%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEV166^5 : TPTP v9.3.1. Released v4.0.0.
% 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 : n005.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 08:36:56 AM UTC 2026
% Result : Theorem 4.66s 1.92s
% Output : Refutation 4.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 5
% Syntax : Number of formulae : 34 ( 14 unt; 0 typ; 4 def)
% Number of atoms : 98 ( 97 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 186 ( 36 ~; 28 |; 14 &; 108 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 104 ( 104 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 4 usr; 5 con; 0-2 aty)
% Number of variables : 74 ( 46 ^; 24 !; 0 ?; 74 :)
% ( 0 !>; 0 ?*; 0 @-; 4 @+)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(sk1_decl,type,
sk1: a ).
thf(sk2_decl,type,
sk2: a ).
thf(sk3_decl,type,
sk3: a ).
thf(sk4_decl,type,
sk4: a ).
thf(sk1_def,definition,
( sk1
= ( @+[A: a] :
~ ! [B: a,C: a,D: a] :
( ( ( ^ [E: a > a > a] : ( E @ A @ B ) )
= ( ^ [E: a > a > a] : ( E @ C @ D ) ) )
= ( ( A = C )
& ( B = D ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: a] :
~ ! [B: a,C: a] :
( ( ( ^ [D: a > a > a] : ( D @ sk1 @ A ) )
= ( ^ [D: a > a > a] : ( D @ B @ C ) ) )
= ( ( sk1 = B )
& ( A = C ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: a] :
~ ! [B: a] :
( ( ( ^ [C: a > a > a] : ( C @ sk1 @ sk2 ) )
= ( ^ [C: a > a > a] : ( C @ A @ B ) ) )
= ( ( sk1 = A )
& ( sk2 = B ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: a] :
( ( ( ^ [B: a > a > a] : ( B @ sk1 @ sk2 ) )
= ( ^ [B: a > a > a] : ( B @ sk3 @ A ) ) )
!= ( ( sk1 = sk3 )
& ( sk2 = A ) ) ) ) ) ).
thf(1,conjecture,
! [A: a,B: a,C: a,D: a] :
( ( ( ^ [E: a > a > a] : ( E @ A @ B ) )
= ( ^ [E: a > a > a] : ( E @ C @ D ) ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM182_pme) ).
thf(2,negated_conjecture,
~ ! [A: a,B: a,C: a,D: a] :
( ( ( ^ [E: a > a > a] : ( E @ A @ B ) )
= ( ^ [E: a > a > a] : ( E @ C @ D ) ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: a,B: a,C: a,D: a] :
( ( ( ^ [E: a > a > a] : ( E @ A @ B ) )
= ( ^ [E: a > a > a] : ( E @ C @ D ) ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
( ( ( ^ [A: a > a > a] : ( A @ sk1 @ sk2 ) )
= ( ^ [A: a > a > a] : ( A @ sk3 @ sk4 ) ) )
!= ( ( sk1 = sk3 )
& ( sk2 = sk4 ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
( ( ( sk1 = sk3 )
& ( sk2 = sk4 ) )
!= ( ( ^ [A: a > a > a] : ( A @ sk1 @ sk2 ) )
= ( ^ [A: a > a > a] : ( A @ sk3 @ sk4 ) ) ) ),
inference(lifteq,[status(thm)],[4]) ).
thf(7,plain,
( ( ( sk1 = sk3 )
& ( sk2 = sk4 ) )
| ( ( ^ [A: a > a > a] : ( A @ sk1 @ sk2 ) )
= ( ^ [A: a > a > a] : ( A @ sk3 @ sk4 ) ) ) ),
inference(bool_ext,[status(thm)],[5]) ).
thf(9,plain,
( ( ( ^ [A: a > a > a] : ( A @ sk3 @ sk4 ) )
= ( ^ [A: a > a > a] : ( A @ sk1 @ sk2 ) ) )
| ( ( sk1 = sk3 )
& ( sk2 = sk4 ) ) ),
inference(lifteq,[status(thm)],[7]) ).
thf(12,plain,
( ( ( ( ^ [A: a > a > a] : ( A @ sk3 @ sk4 ) )
= ( ^ [A: a > a > a] : ( A @ sk1 @ sk2 ) ) )
| ( sk1 = sk3 ) )
& ( ( ( ^ [A: a > a > a] : ( A @ sk3 @ sk4 ) )
= ( ^ [A: a > a > a] : ( A @ sk1 @ sk2 ) ) )
| ( sk2 = sk4 ) ) ),
inference(cnf,[status(esa)],[9]) ).
thf(14,plain,
( ( ( ^ [A: a > a > a] : ( A @ sk3 @ sk4 ) )
= ( ^ [A: a > a > a] : ( A @ sk1 @ sk2 ) ) )
| ( sk2 = sk4 ) ),
inference(cnfConj,[status(thm)],[12]) ).
thf(16,plain,
( ( sk4 = sk2 )
| ( ( ^ [A: a > a > a] : ( A @ sk3 @ sk4 ) )
= ( ^ [A: a > a > a] : ( A @ sk1 @ sk2 ) ) ) ),
inference(lifteq,[status(thm)],[14]) ).
thf(18,plain,
! [A: a > a > a] :
( ( ( A @ sk3 @ sk4 )
= ( A @ sk1 @ sk2 ) )
| ( sk4 = sk2 ) ),
inference(func_ext,[status(esa)],[16]) ).
thf(13,plain,
( ( ( ^ [A: a > a > a] : ( A @ sk3 @ sk4 ) )
= ( ^ [A: a > a > a] : ( A @ sk1 @ sk2 ) ) )
| ( sk1 = sk3 ) ),
inference(cnfConj,[status(thm)],[12]) ).
thf(15,plain,
( ( sk3 = sk1 )
| ( ( ^ [A: a > a > a] : ( A @ sk3 @ sk4 ) )
= ( ^ [A: a > a > a] : ( A @ sk1 @ sk2 ) ) ) ),
inference(lifteq,[status(thm)],[13]) ).
thf(17,plain,
! [A: a > a > a] :
( ( ( A @ sk3 @ sk4 )
= ( A @ sk1 @ sk2 ) )
| ( sk3 = sk1 ) ),
inference(func_ext,[status(esa)],[15]) ).
thf(39,plain,
! [A: a > a > a] :
( ( sk3 = sk1 )
| ( ( A @ sk3 @ sk4 )
!= sk3 )
| ( ( A @ sk1 @ sk2 )
!= sk1 ) ),
inference(eqfactor_ordered,[status(thm)],[17]) ).
thf(43,plain,
sk3 = sk1,
inference(pre_uni,[status(thm)],[39:[bind(A,$thf( ^ [B: a] : ^ [C: a] : B ))]]) ).
thf(99,plain,
! [A: a > a > a] :
( ( ( A @ sk1 @ sk4 )
= ( A @ sk1 @ sk2 ) )
| ( sk4 = sk2 ) ),
inference(rewrite,[status(thm)],[18,43]) ).
thf(6,plain,
( ~ ( ( sk1 = sk3 )
& ( sk2 = sk4 ) )
| ( ( ^ [A: a > a > a] : ( A @ sk1 @ sk2 ) )
!= ( ^ [A: a > a > a] : ( A @ sk3 @ sk4 ) ) ) ),
inference(bool_ext,[status(thm)],[5]) ).
thf(8,plain,
( ( ( ^ [A: a > a > a] : ( A @ sk3 @ sk4 ) )
!= ( ^ [A: a > a > a] : ( A @ sk1 @ sk2 ) ) )
| ~ ( ( sk1 = sk3 )
& ( sk2 = sk4 ) ) ),
inference(lifteq,[status(thm)],[6]) ).
thf(10,plain,
( ( ( ^ [A: a > a > a] : ( A @ sk3 @ sk4 ) )
!= ( ^ [A: a > a > a] : ( A @ sk1 @ sk2 ) ) )
| ( sk1 != sk3 )
| ( sk2 != sk4 ) ),
inference(cnf,[status(esa)],[8]) ).
thf(11,plain,
( ( sk3 != sk1 )
| ( sk4 != sk2 )
| ( ( ^ [A: a > a > a] : ( A @ sk3 @ sk4 ) )
!= ( ^ [A: a > a > a] : ( A @ sk1 @ sk2 ) ) ) ),
inference(lifteq,[status(thm)],[10]) ).
thf(66,plain,
( ( sk3 != sk1 )
| ( sk4 != sk2 )
| ( ( ^ [A: a > a > a] : sk3 )
!= ( ^ [A: a > a > a] : sk1 ) )
| ( ( ^ [A: a > a > a] : sk4 )
!= ( ^ [A: a > a > a] : sk2 ) ) ),
inference(simp,[status(thm)],[11]) ).
thf(81,plain,
( ( sk3 != sk1 )
| ( sk4 != sk2 )
| ( sk3 != sk1 )
| ( sk4 != sk2 ) ),
inference(func_ext,[status(esa)],[66]) ).
thf(88,plain,
( ( sk3 != sk1 )
| ( sk4 != sk2 ) ),
inference(simp,[status(thm)],[81]) ).
thf(97,plain,
( ( sk1 != sk1 )
| ( sk4 != sk2 ) ),
inference(rewrite,[status(thm)],[88,43]) ).
thf(98,plain,
sk4 != sk2,
inference(simp,[status(thm)],[97]) ).
thf(100,plain,
! [A: a > a > a] :
( ( A @ sk1 @ sk4 )
= ( A @ sk1 @ sk2 ) ),
inference(simplifyReflect,[status(thm)],[99,98]) ).
thf(101,plain,
! [A: a > a > a] :
( ( ( A @ sk1 @ sk2 )
!= sk2 )
| ( ( A @ sk1 @ sk4 )
!= sk4 ) ),
inference(paramod_ordered,[status(thm)],[100,98]) ).
thf(107,plain,
sk2 != sk2,
inference(pre_uni,[status(thm)],[101:[bind(A,$thf( ^ [B: a] : ^ [C: a] : C ))]]) ).
thf(108,plain,
$false,
inference(pattern_uni,[status(thm)],[107:[]]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV166^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % 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
% 0.08/0.18 % Computer : n005.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 15:18:01 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 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
% 0.69/0.50 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.91/0.60 % [INFO] Parsing done (95ms).
% 0.91/0.61 % [INFO] Running in sequential loop mode.
% 1.36/0.80 % [INFO] eprover registered as external prover.
% 1.36/0.81 % [INFO] Scanning for conjecture ...
% 1.36/0.85 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.36/0.87 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.36/0.87 % [INFO] Problem is higher-order (TPTP THF).
% 1.36/0.87 % [INFO] Type checking passed.
% 1.36/0.87 % [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 ...
% 4.66/1.92 % [INFO] Killing All external provers ...
% 4.66/1.92 % Time passed: 1636ms (effective reasoning time: 1308ms)
% 4.66/1.92 % 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)>
% 4.66/1.92 % Axioms used in derivation (0):
% 4.66/1.92 % No. of inferences in proof: 30
% 4.66/1.92 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1636 ms resp. 1308 ms w/o parsing
% 4.66/1.98 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.66/1.98 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------