%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU492^1 : TPTP v9.3.1. Released v3.6.0.
% 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 : n013.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 08:28:16 AM UTC 2026
% Result : Theorem 14.46s 4.38s
% Output : Refutation 13.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 22
% Syntax : Number of formulae : 100 ( 48 unt; 0 typ; 21 def)
% Number of atoms : 385 ( 80 equ; 0 cnn)
% Maximal formula atoms : 72 ( 3 avg)
% Number of connectives : 1051 ( 182 ~; 129 |; 51 &; 638 @)
% ( 0 <=>; 51 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 36 ( 36 >; 0 *; 0 +; 0 <<)
% Number of symbols : 28 ( 25 usr; 20 con; 0-2 aty)
% Number of variables : 155 ( 24 ^; 114 !; 0 ?; 155 :)
% ( 0 !>; 0 ?*; 0 @-; 17 @+)
% Comments :
%------------------------------------------------------------------------------
thf(irrefl_decl,type,
irrefl: ( $i > $i > $o ) > $o ).
thf(asymm_decl,type,
asymm: ( $i > $i > $o ) > $o ).
thf(trans_decl,type,
trans: ( $i > $i > $o ) > $o ).
thf(so_decl,type,
so: ( $i > $i > $o ) > $o ).
thf(sk1_decl,type,
sk1: $i > $i > $o ).
thf(sk2_decl,type,
sk2: $i > $i > $o ).
thf(sk3_decl,type,
sk3: $i > $i > $o ).
thf(sk4_decl,type,
sk4: $i ).
thf(sk5_decl,type,
sk5: $i ).
thf(sk6_decl,type,
sk6: $i ).
thf(sk7_decl,type,
sk7: $i ).
thf(sk8_decl,type,
sk8: $i ).
thf(sk9_decl,type,
sk9: $i ).
thf(sk10_decl,type,
sk10: $i ).
thf(sk11_decl,type,
sk11: $i ).
thf(sk12_decl,type,
sk12: $i ).
thf(sk13_decl,type,
sk13: $i ).
thf(sk14_decl,type,
sk14: $i ).
thf(sk15_decl,type,
sk15: $i ).
thf(sk16_decl,type,
sk16: $i ).
thf(sk17_decl,type,
sk17: $i ).
thf(sk18_decl,type,
sk18: $i ).
thf(sk19_decl,type,
sk19: $i ).
thf(sk20_decl,type,
sk20: $i ).
thf(sk21_decl,type,
sk21: $i ).
thf(irrefl_def,definition,
( irrefl
= ( ^ [A: $i > $i > $o] :
! [B: $i] :
~ ( A @ B @ B ) ) ) ).
thf(asymm_def,definition,
( asymm
= ( ^ [A: $i > $i > $o] :
! [B: $i,C: $i] :
( ( A @ B @ C )
=> ~ ( A @ C @ B ) ) ) ) ).
thf(trans_def,definition,
( trans
= ( ^ [A: $i > $i > $o] :
! [B: $i,C: $i,D: $i] :
( ( ( A @ B @ C )
& ( A @ C @ D ) )
=> ( A @ B @ D ) ) ) ) ).
thf(so_def,definition,
( so
= ( ^ [A: $i > $i > $o] :
( ( asymm @ A )
& ( trans @ A ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( @+[A: $i] :
~ ! [B: $i] :
( ( sk2 @ A @ B )
=> ~ ( sk2 @ B @ A ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( @+[A: $i] :
~ ( ( sk2 @ sk5 @ A )
=> ~ ( sk2 @ A @ sk5 ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( @+[A: $i] :
~ ~ ( sk2 @ A @ A ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( @+[A: $i] :
~ ( ( sk3 @ sk4 @ A )
=> ~ ( sk3 @ A @ sk4 ) ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( @+[A: $i] :
~ ! [B: $i] :
( ( sk1 @ A @ B )
=> ~ ( sk1 @ B @ A ) ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( @+[A: $i] :
~ ( ( sk1 @ sk9 @ A )
=> ~ ( sk1 @ A @ sk9 ) ) ) ) ).
thf(sk11_def,definition,
( sk11
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) ) ).
thf(sk12_def,definition,
( sk12
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( sk1 @ sk11 @ A )
& ( sk1 @ A @ B ) )
=> ( sk1 @ sk11 @ B ) ) ) ) ).
thf(sk13_def,definition,
( sk13
= ( @+[A: $i] :
~ ( ( ( sk1 @ sk11 @ sk12 )
& ( sk1 @ sk12 @ A ) )
=> ( sk1 @ sk11 @ A ) ) ) ) ).
thf(sk14_def,definition,
( sk14
= ( @+[A: $i] :
~ ~ ( sk1 @ A @ A ) ) ) ).
thf(sk15_def,definition,
( sk15
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) ) ).
thf(sk16_def,definition,
( sk16
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( sk1 @ sk15 @ A )
& ( sk1 @ A @ B ) )
=> ( sk1 @ sk15 @ B ) ) ) ) ).
thf(sk17_def,definition,
( sk17
= ( @+[A: $i] :
~ ( ( ( sk1 @ sk15 @ sk16 )
& ( sk1 @ sk16 @ A ) )
=> ( sk1 @ sk15 @ A ) ) ) ) ).
thf(sk18_def,definition,
( sk18
= ( @+[A: $i] :
~ ! [B: $i] :
( ( sk1 @ A @ B )
=> ~ ( sk1 @ B @ A ) ) ) ) ).
thf(sk19_def,definition,
( sk19
= ( @+[A: $i] :
~ ( ( sk1 @ sk18 @ A )
=> ~ ( sk1 @ A @ sk18 ) ) ) ) ).
thf(sk20_def,definition,
( sk20
= ( @+[A: $i] :
~ ~ ( sk1 @ A @ A ) ) ) ).
thf(sk21_def,definition,
( sk21
= ( @+[A: $i] :
~ ( ( sk3 @ sk4 @ A )
=> ~ ( sk3 @ A @ sk4 ) ) ) ) ).
thf(1,conjecture,
( so
= ( ^ [A: $i > $i > $o] :
( ( irrefl @ A )
& ( trans @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',alternative_definition_of_strict_order) ).
thf(2,negated_conjecture,
( so
!= ( ^ [A: $i > $i > $o] :
( ( irrefl @ A )
& ( trans @ A ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ^ [A: $i > $i > $o] :
( ! [B: $i,C: $i] :
( ( A @ B @ C )
=> ~ ( A @ C @ B ) )
& ! [B: $i,C: $i,D: $i] :
( ( ( A @ B @ C )
& ( A @ C @ D ) )
=> ( A @ B @ D ) ) ) )
!= ( ^ [A: $i > $i > $o] :
( ! [B: $i] :
~ ( A @ B @ B )
& ! [B: $i,C: $i,D: $i] :
( ( ( A @ B @ C )
& ( A @ C @ D ) )
=> ( A @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
( ( ^ [A: $i > $i > $o] :
( ! [B: $i,C: $i] :
( ( A @ B @ C )
=> ~ ( A @ C @ B ) )
& ! [B: $i,C: $i,D: $i] :
( ( ( A @ B @ C )
& ( A @ C @ D ) )
=> ( A @ B @ D ) ) ) )
!= ( ^ [A: $i > $i > $o] :
( ! [B: $i] :
~ ( A @ B @ B )
& ! [B: $i,C: $i,D: $i] :
( ( ( A @ B @ C )
& ( A @ C @ D ) )
=> ( A @ B @ D ) ) ) ) ),
inference(lifteq,[status(thm)],[3]) ).
thf(5,plain,
( ( ( ^ [A: $i > $i > $o] :
! [B: $i,C: $i] :
( ( A @ B @ C )
=> ~ ( A @ C @ B ) ) )
!= ( ^ [A: $i > $i > $o] :
! [B: $i] :
~ ( A @ B @ B ) ) )
| ( ( ^ [A: $i > $i > $o] :
! [B: $i,C: $i,D: $i] :
( ( ( A @ B @ C )
& ( A @ C @ D ) )
=> ( A @ B @ D ) ) )
!= ( ^ [A: $i > $i > $o] :
! [B: $i,C: $i,D: $i] :
( ( ( A @ B @ C )
& ( A @ C @ D ) )
=> ( A @ B @ D ) ) ) ) ),
inference(simp,[status(thm)],[4]) ).
thf(7,plain,
( ( ^ [A: $i > $i > $o] :
! [B: $i,C: $i] :
( ( A @ B @ C )
=> ~ ( A @ C @ B ) ) )
!= ( ^ [A: $i > $i > $o] :
! [B: $i] :
~ ( A @ B @ B ) ) ),
inference(simp,[status(thm)],[5]) ).
thf(8,plain,
( ( ^ [A: $i > $i > $o,B: $i] :
! [C: $i] :
( ( A @ B @ C )
=> ~ ( A @ C @ B ) ) )
!= ( ^ [A: $i > $i > $o,B: $i] :
~ ( A @ B @ B ) ) ),
inference(simp,[status(thm)],[7]) ).
thf(10,plain,
( ( ! [A: $i] :
( ( sk3 @ sk4 @ A )
=> ~ ( sk3 @ A @ sk4 ) ) )
!= ( ~ ( sk3 @ sk4 @ sk4 ) ) ),
inference(func_ext,[status(esa)],[8]) ).
thf(19,plain,
( ! [A: $i] :
( ( sk3 @ sk4 @ A )
=> ~ ( sk3 @ A @ sk4 ) )
| ~ ( sk3 @ sk4 @ sk4 ) ),
inference(bool_ext,[status(thm)],[10]) ).
thf(23,plain,
! [A: $i] :
( ~ ( sk3 @ sk4 @ A )
| ~ ( sk3 @ A @ sk4 )
| ~ ( sk3 @ sk4 @ sk4 ) ),
inference(cnf,[status(esa)],[19]) ).
thf(213,plain,
! [A: $i] :
( ~ ( sk3 @ sk4 @ A )
| ~ ( sk3 @ sk4 @ sk4 )
| ( ( sk3 @ A @ sk4 )
!= ( sk3 @ sk4 @ A ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[23]) ).
thf(218,plain,
( ~ ( sk3 @ sk4 @ sk4 )
| ~ ( sk3 @ sk4 @ sk4 ) ),
inference(pattern_uni,[status(thm)],[213:[bind(A,$thf( sk4 ))]]) ).
thf(223,plain,
~ ( sk3 @ sk4 @ sk4 ),
inference(simp,[status(thm)],[218]) ).
thf(226,plain,
( ( ! [A: $i] :
( ( sk3 @ sk4 @ A )
=> ~ ( sk3 @ A @ sk4 ) ) )
!= ( ~ $false ) ),
inference(rewrite,[status(thm)],[10,223]) ).
thf(227,plain,
~ ! [A: $i] :
( ( sk3 @ sk4 @ A )
=> ~ ( sk3 @ A @ sk4 ) ),
inference(simp,[status(thm)],[226]) ).
thf(232,plain,
( ( sk3 @ sk4 @ sk21 )
& ( sk3 @ sk21 @ sk4 ) ),
inference(cnf,[status(esa)],[227]) ).
thf(234,plain,
sk3 @ sk21 @ sk4,
inference(cnfConj,[status(thm)],[232]) ).
thf(6,plain,
( ( ! [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ~ ( sk1 @ B @ A ) )
& ! [A: $i,B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) )
!= ( ! [A: $i] :
~ ( sk1 @ A @ A )
& ! [A: $i,B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) ),
inference(func_ext,[status(esa)],[4]) ).
thf(39,plain,
( ( ( ! [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ~ ( sk1 @ B @ A ) ) )
!= ( ! [A: $i] :
~ ( sk1 @ A @ A ) ) )
| ( ( ! [A: $i,B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) )
!= ( ! [A: $i,B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) ) ),
inference(simp,[status(thm)],[6]) ).
thf(42,plain,
( ( ! [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ~ ( sk1 @ B @ A ) ) )
!= ( ! [A: $i] :
~ ( sk1 @ A @ A ) ) ),
inference(simp,[status(thm)],[39]) ).
thf(9,plain,
( ( ! [A: $i,B: $i] :
( ( sk2 @ A @ B )
=> ~ ( sk2 @ B @ A ) ) )
!= ( ! [A: $i] :
~ ( sk2 @ A @ A ) ) ),
inference(func_ext,[status(esa)],[7]) ).
thf(40,plain,
( ~ ( ! [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ~ ( sk1 @ B @ A ) )
& ! [A: $i,B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) )
| ~ ( ! [A: $i] :
~ ( sk1 @ A @ A )
& ! [A: $i,B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) ),
inference(bool_ext,[status(thm)],[6]) ).
thf(43,plain,
( ( ( sk1 @ sk9 @ sk10 )
| ( sk1 @ sk11 @ sk12 )
| ( sk1 @ sk14 @ sk14 )
| ( sk1 @ sk15 @ sk16 ) )
& ( ( sk1 @ sk9 @ sk10 )
| ( sk1 @ sk11 @ sk12 )
| ( sk1 @ sk14 @ sk14 )
| ( sk1 @ sk16 @ sk17 ) )
& ( ( sk1 @ sk9 @ sk10 )
| ( sk1 @ sk11 @ sk12 )
| ( sk1 @ sk14 @ sk14 )
| ~ ( sk1 @ sk15 @ sk17 ) )
& ( ( sk1 @ sk9 @ sk10 )
| ( sk1 @ sk12 @ sk13 )
| ( sk1 @ sk14 @ sk14 )
| ( sk1 @ sk15 @ sk16 ) )
& ( ( sk1 @ sk9 @ sk10 )
| ( sk1 @ sk12 @ sk13 )
| ( sk1 @ sk14 @ sk14 )
| ( sk1 @ sk16 @ sk17 ) )
& ( ( sk1 @ sk9 @ sk10 )
| ( sk1 @ sk12 @ sk13 )
| ( sk1 @ sk14 @ sk14 )
| ~ ( sk1 @ sk15 @ sk17 ) )
& ( ( sk1 @ sk9 @ sk10 )
| ~ ( sk1 @ sk11 @ sk13 )
| ( sk1 @ sk14 @ sk14 )
| ( sk1 @ sk15 @ sk16 ) )
& ( ( sk1 @ sk9 @ sk10 )
| ~ ( sk1 @ sk11 @ sk13 )
| ( sk1 @ sk14 @ sk14 )
| ( sk1 @ sk16 @ sk17 ) )
& ( ( sk1 @ sk9 @ sk10 )
| ~ ( sk1 @ sk11 @ sk13 )
| ( sk1 @ sk14 @ sk14 )
| ~ ( sk1 @ sk15 @ sk17 ) )
& ( ( sk1 @ sk10 @ sk9 )
| ( sk1 @ sk11 @ sk12 )
| ( sk1 @ sk14 @ sk14 )
| ( sk1 @ sk15 @ sk16 ) )
& ( ( sk1 @ sk10 @ sk9 )
| ( sk1 @ sk11 @ sk12 )
| ( sk1 @ sk14 @ sk14 )
| ( sk1 @ sk16 @ sk17 ) )
& ( ( sk1 @ sk10 @ sk9 )
| ( sk1 @ sk11 @ sk12 )
| ( sk1 @ sk14 @ sk14 )
| ~ ( sk1 @ sk15 @ sk17 ) )
& ( ( sk1 @ sk10 @ sk9 )
| ( sk1 @ sk12 @ sk13 )
| ( sk1 @ sk14 @ sk14 )
| ( sk1 @ sk15 @ sk16 ) )
& ( ( sk1 @ sk10 @ sk9 )
| ( sk1 @ sk12 @ sk13 )
| ( sk1 @ sk14 @ sk14 )
| ( sk1 @ sk16 @ sk17 ) )
& ( ( sk1 @ sk10 @ sk9 )
| ( sk1 @ sk12 @ sk13 )
| ( sk1 @ sk14 @ sk14 )
| ~ ( sk1 @ sk15 @ sk17 ) )
& ( ( sk1 @ sk10 @ sk9 )
| ~ ( sk1 @ sk11 @ sk13 )
| ( sk1 @ sk14 @ sk14 )
| ( sk1 @ sk15 @ sk16 ) )
& ( ( sk1 @ sk10 @ sk9 )
| ~ ( sk1 @ sk11 @ sk13 )
| ( sk1 @ sk14 @ sk14 )
| ( sk1 @ sk16 @ sk17 ) )
& ( ( sk1 @ sk10 @ sk9 )
| ~ ( sk1 @ sk11 @ sk13 )
| ( sk1 @ sk14 @ sk14 )
| ~ ( sk1 @ sk15 @ sk17 ) ) ),
inference(cnf,[status(esa)],[40]) ).
thf(44,plain,
( ( sk1 @ sk9 @ sk10 )
| ( sk1 @ sk11 @ sk12 )
| ( sk1 @ sk14 @ sk14 )
| ( sk1 @ sk16 @ sk17 ) ),
inference(cnfConj,[status(thm)],[43]) ).
thf(12,plain,
( ~ ! [A: $i,B: $i] :
( ( sk2 @ A @ B )
=> ~ ( sk2 @ B @ A ) )
| ~ ! [A: $i] :
~ ( sk2 @ A @ A ) ),
inference(bool_ext,[status(thm)],[9]) ).
thf(14,plain,
( ( ( sk2 @ sk5 @ sk6 )
| ( sk2 @ sk7 @ sk7 ) )
& ( ( sk2 @ sk6 @ sk5 )
| ( sk2 @ sk7 @ sk7 ) ) ),
inference(cnf,[status(esa)],[12]) ).
thf(16,plain,
( ( sk2 @ sk6 @ sk5 )
| ( sk2 @ sk7 @ sk7 ) ),
inference(cnfConj,[status(thm)],[14]) ).
thf(13,plain,
( ! [A: $i,B: $i] :
( ( sk2 @ A @ B )
=> ~ ( sk2 @ B @ A ) )
| ! [A: $i] :
~ ( sk2 @ A @ A ) ),
inference(bool_ext,[status(thm)],[9]) ).
thf(17,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( sk2 @ A @ B )
| ~ ( sk2 @ B @ A )
| ~ ( sk2 @ C @ C ) ),
inference(cnf,[status(esa)],[13]) ).
thf(146,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( sk2 @ A @ B )
| ~ ( sk2 @ B @ A )
| ( ( sk2 @ C @ C )
!= ( sk2 @ A @ B ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[17]) ).
thf(149,plain,
! [A: $i] :
( ~ ( sk2 @ A @ A )
| ~ ( sk2 @ A @ A ) ),
inference(pattern_uni,[status(thm)],[146:[bind(A,$thf( C )),bind(B,$thf( C ))]]) ).
thf(154,plain,
! [A: $i] :
~ ( sk2 @ A @ A ),
inference(simp,[status(thm)],[149]) ).
thf(158,plain,
( ( sk2 @ sk6 @ sk5 )
| $false ),
inference(rewrite,[status(thm)],[16,154]) ).
thf(159,plain,
sk2 @ sk6 @ sk5,
inference(simp,[status(thm)],[158]) ).
thf(170,plain,
! [A: $i] :
( ~ $true
| ( ( sk2 @ sk6 @ sk5 )
!= ( sk2 @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[159,154]) ).
thf(171,plain,
! [A: $i] :
( ( sk2 @ sk6 @ sk5 )
!= ( sk2 @ A @ A ) ),
inference(simp,[status(thm)],[170]) ).
thf(173,plain,
! [A: $i] :
( ( sk6 != A )
| ( sk5 != A ) ),
inference(simp,[status(thm)],[171]) ).
thf(177,plain,
sk6 != sk5,
inference(simp,[status(thm)],[173]) ).
thf(18,plain,
( ~ ! [A: $i] :
( ( sk3 @ sk4 @ A )
=> ~ ( sk3 @ A @ sk4 ) )
| ~ ~ ( sk3 @ sk4 @ sk4 ) ),
inference(bool_ext,[status(thm)],[10]) ).
thf(20,plain,
( ( ( sk3 @ sk4 @ sk8 )
| ( sk3 @ sk4 @ sk4 ) )
& ( ( sk3 @ sk8 @ sk4 )
| ( sk3 @ sk4 @ sk4 ) ) ),
inference(cnf,[status(esa)],[18]) ).
thf(22,plain,
( ( sk3 @ sk8 @ sk4 )
| ( sk3 @ sk4 @ sk4 ) ),
inference(cnfConj,[status(thm)],[20]) ).
thf(230,plain,
( ( sk3 @ sk8 @ sk4 )
| $false ),
inference(rewrite,[status(thm)],[22,223]) ).
thf(231,plain,
sk3 @ sk8 @ sk4,
inference(simp,[status(thm)],[230]) ).
thf(72,plain,
( ~ ! [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ~ ( sk1 @ B @ A ) )
| ~ ! [A: $i] :
~ ( sk1 @ A @ A ) ),
inference(bool_ext,[status(thm)],[42]) ).
thf(74,plain,
( ( ( sk1 @ sk18 @ sk19 )
| ( sk1 @ sk20 @ sk20 ) )
& ( ( sk1 @ sk19 @ sk18 )
| ( sk1 @ sk20 @ sk20 ) ) ),
inference(cnf,[status(esa)],[72]) ).
thf(75,plain,
( ( sk1 @ sk18 @ sk19 )
| ( sk1 @ sk20 @ sk20 ) ),
inference(cnfConj,[status(thm)],[74]) ).
thf(124,plain,
( ( sk1 @ sk18 @ sk19 )
| ( ( sk1 @ sk20 @ sk20 )
!= ( sk1 @ sk18 @ sk19 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[75]) ).
thf(125,plain,
( ( sk1 @ sk18 @ sk19 )
| ( ( sk1 @ sk20 @ sk20 )
!= ( sk1 @ sk18 @ sk19 ) ) ),
inference(simp,[status(thm)],[124]) ).
thf(76,plain,
( ( sk1 @ sk19 @ sk18 )
| ( sk1 @ sk20 @ sk20 ) ),
inference(cnfConj,[status(thm)],[74]) ).
thf(194,plain,
( ( sk1 @ sk19 @ sk18 )
| ( ( sk1 @ sk20 @ sk20 )
!= ( sk1 @ sk19 @ sk18 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[76]) ).
thf(196,plain,
( ( sk1 @ sk19 @ sk18 )
| ( sk20 != sk19 )
| ( sk20 != sk18 ) ),
inference(simp,[status(thm)],[194]) ).
thf(21,plain,
( ( sk3 @ sk4 @ sk8 )
| ( sk3 @ sk4 @ sk4 ) ),
inference(cnfConj,[status(thm)],[20]) ).
thf(32,plain,
( ( sk3 @ sk4 @ sk4 )
| ( ( sk3 @ sk4 @ sk8 )
!= ( sk3 @ sk4 @ sk4 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[21]) ).
thf(35,plain,
( ( sk3 @ sk4 @ sk4 )
| ( sk4 != sk4 )
| ( sk8 != sk4 ) ),
inference(simp,[status(thm)],[32]) ).
thf(38,plain,
( ( sk3 @ sk4 @ sk4 )
| ( sk8 != sk4 ) ),
inference(simp,[status(thm)],[35]) ).
thf(78,plain,
( ( sk8 != sk4 )
| ( ( ~ $true )
!= ( ! [A: $i] :
( ( sk3 @ sk4 @ A )
=> ~ ( sk3 @ A @ sk4 ) ) ) )
| ( ( sk3 @ sk4 @ sk4 )
!= ( sk3 @ sk4 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[38,10]) ).
thf(79,plain,
( ( sk8 != sk4 )
| ! [A: $i] :
( ( sk3 @ sk4 @ A )
=> ~ ( sk3 @ A @ sk4 ) )
| ( ( sk3 @ sk4 @ sk4 )
!= ( sk3 @ sk4 @ sk4 ) ) ),
inference(simp,[status(thm)],[78]) ).
thf(80,plain,
( ( sk8 != sk4 )
| ! [A: $i] :
( ( sk3 @ sk4 @ A )
=> ~ ( sk3 @ A @ sk4 ) ) ),
inference(pattern_uni,[status(thm)],[79:[]]) ).
thf(81,plain,
! [A: $i] :
( ( sk8 != sk4 )
| ~ ( sk3 @ sk4 @ A )
| ~ ( sk3 @ A @ sk4 ) ),
inference(cnf,[status(esa)],[80]) ).
thf(96,plain,
! [A: $i] :
( ( sk8 != sk4 )
| ( sk8 != sk4 )
| ~ $true
| ~ ( sk3 @ A @ sk4 )
| ( ( sk3 @ sk4 @ sk4 )
!= ( sk3 @ sk4 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[38,81]) ).
thf(97,plain,
! [A: $i] :
( ( sk8 != sk4 )
| ~ ( sk3 @ A @ sk4 )
| ( ( sk3 @ sk4 @ sk4 )
!= ( sk3 @ sk4 @ A ) ) ),
inference(simp,[status(thm)],[96]) ).
thf(98,plain,
( ( sk8 != sk4 )
| ~ ( sk3 @ sk4 @ sk4 ) ),
inference(pattern_uni,[status(thm)],[97:[bind(A,$thf( sk4 ))]]) ).
thf(115,plain,
( ( sk8 != sk4 )
| ( sk8 != sk4 )
| ~ $true
| ( ( sk3 @ sk4 @ sk4 )
!= ( sk3 @ sk4 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[38,98]) ).
thf(116,plain,
( ( sk8 != sk4 )
| ( ( sk3 @ sk4 @ sk4 )
!= ( sk3 @ sk4 @ sk4 ) ) ),
inference(simp,[status(thm)],[115]) ).
thf(117,plain,
sk8 != sk4,
inference(pattern_uni,[status(thm)],[116:[]]) ).
thf(233,plain,
sk3 @ sk4 @ sk21,
inference(cnfConj,[status(thm)],[232]) ).
thf(228,plain,
( ( sk3 @ sk4 @ sk8 )
| $false ),
inference(rewrite,[status(thm)],[21,223]) ).
thf(229,plain,
sk3 @ sk4 @ sk8,
inference(simp,[status(thm)],[228]) ).
thf(249,plain,
( ~ $true
| ( ( sk3 @ sk4 @ sk21 )
!= ( sk3 @ sk4 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[233,223]) ).
thf(250,plain,
( ( sk3 @ sk4 @ sk21 )
!= ( sk3 @ sk4 @ sk4 ) ),
inference(simp,[status(thm)],[249]) ).
thf(251,plain,
( ( sk4 != sk4 )
| ( sk21 != sk4 ) ),
inference(simp,[status(thm)],[250]) ).
thf(252,plain,
sk21 != sk4,
inference(simp,[status(thm)],[251]) ).
thf(15,plain,
( ( sk2 @ sk5 @ sk6 )
| ( sk2 @ sk7 @ sk7 ) ),
inference(cnfConj,[status(thm)],[14]) ).
thf(160,plain,
( ( sk2 @ sk5 @ sk6 )
| $false ),
inference(rewrite,[status(thm)],[15,154]) ).
thf(161,plain,
sk2 @ sk5 @ sk6,
inference(simp,[status(thm)],[160]) ).
thf(71,plain,
( ( ^ [A: $i] :
! [B: $i] :
( ( sk1 @ A @ B )
=> ~ ( sk1 @ B @ A ) ) )
!= ( ^ [A: $i] :
~ ( sk1 @ A @ A ) ) ),
inference(simp,[status(thm)],[42]) ).
thf(11,plain,
( ( ^ [A: $i] :
! [B: $i] :
( ( sk2 @ A @ B )
=> ~ ( sk2 @ B @ A ) ) )
!= ( ^ [A: $i] :
~ ( sk2 @ A @ A ) ) ),
inference(simp,[status(thm)],[9]) ).
thf(126,plain,
( ( sk1 @ sk18 @ sk19 )
| ( sk20 != sk18 )
| ( sk20 != sk19 ) ),
inference(simp,[status(thm)],[124]) ).
thf(357,plain,
$false,
inference(e,[status(thm)],[234,42,9,44,177,231,125,196,117,233,6,229,252,161,17,71,159,76,7,223,3,154,11,8,75,4,126]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU492^1 : TPTP v9.3.1. Released v3.6.0.
% 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
% 0.09/0.20 % Computer : n013.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.21 % CPULimit : 300
% 0.09/0.21 % WCLimit : 300
% 0.09/0.21 % DateTime : Tue Sep 29 13:45:06 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 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
% 0.87/0.79 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.59/1.06 % [INFO] Parsing done (260ms).
% 1.59/1.07 % [INFO] Running in sequential loop mode.
% 2.25/1.47 % [INFO] eprover registered as external prover.
% 2.25/1.48 % [INFO] Scanning for conjecture ...
% 2.71/1.65 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.71/1.68 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.71/1.68 % [INFO] Problem is higher-order (TPTP THF).
% 2.71/1.69 % [INFO] Type checking passed.
% 2.71/1.69 % [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 ...
% 14.46/4.38 % External prover 'e' found a proof!
% 14.46/4.38 % [INFO] Killing All external provers ...
% 14.46/4.38 % Time passed: 4027ms (effective reasoning time: 3301ms)
% 14.46/4.38 % 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)>
% 14.46/4.38 % Axioms used in derivation (0):
% 14.46/4.38 % No. of inferences in proof: 79
% 14.46/4.38 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 4027 ms resp. 3301 ms w/o parsing
% 13.59/4.46 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 13.59/4.46 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------