TSTP Solution File: SEU671^2 by Leo-III---1.7.15
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.15
% Problem : SEU671^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n026.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 : Mon Jun 24 15:27:50 EDT 2024
% Result : Theorem 21.42s 5.56s
% Output : Refutation 21.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 85 ( 36 unt; 0 typ; 4 def)
% Number of atoms : 230 ( 83 equ; 0 cnn)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 893 ( 92 ~; 88 |; 18 &; 670 @)
% ( 0 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 77 ( 77 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 17 usr; 11 con; 0-3 aty)
% Number of variables : 305 ( 54 ^ 238 !; 13 ?; 305 :)
% Comments :
%------------------------------------------------------------------------------
thf(in_type,type,
in: $i > $i > $o ).
thf(dsetconstr_type,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(dsetconstrER_type,type,
dsetconstrER: $o ).
thf(dsetconstrER_def,definition,
( dsetconstrER
= ( ! [A: $i,B: $i > $o,C: $i] :
( ( in @ C @ ( dsetconstr @ A @ B ) )
=> ( B @ C ) ) ) ) ).
thf(kpair_type,type,
kpair: $i > $i > $i ).
thf(cartprod_type,type,
cartprod: $i > $i > $i ).
thf(setukpairinjL_type,type,
setukpairinjL: $o ).
thf(setukpairinjL_def,definition,
( setukpairinjL
= ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( kpair @ A @ B )
= ( kpair @ C @ D ) )
=> ( A = C ) ) ) ) ).
thf(setukpairinjR_type,type,
setukpairinjR: $o ).
thf(setukpairinjR_def,definition,
( setukpairinjR
= ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( kpair @ A @ B )
= ( kpair @ C @ D ) )
=> ( B = D ) ) ) ) ).
thf(dpsetconstr_type,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(dpsetconstr_def,definition,
( dpsetconstr
= ( ^ [A: $i,B: $i,C: $i > $i > $o] :
( dsetconstr @ ( cartprod @ A @ B )
@ ^ [D: $i] :
? [E: $i] :
( ( in @ E @ A )
& ? [F: $i] :
( ( in @ F @ B )
& ( C @ E @ F )
& ( D
= ( kpair @ E @ F ) ) ) ) ) ) ) ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $i > $i > $o ).
thf(sk4_type,type,
sk4: $i ).
thf(sk5_type,type,
sk5: $i ).
thf(sk6_type,type,
sk6: $i > $i > $i ).
thf(sk7_type,type,
sk7: $i > $i > $i ).
thf(sk8_type,type,
sk8: $i ).
thf(sk9_type,type,
sk9: $i ).
thf(1,conjecture,
( dsetconstrER
=> ( setukpairinjL
=> ( setukpairinjR
=> ! [A: $i,B: $i,C: $i > $i > $o,D: $i,E: $i] :
( ( in @ ( kpair @ D @ E ) @ ( dpsetconstr @ A @ B @ C ) )
=> ( C @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dpsetconstrER) ).
thf(2,negated_conjecture,
~ ( dsetconstrER
=> ( setukpairinjL
=> ( setukpairinjR
=> ! [A: $i,B: $i,C: $i > $i > $o,D: $i,E: $i] :
( ( in @ ( kpair @ D @ E ) @ ( dpsetconstr @ A @ B @ C ) )
=> ( C @ D @ E ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i,B: $i > $o,C: $i] :
( ( in @ C @ ( dsetconstr @ A @ B ) )
=> ( B @ C ) )
=> ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( kpair @ A @ B )
= ( kpair @ C @ D ) )
=> ( A = C ) )
=> ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( kpair @ A @ B )
= ( kpair @ C @ D ) )
=> ( B = D ) )
=> ! [A: $i,B: $i,C: $i > $i > $o,D: $i,E: $i] :
( ( in @ ( kpair @ D @ E )
@ ( dsetconstr @ ( cartprod @ A @ B )
@ ^ [F: $i] :
? [G: $i] :
( ( in @ G @ A )
& ? [H: $i] :
( ( in @ H @ B )
& ( C @ G @ H )
& ( F
= ( kpair @ G @ H ) ) ) ) ) )
=> ( C @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
~ ( ! [A: $i,B: $i > $o,C: $i] :
( ( in @ C @ ( dsetconstr @ A @ B ) )
=> ( B @ C ) )
=> ( ! [A: $i,B: $i,C: $i] :
( ? [D: $i] :
( ( kpair @ A @ B )
= ( kpair @ C @ D ) )
=> ( A = C ) )
=> ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( kpair @ A @ B )
= ( kpair @ C @ D ) )
=> ( B = D ) )
=> ! [A: $i,B: $i,C: $i > $i > $o,D: $i,E: $i] :
( ( in @ ( kpair @ D @ E )
@ ( dsetconstr @ ( cartprod @ A @ B )
@ ^ [F: $i] :
? [G: $i] :
( ( in @ G @ A )
& ? [H: $i] :
( ( in @ H @ B )
& ( C @ G @ H )
& ( F
= ( kpair @ G @ H ) ) ) ) ) )
=> ( C @ D @ E ) ) ) ) ),
inference(miniscope,[status(thm)],[3]) ).
thf(5,plain,
~ ( sk3 @ sk4 @ sk5 ),
inference(cnf,[status(esa)],[4]) ).
thf(6,plain,
( in @ ( kpair @ sk4 @ sk5 )
@ ( dsetconstr @ ( cartprod @ sk1 @ sk2 )
@ ^ [A: $i] :
? [B: $i] :
( ( in @ B @ sk1 )
& ? [C: $i] :
( ( in @ C @ sk2 )
& ( sk3 @ B @ C )
& ( A
= ( kpair @ B @ C ) ) ) ) ) ),
inference(cnf,[status(esa)],[4]) ).
thf(9,plain,
! [C: $i,B: $i > $o,A: $i] :
( ~ ( in @ C @ ( dsetconstr @ A @ B ) )
| ( B @ C ) ),
inference(cnf,[status(esa)],[4]) ).
thf(17,plain,
! [C: $i,B: $i > $o,A: $i] :
( ( B @ C )
| ( ( in @ ( kpair @ sk4 @ sk5 )
@ ( dsetconstr @ ( cartprod @ sk1 @ sk2 )
@ ^ [D: $i] :
? [E: $i] :
( ( in @ E @ sk1 )
& ? [F: $i] :
( ( in @ F @ sk2 )
& ( sk3 @ E @ F )
& ( D
= ( kpair @ E @ F ) ) ) ) ) )
!= ( in @ C @ ( dsetconstr @ A @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[6,9]) ).
thf(18,plain,
? [A: $i] :
( ( in @ A @ sk1 )
& ? [B: $i] :
( ( in @ B @ sk2 )
& ( sk3 @ A @ B )
& ( ( kpair @ sk4 @ sk5 )
= ( kpair @ A @ B ) ) ) ),
inference(pattern_uni,[status(thm)],[17:[bind(A,$thf( cartprod @ sk1 @ sk2 )),bind(B,$thf( ^ [D: $i] : ? [E: $i] : ( ( in @ E @ sk1 ) & ? [F: $i] : ( ( in @ F @ sk2 ) & ( sk3 @ E @ F ) & ( D = ( kpair @ E @ F ) ) ) ) )),bind(C,$thf( kpair @ sk4 @ sk5 ))]]) ).
thf(37,plain,
in @ sk8 @ sk1,
inference(cnf,[status(esa)],[18]) ).
thf(36,plain,
in @ sk9 @ sk2,
inference(cnf,[status(esa)],[18]) ).
thf(21,plain,
! [B: $i,A: $i] :
( ~ ( in @ B
@ ( dsetconstr @ A
@ ^ [C: $i] : $false ) )
| $false ),
inference(prim_subst,[status(thm)],[9:[bind(A,$thf( A )),bind(B,$thf( ^ [D: $i] : $false ))]]) ).
thf(39,plain,
! [B: $i,A: $i] :
~ ( in @ B
@ ( dsetconstr @ A
@ ^ [C: $i] : $false ) ),
inference(simp,[status(thm)],[21]) ).
thf(238,plain,
! [B: $i,A: $i] :
( ( in @ sk9 @ sk2 )
!= ( in @ B
@ ( dsetconstr @ A
@ ^ [C: $i] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[36,39]) ).
thf(241,plain,
! [B: $i,A: $i] :
( ( sk9 != B )
| ( ( dsetconstr @ A
@ ^ [C: $i] : $false )
!= sk2 ) ),
inference(simp,[status(thm)],[238]) ).
thf(253,plain,
! [A: $i] :
( ( dsetconstr @ A
@ ^ [B: $i] : $false )
!= sk2 ),
inference(simp,[status(thm)],[241]) ).
thf(20,plain,
! [C: $i,B: $i > $o,A: $i] :
( ~ ( in @ C @ ( dsetconstr @ A @ B ) )
| ( ( B @ C )
!= ( ~ ( in @ C @ ( dsetconstr @ A @ B ) ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[9]) ).
thf(27,plain,
! [A: $i] :
~ ( in
@ ( dsetconstr @ A
@ ^ [B: $i] :
~ ( in @ B @ B ) )
@ ( dsetconstr @ A
@ ^ [B: $i] :
~ ( in @ B @ B ) ) ),
inference(pre_uni,[status(thm)],[20:[bind(A,$thf( A )),bind(B,$thf( ^ [D: $i] : ~ ( in @ D @ D ) )),bind(C,$thf( dsetconstr @ A @ ^ [D: $i] : ~ ( in @ D @ D ) ))]]) ).
thf(290,plain,
! [D: $i,C: $i,B: $i > $o,A: $i] :
( ~ ( in @ C @ ( dsetconstr @ A @ B ) )
| ( ( B @ C )
!= ( in
@ ( dsetconstr @ D
@ ^ [E: $i] :
~ ( in @ E @ E ) )
@ ( dsetconstr @ D
@ ^ [E: $i] :
~ ( in @ E @ E ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[9,27]) ).
thf(303,plain,
! [B: $i,A: $i] :
~ ( in
@ ( dsetconstr @ B
@ ^ [C: $i] :
~ ( in @ C @ C ) )
@ ( dsetconstr @ A
@ ^ [C: $i] : ( in @ C @ C ) ) ),
inference(pre_uni,[status(thm)],[290:[bind(A,$thf( A )),bind(B,$thf( ^ [E: $i] : ( in @ E @ E ) )),bind(C,$thf( dsetconstr @ D @ ^ [E: $i] : ~ ( in @ E @ E ) )),bind(D,$thf( D ))]]) ).
thf(312,plain,
! [B: $i,A: $i] :
~ ( in
@ ( dsetconstr @ B
@ ^ [C: $i] :
~ ( in @ C @ C ) )
@ ( dsetconstr @ A
@ ^ [C: $i] : ( in @ C @ C ) ) ),
inference(simp,[status(thm)],[303]) ).
thf(62,plain,
! [C: $i,B: $i > $o,A: $i] :
( ( B @ C )
| ( ( in @ sk9 @ sk2 )
!= ( in @ C @ ( dsetconstr @ A @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[36,9]) ).
thf(64,plain,
! [C: $i,B: $i > $o,A: $i] :
( ( B @ C )
| ( sk9 != C )
| ( ( dsetconstr @ A @ B )
!= sk2 ) ),
inference(simp,[status(thm)],[62]) ).
thf(65,plain,
! [B: $i > $o,A: $i] :
( ( B @ sk9 )
| ( ( dsetconstr @ A @ B )
!= sk2 ) ),
inference(simp,[status(thm)],[64]) ).
thf(22,plain,
! [D: $i > $o,C: $i > $o,B: $i,A: $i] :
( ~ ( in @ B
@ ( dsetconstr @ A
@ ^ [E: $i] :
( ( C @ E )
| ( D @ E ) ) ) )
| ( C @ B )
| ( D @ B ) ),
inference(prim_subst,[status(thm)],[9:[bind(A,$thf( A )),bind(B,$thf( ^ [F: $i] : ( ( D @ F ) | ( E @ F ) ) ))]]) ).
thf(40,plain,
! [D: $i > $o,C: $i > $o,B: $i,A: $i] :
( ( C @ B )
| ( D @ B )
| ~ ( in @ B
@ ( dsetconstr @ A
@ ^ [E: $i] :
( ( C @ E )
| ( D @ E ) ) ) ) ),
inference(cnf,[status(esa)],[22]) ).
thf(41,plain,
! [D: $i > $o,C: $i > $o,B: $i,A: $i] :
( ( C @ B )
| ( D @ B )
| ~ ( in @ B
@ ( dsetconstr @ A
@ ^ [E: $i] :
( ( C @ E )
| ( D @ E ) ) ) ) ),
inference(simp,[status(thm)],[40]) ).
thf(7,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( kpair @ A @ B )
!= ( kpair @ C @ D ) )
| ( A = C ) ),
inference(cnf,[status(esa)],[4]) ).
thf(10,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( kpair @ A @ B )
!= ( kpair @ C @ D ) )
| ( A = C ) ),
inference(lifteq,[status(thm)],[7]) ).
thf(11,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( kpair @ A @ B )
!= ( kpair @ C @ D ) )
| ( A = C ) ),
inference(simp,[status(thm)],[10]) ).
thf(12,plain,
! [B: $i,A: $i] :
( ( sk6 @ A @ ( kpair @ B @ A ) )
= B ),
introduced(tautology,[new_symbols(inverse(kpair),[sk6])]) ).
thf(16,plain,
! [C: $i,B: $i > $o,A: $i] :
( ~ ( in @ C @ ( dsetconstr @ A @ B ) )
| ( ( B @ C )
!= ( sk3 @ sk4 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[9,5]) ).
thf(29,plain,
! [A: $i] :
~ ( in @ sk4
@ ( dsetconstr @ A
@ ^ [B: $i] : ( sk3 @ B @ sk5 ) ) ),
inference(pre_uni,[status(thm)],[16:[bind(A,$thf( A )),bind(B,$thf( ^ [D: $i] : ( sk3 @ D @ sk5 ) )),bind(C,$thf( sk4 ))]]) ).
thf(61,plain,
! [A: $i] :
( ( in @ sk9 @ sk2 )
!= ( in @ sk4
@ ( dsetconstr @ A
@ ^ [B: $i] : ( sk3 @ B @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[36,29]) ).
thf(63,plain,
! [A: $i] :
( ( sk9 != sk4 )
| ( ( dsetconstr @ A
@ ^ [B: $i] : ( sk3 @ B @ sk5 ) )
!= sk2 ) ),
inference(simp,[status(thm)],[61]) ).
thf(30,plain,
! [A: $i] :
~ ( in @ sk5 @ ( dsetconstr @ A @ ( sk3 @ sk4 ) ) ),
inference(pre_uni,[status(thm)],[16:[bind(A,$thf( A )),bind(B,$thf( sk3 @ sk4 )),bind(C,$thf( sk5 ))]]) ).
thf(102,plain,
! [D: $i,C: $i,B: $i > $o,A: $i] :
( ~ ( in @ C @ ( dsetconstr @ A @ B ) )
| ( ( B @ C )
!= ( in @ sk5 @ ( dsetconstr @ D @ ( sk3 @ sk4 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[9,30]) ).
thf(106,plain,
! [B: $i,A: $i] :
~ ( in @ ( dsetconstr @ B @ ( sk3 @ sk4 ) ) @ ( dsetconstr @ A @ ( in @ sk5 ) ) ),
inference(pre_uni,[status(thm)],[102:[bind(A,$thf( A )),bind(B,$thf( in @ sk5 )),bind(C,$thf( dsetconstr @ D @ ( sk3 @ sk4 ) )),bind(D,$thf( D ))]]) ).
thf(111,plain,
! [B: $i,A: $i] :
~ ( in @ ( dsetconstr @ B @ ( sk3 @ sk4 ) ) @ ( dsetconstr @ A @ ( in @ sk5 ) ) ),
inference(simp,[status(thm)],[106]) ).
thf(8,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( kpair @ A @ B )
!= ( kpair @ C @ D ) )
| ( B = D ) ),
inference(cnf,[status(esa)],[4]) ).
thf(13,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( kpair @ A @ B )
!= ( kpair @ C @ D ) )
| ( B = D ) ),
inference(lifteq,[status(thm)],[8]) ).
thf(14,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( kpair @ A @ B )
!= ( kpair @ C @ D ) )
| ( B = D ) ),
inference(simp,[status(thm)],[13]) ).
thf(132,plain,
! [E: $i > $o,D: $i > $o,C: $i > $o,B: $i,A: $i] :
( ( D @ B )
| ( E @ B )
| ( C @ B )
| ~ ( in @ B
@ ( dsetconstr @ A
@ ^ [F: $i] :
( ( D @ F )
| ( E @ F )
| ( C @ F ) ) ) ) ),
inference(prim_subst,[status(thm)],[41:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( ^ [G: $i] : ( ( E @ G ) | ( F @ G ) ) ))]]) ).
thf(183,plain,
! [E: $i > $o,D: $i > $o,C: $i > $o,B: $i,A: $i] :
( ~ ( in @ B
@ ( dsetconstr @ A
@ ^ [F: $i] :
( ( D @ F )
| ( E @ F )
| ( C @ F ) ) ) )
| ( C @ B )
| ( D @ B )
| ( E @ B ) ),
inference(cnf,[status(esa)],[132]) ).
thf(184,plain,
! [E: $i > $o,D: $i > $o,C: $i > $o,B: $i,A: $i] :
( ~ ( in @ B
@ ( dsetconstr @ A
@ ^ [F: $i] :
( ( D @ F )
| ( E @ F )
| ( C @ F ) ) ) )
| ( C @ B )
| ( D @ B )
| ( E @ B ) ),
inference(simp,[status(thm)],[183]) ).
thf(103,plain,
! [A: $i] :
( ( in @ sk9 @ sk2 )
!= ( in @ sk5 @ ( dsetconstr @ A @ ( sk3 @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[36,30]) ).
thf(110,plain,
! [A: $i] :
( ( sk9 != sk5 )
| ( ( dsetconstr @ A @ ( sk3 @ sk4 ) )
!= sk2 ) ),
inference(simp,[status(thm)],[103]) ).
thf(49,plain,
! [D: $i,C: $i,B: $i > $o,A: $i] :
( ~ ( in @ C @ ( dsetconstr @ A @ B ) )
| ( ( B @ C )
!= ( in @ sk4
@ ( dsetconstr @ D
@ ^ [E: $i] : ( sk3 @ E @ sk5 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[9,29]) ).
thf(53,plain,
! [B: $i > $i,A: $i] :
~ ( in @ sk4
@ ( dsetconstr @ A
@ ^ [C: $i] :
( in @ C
@ ( dsetconstr @ ( B @ C )
@ ^ [D: $i] : ( sk3 @ D @ sk5 ) ) ) ) ),
inference(pre_uni,[status(thm)],[49:[bind(A,$thf( A )),bind(B,$thf( ^ [F: $i] : ( in @ F @ ( dsetconstr @ ( G @ F ) @ ^ [G: $i] : ( sk3 @ G @ sk5 ) ) ) )),bind(C,$thf( sk4 )),bind(D,$thf( G @ sk4 ))]]) ).
thf(57,plain,
! [B: $i > $i,A: $i] :
~ ( in @ sk4
@ ( dsetconstr @ A
@ ^ [C: $i] :
( in @ C
@ ( dsetconstr @ ( B @ C )
@ ^ [D: $i] : ( sk3 @ D @ sk5 ) ) ) ) ),
inference(simp,[status(thm)],[53]) ).
thf(35,plain,
sk3 @ sk8 @ sk9,
inference(cnf,[status(esa)],[18]) ).
thf(59,plain,
( ( sk3 @ sk8 @ sk9 )
!= ( sk3 @ sk4 @ sk5 ) ),
inference(paramod_ordered,[status(thm)],[35,5]) ).
thf(60,plain,
( ( sk8 != sk4 )
| ( sk9 != sk5 ) ),
inference(simp,[status(thm)],[59]) ).
thf(34,plain,
( ( kpair @ sk4 @ sk5 )
= ( kpair @ sk8 @ sk9 ) ),
inference(cnf,[status(esa)],[18]) ).
thf(38,plain,
( ( kpair @ sk8 @ sk9 )
= ( kpair @ sk4 @ sk5 ) ),
inference(lifteq,[status(thm)],[34]) ).
thf(67,plain,
! [C: $i,B: $i > $o,A: $i] :
( ( B @ C )
| ( ( in @ sk8 @ sk1 )
!= ( in @ C @ ( dsetconstr @ A @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[37,9]) ).
thf(69,plain,
! [C: $i,B: $i > $o,A: $i] :
( ( B @ C )
| ( sk8 != C )
| ( ( dsetconstr @ A @ B )
!= sk1 ) ),
inference(simp,[status(thm)],[67]) ).
thf(70,plain,
! [B: $i > $o,A: $i] :
( ( B @ sk8 )
| ( ( dsetconstr @ A @ B )
!= sk1 ) ),
inference(simp,[status(thm)],[69]) ).
thf(19,plain,
! [F: $i,E: $i > $o,D: $i,C: $i,B: $i > $o,A: $i] :
( ~ ( in @ C @ ( dsetconstr @ A @ B ) )
| ( E @ F )
| ( ( B @ C )
!= ( in @ F @ ( dsetconstr @ D @ E ) ) ) ),
inference(paramod_ordered,[status(thm)],[9,9]) ).
thf(32,plain,
! [D: $i > $i,C: $i > $o,B: $i,A: $i] :
( ~ ( in @ ( dsetconstr @ B @ C )
@ ( dsetconstr @ A
@ ^ [E: $i] : ( in @ ( D @ E ) @ E ) ) )
| ( C @ ( D @ ( dsetconstr @ B @ C ) ) ) ),
inference(pre_uni,[status(thm)],[19:[bind(A,$thf( A )),bind(B,$thf( ^ [H: $i] : ( in @ ( G @ H ) @ H ) )),bind(C,$thf( dsetconstr @ D @ E )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( G @ ( dsetconstr @ D @ E ) ))]]) ).
thf(33,plain,
! [D: $i > $i,C: $i > $o,B: $i,A: $i] :
( ~ ( in @ ( dsetconstr @ B @ C )
@ ( dsetconstr @ A
@ ^ [E: $i] : ( in @ ( D @ E ) @ E ) ) )
| ( C @ ( D @ ( dsetconstr @ B @ C ) ) ) ),
inference(simp,[status(thm)],[32]) ).
thf(15,plain,
! [B: $i,A: $i] :
( ( sk7 @ A @ ( kpair @ A @ B ) )
= B ),
introduced(tautology,[new_symbols(inverse(kpair),[sk7])]) ).
thf(80,plain,
! [B: $i,A: $i] :
( ( ( sk7 @ A @ ( kpair @ sk4 @ sk5 ) )
= B )
| ( ( kpair @ sk8 @ sk9 )
!= ( kpair @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[38,15]) ).
thf(81,plain,
( ( sk7 @ sk8 @ ( kpair @ sk4 @ sk5 ) )
= sk9 ),
inference(pattern_uni,[status(thm)],[80:[bind(A,$thf( sk8 )),bind(B,$thf( sk9 ))]]) ).
thf(362,plain,
! [J: $i > $o,I: $i > $o,H: $i > $o,G: $i,F: $i,E: $i > $o,D: $i > $o,C: $i > $o,B: $i,A: $i] :
( ~ ( in @ B
@ ( dsetconstr @ A
@ ^ [K: $i] :
( ( D @ K )
| ( E @ K )
| ( C @ K ) ) ) )
| ( D @ B )
| ( E @ B )
| ( H @ G )
| ( I @ G )
| ( J @ G )
| ( ( C @ B )
!= ( in @ G
@ ( dsetconstr @ F
@ ^ [K: $i] :
( ( I @ K )
| ( J @ K )
| ( H @ K ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[184,184]) ).
thf(465,plain,
! [I: $i > $i > $o,H: $i > $i > $o,G: $i > $i > $o,F: $i > $i,E: $i > $i,D: $i > $o,C: $i > $o,B: $i,A: $i] :
( ~ ( in @ B
@ ( dsetconstr @ A
@ ^ [J: $i] :
( ( C @ J )
| ( D @ J )
| ( in @ ( E @ J )
@ ( dsetconstr @ ( F @ J )
@ ^ [K: $i] :
( ( H @ J @ K )
| ( I @ J @ K )
| ( G @ J @ K ) ) ) ) ) ) )
| ( C @ B )
| ( D @ B )
| ( G @ B @ ( E @ B ) )
| ( H @ B @ ( E @ B ) )
| ( I @ B @ ( E @ B ) ) ),
inference(pre_uni,[status(thm)],[362:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( ^ [P: $i] : ( in @ ( K @ P ) @ ( dsetconstr @ ( M @ P ) @ ^ [Q: $i] : ( ( Q @ P @ Q ) | ( R @ P @ Q ) | ( P @ P @ Q ) ) ) ) )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( M @ B )),bind(G,$thf( K @ B )),bind(H,$thf( P @ B )),bind(I,$thf( Q @ B )),bind(J,$thf( R @ B ))]]) ).
thf(581,plain,
! [I: $i > $i > $o,H: $i > $i > $o,G: $i > $i > $o,F: $i > $i,E: $i > $i,D: $i > $o,C: $i > $o,B: $i,A: $i] :
( ~ ( in @ B
@ ( dsetconstr @ A
@ ^ [J: $i] :
( ( C @ J )
| ( D @ J )
| ( in @ ( E @ J )
@ ( dsetconstr @ ( F @ J )
@ ^ [K: $i] :
( ( H @ J @ K )
| ( I @ J @ K )
| ( G @ J @ K ) ) ) ) ) ) )
| ( C @ B )
| ( D @ B )
| ( G @ B @ ( E @ B ) )
| ( H @ B @ ( E @ B ) )
| ( I @ B @ ( E @ B ) ) ),
inference(simp,[status(thm)],[465]) ).
thf(100,plain,
! [A: $i] :
( ( in @ sk8 @ sk1 )
!= ( in @ sk5 @ ( dsetconstr @ A @ ( sk3 @ sk4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[37,30]) ).
thf(104,plain,
! [A: $i] :
( ( sk8 != sk5 )
| ( ( dsetconstr @ A @ ( sk3 @ sk4 ) )
!= sk1 ) ),
inference(simp,[status(thm)],[100]) ).
thf(230,plain,
! [B: $i,A: $i] :
( ( in @ sk8 @ sk1 )
!= ( in @ B
@ ( dsetconstr @ A
@ ^ [C: $i] : $false ) ) ),
inference(paramod_ordered,[status(thm)],[37,39]) ).
thf(246,plain,
! [B: $i,A: $i] :
( ( sk8 != B )
| ( ( dsetconstr @ A
@ ^ [C: $i] : $false )
!= sk1 ) ),
inference(simp,[status(thm)],[230]) ).
thf(258,plain,
! [A: $i] :
( ( dsetconstr @ A
@ ^ [B: $i] : $false )
!= sk1 ),
inference(simp,[status(thm)],[246]) ).
thf(51,plain,
! [B: $i,A: $i] :
~ ( in
@ ( dsetconstr @ B
@ ^ [C: $i] : ( sk3 @ C @ sk5 ) )
@ ( dsetconstr @ A @ ( in @ sk4 ) ) ),
inference(pre_uni,[status(thm)],[49:[bind(A,$thf( A )),bind(B,$thf( in @ sk4 )),bind(C,$thf( dsetconstr @ D @ ^ [E: $i] : ( sk3 @ E @ sk5 ) )),bind(D,$thf( D ))]]) ).
thf(55,plain,
! [B: $i,A: $i] :
~ ( in
@ ( dsetconstr @ B
@ ^ [C: $i] : ( sk3 @ C @ sk5 ) )
@ ( dsetconstr @ A @ ( in @ sk4 ) ) ),
inference(simp,[status(thm)],[51]) ).
thf(74,plain,
! [B: $i,A: $i] :
( ( ( sk6 @ A @ ( kpair @ sk4 @ sk5 ) )
= B )
| ( ( kpair @ sk8 @ sk9 )
!= ( kpair @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[38,12]) ).
thf(75,plain,
( ( sk6 @ sk9 @ ( kpair @ sk4 @ sk5 ) )
= sk8 ),
inference(pattern_uni,[status(thm)],[74:[bind(A,$thf( sk9 )),bind(B,$thf( sk8 ))]]) ).
thf(54,plain,
! [B: $i > $i,A: $i] :
~ ( in @ sk5
@ ( dsetconstr @ A
@ ^ [C: $i] :
( in @ sk4
@ ( dsetconstr @ ( B @ C )
@ ^ [D: $i] : ( sk3 @ D @ C ) ) ) ) ),
inference(pre_uni,[status(thm)],[49:[bind(A,$thf( A )),bind(B,$thf( ^ [F: $i] : ( in @ sk4 @ ( dsetconstr @ ( G @ F ) @ ^ [G: $i] : ( sk3 @ G @ F ) ) ) )),bind(C,$thf( sk5 )),bind(D,$thf( G @ sk5 ))]]) ).
thf(58,plain,
! [B: $i > $i,A: $i] :
~ ( in @ sk5
@ ( dsetconstr @ A
@ ^ [C: $i] :
( in @ sk4
@ ( dsetconstr @ ( B @ C )
@ ^ [D: $i] : ( sk3 @ D @ C ) ) ) ) ),
inference(simp,[status(thm)],[54]) ).
thf(66,plain,
! [A: $i] :
( ( in @ sk8 @ sk1 )
!= ( in @ sk4
@ ( dsetconstr @ A
@ ^ [B: $i] : ( sk3 @ B @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[37,29]) ).
thf(68,plain,
! [A: $i] :
( ( sk8 != sk4 )
| ( ( dsetconstr @ A
@ ^ [B: $i] : ( sk3 @ B @ sk5 ) )
!= sk1 ) ),
inference(simp,[status(thm)],[66]) ).
thf(2098,plain,
$false,
inference(e,[status(thm)],[5,37,253,312,65,9,41,27,12,63,11,111,14,184,110,57,29,6,60,38,70,33,81,39,3,35,581,104,258,55,75,58,36,30,15,68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU671^2 : TPTP v8.2.0. Released v3.7.0.
% 0.00/0.11 % Command : run_Leo-III %s %d THM
% 0.11/0.33 % Computer : n026.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 21 16:34:25 EDT 2024
% 0.11/0.33 % CPUTime :
% 0.94/0.86 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.19/0.97 % [INFO] Parsing done (111ms).
% 1.19/0.98 % [INFO] Running in sequential loop mode.
% 1.65/1.20 % [INFO] eprover registered as external prover.
% 1.65/1.21 % [INFO] Scanning for conjecture ...
% 1.80/1.29 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.99/1.31 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.99/1.31 % [INFO] Problem is higher-order (TPTP THF).
% 1.99/1.32 % [INFO] Type checking passed.
% 1.99/1.32 % [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 ...
% 21.42/5.56 % External prover 'e' found a proof!
% 21.42/5.56 % [INFO] Killing All external provers ...
% 21.42/5.56 % Time passed: 5034ms (effective reasoning time: 4576ms)
% 21.42/5.56 % 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)>
% 21.42/5.56 % Axioms used in derivation (0):
% 21.42/5.56 % No. of inferences in proof: 81
% 21.42/5.56 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 5034 ms resp. 4576 ms w/o parsing
% 21.42/5.62 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 21.42/5.62 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------