TSTP Solution File: SYO546^1 by Leo-III---1.7.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : SYO546^1 : TPTP v8.2.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 08:57:20 EDT 2024
% Result : Theorem 21.87s 4.81s
% Output : Refutation 22.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 48
% Number of leaves : 23
% Syntax : Number of formulae : 237 ( 16 unt; 20 typ; 1 def)
% Number of atoms : 1761 ( 629 equ; 66 cnn)
% Maximal formula atoms : 16 ( 8 avg)
% Number of connectives : 1396 ( 446 ~; 586 |; 212 &; 151 @)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 20 usr; 20 con; 0-5 aty)
% Number of variables : 305 ( 268 ^ 35 !; 2 ?; 305 :)
% Comments :
%------------------------------------------------------------------------------
thf(eps_type,type,
eps: ( $i > $o ) > $i ).
thf(case_type,type,
case: ( $o > $o ) > $i > $i > $i > $i > $i ).
thf(case_def,definition,
( case
= ( ^ [A: $o > $o,B: $i,C: $i,D: $i,E: $i] :
( eps
@ ^ [F: $i] :
( ( ( A
= ( ^ [G: $o] : $false ) )
& ( F = B ) )
| ( ( A = (~) )
& ( F = C ) )
| ( ( A
= ( ^ [G: $o] : G ) )
& ( F = D ) )
| ( ( A
= ( ^ [G: $o] : $true ) )
& ( F = E ) ) ) ) ) ) ).
thf(f_type,type,
f: $o > $o ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $o ).
thf(sk3_type,type,
sk3: $o ).
thf(sk5_type,type,
sk5: $o ).
thf(sk6_type,type,
sk6: $o ).
thf(sk7_type,type,
sk7: $o ).
thf(sk8_type,type,
sk8: $o ).
thf(sk9_type,type,
sk9: $o ).
thf(sk10_type,type,
sk10: $o ).
thf(sk11_type,type,
sk11: $o ).
thf(sk12_type,type,
sk12: $o ).
thf(sk15_type,type,
sk15: $o ).
thf(sk16_type,type,
sk16: $o ).
thf(sk20_type,type,
sk20: $o ).
thf(sk21_type,type,
sk21: $o ).
thf(sk23_type,type,
sk23: $o ).
thf(sk26_type,type,
sk26: $o ).
thf(11,axiom,
? [A: ( $i > $o ) > $i] :
! [B: $i > $o] :
( ? [C: $i] : ( B @ C )
=> ( B @ ( A @ B ) ) ),
introduced(axiom_of_choice) ).
thf(12,plain,
! [A: $i] :
( ~ ( ( ( f
= ( ^ [B: $o] : $false ) )
& ( A = sk1 ) )
| ( ( f = (~) )
& ( A = sk1 ) )
| ( ( f
= ( ^ [B: $o] : B ) )
& ( A = sk1 ) )
| ( ( f
= ( ^ [B: $o] : $true ) )
& ( A = sk1 ) ) )
| ( ( f
= ( ^ [B: $o] : $false ) )
& ( ( eps
@ ^ [B: $i] :
( ( ( f
= ( ^ [C: $o] : $false ) )
& ( B = sk1 ) )
| ( ( f = (~) )
& ( B = sk1 ) )
| ( ( f
= ( ^ [C: $o] : C ) )
& ( B = sk1 ) )
| ( ( f
= ( ^ [C: $o] : $true ) )
& ( B = sk1 ) ) ) )
= sk1 ) )
| ( ( f = (~) )
& ( ( eps
@ ^ [B: $i] :
( ( ( f
= ( ^ [C: $o] : $false ) )
& ( B = sk1 ) )
| ( ( f = (~) )
& ( B = sk1 ) )
| ( ( f
= ( ^ [C: $o] : C ) )
& ( B = sk1 ) )
| ( ( f
= ( ^ [C: $o] : $true ) )
& ( B = sk1 ) ) ) )
= sk1 ) )
| ( ( f
= ( ^ [B: $o] : B ) )
& ( ( eps
@ ^ [B: $i] :
( ( ( f
= ( ^ [C: $o] : $false ) )
& ( B = sk1 ) )
| ( ( f = (~) )
& ( B = sk1 ) )
| ( ( f
= ( ^ [C: $o] : C ) )
& ( B = sk1 ) )
| ( ( f
= ( ^ [C: $o] : $true ) )
& ( B = sk1 ) ) ) )
= sk1 ) )
| ( ( f
= ( ^ [B: $o] : $true ) )
& ( ( eps
@ ^ [B: $i] :
( ( ( f
= ( ^ [C: $o] : $false ) )
& ( B = sk1 ) )
| ( ( f = (~) )
& ( B = sk1 ) )
| ( ( f
= ( ^ [C: $o] : C ) )
& ( B = sk1 ) )
| ( ( f
= ( ^ [C: $o] : $true ) )
& ( B = sk1 ) ) ) )
= sk1 ) ) ),
inference(choice,[status(esa)],[11]) ).
thf(31,plain,
! [A: $i] :
( ~ sk2
| ( ( eps
@ ^ [B: $i] :
( ( ( f
= ( ^ [C: $o] : $false ) )
& ( B = sk1 ) )
| ( ( f = (~) )
& ( B = sk1 ) )
| ( ( f
= ( ^ [C: $o] : C ) )
& ( B = sk1 ) )
| ( ( f
= ( ^ [C: $o] : $true ) )
& ( B = sk1 ) ) ) )
= sk1 )
| sk3
| ( f
!= ( ^ [B: $o] : B ) )
| ( A != sk1 ) ),
inference(cnf,[status(esa)],[12]) ).
thf(95,plain,
! [A: $i] :
( ( ( eps
@ ^ [B: $i] :
( ( ( f
= ( ^ [C: $o] : $false ) )
& ( B = sk1 ) )
| ( ( f = (~) )
& ( B = sk1 ) )
| ( ( f
= ( ^ [C: $o] : C ) )
& ( B = sk1 ) )
| ( ( f
= ( ^ [C: $o] : $true ) )
& ( B = sk1 ) ) ) )
= sk1 )
| ( f
!= ( ^ [B: $o] : B ) )
| ( A != sk1 )
| ~ sk2
| sk3 ),
inference(lifteq,[status(thm)],[31]) ).
thf(96,plain,
( ( ( eps
@ ^ [A: $i] :
( ( ( f
= ( ^ [B: $o] : $false ) )
& ( A = sk1 ) )
| ( ( f = (~) )
& ( A = sk1 ) )
| ( ( f
= ( ^ [B: $o] : B ) )
& ( A = sk1 ) )
| ( ( f
= ( ^ [B: $o] : $true ) )
& ( A = sk1 ) ) ) )
= sk1 )
| ( f
!= ( ^ [A: $o] : A ) )
| ~ sk2
| sk3 ),
inference(simp,[status(thm)],[95]) ).
thf(1,conjecture,
! [A: $i] :
( ( case @ f @ A @ A @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( case @ f @ A @ A @ A @ A )
= A ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(4,plain,
~ ! [A: $i] :
( ( eps
@ ^ [B: $i] :
( ( ( f
= ( ^ [C: $o] : $false ) )
& ( B = A ) )
| ( ( f = (~) )
& ( B = A ) )
| ( ( f
= ( ^ [C: $o] : C ) )
& ( B = A ) )
| ( ( f
= ( ^ [C: $o] : $true ) )
& ( B = A ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,plain,
( ( eps
@ ^ [A: $i] :
( ( ( f
= ( ^ [B: $o] : $false ) )
& ( A = sk1 ) )
| ( ( f = (~) )
& ( A = sk1 ) )
| ( ( f
= ( ^ [B: $o] : B ) )
& ( A = sk1 ) )
| ( ( f
= ( ^ [B: $o] : $true ) )
& ( A = sk1 ) ) ) )
!= sk1 ),
inference(cnf,[status(esa)],[4]) ).
thf(6,plain,
( ( eps
@ ^ [A: $i] :
( ( ( f
= ( ^ [B: $o] : $false ) )
& ( A = sk1 ) )
| ( ( f = (~) )
& ( A = sk1 ) )
| ( ( f
= ( ^ [B: $o] : B ) )
& ( A = sk1 ) )
| ( ( f
= ( ^ [B: $o] : $true ) )
& ( A = sk1 ) ) ) )
!= sk1 ),
inference(lifteq,[status(thm)],[5]) ).
thf(548,plain,
( ( f
!= ( ^ [A: $o] : A ) )
| ~ sk2
| sk3 ),
inference(simplifyReflect,[status(thm)],[96,6]) ).
thf(39,plain,
! [A: $i] :
( ( ( eps
@ ^ [B: $i] :
( ( ( f
= ( ^ [C: $o] : $false ) )
& ( B = sk1 ) )
| ( ( f = (~) )
& ( B = sk1 ) )
| ( ( f
= ( ^ [C: $o] : C ) )
& ( B = sk1 ) )
| ( ( f
= ( ^ [C: $o] : $true ) )
& ( B = sk1 ) ) ) )
= sk1 )
| sk2
| ( f
!= ( ^ [B: $o] : $false ) )
| ( A != sk1 ) ),
inference(cnf,[status(esa)],[12]) ).
thf(47,plain,
! [A: $i] :
( ( ( eps
@ ^ [B: $i] :
( ( ( f
= ( ^ [C: $o] : $false ) )
& ( B = sk1 ) )
| ( ( f = (~) )
& ( B = sk1 ) )
| ( ( f
= ( ^ [C: $o] : C ) )
& ( B = sk1 ) )
| ( ( f
= ( ^ [C: $o] : $true ) )
& ( B = sk1 ) ) ) )
= sk1 )
| ( f
!= ( ^ [B: $o] : $false ) )
| ( A != sk1 )
| sk2 ),
inference(lifteq,[status(thm)],[39]) ).
thf(48,plain,
( ( ( eps
@ ^ [A: $i] :
( ( ( f
= ( ^ [B: $o] : $false ) )
& ( A = sk1 ) )
| ( ( f = (~) )
& ( A = sk1 ) )
| ( ( f
= ( ^ [B: $o] : B ) )
& ( A = sk1 ) )
| ( ( f
= ( ^ [B: $o] : $true ) )
& ( A = sk1 ) ) ) )
= sk1 )
| ( f
!= ( ^ [A: $o] : $false ) )
| sk2 ),
inference(simp,[status(thm)],[47]) ).
thf(120,plain,
( ( f
!= ( ^ [A: $o] : $false ) )
| sk2 ),
inference(simplifyReflect,[status(thm)],[48,6]) ).
thf(121,plain,
( ( f @ sk9 )
| sk2 ),
inference(func_ext,[status(esa)],[120]) ).
thf(27,plain,
! [A: $i] :
( ( f
= ( ^ [B: $o] : $false ) )
| sk2
| ( f != (~) )
| ( A != sk1 ) ),
inference(cnf,[status(esa)],[12]) ).
thf(91,plain,
! [A: $i] :
( ( f
= ( ^ [B: $o] : $false ) )
| ( f != (~) )
| ( A != sk1 )
| sk2 ),
inference(lifteq,[status(thm)],[27]) ).
thf(92,plain,
( ( f
= ( ^ [A: $o] : $false ) )
| ( f != (~) )
| sk2 ),
inference(simp,[status(thm)],[91]) ).
thf(111,plain,
! [A: $o] :
( ~ ( f @ A )
| ( ( f @ sk6 )
!= ~ sk6 )
| sk2 ),
inference(func_ext,[status(esa)],[92]) ).
thf(487,plain,
! [A: $o] :
( sk2
| ( ( f @ sk6 )
!= ~ sk6 )
| ( ( f @ sk9 )
!= ( f @ A ) ) ),
inference(paramod_ordered,[status(thm)],[121,111]) ).
thf(488,plain,
( sk2
| ( ( f @ sk6 )
!= ~ sk6 ) ),
inference(pattern_uni,[status(thm)],[487:[bind(A,$thf( sk9 ))]]) ).
thf(518,plain,
( sk2
| sk6
| ( ( f @ sk9 )
!= ( f @ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[121,488]) ).
thf(526,plain,
( sk2
| sk6
| ( sk9 != sk6 ) ),
inference(simp,[status(thm)],[518]) ).
thf(532,plain,
( sk2
| sk6
| sk9
| sk6 ),
inference(bool_ext,[status(thm)],[526]) ).
thf(533,plain,
( sk2
| sk6
| sk9 ),
inference(simp,[status(thm)],[532]) ).
thf(41,plain,
! [A: $i] :
( ( f
= ( ^ [B: $o] : $false ) )
| sk2
| ( f
!= ( ^ [B: $o] : $true ) )
| ( A != sk1 ) ),
inference(cnf,[status(esa)],[12]) ).
thf(79,plain,
! [A: $i] :
( ( f
= ( ^ [B: $o] : $false ) )
| ( f
!= ( ^ [B: $o] : $true ) )
| ( A != sk1 )
| sk2 ),
inference(lifteq,[status(thm)],[41]) ).
thf(80,plain,
( ( f
= ( ^ [A: $o] : $false ) )
| ( f
!= ( ^ [A: $o] : $true ) )
| sk2 ),
inference(simp,[status(thm)],[79]) ).
thf(110,plain,
! [A: $o] :
( ~ ( f @ A )
| ~ ( f @ sk5 )
| sk2 ),
inference(func_ext,[status(esa)],[80]) ).
thf(190,plain,
! [A: $o] :
( sk2
| ~ ( f @ sk5 )
| ( ( f @ sk9 )
!= ( f @ A ) ) ),
inference(paramod_ordered,[status(thm)],[121,110]) ).
thf(191,plain,
( sk2
| ~ ( f @ sk5 ) ),
inference(pattern_uni,[status(thm)],[190:[bind(A,$thf( sk9 ))]]) ).
thf(208,plain,
( sk2
| ( ( f @ sk9 )
!= ( f @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[121,191]) ).
thf(210,plain,
( sk2
| ( sk9 != sk5 ) ),
inference(simp,[status(thm)],[208]) ).
thf(214,plain,
( sk2
| sk9
| sk5 ),
inference(bool_ext,[status(thm)],[210]) ).
thf(21,plain,
! [A: $i] :
( ( ( eps
@ ^ [B: $i] :
( ( ( f
= ( ^ [C: $o] : $false ) )
& ( B = sk1 ) )
| ( ( f = (~) )
& ( B = sk1 ) )
| ( ( f
= ( ^ [C: $o] : C ) )
& ( B = sk1 ) )
| ( ( f
= ( ^ [C: $o] : $true ) )
& ( B = sk1 ) ) ) )
= sk1 )
| sk2
| ( f
!= ( ^ [B: $o] : B ) )
| ( A != sk1 ) ),
inference(cnf,[status(esa)],[12]) ).
thf(69,plain,
! [A: $i] :
( ( ( eps
@ ^ [B: $i] :
( ( ( f
= ( ^ [C: $o] : $false ) )
& ( B = sk1 ) )
| ( ( f = (~) )
& ( B = sk1 ) )
| ( ( f
= ( ^ [C: $o] : C ) )
& ( B = sk1 ) )
| ( ( f
= ( ^ [C: $o] : $true ) )
& ( B = sk1 ) ) ) )
= sk1 )
| ( f
!= ( ^ [B: $o] : B ) )
| ( A != sk1 )
| sk2 ),
inference(lifteq,[status(thm)],[21]) ).
thf(70,plain,
( ( ( eps
@ ^ [A: $i] :
( ( ( f
= ( ^ [B: $o] : $false ) )
& ( A = sk1 ) )
| ( ( f = (~) )
& ( A = sk1 ) )
| ( ( f
= ( ^ [B: $o] : B ) )
& ( A = sk1 ) )
| ( ( f
= ( ^ [B: $o] : $true ) )
& ( A = sk1 ) ) ) )
= sk1 )
| ( f
!= ( ^ [A: $o] : A ) )
| sk2 ),
inference(simp,[status(thm)],[69]) ).
thf(116,plain,
( ( f
!= ( ^ [A: $o] : A ) )
| sk2 ),
inference(simplifyReflect,[status(thm)],[70,6]) ).
thf(117,plain,
( ( ( f @ sk8 )
!= sk8 )
| sk2 ),
inference(func_ext,[status(esa)],[116]) ).
thf(119,plain,
( sk2
| ( f @ sk8 )
| sk8 ),
inference(bool_ext,[status(thm)],[117]) ).
thf(28,plain,
! [A: $i] :
( ( ( eps
@ ^ [B: $i] :
( ( ( f
= ( ^ [C: $o] : $false ) )
& ( B = sk1 ) )
| ( ( f = (~) )
& ( B = sk1 ) )
| ( ( f
= ( ^ [C: $o] : C ) )
& ( B = sk1 ) )
| ( ( f
= ( ^ [C: $o] : $true ) )
& ( B = sk1 ) ) ) )
= sk1 )
| sk2
| ( f
!= ( ^ [B: $o] : $true ) )
| ( A != sk1 ) ),
inference(cnf,[status(esa)],[12]) ).
thf(73,plain,
! [A: $i] :
( ( ( eps
@ ^ [B: $i] :
( ( ( f
= ( ^ [C: $o] : $false ) )
& ( B = sk1 ) )
| ( ( f = (~) )
& ( B = sk1 ) )
| ( ( f
= ( ^ [C: $o] : C ) )
& ( B = sk1 ) )
| ( ( f
= ( ^ [C: $o] : $true ) )
& ( B = sk1 ) ) ) )
= sk1 )
| ( f
!= ( ^ [B: $o] : $true ) )
| ( A != sk1 )
| sk2 ),
inference(lifteq,[status(thm)],[28]) ).
thf(74,plain,
( ( ( eps
@ ^ [A: $i] :
( ( ( f
= ( ^ [B: $o] : $false ) )
& ( A = sk1 ) )
| ( ( f = (~) )
& ( A = sk1 ) )
| ( ( f
= ( ^ [B: $o] : B ) )
& ( A = sk1 ) )
| ( ( f
= ( ^ [B: $o] : $true ) )
& ( A = sk1 ) ) ) )
= sk1 )
| ( f
!= ( ^ [A: $o] : $true ) )
| sk2 ),
inference(simp,[status(thm)],[73]) ).
thf(139,plain,
( ( f
!= ( ^ [A: $o] : $true ) )
| sk2 ),
inference(simplifyReflect,[status(thm)],[74,6]) ).
thf(140,plain,
( ~ ( f @ sk11 )
| sk2 ),
inference(func_ext,[status(esa)],[139]) ).
thf(142,plain,
( sk2
| sk8
| ( ( f @ sk11 )
!= ( f @ sk8 ) ) ),
inference(paramod_ordered,[status(thm)],[119,140]) ).
thf(144,plain,
( sk2
| sk8
| ( sk11 != sk8 ) ),
inference(simp,[status(thm)],[142]) ).
thf(165,plain,
( sk2
| sk8
| sk11
| sk8 ),
inference(bool_ext,[status(thm)],[144]) ).
thf(168,plain,
( sk2
| sk8
| sk11 ),
inference(simp,[status(thm)],[165]) ).
thf(141,plain,
( sk2
| ( ( f @ sk11 )
!= ( f @ sk9 ) ) ),
inference(paramod_ordered,[status(thm)],[121,140]) ).
thf(143,plain,
( sk2
| ( sk11 != sk9 ) ),
inference(simp,[status(thm)],[141]) ).
thf(171,plain,
( sk2
| sk8
| ~ sk9
| ( sk11 != sk11 ) ),
inference(paramod_ordered,[status(thm)],[168,143]) ).
thf(172,plain,
( sk2
| sk8
| ~ sk9 ),
inference(pattern_uni,[status(thm)],[171:[]]) ).
thf(225,plain,
( sk2
| sk5
| sk8
| ( sk9 != sk9 ) ),
inference(paramod_ordered,[status(thm)],[214,172]) ).
thf(226,plain,
( sk2
| sk5
| sk8 ),
inference(pattern_uni,[status(thm)],[225:[]]) ).
thf(118,plain,
( sk2
| ~ ( f @ sk8 )
| ~ sk8 ),
inference(bool_ext,[status(thm)],[117]) ).
thf(122,plain,
( sk2
| ~ sk8
| ( ( f @ sk9 )
!= ( f @ sk8 ) ) ),
inference(paramod_ordered,[status(thm)],[121,118]) ).
thf(125,plain,
( sk2
| ~ sk8
| ( sk9 != sk8 ) ),
inference(simp,[status(thm)],[122]) ).
thf(217,plain,
( sk2
| sk5
| ~ sk8
| ( sk9 != sk9 ) ),
inference(paramod_ordered,[status(thm)],[214,125]) ).
thf(218,plain,
( sk2
| sk5
| ~ sk8 ),
inference(pattern_uni,[status(thm)],[217:[]]) ).
thf(241,plain,
( sk2
| sk5
| ( sk8 != sk8 ) ),
inference(paramod_ordered,[status(thm)],[226,218]) ).
thf(242,plain,
( sk2
| sk5 ),
inference(pattern_uni,[status(thm)],[241:[]]) ).
thf(213,plain,
( sk2
| ~ sk9
| ~ sk5 ),
inference(bool_ext,[status(thm)],[210]) ).
thf(253,plain,
( sk2
| ~ sk9
| ( sk5 != sk5 ) ),
inference(paramod_ordered,[status(thm)],[242,213]) ).
thf(254,plain,
( sk2
| ~ sk9 ),
inference(pattern_uni,[status(thm)],[253:[]]) ).
thf(536,plain,
( sk2
| sk6
| ( sk9 != sk9 ) ),
inference(paramod_ordered,[status(thm)],[533,254]) ).
thf(537,plain,
( sk2
| sk6 ),
inference(pattern_uni,[status(thm)],[536:[]]) ).
thf(517,plain,
( sk2
| ( f @ sk6 )
| ~ sk6 ),
inference(bool_ext,[status(thm)],[488]) ).
thf(530,plain,
( ~ sk6
| ( f @ sk6 )
| sk2 ),
inference(cnf,[status(esa)],[517]) ).
thf(251,plain,
( sk2
| ~ ( f @ $true )
| ( sk5 != sk5 ) ),
inference(paramod_ordered,[status(thm)],[242,191]) ).
thf(252,plain,
( sk2
| ~ ( f @ $true ) ),
inference(pattern_uni,[status(thm)],[251:[]]) ).
thf(571,plain,
( ~ sk6
| sk2
| ( ( f @ sk6 )
!= ( f @ $true ) ) ),
inference(paramod_ordered,[status(thm)],[530,252]) ).
thf(587,plain,
( sk2
| ~ sk6
| ~ sk6 ),
inference(simp,[status(thm)],[571]) ).
thf(592,plain,
( sk2
| ~ sk6 ),
inference(simp,[status(thm)],[587]) ).
thf(594,plain,
( sk2
| ( sk6 != sk6 ) ),
inference(paramod_ordered,[status(thm)],[537,592]) ).
thf(595,plain,
sk2,
inference(pattern_uni,[status(thm)],[594:[]]) ).
thf(634,plain,
( ( f
!= ( ^ [A: $o] : A ) )
| ~ $true
| sk3 ),
inference(rewrite,[status(thm)],[548,595]) ).
thf(635,plain,
( ( f
!= ( ^ [A: $o] : A ) )
| sk3 ),
inference(simp,[status(thm)],[634]) ).
thf(14,plain,
! [A: $i] :
( ~ sk2
| ~ sk3
| ( ( eps
@ ^ [B: $i] :
( ( ( f
= ( ^ [C: $o] : $false ) )
& ( B = sk1 ) )
| ( ( f = (~) )
& ( B = sk1 ) )
| ( ( f
= ( ^ [C: $o] : C ) )
& ( B = sk1 ) )
| ( ( f
= ( ^ [C: $o] : $true ) )
& ( B = sk1 ) ) ) )
= sk1 )
| ( ( eps
@ ^ [B: $i] :
( ( ( f
= ( ^ [C: $o] : $false ) )
& ( B = sk1 ) )
| ( ( f = (~) )
& ( B = sk1 ) )
| ( ( f
= ( ^ [C: $o] : C ) )
& ( B = sk1 ) )
| ( ( f
= ( ^ [C: $o] : $true ) )
& ( B = sk1 ) ) ) )
= sk1 )
| ( f
!= ( ^ [B: $o] : B ) )
| ( A != sk1 ) ),
inference(cnf,[status(esa)],[12]) ).
thf(45,plain,
! [A: $i] :
( ( ( eps
@ ^ [B: $i] :
( ( ( f
= ( ^ [C: $o] : $false ) )
& ( B = sk1 ) )
| ( ( f = (~) )
& ( B = sk1 ) )
| ( ( f
= ( ^ [C: $o] : C ) )
& ( B = sk1 ) )
| ( ( f
= ( ^ [C: $o] : $true ) )
& ( B = sk1 ) ) ) )
= sk1 )
| ( ( eps
@ ^ [B: $i] :
( ( ( f
= ( ^ [C: $o] : $false ) )
& ( B = sk1 ) )
| ( ( f = (~) )
& ( B = sk1 ) )
| ( ( f
= ( ^ [C: $o] : C ) )
& ( B = sk1 ) )
| ( ( f
= ( ^ [C: $o] : $true ) )
& ( B = sk1 ) ) ) )
= sk1 )
| ( f
!= ( ^ [B: $o] : B ) )
| ( A != sk1 )
| ~ sk2
| ~ sk3 ),
inference(lifteq,[status(thm)],[14]) ).
thf(46,plain,
( ( ( eps
@ ^ [A: $i] :
( ( ( f
= ( ^ [B: $o] : $false ) )
& ( A = sk1 ) )
| ( ( f = (~) )
& ( A = sk1 ) )
| ( ( f
= ( ^ [B: $o] : B ) )
& ( A = sk1 ) )
| ( ( f
= ( ^ [B: $o] : $true ) )
& ( A = sk1 ) ) ) )
= sk1 )
| ( f
!= ( ^ [A: $o] : A ) )
| ~ sk2
| ~ sk3 ),
inference(simp,[status(thm)],[45]) ).
thf(112,plain,
( ( f
!= ( ^ [A: $o] : A ) )
| ~ sk2
| ~ sk3 ),
inference(simplifyReflect,[status(thm)],[46,6]) ).
thf(113,plain,
( ( ( f @ sk7 )
!= sk7 )
| ~ sk2
| ~ sk3 ),
inference(func_ext,[status(esa)],[112]) ).
thf(115,plain,
( ~ sk2
| ~ sk3
| ( f @ sk7 )
| sk7 ),
inference(bool_ext,[status(thm)],[113]) ).
thf(38,plain,
! [A: $i] :
( ~ sk2
| ~ sk3
| ( ( eps
@ ^ [B: $i] :
( ( ( f
= ( ^ [C: $o] : $false ) )
& ( B = sk1 ) )
| ( ( f = (~) )
& ( B = sk1 ) )
| ( ( f
= ( ^ [C: $o] : C ) )
& ( B = sk1 ) )
| ( ( f
= ( ^ [C: $o] : $true ) )
& ( B = sk1 ) ) ) )
= sk1 )
| ( ( eps
@ ^ [B: $i] :
( ( ( f
= ( ^ [C: $o] : $false ) )
& ( B = sk1 ) )
| ( ( f = (~) )
& ( B = sk1 ) )
| ( ( f
= ( ^ [C: $o] : C ) )
& ( B = sk1 ) )
| ( ( f
= ( ^ [C: $o] : $true ) )
& ( B = sk1 ) ) ) )
= sk1 )
| ( f
!= ( ^ [B: $o] : $true ) )
| ( A != sk1 ) ),
inference(cnf,[status(esa)],[12]) ).
thf(75,plain,
! [A: $i] :
( ( ( eps
@ ^ [B: $i] :
( ( ( f
= ( ^ [C: $o] : $false ) )
& ( B = sk1 ) )
| ( ( f = (~) )
& ( B = sk1 ) )
| ( ( f
= ( ^ [C: $o] : C ) )
& ( B = sk1 ) )
| ( ( f
= ( ^ [C: $o] : $true ) )
& ( B = sk1 ) ) ) )
= sk1 )
| ( ( eps
@ ^ [B: $i] :
( ( ( f
= ( ^ [C: $o] : $false ) )
& ( B = sk1 ) )
| ( ( f = (~) )
& ( B = sk1 ) )
| ( ( f
= ( ^ [C: $o] : C ) )
& ( B = sk1 ) )
| ( ( f
= ( ^ [C: $o] : $true ) )
& ( B = sk1 ) ) ) )
= sk1 )
| ( f
!= ( ^ [B: $o] : $true ) )
| ( A != sk1 )
| ~ sk2
| ~ sk3 ),
inference(lifteq,[status(thm)],[38]) ).
thf(76,plain,
( ( ( eps
@ ^ [A: $i] :
( ( ( f
= ( ^ [B: $o] : $false ) )
& ( A = sk1 ) )
| ( ( f = (~) )
& ( A = sk1 ) )
| ( ( f
= ( ^ [B: $o] : B ) )
& ( A = sk1 ) )
| ( ( f
= ( ^ [B: $o] : $true ) )
& ( A = sk1 ) ) ) )
= sk1 )
| ( f
!= ( ^ [A: $o] : $true ) )
| ~ sk2
| ~ sk3 ),
inference(simp,[status(thm)],[75]) ).
thf(200,plain,
( ( f
!= ( ^ [A: $o] : $true ) )
| ~ sk2
| ~ sk3 ),
inference(simplifyReflect,[status(thm)],[76,6]) ).
thf(201,plain,
( ~ ( f @ sk12 )
| ~ sk2
| ~ sk3 ),
inference(func_ext,[status(esa)],[200]) ).
thf(323,plain,
( ~ sk2
| ~ sk3
| sk7
| ( ( f @ sk12 )
!= ( f @ sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[115,201]) ).
thf(335,plain,
( sk7
| ~ sk2
| ~ sk3
| ( sk12 != sk7 ) ),
inference(simp,[status(thm)],[323]) ).
thf(1349,plain,
( sk7
| ~ $true
| ~ sk3
| ( sk12 != sk7 ) ),
inference(rewrite,[status(thm)],[335,595]) ).
thf(1350,plain,
( sk7
| ~ sk3
| ( sk12 != sk7 ) ),
inference(simp,[status(thm)],[1349]) ).
thf(1352,plain,
( sk7
| ~ sk3
| sk12
| sk7 ),
inference(bool_ext,[status(thm)],[1350]) ).
thf(1353,plain,
( sk7
| ~ sk3
| sk12 ),
inference(simp,[status(thm)],[1352]) ).
thf(25,plain,
! [A: $i] :
( ~ sk2
| ~ sk3
| ( ( eps
@ ^ [B: $i] :
( ( ( f
= ( ^ [C: $o] : $false ) )
& ( B = sk1 ) )
| ( ( f = (~) )
& ( B = sk1 ) )
| ( ( f
= ( ^ [C: $o] : C ) )
& ( B = sk1 ) )
| ( ( f
= ( ^ [C: $o] : $true ) )
& ( B = sk1 ) ) ) )
= sk1 )
| ( ( eps
@ ^ [B: $i] :
( ( ( f
= ( ^ [C: $o] : $false ) )
& ( B = sk1 ) )
| ( ( f = (~) )
& ( B = sk1 ) )
| ( ( f
= ( ^ [C: $o] : C ) )
& ( B = sk1 ) )
| ( ( f
= ( ^ [C: $o] : $true ) )
& ( B = sk1 ) ) ) )
= sk1 )
| ( f
!= ( ^ [B: $o] : $false ) )
| ( A != sk1 ) ),
inference(cnf,[status(esa)],[12]) ).
thf(63,plain,
! [A: $i] :
( ( ( eps
@ ^ [B: $i] :
( ( ( f
= ( ^ [C: $o] : $false ) )
& ( B = sk1 ) )
| ( ( f = (~) )
& ( B = sk1 ) )
| ( ( f
= ( ^ [C: $o] : C ) )
& ( B = sk1 ) )
| ( ( f
= ( ^ [C: $o] : $true ) )
& ( B = sk1 ) ) ) )
= sk1 )
| ( ( eps
@ ^ [B: $i] :
( ( ( f
= ( ^ [C: $o] : $false ) )
& ( B = sk1 ) )
| ( ( f = (~) )
& ( B = sk1 ) )
| ( ( f
= ( ^ [C: $o] : C ) )
& ( B = sk1 ) )
| ( ( f
= ( ^ [C: $o] : $true ) )
& ( B = sk1 ) ) ) )
= sk1 )
| ( f
!= ( ^ [B: $o] : $false ) )
| ( A != sk1 )
| ~ sk2
| ~ sk3 ),
inference(lifteq,[status(thm)],[25]) ).
thf(64,plain,
( ( ( eps
@ ^ [A: $i] :
( ( ( f
= ( ^ [B: $o] : $false ) )
& ( A = sk1 ) )
| ( ( f = (~) )
& ( A = sk1 ) )
| ( ( f
= ( ^ [B: $o] : B ) )
& ( A = sk1 ) )
| ( ( f
= ( ^ [B: $o] : $true ) )
& ( A = sk1 ) ) ) )
= sk1 )
| ( f
!= ( ^ [A: $o] : $false ) )
| ~ sk2
| ~ sk3 ),
inference(simp,[status(thm)],[63]) ).
thf(137,plain,
( ( f
!= ( ^ [A: $o] : $false ) )
| ~ sk2
| ~ sk3 ),
inference(simplifyReflect,[status(thm)],[64,6]) ).
thf(138,plain,
( ( f @ sk10 )
| ~ sk2
| ~ sk3 ),
inference(func_ext,[status(esa)],[137]) ).
thf(231,plain,
( ~ sk2
| ~ sk3
| ( ( f @ sk12 )
!= ( f @ sk10 ) ) ),
inference(paramod_ordered,[status(thm)],[138,201]) ).
thf(234,plain,
( ~ sk2
| ~ sk3
| ( sk12 != sk10 ) ),
inference(simp,[status(thm)],[231]) ).
thf(236,plain,
( ~ sk2
| ~ sk3
| sk12
| sk10 ),
inference(bool_ext,[status(thm)],[234]) ).
thf(16,plain,
! [A: $i] :
( ~ sk2
| ~ sk3
| ( ( eps
@ ^ [B: $i] :
( ( ( f
= ( ^ [C: $o] : $false ) )
& ( B = sk1 ) )
| ( ( f = (~) )
& ( B = sk1 ) )
| ( ( f
= ( ^ [C: $o] : C ) )
& ( B = sk1 ) )
| ( ( f
= ( ^ [C: $o] : $true ) )
& ( B = sk1 ) ) ) )
= sk1 )
| ( ( eps
@ ^ [B: $i] :
( ( ( f
= ( ^ [C: $o] : $false ) )
& ( B = sk1 ) )
| ( ( f = (~) )
& ( B = sk1 ) )
| ( ( f
= ( ^ [C: $o] : C ) )
& ( B = sk1 ) )
| ( ( f
= ( ^ [C: $o] : $true ) )
& ( B = sk1 ) ) ) )
= sk1 )
| ( f != (~) )
| ( A != sk1 ) ),
inference(cnf,[status(esa)],[12]) ).
thf(93,plain,
! [A: $i] :
( ( ( eps
@ ^ [B: $i] :
( ( ( f
= ( ^ [C: $o] : $false ) )
& ( B = sk1 ) )
| ( ( f = (~) )
& ( B = sk1 ) )
| ( ( f
= ( ^ [C: $o] : C ) )
& ( B = sk1 ) )
| ( ( f
= ( ^ [C: $o] : $true ) )
& ( B = sk1 ) ) ) )
= sk1 )
| ( ( eps
@ ^ [B: $i] :
( ( ( f
= ( ^ [C: $o] : $false ) )
& ( B = sk1 ) )
| ( ( f = (~) )
& ( B = sk1 ) )
| ( ( f
= ( ^ [C: $o] : C ) )
& ( B = sk1 ) )
| ( ( f
= ( ^ [C: $o] : $true ) )
& ( B = sk1 ) ) ) )
= sk1 )
| ( f != (~) )
| ( A != sk1 )
| ~ sk2
| ~ sk3 ),
inference(lifteq,[status(thm)],[16]) ).
thf(94,plain,
( ( ( eps
@ ^ [A: $i] :
( ( ( f
= ( ^ [B: $o] : $false ) )
& ( A = sk1 ) )
| ( ( f = (~) )
& ( A = sk1 ) )
| ( ( f
= ( ^ [B: $o] : B ) )
& ( A = sk1 ) )
| ( ( f
= ( ^ [B: $o] : $true ) )
& ( A = sk1 ) ) ) )
= sk1 )
| ( f != (~) )
| ~ sk2
| ~ sk3 ),
inference(simp,[status(thm)],[93]) ).
thf(262,plain,
( ( f != (~) )
| ~ sk2
| ~ sk3 ),
inference(simplifyReflect,[status(thm)],[94,6]) ).
thf(263,plain,
( ( ( f @ sk15 )
!= ~ sk15 )
| ~ sk2
| ~ sk3 ),
inference(func_ext,[status(esa)],[262]) ).
thf(272,plain,
( ~ sk2
| ~ sk3
| sk15
| ( ( f @ sk15 )
!= ( f @ sk10 ) ) ),
inference(paramod_ordered,[status(thm)],[138,263]) ).
thf(274,plain,
( sk15
| ~ sk2
| ~ sk3
| ( sk15 != sk10 ) ),
inference(simp,[status(thm)],[272]) ).
thf(278,plain,
( sk15
| ~ sk2
| ~ sk3
| sk15
| sk10 ),
inference(bool_ext,[status(thm)],[274]) ).
thf(279,plain,
( sk15
| ~ sk2
| ~ sk3
| sk10 ),
inference(simp,[status(thm)],[278]) ).
thf(270,plain,
( ~ sk2
| ~ sk3
| ( f @ sk15 )
| ~ sk15 ),
inference(bool_ext,[status(thm)],[263]) ).
thf(276,plain,
( ~ sk15
| ( f @ sk15 )
| ~ sk3
| ~ sk2 ),
inference(cnf,[status(esa)],[270]) ).
thf(399,plain,
( ~ sk15
| ~ sk3
| ~ sk2
| ( ( f @ sk15 )
!= ( f @ sk12 ) ) ),
inference(paramod_ordered,[status(thm)],[276,201]) ).
thf(412,plain,
( ~ sk15
| ~ sk3
| ~ sk2
| ( sk15 != sk12 ) ),
inference(simp,[status(thm)],[399]) ).
thf(413,plain,
( ~ sk15
| ~ sk3
| ~ sk2
| ~ sk15
| ~ sk12 ),
inference(bool_ext,[status(thm)],[412]) ).
thf(419,plain,
( ~ sk15
| ~ sk3
| ~ sk2
| ~ sk12 ),
inference(simp,[status(thm)],[413]) ).
thf(436,plain,
( ~ sk2
| ~ sk3
| sk10
| ~ sk12
| ( sk15 != sk15 ) ),
inference(paramod_ordered,[status(thm)],[279,419]) ).
thf(437,plain,
( ~ sk2
| ~ sk3
| sk10
| ~ sk12 ),
inference(pattern_uni,[status(thm)],[436:[]]) ).
thf(455,plain,
( ~ sk2
| ~ sk3
| sk10
| ( sk12 != sk12 ) ),
inference(paramod_ordered,[status(thm)],[236,437]) ).
thf(456,plain,
( ~ sk2
| ~ sk3
| sk10 ),
inference(pattern_uni,[status(thm)],[455:[]]) ).
thf(235,plain,
( ~ sk2
| ~ sk3
| ~ sk12
| ~ sk10 ),
inference(bool_ext,[status(thm)],[234]) ).
thf(462,plain,
( ~ sk2
| ~ sk3
| ~ sk12
| ( sk10 != sk10 ) ),
inference(paramod_ordered,[status(thm)],[456,235]) ).
thf(463,plain,
( ~ sk2
| ~ sk3
| ~ sk12 ),
inference(pattern_uni,[status(thm)],[462:[]]) ).
thf(606,plain,
( ~ $true
| ~ sk3
| ~ sk12 ),
inference(rewrite,[status(thm)],[463,595]) ).
thf(607,plain,
( ~ sk3
| ~ sk12 ),
inference(simp,[status(thm)],[606]) ).
thf(1360,plain,
( sk7
| ~ sk3
| ( sk12 != sk12 ) ),
inference(paramod_ordered,[status(thm)],[1353,607]) ).
thf(1361,plain,
( sk7
| ~ sk3 ),
inference(pattern_uni,[status(thm)],[1360:[]]) ).
thf(155,plain,
( ~ sk2
| ~ sk3
| ~ sk7
| ( ( f @ sk10 )
!= ( f @ sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[138,113]) ).
thf(159,plain,
( ~ sk2
| ~ sk3
| ~ sk7
| ( sk10 != sk7 ) ),
inference(simp,[status(thm)],[155]) ).
thf(460,plain,
( ~ sk2
| ~ sk3
| ~ sk7
| ( sk10 != sk10 ) ),
inference(paramod_ordered,[status(thm)],[456,159]) ).
thf(461,plain,
( ~ sk2
| ~ sk3
| ~ sk7 ),
inference(pattern_uni,[status(thm)],[460:[]]) ).
thf(626,plain,
( ~ $true
| ~ sk3
| ~ sk7 ),
inference(rewrite,[status(thm)],[461,595]) ).
thf(627,plain,
( ~ sk3
| ~ sk7 ),
inference(simp,[status(thm)],[626]) ).
thf(1364,plain,
( ~ sk3
| ( sk7 != sk7 ) ),
inference(paramod_ordered,[status(thm)],[1361,627]) ).
thf(1365,plain,
~ sk3,
inference(pattern_uni,[status(thm)],[1364:[]]) ).
thf(1386,plain,
( ( f
!= ( ^ [A: $o] : A ) )
| $false ),
inference(rewrite,[status(thm)],[635,1365]) ).
thf(1387,plain,
( f
!= ( ^ [A: $o] : A ) ),
inference(simp,[status(thm)],[1386]) ).
thf(1454,plain,
( ( f @ sk26 )
!= sk26 ),
inference(func_ext,[status(esa)],[1387]) ).
thf(1608,plain,
( ( f @ sk26 )
| sk26 ),
inference(bool_ext,[status(thm)],[1454]) ).
thf(42,plain,
! [A: $i] :
( ~ sk2
| ( ( eps
@ ^ [B: $i] :
( ( ( f
= ( ^ [C: $o] : $false ) )
& ( B = sk1 ) )
| ( ( f = (~) )
& ( B = sk1 ) )
| ( ( f
= ( ^ [C: $o] : C ) )
& ( B = sk1 ) )
| ( ( f
= ( ^ [C: $o] : $true ) )
& ( B = sk1 ) ) ) )
= sk1 )
| sk3
| ( f
!= ( ^ [B: $o] : $false ) )
| ( A != sk1 ) ),
inference(cnf,[status(esa)],[12]) ).
thf(57,plain,
! [A: $i] :
( ( ( eps
@ ^ [B: $i] :
( ( ( f
= ( ^ [C: $o] : $false ) )
& ( B = sk1 ) )
| ( ( f = (~) )
& ( B = sk1 ) )
| ( ( f
= ( ^ [C: $o] : C ) )
& ( B = sk1 ) )
| ( ( f
= ( ^ [C: $o] : $true ) )
& ( B = sk1 ) ) ) )
= sk1 )
| ( f
!= ( ^ [B: $o] : $false ) )
| ( A != sk1 )
| ~ sk2
| sk3 ),
inference(lifteq,[status(thm)],[42]) ).
thf(58,plain,
( ( ( eps
@ ^ [A: $i] :
( ( ( f
= ( ^ [B: $o] : $false ) )
& ( A = sk1 ) )
| ( ( f = (~) )
& ( A = sk1 ) )
| ( ( f
= ( ^ [B: $o] : B ) )
& ( A = sk1 ) )
| ( ( f
= ( ^ [B: $o] : $true ) )
& ( A = sk1 ) ) ) )
= sk1 )
| ( f
!= ( ^ [A: $o] : $false ) )
| ~ sk2
| sk3 ),
inference(simp,[status(thm)],[57]) ).
thf(255,plain,
( ( f
!= ( ^ [A: $o] : $false ) )
| ~ sk2
| sk3 ),
inference(simplifyReflect,[status(thm)],[58,6]) ).
thf(636,plain,
( ( f
!= ( ^ [A: $o] : $false ) )
| ~ $true
| sk3 ),
inference(rewrite,[status(thm)],[255,595]) ).
thf(637,plain,
( ( f
!= ( ^ [A: $o] : $false ) )
| sk3 ),
inference(simp,[status(thm)],[636]) ).
thf(671,plain,
( ( f @ sk23 )
| sk3 ),
inference(func_ext,[status(esa)],[637]) ).
thf(37,plain,
! [A: $i] :
( ~ sk2
| ( ( eps
@ ^ [B: $i] :
( ( ( f
= ( ^ [C: $o] : $false ) )
& ( B = sk1 ) )
| ( ( f = (~) )
& ( B = sk1 ) )
| ( ( f
= ( ^ [C: $o] : C ) )
& ( B = sk1 ) )
| ( ( f
= ( ^ [C: $o] : $true ) )
& ( B = sk1 ) ) ) )
= sk1 )
| sk3
| ( f
!= ( ^ [B: $o] : $true ) )
| ( A != sk1 ) ),
inference(cnf,[status(esa)],[12]) ).
thf(61,plain,
! [A: $i] :
( ( ( eps
@ ^ [B: $i] :
( ( ( f
= ( ^ [C: $o] : $false ) )
& ( B = sk1 ) )
| ( ( f = (~) )
& ( B = sk1 ) )
| ( ( f
= ( ^ [C: $o] : C ) )
& ( B = sk1 ) )
| ( ( f
= ( ^ [C: $o] : $true ) )
& ( B = sk1 ) ) ) )
= sk1 )
| ( f
!= ( ^ [B: $o] : $true ) )
| ( A != sk1 )
| ~ sk2
| sk3 ),
inference(lifteq,[status(thm)],[37]) ).
thf(62,plain,
( ( ( eps
@ ^ [A: $i] :
( ( ( f
= ( ^ [B: $o] : $false ) )
& ( A = sk1 ) )
| ( ( f = (~) )
& ( A = sk1 ) )
| ( ( f
= ( ^ [B: $o] : B ) )
& ( A = sk1 ) )
| ( ( f
= ( ^ [B: $o] : $true ) )
& ( A = sk1 ) ) ) )
= sk1 )
| ( f
!= ( ^ [A: $o] : $true ) )
| ~ sk2
| sk3 ),
inference(simp,[status(thm)],[61]) ).
thf(267,plain,
( ( f
!= ( ^ [A: $o] : $true ) )
| ~ sk2
| sk3 ),
inference(simplifyReflect,[status(thm)],[62,6]) ).
thf(268,plain,
( ~ ( f @ sk16 )
| ~ sk2
| sk3 ),
inference(func_ext,[status(esa)],[267]) ).
thf(608,plain,
( ~ ( f @ sk16 )
| ~ $true
| sk3 ),
inference(rewrite,[status(thm)],[268,595]) ).
thf(609,plain,
( ~ ( f @ sk16 )
| sk3 ),
inference(simp,[status(thm)],[608]) ).
thf(690,plain,
( sk3
| ( ( f @ sk23 )
!= ( f @ sk16 ) ) ),
inference(paramod_ordered,[status(thm)],[671,609]) ).
thf(691,plain,
( sk3
| ( sk23 != sk16 ) ),
inference(simp,[status(thm)],[690]) ).
thf(712,plain,
( sk3
| sk23
| sk16 ),
inference(bool_ext,[status(thm)],[691]) ).
thf(745,plain,
( sk3
| sk16
| ( f @ $true )
| ( sk23 != sk23 ) ),
inference(paramod_ordered,[status(thm)],[712,671]) ).
thf(746,plain,
( sk3
| sk16
| ( f @ $true ) ),
inference(pattern_uni,[status(thm)],[745:[]]) ).
thf(1372,plain,
( $false
| sk16
| ( f @ $true ) ),
inference(rewrite,[status(thm)],[746,1365]) ).
thf(1373,plain,
( sk16
| ( f @ $true ) ),
inference(simp,[status(thm)],[1372]) ).
thf(1782,plain,
( sk16
| ~ sk26
| ( ( f @ sk26 )
!= ( f @ $true ) ) ),
inference(paramod_ordered,[status(thm)],[1373,1454]) ).
thf(1790,plain,
( sk16
| ~ sk26
| ~ sk26 ),
inference(simp,[status(thm)],[1782]) ).
thf(1801,plain,
( sk16
| ~ sk26 ),
inference(simp,[status(thm)],[1790]) ).
thf(1442,plain,
( ( f @ sk23 )
| $false ),
inference(rewrite,[status(thm)],[671,1365]) ).
thf(1443,plain,
f @ sk23,
inference(simp,[status(thm)],[1442]) ).
thf(26,plain,
! [A: $i] :
( ~ sk2
| ( ( eps
@ ^ [B: $i] :
( ( ( f
= ( ^ [C: $o] : $false ) )
& ( B = sk1 ) )
| ( ( f = (~) )
& ( B = sk1 ) )
| ( ( f
= ( ^ [C: $o] : C ) )
& ( B = sk1 ) )
| ( ( f
= ( ^ [C: $o] : $true ) )
& ( B = sk1 ) ) ) )
= sk1 )
| sk3
| ( f != (~) )
| ( A != sk1 ) ),
inference(cnf,[status(esa)],[12]) ).
thf(99,plain,
! [A: $i] :
( ( ( eps
@ ^ [B: $i] :
( ( ( f
= ( ^ [C: $o] : $false ) )
& ( B = sk1 ) )
| ( ( f = (~) )
& ( B = sk1 ) )
| ( ( f
= ( ^ [C: $o] : C ) )
& ( B = sk1 ) )
| ( ( f
= ( ^ [C: $o] : $true ) )
& ( B = sk1 ) ) ) )
= sk1 )
| ( f != (~) )
| ( A != sk1 )
| ~ sk2
| sk3 ),
inference(lifteq,[status(thm)],[26]) ).
thf(100,plain,
( ( ( eps
@ ^ [A: $i] :
( ( ( f
= ( ^ [B: $o] : $false ) )
& ( A = sk1 ) )
| ( ( f = (~) )
& ( A = sk1 ) )
| ( ( f
= ( ^ [B: $o] : B ) )
& ( A = sk1 ) )
| ( ( f
= ( ^ [B: $o] : $true ) )
& ( A = sk1 ) ) ) )
= sk1 )
| ( f != (~) )
| ~ sk2
| sk3 ),
inference(simp,[status(thm)],[99]) ).
thf(653,plain,
( ( ( eps
@ ^ [A: $i] :
( ( ( f
= ( ^ [B: $o] : $false ) )
& ( A = sk1 ) )
| ( ( f = (~) )
& ( A = sk1 ) )
| ( ( f
= ( ^ [B: $o] : B ) )
& ( A = sk1 ) )
| ( ( f
= ( ^ [B: $o] : $true ) )
& ( A = sk1 ) ) ) )
= sk1 )
| ( f != (~) )
| ~ $true
| sk3 ),
inference(rewrite,[status(thm)],[100,595]) ).
thf(654,plain,
( ( ( eps
@ ^ [A: $i] :
( ( ( f
= ( ^ [B: $o] : $false ) )
& ( A = sk1 ) )
| ( ( f = (~) )
& ( A = sk1 ) )
| ( ( f
= ( ^ [B: $o] : B ) )
& ( A = sk1 ) )
| ( ( f
= ( ^ [B: $o] : $true ) )
& ( A = sk1 ) ) ) )
= sk1 )
| ( f != (~) )
| sk3 ),
inference(simp,[status(thm)],[653]) ).
thf(655,plain,
( ( f != (~) )
| sk3 ),
inference(simplifyReflect,[status(thm)],[654,6]) ).
thf(656,plain,
( ( ( f @ sk20 )
!= ~ sk20 )
| sk3 ),
inference(func_ext,[status(esa)],[655]) ).
thf(1440,plain,
( ( ( f @ sk20 )
!= ~ sk20 )
| $false ),
inference(rewrite,[status(thm)],[656,1365]) ).
thf(1441,plain,
( ( f @ sk20 )
!= ~ sk20 ),
inference(simp,[status(thm)],[1440]) ).
thf(1618,plain,
( sk20
| ( ( f @ sk23 )
!= ( f @ sk20 ) ) ),
inference(paramod_ordered,[status(thm)],[1443,1441]) ).
thf(1623,plain,
( sk20
| ( sk23 != sk20 ) ),
inference(simp,[status(thm)],[1618]) ).
thf(2108,plain,
( sk20
| sk23
| sk20 ),
inference(bool_ext,[status(thm)],[1623]) ).
thf(2115,plain,
( sk20
| sk23 ),
inference(simp,[status(thm)],[2108]) ).
thf(1388,plain,
( $false
| ( sk23 != sk16 ) ),
inference(rewrite,[status(thm)],[691,1365]) ).
thf(1389,plain,
sk23 != sk16,
inference(simp,[status(thm)],[1388]) ).
thf(2116,plain,
( sk20
| ~ sk16
| ( sk23 != sk23 ) ),
inference(paramod_ordered,[status(thm)],[2115,1389]) ).
thf(2117,plain,
( sk20
| ~ sk16 ),
inference(pattern_uni,[status(thm)],[2116:[]]) ).
thf(1617,plain,
( ( f @ sk20 )
| ~ sk20 ),
inference(bool_ext,[status(thm)],[1441]) ).
thf(1627,plain,
( ~ sk20
| ( f @ sk20 ) ),
inference(cnf,[status(esa)],[1617]) ).
thf(602,plain,
( ( f
!= ( ^ [A: $o] : $true ) )
| ~ $true
| sk3 ),
inference(rewrite,[status(thm)],[267,595]) ).
thf(603,plain,
( ( f
!= ( ^ [A: $o] : $true ) )
| sk3 ),
inference(simp,[status(thm)],[602]) ).
thf(657,plain,
( ~ ( f @ sk21 )
| sk3 ),
inference(func_ext,[status(esa)],[603]) ).
thf(697,plain,
( sk3
| ( ( f @ sk23 )
!= ( f @ sk21 ) ) ),
inference(paramod_ordered,[status(thm)],[671,657]) ).
thf(699,plain,
( sk3
| ( sk23 != sk21 ) ),
inference(simp,[status(thm)],[697]) ).
thf(718,plain,
( sk3
| sk23
| sk21 ),
inference(bool_ext,[status(thm)],[699]) ).
thf(711,plain,
( sk3
| ~ sk23
| ~ sk16 ),
inference(bool_ext,[status(thm)],[691]) ).
thf(877,plain,
( sk3
| sk21
| ~ sk16
| ( sk23 != sk23 ) ),
inference(paramod_ordered,[status(thm)],[718,711]) ).
thf(878,plain,
( sk3
| sk21
| ~ sk16 ),
inference(pattern_uni,[status(thm)],[877:[]]) ).
thf(1398,plain,
( $false
| sk21
| ~ sk16 ),
inference(rewrite,[status(thm)],[878,1365]) ).
thf(1399,plain,
( sk21
| ~ sk16 ),
inference(simp,[status(thm)],[1398]) ).
thf(1410,plain,
( ~ ( f @ sk21 )
| $false ),
inference(rewrite,[status(thm)],[657,1365]) ).
thf(1411,plain,
~ ( f @ sk21 ),
inference(simp,[status(thm)],[1410]) ).
thf(1480,plain,
( ~ sk16
| ~ ( f @ $true )
| ( sk21 != sk21 ) ),
inference(paramod_ordered,[status(thm)],[1399,1411]) ).
thf(1481,plain,
( ~ sk16
| ~ ( f @ $true ) ),
inference(pattern_uni,[status(thm)],[1480:[]]) ).
thf(2415,plain,
( ~ sk20
| ~ sk16
| ( ( f @ sk20 )
!= ( f @ $true ) ) ),
inference(paramod_ordered,[status(thm)],[1627,1481]) ).
thf(2432,plain,
( ~ sk20
| ~ sk16
| ~ sk20 ),
inference(simp,[status(thm)],[2415]) ).
thf(2436,plain,
( ~ sk20
| ~ sk16 ),
inference(simp,[status(thm)],[2432]) ).
thf(2443,plain,
( ~ sk16
| ( sk20 != sk20 ) ),
inference(paramod_ordered,[status(thm)],[2117,2436]) ).
thf(2444,plain,
~ sk16,
inference(pattern_uni,[status(thm)],[2443:[]]) ).
thf(2462,plain,
( $false
| ~ sk26 ),
inference(rewrite,[status(thm)],[1801,2444]) ).
thf(2463,plain,
~ sk26,
inference(simp,[status(thm)],[2462]) ).
thf(2531,plain,
( ( f @ $false )
| $false ),
inference(rewrite,[status(thm)],[1608,2463]) ).
thf(2532,plain,
f @ $false,
inference(simp,[status(thm)],[2531]) ).
thf(1430,plain,
( ~ ( f @ sk16 )
| $false ),
inference(rewrite,[status(thm)],[609,1365]) ).
thf(1431,plain,
~ ( f @ sk16 ),
inference(simp,[status(thm)],[1430]) ).
thf(2476,plain,
~ ( f @ $false ),
inference(rewrite,[status(thm)],[1431,2444]) ).
thf(2631,plain,
$false,
inference(rewrite,[status(thm)],[2532,2476]) ).
thf(2632,plain,
$false,
inference(simp,[status(thm)],[2631]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10 % Problem : SYO546^1 : TPTP v8.2.0. Released v5.2.0.
% 0.09/0.12 % Command : run_Leo-III %s %d
% 0.11/0.32 % Computer : n005.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon May 20 08:50:09 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.94/0.93 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.21/1.09 % [INFO] Parsing done (156ms).
% 1.32/1.10 % [INFO] Running in sequential loop mode.
% 1.79/1.45 % [INFO] eprover registered as external prover.
% 1.79/1.45 % [INFO] cvc4 registered as external prover.
% 1.79/1.46 % [INFO] Scanning for conjecture ...
% 2.04/1.56 % [INFO] Found a conjecture (or negated_conjecture) and 1 axioms. Running axiom selection ...
% 2.04/1.59 % [INFO] Axiom selection finished. Selected 1 axioms (removed 0 axioms).
% 2.04/1.60 % [INFO] Problem is higher-order (TPTP THF).
% 2.04/1.60 % [INFO] Type checking passed.
% 2.04/1.60 % [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 ...
% 21.87/4.80 % [INFO] Killing All external provers ...
% 21.87/4.80 % Time passed: 4331ms (effective reasoning time: 3695ms)
% 21.87/4.80 % 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)>
% 21.87/4.81 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 4331 ms resp. 3695 ms w/o parsing
% 22.06/4.96 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 22.06/4.97 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------