%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP021^3 : TPTP v9.3.1. Bugfixed v7.5.0.
% 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 : 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 08:06:25 AM UTC 2026
% Result : Theorem 36.48s 8.02s
% Output : Refutation 37.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 10
% Syntax : Number of formulae : 113 ( 29 unt; 0 typ; 3 def)
% Number of atoms : 437 ( 119 equ; 0 cnn)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 1128 ( 184 ~; 147 |; 32 &; 744 @)
% ( 0 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 7 con; 0-4 aty)
% Number of variables : 109 ( 0 ^; 106 !; 0 ?; 109 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% Comments :
%------------------------------------------------------------------------------
thf(tyop_2Eextreal_2Eextreal_type,type,
tyop_2Eextreal_2Eextreal: $tType ).
thf(tyop_2Emin_2Ebool_type,type,
tyop_2Emin_2Ebool: $tType ).
thf(c_2Ebool_2ECOND_decl,type,
c_2Ebool_2ECOND:
!>[TA: $tType] : ( $o > TA > TA > TA ) ).
thf(c_2Ebool_2EF_decl,type,
c_2Ebool_2EF: $o ).
thf(c_2Ebool_2ET_decl,type,
c_2Ebool_2ET: $o ).
thf(c_2Eextreal_2Eextreal__le_decl,type,
c_2Eextreal_2Eextreal__le: tyop_2Eextreal_2Eextreal > tyop_2Eextreal_2Eextreal > $o ).
thf(c_2Eextreal_2Eextreal__max_decl,type,
c_2Eextreal_2Eextreal__max: tyop_2Eextreal_2Eextreal > tyop_2Eextreal_2Eextreal > tyop_2Eextreal_2Eextreal ).
thf(sk1_decl,type,
sk1: tyop_2Eextreal_2Eextreal ).
thf(sk2_decl,type,
sk2: tyop_2Eextreal_2Eextreal ).
thf(sk3_decl,type,
sk3: tyop_2Eextreal_2Eextreal ).
thf(sk1_def,definition,
( sk1
= ( @+[A: tyop_2Eextreal_2Eextreal] :
~ ! [B: tyop_2Eextreal_2Eextreal,C: tyop_2Eextreal_2Eextreal] :
( ( c_2Eextreal_2Eextreal__le @ ( c_2Eextreal_2Eextreal__max @ B @ C ) @ A )
= ( ( c_2Eextreal_2Eextreal__le @ B @ A )
& ( c_2Eextreal_2Eextreal__le @ C @ A ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: tyop_2Eextreal_2Eextreal] :
~ ! [B: tyop_2Eextreal_2Eextreal] :
( ( c_2Eextreal_2Eextreal__le @ ( c_2Eextreal_2Eextreal__max @ A @ B ) @ sk1 )
= ( ( c_2Eextreal_2Eextreal__le @ A @ sk1 )
& ( c_2Eextreal_2Eextreal__le @ B @ sk1 ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: tyop_2Eextreal_2Eextreal] :
( ( c_2Eextreal_2Eextreal__le @ ( c_2Eextreal_2Eextreal__max @ sk2 @ A ) @ sk1 )
!= ( ( c_2Eextreal_2Eextreal__le @ sk2 @ sk1 )
& ( c_2Eextreal_2Eextreal__le @ A @ sk1 ) ) ) ) ) ).
thf(16,axiom,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal] :
( ( c_2Eextreal_2Eextreal__le @ A @ B )
| ( c_2Eextreal_2Eextreal__le @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextreal_2Ele__total) ).
thf(102,plain,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal] :
( ( c_2Eextreal_2Eextreal__le @ A @ B )
| ( c_2Eextreal_2Eextreal__le @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(103,plain,
! [B: tyop_2Eextreal_2Eextreal,A: tyop_2Eextreal_2Eextreal] :
( ( c_2Eextreal_2Eextreal__le @ A @ B )
| ( c_2Eextreal_2Eextreal__le @ B @ A ) ),
inference(cnf,[status(esa)],[102]) ).
thf(14,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2ET @ A @ B )
= A )
& ( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2EF @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2ECOND__CLAUSES) ).
thf(94,plain,
! [TA: $tType,A: TA,B: TA] :
( ( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2ET @ A @ B )
= A )
& ( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2EF @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(95,plain,
! [TA: $tType,B: TA,A: TA] :
( ( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2ET @ A @ B )
= A )
& ( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2EF @ A @ B )
= B ) ),
inference(cnf,[status(esa)],[94]) ).
thf(97,plain,
! [TA: $tType,B: TA,A: TA] :
( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2EF @ A @ B )
= B ),
inference(cnfConj,[status(thm)],[95]) ).
thf(99,plain,
! [TA: $tType,B: TA,A: TA] :
( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2EF @ A @ B )
= B ),
inference(lifteq,[status(thm)],[97]) ).
thf(3,axiom,
! [A: $o] :
( ( A
=> c_2Ebool_2EF )
=> ~ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EIMP__F) ).
thf(21,plain,
! [A: $o] :
( ( A
=> c_2Ebool_2EF )
=> ~ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(22,plain,
( ( $true
=> c_2Ebool_2EF )
=> ~ $true ),
inference(instance,[status(thm)],[21]) ).
thf(23,plain,
~ c_2Ebool_2EF,
inference(simp,[status(thm)],[22]) ).
thf(180,plain,
! [TA: $tType,B: TA,A: TA] :
( ( c_2Ebool_2ECOND @ TA @ $false @ A @ B )
= B ),
inference(rewrite,[status(thm)],[99,23]) ).
thf(1,conjecture,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal,C: tyop_2Eextreal_2Eextreal] :
( ( c_2Eextreal_2Eextreal__le @ ( c_2Eextreal_2Eextreal__max @ B @ C ) @ A )
= ( ( c_2Eextreal_2Eextreal__le @ B @ A )
& ( c_2Eextreal_2Eextreal__le @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextreal_2Emax__le) ).
thf(2,negated_conjecture,
~ ! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal,C: tyop_2Eextreal_2Eextreal] :
( ( c_2Eextreal_2Eextreal__le @ ( c_2Eextreal_2Eextreal__max @ B @ C ) @ A )
= ( ( c_2Eextreal_2Eextreal__le @ B @ A )
& ( c_2Eextreal_2Eextreal__le @ C @ A ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(18,plain,
~ ! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal,C: tyop_2Eextreal_2Eextreal] :
( ( c_2Eextreal_2Eextreal__le @ ( c_2Eextreal_2Eextreal__max @ B @ C ) @ A )
= ( ( c_2Eextreal_2Eextreal__le @ B @ A )
& ( c_2Eextreal_2Eextreal__le @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(19,plain,
( ( c_2Eextreal_2Eextreal__le @ ( c_2Eextreal_2Eextreal__max @ sk2 @ sk3 ) @ sk1 )
!= ( ( c_2Eextreal_2Eextreal__le @ sk2 @ sk1 )
& ( c_2Eextreal_2Eextreal__le @ sk3 @ sk1 ) ) ),
inference(cnf,[status(esa)],[18]) ).
thf(20,plain,
( ( c_2Eextreal_2Eextreal__le @ ( c_2Eextreal_2Eextreal__max @ sk2 @ sk3 ) @ sk1 )
!= ( ( c_2Eextreal_2Eextreal__le @ sk2 @ sk1 )
& ( c_2Eextreal_2Eextreal__le @ sk3 @ sk1 ) ) ),
inference(lifteq,[status(thm)],[19]) ).
thf(113,plain,
( ( c_2Eextreal_2Eextreal__le @ ( c_2Eextreal_2Eextreal__max @ sk2 @ sk3 ) @ sk1 )
| ( ( c_2Eextreal_2Eextreal__le @ sk2 @ sk1 )
& ( c_2Eextreal_2Eextreal__le @ sk3 @ sk1 ) ) ),
inference(bool_ext,[status(thm)],[20]) ).
thf(115,plain,
( ( ( c_2Eextreal_2Eextreal__le @ ( c_2Eextreal_2Eextreal__max @ sk2 @ sk3 ) @ sk1 )
| ( c_2Eextreal_2Eextreal__le @ sk2 @ sk1 ) )
& ( ( c_2Eextreal_2Eextreal__le @ ( c_2Eextreal_2Eextreal__max @ sk2 @ sk3 ) @ sk1 )
| ( c_2Eextreal_2Eextreal__le @ sk3 @ sk1 ) ) ),
inference(cnf,[status(esa)],[113]) ).
thf(116,plain,
( ( c_2Eextreal_2Eextreal__le @ ( c_2Eextreal_2Eextreal__max @ sk2 @ sk3 ) @ sk1 )
| ( c_2Eextreal_2Eextreal__le @ sk2 @ sk1 ) ),
inference(cnfConj,[status(thm)],[115]) ).
thf(120,plain,
( ( c_2Eextreal_2Eextreal__le @ sk2 @ sk1 )
| ( ( c_2Eextreal_2Eextreal__le @ ( c_2Eextreal_2Eextreal__max @ sk2 @ sk3 ) @ sk1 )
!= ( c_2Eextreal_2Eextreal__le @ sk2 @ sk1 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[116]) ).
thf(122,plain,
( ( c_2Eextreal_2Eextreal__le @ sk2 @ sk1 )
| ( ( c_2Eextreal_2Eextreal__max @ sk2 @ sk3 )
!= sk2 )
| ( sk1 != sk1 ) ),
inference(simp,[status(thm)],[120]) ).
thf(124,plain,
( ( c_2Eextreal_2Eextreal__le @ sk2 @ sk1 )
| ( ( c_2Eextreal_2Eextreal__max @ sk2 @ sk3 )
!= sk2 ) ),
inference(simp,[status(thm)],[122]) ).
thf(17,axiom,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal] :
( ( c_2Eextreal_2Eextreal__max @ A @ B )
= ( c_2Ebool_2ECOND @ tyop_2Eextreal_2Eextreal @ ( c_2Eextreal_2Eextreal__le @ A @ B ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextreal_2Eextreal__max__def) ).
thf(104,plain,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal] :
( ( c_2Eextreal_2Eextreal__max @ A @ B )
= ( c_2Ebool_2ECOND @ tyop_2Eextreal_2Eextreal @ ( c_2Eextreal_2Eextreal__le @ A @ B ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(105,plain,
! [B: tyop_2Eextreal_2Eextreal,A: tyop_2Eextreal_2Eextreal] :
( ( c_2Eextreal_2Eextreal__max @ A @ B )
= ( c_2Ebool_2ECOND @ tyop_2Eextreal_2Eextreal @ ( c_2Eextreal_2Eextreal__le @ A @ B ) @ B @ A ) ),
inference(cnf,[status(esa)],[104]) ).
thf(106,plain,
! [B: tyop_2Eextreal_2Eextreal,A: tyop_2Eextreal_2Eextreal] :
( ( c_2Eextreal_2Eextreal__max @ A @ B )
= ( c_2Ebool_2ECOND @ tyop_2Eextreal_2Eextreal @ ( c_2Eextreal_2Eextreal__le @ A @ B ) @ B @ A ) ),
inference(lifteq,[status(thm)],[105]) ).
thf(189,plain,
( ( c_2Eextreal_2Eextreal__le @ sk2 @ sk1 )
| ( ( c_2Ebool_2ECOND @ tyop_2Eextreal_2Eextreal @ ( c_2Eextreal_2Eextreal__le @ sk2 @ sk3 ) @ sk3 @ sk2 )
!= sk2 ) ),
inference(rewrite,[status(thm)],[124,106]) ).
thf(112,plain,
( ~ ( c_2Eextreal_2Eextreal__le @ ( c_2Eextreal_2Eextreal__max @ sk2 @ sk3 ) @ sk1 )
| ~ ( ( c_2Eextreal_2Eextreal__le @ sk2 @ sk1 )
& ( c_2Eextreal_2Eextreal__le @ sk3 @ sk1 ) ) ),
inference(bool_ext,[status(thm)],[20]) ).
thf(114,plain,
( ~ ( c_2Eextreal_2Eextreal__le @ ( c_2Eextreal_2Eextreal__max @ sk2 @ sk3 ) @ sk1 )
| ~ ( c_2Eextreal_2Eextreal__le @ sk2 @ sk1 )
| ~ ( c_2Eextreal_2Eextreal__le @ sk3 @ sk1 ) ),
inference(cnf,[status(esa)],[112]) ).
thf(139,plain,
( ~ ( c_2Eextreal_2Eextreal__le @ sk2 @ sk1 )
| ~ ( c_2Eextreal_2Eextreal__le @ sk3 @ sk1 )
| ( ( c_2Eextreal_2Eextreal__le @ ( c_2Eextreal_2Eextreal__max @ sk2 @ sk3 ) @ sk1 )
!= ( c_2Eextreal_2Eextreal__le @ sk2 @ sk1 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[114]) ).
thf(144,plain,
( ~ ( c_2Eextreal_2Eextreal__le @ sk2 @ sk1 )
| ~ ( c_2Eextreal_2Eextreal__le @ sk3 @ sk1 )
| ( ( c_2Eextreal_2Eextreal__max @ sk2 @ sk3 )
!= sk2 )
| ( sk1 != sk1 ) ),
inference(simp,[status(thm)],[139]) ).
thf(146,plain,
( ~ ( c_2Eextreal_2Eextreal__le @ sk2 @ sk1 )
| ~ ( c_2Eextreal_2Eextreal__le @ sk3 @ sk1 )
| ( ( c_2Eextreal_2Eextreal__max @ sk2 @ sk3 )
!= sk2 ) ),
inference(simp,[status(thm)],[144]) ).
thf(190,plain,
( ~ ( c_2Eextreal_2Eextreal__le @ sk2 @ sk1 )
| ~ ( c_2Eextreal_2Eextreal__le @ sk3 @ sk1 )
| ( ( c_2Ebool_2ECOND @ tyop_2Eextreal_2Eextreal @ ( c_2Eextreal_2Eextreal__le @ sk2 @ sk3 ) @ sk3 @ sk2 )
!= sk2 ) ),
inference(rewrite,[status(thm)],[146,106]) ).
thf(2546,plain,
( ( ( c_2Ebool_2ECOND @ tyop_2Eextreal_2Eextreal @ ( c_2Eextreal_2Eextreal__le @ sk2 @ sk3 ) @ sk3 @ sk2 )
!= sk2 )
| ~ $true
| ~ ( c_2Eextreal_2Eextreal__le @ sk3 @ sk1 )
| ( ( c_2Ebool_2ECOND @ tyop_2Eextreal_2Eextreal @ ( c_2Eextreal_2Eextreal__le @ sk2 @ sk3 ) @ sk3 @ sk2 )
!= sk2 )
| ( ( c_2Eextreal_2Eextreal__le @ sk2 @ sk1 )
!= ( c_2Eextreal_2Eextreal__le @ sk2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[189,190]) ).
thf(2547,plain,
( ( ( c_2Ebool_2ECOND @ tyop_2Eextreal_2Eextreal @ ( c_2Eextreal_2Eextreal__le @ sk2 @ sk3 ) @ sk3 @ sk2 )
!= sk2 )
| ~ ( c_2Eextreal_2Eextreal__le @ sk3 @ sk1 )
| ( ( c_2Eextreal_2Eextreal__le @ sk2 @ sk1 )
!= ( c_2Eextreal_2Eextreal__le @ sk2 @ sk1 ) ) ),
inference(simp,[status(thm)],[2546]) ).
thf(2548,plain,
( ( ( c_2Ebool_2ECOND @ tyop_2Eextreal_2Eextreal @ ( c_2Eextreal_2Eextreal__le @ sk2 @ sk3 ) @ sk3 @ sk2 )
!= sk2 )
| ~ ( c_2Eextreal_2Eextreal__le @ sk3 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[2547:[]]) ).
thf(3199,plain,
! [B: tyop_2Eextreal_2Eextreal,A: tyop_2Eextreal_2Eextreal] :
( ( B != sk2 )
| ~ ( c_2Eextreal_2Eextreal__le @ sk3 @ sk1 )
| ( ( c_2Ebool_2ECOND @ tyop_2Eextreal_2Eextreal @ $false @ A @ B )
!= ( c_2Ebool_2ECOND @ tyop_2Eextreal_2Eextreal @ ( c_2Eextreal_2Eextreal__le @ sk2 @ sk3 ) @ sk3 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[180,2548]) ).
thf(3231,plain,
! [A: tyop_2Eextreal_2Eextreal] :
( ~ ( c_2Eextreal_2Eextreal__le @ sk3 @ sk1 )
| ( c_2Eextreal_2Eextreal__le @ sk2 @ sk3 )
| ( A != sk3 )
| ( sk2 != sk2 ) ),
inference(simp,[status(thm)],[3199]) ).
thf(3252,plain,
( ~ ( c_2Eextreal_2Eextreal__le @ sk3 @ sk1 )
| ( c_2Eextreal_2Eextreal__le @ sk2 @ sk3 ) ),
inference(simp,[status(thm)],[3231]) ).
thf(3290,plain,
! [B: tyop_2Eextreal_2Eextreal,A: tyop_2Eextreal_2Eextreal] :
( ( c_2Eextreal_2Eextreal__le @ B @ A )
| ~ $true
| ( c_2Eextreal_2Eextreal__le @ sk2 @ sk3 )
| ( ( c_2Eextreal_2Eextreal__le @ A @ B )
!= ( c_2Eextreal_2Eextreal__le @ sk3 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[103,3252]) ).
thf(3291,plain,
! [B: tyop_2Eextreal_2Eextreal,A: tyop_2Eextreal_2Eextreal] :
( ( c_2Eextreal_2Eextreal__le @ B @ A )
| ( c_2Eextreal_2Eextreal__le @ sk2 @ sk3 )
| ( ( c_2Eextreal_2Eextreal__le @ A @ B )
!= ( c_2Eextreal_2Eextreal__le @ sk3 @ sk1 ) ) ),
inference(simp,[status(thm)],[3290]) ).
thf(3292,plain,
( ( c_2Eextreal_2Eextreal__le @ sk1 @ sk3 )
| ( c_2Eextreal_2Eextreal__le @ sk2 @ sk3 ) ),
inference(pattern_uni,[status(thm)],[3291:[bind(A,$thf( sk3 )),bind(B,$thf( sk1 ))]]) ).
thf(96,plain,
! [TA: $tType,B: TA,A: TA] :
( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2ET @ A @ B )
= A ),
inference(cnfConj,[status(thm)],[95]) ).
thf(98,plain,
! [TA: $tType,B: TA,A: TA] :
( ( c_2Ebool_2ECOND @ TA @ c_2Ebool_2ET @ A @ B )
= A ),
inference(lifteq,[status(thm)],[96]) ).
thf(8,axiom,
! [A: $o] :
( ( ( c_2Ebool_2ET
=> A )
= A )
& ( ( A
=> c_2Ebool_2ET )
= c_2Ebool_2ET )
& ( ( c_2Ebool_2EF
=> A )
= c_2Ebool_2ET )
& ( ( A
=> A )
= c_2Ebool_2ET )
& ( ( A
=> c_2Ebool_2EF )
= ( ~ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EIMP__CLAUSES) ).
thf(51,plain,
! [A: $o] :
( ( ( c_2Ebool_2ET
=> A )
= A )
& ( ( A
=> c_2Ebool_2ET )
= c_2Ebool_2ET )
& ( ( c_2Ebool_2EF
=> A )
= c_2Ebool_2ET )
& c_2Ebool_2ET
& ( ( A
=> c_2Ebool_2EF )
= ( ~ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(52,plain,
( ( ( c_2Ebool_2ET
=> $true )
= $true )
& ( ( $true
=> c_2Ebool_2ET )
= c_2Ebool_2ET )
& ( ( c_2Ebool_2EF
=> $true )
= c_2Ebool_2ET )
& c_2Ebool_2ET
& ( ( $true
=> c_2Ebool_2EF )
= ( ~ $true ) ) ),
inference(instance,[status(thm)],[51]) ).
thf(53,plain,
( c_2Ebool_2ET
& c_2Ebool_2ET
& ~ c_2Ebool_2EF ),
inference(simp,[status(thm)],[52]) ).
thf(56,plain,
( c_2Ebool_2ET
& c_2Ebool_2ET
& ~ c_2Ebool_2EF ),
inference(cnf,[status(esa)],[53]) ).
thf(57,plain,
c_2Ebool_2ET,
inference(cnfConj,[status(thm)],[56]) ).
thf(179,plain,
! [TA: $tType,B: TA,A: TA] :
( ( c_2Ebool_2ECOND @ TA @ $true @ A @ B )
= A ),
inference(rewrite,[status(thm)],[98,57]) ).
thf(520,plain,
! [B: tyop_2Eextreal_2Eextreal,A: tyop_2Eextreal_2Eextreal] :
( ( c_2Eextreal_2Eextreal__le @ sk2 @ sk1 )
| ( B != sk2 )
| ( ( c_2Ebool_2ECOND @ tyop_2Eextreal_2Eextreal @ $false @ A @ B )
!= ( c_2Ebool_2ECOND @ tyop_2Eextreal_2Eextreal @ ( c_2Eextreal_2Eextreal__le @ sk2 @ sk3 ) @ sk3 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[180,189]) ).
thf(557,plain,
! [A: tyop_2Eextreal_2Eextreal] :
( ( c_2Eextreal_2Eextreal__le @ sk2 @ sk1 )
| ( c_2Eextreal_2Eextreal__le @ sk2 @ sk3 )
| ( A != sk3 )
| ( sk2 != sk2 ) ),
inference(simp,[status(thm)],[520]) ).
thf(574,plain,
( ( c_2Eextreal_2Eextreal__le @ sk2 @ sk1 )
| ( c_2Eextreal_2Eextreal__le @ sk2 @ sk3 ) ),
inference(simp,[status(thm)],[557]) ).
thf(117,plain,
( ( c_2Eextreal_2Eextreal__le @ ( c_2Eextreal_2Eextreal__max @ sk2 @ sk3 ) @ sk1 )
| ( c_2Eextreal_2Eextreal__le @ sk3 @ sk1 ) ),
inference(cnfConj,[status(thm)],[115]) ).
thf(170,plain,
( ( c_2Eextreal_2Eextreal__le @ sk3 @ sk1 )
| ( ( c_2Eextreal_2Eextreal__le @ ( c_2Eextreal_2Eextreal__max @ sk2 @ sk3 ) @ sk1 )
!= ( c_2Eextreal_2Eextreal__le @ sk3 @ sk1 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[117]) ).
thf(172,plain,
( ( c_2Eextreal_2Eextreal__le @ sk3 @ sk1 )
| ( ( c_2Eextreal_2Eextreal__max @ sk2 @ sk3 )
!= sk3 )
| ( sk1 != sk1 ) ),
inference(simp,[status(thm)],[170]) ).
thf(176,plain,
( ( c_2Eextreal_2Eextreal__le @ sk3 @ sk1 )
| ( ( c_2Eextreal_2Eextreal__max @ sk2 @ sk3 )
!= sk3 ) ),
inference(simp,[status(thm)],[172]) ).
thf(205,plain,
( ( c_2Eextreal_2Eextreal__le @ sk3 @ sk1 )
| ( ( c_2Ebool_2ECOND @ tyop_2Eextreal_2Eextreal @ ( c_2Eextreal_2Eextreal__le @ sk2 @ sk3 ) @ sk3 @ sk2 )
!= sk3 ) ),
inference(rewrite,[status(thm)],[176,106]) ).
thf(15,axiom,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal,C: tyop_2Eextreal_2Eextreal] :
( ( ( c_2Eextreal_2Eextreal__le @ A @ B )
& ( c_2Eextreal_2Eextreal__le @ B @ C ) )
=> ( c_2Eextreal_2Eextreal__le @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eextreal_2Ele__trans) ).
thf(100,plain,
! [A: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal,C: tyop_2Eextreal_2Eextreal] :
( ( ( c_2Eextreal_2Eextreal__le @ A @ B )
& ( c_2Eextreal_2Eextreal__le @ B @ C ) )
=> ( c_2Eextreal_2Eextreal__le @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(101,plain,
! [C: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal,A: tyop_2Eextreal_2Eextreal] :
( ~ ( c_2Eextreal_2Eextreal__le @ A @ B )
| ~ ( c_2Eextreal_2Eextreal__le @ B @ C )
| ( c_2Eextreal_2Eextreal__le @ A @ C ) ),
inference(cnf,[status(esa)],[100]) ).
thf(379,plain,
! [C: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal,A: tyop_2Eextreal_2Eextreal] :
( ( ( c_2Ebool_2ECOND @ tyop_2Eextreal_2Eextreal @ ( c_2Eextreal_2Eextreal__le @ sk2 @ sk3 ) @ sk3 @ sk2 )
!= sk3 )
| ~ ( c_2Eextreal_2Eextreal__le @ A @ B )
| ~ $true
| ( c_2Eextreal_2Eextreal__le @ A @ C )
| ( ( c_2Eextreal_2Eextreal__le @ sk3 @ sk1 )
!= ( c_2Eextreal_2Eextreal__le @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[205,101]) ).
thf(380,plain,
! [C: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal,A: tyop_2Eextreal_2Eextreal] :
( ( ( c_2Ebool_2ECOND @ tyop_2Eextreal_2Eextreal @ ( c_2Eextreal_2Eextreal__le @ sk2 @ sk3 ) @ sk3 @ sk2 )
!= sk3 )
| ~ ( c_2Eextreal_2Eextreal__le @ A @ B )
| ( c_2Eextreal_2Eextreal__le @ A @ C )
| ( ( c_2Eextreal_2Eextreal__le @ sk3 @ sk1 )
!= ( c_2Eextreal_2Eextreal__le @ B @ C ) ) ),
inference(simp,[status(thm)],[379]) ).
thf(381,plain,
! [A: tyop_2Eextreal_2Eextreal] :
( ( ( c_2Ebool_2ECOND @ tyop_2Eextreal_2Eextreal @ ( c_2Eextreal_2Eextreal__le @ sk2 @ sk3 ) @ sk3 @ sk2 )
!= sk3 )
| ~ ( c_2Eextreal_2Eextreal__le @ A @ sk3 )
| ( c_2Eextreal_2Eextreal__le @ A @ sk1 ) ),
inference(pattern_uni,[status(thm)],[380:[bind(A,$thf( A )),bind(B,$thf( sk3 )),bind(C,$thf( sk1 ))]]) ).
thf(14898,plain,
! [A: tyop_2Eextreal_2Eextreal] :
( ( c_2Eextreal_2Eextreal__le @ sk2 @ sk1 )
| ( ( c_2Ebool_2ECOND @ tyop_2Eextreal_2Eextreal @ ( c_2Eextreal_2Eextreal__le @ sk2 @ sk3 ) @ sk3 @ sk2 )
!= sk3 )
| ~ $true
| ( c_2Eextreal_2Eextreal__le @ A @ sk1 )
| ( ( c_2Eextreal_2Eextreal__le @ sk2 @ sk3 )
!= ( c_2Eextreal_2Eextreal__le @ A @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[574,381]) ).
thf(14899,plain,
! [A: tyop_2Eextreal_2Eextreal] :
( ( c_2Eextreal_2Eextreal__le @ sk2 @ sk1 )
| ( ( c_2Ebool_2ECOND @ tyop_2Eextreal_2Eextreal @ ( c_2Eextreal_2Eextreal__le @ sk2 @ sk3 ) @ sk3 @ sk2 )
!= sk3 )
| ( c_2Eextreal_2Eextreal__le @ A @ sk1 )
| ( ( c_2Eextreal_2Eextreal__le @ sk2 @ sk3 )
!= ( c_2Eextreal_2Eextreal__le @ A @ sk3 ) ) ),
inference(simp,[status(thm)],[14898]) ).
thf(14900,plain,
( ( c_2Eextreal_2Eextreal__le @ sk2 @ sk1 )
| ( ( c_2Ebool_2ECOND @ tyop_2Eextreal_2Eextreal @ ( c_2Eextreal_2Eextreal__le @ sk2 @ sk3 ) @ sk3 @ sk2 )
!= sk3 )
| ( c_2Eextreal_2Eextreal__le @ sk2 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[14899:[bind(A,$thf( sk2 ))]]) ).
thf(15053,plain,
( ( c_2Eextreal_2Eextreal__le @ sk2 @ sk1 )
| ( ( c_2Ebool_2ECOND @ tyop_2Eextreal_2Eextreal @ ( c_2Eextreal_2Eextreal__le @ sk2 @ sk3 ) @ sk3 @ sk2 )
!= sk3 ) ),
inference(simp,[status(thm)],[14900]) ).
thf(140,plain,
( ~ ( c_2Eextreal_2Eextreal__le @ sk2 @ sk1 )
| ~ ( c_2Eextreal_2Eextreal__le @ sk3 @ sk1 )
| ( ( c_2Eextreal_2Eextreal__le @ ( c_2Eextreal_2Eextreal__max @ sk2 @ sk3 ) @ sk1 )
!= ( c_2Eextreal_2Eextreal__le @ sk3 @ sk1 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[114]) ).
thf(142,plain,
( ~ ( c_2Eextreal_2Eextreal__le @ sk2 @ sk1 )
| ~ ( c_2Eextreal_2Eextreal__le @ sk3 @ sk1 )
| ( ( c_2Eextreal_2Eextreal__max @ sk2 @ sk3 )
!= sk3 )
| ( sk1 != sk1 ) ),
inference(simp,[status(thm)],[140]) ).
thf(148,plain,
( ~ ( c_2Eextreal_2Eextreal__le @ sk2 @ sk1 )
| ~ ( c_2Eextreal_2Eextreal__le @ sk3 @ sk1 )
| ( ( c_2Eextreal_2Eextreal__max @ sk2 @ sk3 )
!= sk3 ) ),
inference(simp,[status(thm)],[142]) ).
thf(223,plain,
( ~ ( c_2Eextreal_2Eextreal__le @ sk2 @ sk1 )
| ~ ( c_2Eextreal_2Eextreal__le @ sk3 @ sk1 )
| ( ( c_2Ebool_2ECOND @ tyop_2Eextreal_2Eextreal @ ( c_2Eextreal_2Eextreal__le @ sk2 @ sk3 ) @ sk3 @ sk2 )
!= sk3 ) ),
inference(rewrite,[status(thm)],[148,106]) ).
thf(226,plain,
( ( ( c_2Ebool_2ECOND @ tyop_2Eextreal_2Eextreal @ ( c_2Eextreal_2Eextreal__le @ sk2 @ sk3 ) @ sk3 @ sk2 )
!= sk3 )
| ~ ( c_2Eextreal_2Eextreal__le @ sk2 @ sk1 )
| ~ $true
| ( ( c_2Ebool_2ECOND @ tyop_2Eextreal_2Eextreal @ ( c_2Eextreal_2Eextreal__le @ sk2 @ sk3 ) @ sk3 @ sk2 )
!= sk3 )
| ( ( c_2Eextreal_2Eextreal__le @ sk3 @ sk1 )
!= ( c_2Eextreal_2Eextreal__le @ sk3 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[205,223]) ).
thf(227,plain,
( ( ( c_2Ebool_2ECOND @ tyop_2Eextreal_2Eextreal @ ( c_2Eextreal_2Eextreal__le @ sk2 @ sk3 ) @ sk3 @ sk2 )
!= sk3 )
| ~ ( c_2Eextreal_2Eextreal__le @ sk2 @ sk1 )
| ( ( c_2Eextreal_2Eextreal__le @ sk3 @ sk1 )
!= ( c_2Eextreal_2Eextreal__le @ sk3 @ sk1 ) ) ),
inference(simp,[status(thm)],[226]) ).
thf(228,plain,
( ( ( c_2Ebool_2ECOND @ tyop_2Eextreal_2Eextreal @ ( c_2Eextreal_2Eextreal__le @ sk2 @ sk3 ) @ sk3 @ sk2 )
!= sk3 )
| ~ ( c_2Eextreal_2Eextreal__le @ sk2 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[227:[]]) ).
thf(15114,plain,
( ( ( c_2Ebool_2ECOND @ tyop_2Eextreal_2Eextreal @ ( c_2Eextreal_2Eextreal__le @ sk2 @ sk3 ) @ sk3 @ sk2 )
!= sk3 )
| ( ( c_2Ebool_2ECOND @ tyop_2Eextreal_2Eextreal @ ( c_2Eextreal_2Eextreal__le @ sk2 @ sk3 ) @ sk3 @ sk2 )
!= sk3 )
| ~ $true
| ( ( c_2Eextreal_2Eextreal__le @ sk2 @ sk1 )
!= ( c_2Eextreal_2Eextreal__le @ sk2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[15053,228]) ).
thf(15115,plain,
( ( ( c_2Ebool_2ECOND @ tyop_2Eextreal_2Eextreal @ ( c_2Eextreal_2Eextreal__le @ sk2 @ sk3 ) @ sk3 @ sk2 )
!= sk3 )
| ( ( c_2Eextreal_2Eextreal__le @ sk2 @ sk1 )
!= ( c_2Eextreal_2Eextreal__le @ sk2 @ sk1 ) ) ),
inference(simp,[status(thm)],[15114]) ).
thf(15116,plain,
( ( c_2Ebool_2ECOND @ tyop_2Eextreal_2Eextreal @ ( c_2Eextreal_2Eextreal__le @ sk2 @ sk3 ) @ sk3 @ sk2 )
!= sk3 ),
inference(pattern_uni,[status(thm)],[15115:[]]) ).
thf(15530,plain,
! [B: tyop_2Eextreal_2Eextreal,A: tyop_2Eextreal_2Eextreal] :
( ( A != sk3 )
| ( ( c_2Ebool_2ECOND @ tyop_2Eextreal_2Eextreal @ $true @ A @ B )
!= ( c_2Ebool_2ECOND @ tyop_2Eextreal_2Eextreal @ ( c_2Eextreal_2Eextreal__le @ sk2 @ sk3 ) @ sk3 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[179,15116]) ).
thf(15557,plain,
! [A: tyop_2Eextreal_2Eextreal] :
( ~ ( c_2Eextreal_2Eextreal__le @ sk2 @ sk3 )
| ( sk3 != sk3 )
| ( A != sk2 ) ),
inference(simp,[status(thm)],[15530]) ).
thf(15588,plain,
~ ( c_2Eextreal_2Eextreal__le @ sk2 @ sk3 ),
inference(simp,[status(thm)],[15557]) ).
thf(15612,plain,
( ( c_2Eextreal_2Eextreal__le @ sk1 @ sk3 )
| $false ),
inference(rewrite,[status(thm)],[3292,15588]) ).
thf(15613,plain,
c_2Eextreal_2Eextreal__le @ sk1 @ sk3,
inference(simp,[status(thm)],[15612]) ).
thf(210,plain,
! [B: tyop_2Eextreal_2Eextreal,A: tyop_2Eextreal_2Eextreal] :
( ( c_2Eextreal_2Eextreal__le @ sk3 @ sk1 )
| ( A != sk3 )
| ( ( c_2Ebool_2ECOND @ tyop_2Eextreal_2Eextreal @ $true @ A @ B )
!= ( c_2Ebool_2ECOND @ tyop_2Eextreal_2Eextreal @ ( c_2Eextreal_2Eextreal__le @ sk2 @ sk3 ) @ sk3 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[179,205]) ).
thf(217,plain,
! [A: tyop_2Eextreal_2Eextreal] :
( ( c_2Eextreal_2Eextreal__le @ sk3 @ sk1 )
| ~ ( c_2Eextreal_2Eextreal__le @ sk2 @ sk3 )
| ( sk3 != sk3 )
| ( A != sk2 ) ),
inference(simp,[status(thm)],[210]) ).
thf(222,plain,
( ( c_2Eextreal_2Eextreal__le @ sk3 @ sk1 )
| ~ ( c_2Eextreal_2Eextreal__le @ sk2 @ sk3 ) ),
inference(simp,[status(thm)],[217]) ).
thf(231,plain,
! [B: tyop_2Eextreal_2Eextreal,A: tyop_2Eextreal_2Eextreal] :
( ~ ( c_2Eextreal_2Eextreal__le @ sk2 @ sk1 )
| ~ ( c_2Eextreal_2Eextreal__le @ sk3 @ sk1 )
| ( A != sk3 )
| ( ( c_2Ebool_2ECOND @ tyop_2Eextreal_2Eextreal @ $true @ A @ B )
!= ( c_2Ebool_2ECOND @ tyop_2Eextreal_2Eextreal @ ( c_2Eextreal_2Eextreal__le @ sk2 @ sk3 ) @ sk3 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[179,223]) ).
thf(238,plain,
! [A: tyop_2Eextreal_2Eextreal] :
( ~ ( c_2Eextreal_2Eextreal__le @ sk2 @ sk1 )
| ~ ( c_2Eextreal_2Eextreal__le @ sk3 @ sk1 )
| ~ ( c_2Eextreal_2Eextreal__le @ sk2 @ sk3 )
| ( sk3 != sk3 )
| ( A != sk2 ) ),
inference(simp,[status(thm)],[231]) ).
thf(245,plain,
( ~ ( c_2Eextreal_2Eextreal__le @ sk2 @ sk1 )
| ~ ( c_2Eextreal_2Eextreal__le @ sk3 @ sk1 )
| ~ ( c_2Eextreal_2Eextreal__le @ sk2 @ sk3 ) ),
inference(simp,[status(thm)],[238]) ).
thf(318,plain,
( ~ ( c_2Eextreal_2Eextreal__le @ sk2 @ sk3 )
| ~ ( c_2Eextreal_2Eextreal__le @ sk2 @ sk1 )
| ~ $true
| ~ ( c_2Eextreal_2Eextreal__le @ sk2 @ sk3 )
| ( ( c_2Eextreal_2Eextreal__le @ sk3 @ sk1 )
!= ( c_2Eextreal_2Eextreal__le @ sk3 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[222,245]) ).
thf(319,plain,
( ~ ( c_2Eextreal_2Eextreal__le @ sk2 @ sk3 )
| ~ ( c_2Eextreal_2Eextreal__le @ sk2 @ sk1 )
| ( ( c_2Eextreal_2Eextreal__le @ sk3 @ sk1 )
!= ( c_2Eextreal_2Eextreal__le @ sk3 @ sk1 ) ) ),
inference(simp,[status(thm)],[318]) ).
thf(320,plain,
( ~ ( c_2Eextreal_2Eextreal__le @ sk2 @ sk3 )
| ~ ( c_2Eextreal_2Eextreal__le @ sk2 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[319:[]]) ).
thf(368,plain,
! [C: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal,A: tyop_2Eextreal_2Eextreal] :
( ~ ( c_2Eextreal_2Eextreal__le @ A @ B )
| ~ ( c_2Eextreal_2Eextreal__le @ B @ C )
| ~ $true
| ~ ( c_2Eextreal_2Eextreal__le @ sk2 @ sk1 )
| ( ( c_2Eextreal_2Eextreal__le @ A @ C )
!= ( c_2Eextreal_2Eextreal__le @ sk2 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[101,320]) ).
thf(369,plain,
! [C: tyop_2Eextreal_2Eextreal,B: tyop_2Eextreal_2Eextreal,A: tyop_2Eextreal_2Eextreal] :
( ~ ( c_2Eextreal_2Eextreal__le @ A @ B )
| ~ ( c_2Eextreal_2Eextreal__le @ B @ C )
| ~ ( c_2Eextreal_2Eextreal__le @ sk2 @ sk1 )
| ( ( c_2Eextreal_2Eextreal__le @ A @ C )
!= ( c_2Eextreal_2Eextreal__le @ sk2 @ sk3 ) ) ),
inference(simp,[status(thm)],[368]) ).
thf(370,plain,
! [A: tyop_2Eextreal_2Eextreal] :
( ~ ( c_2Eextreal_2Eextreal__le @ sk2 @ A )
| ~ ( c_2Eextreal_2Eextreal__le @ A @ sk3 )
| ~ ( c_2Eextreal_2Eextreal__le @ sk2 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[369:[bind(A,$thf( sk2 )),bind(B,$thf( B )),bind(C,$thf( sk3 ))]]) ).
thf(420,plain,
! [A: tyop_2Eextreal_2Eextreal] :
( ~ ( c_2Eextreal_2Eextreal__le @ sk2 @ A )
| ~ ( c_2Eextreal_2Eextreal__le @ A @ sk3 )
| ~ ( c_2Eextreal_2Eextreal__le @ sk2 @ sk1 ) ),
inference(simp,[status(thm)],[370]) ).
thf(623,plain,
( ( c_2Eextreal_2Eextreal__le @ sk2 @ sk1 )
| ( ( c_2Eextreal_2Eextreal__le @ sk2 @ sk3 )
!= ( c_2Eextreal_2Eextreal__le @ sk2 @ sk1 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[574]) ).
thf(624,plain,
( ( c_2Eextreal_2Eextreal__le @ sk2 @ sk1 )
| ( ( c_2Eextreal_2Eextreal__le @ sk2 @ sk3 )
!= ( c_2Eextreal_2Eextreal__le @ sk2 @ sk1 ) ) ),
inference(simp,[status(thm)],[623]) ).
thf(15616,plain,
( ( c_2Eextreal_2Eextreal__le @ sk2 @ sk1 )
| ( c_2Eextreal_2Eextreal__le @ sk2 @ sk1 ) ),
inference(rewrite,[status(thm)],[624,15588]) ).
thf(15617,plain,
c_2Eextreal_2Eextreal__le @ sk2 @ sk1,
inference(simp,[status(thm)],[15616]) ).
thf(16892,plain,
! [A: tyop_2Eextreal_2Eextreal] :
( ~ ( c_2Eextreal_2Eextreal__le @ sk2 @ A )
| ~ ( c_2Eextreal_2Eextreal__le @ A @ sk3 )
| ~ $true ),
inference(rewrite,[status(thm)],[420,15617]) ).
thf(16893,plain,
! [A: tyop_2Eextreal_2Eextreal] :
( ~ ( c_2Eextreal_2Eextreal__le @ sk2 @ A )
| ~ ( c_2Eextreal_2Eextreal__le @ A @ sk3 ) ),
inference(simp,[status(thm)],[16892]) ).
thf(16936,plain,
! [A: tyop_2Eextreal_2Eextreal] :
( ~ ( c_2Eextreal_2Eextreal__le @ sk2 @ A )
| ~ $true
| ( ( c_2Eextreal_2Eextreal__le @ sk1 @ sk3 )
!= ( c_2Eextreal_2Eextreal__le @ A @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[15613,16893]) ).
thf(16937,plain,
! [A: tyop_2Eextreal_2Eextreal] :
( ~ ( c_2Eextreal_2Eextreal__le @ sk2 @ A )
| ( ( c_2Eextreal_2Eextreal__le @ sk1 @ sk3 )
!= ( c_2Eextreal_2Eextreal__le @ A @ sk3 ) ) ),
inference(simp,[status(thm)],[16936]) ).
thf(16938,plain,
~ ( c_2Eextreal_2Eextreal__le @ sk2 @ sk1 ),
inference(pattern_uni,[status(thm)],[16937:[bind(A,$thf( sk1 ))]]) ).
thf(16975,plain,
~ $true,
inference(rewrite,[status(thm)],[16938,15617]) ).
thf(16976,plain,
$false,
inference(simp,[status(thm)],[16975]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP021^3 : TPTP v9.3.1. Bugfixed v7.5.0.
% 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
% 0.11/0.22 % Computer : n013.cluster.edu
% 0.11/0.22 % Model : x86_64 x86_64
% 0.11/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.22 % Memory : 8046.5625MB
% 0.11/0.22 % OS : Linux 6.8.0-71-generic
% 0.11/0.22 % CPULimit : 300
% 0.11/0.22 % WCLimit : 300
% 0.11/0.22 % DateTime : Tue Sep 29 19:33:36 UTC 2026
% 0.11/0.22 % CPUTime :
% 0.11/0.22 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
% 1.03/0.80 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.49/1.04 % [INFO] Parsing done (239ms).
% 1.49/1.06 % [INFO] Running in sequential loop mode.
% 2.09/1.45 % [INFO] eprover registered as external prover.
% 2.09/1.46 % [INFO] Scanning for conjecture ...
% 2.28/1.56 % [INFO] Found a conjecture (or negated_conjecture) and 34 axioms. Running axiom selection ...
% 2.46/1.62 % [INFO] Axiom selection finished. Selected 15 axioms (removed 19 axioms).
% 2.46/1.65 % [INFO] Problem is higher-order (TPTP THF).
% 2.46/1.66 % [INFO] Type checking passed.
% 2.46/1.66 % [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 ...
% 36.48/8.01 % [INFO] Killing All external provers ...
% 36.48/8.02 % Time passed: 7648ms (effective reasoning time: 6950ms)
% 36.48/8.02 % 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)>
% 36.48/8.02 % Axioms used in derivation (6): thm_2Ebool_2EIMP__F, thm_2Eextreal_2Ele__trans, thm_2Ebool_2ECOND__CLAUSES, thm_2Ebool_2EIMP__CLAUSES, thm_2Eextreal_2Ele__total, thm_2Eextreal_2Eextreal__max__def
% 36.48/8.02 % No. of inferences in proof: 110
% 36.48/8.02 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 7648 ms resp. 6950 ms w/o parsing
% 37.29/8.08 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 37.29/8.08 % [INFO] Killing All external provers ...
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