TSTP Solution File: SEV208^5 by Leo-III---1.7.15
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.15
% Problem : SEV208^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n029.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 15:58:30 EDT 2024
% Result : Theorem 71.86s 22.85s
% Output : Refutation 71.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 1
% Syntax : Number of formulae : 131 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 596 ( 261 equ; 0 cnn)
% Maximal formula atoms : 24 ( 4 avg)
% Number of connectives : 1962 ( 266 ~; 268 |; 82 &;1318 @)
% ( 0 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 9 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 192 ( 192 >; 0 *; 0 +; 0 <<)
% Number of symbols : 30 ( 27 usr; 13 con; 0-3 aty)
% Number of variables : 569 ( 336 ^ 161 !; 72 ?; 569 :)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(z_type,type,
z: a ).
thf(y_type,type,
y: a ).
thf(cP_type,type,
cP: a > a > a ).
thf(w_type,type,
w: a ).
thf(x_type,type,
x: a ).
thf(c0_type,type,
c0: a ).
thf(sk1_type,type,
sk1: ( a > a > a > $o ) > a ).
thf(sk2_type,type,
sk2: ( a > a > a > $o ) > a ).
thf(sk3_type,type,
sk3: ( a > a > a > $o ) > a ).
thf(sk4_type,type,
sk4: ( a > a > a > $o ) > $o ).
thf(sk5_type,type,
sk5: ( a > a > a > $o ) > $o ).
thf(sk12_type,type,
sk12: ( a > a > a > $o ) > a ).
thf(sk13_type,type,
sk13: ( a > a > a > $o ) > a ).
thf(sk14_type,type,
sk14: ( a > a > a > $o ) > a ).
thf(sk15_type,type,
sk15: ( a > a > a > $o ) > $o ).
thf(sk16_type,type,
sk16: ( a > a > a > $o ) > $o ).
thf(sk19_type,type,
sk19: ( a > a > a > $o ) > a ).
thf(sk20_type,type,
sk20: ( a > a > a > $o ) > a ).
thf(sk21_type,type,
sk21: ( a > a > a > $o ) > a ).
thf(sk22_type,type,
sk22: ( a > a > a > $o ) > a ).
thf(sk23_type,type,
sk23: a > a > a > $o ).
thf(1,conjecture,
( ( ! [A: a > a > a > $o] :
( ( $true
& ! [B: a,C: a,D: a] :
( ( ( ( B = c0 )
& ( C = D ) )
| ( ( C = c0 )
& ( B = D ) )
| ? [E: a,F: a,G: a,H: a,I: a,J: a] :
( ( B
= ( cP @ E @ F ) )
& ( C
= ( cP @ G @ H ) )
& ( D
= ( cP @ I @ J ) )
& ( A @ E @ G @ I )
& ( A @ F @ H @ J ) ) )
=> ( A @ B @ C @ D ) ) )
=> ( A @ x @ y @ y ) )
& ! [A: a > a > a > $o] :
( ( $true
& ! [B: a,C: a,D: a] :
( ( ( ( B = c0 )
& ( C = D ) )
| ( ( C = c0 )
& ( B = D ) )
| ? [E: a,F: a,G: a,H: a,I: a,J: a] :
( ( B
= ( cP @ E @ F ) )
& ( C
= ( cP @ G @ H ) )
& ( D
= ( cP @ I @ J ) )
& ( A @ E @ G @ I )
& ( A @ F @ H @ J ) ) )
=> ( A @ B @ C @ D ) ) )
=> ( A @ w @ z @ z ) ) )
=> ! [A: a > a > a > $o] :
( ( $true
& ! [B: a,C: a,D: a] :
( ( ( ( B = c0 )
& ( C = D ) )
| ( ( C = c0 )
& ( B = D ) )
| ? [E: a,F: a,G: a,H: a,I: a,J: a] :
( ( B
= ( cP @ E @ F ) )
& ( C
= ( cP @ G @ H ) )
& ( D
= ( cP @ I @ J ) )
& ( A @ E @ G @ I )
& ( A @ F @ H @ J ) ) )
=> ( A @ B @ C @ D ) ) )
=> ( A @ ( cP @ x @ w ) @ ( cP @ y @ z ) @ ( cP @ y @ z ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cS_INCL_LEM1_pme) ).
thf(2,negated_conjecture,
~ ( ( ! [A: a > a > a > $o] :
( ( $true
& ! [B: a,C: a,D: a] :
( ( ( ( B = c0 )
& ( C = D ) )
| ( ( C = c0 )
& ( B = D ) )
| ? [E: a,F: a,G: a,H: a,I: a,J: a] :
( ( B
= ( cP @ E @ F ) )
& ( C
= ( cP @ G @ H ) )
& ( D
= ( cP @ I @ J ) )
& ( A @ E @ G @ I )
& ( A @ F @ H @ J ) ) )
=> ( A @ B @ C @ D ) ) )
=> ( A @ x @ y @ y ) )
& ! [A: a > a > a > $o] :
( ( $true
& ! [B: a,C: a,D: a] :
( ( ( ( B = c0 )
& ( C = D ) )
| ( ( C = c0 )
& ( B = D ) )
| ? [E: a,F: a,G: a,H: a,I: a,J: a] :
( ( B
= ( cP @ E @ F ) )
& ( C
= ( cP @ G @ H ) )
& ( D
= ( cP @ I @ J ) )
& ( A @ E @ G @ I )
& ( A @ F @ H @ J ) ) )
=> ( A @ B @ C @ D ) ) )
=> ( A @ w @ z @ z ) ) )
=> ! [A: a > a > a > $o] :
( ( $true
& ! [B: a,C: a,D: a] :
( ( ( ( B = c0 )
& ( C = D ) )
| ( ( C = c0 )
& ( B = D ) )
| ? [E: a,F: a,G: a,H: a,I: a,J: a] :
( ( B
= ( cP @ E @ F ) )
& ( C
= ( cP @ G @ H ) )
& ( D
= ( cP @ I @ J ) )
& ( A @ E @ G @ I )
& ( A @ F @ H @ J ) ) )
=> ( A @ B @ C @ D ) ) )
=> ( A @ ( cP @ x @ w ) @ ( cP @ y @ z ) @ ( cP @ y @ z ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ( ! [A: a > a > a > $o] :
( ! [B: a,C: a,D: a] :
( ( ( ( B = c0 )
& ( C = D ) )
| ( ( C = c0 )
& ( B = D ) )
| ? [E: a,F: a,G: a,H: a,I: a,J: a] :
( ( B
= ( cP @ E @ F ) )
& ( C
= ( cP @ G @ H ) )
& ( D
= ( cP @ I @ J ) )
& ( A @ E @ G @ I )
& ( A @ F @ H @ J ) ) )
=> ( A @ B @ C @ D ) )
=> ( A @ x @ y @ y ) )
& ! [A: a > a > a > $o] :
( ! [B: a,C: a,D: a] :
( ( ( ( B = c0 )
& ( C = D ) )
| ( ( C = c0 )
& ( B = D ) )
| ? [E: a,F: a,G: a,H: a,I: a,J: a] :
( ( B
= ( cP @ E @ F ) )
& ( C
= ( cP @ G @ H ) )
& ( D
= ( cP @ I @ J ) )
& ( A @ E @ G @ I )
& ( A @ F @ H @ J ) ) )
=> ( A @ B @ C @ D ) )
=> ( A @ w @ z @ z ) ) )
=> ! [A: a > a > a > $o] :
( ! [B: a,C: a,D: a] :
( ( ( ( B = c0 )
& ( C = D ) )
| ( ( C = c0 )
& ( B = D ) )
| ? [E: a,F: a,G: a,H: a,I: a,J: a] :
( ( B
= ( cP @ E @ F ) )
& ( C
= ( cP @ G @ H ) )
& ( D
= ( cP @ I @ J ) )
& ( A @ E @ G @ I )
& ( A @ F @ H @ J ) ) )
=> ( A @ B @ C @ D ) )
=> ( A @ ( cP @ x @ w ) @ ( cP @ y @ z ) @ ( cP @ y @ z ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
~ ( ( ! [A: a > a > a > $o] :
( ! [B: a,C: a,D: a] :
( ( ( ( B = c0 )
& ( C = D ) )
| ( ( C = c0 )
& ( B = D ) )
| ? [E: a,F: a] :
( ( B
= ( cP @ E @ F ) )
& ? [G: a,H: a] :
( ( C
= ( cP @ G @ H ) )
& ? [I: a,J: a] :
( ( D
= ( cP @ I @ J ) )
& ( A @ E @ G @ I )
& ( A @ F @ H @ J ) ) ) ) )
=> ( A @ B @ C @ D ) )
=> ( A @ x @ y @ y ) )
& ! [A: a > a > a > $o] :
( ! [B: a,C: a,D: a] :
( ( ( ( B = c0 )
& ( C = D ) )
| ( ( C = c0 )
& ( B = D ) )
| ? [E: a,F: a] :
( ( B
= ( cP @ E @ F ) )
& ? [G: a,H: a] :
( ( C
= ( cP @ G @ H ) )
& ? [I: a,J: a] :
( ( D
= ( cP @ I @ J ) )
& ( A @ E @ G @ I )
& ( A @ F @ H @ J ) ) ) ) )
=> ( A @ B @ C @ D ) )
=> ( A @ w @ z @ z ) ) )
=> ! [A: a > a > a > $o] :
( ! [B: a,C: a,D: a] :
( ( ( ( B = c0 )
& ( C = D ) )
| ( ( C = c0 )
& ( B = D ) )
| ? [E: a,F: a] :
( ( B
= ( cP @ E @ F ) )
& ? [G: a,H: a] :
( ( C
= ( cP @ G @ H ) )
& ? [I: a,J: a] :
( ( D
= ( cP @ I @ J ) )
& ( A @ E @ G @ I )
& ( A @ F @ H @ J ) ) ) ) )
=> ( A @ B @ C @ D ) )
=> ( A @ ( cP @ x @ w ) @ ( cP @ y @ z ) @ ( cP @ y @ z ) ) ) ),
inference(miniscope,[status(thm)],[3]) ).
thf(11,plain,
! [A: a > a > a > $o] :
( ~ ( A @ ( sk12 @ A ) @ ( sk13 @ A ) @ ( sk14 @ A ) )
| ( A @ w @ z @ z ) ),
inference(cnf,[status(esa)],[4]) ).
thf(45,plain,
! [A: a > a > a > $o] :
( ~ ( A @ ( sk12 @ A ) @ ( sk13 @ A ) @ ( sk14 @ A ) )
| ( A @ w @ z @ z ) ),
inference(simp,[status(thm)],[11]) ).
thf(393,plain,
! [A: a > a > a > $o] :
( ~ ~ ( A
@ ( sk12
@ ^ [B: a,C: a,D: a] :
~ ( A @ B @ C @ D ) )
@ ( sk13
@ ^ [B: a,C: a,D: a] :
~ ( A @ B @ C @ D ) )
@ ( sk14
@ ^ [B: a,C: a,D: a] :
~ ( A @ B @ C @ D ) ) )
| ~ ( A @ w @ z @ z ) ),
inference(prim_subst,[status(thm)],[45:[bind(A,$thf( ^ [C: a] : ^ [D: a] : ^ [E: a] : ~ ( B @ C @ D @ E ) ))]]) ).
thf(416,plain,
! [A: a > a > a > $o] :
( ~ ( A @ w @ z @ z )
| ( A
@ ( sk12
@ ^ [B: a,C: a,D: a] :
~ ( A @ B @ C @ D ) )
@ ( sk13
@ ^ [B: a,C: a,D: a] :
~ ( A @ B @ C @ D ) )
@ ( sk14
@ ^ [B: a,C: a,D: a] :
~ ( A @ B @ C @ D ) ) ) ),
inference(cnf,[status(esa)],[393]) ).
thf(417,plain,
! [A: a > a > a > $o] :
( ~ ( A @ w @ z @ z )
| ( A
@ ( sk12
@ ^ [B: a,C: a,D: a] :
~ ( A @ B @ C @ D ) )
@ ( sk13
@ ^ [B: a,C: a,D: a] :
~ ( A @ B @ C @ D ) )
@ ( sk14
@ ^ [B: a,C: a,D: a] :
~ ( A @ B @ C @ D ) ) ) ),
inference(simp,[status(thm)],[416]) ).
thf(27,plain,
! [A: a > a > a > $o] :
( ( ( sk12 @ A )
= c0 )
| ( sk15 @ A )
| ( A @ w @ z @ z ) ),
inference(cnf,[status(esa)],[4]) ).
thf(54,plain,
! [A: a > a > a > $o] :
( ( ( sk12 @ A )
= c0 )
| ( sk15 @ A )
| ( A @ w @ z @ z ) ),
inference(lifteq,[status(thm)],[27]) ).
thf(55,plain,
! [A: a > a > a > $o] :
( ( ( sk12 @ A )
= c0 )
| ( sk15 @ A )
| ( A @ w @ z @ z ) ),
inference(simp,[status(thm)],[54]) ).
thf(101,plain,
( ( ( sk12 @ sk23 )
= c0 )
| ( sk15 @ sk23 )
| ( sk23 @ w @ z @ z ) ),
inference(prim_subst,[status(thm)],[55:[bind(A,$thf( sk23 ))]]) ).
thf(453,plain,
! [A: a > a > a > $o] :
( ( ( sk12 @ sk23 )
= c0 )
| ( sk15 @ sk23 )
| ( A @ w @ z @ z )
| ( ( sk23 @ w @ z @ z )
!= ( A @ ( sk12 @ A ) @ ( sk13 @ A ) @ ( sk14 @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[101,45]) ).
thf(460,plain,
( ( ( sk12 @ sk23 )
= c0 )
| ( sk15 @ sk23 )
| ( sk23 @ w @ z @ z ) ),
inference(pre_uni,[status(thm)],[453:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ^ [D: a] : ( sk23 @ w @ z @ z ) ))]]) ).
thf(6,plain,
~ ( sk23 @ ( cP @ x @ w ) @ ( cP @ y @ z ) @ ( cP @ y @ z ) ),
inference(cnf,[status(esa)],[4]) ).
thf(21,plain,
! [A: a > a > a > $o] :
( ~ ( A @ ( sk1 @ A ) @ ( sk2 @ A ) @ ( sk3 @ A ) )
| ( A @ x @ y @ y ) ),
inference(cnf,[status(esa)],[4]) ).
thf(318,plain,
! [A: a > a > a > $o] :
( ~ ~ ( A
@ ( sk1
@ ^ [B: a,C: a,D: a] :
~ ( A @ B @ C @ D ) )
@ ( sk2
@ ^ [B: a,C: a,D: a] :
~ ( A @ B @ C @ D ) )
@ ( sk3
@ ^ [B: a,C: a,D: a] :
~ ( A @ B @ C @ D ) ) )
| ~ ( A @ x @ y @ y ) ),
inference(prim_subst,[status(thm)],[21:[bind(A,$thf( ^ [C: a] : ^ [D: a] : ^ [E: a] : ~ ( B @ C @ D @ E ) ))]]) ).
thf(349,plain,
! [A: a > a > a > $o] :
( ~ ( A @ x @ y @ y )
| ( A
@ ( sk1
@ ^ [B: a,C: a,D: a] :
~ ( A @ B @ C @ D ) )
@ ( sk2
@ ^ [B: a,C: a,D: a] :
~ ( A @ B @ C @ D ) )
@ ( sk3
@ ^ [B: a,C: a,D: a] :
~ ( A @ B @ C @ D ) ) ) ),
inference(cnf,[status(esa)],[318]) ).
thf(350,plain,
! [A: a > a > a > $o] :
( ~ ( A @ x @ y @ y )
| ( A
@ ( sk1
@ ^ [B: a,C: a,D: a] :
~ ( A @ B @ C @ D ) )
@ ( sk2
@ ^ [B: a,C: a,D: a] :
~ ( A @ B @ C @ D ) )
@ ( sk3
@ ^ [B: a,C: a,D: a] :
~ ( A @ B @ C @ D ) ) ) ),
inference(simp,[status(thm)],[349]) ).
thf(7,plain,
! [C: a,B: a,A: a] :
( ( A != c0 )
| ( B != C )
| ( sk23 @ A @ B @ C ) ),
inference(cnf,[status(esa)],[4]) ).
thf(42,plain,
! [C: a,B: a,A: a] :
( ( A != c0 )
| ( B != C )
| ( sk23 @ A @ B @ C ) ),
inference(lifteq,[status(thm)],[7]) ).
thf(43,plain,
! [A: a] : ( sk23 @ c0 @ A @ A ),
inference(simp,[status(thm)],[42]) ).
thf(10,plain,
! [I: a,H: a,G: a,F: a,E: a,D: a,C: a,B: a,A: a] :
( ( A
!= ( cP @ D @ E ) )
| ( B
!= ( cP @ F @ G ) )
| ( C
!= ( cP @ H @ I ) )
| ~ ( sk23 @ D @ F @ H )
| ~ ( sk23 @ E @ G @ I )
| ( sk23 @ A @ B @ C ) ),
inference(cnf,[status(esa)],[4]) ).
thf(29,plain,
! [I: a,H: a,G: a,F: a,E: a,D: a,C: a,B: a,A: a] :
( ( A
!= ( cP @ D @ E ) )
| ( B
!= ( cP @ F @ G ) )
| ( C
!= ( cP @ H @ I ) )
| ~ ( sk23 @ D @ F @ H )
| ~ ( sk23 @ E @ G @ I )
| ( sk23 @ A @ B @ C ) ),
inference(lifteq,[status(thm)],[10]) ).
thf(30,plain,
! [F: a,E: a,D: a,C: a,B: a,A: a] :
( ~ ( sk23 @ A @ C @ E )
| ~ ( sk23 @ B @ D @ F )
| ( sk23 @ ( cP @ A @ B ) @ ( cP @ C @ D ) @ ( cP @ E @ F ) ) ),
inference(simp,[status(thm)],[29]) ).
thf(471,plain,
! [F: a,E: a,D: a,C: a,B: a,A: a] :
( ~ ( sk23 @ A @ C @ E )
| ~ ( sk23 @ B @ D @ F )
| ( ( sk23 @ ( cP @ A @ B ) @ ( cP @ C @ D ) @ ( cP @ E @ F ) )
!= ( sk23 @ ( cP @ x @ w ) @ ( cP @ y @ z ) @ ( cP @ y @ z ) ) ) ),
inference(paramod_ordered,[status(thm)],[30,6]) ).
thf(472,plain,
( ~ ( sk23 @ x @ y @ y )
| ~ ( sk23 @ w @ z @ z ) ),
inference(pattern_uni,[status(thm)],[471:[bind(A,$thf( x )),bind(B,$thf( w )),bind(C,$thf( y )),bind(D,$thf( z )),bind(E,$thf( y )),bind(F,$thf( z ))]]) ).
thf(527,plain,
! [A: a] :
( ~ ( sk23 @ x @ y @ y )
| ( ( sk23 @ c0 @ A @ A )
!= ( sk23 @ w @ z @ z ) ) ),
inference(paramod_ordered,[status(thm)],[43,472]) ).
thf(538,plain,
! [A: a] :
( ~ ( sk23 @ x @ y @ y )
| ( c0 != w )
| ( A != z )
| ( A != z ) ),
inference(simp,[status(thm)],[527]) ).
thf(553,plain,
( ~ ( sk23 @ x @ y @ y )
| ( c0 != w ) ),
inference(simp,[status(thm)],[538]) ).
thf(315,plain,
! [A: a > a > a > a > a > a > $o] :
( ~ ( sk16
@ ( A
@ ( sk1
@ ^ [B: a,C: a,D: a] : ( sk16 @ ( A @ B @ C @ D ) ) )
@ ( sk2
@ ^ [B: a,C: a,D: a] : ( sk16 @ ( A @ B @ C @ D ) ) )
@ ( sk3
@ ^ [B: a,C: a,D: a] : ( sk16 @ ( A @ B @ C @ D ) ) ) ) )
| ( sk16 @ ( A @ x @ y @ y ) ) ),
inference(prim_subst,[status(thm)],[21:[bind(A,$thf( ^ [C: a] : ^ [D: a] : ^ [E: a] : ( sk16 @ ( B @ C @ D @ E ) ) ))]]) ).
thf(347,plain,
! [A: a > a > a > a > a > a > $o] :
( ~ ( sk16
@ ( A
@ ( sk1
@ ^ [B: a,C: a,D: a] : ( sk16 @ ( A @ B @ C @ D ) ) )
@ ( sk2
@ ^ [B: a,C: a,D: a] : ( sk16 @ ( A @ B @ C @ D ) ) )
@ ( sk3
@ ^ [B: a,C: a,D: a] : ( sk16 @ ( A @ B @ C @ D ) ) ) ) )
| ( sk16 @ ( A @ x @ y @ y ) ) ),
inference(simp,[status(thm)],[315]) ).
thf(526,plain,
! [A: a] :
( ~ ( sk23 @ w @ z @ z )
| ( ( sk23 @ c0 @ A @ A )
!= ( sk23 @ x @ y @ y ) ) ),
inference(paramod_ordered,[status(thm)],[43,472]) ).
thf(541,plain,
! [A: a] :
( ~ ( sk23 @ w @ z @ z )
| ( c0 != x )
| ( A != y )
| ( A != y ) ),
inference(simp,[status(thm)],[526]) ).
thf(555,plain,
( ~ ( sk23 @ w @ z @ z )
| ( c0 != x ) ),
inference(simp,[status(thm)],[541]) ).
thf(5,plain,
! [A: a > a > a > $o] :
( ~ ( sk4 @ A )
| ~ ( sk5 @ A )
| ( A @ ( sk6 @ A ) @ ( sk8 @ A ) @ ( sk10 @ A ) )
| ( A @ x @ y @ y ) ),
inference(cnf,[status(esa)],[4]) ).
thf(13,plain,
! [A: a > a > a > $o] :
( ~ ( sk15 @ A )
| ( ( sk13 @ A )
= c0 )
| ( sk16 @ A )
| ( A @ w @ z @ z ) ),
inference(cnf,[status(esa)],[4]) ).
thf(37,plain,
! [A: a > a > a > $o] :
( ( ( sk13 @ A )
= c0 )
| ~ ( sk15 @ A )
| ( sk16 @ A )
| ( A @ w @ z @ z ) ),
inference(lifteq,[status(thm)],[13]) ).
thf(38,plain,
! [A: a > a > a > $o] :
( ( ( sk13 @ A )
= c0 )
| ~ ( sk15 @ A )
| ( sk16 @ A )
| ( A @ w @ z @ z ) ),
inference(simp,[status(thm)],[37]) ).
thf(1763,plain,
( ( ( sk13
@ ^ [A: a,B: a,C: a] : $false )
= c0 )
| ~ ( sk15
@ ^ [A: a,B: a,C: a] : $false )
| ( sk16
@ ^ [A: a,B: a,C: a] : $false )
| $false ),
inference(prim_subst,[status(thm)],[38:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ^ [D: a] : $false ))]]) ).
thf(1793,plain,
( ( ( sk13
@ ^ [A: a,B: a,C: a] : $false )
= c0 )
| ~ ( sk15
@ ^ [A: a,B: a,C: a] : $false )
| ( sk16
@ ^ [A: a,B: a,C: a] : $false ) ),
inference(simp,[status(thm)],[1763]) ).
thf(535,plain,
( ~ ( sk23 @ w @ z @ z )
| ( ( sk23 @ x @ y @ y )
!= ( sk23 @ w @ z @ z ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[472]) ).
thf(544,plain,
( ~ ( sk23 @ w @ z @ z )
| ( x != w )
| ( y != z )
| ( y != z ) ),
inference(simp,[status(thm)],[535]) ).
thf(550,plain,
( ~ ( sk23 @ w @ z @ z )
| ( x != w )
| ( y != z ) ),
inference(simp,[status(thm)],[544]) ).
thf(543,plain,
( ~ ( sk23 @ w @ z @ z )
| ( ( sk23 @ x @ y @ y )
!= ( sk23 @ w @ z @ z ) ) ),
inference(simp,[status(thm)],[535]) ).
thf(761,plain,
! [A: a] :
( ( ( sk23 @ x @ y @ y )
!= ( sk23 @ w @ z @ z ) )
| ( ( sk23 @ c0 @ A @ A )
!= ( sk23 @ w @ z @ z ) ) ),
inference(paramod_ordered,[status(thm)],[43,543]) ).
thf(769,plain,
! [A: a] :
( ( ( sk23 @ x @ y @ y )
!= ( sk23 @ w @ z @ z ) )
| ( c0 != w )
| ( A != z )
| ( A != z ) ),
inference(simp,[status(thm)],[761]) ).
thf(789,plain,
( ( ( sk23 @ x @ y @ y )
!= ( sk23 @ w @ z @ z ) )
| ( c0 != w ) ),
inference(simp,[status(thm)],[769]) ).
thf(316,plain,
! [A: a > a > a > a > a > a > $o] :
( ~ ( sk15
@ ( A
@ ( sk1
@ ^ [B: a,C: a,D: a] : ( sk15 @ ( A @ B @ C @ D ) ) )
@ ( sk2
@ ^ [B: a,C: a,D: a] : ( sk15 @ ( A @ B @ C @ D ) ) )
@ ( sk3
@ ^ [B: a,C: a,D: a] : ( sk15 @ ( A @ B @ C @ D ) ) ) ) )
| ( sk15 @ ( A @ x @ y @ y ) ) ),
inference(prim_subst,[status(thm)],[21:[bind(A,$thf( ^ [C: a] : ^ [D: a] : ^ [E: a] : ( sk15 @ ( B @ C @ D @ E ) ) ))]]) ).
thf(348,plain,
! [A: a > a > a > a > a > a > $o] :
( ~ ( sk15
@ ( A
@ ( sk1
@ ^ [B: a,C: a,D: a] : ( sk15 @ ( A @ B @ C @ D ) ) )
@ ( sk2
@ ^ [B: a,C: a,D: a] : ( sk15 @ ( A @ B @ C @ D ) ) )
@ ( sk3
@ ^ [B: a,C: a,D: a] : ( sk15 @ ( A @ B @ C @ D ) ) ) ) )
| ( sk15 @ ( A @ x @ y @ y ) ) ),
inference(simp,[status(thm)],[316]) ).
thf(14,plain,
! [C: a,B: a,A: a] :
( ( B != c0 )
| ( A != C )
| ( sk23 @ A @ B @ C ) ),
inference(cnf,[status(esa)],[4]) ).
thf(31,plain,
! [C: a,B: a,A: a] :
( ( B != c0 )
| ( A != C )
| ( sk23 @ A @ B @ C ) ),
inference(lifteq,[status(thm)],[14]) ).
thf(32,plain,
! [A: a] : ( sk23 @ A @ c0 @ A ),
inference(simp,[status(thm)],[31]) ).
thf(59,plain,
! [A: a] :
( ( sk23 @ A @ c0 @ A )
!= ( sk23 @ ( cP @ x @ w ) @ ( cP @ y @ z ) @ ( cP @ y @ z ) ) ),
inference(paramod_ordered,[status(thm)],[32,6]) ).
thf(61,plain,
! [A: a] :
( ( A
!= ( cP @ x @ w ) )
| ( ( cP @ y @ z )
!= c0 )
| ( A
!= ( cP @ y @ z ) ) ),
inference(simp,[status(thm)],[59]) ).
thf(63,plain,
( ( ( cP @ y @ z )
!= c0 )
| ( ( cP @ x @ w )
!= ( cP @ y @ z ) ) ),
inference(simp,[status(thm)],[61]) ).
thf(65,plain,
( ( ( cP @ y @ z )
!= c0 )
| ( x != y )
| ( w != z ) ),
inference(simp,[status(thm)],[63]) ).
thf(531,plain,
! [A: a] :
( ~ ( sk23 @ w @ z @ z )
| ( ( sk23 @ A @ c0 @ A )
!= ( sk23 @ x @ y @ y ) ) ),
inference(paramod_ordered,[status(thm)],[32,472]) ).
thf(545,plain,
! [A: a] :
( ~ ( sk23 @ w @ z @ z )
| ( A != x )
| ( c0 != y )
| ( A != y ) ),
inference(simp,[status(thm)],[531]) ).
thf(551,plain,
( ~ ( sk23 @ w @ z @ z )
| ( c0 != y )
| ( x != y ) ),
inference(simp,[status(thm)],[545]) ).
thf(60,plain,
! [A: a] :
( ( sk23 @ c0 @ A @ A )
!= ( sk23 @ ( cP @ x @ w ) @ ( cP @ y @ z ) @ ( cP @ y @ z ) ) ),
inference(paramod_ordered,[status(thm)],[43,6]) ).
thf(62,plain,
! [A: a] :
( ( ( cP @ x @ w )
!= c0 )
| ( A
!= ( cP @ y @ z ) )
| ( A
!= ( cP @ y @ z ) ) ),
inference(simp,[status(thm)],[60]) ).
thf(64,plain,
( ( cP @ x @ w )
!= c0 ),
inference(simp,[status(thm)],[62]) ).
thf(560,plain,
! [A: a] :
( ( c0 != w )
| ( ( sk23 @ c0 @ A @ A )
!= ( sk23 @ x @ y @ y ) ) ),
inference(paramod_ordered,[status(thm)],[43,553]) ).
thf(570,plain,
! [A: a] :
( ( c0 != w )
| ( c0 != x )
| ( A != y )
| ( A != y ) ),
inference(simp,[status(thm)],[560]) ).
thf(573,plain,
( ( c0 != w )
| ( c0 != x ) ),
inference(simp,[status(thm)],[570]) ).
thf(20,plain,
! [A: a > a > a > $o] :
( ~ ( sk15 @ A )
| ( ( sk12 @ A )
= ( sk14 @ A ) )
| ( sk16 @ A )
| ( A @ w @ z @ z ) ),
inference(cnf,[status(esa)],[4]) ).
thf(33,plain,
! [A: a > a > a > $o] :
( ( ( sk14 @ A )
= ( sk12 @ A ) )
| ~ ( sk15 @ A )
| ( sk16 @ A )
| ( A @ w @ z @ z ) ),
inference(lifteq,[status(thm)],[20]) ).
thf(34,plain,
! [A: a > a > a > $o] :
( ( ( sk14 @ A )
= ( sk12 @ A ) )
| ~ ( sk15 @ A )
| ( sk16 @ A )
| ( A @ w @ z @ z ) ),
inference(simp,[status(thm)],[33]) ).
thf(25,plain,
! [A: a > a > a > $o] :
( ( ( sk1 @ A )
= c0 )
| ( sk4 @ A )
| ( A @ x @ y @ y ) ),
inference(cnf,[status(esa)],[4]) ).
thf(51,plain,
! [A: a > a > a > $o] :
( ( ( sk1 @ A )
= c0 )
| ( sk4 @ A )
| ( A @ x @ y @ y ) ),
inference(lifteq,[status(thm)],[25]) ).
thf(68,plain,
( ( ( sk1 @ sk23 )
= c0 )
| ( sk4 @ sk23 )
| ( sk23 @ x @ y @ y ) ),
inference(prim_subst,[status(thm)],[51:[bind(A,$thf( sk23 ))]]) ).
thf(561,plain,
( ( ( sk1 @ sk23 )
= c0 )
| ( sk4 @ sk23 )
| ( c0 != w )
| ( ( sk23 @ x @ y @ y )
!= ( sk23 @ x @ y @ y ) ) ),
inference(paramod_ordered,[status(thm)],[68,553]) ).
thf(562,plain,
( ( ( sk1 @ sk23 )
= c0 )
| ( sk4 @ sk23 )
| ( c0 != w ) ),
inference(pattern_uni,[status(thm)],[561:[]]) ).
thf(578,plain,
( ( ( sk12 @ sk23 )
= c0 )
| ( sk15 @ sk23 )
| ( c0 != x )
| ( ( sk23 @ w @ z @ z )
!= ( sk23 @ w @ z @ z ) ) ),
inference(paramod_ordered,[status(thm)],[101,555]) ).
thf(579,plain,
( ( ( sk12 @ sk23 )
= c0 )
| ( sk15 @ sk23 )
| ( c0 != x ) ),
inference(pattern_uni,[status(thm)],[578:[]]) ).
thf(390,plain,
! [A: a > a > a > a > a > a > $o] :
( ~ ( sk5
@ ( A
@ ( sk12
@ ^ [B: a,C: a,D: a] : ( sk5 @ ( A @ B @ C @ D ) ) )
@ ( sk13
@ ^ [B: a,C: a,D: a] : ( sk5 @ ( A @ B @ C @ D ) ) )
@ ( sk14
@ ^ [B: a,C: a,D: a] : ( sk5 @ ( A @ B @ C @ D ) ) ) ) )
| ( sk5 @ ( A @ w @ z @ z ) ) ),
inference(prim_subst,[status(thm)],[45:[bind(A,$thf( ^ [C: a] : ^ [D: a] : ^ [E: a] : ( sk5 @ ( B @ C @ D @ E ) ) ))]]) ).
thf(413,plain,
! [A: a > a > a > a > a > a > $o] :
( ~ ( sk5
@ ( A
@ ( sk12
@ ^ [B: a,C: a,D: a] : ( sk5 @ ( A @ B @ C @ D ) ) )
@ ( sk13
@ ^ [B: a,C: a,D: a] : ( sk5 @ ( A @ B @ C @ D ) ) )
@ ( sk14
@ ^ [B: a,C: a,D: a] : ( sk5 @ ( A @ B @ C @ D ) ) ) ) )
| ( sk5 @ ( A @ w @ z @ z ) ) ),
inference(simp,[status(thm)],[390]) ).
thf(890,plain,
( ~ ( sk23 @ x @ y @ y )
| ( sk23
@ ( sk1
@ ^ [A: a,B: a,C: a] :
~ ( sk23 @ A @ B @ C ) )
@ ( sk2
@ ^ [A: a,B: a,C: a] :
~ ( sk23 @ A @ B @ C ) )
@ ( sk3
@ ^ [A: a,B: a,C: a] :
~ ( sk23 @ A @ B @ C ) ) ) ),
inference(prim_subst,[status(thm)],[350:[bind(A,$thf( sk23 ))]]) ).
thf(532,plain,
! [A: a] :
( ~ ( sk23 @ x @ y @ y )
| ( ( sk23 @ A @ c0 @ A )
!= ( sk23 @ w @ z @ z ) ) ),
inference(paramod_ordered,[status(thm)],[32,472]) ).
thf(548,plain,
! [A: a] :
( ~ ( sk23 @ x @ y @ y )
| ( A != w )
| ( c0 != z )
| ( A != z ) ),
inference(simp,[status(thm)],[532]) ).
thf(552,plain,
( ~ ( sk23 @ x @ y @ y )
| ( c0 != z )
| ( w != z ) ),
inference(simp,[status(thm)],[548]) ).
thf(99,plain,
( ( ( sk12
@ ^ [A: a,B: a,C: a] : $false )
= c0 )
| ( sk15
@ ^ [A: a,B: a,C: a] : $false )
| $false ),
inference(prim_subst,[status(thm)],[55:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ^ [D: a] : $false ))]]) ).
thf(108,plain,
( ( ( sk12
@ ^ [A: a,B: a,C: a] : $false )
= c0 )
| ( sk15
@ ^ [A: a,B: a,C: a] : $false ) ),
inference(simp,[status(thm)],[99]) ).
thf(394,plain,
( ~ ( sk23 @ ( sk12 @ sk23 ) @ ( sk13 @ sk23 ) @ ( sk14 @ sk23 ) )
| ( sk23 @ w @ z @ z ) ),
inference(prim_subst,[status(thm)],[45:[bind(A,$thf( sk23 ))]]) ).
thf(1745,plain,
! [A: a > a > a > $o] :
( ( ( sk12
@ ^ [B: a,C: a,D: a] : $false )
= c0 )
| ( ( sk13 @ A )
= c0 )
| ( sk16 @ A )
| ( A @ w @ z @ z )
| ( ( sk15
@ ^ [B: a,C: a,D: a] : $false )
!= ( sk15 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[108,38]) ).
thf(1746,plain,
( ( ( sk12
@ ^ [A: a,B: a,C: a] : $false )
= c0 )
| ( ( sk13
@ ^ [A: a,B: a,C: a] : $false )
= c0 )
| ( sk16
@ ^ [A: a,B: a,C: a] : $false )
| $false ),
inference(pattern_uni,[status(thm)],[1745:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ^ [D: a] : $false ))]]) ).
thf(1780,plain,
( ( ( sk12
@ ^ [A: a,B: a,C: a] : $false )
= c0 )
| ( ( sk13
@ ^ [A: a,B: a,C: a] : $false )
= c0 )
| ( sk16
@ ^ [A: a,B: a,C: a] : $false ) ),
inference(simp,[status(thm)],[1746]) ).
thf(16,plain,
! [A: a > a > a > $o] :
( ~ ( sk4 @ A )
| ~ ( sk5 @ A )
| ( A @ ( sk7 @ A ) @ ( sk9 @ A ) @ ( sk11 @ A ) )
| ( A @ x @ y @ y ) ),
inference(cnf,[status(esa)],[4]) ).
thf(321,plain,
! [A: a > a > a > a > a > a > $o] :
( ~ ( sk5
@ ( A
@ ( sk1
@ ^ [B: a,C: a,D: a] : ( sk5 @ ( A @ B @ C @ D ) ) )
@ ( sk2
@ ^ [B: a,C: a,D: a] : ( sk5 @ ( A @ B @ C @ D ) ) )
@ ( sk3
@ ^ [B: a,C: a,D: a] : ( sk5 @ ( A @ B @ C @ D ) ) ) ) )
| ( sk5 @ ( A @ x @ y @ y ) ) ),
inference(prim_subst,[status(thm)],[21:[bind(A,$thf( ^ [C: a] : ^ [D: a] : ^ [E: a] : ( sk5 @ ( B @ C @ D @ E ) ) ))]]) ).
thf(338,plain,
! [A: a > a > a > a > a > a > $o] :
( ~ ( sk5
@ ( A
@ ( sk1
@ ^ [B: a,C: a,D: a] : ( sk5 @ ( A @ B @ C @ D ) ) )
@ ( sk2
@ ^ [B: a,C: a,D: a] : ( sk5 @ ( A @ B @ C @ D ) ) )
@ ( sk3
@ ^ [B: a,C: a,D: a] : ( sk5 @ ( A @ B @ C @ D ) ) ) ) )
| ( sk5 @ ( A @ x @ y @ y ) ) ),
inference(simp,[status(thm)],[321]) ).
thf(563,plain,
! [A: a] :
( ( c0 != w )
| ( ( sk23 @ A @ c0 @ A )
!= ( sk23 @ x @ y @ y ) ) ),
inference(paramod_ordered,[status(thm)],[32,553]) ).
thf(567,plain,
! [A: a] :
( ( c0 != w )
| ( A != x )
| ( c0 != y )
| ( A != y ) ),
inference(simp,[status(thm)],[563]) ).
thf(571,plain,
( ( c0 != w )
| ( c0 != y )
| ( x != y ) ),
inference(simp,[status(thm)],[567]) ).
thf(580,plain,
! [A: a] :
( ( c0 != x )
| ( ( sk23 @ A @ c0 @ A )
!= ( sk23 @ w @ z @ z ) ) ),
inference(paramod_ordered,[status(thm)],[32,555]) ).
thf(583,plain,
! [A: a] :
( ( c0 != x )
| ( A != w )
| ( c0 != z )
| ( A != z ) ),
inference(simp,[status(thm)],[580]) ).
thf(588,plain,
( ( c0 != x )
| ( c0 != z )
| ( w != z ) ),
inference(simp,[status(thm)],[583]) ).
thf(17,plain,
! [A: a > a > a > $o] :
( ~ ( sk15 @ A )
| ~ ( sk16 @ A )
| ( ( sk13 @ A )
= ( cP @ ( sk19 @ A ) @ ( sk20 @ A ) ) )
| ( A @ w @ z @ z ) ),
inference(cnf,[status(esa)],[4]) ).
thf(39,plain,
! [A: a > a > a > $o] :
( ( ( cP @ ( sk19 @ A ) @ ( sk20 @ A ) )
= ( sk13 @ A ) )
| ~ ( sk15 @ A )
| ~ ( sk16 @ A )
| ( A @ w @ z @ z ) ),
inference(lifteq,[status(thm)],[17]) ).
thf(40,plain,
! [A: a > a > a > $o] :
( ( ( cP @ ( sk19 @ A ) @ ( sk20 @ A ) )
= ( sk13 @ A ) )
| ~ ( sk15 @ A )
| ~ ( sk16 @ A )
| ( A @ w @ z @ z ) ),
inference(simp,[status(thm)],[39]) ).
thf(72,plain,
( ( ( sk1
@ ^ [A: a,B: a,C: a] : $false )
= c0 )
| ( sk4
@ ^ [A: a,B: a,C: a] : $false )
| $false ),
inference(prim_subst,[status(thm)],[51:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ^ [D: a] : $false ))]]) ).
thf(82,plain,
( ( ( sk1
@ ^ [A: a,B: a,C: a] : $false )
= c0 )
| ( sk4
@ ^ [A: a,B: a,C: a] : $false ) ),
inference(simp,[status(thm)],[72]) ).
thf(119,plain,
! [A: a > a > a > $o] :
( ( ( sk1
@ ^ [B: a,C: a,D: a] : $false )
= c0 )
| ~ ( sk5 @ A )
| ( A @ ( sk6 @ A ) @ ( sk8 @ A ) @ ( sk10 @ A ) )
| ( A @ x @ y @ y )
| ( ( sk4
@ ^ [B: a,C: a,D: a] : $false )
!= ( sk4 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[82,5]) ).
thf(120,plain,
( ( ( sk1
@ ^ [A: a,B: a,C: a] : $false )
= c0 )
| ~ ( sk5
@ ^ [A: a,B: a,C: a] : $false )
| $false
| $false ),
inference(pattern_uni,[status(thm)],[119:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ^ [D: a] : $false ))]]) ).
thf(158,plain,
( ( ( sk1
@ ^ [A: a,B: a,C: a] : $false )
= c0 )
| ~ ( sk5
@ ^ [A: a,B: a,C: a] : $false ) ),
inference(simp,[status(thm)],[120]) ).
thf(314,plain,
! [A: a > a > a > a > a > a > $o] :
( ~ ( sk4
@ ( A
@ ( sk1
@ ^ [B: a,C: a,D: a] : ( sk4 @ ( A @ B @ C @ D ) ) )
@ ( sk2
@ ^ [B: a,C: a,D: a] : ( sk4 @ ( A @ B @ C @ D ) ) )
@ ( sk3
@ ^ [B: a,C: a,D: a] : ( sk4 @ ( A @ B @ C @ D ) ) ) ) )
| ( sk4 @ ( A @ x @ y @ y ) ) ),
inference(prim_subst,[status(thm)],[21:[bind(A,$thf( ^ [C: a] : ^ [D: a] : ^ [E: a] : ( sk4 @ ( B @ C @ D @ E ) ) ))]]) ).
thf(346,plain,
! [A: a > a > a > a > a > a > $o] :
( ~ ( sk4
@ ( A
@ ( sk1
@ ^ [B: a,C: a,D: a] : ( sk4 @ ( A @ B @ C @ D ) ) )
@ ( sk2
@ ^ [B: a,C: a,D: a] : ( sk4 @ ( A @ B @ C @ D ) ) )
@ ( sk3
@ ^ [B: a,C: a,D: a] : ( sk4 @ ( A @ B @ C @ D ) ) ) ) )
| ( sk4 @ ( A @ x @ y @ y ) ) ),
inference(simp,[status(thm)],[314]) ).
thf(759,plain,
! [A: a] :
( ( ( sk23 @ x @ y @ y )
!= ( sk23 @ w @ z @ z ) )
| ( ( sk23 @ A @ c0 @ A )
!= ( sk23 @ w @ z @ z ) ) ),
inference(paramod_ordered,[status(thm)],[32,543]) ).
thf(783,plain,
! [A: a] :
( ( x != w )
| ( y != z )
| ( y != z )
| ( A != w )
| ( c0 != z )
| ( A != z ) ),
inference(simp,[status(thm)],[759]) ).
thf(800,plain,
( ( x != w )
| ( y != z )
| ( c0 != z )
| ( w != z ) ),
inference(simp,[status(thm)],[783]) ).
thf(1008,plain,
! [A: a] :
( ( sk23
@ ( sk1
@ ^ [B: a,C: a,D: a] :
~ ( sk23 @ B @ C @ D ) )
@ ( sk2
@ ^ [B: a,C: a,D: a] :
~ ( sk23 @ B @ C @ D ) )
@ ( sk3
@ ^ [B: a,C: a,D: a] :
~ ( sk23 @ B @ C @ D ) ) )
| ( ( sk23 @ c0 @ A @ A )
!= ( sk23 @ x @ y @ y ) ) ),
inference(paramod_ordered,[status(thm)],[43,890]) ).
thf(1035,plain,
! [A: a] :
( ( sk23
@ ( sk1
@ ^ [B: a,C: a,D: a] :
~ ( sk23 @ B @ C @ D ) )
@ ( sk2
@ ^ [B: a,C: a,D: a] :
~ ( sk23 @ B @ C @ D ) )
@ ( sk3
@ ^ [B: a,C: a,D: a] :
~ ( sk23 @ B @ C @ D ) ) )
| ( c0 != x )
| ( A != y )
| ( A != y ) ),
inference(simp,[status(thm)],[1008]) ).
thf(1045,plain,
( ( sk23
@ ( sk1
@ ^ [A: a,B: a,C: a] :
~ ( sk23 @ A @ B @ C ) )
@ ( sk2
@ ^ [A: a,B: a,C: a] :
~ ( sk23 @ A @ B @ C ) )
@ ( sk3
@ ^ [A: a,B: a,C: a] :
~ ( sk23 @ A @ B @ C ) ) )
| ( c0 != x ) ),
inference(simp,[status(thm)],[1035]) ).
thf(135,plain,
( ~ ( sk4
@ ^ [A: a,B: a,C: a] : $false )
| ~ ( sk5
@ ^ [A: a,B: a,C: a] : $false )
| $false
| $false ),
inference(prim_subst,[status(thm)],[5:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ^ [D: a] : $false ))]]) ).
thf(151,plain,
( ~ ( sk4
@ ^ [A: a,B: a,C: a] : $false )
| ~ ( sk5
@ ^ [A: a,B: a,C: a] : $false ) ),
inference(simp,[status(thm)],[135]) ).
thf(9,plain,
! [A: a > a > a > $o] :
( ~ ( sk15 @ A )
| ~ ( sk16 @ A )
| ( ( sk14 @ A )
= ( cP @ ( sk21 @ A ) @ ( sk22 @ A ) ) )
| ( A @ w @ z @ z ) ),
inference(cnf,[status(esa)],[4]) ).
thf(35,plain,
! [A: a > a > a > $o] :
( ( ( cP @ ( sk21 @ A ) @ ( sk22 @ A ) )
= ( sk14 @ A ) )
| ~ ( sk15 @ A )
| ~ ( sk16 @ A )
| ( A @ w @ z @ z ) ),
inference(lifteq,[status(thm)],[9]) ).
thf(36,plain,
! [A: a > a > a > $o] :
( ( ( cP @ ( sk21 @ A ) @ ( sk22 @ A ) )
= ( sk14 @ A ) )
| ~ ( sk15 @ A )
| ~ ( sk16 @ A )
| ( A @ w @ z @ z ) ),
inference(simp,[status(thm)],[35]) ).
thf(770,plain,
! [A: a] :
( ( x != w )
| ( y != z )
| ( y != z )
| ( c0 != w )
| ( A != z )
| ( A != z ) ),
inference(simp,[status(thm)],[761]) ).
thf(790,plain,
( ( x != w )
| ( y != z )
| ( c0 != w ) ),
inference(simp,[status(thm)],[770]) ).
thf(719,plain,
( ( ( sk14
@ ^ [A: a,B: a,C: a] : $false )
= ( sk12
@ ^ [A: a,B: a,C: a] : $false ) )
| ~ ( sk15
@ ^ [A: a,B: a,C: a] : $false )
| ( sk16
@ ^ [A: a,B: a,C: a] : $false )
| $false ),
inference(prim_subst,[status(thm)],[34:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ^ [D: a] : $false ))]]) ).
thf(735,plain,
( ( ( sk14
@ ^ [A: a,B: a,C: a] : $false )
= ( sk12
@ ^ [A: a,B: a,C: a] : $false ) )
| ~ ( sk15
@ ^ [A: a,B: a,C: a] : $false )
| ( sk16
@ ^ [A: a,B: a,C: a] : $false ) ),
inference(simp,[status(thm)],[719]) ).
thf(1268,plain,
( ~ ( sk23 @ w @ z @ z )
| ( sk23
@ ( sk12
@ ^ [A: a,B: a,C: a] :
~ ( sk23 @ A @ B @ C ) )
@ ( sk13
@ ^ [A: a,B: a,C: a] :
~ ( sk23 @ A @ B @ C ) )
@ ( sk14
@ ^ [A: a,B: a,C: a] :
~ ( sk23 @ A @ B @ C ) ) ) ),
inference(prim_subst,[status(thm)],[417:[bind(A,$thf( sk23 ))]]) ).
thf(1395,plain,
! [A: a] :
( ( sk23
@ ( sk12
@ ^ [B: a,C: a,D: a] :
~ ( sk23 @ B @ C @ D ) )
@ ( sk13
@ ^ [B: a,C: a,D: a] :
~ ( sk23 @ B @ C @ D ) )
@ ( sk14
@ ^ [B: a,C: a,D: a] :
~ ( sk23 @ B @ C @ D ) ) )
| ( ( sk23 @ c0 @ A @ A )
!= ( sk23 @ w @ z @ z ) ) ),
inference(paramod_ordered,[status(thm)],[43,1268]) ).
thf(1413,plain,
! [A: a] :
( ( sk23
@ ( sk12
@ ^ [B: a,C: a,D: a] :
~ ( sk23 @ B @ C @ D ) )
@ ( sk13
@ ^ [B: a,C: a,D: a] :
~ ( sk23 @ B @ C @ D ) )
@ ( sk14
@ ^ [B: a,C: a,D: a] :
~ ( sk23 @ B @ C @ D ) ) )
| ( c0 != w )
| ( A != z )
| ( A != z ) ),
inference(simp,[status(thm)],[1395]) ).
thf(1436,plain,
( ( sk23
@ ( sk12
@ ^ [A: a,B: a,C: a] :
~ ( sk23 @ A @ B @ C ) )
@ ( sk13
@ ^ [A: a,B: a,C: a] :
~ ( sk23 @ A @ B @ C ) )
@ ( sk14
@ ^ [A: a,B: a,C: a] :
~ ( sk23 @ A @ B @ C ) ) )
| ( c0 != w ) ),
inference(simp,[status(thm)],[1413]) ).
thf(305,plain,
! [A: a > a > a > $o] :
( ( ( sk1 @ sk23 )
= c0 )
| ( sk4 @ sk23 )
| ( A @ x @ y @ y )
| ( ( sk23 @ x @ y @ y )
!= ( A @ ( sk1 @ A ) @ ( sk2 @ A ) @ ( sk3 @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[68,21]) ).
thf(326,plain,
( ( ( sk1 @ sk23 )
= c0 )
| ( sk4 @ sk23 )
| ( sk23 @ x @ y @ y ) ),
inference(pre_uni,[status(thm)],[305:[bind(A,$thf( ^ [B: a] : ^ [C: a] : ^ [D: a] : ( sk23 @ x @ y @ y ) ))]]) ).
thf(322,plain,
( ~ ( sk23 @ ( sk1 @ sk23 ) @ ( sk2 @ sk23 ) @ ( sk3 @ sk23 ) )
| ( sk23 @ x @ y @ y ) ),
inference(prim_subst,[status(thm)],[21:[bind(A,$thf( sk23 ))]]) ).
thf(2308,plain,
$false,
inference(e,[status(thm)],[417,460,6,350,553,101,347,555,5,1793,550,472,789,348,38,21,65,551,45,64,573,32,34,562,579,413,890,552,108,394,3,63,1780,16,338,571,43,588,40,158,55,346,800,82,1045,151,36,30,51,790,735,1436,326,1268,68,322,543]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SEV208^5 : TPTP v8.2.0. Released v4.0.0.
% 0.12/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.33 % Computer : n029.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 21 18:29:25 EDT 2024
% 0.20/0.33 % CPUTime :
% 0.99/0.87 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.22/0.98 % [INFO] Parsing done (111ms).
% 1.22/0.99 % [INFO] Running in sequential loop mode.
% 1.75/1.21 % [INFO] eprover registered as external prover.
% 1.75/1.21 % [INFO] Scanning for conjecture ...
% 1.91/1.30 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.16/1.33 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.16/1.33 % [INFO] Problem is higher-order (TPTP THF).
% 2.16/1.33 % [INFO] Type checking passed.
% 2.16/1.34 % [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 ...
% 71.86/22.85 % External prover 'e' found a proof!
% 71.86/22.85 % [INFO] Killing All external provers ...
% 71.86/22.85 % Time passed: 22319ms (effective reasoning time: 21859ms)
% 71.86/22.85 % 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)>
% 71.86/22.85 % Axioms used in derivation (0):
% 71.86/22.85 % No. of inferences in proof: 131
% 71.86/22.85 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 22319 ms resp. 21859 ms w/o parsing
% 71.93/22.92 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 71.93/22.92 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------