%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU150+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 : n020.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 08:37:46 AM UTC 2026
% Result : Theorem 5.83s 3.25s
% Output : Refutation 6.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 30 ( 16 unt; 0 typ; 3 def)
% Number of atoms : 52 ( 51 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 121 ( 18 ~; 9 |; 1 &; 84 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 48 ( 0 ^; 44 !; 1 ?; 48 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% Comments :
%------------------------------------------------------------------------------
thf(singleton_decl,type,
singleton: $i > $i ).
thf(unordered_pair_decl,type,
unordered_pair: $i > $i > $i ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( ( A @ singleton )
= ( C @ ( B @ unordered_pair ) ) )
=> ( B = C ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( sk1 @ singleton )
= ( B @ ( A @ unordered_pair ) ) )
=> ( A = B ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ( ( ( sk1 @ singleton )
= ( A @ ( sk2 @ unordered_pair ) ) )
=> ( sk2 = A ) ) ) ) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i] :
( ( ( A @ singleton )
= ( C @ ( B @ unordered_pair ) ) )
=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_zfmisc_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( ( A @ singleton )
= ( C @ ( B @ unordered_pair ) ) )
=> ( B = C ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(7,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( ( A @ singleton )
= ( C @ ( B @ unordered_pair ) ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,plain,
( ( sk2 != sk3 )
& ( ( sk1 @ singleton )
= ( sk3 @ ( sk2 @ unordered_pair ) ) ) ),
inference(cnf,[status(esa)],[7]) ).
thf(9,plain,
( ( sk1 @ singleton )
= ( sk3 @ ( sk2 @ unordered_pair ) ) ),
inference(cnfConj,[status(thm)],[8]) ).
thf(11,plain,
( ( sk3 @ ( sk2 @ unordered_pair ) )
= ( sk1 @ singleton ) ),
inference(lifteq,[status(thm)],[9]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ singleton )
= ( C @ ( B @ unordered_pair ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_zfmisc_1) ).
thf(18,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ singleton )
= ( C @ ( B @ unordered_pair ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(19,plain,
! [A: $i,B: $i] :
( ? [C: $i] :
( ( A @ singleton )
= ( C @ ( B @ unordered_pair ) ) )
=> ( A = B ) ),
inference(miniscope,[status(thm)],[18]) ).
thf(20,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( ( A @ singleton )
!= ( C @ ( B @ unordered_pair ) ) ) ),
inference(cnf,[status(esa)],[19]) ).
thf(21,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( ( A @ singleton )
!= ( C @ ( B @ unordered_pair ) ) ) ),
inference(lifteq,[status(thm)],[20]) ).
thf(42,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( sk2 @ unordered_pair ) )
!= ( C @ ( B @ unordered_pair ) ) )
| ( A = B )
| ( ( sk1 @ singleton )
!= ( A @ singleton ) ) ),
inference(paramod_ordered,[status(thm)],[11,21]) ).
thf(43,plain,
! [A: $i] :
( ( A = sk2 )
| ( ( sk1 @ singleton )
!= ( A @ singleton ) ) ),
inference(pattern_uni,[status(thm)],[42:[bind(A,$thf( A )),bind(B,$thf( sk2 )),bind(C,$thf( sk3 ))]]) ).
thf(87,plain,
sk2 = sk1,
inference(pattern_uni,[status(thm)],[43:[bind(A,$thf( sk1 ))]]) ).
thf(10,plain,
sk2 != sk3,
inference(cnfConj,[status(thm)],[8]) ).
thf(12,plain,
sk3 != sk2,
inference(lifteq,[status(thm)],[10]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ unordered_pair ) )
= ( A @ ( B @ unordered_pair ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(13,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ unordered_pair ) )
= ( A @ ( B @ unordered_pair ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(14,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) )
= ( A @ ( B @ unordered_pair ) ) ),
inference(cnf,[status(esa)],[13]) ).
thf(15,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) )
= ( A @ ( B @ unordered_pair ) ) ),
inference(lifteq,[status(thm)],[14]) ).
thf(24,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk2 @ unordered_pair ) )
!= ( B @ ( A @ unordered_pair ) ) )
| ( ( A @ ( B @ unordered_pair ) )
= ( sk1 @ singleton ) ) ),
inference(paramod_ordered,[status(thm)],[11,15]) ).
thf(25,plain,
( ( sk2 @ ( sk3 @ unordered_pair ) )
= ( sk1 @ singleton ) ),
inference(pattern_uni,[status(thm)],[24:[bind(A,$thf( sk2 )),bind(B,$thf( sk3 ))]]) ).
thf(40,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk3 @ unordered_pair ) )
!= ( C @ ( B @ unordered_pair ) ) )
| ( A = B )
| ( ( sk1 @ singleton )
!= ( A @ singleton ) ) ),
inference(paramod_ordered,[status(thm)],[25,21]) ).
thf(41,plain,
! [A: $i] :
( ( A = sk3 )
| ( ( sk1 @ singleton )
!= ( A @ singleton ) ) ),
inference(pattern_uni,[status(thm)],[40:[bind(A,$thf( A )),bind(B,$thf( sk3 )),bind(C,$thf( sk2 ))]]) ).
thf(49,plain,
sk3 = sk1,
inference(pattern_uni,[status(thm)],[41:[bind(A,$thf( sk1 ))]]) ).
thf(53,plain,
sk2 != sk1,
inference(rewrite,[status(thm)],[12,49]) ).
thf(91,plain,
$false,
inference(simplifyReflect,[status(thm)],[87,53]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU150+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
% 0.13/0.39 % Computer : n020.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sat Sep 26 08:41:34 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 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
% 1.08/1.12 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.56/1.30 % [INFO] Parsing done (178ms).
% 1.56/1.32 % [INFO] Running in sequential loop mode.
% 2.30/1.87 % [INFO] eprover registered as external prover.
% 2.30/1.88 % [INFO] Scanning for conjecture ...
% 2.54/1.97 % [INFO] Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ...
% 2.54/2.00 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 2.54/2.01 % [INFO] Problem is first-order (TPTP FOF).
% 2.54/2.02 % [INFO] Type checking passed.
% 2.54/2.02 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 5.83/3.24 % [INFO] Killing All external provers ...
% 5.83/3.25 % Time passed: 2636ms (effective reasoning time: 1923ms)
% 5.83/3.25 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 5.83/3.25 % Axioms used in derivation (2): t8_zfmisc_1, commutativity_k2_tarski
% 5.83/3.25 % No. of inferences in proof: 27
% 5.83/3.25 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2636 ms resp. 1923 ms w/o parsing
% 6.22/3.32 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.22/3.32 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------