%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : QUA002^1 : TPTP v9.3.1. Released v4.1.0.
% 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 : n010.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 : Wed Sep 30 08:21:21 AM UTC 2026
% Result : Theorem 11.52s 3.91s
% Output : Refutation 11.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 25 ( 15 unt; 0 typ; 5 def)
% Number of atoms : 85 ( 79 equ; 0 cnn)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 92 ( 28 ~; 36 |; 3 &; 25 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 28 ( 19 ^; 7 !; 0 ?; 28 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(union_decl,type,
union: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(singleton_decl,type,
singleton: $i > $i > $o ).
thf(sup_decl,type,
sup: ( $i > $o ) > $i ).
thf(addition_decl,type,
addition: $i > $i > $i ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(union_def,definition,
( union
= ( ^ [A: $i > $o,B: $i > $o,C: $i] :
( ( A @ C )
| ( B @ C ) ) ) ) ).
thf(singleton_def,definition,
( singleton
= ( ^ [A: $i,B: $i] : ( B = A ) ) ) ).
thf(addition_def,definition,
( addition
= ( ^ [A: $i,B: $i] : ( sup @ ( union @ ( singleton @ A ) @ ( singleton @ B ) ) ) ) ) ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i] :
( ( sup
@ ^ [C: $i] :
( ( C = A )
| ( C = B ) ) )
= ( sup
@ ^ [C: $i] :
( ( C = B )
| ( C = A ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
( ( sup
@ ^ [B: $i] :
( ( B = sk1 )
| ( B = A ) ) )
!= ( sup
@ ^ [B: $i] :
( ( B = A )
| ( B = sk1 ) ) ) ) ) ) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',addition_comm) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(10,plain,
~ ! [A: $i,B: $i] :
( ( sup
@ ^ [C: $i] :
( ( C = A )
| ( C = B ) ) )
= ( sup
@ ^ [C: $i] :
( ( C = B )
| ( C = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(11,plain,
( ( sup
@ ^ [A: $i] :
( ( A = sk1 )
| ( A = sk2 ) ) )
!= ( sup
@ ^ [A: $i] :
( ( A = sk2 )
| ( A = sk1 ) ) ) ),
inference(cnf,[status(esa)],[10]) ).
thf(12,plain,
( ( sup
@ ^ [A: $i] :
( ( A = sk1 )
| ( A = sk2 ) ) )
!= ( sup
@ ^ [A: $i] :
( ( A = sk2 )
| ( A = sk1 ) ) ) ),
inference(lifteq,[status(thm)],[11]) ).
thf(50,plain,
( ( ^ [A: $i] :
( ( A = sk1 )
| ( A = sk2 ) ) )
!= ( ^ [A: $i] :
( ( A = sk2 )
| ( A = sk1 ) ) ) ),
inference(simp,[status(thm)],[12]) ).
thf(68,plain,
( ( ( sk3 = sk1 )
| ( sk3 = sk2 ) )
!= ( ( sk3 = sk2 )
| ( sk3 = sk1 ) ) ),
inference(func_ext,[status(esa)],[50]) ).
thf(305,plain,
( ( sk3 = sk1 )
| ( sk3 = sk2 )
| ( sk3 = sk2 )
| ( sk3 = sk1 ) ),
inference(bool_ext,[status(thm)],[68]) ).
thf(347,plain,
( ( sk3 = sk1 )
| ( sk3 = sk2 )
| ( sk3 = sk2 )
| ( sk3 = sk1 ) ),
inference(cnf,[status(esa)],[305]) ).
thf(348,plain,
( ( sk3 = sk1 )
| ( sk3 = sk2 )
| ( sk3 = sk2 )
| ( sk3 = sk1 ) ),
inference(lifteq,[status(thm)],[347]) ).
thf(349,plain,
( ( sk3 = sk1 )
| ( sk3 = sk2 ) ),
inference(simp,[status(thm)],[348]) ).
thf(304,plain,
( ~ ( ( sk3 = sk1 )
| ( sk3 = sk2 ) )
| ~ ( ( sk3 = sk2 )
| ( sk3 = sk1 ) ) ),
inference(bool_ext,[status(thm)],[68]) ).
thf(338,plain,
( ( ( sk3 != sk1 )
| ( sk3 != sk2 ) )
& ( ( sk3 != sk1 )
| ( sk3 != sk1 ) )
& ( ( sk3 != sk2 )
| ( sk3 != sk2 ) )
& ( ( sk3 != sk2 )
| ( sk3 != sk1 ) ) ),
inference(cnf,[status(esa)],[304]) ).
thf(340,plain,
( ( sk3 != sk1 )
| ( sk3 != sk1 ) ),
inference(cnfConj,[status(thm)],[338]) ).
thf(343,plain,
( ( sk3 != sk1 )
| ( sk3 != sk1 ) ),
inference(lifteq,[status(thm)],[340]) ).
thf(344,plain,
sk3 != sk1,
inference(simp,[status(thm)],[343]) ).
thf(341,plain,
( ( sk3 != sk2 )
| ( sk3 != sk2 ) ),
inference(cnfConj,[status(thm)],[338]) ).
thf(345,plain,
( ( sk3 != sk2 )
| ( sk3 != sk2 ) ),
inference(lifteq,[status(thm)],[341]) ).
thf(346,plain,
sk3 != sk2,
inference(simp,[status(thm)],[345]) ).
thf(353,plain,
$false,
inference(simplifyReflect,[status(thm)],[349,344,346]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : QUA002^1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.08 % 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
% 0.11/0.21 % Computer : n010.cluster.edu
% 0.11/0.21 % Model : x86_64 x86_64
% 0.11/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.21 % Memory : 8046.5625MB
% 0.11/0.21 % OS : Linux 6.8.0-71-generic
% 0.11/0.21 % CPULimit : 300
% 0.11/0.21 % WCLimit : 300
% 0.11/0.21 % DateTime : Tue Sep 29 13:29:26 UTC 2026
% 0.11/0.22 % CPUTime :
% 0.11/0.22 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
% 0.90/0.79 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.25/1.01 % [INFO] Parsing done (216ms).
% 1.25/1.03 % [INFO] Running in sequential loop mode.
% 2.17/1.41 % [INFO] eprover registered as external prover.
% 2.17/1.42 % [INFO] Scanning for conjecture ...
% 2.34/1.54 % [INFO] Found a conjecture (or negated_conjecture) and 7 axioms. Running axiom selection ...
% 2.34/1.57 % [INFO] Axiom selection finished. Selected 7 axioms (removed 0 axioms).
% 2.34/1.59 % [INFO] Problem is higher-order (TPTP THF).
% 2.34/1.59 % [INFO] Type checking passed.
% 2.34/1.60 % [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 ...
% 11.52/3.90 % [INFO] Killing All external provers ...
% 11.52/3.90 % Time passed: 3547ms (effective reasoning time: 2867ms)
% 11.52/3.90 % 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)>
% 11.52/3.90 % Axioms used in derivation (0):
% 11.52/3.91 % No. of inferences in proof: 20
% 11.52/3.91 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3547 ms resp. 2867 ms w/o parsing
% 11.52/3.95 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 11.52/3.95 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------