%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEV065^5 : 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 : n011.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 08:36:47 AM UTC 2026
% Result : Theorem 6.56s 3.07s
% Output : Refutation 6.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 4
% Syntax : Number of formulae : 45 ( 19 unt; 0 typ; 3 def)
% Number of atoms : 193 ( 126 equ; 0 cnn)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 343 ( 79 ~; 68 |; 50 &; 140 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 6 con; 0-2 aty)
% Number of variables : 33 ( 18 ^; 12 !; 0 ?; 33 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% Comments :
%------------------------------------------------------------------------------
thf(b_type,type,
b: $tType ).
thf(a_type,type,
a: $tType ).
thf(sk1_decl,type,
sk1: b ).
thf(sk2_decl,type,
sk2: a ).
thf(sk3_decl,type,
sk3: b > a > $o ).
thf(sk4_decl,type,
sk4: b ).
thf(sk5_decl,type,
sk5: a ).
thf(sk1_def,definition,
( sk1
= ( @+[A: b] :
~ ! [B: a,C: b > a > $o] :
( ( C @ A @ B )
=> ( ( ^ [D: b,E: a] :
( ( ( C @ D @ E )
& ~ ( ( D = A )
& ( E = B ) ) )
| ( ( D = A )
& ( E = B ) ) ) )
= C ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: a] :
~ ! [B: b > a > $o] :
( ( B @ sk1 @ A )
=> ( ( ^ [C: b,D: a] :
( ( ( B @ C @ D )
& ~ ( ( C = sk1 )
& ( D = A ) ) )
| ( ( C = sk1 )
& ( D = A ) ) ) )
= B ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: b > a > $o] :
~ ( ( A @ sk1 @ sk2 )
=> ( ( ^ [B: b,C: a] :
( ( ( A @ B @ C )
& ~ ( ( B = sk1 )
& ( C = sk2 ) ) )
| ( ( B = sk1 )
& ( C = sk2 ) ) ) )
= A ) ) ) ) ).
thf(1,conjecture,
! [A: b,B: a,C: b > a > $o] :
( ( C @ A @ B )
=> ( ( ^ [D: b,E: a] :
( ( ( C @ D @ E )
& ~ ( ( D = A )
& ( E = B ) ) )
| ( ( D = A )
& ( E = B ) ) ) )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM177_pme) ).
thf(2,negated_conjecture,
~ ! [A: b,B: a,C: b > a > $o] :
( ( C @ A @ B )
=> ( ( ^ [D: b,E: a] :
( ( ( C @ D @ E )
& ~ ( ( D = A )
& ( E = B ) ) )
| ( ( D = A )
& ( E = B ) ) ) )
= C ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: b,B: a,C: b > a > $o] :
( ( C @ A @ B )
=> ( ( ^ [D: b,E: a] :
( ( ( C @ D @ E )
& ~ ( ( D = A )
& ( E = B ) ) )
| ( ( D = A )
& ( E = B ) ) ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
( ( sk3 @ sk1 @ sk2 )
& ( ( ^ [A: b,B: a] :
( ( ( sk3 @ A @ B )
& ~ ( ( A = sk1 )
& ( B = sk2 ) ) )
| ( ( A = sk1 )
& ( B = sk2 ) ) ) )
!= sk3 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
sk3 @ sk1 @ sk2,
inference(cnfConj,[status(thm)],[4]) ).
thf(6,plain,
( ( ^ [A: b,B: a] :
( ( ( sk3 @ A @ B )
& ~ ( ( A = sk1 )
& ( B = sk2 ) ) )
| ( ( A = sk1 )
& ( B = sk2 ) ) ) )
!= sk3 ),
inference(cnfConj,[status(thm)],[4]) ).
thf(7,plain,
( ( ^ [A: b,B: a] :
( ( ( sk3 @ A @ B )
& ~ ( ( A = sk1 )
& ( B = sk2 ) ) )
| ( ( A = sk1 )
& ( B = sk2 ) ) ) )
!= sk3 ),
inference(lifteq,[status(thm)],[6]) ).
thf(8,plain,
( ( ( ( sk3 @ sk4 @ sk5 )
& ~ ( ( sk4 = sk1 )
& ( sk5 = sk2 ) ) )
| ( ( sk4 = sk1 )
& ( sk5 = sk2 ) ) )
!= ( sk3 @ sk4 @ sk5 ) ),
inference(func_ext,[status(esa)],[7]) ).
thf(11,plain,
( ( ( sk3 @ sk4 @ sk5 )
!= ( ( $true
& ~ ( ( sk4 = sk1 )
& ( sk5 = sk2 ) ) )
| ( ( sk4 = sk1 )
& ( sk5 = sk2 ) ) ) )
| ( ( sk3 @ sk4 @ sk5 )
!= ( sk3 @ sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[5,8]) ).
thf(12,plain,
( ~ ( sk3 @ sk4 @ sk5 )
| ( ( sk3 @ sk4 @ sk5 )
!= ( sk3 @ sk1 @ sk2 ) ) ),
inference(simp,[status(thm)],[11]) ).
thf(13,plain,
( ~ ( sk3 @ sk4 @ sk5 )
| ( sk4 != sk1 )
| ( sk5 != sk2 ) ),
inference(simp,[status(thm)],[12]) ).
thf(47,plain,
( ~ $true
| ( sk4 != sk1 )
| ( sk5 != sk2 )
| ( ( sk3 @ sk4 @ sk5 )
!= ( sk3 @ sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[5,13]) ).
thf(48,plain,
( ( sk4 != sk1 )
| ( sk5 != sk2 )
| ( ( sk3 @ sk4 @ sk5 )
!= ( sk3 @ sk1 @ sk2 ) ) ),
inference(simp,[status(thm)],[47]) ).
thf(54,plain,
( ( sk4 != sk1 )
| ( sk5 != sk2 )
| ( sk4 != sk1 )
| ( sk5 != sk2 ) ),
inference(simp,[status(thm)],[48]) ).
thf(55,plain,
( ( sk4 != sk1 )
| ( sk5 != sk2 ) ),
inference(simp,[status(thm)],[54]) ).
thf(10,plain,
( ( ( sk3 @ sk4 @ sk5 )
& ~ ( ( sk4 = sk1 )
& ( sk5 = sk2 ) ) )
| ( ( sk4 = sk1 )
& ( sk5 = sk2 ) )
| ( sk3 @ sk4 @ sk5 ) ),
inference(bool_ext,[status(thm)],[8]) ).
thf(23,plain,
( ( ( sk3 @ sk4 @ sk5 )
| ( sk4 = sk1 )
| ( sk3 @ sk4 @ sk5 ) )
& ( ( sk3 @ sk4 @ sk5 )
| ( sk5 = sk2 )
| ( sk3 @ sk4 @ sk5 ) )
& ( ( sk4 != sk1 )
| ( sk5 != sk2 )
| ( sk4 = sk1 )
| ( sk3 @ sk4 @ sk5 ) )
& ( ( sk4 != sk1 )
| ( sk5 != sk2 )
| ( sk5 = sk2 )
| ( sk3 @ sk4 @ sk5 ) ) ),
inference(cnf,[status(esa)],[10]) ).
thf(24,plain,
( ( sk3 @ sk4 @ sk5 )
| ( sk4 = sk1 )
| ( sk3 @ sk4 @ sk5 ) ),
inference(cnfConj,[status(thm)],[23]) ).
thf(28,plain,
( ( sk4 = sk1 )
| ( sk3 @ sk4 @ sk5 )
| ( sk3 @ sk4 @ sk5 ) ),
inference(lifteq,[status(thm)],[24]) ).
thf(29,plain,
( ( sk4 = sk1 )
| ( sk3 @ sk4 @ sk5 ) ),
inference(simp,[status(thm)],[28]) ).
thf(9,plain,
( ~ ( ( ( sk3 @ sk4 @ sk5 )
& ~ ( ( sk4 = sk1 )
& ( sk5 = sk2 ) ) )
| ( ( sk4 = sk1 )
& ( sk5 = sk2 ) ) )
| ~ ( sk3 @ sk4 @ sk5 ) ),
inference(bool_ext,[status(thm)],[8]) ).
thf(14,plain,
( ( ~ ( sk3 @ sk4 @ sk5 )
| ( sk4 = sk1 )
| ~ ( sk3 @ sk4 @ sk5 ) )
& ( ~ ( sk3 @ sk4 @ sk5 )
| ( sk5 = sk2 )
| ~ ( sk3 @ sk4 @ sk5 ) )
& ( ( sk4 != sk1 )
| ( sk5 != sk2 )
| ~ ( sk3 @ sk4 @ sk5 ) ) ),
inference(cnf,[status(esa)],[9]) ).
thf(15,plain,
( ~ ( sk3 @ sk4 @ sk5 )
| ( sk4 = sk1 )
| ~ ( sk3 @ sk4 @ sk5 ) ),
inference(cnfConj,[status(thm)],[14]) ).
thf(18,plain,
( ( sk4 = sk1 )
| ~ ( sk3 @ sk4 @ sk5 )
| ~ ( sk3 @ sk4 @ sk5 ) ),
inference(lifteq,[status(thm)],[15]) ).
thf(19,plain,
( ( sk4 = sk1 )
| ~ ( sk3 @ sk4 @ sk5 ) ),
inference(simp,[status(thm)],[18]) ).
thf(80,plain,
( ( sk4 = sk1 )
| ( sk4 = sk1 )
| ~ $true
| ( ( sk3 @ sk4 @ sk5 )
!= ( sk3 @ sk4 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[29,19]) ).
thf(81,plain,
( ( sk4 = sk1 )
| ( ( sk3 @ sk4 @ sk5 )
!= ( sk3 @ sk4 @ sk5 ) ) ),
inference(simp,[status(thm)],[80]) ).
thf(82,plain,
sk4 = sk1,
inference(pattern_uni,[status(thm)],[81:[]]) ).
thf(88,plain,
( ( sk1 != sk1 )
| ( sk5 != sk2 ) ),
inference(rewrite,[status(thm)],[55,82]) ).
thf(89,plain,
sk5 != sk2,
inference(simp,[status(thm)],[88]) ).
thf(90,plain,
( ( ( ( sk3 @ sk1 @ sk5 )
& ~ ( ( sk1 = sk1 )
& ( sk5 = sk2 ) ) )
| ( ( sk1 = sk1 )
& ( sk5 = sk2 ) ) )
!= ( sk3 @ sk1 @ sk5 ) ),
inference(rewrite,[status(thm)],[8,82]) ).
thf(91,plain,
( ( ( ( sk3 @ sk1 @ sk5 )
& ( sk5 != sk2 ) )
| ( sk5 = sk2 ) )
!= ( sk3 @ sk1 @ sk5 ) ),
inference(simp,[status(thm)],[90]) ).
thf(16,plain,
( ~ ( sk3 @ sk4 @ sk5 )
| ( sk5 = sk2 )
| ~ ( sk3 @ sk4 @ sk5 ) ),
inference(cnfConj,[status(thm)],[14]) ).
thf(20,plain,
( ( sk5 = sk2 )
| ~ ( sk3 @ sk4 @ sk5 )
| ~ ( sk3 @ sk4 @ sk5 ) ),
inference(lifteq,[status(thm)],[16]) ).
thf(21,plain,
( ( sk5 = sk2 )
| ~ ( sk3 @ sk4 @ sk5 ) ),
inference(simp,[status(thm)],[20]) ).
thf(92,plain,
( ( sk5 = sk2 )
| ~ ( sk3 @ sk1 @ sk5 ) ),
inference(rewrite,[status(thm)],[21,82]) ).
thf(93,plain,
~ ( sk3 @ sk1 @ sk5 ),
inference(simplifyReflect,[status(thm)],[92,89]) ).
thf(98,plain,
( ( $false
& ( sk5 != sk2 ) )
| ( sk5 = sk2 ) ),
inference(rewrite,[status(thm)],[91,93]) ).
thf(99,plain,
sk5 = sk2,
inference(simp,[status(thm)],[98]) ).
thf(100,plain,
sk5 = sk2,
inference(lifteq,[status(thm)],[99]) ).
thf(102,plain,
sk2 != sk2,
inference(rewrite,[status(thm)],[89,100]) ).
thf(103,plain,
$false,
inference(simp,[status(thm)],[102]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV065^5 : 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
% 0.08/0.19 % Computer : n011.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 15:06:16 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
% 1.06/0.81 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.27/1.01 % [INFO] Parsing done (198ms).
% 1.27/1.03 % [INFO] Running in sequential loop mode.
% 2.29/1.52 % [INFO] eprover registered as external prover.
% 2.29/1.53 % [INFO] Scanning for conjecture ...
% 2.47/1.63 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.47/1.68 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.47/1.68 % [INFO] Problem is higher-order (TPTP THF).
% 2.47/1.68 % [INFO] Type checking passed.
% 2.47/1.69 % [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 ...
% 6.56/3.06 % [INFO] Killing All external provers ...
% 6.56/3.07 % Time passed: 2726ms (effective reasoning time: 2031ms)
% 6.56/3.07 % 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)>
% 6.56/3.07 % Axioms used in derivation (0):
% 6.56/3.07 % No. of inferences in proof: 42
% 6.56/3.07 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2726 ms resp. 2031 ms w/o parsing
% 6.33/3.18 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.33/3.18 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------