%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET636^5 : TPTP v9.3.1. Released v4.0.0.
% 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 : n017.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 08:23:05 AM UTC 2026
% Result : Theorem 5.55s 2.97s
% Output : Refutation 6.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 4
% Syntax : Number of formulae : 58 ( 15 unt; 0 typ; 3 def)
% Number of atoms : 310 ( 65 equ; 0 cnn)
% Maximal formula atoms : 5 ( 5 avg)
% Number of connectives : 439 ( 88 ~; 76 |; 65 &; 210 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 5 con; 0-2 aty)
% Number of variables : 123 ( 88 ^; 20 !; 12 ?; 123 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(sk1_decl,type,
sk1: a > $o ).
thf(sk2_decl,type,
sk2: a > $o ).
thf(sk3_decl,type,
sk3: a ).
thf(sk4_decl,type,
sk4: a ).
thf(sk6_decl,type,
sk6: a ).
thf(sk1_def,definition,
( sk1
= ( @+[A: a > $o] :
~ ! [B: a > $o] :
( ( ~ ? [C: a] :
( ( A @ C )
& ( B @ C ) ) )
= ( ( ^ [C: a] :
( ( A @ C )
& ( B @ C ) ) )
= ( ^ [C: a] : $false ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: a > $o] :
( ( ~ ? [B: a] :
( ( sk1 @ B )
& ( A @ B ) ) )
!= ( ( ^ [B: a] :
( ( sk1 @ B )
& ( A @ B ) ) )
= ( ^ [B: a] : $false ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: a] :
( ( sk1 @ A )
& ( sk2 @ A ) ) ) ) ).
thf(1,conjecture,
! [A: a > $o,B: a > $o] :
( ( ~ ? [C: a] :
( ( A @ C )
& ( B @ C ) ) )
= ( ( ^ [C: a] :
( ( A @ C )
& ( B @ C ) ) )
= ( ^ [C: a] : $false ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBOOL_PROP_118_pme) ).
thf(2,negated_conjecture,
~ ! [A: a > $o,B: a > $o] :
( ( ~ ? [C: a] :
( ( A @ C )
& ( B @ C ) ) )
= ( ( ^ [C: a] :
( ( A @ C )
& ( B @ C ) ) )
= ( ^ [C: a] : $false ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: a > $o,B: a > $o] :
( ( ~ ? [C: a] :
( ( A @ C )
& ( B @ C ) ) )
= ( ( ^ [C: a] :
( ( A @ C )
& ( B @ C ) ) )
= ( ^ [C: a] : $false ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
( ( ~ ? [A: a] :
( ( sk1 @ A )
& ( sk2 @ A ) ) )
!= ( ( ^ [A: a] :
( ( sk1 @ A )
& ( sk2 @ A ) ) )
= ( ^ [A: a] : $false ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
( ( ~ ? [A: a] :
( ( sk1 @ A )
& ( sk2 @ A ) ) )
!= ( ( ^ [A: a] :
( ( sk1 @ A )
& ( sk2 @ A ) ) )
= ( ^ [A: a] : $false ) ) ),
inference(lifteq,[status(thm)],[4]) ).
thf(6,plain,
( ~ ~ ? [A: a] :
( ( sk1 @ A )
& ( sk2 @ A ) )
| ( ( ^ [A: a] :
( ( sk1 @ A )
& ( sk2 @ A ) ) )
!= ( ^ [A: a] : $false ) ) ),
inference(bool_ext,[status(thm)],[5]) ).
thf(8,plain,
( ( ( ^ [A: a] :
( ( sk1 @ A )
& ( sk2 @ A ) ) )
!= ( ^ [A: a] : $false ) )
| ~ ~ ? [A: a] :
( ( sk1 @ A )
& ( sk2 @ A ) ) ),
inference(lifteq,[status(thm)],[6]) ).
thf(10,plain,
( ( ( ( ^ [A: a] :
( ( sk1 @ A )
& ( sk2 @ A ) ) )
!= ( ^ [A: a] : $false ) )
| ( sk1 @ sk3 ) )
& ( ( ( ^ [A: a] :
( ( sk1 @ A )
& ( sk2 @ A ) ) )
!= ( ^ [A: a] : $false ) )
| ( sk2 @ sk3 ) ) ),
inference(cnf,[status(esa)],[8]) ).
thf(12,plain,
( ( ( ^ [A: a] :
( ( sk1 @ A )
& ( sk2 @ A ) ) )
!= ( ^ [A: a] : $false ) )
| ( sk2 @ sk3 ) ),
inference(cnfConj,[status(thm)],[10]) ).
thf(87,plain,
( ( ( sk1 @ sk6 )
& ( sk2 @ sk6 ) )
| ( sk2 @ sk3 ) ),
inference(func_ext,[status(esa)],[12]) ).
thf(91,plain,
( ( ( sk1 @ sk6 )
| ( sk2 @ sk3 ) )
& ( ( sk2 @ sk6 )
| ( sk2 @ sk3 ) ) ),
inference(cnf,[status(esa)],[87]) ).
thf(92,plain,
( ( sk1 @ sk6 )
| ( sk2 @ sk3 ) ),
inference(cnfConj,[status(thm)],[91]) ).
thf(11,plain,
( ( ( ^ [A: a] :
( ( sk1 @ A )
& ( sk2 @ A ) ) )
!= ( ^ [A: a] : $false ) )
| ( sk1 @ sk3 ) ),
inference(cnfConj,[status(thm)],[10]) ).
thf(14,plain,
( ( ( sk1 @ sk4 )
& ( sk2 @ sk4 ) )
| ( sk1 @ sk3 ) ),
inference(func_ext,[status(esa)],[11]) ).
thf(15,plain,
( ( ( sk1 @ sk4 )
| ( sk1 @ sk3 ) )
& ( ( sk2 @ sk4 )
| ( sk1 @ sk3 ) ) ),
inference(cnf,[status(esa)],[14]) ).
thf(16,plain,
( ( sk1 @ sk4 )
| ( sk1 @ sk3 ) ),
inference(cnfConj,[status(thm)],[15]) ).
thf(17,plain,
( ( sk2 @ sk4 )
| ( sk1 @ sk3 ) ),
inference(cnfConj,[status(thm)],[15]) ).
thf(7,plain,
( ~ ? [A: a] :
( ( sk1 @ A )
& ( sk2 @ A ) )
| ( ( ^ [A: a] :
( ( sk1 @ A )
& ( sk2 @ A ) ) )
= ( ^ [A: a] : $false ) ) ),
inference(bool_ext,[status(thm)],[5]) ).
thf(9,plain,
( ( ( ^ [A: a] :
( ( sk1 @ A )
& ( sk2 @ A ) ) )
= ( ^ [A: a] : $false ) )
| ~ ? [A: a] :
( ( sk1 @ A )
& ( sk2 @ A ) ) ),
inference(lifteq,[status(thm)],[7]) ).
thf(13,plain,
! [A: a] :
( ( ( ^ [B: a] :
( ( sk1 @ B )
& ( sk2 @ B ) ) )
= ( ^ [B: a] : $false ) )
| ~ ( sk1 @ A )
| ~ ( sk2 @ A ) ),
inference(cnf,[status(esa)],[9]) ).
thf(25,plain,
! [A: a] :
( ( sk1 @ sk3 )
| ( ( ^ [B: a] :
( ( sk1 @ B )
& ( sk2 @ B ) ) )
= ( ^ [B: a] : $false ) )
| ~ ( sk1 @ A )
| ~ $true
| ( ( sk2 @ sk4 )
!= ( sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[17,13]) ).
thf(26,plain,
! [A: a] :
( ( sk1 @ sk3 )
| ( ( ^ [B: a] :
( ( sk1 @ B )
& ( sk2 @ B ) ) )
= ( ^ [B: a] : $false ) )
| ~ ( sk1 @ A )
| ( ( sk2 @ sk4 )
!= ( sk2 @ A ) ) ),
inference(simp,[status(thm)],[25]) ).
thf(27,plain,
( ( sk1 @ sk3 )
| ( ( ^ [A: a] :
( ( sk1 @ A )
& ( sk2 @ A ) ) )
= ( ^ [A: a] : $false ) )
| ~ ( sk1 @ sk4 ) ),
inference(pattern_uni,[status(thm)],[26:[bind(A,$thf( sk4 ))]]) ).
thf(62,plain,
( ( sk1 @ sk3 )
| ~ ( sk1 @ sk4 )
| ( ( ^ [A: a] : $false )
!= ( ^ [A: a] : $false ) )
| ( sk1 @ sk3 )
| ( ( ^ [A: a] :
( ( sk1 @ A )
& ( sk2 @ A ) ) )
!= ( ^ [A: a] :
( ( sk1 @ A )
& ( sk2 @ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[27,11]) ).
thf(63,plain,
( ( sk1 @ sk3 )
| ~ ( sk1 @ sk4 )
| ( ( ^ [A: a] :
( ( sk1 @ A )
& ( sk2 @ A ) ) )
!= ( ^ [A: a] :
( ( sk1 @ A )
& ( sk2 @ A ) ) ) ) ),
inference(simp,[status(thm)],[62]) ).
thf(64,plain,
( ( sk1 @ sk3 )
| ~ ( sk1 @ sk4 ) ),
inference(pattern_uni,[status(thm)],[63:[]]) ).
thf(82,plain,
( ( sk1 @ sk3 )
| ( sk1 @ sk3 )
| ~ $true
| ( ( sk1 @ sk4 )
!= ( sk1 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[16,64]) ).
thf(83,plain,
( ( sk1 @ sk3 )
| ( ( sk1 @ sk4 )
!= ( sk1 @ sk4 ) ) ),
inference(simp,[status(thm)],[82]) ).
thf(84,plain,
sk1 @ sk3,
inference(pattern_uni,[status(thm)],[83:[]]) ).
thf(94,plain,
! [A: a] :
( ( ( ^ [B: a] :
( ( sk1 @ B )
& ( sk2 @ B ) ) )
= ( ^ [B: a] : $false ) )
| ~ $true
| ~ ( sk2 @ A )
| ( ( sk1 @ sk3 )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[84,13]) ).
thf(95,plain,
! [A: a] :
( ( ( ^ [B: a] :
( ( sk1 @ B )
& ( sk2 @ B ) ) )
= ( ^ [B: a] : $false ) )
| ~ ( sk2 @ A )
| ( ( sk1 @ sk3 )
!= ( sk1 @ A ) ) ),
inference(simp,[status(thm)],[94]) ).
thf(96,plain,
( ( ( ^ [A: a] :
( ( sk1 @ A )
& ( sk2 @ A ) ) )
= ( ^ [A: a] : $false ) )
| ~ ( sk2 @ sk3 ) ),
inference(pattern_uni,[status(thm)],[95:[bind(A,$thf( sk3 ))]]) ).
thf(22,plain,
! [A: a] :
( ~ ( sk1 @ A )
| ~ ( sk2 @ A )
| ( ( ~ ? [B: a] : $false )
!= ( ( ^ [B: a] :
( ( sk1 @ B )
& ( sk2 @ B ) ) )
= ( ^ [B: a] : $false ) ) )
| ( ( ^ [B: a] :
( ( sk1 @ B )
& ( sk2 @ B ) ) )
!= ( ^ [B: a] :
( ( sk1 @ B )
& ( sk2 @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[13,5]) ).
thf(23,plain,
! [A: a] :
( ~ ( sk1 @ A )
| ~ ( sk2 @ A )
| ( ( ^ [B: a] :
( ( sk1 @ B )
& ( sk2 @ B ) ) )
!= ( ^ [B: a] : $false ) )
| ( ( ^ [B: a] :
( ( sk1 @ B )
& ( sk2 @ B ) ) )
!= ( ^ [B: a] :
( ( sk1 @ B )
& ( sk2 @ B ) ) ) ) ),
inference(simp,[status(thm)],[22]) ).
thf(24,plain,
! [A: a] :
( ~ ( sk1 @ A )
| ~ ( sk2 @ A )
| ( ( ^ [B: a] :
( ( sk1 @ B )
& ( sk2 @ B ) ) )
!= ( ^ [B: a] : $false ) ) ),
inference(pattern_uni,[status(thm)],[23:[]]) ).
thf(34,plain,
! [A: a] :
( ( ( ^ [B: a] :
( ( sk1 @ B )
& ( sk2 @ B ) ) )
!= ( ^ [B: a] : $false ) )
| ~ ( sk1 @ A )
| ~ ( sk2 @ A ) ),
inference(lifteq,[status(thm)],[24]) ).
thf(97,plain,
! [A: a] :
( ( ( ^ [B: a] :
( ( sk1 @ B )
& ( sk2 @ B ) ) )
!= ( ^ [B: a] : $false ) )
| ~ $true
| ~ ( sk2 @ A )
| ( ( sk1 @ sk3 )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[84,34]) ).
thf(98,plain,
! [A: a] :
( ( ( ^ [B: a] :
( ( sk1 @ B )
& ( sk2 @ B ) ) )
!= ( ^ [B: a] : $false ) )
| ~ ( sk2 @ A )
| ( ( sk1 @ sk3 )
!= ( sk1 @ A ) ) ),
inference(simp,[status(thm)],[97]) ).
thf(99,plain,
( ( ( ^ [A: a] :
( ( sk1 @ A )
& ( sk2 @ A ) ) )
!= ( ^ [A: a] : $false ) )
| ~ ( sk2 @ sk3 ) ),
inference(pattern_uni,[status(thm)],[98:[bind(A,$thf( sk3 ))]]) ).
thf(275,plain,
( ~ ( sk2 @ sk3 )
| ( ( ^ [A: a] : $false )
!= ( ^ [A: a] : $false ) )
| ~ ( sk2 @ sk3 )
| ( ( ^ [A: a] :
( ( sk1 @ A )
& ( sk2 @ A ) ) )
!= ( ^ [A: a] :
( ( sk1 @ A )
& ( sk2 @ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[96,99]) ).
thf(276,plain,
( ~ ( sk2 @ sk3 )
| ( ( ^ [A: a] :
( ( sk1 @ A )
& ( sk2 @ A ) ) )
!= ( ^ [A: a] :
( ( sk1 @ A )
& ( sk2 @ A ) ) ) ) ),
inference(simp,[status(thm)],[275]) ).
thf(277,plain,
~ ( sk2 @ sk3 ),
inference(pattern_uni,[status(thm)],[276:[]]) ).
thf(299,plain,
( ( sk1 @ sk6 )
| $false ),
inference(rewrite,[status(thm)],[92,277]) ).
thf(300,plain,
sk1 @ sk6,
inference(simp,[status(thm)],[299]) ).
thf(316,plain,
! [A: a] :
( ( ( ^ [B: a] :
( ( sk1 @ B )
& ( sk2 @ B ) ) )
= ( ^ [B: a] : $false ) )
| ~ $true
| ~ ( sk2 @ A )
| ( ( sk1 @ sk6 )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[300,13]) ).
thf(317,plain,
! [A: a] :
( ( ( ^ [B: a] :
( ( sk1 @ B )
& ( sk2 @ B ) ) )
= ( ^ [B: a] : $false ) )
| ~ ( sk2 @ A )
| ( ( sk1 @ sk6 )
!= ( sk1 @ A ) ) ),
inference(simp,[status(thm)],[316]) ).
thf(318,plain,
( ( ( ^ [A: a] :
( ( sk1 @ A )
& ( sk2 @ A ) ) )
= ( ^ [A: a] : $false ) )
| ~ ( sk2 @ sk6 ) ),
inference(pattern_uni,[status(thm)],[317:[bind(A,$thf( sk6 ))]]) ).
thf(93,plain,
( ( sk2 @ sk6 )
| ( sk2 @ sk3 ) ),
inference(cnfConj,[status(thm)],[91]) ).
thf(303,plain,
( ( sk2 @ sk6 )
| $false ),
inference(rewrite,[status(thm)],[93,277]) ).
thf(304,plain,
sk2 @ sk6,
inference(simp,[status(thm)],[303]) ).
thf(390,plain,
( ( ( ^ [A: a] :
( ( sk1 @ A )
& ( sk2 @ A ) ) )
= ( ^ [A: a] : $false ) )
| ~ $true ),
inference(rewrite,[status(thm)],[318,304]) ).
thf(391,plain,
( ( ^ [A: a] :
( ( sk1 @ A )
& ( sk2 @ A ) ) )
= ( ^ [A: a] : $false ) ),
inference(simp,[status(thm)],[390]) ).
thf(301,plain,
( ( ( ^ [A: a] :
( ( sk1 @ A )
& ( sk2 @ A ) ) )
!= ( ^ [A: a] : $false ) )
| $false ),
inference(rewrite,[status(thm)],[12,277]) ).
thf(302,plain,
( ( ^ [A: a] :
( ( sk1 @ A )
& ( sk2 @ A ) ) )
!= ( ^ [A: a] : $false ) ),
inference(simp,[status(thm)],[301]) ).
thf(392,plain,
$false,
inference(simplifyReflect,[status(thm)],[391,302]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET636^5 : TPTP v9.3.1. Released v4.0.0.
% 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
% 0.12/0.24 % Computer : n017.cluster.edu
% 0.12/0.24 % Model : x86_64 x86_64
% 0.12/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.24 % Memory : 8046.5625MB
% 0.12/0.24 % OS : Linux 6.8.0-71-generic
% 0.12/0.24 % CPULimit : 300
% 0.12/0.24 % WCLimit : 300
% 0.12/0.24 % DateTime : Tue Sep 29 13:35:37 UTC 2026
% 0.12/0.24 % CPUTime :
% 0.12/0.24 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
% 1.02/0.82 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.21/1.01 % [INFO] Parsing done (184ms).
% 1.21/1.03 % [INFO] Running in sequential loop mode.
% 1.99/1.44 % [INFO] eprover registered as external prover.
% 1.99/1.44 % [INFO] Scanning for conjecture ...
% 2.19/1.53 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.19/1.57 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.19/1.57 % [INFO] Problem is higher-order (TPTP THF).
% 2.19/1.57 % [INFO] Type checking passed.
% 2.19/1.58 % [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 ...
% 5.55/2.96 % [INFO] Killing All external provers ...
% 5.55/2.96 % Time passed: 2573ms (effective reasoning time: 1927ms)
% 5.55/2.96 % 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)>
% 5.55/2.97 % Axioms used in derivation (0):
% 5.55/2.97 % No. of inferences in proof: 55
% 5.55/2.97 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2573 ms resp. 1927 ms w/o parsing
% 6.94/3.04 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.94/3.04 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------