%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET623^3 : TPTP v9.3.1. Released v3.6.0.
% 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 : n002.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 08:23:03 AM UTC 2026
% Result : Theorem 12.93s 4.70s
% Output : Refutation 13.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 5
% Syntax : Number of formulae : 63 ( 17 unt; 0 typ; 4 def)
% Number of atoms : 2328 ( 44 equ; 0 cnn)
% Maximal formula atoms : 1560 ( 36 avg)
% Number of connectives : 5762 (1197 ~;1745 |; 492 &;2328 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 231 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 17 ( 17 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 3 con; 0-3 aty)
% Number of variables : 30 ( 15 ^; 12 !; 0 ?; 30 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% Comments :
%------------------------------------------------------------------------------
thf(excl_union_decl,type,
excl_union: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(sk1_decl,type,
sk1: $i > $o ).
thf(sk2_decl,type,
sk2: $i > $o ).
thf(sk3_decl,type,
sk3: $i > $o ).
thf(sk4_decl,type,
sk4: $i ).
thf(excl_union_def,definition,
( excl_union
= ( ^ [A: $i > $o,B: $i > $o,C: $i] :
( ( ( A @ C )
& ~ ( B @ C ) )
| ( ~ ( A @ C )
& ( B @ C ) ) ) ) ) ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i > $o] :
~ ! [B: $i > $o,C: $i > $o] :
( ( ^ [D: $i] :
( ( ( ( ( A @ D )
& ~ ( B @ D ) )
| ( ~ ( A @ D )
& ( B @ D ) ) )
& ~ ( C @ D ) )
| ( ~ ( ( ( A @ D )
& ~ ( B @ D ) )
| ( ~ ( A @ D )
& ( B @ D ) ) )
& ( C @ D ) ) ) )
= ( ^ [D: $i] :
( ( ( A @ D )
& ~ ( ( ( B @ D )
& ~ ( C @ D ) )
| ( ~ ( B @ D )
& ( C @ D ) ) ) )
| ( ~ ( A @ D )
& ( ( ( B @ D )
& ~ ( C @ D ) )
| ( ~ ( B @ D )
& ( C @ D ) ) ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i > $o] :
~ ! [B: $i > $o] :
( ( ^ [C: $i] :
( ( ( ( ( sk1 @ C )
& ~ ( A @ C ) )
| ( ~ ( sk1 @ C )
& ( A @ C ) ) )
& ~ ( B @ C ) )
| ( ~ ( ( ( sk1 @ C )
& ~ ( A @ C ) )
| ( ~ ( sk1 @ C )
& ( A @ C ) ) )
& ( B @ C ) ) ) )
= ( ^ [C: $i] :
( ( ( sk1 @ C )
& ~ ( ( ( A @ C )
& ~ ( B @ C ) )
| ( ~ ( A @ C )
& ( B @ C ) ) ) )
| ( ~ ( sk1 @ C )
& ( ( ( A @ C )
& ~ ( B @ C ) )
| ( ~ ( A @ C )
& ( B @ C ) ) ) ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i > $o] :
( ( ^ [B: $i] :
( ( ( ( ( sk1 @ B )
& ~ ( sk2 @ B ) )
| ( ~ ( sk1 @ B )
& ( sk2 @ B ) ) )
& ~ ( A @ B ) )
| ( ~ ( ( ( sk1 @ B )
& ~ ( sk2 @ B ) )
| ( ~ ( sk1 @ B )
& ( sk2 @ B ) ) )
& ( A @ B ) ) ) )
!= ( ^ [B: $i] :
( ( ( sk1 @ B )
& ~ ( ( ( sk2 @ B )
& ~ ( A @ B ) )
| ( ~ ( sk2 @ B )
& ( A @ B ) ) ) )
| ( ~ ( sk1 @ B )
& ( ( ( sk2 @ B )
& ~ ( A @ B ) )
| ( ~ ( sk2 @ B )
& ( A @ B ) ) ) ) ) ) ) ) ) ).
thf(1,conjecture,
! [A: $i > $o,B: $i > $o,C: $i > $o] :
( ( excl_union @ ( excl_union @ A @ B ) @ C )
= ( excl_union @ A @ ( excl_union @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(2,negated_conjecture,
~ ! [A: $i > $o,B: $i > $o,C: $i > $o] :
( ( excl_union @ ( excl_union @ A @ B ) @ C )
= ( excl_union @ A @ ( excl_union @ B @ C ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: $i > $o,B: $i > $o,C: $i > $o] :
( ( ^ [D: $i] :
( ( ( ( ( A @ D )
& ~ ( B @ D ) )
| ( ~ ( A @ D )
& ( B @ D ) ) )
& ~ ( C @ D ) )
| ( ~ ( ( ( A @ D )
& ~ ( B @ D ) )
| ( ~ ( A @ D )
& ( B @ D ) ) )
& ( C @ D ) ) ) )
= ( ^ [D: $i] :
( ( ( A @ D )
& ~ ( ( ( B @ D )
& ~ ( C @ D ) )
| ( ~ ( B @ D )
& ( C @ D ) ) ) )
| ( ~ ( A @ D )
& ( ( ( B @ D )
& ~ ( C @ D ) )
| ( ~ ( B @ D )
& ( C @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
( ( ^ [A: $i] :
( ( ( ( ( sk1 @ A )
& ~ ( sk2 @ A ) )
| ( ~ ( sk1 @ A )
& ( sk2 @ A ) ) )
& ~ ( sk3 @ A ) )
| ( ~ ( ( ( sk1 @ A )
& ~ ( sk2 @ A ) )
| ( ~ ( sk1 @ A )
& ( sk2 @ A ) ) )
& ( sk3 @ A ) ) ) )
!= ( ^ [A: $i] :
( ( ( sk1 @ A )
& ~ ( ( ( sk2 @ A )
& ~ ( sk3 @ A ) )
| ( ~ ( sk2 @ A )
& ( sk3 @ A ) ) ) )
| ( ~ ( sk1 @ A )
& ( ( ( sk2 @ A )
& ~ ( sk3 @ A ) )
| ( ~ ( sk2 @ A )
& ( sk3 @ A ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
( ( ^ [A: $i] :
( ( ( sk1 @ A )
& ~ ( ( ( sk2 @ A )
& ~ ( sk3 @ A ) )
| ( ~ ( sk2 @ A )
& ( sk3 @ A ) ) ) )
| ( ~ ( sk1 @ A )
& ( ( ( sk2 @ A )
& ~ ( sk3 @ A ) )
| ( ~ ( sk2 @ A )
& ( sk3 @ A ) ) ) ) ) )
!= ( ^ [A: $i] :
( ( ( ( ( sk1 @ A )
& ~ ( sk2 @ A ) )
| ( ~ ( sk1 @ A )
& ( sk2 @ A ) ) )
& ~ ( sk3 @ A ) )
| ( ~ ( ( ( sk1 @ A )
& ~ ( sk2 @ A ) )
| ( ~ ( sk1 @ A )
& ( sk2 @ A ) ) )
& ( sk3 @ A ) ) ) ) ),
inference(lifteq,[status(thm)],[4]) ).
thf(7,plain,
( ( ( ( sk1 @ sk4 )
& ~ ( ( ( sk2 @ sk4 )
& ~ ( sk3 @ sk4 ) )
| ( ~ ( sk2 @ sk4 )
& ( sk3 @ sk4 ) ) ) )
| ( ~ ( sk1 @ sk4 )
& ( ( ( sk2 @ sk4 )
& ~ ( sk3 @ sk4 ) )
| ( ~ ( sk2 @ sk4 )
& ( sk3 @ sk4 ) ) ) ) )
!= ( ( ( ( ( sk1 @ sk4 )
& ~ ( sk2 @ sk4 ) )
| ( ~ ( sk1 @ sk4 )
& ( sk2 @ sk4 ) ) )
& ~ ( sk3 @ sk4 ) )
| ( ~ ( ( ( sk1 @ sk4 )
& ~ ( sk2 @ sk4 ) )
| ( ~ ( sk1 @ sk4 )
& ( sk2 @ sk4 ) ) )
& ( sk3 @ sk4 ) ) ) ),
inference(func_ext,[status(esa)],[5]) ).
thf(8,plain,
( ( ( ( sk1 @ sk4 )
& ~ ( ( ( sk2 @ sk4 )
& ~ ( sk3 @ sk4 ) )
| ( ~ ( sk2 @ sk4 )
& ( sk3 @ sk4 ) ) ) )
!= ( ( ( ( sk1 @ sk4 )
& ~ ( sk2 @ sk4 ) )
| ( ~ ( sk1 @ sk4 )
& ( sk2 @ sk4 ) ) )
& ~ ( sk3 @ sk4 ) ) )
| ( ( ~ ( sk1 @ sk4 )
& ( ( ( sk2 @ sk4 )
& ~ ( sk3 @ sk4 ) )
| ( ~ ( sk2 @ sk4 )
& ( sk3 @ sk4 ) ) ) )
!= ( ~ ( ( ( sk1 @ sk4 )
& ~ ( sk2 @ sk4 ) )
| ( ~ ( sk1 @ sk4 )
& ( sk2 @ sk4 ) ) )
& ( sk3 @ sk4 ) ) ) ),
inference(simp,[status(thm)],[7]) ).
thf(192,plain,
( ( ( sk1 @ sk4 )
& ~ ( ( ( sk2 @ sk4 )
& ~ ( sk3 @ sk4 ) )
| ( ~ ( sk2 @ sk4 )
& ( sk3 @ sk4 ) ) ) )
| ( ( ( ( sk1 @ sk4 )
& ~ ( sk2 @ sk4 ) )
| ( ~ ( sk1 @ sk4 )
& ( sk2 @ sk4 ) ) )
& ~ ( sk3 @ sk4 ) )
| ( ~ ( sk1 @ sk4 )
& ( ( ( sk2 @ sk4 )
& ~ ( sk3 @ sk4 ) )
| ( ~ ( sk2 @ sk4 )
& ( sk3 @ sk4 ) ) ) )
| ( ~ ( ( ( sk1 @ sk4 )
& ~ ( sk2 @ sk4 ) )
| ( ~ ( sk1 @ sk4 )
& ( sk2 @ sk4 ) ) )
& ( sk3 @ sk4 ) ) ),
inference(bool_ext,[status(thm)],[8]) ).
thf(209,plain,
( ( ( sk1 @ sk4 )
| ( sk1 @ sk4 )
| ~ ( sk1 @ sk4 )
| ~ ( sk1 @ sk4 )
| ~ ( sk1 @ sk4 )
| ( sk2 @ sk4 ) )
& ( ( sk1 @ sk4 )
| ( sk1 @ sk4 )
| ~ ( sk1 @ sk4 )
| ~ ( sk1 @ sk4 )
| ( sk1 @ sk4 )
| ~ ( sk2 @ sk4 ) )
& ( ( sk1 @ sk4 )
| ( sk1 @ sk4 )
| ~ ( sk1 @ sk4 )
| ~ ( sk1 @ sk4 )
| ( sk3 @ sk4 ) )
& ( ( sk1 @ sk4 )
| ( sk1 @ sk4 )
| ~ ( sk1 @ sk4 )
| ( sk2 @ sk4 )
| ~ ( sk2 @ sk4 )
| ~ ( sk1 @ sk4 )
| ( sk2 @ sk4 ) )
& ( ( sk1 @ sk4 )
| ( sk1 @ sk4 )
| ~ ( sk1 @ sk4 )
| ( sk2 @ sk4 )
| ~ ( sk2 @ sk4 )
| ( sk1 @ sk4 )
| ~ ( sk2 @ sk4 ) )
& ( ( sk1 @ sk4 )
| ( sk1 @ sk4 )
| ~ ( sk1 @ sk4 )
| ( sk2 @ sk4 )
| ~ ( sk2 @ sk4 )
| ( sk3 @ sk4 ) )
& ( ( sk1 @ sk4 )
| ( sk1 @ sk4 )
| ~ ( sk1 @ sk4 )
| ( sk2 @ sk4 )
| ( sk3 @ sk4 )
| ~ ( sk1 @ sk4 )
| ( sk2 @ sk4 ) )
& ( ( sk1 @ sk4 )
| ( sk1 @ sk4 )
| ~ ( sk1 @ sk4 )
| ( sk2 @ sk4 )
| ( sk3 @ sk4 )
| ( sk1 @ sk4 )
| ~ ( sk2 @ sk4 ) )
& ( ( sk1 @ sk4 )
| ( sk1 @ sk4 )
| ~ ( sk1 @ sk4 )
| ( sk2 @ sk4 )
| ( sk3 @ sk4 )
| ( sk3 @ sk4 ) )
& ( ( sk1 @ sk4 )
| ( sk1 @ sk4 )
| ~ ( sk1 @ sk4 )
| ~ ( sk3 @ sk4 )
| ~ ( sk2 @ sk4 )
| ~ ( sk1 @ sk4 )
| ( sk2 @ sk4 ) )
& ( ( sk1 @ sk4 )
| ( sk1 @ sk4 )
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| ~ ( sk3 @ sk4 )
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& ( ( sk1 @ sk4 )
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& ( ( sk1 @ sk4 )
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& ( ( sk1 @ sk4 )
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& ( ( sk1 @ sk4 )
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| ( sk2 @ sk4 )
| ( sk3 @ sk4 )
| ( sk1 @ sk4 )
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& ( ( sk2 @ sk4 )
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& ( ( sk2 @ sk4 )
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& ( ( sk2 @ sk4 )
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& ( ( sk2 @ sk4 )
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& ( ( sk2 @ sk4 )
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& ( ( sk2 @ sk4 )
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& ( ( sk2 @ sk4 )
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| ( sk1 @ sk4 )
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& ( ( sk2 @ sk4 )
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& ( ( sk2 @ sk4 )
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| ( sk2 @ sk4 )
| ( sk3 @ sk4 )
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| ( sk2 @ sk4 ) )
& ( ( sk2 @ sk4 )
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| ( sk2 @ sk4 )
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& ( ( sk2 @ sk4 )
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| ( sk2 @ sk4 )
| ( sk3 @ sk4 )
| ( sk3 @ sk4 ) )
& ( ( sk2 @ sk4 )
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| ~ ( sk3 @ sk4 )
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| ~ ( sk2 @ sk4 )
| ~ ( sk1 @ sk4 )
| ( sk2 @ sk4 ) )
& ( ( sk2 @ sk4 )
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| ~ ( sk3 @ sk4 )
| ~ ( sk3 @ sk4 )
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| ( sk1 @ sk4 )
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& ( ( sk2 @ sk4 )
| ~ ( sk3 @ sk4 )
| ~ ( sk3 @ sk4 )
| ~ ( sk3 @ sk4 )
| ~ ( sk2 @ sk4 )
| ( sk3 @ sk4 ) )
& ( ( sk2 @ sk4 )
| ~ ( sk3 @ sk4 )
| ~ ( sk3 @ sk4 )
| ~ ( sk3 @ sk4 )
| ( sk3 @ sk4 )
| ~ ( sk1 @ sk4 )
| ( sk2 @ sk4 ) )
& ( ( sk2 @ sk4 )
| ~ ( sk3 @ sk4 )
| ~ ( sk3 @ sk4 )
| ~ ( sk3 @ sk4 )
| ( sk3 @ sk4 )
| ( sk1 @ sk4 )
| ~ ( sk2 @ sk4 ) )
& ( ( sk2 @ sk4 )
| ~ ( sk3 @ sk4 )
| ~ ( sk3 @ sk4 )
| ~ ( sk3 @ sk4 )
| ( sk3 @ sk4 )
| ( sk3 @ sk4 ) ) ),
inference(cnf,[status(esa)],[192]) ).
thf(295,plain,
( ( sk1 @ sk4 )
| ( sk1 @ sk4 )
| ( sk2 @ sk4 )
| ( sk2 @ sk4 )
| ( sk3 @ sk4 )
| ( sk3 @ sk4 ) ),
inference(cnfConj,[status(thm)],[209]) ).
thf(553,plain,
( ( sk1 @ sk4 )
| ( sk2 @ sk4 )
| ( sk3 @ sk4 ) ),
inference(simp,[status(thm)],[295]) ).
thf(9,plain,
( ~ ( ( ( sk1 @ sk4 )
& ~ ( ( ( sk2 @ sk4 )
& ~ ( sk3 @ sk4 ) )
| ( ~ ( sk2 @ sk4 )
& ( sk3 @ sk4 ) ) ) )
| ( ~ ( sk1 @ sk4 )
& ( ( ( sk2 @ sk4 )
& ~ ( sk3 @ sk4 ) )
| ( ~ ( sk2 @ sk4 )
& ( sk3 @ sk4 ) ) ) ) )
| ~ ( ( ( ( ( sk1 @ sk4 )
& ~ ( sk2 @ sk4 ) )
| ( ~ ( sk1 @ sk4 )
& ( sk2 @ sk4 ) ) )
& ~ ( sk3 @ sk4 ) )
| ( ~ ( ( ( sk1 @ sk4 )
& ~ ( sk2 @ sk4 ) )
| ( ~ ( sk1 @ sk4 )
& ( sk2 @ sk4 ) ) )
& ( sk3 @ sk4 ) ) ) ),
inference(bool_ext,[status(thm)],[7]) ).
thf(11,plain,
( ( ~ ( sk1 @ sk4 )
| ( sk2 @ sk4 )
| ~ ( sk2 @ sk4 )
| ~ ( sk1 @ sk4 )
| ( sk2 @ sk4 )
| ( sk3 @ sk4 ) )
& ( ~ ( sk1 @ sk4 )
| ( sk2 @ sk4 )
| ~ ( sk2 @ sk4 )
| ( sk1 @ sk4 )
| ~ ( sk2 @ sk4 )
| ( sk3 @ sk4 ) )
& ( ~ ( sk1 @ sk4 )
| ( sk2 @ sk4 )
| ~ ( sk2 @ sk4 )
| ( sk1 @ sk4 )
| ~ ( sk1 @ sk4 )
| ~ ( sk3 @ sk4 ) )
& ( ~ ( sk1 @ sk4 )
| ( sk2 @ sk4 )
| ~ ( sk2 @ sk4 )
| ( sk1 @ sk4 )
| ( sk2 @ sk4 )
| ~ ( sk3 @ sk4 ) )
& ( ~ ( sk1 @ sk4 )
| ( sk2 @ sk4 )
| ~ ( sk2 @ sk4 )
| ~ ( sk2 @ sk4 )
| ~ ( sk1 @ sk4 )
| ~ ( sk3 @ sk4 ) )
& ( ~ ( sk1 @ sk4 )
| ( sk2 @ sk4 )
| ~ ( sk2 @ sk4 )
| ~ ( sk2 @ sk4 )
| ( sk2 @ sk4 )
| ~ ( sk3 @ sk4 ) )
& ( ~ ( sk1 @ sk4 )
| ( sk2 @ sk4 )
| ( sk3 @ sk4 )
| ~ ( sk1 @ sk4 )
| ( sk2 @ sk4 )
| ( sk3 @ sk4 ) )
& ( ~ ( sk1 @ sk4 )
| ( sk2 @ sk4 )
| ( sk3 @ sk4 )
| ( sk1 @ sk4 )
| ~ ( sk2 @ sk4 )
| ( sk3 @ sk4 ) )
& ( ~ ( sk1 @ sk4 )
| ( sk2 @ sk4 )
| ( sk3 @ sk4 )
| ( sk1 @ sk4 )
| ~ ( sk1 @ sk4 )
| ~ ( sk3 @ sk4 ) )
& ( ~ ( sk1 @ sk4 )
| ( sk2 @ sk4 )
| ( sk3 @ sk4 )
| ( sk1 @ sk4 )
| ( sk2 @ sk4 )
| ~ ( sk3 @ sk4 ) )
& ( ~ ( sk1 @ sk4 )
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| ( sk3 @ sk4 )
| ~ ( sk2 @ sk4 )
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& ( ~ ( sk1 @ sk4 )
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| ( sk2 @ sk4 )
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& ( ~ ( sk1 @ sk4 )
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| ~ ( sk1 @ sk4 )
| ( sk2 @ sk4 )
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& ( ~ ( sk1 @ sk4 )
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| ( sk1 @ sk4 )
| ~ ( sk2 @ sk4 )
| ( sk3 @ sk4 ) )
& ( ~ ( sk1 @ sk4 )
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| ~ ( sk2 @ sk4 )
| ( sk1 @ sk4 )
| ~ ( sk1 @ sk4 )
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& ( ~ ( sk1 @ sk4 )
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| ~ ( sk2 @ sk4 )
| ( sk1 @ sk4 )
| ( sk2 @ sk4 )
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& ( ~ ( sk1 @ sk4 )
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| ~ ( sk2 @ sk4 )
| ~ ( sk2 @ sk4 )
| ~ ( sk1 @ sk4 )
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& ( ~ ( sk1 @ sk4 )
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| ~ ( sk2 @ sk4 )
| ( sk2 @ sk4 )
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& ( ~ ( sk1 @ sk4 )
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| ( sk3 @ sk4 )
| ~ ( sk1 @ sk4 )
| ( sk2 @ sk4 )
| ( sk3 @ sk4 ) )
& ( ~ ( sk1 @ sk4 )
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| ( sk3 @ sk4 )
| ( sk1 @ sk4 )
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| ( sk3 @ sk4 ) )
& ( ~ ( sk1 @ sk4 )
| ~ ( sk3 @ sk4 )
| ( sk3 @ sk4 )
| ( sk1 @ sk4 )
| ~ ( sk1 @ sk4 )
| ~ ( sk3 @ sk4 ) )
& ( ~ ( sk1 @ sk4 )
| ~ ( sk3 @ sk4 )
| ( sk3 @ sk4 )
| ( sk1 @ sk4 )
| ( sk2 @ sk4 )
| ~ ( sk3 @ sk4 ) )
& ( ~ ( sk1 @ sk4 )
| ~ ( sk3 @ sk4 )
| ( sk3 @ sk4 )
| ~ ( sk2 @ sk4 )
| ~ ( sk1 @ sk4 )
| ~ ( sk3 @ sk4 ) )
& ( ~ ( sk1 @ sk4 )
| ~ ( sk3 @ sk4 )
| ( sk3 @ sk4 )
| ~ ( sk2 @ sk4 )
| ( sk2 @ sk4 )
| ~ ( sk3 @ sk4 ) )
& ( ( sk1 @ sk4 )
| ~ ( sk2 @ sk4 )
| ( sk3 @ sk4 )
| ~ ( sk1 @ sk4 )
| ( sk2 @ sk4 )
| ( sk3 @ sk4 ) )
& ( ( sk1 @ sk4 )
| ~ ( sk2 @ sk4 )
| ( sk3 @ sk4 )
| ( sk1 @ sk4 )
| ~ ( sk2 @ sk4 )
| ( sk3 @ sk4 ) )
& ( ( sk1 @ sk4 )
| ~ ( sk2 @ sk4 )
| ( sk3 @ sk4 )
| ( sk1 @ sk4 )
| ~ ( sk1 @ sk4 )
| ~ ( sk3 @ sk4 ) )
& ( ( sk1 @ sk4 )
| ~ ( sk2 @ sk4 )
| ( sk3 @ sk4 )
| ( sk1 @ sk4 )
| ( sk2 @ sk4 )
| ~ ( sk3 @ sk4 ) )
& ( ( sk1 @ sk4 )
| ~ ( sk2 @ sk4 )
| ( sk3 @ sk4 )
| ~ ( sk2 @ sk4 )
| ~ ( sk1 @ sk4 )
| ~ ( sk3 @ sk4 ) )
& ( ( sk1 @ sk4 )
| ~ ( sk2 @ sk4 )
| ( sk3 @ sk4 )
| ~ ( sk2 @ sk4 )
| ( sk2 @ sk4 )
| ~ ( sk3 @ sk4 ) )
& ( ( sk1 @ sk4 )
| ( sk2 @ sk4 )
| ~ ( sk3 @ sk4 )
| ~ ( sk1 @ sk4 )
| ( sk2 @ sk4 )
| ( sk3 @ sk4 ) )
& ( ( sk1 @ sk4 )
| ( sk2 @ sk4 )
| ~ ( sk3 @ sk4 )
| ( sk1 @ sk4 )
| ~ ( sk2 @ sk4 )
| ( sk3 @ sk4 ) )
& ( ( sk1 @ sk4 )
| ( sk2 @ sk4 )
| ~ ( sk3 @ sk4 )
| ( sk1 @ sk4 )
| ~ ( sk1 @ sk4 )
| ~ ( sk3 @ sk4 ) )
& ( ( sk1 @ sk4 )
| ( sk2 @ sk4 )
| ~ ( sk3 @ sk4 )
| ( sk1 @ sk4 )
| ( sk2 @ sk4 )
| ~ ( sk3 @ sk4 ) )
& ( ( sk1 @ sk4 )
| ( sk2 @ sk4 )
| ~ ( sk3 @ sk4 )
| ~ ( sk2 @ sk4 )
| ~ ( sk1 @ sk4 )
| ~ ( sk3 @ sk4 ) )
& ( ( sk1 @ sk4 )
| ( sk2 @ sk4 )
| ~ ( sk3 @ sk4 )
| ~ ( sk2 @ sk4 )
| ( sk2 @ sk4 )
| ~ ( sk3 @ sk4 ) ) ),
inference(cnf,[status(esa)],[9]) ).
thf(21,plain,
( ( sk1 @ sk4 )
| ( sk2 @ sk4 )
| ~ ( sk3 @ sk4 )
| ( sk1 @ sk4 )
| ( sk2 @ sk4 )
| ~ ( sk3 @ sk4 ) ),
inference(cnfConj,[status(thm)],[11]) ).
thf(53,plain,
( ( sk1 @ sk4 )
| ( sk2 @ sk4 )
| ~ ( sk3 @ sk4 ) ),
inference(simp,[status(thm)],[21]) ).
thf(2782,plain,
( ( sk1 @ sk4 )
| ( sk2 @ sk4 )
| ( sk1 @ sk4 )
| ( sk2 @ sk4 )
| ~ $true
| ( ( sk3 @ sk4 )
!= ( sk3 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[553,53]) ).
thf(2783,plain,
( ( sk1 @ sk4 )
| ( sk2 @ sk4 )
| ( ( sk3 @ sk4 )
!= ( sk3 @ sk4 ) ) ),
inference(simp,[status(thm)],[2782]) ).
thf(2784,plain,
( ( sk1 @ sk4 )
| ( sk2 @ sk4 ) ),
inference(pattern_uni,[status(thm)],[2783:[]]) ).
thf(26,plain,
( ( sk1 @ sk4 )
| ~ ( sk2 @ sk4 )
| ( sk3 @ sk4 )
| ( sk1 @ sk4 )
| ~ ( sk2 @ sk4 )
| ( sk3 @ sk4 ) ),
inference(cnfConj,[status(thm)],[11]) ).
thf(67,plain,
( ( sk1 @ sk4 )
| ~ ( sk2 @ sk4 )
| ( sk3 @ sk4 ) ),
inference(simp,[status(thm)],[26]) ).
thf(2913,plain,
( ( sk1 @ sk4 )
| ( sk1 @ sk4 )
| ~ $true
| ( sk3 @ sk4 )
| ( ( sk2 @ sk4 )
!= ( sk2 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[2784,67]) ).
thf(2914,plain,
( ( sk1 @ sk4 )
| ( sk3 @ sk4 )
| ( ( sk2 @ sk4 )
!= ( sk2 @ sk4 ) ) ),
inference(simp,[status(thm)],[2913]) ).
thf(2915,plain,
( ( sk1 @ sk4 )
| ( sk3 @ sk4 ) ),
inference(pattern_uni,[status(thm)],[2914:[]]) ).
thf(3070,plain,
( ( sk1 @ sk4 )
| ( ( ( ( ( sk1 @ sk4 )
& ~ ( sk2 @ sk4 ) )
| ( ~ ( sk1 @ sk4 )
& ( sk2 @ sk4 ) ) )
& ~ $true )
!= ( ( sk1 @ sk4 )
& ~ ( ( ( sk2 @ sk4 )
& ~ ( sk3 @ sk4 ) )
| ( ~ ( sk2 @ sk4 )
& ( sk3 @ sk4 ) ) ) ) )
| ( ( ~ ( sk1 @ sk4 )
& ( ( ( sk2 @ sk4 )
& ~ ( sk3 @ sk4 ) )
| ( ~ ( sk2 @ sk4 )
& ( sk3 @ sk4 ) ) ) )
!= ( ~ ( ( ( sk1 @ sk4 )
& ~ ( sk2 @ sk4 ) )
| ( ~ ( sk1 @ sk4 )
& ( sk2 @ sk4 ) ) )
& ( sk3 @ sk4 ) ) )
| ( ( sk3 @ sk4 )
!= ( sk3 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[2915,8]) ).
thf(3071,plain,
( ( sk1 @ sk4 )
| ( ( sk1 @ sk4 )
& ~ ( ( ( sk2 @ sk4 )
& ~ ( sk3 @ sk4 ) )
| ( ~ ( sk2 @ sk4 )
& ( sk3 @ sk4 ) ) ) )
| ( ( ~ ( sk1 @ sk4 )
& ( ( ( sk2 @ sk4 )
& ~ ( sk3 @ sk4 ) )
| ( ~ ( sk2 @ sk4 )
& ( sk3 @ sk4 ) ) ) )
!= ( ~ ( ( ( sk1 @ sk4 )
& ~ ( sk2 @ sk4 ) )
| ( ~ ( sk1 @ sk4 )
& ( sk2 @ sk4 ) ) )
& ( sk3 @ sk4 ) ) )
| ( ( sk3 @ sk4 )
!= ( sk3 @ sk4 ) ) ),
inference(simp,[status(thm)],[3070]) ).
thf(3072,plain,
( ( sk1 @ sk4 )
| ( ( sk1 @ sk4 )
& ~ ( ( ( sk2 @ sk4 )
& ~ ( sk3 @ sk4 ) )
| ( ~ ( sk2 @ sk4 )
& ( sk3 @ sk4 ) ) ) )
| ( ( ~ ( sk1 @ sk4 )
& ( ( ( sk2 @ sk4 )
& ~ ( sk3 @ sk4 ) )
| ( ~ ( sk2 @ sk4 )
& ( sk3 @ sk4 ) ) ) )
!= ( ~ ( ( ( sk1 @ sk4 )
& ~ ( sk2 @ sk4 ) )
| ( ~ ( sk1 @ sk4 )
& ( sk2 @ sk4 ) ) )
& ( sk3 @ sk4 ) ) ) ),
inference(pattern_uni,[status(thm)],[3071:[]]) ).
thf(3110,plain,
( ( ( sk1 @ sk4 )
| ( sk1 @ sk4 )
| ( ( ~ ( sk1 @ sk4 )
& ( ( ( sk2 @ sk4 )
& ~ ( sk3 @ sk4 ) )
| ( ~ ( sk2 @ sk4 )
& ( sk3 @ sk4 ) ) ) )
!= ( ~ ( ( ( sk1 @ sk4 )
& ~ ( sk2 @ sk4 ) )
| ( ~ ( sk1 @ sk4 )
& ( sk2 @ sk4 ) ) )
& ( sk3 @ sk4 ) ) ) )
& ( ( sk1 @ sk4 )
| ~ ( sk2 @ sk4 )
| ( sk3 @ sk4 )
| ( ( ~ ( sk1 @ sk4 )
& ( ( ( sk2 @ sk4 )
& ~ ( sk3 @ sk4 ) )
| ( ~ ( sk2 @ sk4 )
& ( sk3 @ sk4 ) ) ) )
!= ( ~ ( ( ( sk1 @ sk4 )
& ~ ( sk2 @ sk4 ) )
| ( ~ ( sk1 @ sk4 )
& ( sk2 @ sk4 ) ) )
& ( sk3 @ sk4 ) ) ) )
& ( ( sk1 @ sk4 )
| ( sk2 @ sk4 )
| ~ ( sk3 @ sk4 )
| ( ( ~ ( sk1 @ sk4 )
& ( ( ( sk2 @ sk4 )
& ~ ( sk3 @ sk4 ) )
| ( ~ ( sk2 @ sk4 )
& ( sk3 @ sk4 ) ) ) )
!= ( ~ ( ( ( sk1 @ sk4 )
& ~ ( sk2 @ sk4 ) )
| ( ~ ( sk1 @ sk4 )
& ( sk2 @ sk4 ) ) )
& ( sk3 @ sk4 ) ) ) ) ),
inference(cnf,[status(esa)],[3072]) ).
thf(3111,plain,
( ( sk1 @ sk4 )
| ( sk1 @ sk4 )
| ( ( ~ ( sk1 @ sk4 )
& ( ( ( sk2 @ sk4 )
& ~ ( sk3 @ sk4 ) )
| ( ~ ( sk2 @ sk4 )
& ( sk3 @ sk4 ) ) ) )
!= ( ~ ( ( ( sk1 @ sk4 )
& ~ ( sk2 @ sk4 ) )
| ( ~ ( sk1 @ sk4 )
& ( sk2 @ sk4 ) ) )
& ( sk3 @ sk4 ) ) ) ),
inference(cnfConj,[status(thm)],[3110]) ).
thf(3114,plain,
( ( sk1 @ sk4 )
| ( ( ~ ( sk1 @ sk4 )
& ( ( ( sk2 @ sk4 )
& ~ ( sk3 @ sk4 ) )
| ( ~ ( sk2 @ sk4 )
& ( sk3 @ sk4 ) ) ) )
!= ( ~ ( ( ( sk1 @ sk4 )
& ~ ( sk2 @ sk4 ) )
| ( ~ ( sk1 @ sk4 )
& ( sk2 @ sk4 ) ) )
& ( sk3 @ sk4 ) ) ) ),
inference(simp,[status(thm)],[3111]) ).
thf(3298,plain,
( ( sk1 @ sk4 )
| ( sk1 @ sk4 )
| ( ( ~ ( sk1 @ sk4 )
& ( ( ( sk2 @ sk4 )
& ~ $true )
| ( ~ ( sk2 @ sk4 )
& ( sk3 @ sk4 ) ) ) )
!= ( ~ ( ( ( sk1 @ sk4 )
& ~ ( sk2 @ sk4 ) )
| ( ~ ( sk1 @ sk4 )
& ( sk2 @ sk4 ) ) )
& ( sk3 @ sk4 ) ) )
| ( ( sk3 @ sk4 )
!= ( sk3 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[2915,3114]) ).
thf(3299,plain,
( ( sk1 @ sk4 )
| ( ( ~ ( sk1 @ sk4 )
& ~ ( sk2 @ sk4 )
& ( sk3 @ sk4 ) )
!= ( ~ ( ( ( sk1 @ sk4 )
& ~ ( sk2 @ sk4 ) )
| ( ~ ( sk1 @ sk4 )
& ( sk2 @ sk4 ) ) )
& ( sk3 @ sk4 ) ) )
| ( ( sk3 @ sk4 )
!= ( sk3 @ sk4 ) ) ),
inference(simp,[status(thm)],[3298]) ).
thf(3300,plain,
( ( sk1 @ sk4 )
| ( ( ~ ( sk1 @ sk4 )
& ~ ( sk2 @ sk4 )
& ( sk3 @ sk4 ) )
!= ( ~ ( ( ( sk1 @ sk4 )
& ~ ( sk2 @ sk4 ) )
| ( ~ ( sk1 @ sk4 )
& ( sk2 @ sk4 ) ) )
& ( sk3 @ sk4 ) ) ) ),
inference(pattern_uni,[status(thm)],[3299:[]]) ).
thf(3362,plain,
( ( sk1 @ sk4 )
| ( ~ ( sk1 @ sk4 )
& ~ ( sk2 @ sk4 )
& ( sk3 @ sk4 ) )
| ( ~ ( ( ( sk1 @ sk4 )
& ~ ( sk2 @ sk4 ) )
| ( ~ ( sk1 @ sk4 )
& ( sk2 @ sk4 ) ) )
& ( sk3 @ sk4 ) ) ),
inference(bool_ext,[status(thm)],[3300]) ).
thf(3385,plain,
( ( ( sk1 @ sk4 )
| ~ ( sk1 @ sk4 )
| ~ ( sk1 @ sk4 )
| ( sk2 @ sk4 ) )
& ( ( sk1 @ sk4 )
| ~ ( sk1 @ sk4 )
| ( sk1 @ sk4 )
| ~ ( sk2 @ sk4 ) )
& ( ( sk1 @ sk4 )
| ~ ( sk1 @ sk4 )
| ( sk3 @ sk4 ) )
& ( ( sk1 @ sk4 )
| ~ ( sk2 @ sk4 )
| ~ ( sk1 @ sk4 )
| ( sk2 @ sk4 ) )
& ( ( sk1 @ sk4 )
| ~ ( sk2 @ sk4 )
| ( sk1 @ sk4 )
| ~ ( sk2 @ sk4 ) )
& ( ( sk1 @ sk4 )
| ~ ( sk2 @ sk4 )
| ( sk3 @ sk4 ) )
& ( ( sk1 @ sk4 )
| ( sk3 @ sk4 )
| ~ ( sk1 @ sk4 )
| ( sk2 @ sk4 ) )
& ( ( sk1 @ sk4 )
| ( sk3 @ sk4 )
| ( sk1 @ sk4 )
| ~ ( sk2 @ sk4 ) )
& ( ( sk1 @ sk4 )
| ( sk3 @ sk4 )
| ( sk3 @ sk4 ) ) ),
inference(cnf,[status(esa)],[3362]) ).
thf(3394,plain,
( ( sk1 @ sk4 )
| ~ ( sk2 @ sk4 )
| ( sk1 @ sk4 )
| ~ ( sk2 @ sk4 ) ),
inference(cnfConj,[status(thm)],[3385]) ).
thf(3399,plain,
( ( sk1 @ sk4 )
| ~ ( sk2 @ sk4 ) ),
inference(simp,[status(thm)],[3394]) ).
thf(3408,plain,
( ( sk1 @ sk4 )
| ( sk1 @ sk4 )
| ~ $true
| ( ( sk2 @ sk4 )
!= ( sk2 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[2784,3399]) ).
thf(3409,plain,
( ( sk1 @ sk4 )
| ( ( sk2 @ sk4 )
!= ( sk2 @ sk4 ) ) ),
inference(simp,[status(thm)],[3408]) ).
thf(3410,plain,
sk1 @ sk4,
inference(pattern_uni,[status(thm)],[3409:[]]) ).
thf(3419,plain,
( ( ( $true
& ~ ( ( ( sk2 @ sk4 )
& ~ ( sk3 @ sk4 ) )
| ( ~ ( sk2 @ sk4 )
& ( sk3 @ sk4 ) ) ) )
| ( ~ $true
& ( ( ( sk2 @ sk4 )
& ~ ( sk3 @ sk4 ) )
| ( ~ ( sk2 @ sk4 )
& ( sk3 @ sk4 ) ) ) ) )
!= ( ( ( ( $true
& ~ ( sk2 @ sk4 ) )
| ( ~ $true
& ( sk2 @ sk4 ) ) )
& ~ ( sk3 @ sk4 ) )
| ( ~ ( ( $true
& ~ ( sk2 @ sk4 ) )
| ( ~ $true
& ( sk2 @ sk4 ) ) )
& ( sk3 @ sk4 ) ) ) ),
inference(rewrite,[status(thm)],[7,3410]) ).
thf(3420,plain,
( ( ~ ( ( ( sk2 @ sk4 )
& ~ ( sk3 @ sk4 ) )
| ( ~ ( sk2 @ sk4 )
& ( sk3 @ sk4 ) ) ) )
!= ( ( ~ ( sk2 @ sk4 )
& ~ ( sk3 @ sk4 ) )
| ( ( sk2 @ sk4 )
& ( sk3 @ sk4 ) ) ) ),
inference(simp,[status(thm)],[3419]) ).
thf(34,plain,
( ~ ( sk1 @ sk4 )
| ( sk2 @ sk4 )
| ( sk3 @ sk4 )
| ~ ( sk1 @ sk4 )
| ( sk2 @ sk4 )
| ( sk3 @ sk4 ) ),
inference(cnfConj,[status(thm)],[11]) ).
thf(61,plain,
( ~ ( sk1 @ sk4 )
| ( sk2 @ sk4 )
| ( sk3 @ sk4 ) ),
inference(simp,[status(thm)],[34]) ).
thf(379,plain,
( ( sk2 @ sk4 )
| ~ ( sk3 @ sk4 )
| ~ ( sk3 @ sk4 )
| ~ ( sk1 @ sk4 )
| ~ ( sk1 @ sk4 )
| ( sk2 @ sk4 ) ),
inference(cnfConj,[status(thm)],[209]) ).
thf(424,plain,
( ( sk2 @ sk4 )
| ~ ( sk3 @ sk4 )
| ~ ( sk1 @ sk4 ) ),
inference(simp,[status(thm)],[379]) ).
thf(2522,plain,
( ~ ( sk1 @ sk4 )
| ( sk2 @ sk4 )
| ( sk2 @ sk4 )
| ~ $true
| ~ ( sk1 @ sk4 )
| ( ( sk3 @ sk4 )
!= ( sk3 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[61,424]) ).
thf(2523,plain,
( ~ ( sk1 @ sk4 )
| ( sk2 @ sk4 )
| ( ( sk3 @ sk4 )
!= ( sk3 @ sk4 ) ) ),
inference(simp,[status(thm)],[2522]) ).
thf(2524,plain,
( ~ ( sk1 @ sk4 )
| ( sk2 @ sk4 ) ),
inference(pattern_uni,[status(thm)],[2523:[]]) ).
thf(3417,plain,
( ~ $true
| ( sk2 @ sk4 ) ),
inference(rewrite,[status(thm)],[2524,3410]) ).
thf(3418,plain,
sk2 @ sk4,
inference(simp,[status(thm)],[3417]) ).
thf(27,plain,
( ~ ( sk1 @ sk4 )
| ~ ( sk3 @ sk4 )
| ~ ( sk2 @ sk4 )
| ~ ( sk2 @ sk4 )
| ~ ( sk1 @ sk4 )
| ~ ( sk3 @ sk4 ) ),
inference(cnfConj,[status(thm)],[11]) ).
thf(63,plain,
( ~ ( sk1 @ sk4 )
| ~ ( sk3 @ sk4 )
| ~ ( sk2 @ sk4 ) ),
inference(simp,[status(thm)],[27]) ).
thf(2540,plain,
( ~ ( sk1 @ sk4 )
| ~ ( sk1 @ sk4 )
| ~ ( sk3 @ sk4 )
| ~ $true
| ( ( sk2 @ sk4 )
!= ( sk2 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[2524,63]) ).
thf(2541,plain,
( ~ ( sk1 @ sk4 )
| ~ ( sk3 @ sk4 )
| ( ( sk2 @ sk4 )
!= ( sk2 @ sk4 ) ) ),
inference(simp,[status(thm)],[2540]) ).
thf(2542,plain,
( ~ ( sk1 @ sk4 )
| ~ ( sk3 @ sk4 ) ),
inference(pattern_uni,[status(thm)],[2541:[]]) ).
thf(3421,plain,
( ~ $true
| ~ ( sk3 @ sk4 ) ),
inference(rewrite,[status(thm)],[2542,3410]) ).
thf(3422,plain,
~ ( sk3 @ sk4 ),
inference(simp,[status(thm)],[3421]) ).
thf(3587,plain,
( ( ( ~ $true
& ~ $false )
| ( $true
& $false ) )
!= ( ~ ( ( $true
& ~ $false )
| ( ~ $true
& $false ) ) ) ),
inference(rewrite,[status(thm)],[3420,3418,3422]) ).
thf(3588,plain,
$false,
inference(simp,[status(thm)],[3587]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET623^3 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.07 % 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
% 0.11/0.19 % Computer : n002.cluster.edu
% 0.11/0.19 % Model : x86_64 x86_64
% 0.11/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.19 % Memory : 8046.5625MB
% 0.11/0.19 % OS : Linux 6.8.0-71-generic
% 0.11/0.19 % CPULimit : 300
% 0.11/0.19 % WCLimit : 300
% 0.11/0.19 % DateTime : Tue Sep 29 13:42:22 UTC 2026
% 0.11/0.20 % CPUTime :
% 0.11/0.20 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
% 0.89/0.76 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.24/0.98 % [INFO] Parsing done (220ms).
% 1.24/1.00 % [INFO] Running in sequential loop mode.
% 2.24/1.41 % [INFO] eprover registered as external prover.
% 2.24/1.42 % [INFO] Scanning for conjecture ...
% 2.46/1.54 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.46/1.57 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.46/1.58 % [INFO] Problem is higher-order (TPTP THF).
% 2.46/1.58 % [INFO] Type checking passed.
% 2.46/1.58 % [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 ...
% 14.91/4.69 % [INFO] Killing All external provers ...
% 12.93/4.70 % Time passed: 4371ms (effective reasoning time: 3694ms)
% 12.93/4.70 % 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)>
% 12.93/4.70 % Axioms used in derivation (0):
% 12.93/4.70 % No. of inferences in proof: 59
% 12.93/4.70 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4371 ms resp. 3694 ms w/o parsing
% 13.40/4.87 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 13.40/4.87 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------