TSTP Solution File: SEV428^1 by Leo-III---1.7.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : SEV428^1 : TPTP v8.2.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n032.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 04:10:31 EDT 2024
% Result : Theorem 16.16s 4.38s
% Output : Refutation 16.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 21
% Syntax : Number of formulae : 84 ( 12 unt; 14 typ; 2 def)
% Number of atoms : 381 ( 38 equ; 0 cnn)
% Maximal formula atoms : 13 ( 5 avg)
% Number of connectives : 1050 ( 104 ~; 107 |; 95 &; 739 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 130 ( 130 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 14 usr; 9 con; 0-2 aty)
% Number of variables : 156 ( 114 ^ 31 !; 11 ?; 156 :)
% Comments :
%------------------------------------------------------------------------------
thf(eps_type,type,
eps: ( $i > $o ) > $i ).
thf(epsio_type,type,
epsio: ( ( $i > $o ) > $o ) > $i > $o ).
thf(setunion_type,type,
setunion: ( ( $i > $o ) > $o ) > $i > $o ).
thf(setunion_def,definition,
( setunion
= ( ^ [A: ( $i > $o ) > $o,B: $i] :
? [C: $i > $o] :
( ( A @ C )
& ( C @ B ) ) ) ) ).
thf(choosenonempty_type,type,
choosenonempty: ( ( $i > $o ) > $o ) > $i > $o ).
thf(choosenonempty_def,definition,
( choosenonempty
= ( ^ [A: ( $i > $o ) > $o] :
( epsio
@ ^ [B: $i > $o] :
( ( A @ B )
& ( B @ ( eps @ B ) ) ) ) ) ) ).
thf(c_type,type,
c: ( $i > $o ) > $o ).
thf(a_type,type,
a: $i ).
thf(sk1_type,type,
sk1: $i > $o ).
thf(sk2_type,type,
sk2: $i > $i ).
thf(sk4_type,type,
sk4: $i ).
thf(sk5_type,type,
sk5: $i ).
thf(sk8_type,type,
sk8: $i ).
thf(sk9_type,type,
sk9: $i ).
thf(sk11_type,type,
sk11: $i ).
thf(sk13_type,type,
sk13: $i ).
thf(4,axiom,
! [A: ( $i > $o ) > $o] :
( ? [B: $i > $o] : ( A @ B )
=> ( A @ ( epsio @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',choiceaxio) ).
thf(10,plain,
! [A: ( $i > $o ) > $o] :
( ? [B: $i > $o] : ( A @ B )
=> ( A @ ( epsio @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(1,conjecture,
( ( c @ ( choosenonempty @ c ) )
& ? [A: $i] : ( choosenonempty @ c @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(2,negated_conjecture,
~ ( ( c @ ( choosenonempty @ c ) )
& ? [A: $i] : ( choosenonempty @ c @ A ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(6,plain,
~ ( ( c
@ ( epsio
@ ^ [A: $i > $o] :
( ( c @ A )
& ( A @ ( eps @ A ) ) ) ) )
& ? [A: $i] :
( epsio
@ ^ [B: $i > $o] :
( ( c @ B )
& ( B @ ( eps @ B ) ) )
@ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(20,axiom,
? [A: ( ( $i > $o ) > $o ) > $i > $o] :
! [B: ( $i > $o ) > $o] :
( ? [C: $i > $o] : ( B @ C )
=> ( B @ ( A @ B ) ) ),
introduced(axiom_of_choice) ).
thf(21,plain,
! [A: $i > $o] :
( ~ ( ( c @ A )
& ( A @ ( eps @ A ) ) )
| ( ( c
@ ( epsio
@ ^ [B: $i > $o] :
( ( c @ B )
& ( B @ ( eps @ B ) ) ) ) )
& ( epsio
@ ^ [B: $i > $o] :
( ( c @ B )
& ( B @ ( eps @ B ) ) )
@ ( eps
@ ( epsio
@ ^ [B: $i > $o] :
( ( c @ B )
& ( B @ ( eps @ B ) ) ) ) ) ) ) ),
inference(choice,[status(esa)],[20]) ).
thf(24,plain,
! [A: $i > $o] :
( ( c
@ ( epsio
@ ^ [B: $i > $o] :
( ( c @ B )
& ( B @ ( eps @ B ) ) ) ) )
| ~ ( c @ A )
| ~ ( A @ ( eps @ A ) ) ),
inference(cnf,[status(esa)],[21]) ).
thf(205,plain,
( ( c
@ ( epsio
@ ^ [A: $i > $o] :
( ( c @ A )
& ( A @ ( eps @ A ) ) ) ) )
| ~ ( c
@ ^ [A: $i] : $true )
| ~ $true ),
inference(prim_subst,[status(thm)],[24:[bind(A,$thf( ^ [B: $i] : $true ))]]) ).
thf(221,plain,
( ( c
@ ( epsio
@ ^ [A: $i > $o] :
( ( c @ A )
& ( A @ ( eps @ A ) ) ) ) )
| ~ ( c
@ ^ [A: $i] : $true ) ),
inference(simp,[status(thm)],[205]) ).
thf(23,plain,
! [A: $i > $o] :
( ( epsio
@ ^ [B: $i > $o] :
( ( c @ B )
& ( B @ ( eps @ B ) ) )
@ ( eps
@ ( epsio
@ ^ [B: $i > $o] :
( ( c @ B )
& ( B @ ( eps @ B ) ) ) ) ) )
| ~ ( c @ A )
| ~ ( A @ ( eps @ A ) ) ),
inference(cnf,[status(esa)],[21]) ).
thf(74,plain,
( ( epsio
@ ^ [A: $i > $o] :
( ( c @ A )
& ( A @ ( eps @ A ) ) )
@ ( eps
@ ( epsio
@ ^ [A: $i > $o] :
( ( c @ A )
& ( A @ ( eps @ A ) ) ) ) ) )
| ~ ( c
@ ^ [A: $i] : $true )
| ~ $true ),
inference(prim_subst,[status(thm)],[23:[bind(A,$thf( ^ [B: $i] : $true ))]]) ).
thf(93,plain,
( ( epsio
@ ^ [A: $i > $o] :
( ( c @ A )
& ( A @ ( eps @ A ) ) )
@ ( eps
@ ( epsio
@ ^ [A: $i > $o] :
( ( c @ A )
& ( A @ ( eps @ A ) ) ) ) ) )
| ~ ( c
@ ^ [A: $i] : $true ) ),
inference(simp,[status(thm)],[74]) ).
thf(7,plain,
! [A: $i] :
( ~ ( c
@ ( epsio
@ ^ [B: $i > $o] :
( ( c @ B )
& ( B @ ( eps @ B ) ) ) ) )
| ~ ( epsio
@ ^ [B: $i > $o] :
( ( c @ B )
& ( B @ ( eps @ B ) ) )
@ A ) ),
inference(cnf,[status(esa)],[6]) ).
thf(105,plain,
! [A: $i] :
( ~ ( c
@ ^ [B: $i] : $true )
| ~ ( c
@ ( epsio
@ ^ [B: $i > $o] :
( ( c @ B )
& ( B @ ( eps @ B ) ) ) ) )
| ( ( epsio
@ ^ [B: $i > $o] :
( ( c @ B )
& ( B @ ( eps @ B ) ) )
@ ( eps
@ ( epsio
@ ^ [B: $i > $o] :
( ( c @ B )
& ( B @ ( eps @ B ) ) ) ) ) )
!= ( epsio
@ ^ [B: $i > $o] :
( ( c @ B )
& ( B @ ( eps @ B ) ) )
@ A ) ) ),
inference(paramod_ordered,[status(thm)],[93,7]) ).
thf(106,plain,
( ~ ( c
@ ^ [A: $i] : $true )
| ~ ( c
@ ( epsio
@ ^ [A: $i > $o] :
( ( c @ A )
& ( A @ ( eps @ A ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[105:[bind(A,$thf( eps @ ( epsio @ ^ [B: $i > $o] : ( ( c @ B ) & ( B @ ( eps @ B ) ) ) ) ))]]) ).
thf(359,plain,
( ~ ( c
@ ^ [A: $i] : $true )
| ( ( c
@ ( epsio
@ ^ [A: $i > $o] :
( ( c @ A )
& ( A @ ( eps @ A ) ) ) ) )
!= ( c
@ ( epsio
@ ^ [A: $i > $o] :
( ( c @ A )
& ( A @ ( eps @ A ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[221,106]) ).
thf(360,plain,
~ ( c
@ ^ [A: $i] : $true ),
inference(pattern_uni,[status(thm)],[359:[]]) ).
thf(5,axiom,
setunion @ c @ a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ca) ).
thf(12,plain,
? [A: $i > $o] :
( ( c @ A )
& ( A @ a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(14,plain,
c @ sk1,
inference(cnf,[status(esa)],[12]) ).
thf(19,plain,
! [A: $i] :
( ~ ( epsio
@ ^ [B: $i > $o] :
( ( c @ B )
& ( B @ ( eps @ B ) ) )
@ A )
| ( ( c
@ ( epsio
@ ^ [B: $i > $o] :
( ( c @ B )
& ( B @ ( eps @ B ) ) ) ) )
!= ( c @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[14,7]) ).
thf(22,plain,
! [A: $i] :
( ~ ( epsio
@ ^ [B: $i > $o] :
( ( c @ B )
& ( B @ ( eps @ B ) ) )
@ A )
| ( ( epsio
@ ^ [B: $i > $o] :
( ( c @ B )
& ( B @ ( eps @ B ) ) ) )
!= sk1 ) ),
inference(simp,[status(thm)],[19]) ).
thf(25,plain,
! [A: $i] :
( ( ( epsio
@ ^ [B: $i > $o] :
( ( c @ B )
& ( B @ ( eps @ B ) ) )
@ ( sk2 @ A ) )
!= ( sk1 @ ( sk2 @ A ) ) )
| ~ ( epsio
@ ^ [B: $i > $o] :
( ( c @ B )
& ( B @ ( eps @ B ) ) )
@ A ) ),
inference(func_ext,[status(esa)],[22]) ).
thf(27,plain,
! [A: $i] :
( ~ ( epsio
@ ^ [B: $i > $o] :
( ( c @ B )
& ( B @ ( eps @ B ) ) )
@ A )
| ( epsio
@ ^ [B: $i > $o] :
( ( c @ B )
& ( B @ ( eps @ B ) ) )
@ ( sk2 @ A ) )
| ( sk1 @ ( sk2 @ A ) ) ),
inference(bool_ext,[status(thm)],[25]) ).
thf(46,plain,
! [B: $i,A: $i] :
( ~ ( epsio
@ ^ [C: $i > $o] :
( ( c @ C )
& ( C @ ( eps @ C ) ) )
@ A )
| ( sk1 @ ( sk2 @ A ) )
| ( epsio
@ ^ [C: $i > $o] :
( ( c @ C )
& ( C @ ( eps @ C ) ) )
@ ( sk2 @ B ) )
| ( sk1 @ ( sk2 @ B ) )
| ( ( epsio
@ ^ [C: $i > $o] :
( ( c @ C )
& ( C @ ( eps @ C ) ) )
@ ( sk2 @ A ) )
!= ( epsio
@ ^ [C: $i > $o] :
( ( c @ C )
& ( C @ ( eps @ C ) ) )
@ B ) ) ),
inference(paramod_ordered,[status(thm)],[27,27]) ).
thf(47,plain,
! [A: $i] :
( ~ ( epsio
@ ^ [B: $i > $o] :
( ( c @ B )
& ( B @ ( eps @ B ) ) )
@ A )
| ( sk1 @ ( sk2 @ A ) )
| ( epsio
@ ^ [B: $i > $o] :
( ( c @ B )
& ( B @ ( eps @ B ) ) )
@ ( sk2 @ ( sk2 @ A ) ) )
| ( sk1 @ ( sk2 @ ( sk2 @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[46:[bind(A,$thf( C )),bind(B,$thf( sk2 @ C ))]]) ).
thf(52,plain,
! [A: $i] :
( ~ ( epsio
@ ^ [B: $i > $o] :
( ( c @ B )
& ( B @ ( eps @ B ) ) )
@ A )
| ( sk1 @ ( sk2 @ A ) )
| ( epsio
@ ^ [B: $i > $o] :
( ( c @ B )
& ( B @ ( eps @ B ) ) )
@ ( sk2 @ ( sk2 @ A ) ) )
| ( sk1 @ ( sk2 @ ( sk2 @ A ) ) ) ),
inference(simp,[status(thm)],[47]) ).
thf(145,plain,
! [B: $i,A: $i] :
( ~ ( epsio
@ ^ [C: $i > $o] :
( ( c @ C )
& ( C @ ( eps @ C ) ) )
@ A )
| ( sk1 @ ( sk2 @ A ) )
| ( sk1 @ ( sk2 @ ( sk2 @ A ) ) )
| ( sk1 @ ( sk2 @ B ) )
| ( epsio
@ ^ [C: $i > $o] :
( ( c @ C )
& ( C @ ( eps @ C ) ) )
@ ( sk2 @ ( sk2 @ B ) ) )
| ( sk1 @ ( sk2 @ ( sk2 @ B ) ) )
| ( ( epsio
@ ^ [C: $i > $o] :
( ( c @ C )
& ( C @ ( eps @ C ) ) )
@ ( sk2 @ ( sk2 @ A ) ) )
!= ( epsio
@ ^ [C: $i > $o] :
( ( c @ C )
& ( C @ ( eps @ C ) ) )
@ B ) ) ),
inference(paramod_ordered,[status(thm)],[52,52]) ).
thf(146,plain,
! [A: $i] :
( ~ ( epsio
@ ^ [B: $i > $o] :
( ( c @ B )
& ( B @ ( eps @ B ) ) )
@ A )
| ( sk1 @ ( sk2 @ A ) )
| ( sk1 @ ( sk2 @ ( sk2 @ A ) ) )
| ( sk1 @ ( sk2 @ ( sk2 @ ( sk2 @ A ) ) ) )
| ( epsio
@ ^ [B: $i > $o] :
( ( c @ B )
& ( B @ ( eps @ B ) ) )
@ ( sk2 @ ( sk2 @ ( sk2 @ ( sk2 @ A ) ) ) ) )
| ( sk1 @ ( sk2 @ ( sk2 @ ( sk2 @ ( sk2 @ A ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[145:[bind(A,$thf( D )),bind(B,$thf( sk2 @ ( sk2 @ D ) ))]]) ).
thf(161,plain,
! [A: $i] :
( ~ ( epsio
@ ^ [B: $i > $o] :
( ( c @ B )
& ( B @ ( eps @ B ) ) )
@ A )
| ( sk1 @ ( sk2 @ A ) )
| ( sk1 @ ( sk2 @ ( sk2 @ A ) ) )
| ( sk1 @ ( sk2 @ ( sk2 @ ( sk2 @ A ) ) ) )
| ( epsio
@ ^ [B: $i > $o] :
( ( c @ B )
& ( B @ ( eps @ B ) ) )
@ ( sk2 @ ( sk2 @ ( sk2 @ ( sk2 @ A ) ) ) ) )
| ( sk1 @ ( sk2 @ ( sk2 @ ( sk2 @ ( sk2 @ A ) ) ) ) ) ),
inference(simp,[status(thm)],[146]) ).
thf(123,plain,
( ~ ( c
@ ^ [A: $i] : $true )
| ( ( c
@ ( epsio
@ ^ [A: $i > $o] :
( ( c @ A )
& ( A @ ( eps @ A ) ) ) ) )
!= ( c
@ ^ [A: $i] : $true ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[106]) ).
thf(127,plain,
( ~ ( c
@ ^ [A: $i] : $true )
| ( ( epsio
@ ^ [A: $i > $o] :
( ( c @ A )
& ( A @ ( eps @ A ) ) ) )
!= ( ^ [A: $i] : $true ) ) ),
inference(simp,[status(thm)],[123]) ).
thf(134,plain,
( ~ ( epsio
@ ^ [A: $i > $o] :
( ( c @ A )
& ( A @ ( eps @ A ) ) )
@ sk5 )
| ~ ( c
@ ^ [A: $i] : $true ) ),
inference(func_ext,[status(esa)],[127]) ).
thf(230,plain,
( ~ ( epsio
@ ^ [A: $i > $o] :
( ( c @ A )
& ( A @ ( eps @ A ) ) )
@ sk5 )
| ( ( c @ sk1 )
!= ( c
@ ^ [A: $i] : $true ) ) ),
inference(paramod_ordered,[status(thm)],[14,134]) ).
thf(235,plain,
( ~ ( epsio
@ ^ [A: $i > $o] :
( ( c @ A )
& ( A @ ( eps @ A ) ) )
@ sk5 )
| ( sk1
!= ( ^ [A: $i] : $true ) ) ),
inference(simp,[status(thm)],[230]) ).
thf(251,plain,
( ~ ( sk1 @ sk11 )
| ~ ( epsio
@ ^ [A: $i > $o] :
( ( c @ A )
& ( A @ ( eps @ A ) ) )
@ sk5 ) ),
inference(func_ext,[status(esa)],[235]) ).
thf(26,plain,
! [A: $i] :
( ~ ( epsio
@ ^ [B: $i > $o] :
( ( c @ B )
& ( B @ ( eps @ B ) ) )
@ A )
| ~ ( epsio
@ ^ [B: $i > $o] :
( ( c @ B )
& ( B @ ( eps @ B ) ) )
@ ( sk2 @ A ) )
| ~ ( sk1 @ ( sk2 @ A ) ) ),
inference(bool_ext,[status(thm)],[25]) ).
thf(29,plain,
! [A: $i] :
( ~ ( epsio
@ ^ [B: $i > $o] :
( ( c @ B )
& ( B @ ( eps @ B ) ) )
@ A )
| ~ ( sk1 @ ( sk2 @ A ) )
| ( ( epsio
@ ^ [B: $i > $o] :
( ( c @ B )
& ( B @ ( eps @ B ) ) )
@ ( sk2 @ A ) )
!= ( epsio
@ ^ [B: $i > $o] :
( ( c @ B )
& ( B @ ( eps @ B ) ) )
@ A ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[26]) ).
thf(31,plain,
! [A: $i] :
( ~ ( epsio
@ ^ [B: $i > $o] :
( ( c @ B )
& ( B @ ( eps @ B ) ) )
@ A )
| ~ ( sk1 @ ( sk2 @ A ) )
| ( ( epsio
@ ^ [B: $i > $o] :
( ( c @ B )
& ( B @ ( eps @ B ) ) )
@ ( sk2 @ A ) )
!= ( epsio
@ ^ [B: $i > $o] :
( ( c @ B )
& ( B @ ( eps @ B ) ) )
@ A ) ) ),
inference(simp,[status(thm)],[29]) ).
thf(3,axiom,
! [A: $i > $o] :
( ? [B: $i] : ( A @ B )
=> ( A @ ( eps @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',choiceax) ).
thf(8,plain,
! [A: $i > $o] :
( ? [B: $i] : ( A @ B )
=> ( A @ ( eps @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(13,plain,
sk1 @ a,
inference(cnf,[status(esa)],[12]) ).
thf(28,plain,
! [A: $i] :
( ~ ( epsio
@ ^ [B: $i > $o] :
( ( c @ B )
& ( B @ ( eps @ B ) ) )
@ A )
| ~ ( epsio
@ ^ [B: $i > $o] :
( ( c @ B )
& ( B @ ( eps @ B ) ) )
@ ( sk2 @ A ) )
| ( ( sk1 @ ( sk2 @ A ) )
!= ( sk1 @ a ) ) ),
inference(paramod_ordered,[status(thm)],[13,26]) ).
thf(30,plain,
! [A: $i] :
( ~ ( epsio
@ ^ [B: $i > $o] :
( ( c @ B )
& ( B @ ( eps @ B ) ) )
@ A )
| ~ ( epsio
@ ^ [B: $i > $o] :
( ( c @ B )
& ( B @ ( eps @ B ) ) )
@ ( sk2 @ A ) )
| ( ( sk2 @ A )
!= a ) ),
inference(simp,[status(thm)],[28]) ).
thf(121,plain,
( ~ ( c
@ ( epsio
@ ^ [A: $i > $o] :
( ( c @ A )
& ( A @ ( eps @ A ) ) ) ) )
| ( ( c @ sk1 )
!= ( c
@ ^ [A: $i] : $true ) ) ),
inference(paramod_ordered,[status(thm)],[14,106]) ).
thf(124,plain,
( ~ ( c
@ ( epsio
@ ^ [A: $i > $o] :
( ( c @ A )
& ( A @ ( eps @ A ) ) ) ) )
| ( sk1
!= ( ^ [A: $i] : $true ) ) ),
inference(simp,[status(thm)],[121]) ).
thf(131,plain,
( ~ ( sk1 @ sk4 )
| ~ ( c
@ ( epsio
@ ^ [A: $i > $o] :
( ( c @ A )
& ( A @ ( eps @ A ) ) ) ) ) ),
inference(func_ext,[status(esa)],[124]) ).
thf(168,plain,
( ~ ( c
@ ( epsio
@ ^ [A: $i > $o] :
( ( c @ A )
& ( A @ ( eps @ A ) ) ) ) )
| ( ( sk1 @ sk4 )
!= ( sk1 @ a ) ) ),
inference(paramod_ordered,[status(thm)],[13,131]) ).
thf(170,plain,
( ~ ( c
@ ( epsio
@ ^ [A: $i > $o] :
( ( c @ A )
& ( A @ ( eps @ A ) ) ) ) )
| ( sk4 != a ) ),
inference(simp,[status(thm)],[168]) ).
thf(246,plain,
( ( sk4 != a )
| ( ( c
@ ( epsio
@ ^ [A: $i > $o] :
( ( c @ A )
& ( A @ ( eps @ A ) ) ) ) )
!= ( c @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[14,170]) ).
thf(247,plain,
( ( sk4 != a )
| ( ( epsio
@ ^ [A: $i > $o] :
( ( c @ A )
& ( A @ ( eps @ A ) ) ) )
!= sk1 ) ),
inference(simp,[status(thm)],[246]) ).
thf(391,plain,
( ( c @ sk1 )
!= ( c
@ ^ [A: $i] : $true ) ),
inference(paramod_ordered,[status(thm)],[14,360]) ).
thf(393,plain,
( sk1
!= ( ^ [A: $i] : $true ) ),
inference(simp,[status(thm)],[391]) ).
thf(394,plain,
~ ( sk1 @ sk13 ),
inference(func_ext,[status(esa)],[393]) ).
thf(395,plain,
( ( sk1 @ sk13 )
!= ( sk1 @ a ) ),
inference(paramod_ordered,[status(thm)],[13,394]) ).
thf(396,plain,
sk13 != a,
inference(simp,[status(thm)],[395]) ).
thf(135,plain,
( ( ( epsio
@ ^ [A: $i > $o] :
( ( c @ A )
& ( A @ ( eps @ A ) ) ) )
!= ( ^ [A: $i] : $true ) )
| ( ( c @ sk1 )
!= ( c
@ ^ [A: $i] : $true ) ) ),
inference(paramod_ordered,[status(thm)],[14,127]) ).
thf(136,plain,
( ( ( epsio
@ ^ [A: $i > $o] :
( ( c @ A )
& ( A @ ( eps @ A ) ) ) )
!= ( ^ [A: $i] : $true ) )
| ( sk1
!= ( ^ [A: $i] : $true ) ) ),
inference(simp,[status(thm)],[135]) ).
thf(243,plain,
( ~ ( epsio
@ ^ [A: $i > $o] :
( ( c @ A )
& ( A @ ( eps @ A ) ) )
@ sk8 )
| ~ ( sk1 @ sk9 ) ),
inference(func_ext,[status(esa)],[136]) ).
thf(308,plain,
( ~ ( epsio
@ ^ [A: $i > $o] :
( ( c @ A )
& ( A @ ( eps @ A ) ) )
@ sk8 )
| ( ( sk1 @ sk9 )
!= ( sk1 @ a ) ) ),
inference(paramod_ordered,[status(thm)],[13,243]) ).
thf(313,plain,
( ~ ( epsio
@ ^ [A: $i > $o] :
( ( c @ A )
& ( A @ ( eps @ A ) ) )
@ sk8 )
| ( sk9 != a ) ),
inference(simp,[status(thm)],[308]) ).
thf(267,plain,
! [B: $i,A: $i] :
( ~ ( epsio
@ ^ [C: $i > $o] :
( ( c @ C )
& ( C @ ( eps @ C ) ) )
@ A )
| ( sk1 @ ( sk2 @ A ) )
| ( sk1 @ ( sk2 @ ( sk2 @ A ) ) )
| ( sk1 @ ( sk2 @ ( sk2 @ ( sk2 @ A ) ) ) )
| ( sk1 @ ( sk2 @ ( sk2 @ ( sk2 @ ( sk2 @ A ) ) ) ) )
| ( sk1 @ ( sk2 @ B ) )
| ( sk1 @ ( sk2 @ ( sk2 @ B ) ) )
| ( sk1 @ ( sk2 @ ( sk2 @ ( sk2 @ B ) ) ) )
| ( epsio
@ ^ [C: $i > $o] :
( ( c @ C )
& ( C @ ( eps @ C ) ) )
@ ( sk2 @ ( sk2 @ ( sk2 @ ( sk2 @ B ) ) ) ) )
| ( sk1 @ ( sk2 @ ( sk2 @ ( sk2 @ ( sk2 @ B ) ) ) ) )
| ( ( epsio
@ ^ [C: $i > $o] :
( ( c @ C )
& ( C @ ( eps @ C ) ) )
@ ( sk2 @ ( sk2 @ ( sk2 @ ( sk2 @ A ) ) ) ) )
!= ( epsio
@ ^ [C: $i > $o] :
( ( c @ C )
& ( C @ ( eps @ C ) ) )
@ B ) ) ),
inference(paramod_ordered,[status(thm)],[161,161]) ).
thf(268,plain,
! [A: $i] :
( ~ ( epsio
@ ^ [B: $i > $o] :
( ( c @ B )
& ( B @ ( eps @ B ) ) )
@ A )
| ( sk1 @ ( sk2 @ A ) )
| ( sk1 @ ( sk2 @ ( sk2 @ A ) ) )
| ( sk1 @ ( sk2 @ ( sk2 @ ( sk2 @ A ) ) ) )
| ( sk1 @ ( sk2 @ ( sk2 @ ( sk2 @ ( sk2 @ A ) ) ) ) )
| ( sk1 @ ( sk2 @ ( sk2 @ ( sk2 @ ( sk2 @ ( sk2 @ A ) ) ) ) ) )
| ( sk1 @ ( sk2 @ ( sk2 @ ( sk2 @ ( sk2 @ ( sk2 @ ( sk2 @ A ) ) ) ) ) ) )
| ( sk1 @ ( sk2 @ ( sk2 @ ( sk2 @ ( sk2 @ ( sk2 @ ( sk2 @ ( sk2 @ A ) ) ) ) ) ) ) )
| ( epsio
@ ^ [B: $i > $o] :
( ( c @ B )
& ( B @ ( eps @ B ) ) )
@ ( sk2 @ ( sk2 @ ( sk2 @ ( sk2 @ ( sk2 @ ( sk2 @ ( sk2 @ ( sk2 @ A ) ) ) ) ) ) ) ) )
| ( sk1 @ ( sk2 @ ( sk2 @ ( sk2 @ ( sk2 @ ( sk2 @ ( sk2 @ ( sk2 @ ( sk2 @ A ) ) ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[267:[bind(A,$thf( F )),bind(B,$thf( sk2 @ ( sk2 @ ( sk2 @ ( sk2 @ F ) ) ) ))]]) ).
thf(299,plain,
! [A: $i] :
( ~ ( epsio
@ ^ [B: $i > $o] :
( ( c @ B )
& ( B @ ( eps @ B ) ) )
@ A )
| ( sk1 @ ( sk2 @ A ) )
| ( sk1 @ ( sk2 @ ( sk2 @ A ) ) )
| ( sk1 @ ( sk2 @ ( sk2 @ ( sk2 @ A ) ) ) )
| ( sk1 @ ( sk2 @ ( sk2 @ ( sk2 @ ( sk2 @ A ) ) ) ) )
| ( sk1 @ ( sk2 @ ( sk2 @ ( sk2 @ ( sk2 @ ( sk2 @ A ) ) ) ) ) )
| ( sk1 @ ( sk2 @ ( sk2 @ ( sk2 @ ( sk2 @ ( sk2 @ ( sk2 @ A ) ) ) ) ) ) )
| ( sk1 @ ( sk2 @ ( sk2 @ ( sk2 @ ( sk2 @ ( sk2 @ ( sk2 @ ( sk2 @ A ) ) ) ) ) ) ) )
| ( epsio
@ ^ [B: $i > $o] :
( ( c @ B )
& ( B @ ( eps @ B ) ) )
@ ( sk2 @ ( sk2 @ ( sk2 @ ( sk2 @ ( sk2 @ ( sk2 @ ( sk2 @ ( sk2 @ A ) ) ) ) ) ) ) ) )
| ( sk1 @ ( sk2 @ ( sk2 @ ( sk2 @ ( sk2 @ ( sk2 @ ( sk2 @ ( sk2 @ ( sk2 @ A ) ) ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[268]) ).
thf(169,plain,
( ~ ( sk1 @ sk4 )
| ( ( c
@ ( epsio
@ ^ [A: $i > $o] :
( ( c @ A )
& ( A @ ( eps @ A ) ) ) ) )
!= ( c @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[14,131]) ).
thf(171,plain,
( ~ ( sk1 @ sk4 )
| ( ( epsio
@ ^ [A: $i > $o] :
( ( c @ A )
& ( A @ ( eps @ A ) ) ) )
!= sk1 ) ),
inference(simp,[status(thm)],[169]) ).
thf(534,plain,
$false,
inference(e,[status(thm)],[10,6,360,161,7,251,31,8,30,131,170,247,24,25,52,14,396,243,393,13,22,27,12,313,394,299,26,171,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV428^1 : TPTP v8.2.0. Released v5.2.0.
% 0.11/0.13 % Command : run_Leo-III %s %d
% 0.12/0.34 % Computer : n032.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sun May 19 18:38:24 EDT 2024
% 0.12/0.34 % CPUTime :
% 1.04/0.97 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.36/1.14 % [INFO] Parsing done (168ms).
% 1.36/1.15 % [INFO] Running in sequential loop mode.
% 1.92/1.52 % [INFO] eprover registered as external prover.
% 1.92/1.52 % [INFO] cvc4 registered as external prover.
% 1.92/1.53 % [INFO] Scanning for conjecture ...
% 2.07/1.62 % [INFO] Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ...
% 2.07/1.66 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 2.07/1.66 % [INFO] Problem is higher-order (TPTP THF).
% 2.25/1.67 % [INFO] Type checking passed.
% 2.25/1.67 % [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 ...
% 16.16/4.37 % External prover 'e' found a proof!
% 16.16/4.37 % [INFO] Killing All external provers ...
% 16.16/4.37 % Time passed: 3881ms (effective reasoning time: 3211ms)
% 16.16/4.37 % 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)>
% 16.16/4.38 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3881 ms resp. 3211 ms w/o parsing
% 16.52/4.47 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 16.52/4.47 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------