( sk2 @ in ) )
| ( sk3 != sk3 )
| ~ ( sk4 @ singleton @ ( sk3 @ disjoint ) ) ),
inference(pattern_uni,[status(thm)],[159:[bind(A,$thf( sk3 )),bind(B,$thf( sk4 @ singleton ))]]) ).
thf(161,plain,
( ( sk1 @ ( sk2 @ in ) )
| ~ ( sk4 @ singleton @ ( sk3 @ disjoint ) ) ),
inference(simp,[status(thm)],[160]) ).
thf(281,plain,
! [B: $i,A: $i] :
( ( ( B @ singleton @ ( A @ disjoint ) )
!= ( sk4 @ singleton @ ( sk3 @ disjoint ) ) )
| ( sk1 @ ( sk2 @ in ) )
| ~ $true
| ( A @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[99,161]) ).
thf(282,plain,
! [B: $i,A: $i] :
( ( ( B @ singleton @ ( A @ disjoint ) )
!= ( sk4 @ singleton @ ( sk3 @ disjoint ) ) )
| ( sk1 @ ( sk2 @ in ) )
| ( A @ ( B @ in ) ) ),
inference(simp,[status(thm)],[281]) ).
thf(283,plain,
( ( sk1 @ ( sk2 @ in ) )
| ( sk3 @ ( sk4 @ in ) ) ),
inference(pattern_uni,[status(thm)],[282:[bind(A,$thf( sk3 )),bind(B,$thf( sk4 ))]]) ).
thf(15,plain,
( ~ ( sk3 @ ( sk4 @ in ) )
| ( sk1 @ ( sk2 @ in ) ) ),
inference(cnfConj,[status(thm)],[12]) ).
thf(302,plain,
( ( ( sk3 @ ( sk4 @ in ) )
!= ( sk3 @ ( sk4 @ in ) ) )
| ~ $true
| ( sk1 @ ( sk2 @ in ) )
| ( sk1 @ ( sk2 @ in ) ) ),
inference(paramod_ordered,[status(thm)],[283,15]) ).
thf(303,plain,
( ( ( sk3 @ ( sk4 @ in ) )
!= ( sk3 @ ( sk4 @ in ) ) )
| ( sk1 @ ( sk2 @ in ) ) ),
inference(simp,[status(thm)],[302]) ).
thf(304,plain,
sk1 @ ( sk2 @ in ),
inference(pattern_uni,[status(thm)],[303:[]]) ).
thf(6,axiom,
! [A: $i,B: $i] :
~ ( ( B @ ( A @ in ) )
& ( B @ ( A @ singleton @ disjoint ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l25_zfmisc_1) ).
thf(24,plain,
! [A: $i,B: $i] :
~ ( ( B @ ( A @ in ) )
& ( B @ ( A @ singleton @ disjoint ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(25,plain,
~ ? [A: $i,B: $i] :
( ( B @ ( A @ in ) )
& ( B @ ( A @ singleton @ disjoint ) ) ),
inference(miniscope,[status(thm)],[24]) ).
thf(26,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ in ) )
| ~ ( B @ ( A @ singleton @ disjoint ) ) ),
inference(cnf,[status(esa)],[25]) ).
thf(332,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ in ) )
!= ( B @ ( A @ in ) ) )
| ~ $true
| ~ ( B @ ( A @ singleton @ disjoint ) ) ),
inference(paramod_ordered,[status(thm)],[304,26]) ).
thf(333,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ in ) )
!= ( B @ ( A @ in ) ) )
| ~ ( B @ ( A @ singleton @ disjoint ) ) ),
inference(simp,[status(thm)],[332]) ).
thf(334,plain,
~ ( sk1 @ ( sk2 @ singleton @ disjoint ) ),
inference(pattern_uni,[status(thm)],[333:[bind(A,$thf( sk2 )),bind(B,$thf( sk1 ))]]) ).
thf(356,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ disjoint ) )
!= ( sk1 @ ( sk2 @ singleton @ disjoint ) ) )
| ~ $true
| ~ ( B @ ( A @ disjoint ) ) ),
inference(paramod_ordered,[status(thm)],[30,334]) ).
thf(357,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ disjoint ) )
!= ( sk1 @ ( sk2 @ singleton @ disjoint ) ) )
| ~ ( B @ ( A @ disjoint ) ) ),
inference(simp,[status(thm)],[356]) ).
thf(358,plain,
~ ( sk2 @ singleton @ ( sk1 @ disjoint ) ),
inference(pattern_uni,[status(thm)],[357:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 @ singleton ))]]) ).
thf(368,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ disjoint ) )
!= ( sk2 @ singleton @ ( sk1 @ disjoint ) ) )
| ~ $true
| ( ( B @ ( A @ set_difference ) )
!= A ) ),
inference(paramod_ordered,[status(thm)],[38,358]) ).
thf(369,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ disjoint ) )
!= ( sk2 @ singleton @ ( sk1 @ disjoint ) ) )
| ( ( B @ ( A @ set_difference ) )
!= A ) ),
inference(simp,[status(thm)],[368]) ).
thf(370,plain,
( ( sk2 @ singleton @ ( sk1 @ set_difference ) )
!= sk1 ),
inference(pattern_uni,[status(thm)],[369:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 @ singleton ))]]) ).
thf(378,plain,
( ( sk4 @ singleton @ ( sk3 @ set_difference ) )
!= sk3 ),
inference(simplifyReflect,[status(thm)],[18,370]) ).
thf(388,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ set_difference ) )
!= ( sk4 @ singleton @ ( sk3 @ set_difference ) ) )
| ( A != sk3 )
| ~ ( B @ ( A @ disjoint ) ) ),
inference(paramod_ordered,[status(thm)],[36,378]) ).
thf(389,plain,
( ( sk3 != sk3 )
| ~ ( sk4 @ singleton @ ( sk3 @ disjoint ) ) ),
inference(pattern_uni,[status(thm)],[388:[bind(A,$thf( sk3 )),bind(B,$thf( sk4 @ singleton ))]]) ).
thf(390,plain,
~ ( sk4 @ singleton @ ( sk3 @ disjoint ) ),
inference(simp,[status(thm)],[389]) ).
thf(394,plain,
! [B: $i,A: $i] :
( ( ( B @ singleton @ ( A @ disjoint ) )
!= ( sk4 @ singleton @ ( sk3 @ disjoint ) ) )
| ~ $true
| ( A @ ( B @ in ) ) ),
inference(paramod_ordered,[status(thm)],[99,390]) ).
thf(395,plain,
! [B: $i,A: $i] :
( ( ( B @ singleton @ ( A @ disjoint ) )
!= ( sk4 @ singleton @ ( sk3 @ disjoint ) ) )
| ( A @ ( B @ in ) ) ),
inference(simp,[status(thm)],[394]) ).
thf(396,plain,
sk3 @ ( sk4 @ in ),
inference(pattern_uni,[status(thm)],[395:[bind(A,$thf( sk3 )),bind(B,$thf( sk4 ))]]) ).
thf(13,plain,
( ~ ( sk3 @ ( sk4 @ in ) )
| ( ( sk2 @ singleton @ ( sk1 @ set_difference ) )
= sk1 ) ),
inference(cnfConj,[status(thm)],[12]) ).
thf(17,plain,
( ~ ( sk3 @ ( sk4 @ in ) )
| ( ( sk2 @ singleton @ ( sk1 @ set_difference ) )
= sk1 ) ),
inference(lifteq,[status(thm)],[13]) ).
thf(377,plain,
~ ( sk3 @ ( sk4 @ in ) ),
inference(simplifyReflect,[status(thm)],[17,370]) ).
thf(408,plain,
$false,
inference(rewrite,[status(thm)],[396,377]) ).
thf(409,plain,
$false,
inference(simp,[status(thm)],[408]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU162+1 : TPTP v9.3.1. Released v3.3.0.
% 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
% 0.17/5.43 % Computer : n026.cluster.edu
% 0.17/5.43 % Model : x86_64 x86_64
% 0.17/5.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/5.43 % Memory : 8046.5625MB
% 0.17/5.43 % OS : Linux 6.8.0-71-generic
% 0.17/5.43 % CPULimit : 300
% 0.17/5.43 % WCLimit : 300
% 0.17/5.43 % DateTime : Sat Sep 26 08:45:32 UTC 2026
% 0.17/5.43 % CPUTime :
% 0.17/5.43 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
% 1.29/6.27 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.83/6.53 % [INFO] Parsing done (259ms).
% 1.83/6.55 % [INFO] Running in sequential loop mode.
% 2.86/7.16 % [INFO] eprover registered as external prover.
% 2.86/7.17 % [INFO] Scanning for conjecture ...
% 3.12/7.30 % [INFO] Found a conjecture (or negated_conjecture) and 7 axioms. Running axiom selection ...
% 3.12/7.35 % [INFO] Axiom selection finished. Selected 7 axioms (removed 0 axioms).
% 3.12/7.37 % [INFO] Problem is first-order (TPTP FOF).
% 3.12/7.38 % [INFO] Type checking passed.
% 3.12/7.38 % [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 ...
% 10.60/9.73 % [INFO] Killing All external provers ...
% 10.60/9.74 % Time passed: 4089ms (effective reasoning time: 3172ms)
% 10.60/9.74 % 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)>
% 10.60/9.74 % Axioms used in derivation (4): l28_zfmisc_1, symmetry_r1_xboole_0, t83_xboole_1, l25_zfmisc_1
% 10.60/9.74 % No. of inferences in proof: 63
% 10.60/9.74 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4089 ms resp. 3172 ms w/o parsing
% 11.08/9.84 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 11.08/9.84 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------