TSTP Solution File: SYO546^1 by Leo-III-SAT---1.7.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III-SAT---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 : n021.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 09:00:53 EDT 2024
% Result : Theorem 22.62s 4.39s
% Output : Refutation 23.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 56
% Number of leaves : 25
% Syntax : Number of formulae : 270 ( 13 unt; 22 typ; 1 def)
% Number of atoms : 1961 ( 661 equ; 72 cnn)
% Maximal formula atoms : 16 ( 7 avg)
% Number of connectives : 1605 ( 532 ~; 671 |; 216 &; 185 @)
% ( 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 : 26 ( 22 usr; 22 con; 0-5 aty)
% Number of variables : 314 ( 273 ^ 39 !; 2 ?; 314 :)
% 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(sk10_type,type,
sk10: $o ).
thf(sk12_type,type,
sk12: $o ).
thf(sk13_type,type,
sk13: $o ).
thf(sk14_type,type,
sk14: $o ).
thf(sk15_type,type,
sk15: $o ).
thf(sk18_type,type,
sk18: $o ).
thf(sk19_type,type,
sk19: $o ).
thf(sk20_type,type,
sk20: $o ).
thf(sk21_type,type,
sk21: $o ).
thf(sk23_type,type,
sk23: $o ).
thf(sk24_type,type,
sk24: $o ).
thf(sk25_type,type,
sk25: $o ).
thf(10,axiom,
? [A: ( $i > $o ) > $i] :
! [B: $i > $o] :
( ? [C: $i] : ( B @ C )
=> ( B @ ( A @ B ) ) ),
introduced(axiom_of_choice) ).
thf(11,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)],[10]) ).
thf(18,plain,
! [A: $i] :
( ~ sk2
| ( f = (~) )
| sk3
| ( f
!= ( ^ [B: $o] : $true ) )
| ( A != sk1 ) ),
inference(cnf,[status(esa)],[11]) ).
thf(52,plain,
! [A: $i] :
( ( f = (~) )
| ( f
!= ( ^ [B: $o] : $true ) )
| ( A != sk1 )
| ~ sk2
| sk3 ),
inference(lifteq,[status(thm)],[18]) ).
thf(53,plain,
( ( f = (~) )
| ( f
!= ( ^ [A: $o] : $true ) )
| ~ sk2
| sk3 ),
inference(simp,[status(thm)],[52]) ).
thf(271,plain,
! [A: $o] :
( ( ( f @ A )
= ~ A )
| ~ ( f @ sk13 )
| ~ sk2
| sk3 ),
inference(func_ext,[status(esa)],[53]) ).
thf(38,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)],[11]) ).
thf(76,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)],[38]) ).
thf(77,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)],[76]) ).
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(235,plain,
( ( f
!= ( ^ [A: $o] : $false ) )
| sk2 ),
inference(simplifyReflect,[status(thm)],[77,6]) ).
thf(236,plain,
( ( f @ sk12 )
| sk2 ),
inference(func_ext,[status(esa)],[235]) ).
thf(26,plain,
! [A: $i] :
( ( f
= ( ^ [B: $o] : $false ) )
| sk2
| ( f != (~) )
| ( A != sk1 ) ),
inference(cnf,[status(esa)],[11]) ).
thf(98,plain,
! [A: $i] :
( ( f
= ( ^ [B: $o] : $false ) )
| ( f != (~) )
| ( A != sk1 )
| sk2 ),
inference(lifteq,[status(thm)],[26]) ).
thf(99,plain,
( ( f
= ( ^ [A: $o] : $false ) )
| ( f != (~) )
| sk2 ),
inference(simp,[status(thm)],[98]) ).
thf(110,plain,
! [A: $o] :
( ~ ( f @ A )
| ( ( f @ sk6 )
!= ~ sk6 )
| sk2 ),
inference(func_ext,[status(esa)],[99]) ).
thf(240,plain,
! [A: $o] :
( sk2
| ( ( f @ sk6 )
!= ~ sk6 )
| ( ( f @ sk12 )
!= ( f @ A ) ) ),
inference(paramod_ordered,[status(thm)],[236,110]) ).
thf(241,plain,
( sk2
| ( ( f @ sk6 )
!= ~ sk6 ) ),
inference(pattern_uni,[status(thm)],[240:[bind(A,$thf( sk12 ))]]) ).
thf(284,plain,
( sk2
| sk6
| ( ( f @ sk12 )
!= ( f @ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[236,241]) ).
thf(286,plain,
( sk2
| sk6
| ( sk12 != sk6 ) ),
inference(simp,[status(thm)],[284]) ).
thf(374,plain,
( sk2
| sk6
| sk12
| sk6 ),
inference(bool_ext,[status(thm)],[286]) ).
thf(375,plain,
( sk2
| sk6
| sk12 ),
inference(simp,[status(thm)],[374]) ).
thf(40,plain,
! [A: $i] :
( ( f
= ( ^ [B: $o] : $false ) )
| sk2
| ( f
!= ( ^ [B: $o] : $true ) )
| ( A != sk1 ) ),
inference(cnf,[status(esa)],[11]) ).
thf(96,plain,
! [A: $i] :
( ( f
= ( ^ [B: $o] : $false ) )
| ( f
!= ( ^ [B: $o] : $true ) )
| ( A != sk1 )
| sk2 ),
inference(lifteq,[status(thm)],[40]) ).
thf(97,plain,
( ( f
= ( ^ [A: $o] : $false ) )
| ( f
!= ( ^ [A: $o] : $true ) )
| sk2 ),
inference(simp,[status(thm)],[96]) ).
thf(109,plain,
! [A: $o] :
( ~ ( f @ A )
| ~ ( f @ sk5 )
| sk2 ),
inference(func_ext,[status(esa)],[97]) ).
thf(128,plain,
! [A: $o] :
( ~ ( f @ A )
| sk2
| ( ( f @ sk5 )
!= ( f @ A ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[109]) ).
thf(130,plain,
( ~ ( f @ sk5 )
| sk2 ),
inference(pattern_uni,[status(thm)],[128:[bind(A,$thf( sk5 ))]]) ).
thf(256,plain,
( sk2
| ( ( f @ sk12 )
!= ( f @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[236,130]) ).
thf(262,plain,
( sk2
| ( sk12 != sk5 ) ),
inference(simp,[status(thm)],[256]) ).
thf(269,plain,
( sk2
| sk12
| sk5 ),
inference(bool_ext,[status(thm)],[262]) ).
thf(20,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)],[11]) ).
thf(66,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)],[20]) ).
thf(67,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)],[66]) ).
thf(115,plain,
( ( f
!= ( ^ [A: $o] : A ) )
| sk2 ),
inference(simplifyReflect,[status(thm)],[67,6]) ).
thf(116,plain,
( ( ( f @ sk8 )
!= sk8 )
| sk2 ),
inference(func_ext,[status(esa)],[115]) ).
thf(118,plain,
( sk2
| ( f @ sk8 )
| sk8 ),
inference(bool_ext,[status(thm)],[116]) ).
thf(131,plain,
( sk2
| sk8
| ( ( f @ sk8 )
!= ( f @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[118,130]) ).
thf(132,plain,
( sk2
| sk8
| ( sk8 != sk5 ) ),
inference(simp,[status(thm)],[131]) ).
thf(137,plain,
( sk2
| sk8
| sk8
| sk5 ),
inference(bool_ext,[status(thm)],[132]) ).
thf(138,plain,
( sk2
| sk8
| sk5 ),
inference(simp,[status(thm)],[137]) ).
thf(117,plain,
( sk2
| ~ ( f @ sk8 )
| ~ sk8 ),
inference(bool_ext,[status(thm)],[116]) ).
thf(147,plain,
( sk2
| sk5
| ~ ( f @ sk8 )
| ( sk8 != sk8 ) ),
inference(paramod_ordered,[status(thm)],[138,117]) ).
thf(148,plain,
( sk2
| sk5
| ~ ( f @ sk8 ) ),
inference(pattern_uni,[status(thm)],[147:[]]) ).
thf(149,plain,
( sk2
| sk5
| ~ ( f @ $true )
| ( sk8 != sk8 ) ),
inference(paramod_ordered,[status(thm)],[138,148]) ).
thf(150,plain,
( sk2
| sk5
| ~ ( f @ $true ) ),
inference(pattern_uni,[status(thm)],[149:[]]) ).
thf(247,plain,
( sk2
| sk5
| ( ( f @ sk12 )
!= ( f @ $true ) ) ),
inference(paramod_ordered,[status(thm)],[236,150]) ).
thf(258,plain,
( sk2
| sk5
| ~ sk12 ),
inference(simp,[status(thm)],[247]) ).
thf(294,plain,
( sk2
| sk5
| ( sk12 != sk12 ) ),
inference(paramod_ordered,[status(thm)],[269,258]) ).
thf(295,plain,
( sk2
| sk5 ),
inference(pattern_uni,[status(thm)],[294:[]]) ).
thf(268,plain,
( sk2
| ~ sk12
| ~ sk5 ),
inference(bool_ext,[status(thm)],[262]) ).
thf(316,plain,
( sk2
| ~ sk12
| ( sk5 != sk5 ) ),
inference(paramod_ordered,[status(thm)],[295,268]) ).
thf(317,plain,
( sk2
| ~ sk12 ),
inference(pattern_uni,[status(thm)],[316:[]]) ).
thf(378,plain,
( sk2
| sk6
| ( sk12 != sk12 ) ),
inference(paramod_ordered,[status(thm)],[375,317]) ).
thf(379,plain,
( sk2
| sk6 ),
inference(pattern_uni,[status(thm)],[378:[]]) ).
thf(281,plain,
( sk2
| ( f @ sk6 )
| ~ sk6 ),
inference(bool_ext,[status(thm)],[241]) ).
thf(289,plain,
( ~ sk6
| ( f @ sk6 )
| sk2 ),
inference(cnf,[status(esa)],[281]) ).
thf(314,plain,
( sk2
| ~ ( f @ $true )
| ( sk5 != sk5 ) ),
inference(paramod_ordered,[status(thm)],[295,130]) ).
thf(315,plain,
( sk2
| ~ ( f @ $true ) ),
inference(pattern_uni,[status(thm)],[314:[]]) ).
thf(433,plain,
( ~ sk6
| sk2
| ( ( f @ sk6 )
!= ( f @ $true ) ) ),
inference(paramod_ordered,[status(thm)],[289,315]) ).
thf(438,plain,
( sk2
| ~ sk6
| ~ sk6 ),
inference(simp,[status(thm)],[433]) ).
thf(440,plain,
( sk2
| ~ sk6 ),
inference(simp,[status(thm)],[438]) ).
thf(441,plain,
( sk2
| ( sk6 != sk6 ) ),
inference(paramod_ordered,[status(thm)],[379,440]) ).
thf(442,plain,
sk2,
inference(pattern_uni,[status(thm)],[441:[]]) ).
thf(2797,plain,
! [A: $o] :
( ( ( f @ A )
= ~ A )
| ~ ( f @ sk13 )
| ~ $true
| sk3 ),
inference(rewrite,[status(thm)],[271,442]) ).
thf(2798,plain,
! [A: $o] :
( ( ( f @ A )
= ~ A )
| ~ ( f @ sk13 )
| sk3 ),
inference(simp,[status(thm)],[2797]) ).
thf(25,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)],[11]) ).
thf(64,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)],[25]) ).
thf(65,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)],[64]) ).
thf(392,plain,
( ( f != (~) )
| ~ sk2
| sk3 ),
inference(simplifyReflect,[status(thm)],[65,6]) ).
thf(447,plain,
( ( f != (~) )
| ~ $true
| sk3 ),
inference(rewrite,[status(thm)],[392,442]) ).
thf(448,plain,
( ( f != (~) )
| sk3 ),
inference(simp,[status(thm)],[447]) ).
thf(480,plain,
( ( ( f @ sk20 )
!= ~ sk20 )
| sk3 ),
inference(func_ext,[status(esa)],[448]) ).
thf(2868,plain,
! [A: $o] :
( ~ ( f @ sk13 )
| sk3
| ( A != sk20 )
| ( ( f @ A )
!= ( f @ sk20 ) ) ),
inference(paramod_ordered,[status(thm)],[2798,480]) ).
thf(2869,plain,
( ~ ( f @ sk13 )
| sk3
| ( sk20 != sk20 ) ),
inference(pattern_uni,[status(thm)],[2868:[bind(A,$thf( sk20 ))]]) ).
thf(2981,plain,
( ~ ( f @ sk13 )
| sk3 ),
inference(simp,[status(thm)],[2869]) ).
thf(13,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)],[11]) ).
thf(78,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)],[13]) ).
thf(79,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)],[78]) ).
thf(111,plain,
( ( f
!= ( ^ [A: $o] : A ) )
| ~ sk2
| ~ sk3 ),
inference(simplifyReflect,[status(thm)],[79,6]) ).
thf(112,plain,
( ( ( f @ sk7 )
!= sk7 )
| ~ sk2
| ~ sk3 ),
inference(func_ext,[status(esa)],[111]) ).
thf(114,plain,
( ~ sk2
| ~ sk3
| ( f @ sk7 )
| sk7 ),
inference(bool_ext,[status(thm)],[112]) ).
thf(459,plain,
( ~ $true
| ~ sk3
| ( f @ sk7 )
| sk7 ),
inference(rewrite,[status(thm)],[114,442]) ).
thf(460,plain,
( ~ sk3
| ( f @ sk7 )
| sk7 ),
inference(simp,[status(thm)],[459]) ).
thf(37,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)],[11]) ).
thf(62,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)],[37]) ).
thf(63,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)],[62]) ).
thf(388,plain,
( ( f
!= ( ^ [A: $o] : $true ) )
| ~ sk2
| ~ sk3 ),
inference(simplifyReflect,[status(thm)],[63,6]) ).
thf(467,plain,
( ( f
!= ( ^ [A: $o] : $true ) )
| ~ $true
| ~ sk3 ),
inference(rewrite,[status(thm)],[388,442]) ).
thf(468,plain,
( ( f
!= ( ^ [A: $o] : $true ) )
| ~ sk3 ),
inference(simp,[status(thm)],[467]) ).
thf(484,plain,
( ~ ( f @ sk21 )
| ~ sk3 ),
inference(func_ext,[status(esa)],[468]) ).
thf(934,plain,
( ~ sk3
| sk7
| ( ( f @ sk21 )
!= ( f @ sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[460,484]) ).
thf(944,plain,
( sk7
| ~ sk3
| ( sk21 != sk7 ) ),
inference(simp,[status(thm)],[934]) ).
thf(3471,plain,
( sk7
| ~ sk3
| sk21
| sk7 ),
inference(bool_ext,[status(thm)],[944]) ).
thf(3472,plain,
( sk7
| ~ sk3
| sk21 ),
inference(simp,[status(thm)],[3471]) ).
thf(24,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)],[11]) ).
thf(60,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)],[24]) ).
thf(61,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)],[60]) ).
thf(368,plain,
( ( f
!= ( ^ [A: $o] : $false ) )
| ~ sk2
| ~ sk3 ),
inference(simplifyReflect,[status(thm)],[61,6]) ).
thf(369,plain,
( ( f @ sk14 )
| ~ sk2
| ~ sk3 ),
inference(func_ext,[status(esa)],[368]) ).
thf(599,plain,
( ( f @ sk14 )
| ~ $true
| ~ sk3 ),
inference(rewrite,[status(thm)],[369,442]) ).
thf(600,plain,
( ( f @ sk14 )
| ~ sk3 ),
inference(simp,[status(thm)],[599]) ).
thf(389,plain,
( ~ ( f @ sk15 )
| ~ sk2
| ~ sk3 ),
inference(func_ext,[status(esa)],[388]) ).
thf(443,plain,
( ~ ( f @ sk15 )
| ~ $true
| ~ sk3 ),
inference(rewrite,[status(thm)],[389,442]) ).
thf(444,plain,
( ~ ( f @ sk15 )
| ~ sk3 ),
inference(simp,[status(thm)],[443]) ).
thf(603,plain,
( ~ sk3
| ( ( f @ sk15 )
!= ( f @ sk14 ) ) ),
inference(paramod_ordered,[status(thm)],[600,444]) ).
thf(616,plain,
( ~ sk3
| ( sk15 != sk14 ) ),
inference(simp,[status(thm)],[603]) ).
thf(619,plain,
( ~ sk3
| sk15
| sk14 ),
inference(bool_ext,[status(thm)],[616]) ).
thf(457,plain,
( ( f
!= ( ^ [A: $o] : $false ) )
| ~ $true
| ~ sk3 ),
inference(rewrite,[status(thm)],[368,442]) ).
thf(458,plain,
( ( f
!= ( ^ [A: $o] : $false ) )
| ~ sk3 ),
inference(simp,[status(thm)],[457]) ).
thf(478,plain,
( ( f @ sk19 )
| ~ sk3 ),
inference(func_ext,[status(esa)],[458]) ).
thf(15,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)],[11]) ).
thf(56,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)],[15]) ).
thf(57,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)],[56]) ).
thf(134,plain,
( ( f != (~) )
| ~ sk2
| ~ sk3 ),
inference(simplifyReflect,[status(thm)],[57,6]) ).
thf(449,plain,
( ( f != (~) )
| ~ $true
| ~ sk3 ),
inference(rewrite,[status(thm)],[134,442]) ).
thf(450,plain,
( ( f != (~) )
| ~ sk3 ),
inference(simp,[status(thm)],[449]) ).
thf(477,plain,
( ( ( f @ sk18 )
!= ~ sk18 )
| ~ sk3 ),
inference(func_ext,[status(esa)],[450]) ).
thf(521,plain,
( ~ sk3
| sk18
| ( ( f @ sk19 )
!= ( f @ sk18 ) ) ),
inference(paramod_ordered,[status(thm)],[478,477]) ).
thf(522,plain,
( sk18
| ~ sk3
| ( sk19 != sk18 ) ),
inference(simp,[status(thm)],[521]) ).
thf(1879,plain,
( sk18
| ~ sk3
| sk19
| sk18 ),
inference(bool_ext,[status(thm)],[522]) ).
thf(1892,plain,
( sk18
| ~ sk3
| sk19 ),
inference(simp,[status(thm)],[1879]) ).
thf(485,plain,
( ~ sk3
| ( ( f @ sk19 )
!= ( f @ sk15 ) ) ),
inference(paramod_ordered,[status(thm)],[478,444]) ).
thf(486,plain,
( ~ sk3
| ( sk19 != sk15 ) ),
inference(simp,[status(thm)],[485]) ).
thf(489,plain,
( ~ sk3
| ~ sk19
| ~ sk15 ),
inference(bool_ext,[status(thm)],[486]) ).
thf(1902,plain,
( sk18
| ~ sk3
| ~ sk15
| ( sk19 != sk19 ) ),
inference(paramod_ordered,[status(thm)],[1892,489]) ).
thf(1903,plain,
( sk18
| ~ sk3
| ~ sk15 ),
inference(pattern_uni,[status(thm)],[1902:[]]) ).
thf(520,plain,
( ~ sk3
| ( f @ sk18 )
| ~ sk18 ),
inference(bool_ext,[status(thm)],[477]) ).
thf(524,plain,
( ~ sk18
| ( f @ sk18 )
| ~ sk3 ),
inference(cnf,[status(esa)],[520]) ).
thf(487,plain,
( ~ sk3
| ( ( f @ sk21 )
!= ( f @ sk19 ) ) ),
inference(paramod_ordered,[status(thm)],[478,484]) ).
thf(488,plain,
( ~ sk3
| ( sk21 != sk19 ) ),
inference(simp,[status(thm)],[487]) ).
thf(492,plain,
( ~ sk3
| sk21
| sk19 ),
inference(bool_ext,[status(thm)],[488]) ).
thf(530,plain,
( ~ sk3
| sk19
| ~ ( f @ $true )
| ( sk21 != sk21 ) ),
inference(paramod_ordered,[status(thm)],[492,484]) ).
thf(531,plain,
( ~ sk3
| sk19
| ~ ( f @ $true ) ),
inference(pattern_uni,[status(thm)],[530:[]]) ).
thf(2275,plain,
( ~ sk18
| ~ sk3
| sk19
| ( ( f @ sk18 )
!= ( f @ $true ) ) ),
inference(paramod_ordered,[status(thm)],[524,531]) ).
thf(2284,plain,
( sk19
| ~ sk18
| ~ sk3
| ~ sk18 ),
inference(simp,[status(thm)],[2275]) ).
thf(2291,plain,
( sk19
| ~ sk18
| ~ sk3 ),
inference(simp,[status(thm)],[2284]) ).
thf(2300,plain,
( ~ sk18
| ~ sk3
| ~ sk15
| ( sk19 != sk19 ) ),
inference(paramod_ordered,[status(thm)],[2291,489]) ).
thf(2301,plain,
( ~ sk18
| ~ sk3
| ~ sk15 ),
inference(pattern_uni,[status(thm)],[2300:[]]) ).
thf(2336,plain,
( ~ sk3
| ~ sk15
| ( sk18 != sk18 ) ),
inference(paramod_ordered,[status(thm)],[1903,2301]) ).
thf(2337,plain,
( ~ sk3
| ~ sk15 ),
inference(pattern_uni,[status(thm)],[2336:[]]) ).
thf(2378,plain,
( ~ sk3
| sk14
| ( sk15 != sk15 ) ),
inference(paramod_ordered,[status(thm)],[619,2337]) ).
thf(2379,plain,
( ~ sk3
| sk14 ),
inference(pattern_uni,[status(thm)],[2378:[]]) ).
thf(607,plain,
( ~ sk3
| ( ( f @ sk21 )
!= ( f @ sk14 ) ) ),
inference(paramod_ordered,[status(thm)],[600,484]) ).
thf(617,plain,
( ~ sk3
| ( sk21 != sk14 ) ),
inference(simp,[status(thm)],[607]) ).
thf(620,plain,
( ~ sk3
| ~ sk21
| ~ sk14 ),
inference(bool_ext,[status(thm)],[617]) ).
thf(2388,plain,
( ~ sk3
| ~ sk21
| ( sk14 != sk14 ) ),
inference(paramod_ordered,[status(thm)],[2379,620]) ).
thf(2389,plain,
( ~ sk3
| ~ sk21 ),
inference(pattern_uni,[status(thm)],[2388:[]]) ).
thf(3485,plain,
( sk7
| ~ sk3
| ( sk21 != sk21 ) ),
inference(paramod_ordered,[status(thm)],[3472,2389]) ).
thf(3486,plain,
( sk7
| ~ sk3 ),
inference(pattern_uni,[status(thm)],[3485:[]]) ).
thf(135,plain,
( ( ( f @ sk10 )
!= ~ sk10 )
| ~ sk2
| ~ sk3 ),
inference(func_ext,[status(esa)],[134]) ).
thf(453,plain,
( ( ( f @ sk10 )
!= ~ sk10 )
| ~ $true
| ~ sk3 ),
inference(rewrite,[status(thm)],[135,442]) ).
thf(454,plain,
( ( ( f @ sk10 )
!= ~ sk10 )
| ~ sk3 ),
inference(simp,[status(thm)],[453]) ).
thf(515,plain,
( ~ sk3
| sk10
| ( ( f @ sk19 )
!= ( f @ sk10 ) ) ),
inference(paramod_ordered,[status(thm)],[478,454]) ).
thf(516,plain,
( sk10
| ~ sk3
| ( sk19 != sk10 ) ),
inference(simp,[status(thm)],[515]) ).
thf(1038,plain,
( sk10
| ~ sk3
| sk19
| sk10 ),
inference(bool_ext,[status(thm)],[516]) ).
thf(1045,plain,
( sk10
| ~ sk3
| sk19 ),
inference(simp,[status(thm)],[1038]) ).
thf(455,plain,
( ( ( f @ sk7 )
!= sk7 )
| ~ $true
| ~ sk3 ),
inference(rewrite,[status(thm)],[112,442]) ).
thf(456,plain,
( ( ( f @ sk7 )
!= sk7 )
| ~ sk3 ),
inference(simp,[status(thm)],[455]) ).
thf(507,plain,
( ~ sk3
| ~ sk7
| ( ( f @ sk19 )
!= ( f @ sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[478,456]) ).
thf(508,plain,
( ~ sk3
| ~ sk7
| ( sk19 != sk7 ) ),
inference(simp,[status(thm)],[507]) ).
thf(764,plain,
( ~ sk3
| ~ sk7
| ~ sk19
| ~ sk7 ),
inference(bool_ext,[status(thm)],[508]) ).
thf(770,plain,
( ~ sk3
| ~ sk7
| ~ sk19 ),
inference(simp,[status(thm)],[764]) ).
thf(1050,plain,
( sk10
| ~ sk3
| ~ sk7
| ( sk19 != sk19 ) ),
inference(paramod_ordered,[status(thm)],[1045,770]) ).
thf(1051,plain,
( sk10
| ~ sk3
| ~ sk7 ),
inference(pattern_uni,[status(thm)],[1050:[]]) ).
thf(161,plain,
( ~ sk2
| ~ sk3
| ( f @ sk10 )
| ~ sk10 ),
inference(bool_ext,[status(thm)],[135]) ).
thf(164,plain,
( ~ sk10
| ( f @ sk10 )
| ~ sk3
| ~ sk2 ),
inference(cnf,[status(esa)],[161]) ).
thf(113,plain,
( ~ sk2
| ~ sk3
| ~ ( f @ sk7 )
| ~ sk7 ),
inference(bool_ext,[status(thm)],[112]) ).
thf(173,plain,
( ~ sk10
| ~ sk3
| ~ sk2
| ~ sk7
| ( ( f @ sk10 )
!= ( f @ sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[164,113]) ).
thf(187,plain,
( ~ sk10
| ~ sk3
| ~ sk2
| ~ sk7
| ( sk10 != sk7 ) ),
inference(simp,[status(thm)],[173]) ).
thf(237,plain,
( ~ sk10
| ~ sk3
| ~ sk2
| ~ sk7
| ~ sk10
| ~ sk7 ),
inference(bool_ext,[status(thm)],[187]) ).
thf(239,plain,
( ~ sk10
| ~ sk3
| ~ sk2
| ~ sk7 ),
inference(simp,[status(thm)],[237]) ).
thf(461,plain,
( ~ sk10
| ~ sk3
| ~ $true
| ~ sk7 ),
inference(rewrite,[status(thm)],[239,442]) ).
thf(462,plain,
( ~ sk10
| ~ sk3
| ~ sk7 ),
inference(simp,[status(thm)],[461]) ).
thf(1090,plain,
( ~ sk3
| ~ sk7
| ( sk10 != sk10 ) ),
inference(paramod_ordered,[status(thm)],[1051,462]) ).
thf(1091,plain,
( ~ sk3
| ~ sk7 ),
inference(pattern_uni,[status(thm)],[1090:[]]) ).
thf(3489,plain,
( ~ sk3
| ( sk7 != sk7 ) ),
inference(paramod_ordered,[status(thm)],[3486,1091]) ).
thf(3490,plain,
~ sk3,
inference(pattern_uni,[status(thm)],[3489:[]]) ).
thf(3565,plain,
( ~ ( f @ sk13 )
| $false ),
inference(rewrite,[status(thm)],[2981,3490]) ).
thf(3566,plain,
~ ( f @ sk13 ),
inference(simp,[status(thm)],[3565]) ).
thf(41,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)],[11]) ).
thf(80,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)],[41]) ).
thf(81,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)],[80]) ).
thf(538,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 ) )
| ~ $true
| sk3 ),
inference(rewrite,[status(thm)],[81,442]) ).
thf(539,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 ) )
| sk3 ),
inference(simp,[status(thm)],[538]) ).
thf(540,plain,
( ( f
!= ( ^ [A: $o] : $false ) )
| sk3 ),
inference(simplifyReflect,[status(thm)],[539,6]) ).
thf(541,plain,
( ( f @ sk23 )
| sk3 ),
inference(func_ext,[status(esa)],[540]) ).
thf(551,plain,
( sk3
| sk20
| ( ( f @ sk23 )
!= ( f @ sk20 ) ) ),
inference(paramod_ordered,[status(thm)],[541,480]) ).
thf(553,plain,
( sk3
| sk20
| ( sk23 != sk20 ) ),
inference(simp,[status(thm)],[551]) ).
thf(2521,plain,
( sk3
| sk20
| sk23
| sk20 ),
inference(bool_ext,[status(thm)],[553]) ).
thf(2522,plain,
( sk3
| sk20
| sk23 ),
inference(simp,[status(thm)],[2521]) ).
thf(2526,plain,
( sk3
| sk20
| ( f @ $true )
| ( sk23 != sk23 ) ),
inference(paramod_ordered,[status(thm)],[2522,541]) ).
thf(2527,plain,
( sk3
| sk20
| ( f @ $true ) ),
inference(pattern_uni,[status(thm)],[2526:[]]) ).
thf(2990,plain,
( sk3
| sk20
| ( ( f @ sk13 )
!= ( f @ $true ) ) ),
inference(paramod_ordered,[status(thm)],[2527,2981]) ).
thf(3027,plain,
( sk3
| sk20
| ~ sk13 ),
inference(simp,[status(thm)],[2990]) ).
thf(550,plain,
( sk3
| ( f @ sk20 )
| ~ sk20 ),
inference(bool_ext,[status(thm)],[480]) ).
thf(555,plain,
( ~ sk20
| ( f @ sk20 )
| sk3 ),
inference(cnf,[status(esa)],[550]) ).
thf(36,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)],[11]) ).
thf(102,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)],[36]) ).
thf(103,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)],[102]) ).
thf(849,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 ) )
| ~ $true
| sk3 ),
inference(rewrite,[status(thm)],[103,442]) ).
thf(850,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 ) )
| sk3 ),
inference(simp,[status(thm)],[849]) ).
thf(851,plain,
( ( f
!= ( ^ [A: $o] : $true ) )
| sk3 ),
inference(simplifyReflect,[status(thm)],[850,6]) ).
thf(852,plain,
( ~ ( f @ sk24 )
| sk3 ),
inference(func_ext,[status(esa)],[851]) ).
thf(862,plain,
( sk3
| ( ( f @ sk24 )
!= ( f @ sk23 ) ) ),
inference(paramod_ordered,[status(thm)],[541,852]) ).
thf(865,plain,
( sk3
| ( sk24 != sk23 ) ),
inference(simp,[status(thm)],[862]) ).
thf(868,plain,
( sk3
| sk24
| sk23 ),
inference(bool_ext,[status(thm)],[865]) ).
thf(880,plain,
( sk3
| sk23
| ~ ( f @ $true )
| ( sk24 != sk24 ) ),
inference(paramod_ordered,[status(thm)],[868,852]) ).
thf(881,plain,
( sk3
| sk23
| ~ ( f @ $true ) ),
inference(pattern_uni,[status(thm)],[880:[]]) ).
thf(3195,plain,
( ~ sk20
| sk3
| sk23
| ( ( f @ sk20 )
!= ( f @ $true ) ) ),
inference(paramod_ordered,[status(thm)],[555,881]) ).
thf(3224,plain,
( sk3
| sk23
| ~ sk20
| ~ sk20 ),
inference(simp,[status(thm)],[3195]) ).
thf(3240,plain,
( sk3
| sk23
| ~ sk20 ),
inference(simp,[status(thm)],[3224]) ).
thf(2999,plain,
( sk3
| ( ( f @ sk23 )
!= ( f @ sk13 ) ) ),
inference(paramod_ordered,[status(thm)],[541,2981]) ).
thf(3022,plain,
( sk3
| ( sk23 != sk13 ) ),
inference(simp,[status(thm)],[2999]) ).
thf(3245,plain,
( sk3
| ~ sk20
| ~ sk13
| ( sk23 != sk23 ) ),
inference(paramod_ordered,[status(thm)],[3240,3022]) ).
thf(3246,plain,
( sk3
| ~ sk20
| ~ sk13 ),
inference(pattern_uni,[status(thm)],[3245:[]]) ).
thf(3373,plain,
( sk3
| ~ sk13
| ( sk20 != sk20 ) ),
inference(paramod_ordered,[status(thm)],[3027,3246]) ).
thf(3374,plain,
( sk3
| ~ sk13 ),
inference(pattern_uni,[status(thm)],[3373:[]]) ).
thf(3531,plain,
( $false
| ~ sk13 ),
inference(rewrite,[status(thm)],[3374,3490]) ).
thf(3532,plain,
~ sk13,
inference(simp,[status(thm)],[3531]) ).
thf(3618,plain,
~ ( f @ $false ),
inference(rewrite,[status(thm)],[3566,3532]) ).
thf(30,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)],[11]) ).
thf(104,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)],[30]) ).
thf(105,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)],[104]) ).
thf(906,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 ) )
| ~ $true
| sk3 ),
inference(rewrite,[status(thm)],[105,442]) ).
thf(907,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 ) )
| sk3 ),
inference(simp,[status(thm)],[906]) ).
thf(908,plain,
( ( f
!= ( ^ [A: $o] : A ) )
| sk3 ),
inference(simplifyReflect,[status(thm)],[907,6]) ).
thf(909,plain,
( ( ( f @ sk25 )
!= sk25 )
| sk3 ),
inference(func_ext,[status(esa)],[908]) ).
thf(3513,plain,
( ( ( f @ sk25 )
!= sk25 )
| $false ),
inference(rewrite,[status(thm)],[909,3490]) ).
thf(3514,plain,
( ( f @ sk25 )
!= sk25 ),
inference(simp,[status(thm)],[3513]) ).
thf(3032,plain,
( sk3
| sk23
| sk13 ),
inference(bool_ext,[status(thm)],[3022]) ).
thf(3107,plain,
( sk3
| sk13
| ( f @ $true )
| ( sk23 != sk23 ) ),
inference(paramod_ordered,[status(thm)],[3032,541]) ).
thf(3108,plain,
( sk3
| sk13
| ( f @ $true ) ),
inference(pattern_uni,[status(thm)],[3107:[]]) ).
thf(3138,plain,
( sk3
| sk13
| ~ sk25
| ( ( f @ sk25 )
!= ( f @ $true ) ) ),
inference(paramod_ordered,[status(thm)],[3108,909]) ).
thf(3171,plain,
( sk3
| sk13
| ~ sk25
| ~ sk25 ),
inference(simp,[status(thm)],[3138]) ).
thf(3174,plain,
( sk3
| sk13
| ~ sk25 ),
inference(simp,[status(thm)],[3171]) ).
thf(3505,plain,
( $false
| sk13
| ~ sk25 ),
inference(rewrite,[status(thm)],[3174,3490]) ).
thf(3506,plain,
( sk13
| ~ sk25 ),
inference(simp,[status(thm)],[3505]) ).
thf(3611,plain,
( $false
| ~ sk25 ),
inference(rewrite,[status(thm)],[3506,3532]) ).
thf(3612,plain,
~ sk25,
inference(simp,[status(thm)],[3611]) ).
thf(3646,plain,
f @ $false,
inference(rewrite,[status(thm)],[3514,3612]) ).
thf(3647,plain,
~ $true,
inference(rewrite,[status(thm)],[3618,3646]) ).
thf(3648,plain,
$false,
inference(simp,[status(thm)],[3647]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYO546^1 : TPTP v8.2.0. Released v5.2.0.
% 0.13/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n021.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Mon May 20 08:50:09 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.95/0.86 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.21/0.96 % [INFO] Parsing done (97ms).
% 1.21/0.96 % [INFO] Running in sequential loop mode.
% 1.44/1.16 % [INFO] nitpick registered as external prover.
% 1.44/1.16 % [INFO] Scanning for conjecture ...
% 1.71/1.23 % [INFO] Found a conjecture (or negated_conjecture) and 1 axioms. Running axiom selection ...
% 1.82/1.24 % [INFO] Axiom selection finished. Selected 1 axioms (removed 0 axioms).
% 1.82/1.25 % [INFO] Problem is higher-order (TPTP THF).
% 1.82/1.25 % [INFO] Type checking passed.
% 1.82/1.25 % [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 ...
% 22.62/4.38 % [INFO] Killing All external provers ...
% 22.62/4.38 % Time passed: 3856ms (effective reasoning time: 3413ms)
% 22.62/4.38 % 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)>
% 22.62/4.39 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3856 ms resp. 3413 ms w/o parsing
% 23.08/4.66 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 23.08/4.68 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------