TSTP Solution File: SEV515+1 by Leo-III-SAT---1.7.15
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.15
% Problem : SEV515+1 : TPTP v8.2.0. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d SAT
% Computer : n023.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 16:00:27 EDT 2024
% Result : Theorem 94.31s 16.52s
% Output : Refutation 94.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 5
% Syntax : Number of formulae : 194 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 862 ( 51 equ; 0 cnn)
% Maximal formula atoms : 24 ( 4 avg)
% Number of connectives : 2697 ( 311 ~; 486 |; 65 &;1820 @)
% ( 3 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 5 con; 0-2 aty)
% Number of variables : 230 ( 0 ^ 206 !; 24 ?; 230 :)
% Comments :
%------------------------------------------------------------------------------
thf(g_true_only_type,type,
g_true_only: $i > $i > $o ).
thf(g_both_type,type,
g_both: $i > $i > $o ).
thf(g_false_only_type,type,
g_false_only: $i > $i > $o ).
thf(g_true_type,type,
g_true: $i > $i > $o ).
thf(g_false_type,type,
g_false: $i > $i > $o ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $o ).
thf(sk3_type,type,
sk3: $i > $o ).
thf(sk4_type,type,
sk4: $i > $i ).
thf(sk5_type,type,
sk5: $i > $i ).
thf(sk6_type,type,
sk6: $i > $i ).
thf(sk7_type,type,
sk7: $i ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( g_true_only @ A @ B )
| ( g_both @ A @ B )
| ( g_false_only @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exhaustion_g) ).
thf(57,plain,
! [A: $i,B: $i] :
( ( g_true_only @ A @ B )
| ( g_both @ A @ B )
| ( g_false_only @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(58,plain,
! [B: $i,A: $i] :
( ( g_true_only @ A @ B )
| ( g_both @ A @ B )
| ( g_false_only @ A @ B ) ),
inference(cnf,[status(esa)],[57]) ).
thf(1,conjecture,
( ! [A: $i] :
? [B: $i] :
( ( ( g_true_only @ B @ A )
& ( ( g_both @ B @ B )
| ( g_true_only @ B @ B ) ) )
| ( ( g_both @ B @ A )
& ( ( g_false_only @ B @ B )
| ( g_true_only @ B @ B ) ) )
| ( ( g_false_only @ B @ A )
& ( ( g_false_only @ B @ B )
| ( g_both @ B @ B ) ) ) )
| ( ? [A: $i] :
( ? [B: $i] :
( ( g_both @ B @ A )
& ( g_both @ B @ B ) )
& ~ ? [B: $i] :
( ( ( g_true_only @ B @ A )
& ( ( g_both @ B @ B )
| ( g_true_only @ B @ B ) ) )
| ( ( g_both @ B @ A )
& ( ( g_false_only @ B @ B )
| ( g_true_only @ B @ B ) ) )
| ( ( g_false_only @ B @ A )
& ( ( g_false_only @ B @ B )
| ( g_both @ B @ B ) ) ) ) )
& ~ ? [A: $i] :
! [B: $i] :
( ( ( g_true_only @ B @ A )
& ( g_false_only @ B @ B ) )
| ( ( g_false_only @ B @ A )
& ( g_true_only @ B @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nc1) ).
thf(2,negated_conjecture,
~ ( ! [A: $i] :
? [B: $i] :
( ( ( g_true_only @ B @ A )
& ( ( g_both @ B @ B )
| ( g_true_only @ B @ B ) ) )
| ( ( g_both @ B @ A )
& ( ( g_false_only @ B @ B )
| ( g_true_only @ B @ B ) ) )
| ( ( g_false_only @ B @ A )
& ( ( g_false_only @ B @ B )
| ( g_both @ B @ B ) ) ) )
| ( ? [A: $i] :
( ? [B: $i] :
( ( g_both @ B @ A )
& ( g_both @ B @ B ) )
& ~ ? [B: $i] :
( ( ( g_true_only @ B @ A )
& ( ( g_both @ B @ B )
| ( g_true_only @ B @ B ) ) )
| ( ( g_both @ B @ A )
& ( ( g_false_only @ B @ B )
| ( g_true_only @ B @ B ) ) )
| ( ( g_false_only @ B @ A )
& ( ( g_false_only @ B @ B )
| ( g_both @ B @ B ) ) ) ) )
& ~ ? [A: $i] :
! [B: $i] :
( ( ( g_true_only @ B @ A )
& ( g_false_only @ B @ B ) )
| ( ( g_false_only @ B @ A )
& ( g_true_only @ B @ B ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(7,plain,
~ ( ! [A: $i] :
? [B: $i] :
( ( ( g_true_only @ B @ A )
& ( ( g_both @ B @ B )
| ( g_true_only @ B @ B ) ) )
| ( ( g_both @ B @ A )
& ( ( g_false_only @ B @ B )
| ( g_true_only @ B @ B ) ) )
| ( ( g_false_only @ B @ A )
& ( ( g_false_only @ B @ B )
| ( g_both @ B @ B ) ) ) )
| ( ? [A: $i] :
( ? [B: $i] :
( ( g_both @ B @ A )
& ( g_both @ B @ B ) )
& ~ ? [B: $i] :
( ( ( g_true_only @ B @ A )
& ( ( g_both @ B @ B )
| ( g_true_only @ B @ B ) ) )
| ( ( g_both @ B @ A )
& ( ( g_false_only @ B @ B )
| ( g_true_only @ B @ B ) ) )
| ( ( g_false_only @ B @ A )
& ( ( g_false_only @ B @ B )
| ( g_both @ B @ B ) ) ) ) )
& ~ ? [A: $i] :
! [B: $i] :
( ( ( g_true_only @ B @ A )
& ( g_false_only @ B @ B ) )
| ( ( g_false_only @ B @ A )
& ( g_true_only @ B @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,plain,
~ ( ! [A: $i] :
( ? [B: $i] :
( ( g_true_only @ B @ A )
& ( ( g_both @ B @ B )
| ( g_true_only @ B @ B ) ) )
| ? [B: $i] :
( ( g_both @ B @ A )
& ( ( g_false_only @ B @ B )
| ( g_true_only @ B @ B ) ) )
| ? [B: $i] :
( ( g_false_only @ B @ A )
& ( ( g_false_only @ B @ B )
| ( g_both @ B @ B ) ) ) )
| ( ? [A: $i] :
( ? [B: $i] :
( ( g_both @ B @ A )
& ( g_both @ B @ B ) )
& ~ ( ? [B: $i] :
( ( g_true_only @ B @ A )
& ( ( g_both @ B @ B )
| ( g_true_only @ B @ B ) ) )
| ? [B: $i] :
( ( g_both @ B @ A )
& ( ( g_false_only @ B @ B )
| ( g_true_only @ B @ B ) ) )
| ? [B: $i] :
( ( g_false_only @ B @ A )
& ( ( g_false_only @ B @ B )
| ( g_both @ B @ B ) ) ) ) )
& ~ ? [A: $i] :
! [B: $i] :
( ( ( g_true_only @ B @ A )
& ( g_false_only @ B @ B ) )
| ( ( g_false_only @ B @ A )
& ( g_true_only @ B @ B ) ) ) ) ),
inference(miniscope,[status(thm)],[7]) ).
thf(11,plain,
! [A: $i] :
( ~ ( g_false_only @ A @ sk1 )
| ~ ( g_false_only @ A @ A ) ),
inference(cnf,[status(esa)],[8]) ).
thf(36,plain,
! [A: $i] :
( ~ ( g_false_only @ A @ sk1 )
| ~ ( g_false_only @ A @ A ) ),
inference(simp,[status(thm)],[11]) ).
thf(69,plain,
! [A: $i] :
( ~ ( g_false_only @ A @ sk1 )
| ( ( g_false_only @ A @ A )
!= ( g_false_only @ A @ sk1 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[36]) ).
thf(71,plain,
~ ( g_false_only @ sk1 @ sk1 ),
inference(pattern_uni,[status(thm)],[69:[bind(A,$thf( sk1 ))]]) ).
thf(452,plain,
! [B: $i,A: $i] :
( ( g_true_only @ A @ B )
| ( g_both @ A @ B )
| ( ( g_false_only @ A @ B )
!= ( g_false_only @ sk1 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[58,71]) ).
thf(453,plain,
( ( g_true_only @ sk1 @ sk1 )
| ( g_both @ sk1 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[452:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(19,plain,
! [A: $i] :
( ~ ( g_true_only @ A @ sk1 )
| ~ ( g_true_only @ A @ A ) ),
inference(cnf,[status(esa)],[8]) ).
thf(59,plain,
! [A: $i] :
( ~ ( g_true_only @ A @ sk1 )
| ( ( g_true_only @ A @ A )
!= ( g_true_only @ A @ sk1 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[19]) ).
thf(60,plain,
~ ( g_true_only @ sk1 @ sk1 ),
inference(pattern_uni,[status(thm)],[59:[bind(A,$thf( sk1 ))]]) ).
thf(467,plain,
( $false
| ( g_both @ sk1 @ sk1 ) ),
inference(rewrite,[status(thm)],[453,60]) ).
thf(468,plain,
g_both @ sk1 @ sk1,
inference(simp,[status(thm)],[467]) ).
thf(24,plain,
! [B: $i,A: $i] :
( ~ ( g_both @ B @ A )
| ~ ( g_both @ B @ B )
| ~ ( sk3 @ A )
| ( g_false_only @ ( sk5 @ A ) @ ( sk5 @ A ) )
| ( g_true_only @ ( sk5 @ A ) @ ( sk5 @ A ) )
| ( g_false_only @ ( sk6 @ A ) @ ( sk6 @ A ) )
| ( g_both @ ( sk6 @ A ) @ ( sk6 @ A ) )
| ~ sk2 ),
inference(cnf,[status(esa)],[8]) ).
thf(26,plain,
! [B: $i,A: $i] :
( ~ ( g_both @ B @ A )
| ~ ( g_both @ B @ B )
| ~ ( sk3 @ A )
| ( g_false_only @ ( sk5 @ A ) @ ( sk5 @ A ) )
| ( g_true_only @ ( sk5 @ A ) @ ( sk5 @ A ) )
| ( g_false_only @ ( sk6 @ A ) @ ( sk6 @ A ) )
| ( g_both @ ( sk6 @ A ) @ ( sk6 @ A ) )
| ~ sk2 ),
inference(simp,[status(thm)],[24]) ).
thf(146,plain,
! [B: $i,A: $i] :
( ~ ( g_both @ B @ A )
| ~ ( g_both @ B @ B )
| ~ ( sk3 @ A )
| ( g_false_only @ ( sk5 @ A ) @ ( sk5 @ A ) )
| ( g_true_only @ ( sk5 @ A ) @ ( sk5 @ A ) )
| ( g_both @ ( sk6 @ A ) @ ( sk6 @ A ) )
| ~ sk2
| ( ( g_false_only @ ( sk6 @ A ) @ ( sk6 @ A ) )
!= ( g_false_only @ ( sk5 @ A ) @ ( sk5 @ A ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[26]) ).
thf(150,plain,
! [B: $i,A: $i] :
( ( g_false_only @ ( sk5 @ A ) @ ( sk5 @ A ) )
| ( g_true_only @ ( sk5 @ A ) @ ( sk5 @ A ) )
| ( g_both @ ( sk6 @ A ) @ ( sk6 @ A ) )
| ~ ( g_both @ B @ A )
| ~ ( g_both @ B @ B )
| ~ ( sk3 @ A )
| ~ sk2
| ( ( g_false_only @ ( sk6 @ A ) @ ( sk6 @ A ) )
!= ( g_false_only @ ( sk5 @ A ) @ ( sk5 @ A ) ) ) ),
inference(simp,[status(thm)],[146]) ).
thf(17,plain,
! [A: $i] :
( sk2
| ( g_false_only @ A @ A )
| ( g_false_only @ A @ sk7 ) ),
inference(cnf,[status(esa)],[8]) ).
thf(32,plain,
! [A: $i] :
( sk2
| ( g_false_only @ A @ A )
| ( g_false_only @ A @ sk7 ) ),
inference(simp,[status(thm)],[17]) ).
thf(209,plain,
! [A: $i] :
( sk2
| ( g_false_only @ A @ A )
| ( ( g_false_only @ A @ sk7 )
!= ( g_false_only @ A @ A ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[32]) ).
thf(212,plain,
( sk2
| ( g_false_only @ sk7 @ sk7 ) ),
inference(pattern_uni,[status(thm)],[209:[bind(A,$thf( sk7 ))]]) ).
thf(9,plain,
! [A: $i] :
( sk2
| ( g_true_only @ A @ sk7 )
| ( g_true_only @ A @ A ) ),
inference(cnf,[status(esa)],[8]) ).
thf(30,plain,
! [A: $i] :
( sk2
| ( g_true_only @ A @ sk7 )
| ( g_true_only @ A @ A ) ),
inference(simp,[status(thm)],[9]) ).
thf(109,plain,
! [A: $i] :
( sk2
| ( g_true_only @ A @ sk7 )
| ( ( g_true_only @ A @ A )
!= ( g_true_only @ A @ sk7 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[30]) ).
thf(112,plain,
( sk2
| ( g_true_only @ sk7 @ sk7 ) ),
inference(pattern_uni,[status(thm)],[109:[bind(A,$thf( sk7 ))]]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( g_true_only @ A @ B )
<=> ( ( g_true @ A @ B )
& ~ ( g_false @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',true_only_g) ).
thf(39,plain,
! [A: $i,B: $i] :
( ( ( g_true_only @ A @ B )
=> ( ( g_true @ A @ B )
& ~ ( g_false @ A @ B ) ) )
& ( ( ( g_true @ A @ B )
& ~ ( g_false @ A @ B ) )
=> ( g_true_only @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(40,plain,
( ! [A: $i,B: $i] :
( ( g_true_only @ A @ B )
=> ( ( g_true @ A @ B )
& ~ ( g_false @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ( ( g_true @ A @ B )
& ~ ( g_false @ A @ B ) )
=> ( g_true_only @ A @ B ) ) ),
inference(miniscope,[status(thm)],[39]) ).
thf(42,plain,
! [B: $i,A: $i] :
( ~ ( g_true_only @ A @ B )
| ( g_true @ A @ B ) ),
inference(cnf,[status(esa)],[40]) ).
thf(122,plain,
! [B: $i,A: $i] :
( sk2
| ( g_true @ A @ B )
| ( ( g_true_only @ sk7 @ sk7 )
!= ( g_true_only @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[112,42]) ).
thf(123,plain,
( sk2
| ( g_true @ sk7 @ sk7 ) ),
inference(pattern_uni,[status(thm)],[122:[bind(A,$thf( sk7 )),bind(B,$thf( sk7 ))]]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( g_false_only @ A @ B )
<=> ( ( g_false @ A @ B )
& ~ ( g_true @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',false_only_g) ).
thf(51,plain,
! [A: $i,B: $i] :
( ( ( g_false_only @ A @ B )
=> ( ( g_false @ A @ B )
& ~ ( g_true @ A @ B ) ) )
& ( ( ( g_false @ A @ B )
& ~ ( g_true @ A @ B ) )
=> ( g_false_only @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(52,plain,
( ! [A: $i,B: $i] :
( ( g_false_only @ A @ B )
=> ( ( g_false @ A @ B )
& ~ ( g_true @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ( ( g_false @ A @ B )
& ~ ( g_true @ A @ B ) )
=> ( g_false_only @ A @ B ) ) ),
inference(miniscope,[status(thm)],[51]) ).
thf(55,plain,
! [B: $i,A: $i] :
( ~ ( g_false_only @ A @ B )
| ~ ( g_true @ A @ B ) ),
inference(cnf,[status(esa)],[52]) ).
thf(161,plain,
! [B: $i,A: $i] :
( sk2
| ~ ( g_false_only @ A @ B )
| ( ( g_true @ sk7 @ sk7 )
!= ( g_true @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[123,55]) ).
thf(162,plain,
( sk2
| ~ ( g_false_only @ sk7 @ sk7 ) ),
inference(pattern_uni,[status(thm)],[161:[bind(A,$thf( sk7 )),bind(B,$thf( sk7 ))]]) ).
thf(270,plain,
( sk2
| ( ( g_false_only @ sk7 @ sk7 )
!= ( g_false_only @ sk7 @ sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[212,162]) ).
thf(271,plain,
sk2,
inference(pattern_uni,[status(thm)],[270:[]]) ).
thf(1102,plain,
! [B: $i,A: $i] :
( ( g_false_only @ ( sk5 @ A ) @ ( sk5 @ A ) )
| ( g_true_only @ ( sk5 @ A ) @ ( sk5 @ A ) )
| ( g_both @ ( sk6 @ A ) @ ( sk6 @ A ) )
| ~ ( g_both @ B @ A )
| ~ ( g_both @ B @ B )
| ~ ( sk3 @ A )
| ~ $true
| ( ( g_false_only @ ( sk6 @ A ) @ ( sk6 @ A ) )
!= ( g_false_only @ ( sk5 @ A ) @ ( sk5 @ A ) ) ) ),
inference(rewrite,[status(thm)],[150,271]) ).
thf(1103,plain,
! [B: $i,A: $i] :
( ( g_false_only @ ( sk5 @ A ) @ ( sk5 @ A ) )
| ( g_true_only @ ( sk5 @ A ) @ ( sk5 @ A ) )
| ( g_both @ ( sk6 @ A ) @ ( sk6 @ A ) )
| ~ ( g_both @ B @ A )
| ~ ( g_both @ B @ B )
| ~ ( sk3 @ A )
| ( ( g_false_only @ ( sk6 @ A ) @ ( sk6 @ A ) )
!= ( g_false_only @ ( sk5 @ A ) @ ( sk5 @ A ) ) ) ),
inference(simp,[status(thm)],[1102]) ).
thf(1110,plain,
! [B: $i,A: $i] :
( ( g_false_only @ ( sk5 @ A ) @ ( sk5 @ A ) )
| ( g_true_only @ ( sk5 @ A ) @ ( sk5 @ A ) )
| ( g_both @ ( sk6 @ A ) @ ( sk6 @ A ) )
| ~ ( g_both @ B @ B )
| ~ ( sk3 @ A )
| ( ( g_false_only @ ( sk6 @ A ) @ ( sk6 @ A ) )
!= ( g_false_only @ ( sk5 @ A ) @ ( sk5 @ A ) ) )
| ( ( g_both @ sk1 @ sk1 )
!= ( g_both @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[468,1103]) ).
thf(1111,plain,
( ( g_false_only @ ( sk5 @ sk1 ) @ ( sk5 @ sk1 ) )
| ( g_true_only @ ( sk5 @ sk1 ) @ ( sk5 @ sk1 ) )
| ( g_both @ ( sk6 @ sk1 ) @ ( sk6 @ sk1 ) )
| ~ ( g_both @ sk1 @ sk1 )
| ~ ( sk3 @ sk1 )
| ( ( g_false_only @ ( sk6 @ sk1 ) @ ( sk6 @ sk1 ) )
!= ( g_false_only @ ( sk5 @ sk1 ) @ ( sk5 @ sk1 ) ) ) ),
inference(pattern_uni,[status(thm)],[1110:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(23,plain,
! [B: $i,A: $i] :
( ~ ( g_both @ B @ A )
| ~ ( g_both @ B @ B )
| ~ ( sk3 @ A )
| ( g_false_only @ ( sk5 @ A ) @ ( sk5 @ A ) )
| ( g_true_only @ ( sk5 @ A ) @ ( sk5 @ A ) )
| ( g_false_only @ ( sk6 @ A ) @ A )
| ~ sk2 ),
inference(cnf,[status(esa)],[8]) ).
thf(37,plain,
! [B: $i,A: $i] :
( ~ ( g_both @ B @ A )
| ~ ( g_both @ B @ B )
| ~ ( sk3 @ A )
| ( g_false_only @ ( sk5 @ A ) @ ( sk5 @ A ) )
| ( g_true_only @ ( sk5 @ A ) @ ( sk5 @ A ) )
| ( g_false_only @ ( sk6 @ A ) @ A )
| ~ sk2 ),
inference(simp,[status(thm)],[23]) ).
thf(514,plain,
! [B: $i,A: $i] :
( ~ ( g_both @ B @ A )
| ~ ( g_both @ B @ B )
| ~ ( sk3 @ A )
| ( g_false_only @ ( sk5 @ A ) @ ( sk5 @ A ) )
| ( g_true_only @ ( sk5 @ A ) @ ( sk5 @ A ) )
| ( g_false_only @ ( sk6 @ A ) @ A )
| ~ $true ),
inference(rewrite,[status(thm)],[37,271]) ).
thf(515,plain,
! [B: $i,A: $i] :
( ~ ( g_both @ B @ A )
| ~ ( g_both @ B @ B )
| ~ ( sk3 @ A )
| ( g_false_only @ ( sk5 @ A ) @ ( sk5 @ A ) )
| ( g_true_only @ ( sk5 @ A ) @ ( sk5 @ A ) )
| ( g_false_only @ ( sk6 @ A ) @ A ) ),
inference(simp,[status(thm)],[514]) ).
thf(526,plain,
! [B: $i,A: $i] :
( ~ ( g_both @ B @ B )
| ~ ( sk3 @ A )
| ( g_false_only @ ( sk5 @ A ) @ ( sk5 @ A ) )
| ( g_true_only @ ( sk5 @ A ) @ ( sk5 @ A ) )
| ( g_false_only @ ( sk6 @ A ) @ A )
| ( ( g_both @ sk1 @ sk1 )
!= ( g_both @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[468,515]) ).
thf(527,plain,
( ~ ( g_both @ sk1 @ sk1 )
| ~ ( sk3 @ sk1 )
| ( g_false_only @ ( sk5 @ sk1 ) @ ( sk5 @ sk1 ) )
| ( g_true_only @ ( sk5 @ sk1 ) @ ( sk5 @ sk1 ) )
| ( g_false_only @ ( sk6 @ sk1 ) @ sk1 ) ),
inference(pattern_uni,[status(thm)],[526:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(10,plain,
! [B: $i,A: $i] :
( ~ ( g_both @ B @ A )
| ~ ( g_both @ B @ B )
| ( g_true_only @ ( sk4 @ A ) @ A )
| ( sk3 @ A )
| ~ sk2 ),
inference(cnf,[status(esa)],[8]) ).
thf(25,plain,
! [B: $i,A: $i] :
( ~ ( g_both @ B @ A )
| ~ ( g_both @ B @ B )
| ( g_true_only @ ( sk4 @ A ) @ A )
| ( sk3 @ A )
| ~ sk2 ),
inference(simp,[status(thm)],[10]) ).
thf(73,plain,
! [B: $i,A: $i] :
( ~ ( g_both @ B @ A )
| ( g_true_only @ ( sk4 @ A ) @ A )
| ( sk3 @ A )
| ~ sk2
| ( ( g_both @ B @ B )
!= ( g_both @ B @ A ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[25]) ).
thf(74,plain,
! [A: $i] :
( ~ ( g_both @ A @ A )
| ( g_true_only @ ( sk4 @ A ) @ A )
| ( sk3 @ A )
| ~ sk2 ),
inference(pattern_uni,[status(thm)],[73:[bind(A,$thf( B ))]]) ).
thf(75,plain,
! [A: $i] :
( ~ ( g_both @ A @ A )
| ( g_true_only @ ( sk4 @ A ) @ A )
| ( sk3 @ A )
| ~ sk2 ),
inference(simp,[status(thm)],[74]) ).
thf(942,plain,
! [A: $i] :
( ~ ( g_both @ A @ A )
| ( g_true_only @ ( sk4 @ A ) @ A )
| ( sk3 @ A )
| ~ $true ),
inference(rewrite,[status(thm)],[75,271]) ).
thf(943,plain,
! [A: $i] :
( ~ ( g_both @ A @ A )
| ( g_true_only @ ( sk4 @ A ) @ A )
| ( sk3 @ A ) ),
inference(simp,[status(thm)],[942]) ).
thf(944,plain,
! [A: $i] :
( ( g_true_only @ ( sk4 @ A ) @ A )
| ( sk3 @ A )
| ( ( g_both @ sk1 @ sk1 )
!= ( g_both @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[468,943]) ).
thf(945,plain,
( ( g_true_only @ ( sk4 @ sk1 ) @ sk1 )
| ( sk3 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[944:[bind(A,$thf( sk1 ))]]) ).
thf(14,plain,
! [B: $i,A: $i] :
( ~ ( g_both @ B @ A )
| ~ ( g_both @ B @ B )
| ( g_both @ ( sk4 @ A ) @ ( sk4 @ A ) )
| ( g_true_only @ ( sk4 @ A ) @ ( sk4 @ A ) )
| ( sk3 @ A )
| ~ sk2 ),
inference(cnf,[status(esa)],[8]) ).
thf(27,plain,
! [B: $i,A: $i] :
( ~ ( g_both @ B @ A )
| ~ ( g_both @ B @ B )
| ( g_both @ ( sk4 @ A ) @ ( sk4 @ A ) )
| ( g_true_only @ ( sk4 @ A ) @ ( sk4 @ A ) )
| ( sk3 @ A )
| ~ sk2 ),
inference(simp,[status(thm)],[14]) ).
thf(12,plain,
! [A: $i] :
( ~ ( g_true_only @ A @ sk1 )
| ~ ( g_both @ A @ A ) ),
inference(cnf,[status(esa)],[8]) ).
thf(238,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( g_both @ B @ A )
| ~ ( g_both @ B @ B )
| ( g_true_only @ ( sk4 @ A ) @ ( sk4 @ A ) )
| ( sk3 @ A )
| ~ sk2
| ~ ( g_true_only @ C @ sk1 )
| ( ( g_both @ ( sk4 @ A ) @ ( sk4 @ A ) )
!= ( g_both @ C @ C ) ) ),
inference(paramod_ordered,[status(thm)],[27,12]) ).
thf(239,plain,
! [B: $i,A: $i] :
( ~ ( g_both @ A @ B )
| ~ ( g_both @ A @ A )
| ( g_true_only @ ( sk4 @ B ) @ ( sk4 @ B ) )
| ( sk3 @ B )
| ~ sk2
| ~ ( g_true_only @ ( sk4 @ B ) @ sk1 ) ),
inference(pattern_uni,[status(thm)],[238:[bind(A,$thf( D )),bind(B,$thf( B )),bind(C,$thf( sk4 @ D ))]]) ).
thf(257,plain,
! [B: $i,A: $i] :
( ~ ( g_both @ A @ B )
| ~ ( g_both @ A @ A )
| ( g_true_only @ ( sk4 @ B ) @ ( sk4 @ B ) )
| ( sk3 @ B )
| ~ sk2
| ~ ( g_true_only @ ( sk4 @ B ) @ sk1 ) ),
inference(simp,[status(thm)],[239]) ).
thf(3516,plain,
! [B: $i,A: $i] :
( ~ ( g_both @ A @ B )
| ~ ( g_both @ A @ A )
| ( g_true_only @ ( sk4 @ B ) @ ( sk4 @ B ) )
| ( sk3 @ B )
| ~ $true
| ~ ( g_true_only @ ( sk4 @ B ) @ sk1 ) ),
inference(rewrite,[status(thm)],[257,271]) ).
thf(3517,plain,
! [B: $i,A: $i] :
( ~ ( g_both @ A @ B )
| ~ ( g_both @ A @ A )
| ( g_true_only @ ( sk4 @ B ) @ ( sk4 @ B ) )
| ( sk3 @ B )
| ~ ( g_true_only @ ( sk4 @ B ) @ sk1 ) ),
inference(simp,[status(thm)],[3516]) ).
thf(3518,plain,
! [B: $i,A: $i] :
( ~ ( g_both @ A @ A )
| ( g_true_only @ ( sk4 @ B ) @ ( sk4 @ B ) )
| ( sk3 @ B )
| ~ ( g_true_only @ ( sk4 @ B ) @ sk1 )
| ( ( g_both @ sk1 @ sk1 )
!= ( g_both @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[468,3517]) ).
thf(3519,plain,
( ~ ( g_both @ sk1 @ sk1 )
| ( g_true_only @ ( sk4 @ sk1 ) @ ( sk4 @ sk1 ) )
| ( sk3 @ sk1 )
| ~ ( g_true_only @ ( sk4 @ sk1 ) @ sk1 ) ),
inference(pattern_uni,[status(thm)],[3518:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(4611,plain,
( ~ $true
| ( g_true_only @ ( sk4 @ sk1 ) @ ( sk4 @ sk1 ) )
| ( sk3 @ sk1 )
| ~ ( g_true_only @ ( sk4 @ sk1 ) @ sk1 ) ),
inference(rewrite,[status(thm)],[3519,468]) ).
thf(4612,plain,
( ( g_true_only @ ( sk4 @ sk1 ) @ ( sk4 @ sk1 ) )
| ( sk3 @ sk1 )
| ~ ( g_true_only @ ( sk4 @ sk1 ) @ sk1 ) ),
inference(simp,[status(thm)],[4611]) ).
thf(965,plain,
! [A: $i] :
( ( sk3 @ sk1 )
| ~ ( g_true_only @ A @ A )
| ( ( g_true_only @ ( sk4 @ sk1 ) @ sk1 )
!= ( g_true_only @ A @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[945,19]) ).
thf(966,plain,
( ( sk3 @ sk1 )
| ~ ( g_true_only @ ( sk4 @ sk1 ) @ ( sk4 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[965:[bind(A,$thf( sk4 @ sk1 ))]]) ).
thf(4625,plain,
( ( sk3 @ sk1 )
| ~ ( g_true_only @ ( sk4 @ sk1 ) @ sk1 )
| ( ( g_true_only @ ( sk4 @ sk1 ) @ ( sk4 @ sk1 ) )
!= ( g_true_only @ ( sk4 @ sk1 ) @ ( sk4 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[4612,966]) ).
thf(4626,plain,
( ( sk3 @ sk1 )
| ~ ( g_true_only @ ( sk4 @ sk1 ) @ sk1 ) ),
inference(pattern_uni,[status(thm)],[4625:[]]) ).
thf(4667,plain,
( ( sk3 @ sk1 )
| ( ( g_true_only @ ( sk4 @ sk1 ) @ sk1 )
!= ( g_true_only @ ( sk4 @ sk1 ) @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[945,4626]) ).
thf(4668,plain,
sk3 @ sk1,
inference(pattern_uni,[status(thm)],[4667:[]]) ).
thf(14288,plain,
( ~ $true
| ~ $true
| ( g_false_only @ ( sk5 @ sk1 ) @ ( sk5 @ sk1 ) )
| ( g_true_only @ ( sk5 @ sk1 ) @ ( sk5 @ sk1 ) )
| ( g_false_only @ ( sk6 @ sk1 ) @ sk1 ) ),
inference(rewrite,[status(thm)],[527,468,4668]) ).
thf(14289,plain,
( ( g_false_only @ ( sk5 @ sk1 ) @ ( sk5 @ sk1 ) )
| ( g_true_only @ ( sk5 @ sk1 ) @ ( sk5 @ sk1 ) )
| ( g_false_only @ ( sk6 @ sk1 ) @ sk1 ) ),
inference(simp,[status(thm)],[14288]) ).
thf(54,plain,
! [B: $i,A: $i] :
( ~ ( g_false_only @ A @ B )
| ( g_false @ A @ B ) ),
inference(cnf,[status(esa)],[52]) ).
thf(14308,plain,
! [B: $i,A: $i] :
( ( g_false_only @ ( sk5 @ sk1 ) @ ( sk5 @ sk1 ) )
| ( g_true_only @ ( sk5 @ sk1 ) @ ( sk5 @ sk1 ) )
| ( g_false @ A @ B )
| ( ( g_false_only @ ( sk6 @ sk1 ) @ sk1 )
!= ( g_false_only @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[14289,54]) ).
thf(14309,plain,
( ( g_false_only @ ( sk5 @ sk1 ) @ ( sk5 @ sk1 ) )
| ( g_true_only @ ( sk5 @ sk1 ) @ ( sk5 @ sk1 ) )
| ( g_false @ ( sk6 @ sk1 ) @ sk1 ) ),
inference(pattern_uni,[status(thm)],[14308:[bind(A,$thf( sk6 @ sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(15,plain,
! [B: $i,A: $i] :
( ~ ( g_both @ B @ A )
| ~ ( g_both @ B @ B )
| ~ ( sk3 @ A )
| ( g_both @ ( sk5 @ A ) @ A )
| ( g_false_only @ ( sk6 @ A ) @ ( sk6 @ A ) )
| ( g_both @ ( sk6 @ A ) @ ( sk6 @ A ) )
| ~ sk2 ),
inference(cnf,[status(esa)],[8]) ).
thf(38,plain,
! [B: $i,A: $i] :
( ~ ( g_both @ B @ A )
| ~ ( g_both @ B @ B )
| ~ ( sk3 @ A )
| ( g_both @ ( sk5 @ A ) @ A )
| ( g_false_only @ ( sk6 @ A ) @ ( sk6 @ A ) )
| ( g_both @ ( sk6 @ A ) @ ( sk6 @ A ) )
| ~ sk2 ),
inference(simp,[status(thm)],[15]) ).
thf(632,plain,
! [B: $i,A: $i] :
( ~ ( g_both @ B @ A )
| ~ ( g_both @ B @ B )
| ~ ( sk3 @ A )
| ( g_both @ ( sk5 @ A ) @ A )
| ( g_false_only @ ( sk6 @ A ) @ ( sk6 @ A ) )
| ( g_both @ ( sk6 @ A ) @ ( sk6 @ A ) )
| ~ $true ),
inference(rewrite,[status(thm)],[38,271]) ).
thf(633,plain,
! [B: $i,A: $i] :
( ~ ( g_both @ B @ A )
| ~ ( g_both @ B @ B )
| ~ ( sk3 @ A )
| ( g_both @ ( sk5 @ A ) @ A )
| ( g_false_only @ ( sk6 @ A ) @ ( sk6 @ A ) )
| ( g_both @ ( sk6 @ A ) @ ( sk6 @ A ) ) ),
inference(simp,[status(thm)],[632]) ).
thf(643,plain,
! [B: $i,A: $i] :
( ~ ( g_both @ B @ B )
| ~ ( sk3 @ A )
| ( g_both @ ( sk5 @ A ) @ A )
| ( g_false_only @ ( sk6 @ A ) @ ( sk6 @ A ) )
| ( g_both @ ( sk6 @ A ) @ ( sk6 @ A ) )
| ( ( g_both @ sk1 @ sk1 )
!= ( g_both @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[468,633]) ).
thf(644,plain,
( ~ ( g_both @ sk1 @ sk1 )
| ~ ( sk3 @ sk1 )
| ( g_both @ ( sk5 @ sk1 ) @ sk1 )
| ( g_false_only @ ( sk6 @ sk1 ) @ ( sk6 @ sk1 ) )
| ( g_both @ ( sk6 @ sk1 ) @ ( sk6 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[643:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(18952,plain,
( ~ $true
| ~ $true
| ( g_both @ ( sk5 @ sk1 ) @ sk1 )
| ( g_false_only @ ( sk6 @ sk1 ) @ ( sk6 @ sk1 ) )
| ( g_both @ ( sk6 @ sk1 ) @ ( sk6 @ sk1 ) ) ),
inference(rewrite,[status(thm)],[644,468,4668]) ).
thf(18953,plain,
( ( g_both @ ( sk5 @ sk1 ) @ sk1 )
| ( g_false_only @ ( sk6 @ sk1 ) @ ( sk6 @ sk1 ) )
| ( g_both @ ( sk6 @ sk1 ) @ ( sk6 @ sk1 ) ) ),
inference(simp,[status(thm)],[18952]) ).
thf(13,plain,
! [B: $i,A: $i] :
( ~ ( g_both @ B @ A )
| ~ ( g_both @ B @ B )
| ~ ( sk3 @ A )
| ( g_both @ ( sk5 @ A ) @ A )
| ( g_false_only @ ( sk6 @ A ) @ A )
| ~ sk2 ),
inference(cnf,[status(esa)],[8]) ).
thf(31,plain,
! [B: $i,A: $i] :
( ~ ( g_both @ B @ A )
| ~ ( g_both @ B @ B )
| ~ ( sk3 @ A )
| ( g_both @ ( sk5 @ A ) @ A )
| ( g_false_only @ ( sk6 @ A ) @ A )
| ~ sk2 ),
inference(simp,[status(thm)],[13]) ).
thf(302,plain,
! [B: $i,A: $i] :
( ~ ( g_both @ B @ A )
| ~ ( g_both @ B @ B )
| ~ ( sk3 @ A )
| ( g_both @ ( sk5 @ A ) @ A )
| ( g_false_only @ ( sk6 @ A ) @ A )
| ~ $true ),
inference(rewrite,[status(thm)],[31,271]) ).
thf(303,plain,
! [B: $i,A: $i] :
( ~ ( g_both @ B @ A )
| ~ ( g_both @ B @ B )
| ~ ( sk3 @ A )
| ( g_both @ ( sk5 @ A ) @ A )
| ( g_false_only @ ( sk6 @ A ) @ A ) ),
inference(simp,[status(thm)],[302]) ).
thf(497,plain,
! [B: $i,A: $i] :
( ~ ( g_both @ B @ B )
| ~ ( sk3 @ A )
| ( g_both @ ( sk5 @ A ) @ A )
| ( g_false_only @ ( sk6 @ A ) @ A )
| ( ( g_both @ sk1 @ sk1 )
!= ( g_both @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[468,303]) ).
thf(498,plain,
( ~ ( g_both @ sk1 @ sk1 )
| ~ ( sk3 @ sk1 )
| ( g_both @ ( sk5 @ sk1 ) @ sk1 )
| ( g_false_only @ ( sk6 @ sk1 ) @ sk1 ) ),
inference(pattern_uni,[status(thm)],[497:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(1642,plain,
( ~ $true
| ~ ( sk3 @ sk1 )
| ( g_both @ ( sk5 @ sk1 ) @ sk1 )
| ( g_false_only @ ( sk6 @ sk1 ) @ sk1 ) ),
inference(rewrite,[status(thm)],[498,468]) ).
thf(1643,plain,
( ~ ( sk3 @ sk1 )
| ( g_both @ ( sk5 @ sk1 ) @ sk1 )
| ( g_false_only @ ( sk6 @ sk1 ) @ sk1 ) ),
inference(simp,[status(thm)],[1642]) ).
thf(1664,plain,
! [A: $i] :
( ~ ( sk3 @ sk1 )
| ( g_both @ ( sk5 @ sk1 ) @ sk1 )
| ~ ( g_false_only @ A @ A )
| ( ( g_false_only @ ( sk6 @ sk1 ) @ sk1 )
!= ( g_false_only @ A @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[1643,36]) ).
thf(1665,plain,
( ~ ( sk3 @ sk1 )
| ( g_both @ ( sk5 @ sk1 ) @ sk1 )
| ~ ( g_false_only @ ( sk6 @ sk1 ) @ ( sk6 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[1664:[bind(A,$thf( sk6 @ sk1 ))]]) ).
thf(4673,plain,
( ~ $true
| ( g_both @ ( sk5 @ sk1 ) @ sk1 )
| ~ ( g_false_only @ ( sk6 @ sk1 ) @ ( sk6 @ sk1 ) ) ),
inference(rewrite,[status(thm)],[1665,4668]) ).
thf(4674,plain,
( ( g_both @ ( sk5 @ sk1 ) @ sk1 )
| ~ ( g_false_only @ ( sk6 @ sk1 ) @ ( sk6 @ sk1 ) ) ),
inference(simp,[status(thm)],[4673]) ).
thf(19003,plain,
( ( g_both @ ( sk5 @ sk1 ) @ sk1 )
| ( g_both @ ( sk6 @ sk1 ) @ ( sk6 @ sk1 ) )
| ( ( g_false_only @ ( sk6 @ sk1 ) @ ( sk6 @ sk1 ) )
!= ( g_false_only @ ( sk6 @ sk1 ) @ ( sk6 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[18953,4674]) ).
thf(19004,plain,
( ( g_both @ ( sk5 @ sk1 ) @ sk1 )
| ( g_both @ ( sk6 @ sk1 ) @ ( sk6 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[19003:[]]) ).
thf(16,plain,
! [A: $i] :
( ~ ( g_false_only @ A @ sk1 )
| ~ ( g_both @ A @ A ) ),
inference(cnf,[status(esa)],[8]) ).
thf(35,plain,
! [A: $i] :
( ~ ( g_false_only @ A @ sk1 )
| ~ ( g_both @ A @ A ) ),
inference(simp,[status(thm)],[16]) ).
thf(1658,plain,
! [A: $i] :
( ~ ( sk3 @ sk1 )
| ( g_both @ ( sk5 @ sk1 ) @ sk1 )
| ~ ( g_both @ A @ A )
| ( ( g_false_only @ ( sk6 @ sk1 ) @ sk1 )
!= ( g_false_only @ A @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[1643,35]) ).
thf(1659,plain,
( ~ ( sk3 @ sk1 )
| ( g_both @ ( sk5 @ sk1 ) @ sk1 )
| ~ ( g_both @ ( sk6 @ sk1 ) @ ( sk6 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[1658:[bind(A,$thf( sk6 @ sk1 ))]]) ).
thf(4671,plain,
( ~ $true
| ( g_both @ ( sk5 @ sk1 ) @ sk1 )
| ~ ( g_both @ ( sk6 @ sk1 ) @ ( sk6 @ sk1 ) ) ),
inference(rewrite,[status(thm)],[1659,4668]) ).
thf(4672,plain,
( ( g_both @ ( sk5 @ sk1 ) @ sk1 )
| ~ ( g_both @ ( sk6 @ sk1 ) @ ( sk6 @ sk1 ) ) ),
inference(simp,[status(thm)],[4671]) ).
thf(19184,plain,
( ( g_both @ ( sk5 @ sk1 ) @ sk1 )
| ( ( g_both @ ( sk6 @ sk1 ) @ ( sk6 @ sk1 ) )
!= ( g_both @ ( sk6 @ sk1 ) @ ( sk6 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[19004,4672]) ).
thf(19185,plain,
g_both @ ( sk5 @ sk1 ) @ sk1,
inference(pattern_uni,[status(thm)],[19184:[]]) ).
thf(20,plain,
! [A: $i] :
( ~ ( g_both @ A @ sk1 )
| ~ ( g_true_only @ A @ A ) ),
inference(cnf,[status(esa)],[8]) ).
thf(28,plain,
! [A: $i] :
( ~ ( g_both @ A @ sk1 )
| ~ ( g_true_only @ A @ A ) ),
inference(simp,[status(thm)],[20]) ).
thf(19448,plain,
! [A: $i] :
( ~ ( g_true_only @ A @ A )
| ( ( g_both @ ( sk5 @ sk1 ) @ sk1 )
!= ( g_both @ A @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[19185,28]) ).
thf(19449,plain,
~ ( g_true_only @ ( sk5 @ sk1 ) @ ( sk5 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[19448:[bind(A,$thf( sk5 @ sk1 ))]]) ).
thf(20037,plain,
( ( g_false_only @ ( sk5 @ sk1 ) @ ( sk5 @ sk1 ) )
| $false
| ( g_false @ ( sk6 @ sk1 ) @ sk1 ) ),
inference(rewrite,[status(thm)],[14309,19449]) ).
thf(20038,plain,
( ( g_false_only @ ( sk5 @ sk1 ) @ ( sk5 @ sk1 ) )
| ( g_false @ ( sk6 @ sk1 ) @ sk1 ) ),
inference(simp,[status(thm)],[20037]) ).
thf(18,plain,
! [A: $i] :
( ~ ( g_both @ A @ sk1 )
| ~ ( g_false_only @ A @ A ) ),
inference(cnf,[status(esa)],[8]) ).
thf(34,plain,
! [A: $i] :
( ~ ( g_both @ A @ sk1 )
| ~ ( g_false_only @ A @ A ) ),
inference(simp,[status(thm)],[18]) ).
thf(19501,plain,
! [A: $i] :
( ~ ( g_false_only @ A @ A )
| ( ( g_both @ ( sk5 @ sk1 ) @ sk1 )
!= ( g_both @ A @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[19185,34]) ).
thf(19502,plain,
~ ( g_false_only @ ( sk5 @ sk1 ) @ ( sk5 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[19501:[bind(A,$thf( sk5 @ sk1 ))]]) ).
thf(21849,plain,
( $false
| ( g_false @ ( sk6 @ sk1 ) @ sk1 ) ),
inference(rewrite,[status(thm)],[20038,19502]) ).
thf(21850,plain,
g_false @ ( sk6 @ sk1 ) @ sk1,
inference(simp,[status(thm)],[21849]) ).
thf(53,plain,
! [B: $i,A: $i] :
( ~ ( g_false @ A @ B )
| ( g_true @ A @ B )
| ( g_false_only @ A @ B ) ),
inference(cnf,[status(esa)],[52]) ).
thf(56,plain,
! [B: $i,A: $i] :
( ~ ( g_false @ A @ B )
| ( g_true @ A @ B )
| ( g_false_only @ A @ B ) ),
inference(simp,[status(thm)],[53]) ).
thf(21851,plain,
! [B: $i,A: $i] :
( ( g_true @ A @ B )
| ( g_false_only @ A @ B )
| ( ( g_false @ ( sk6 @ sk1 ) @ sk1 )
!= ( g_false @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[21850,56]) ).
thf(21852,plain,
( ( g_true @ ( sk6 @ sk1 ) @ sk1 )
| ( g_false_only @ ( sk6 @ sk1 ) @ sk1 ) ),
inference(pattern_uni,[status(thm)],[21851:[bind(A,$thf( sk6 @ sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( g_both @ A @ B )
<=> ( ( g_true @ A @ B )
& ( g_false @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',both_g) ).
thf(45,plain,
! [A: $i,B: $i] :
( ( ( g_both @ A @ B )
=> ( ( g_true @ A @ B )
& ( g_false @ A @ B ) ) )
& ( ( ( g_true @ A @ B )
& ( g_false @ A @ B ) )
=> ( g_both @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(46,plain,
( ! [A: $i,B: $i] :
( ( g_both @ A @ B )
=> ( ( g_true @ A @ B )
& ( g_false @ A @ B ) ) )
& ! [A: $i,B: $i] :
( ( ( g_true @ A @ B )
& ( g_false @ A @ B ) )
=> ( g_both @ A @ B ) ) ),
inference(miniscope,[status(thm)],[45]) ).
thf(47,plain,
! [B: $i,A: $i] :
( ~ ( g_true @ A @ B )
| ~ ( g_false @ A @ B )
| ( g_both @ A @ B ) ),
inference(cnf,[status(esa)],[46]) ).
thf(50,plain,
! [B: $i,A: $i] :
( ~ ( g_true @ A @ B )
| ~ ( g_false @ A @ B )
| ( g_both @ A @ B ) ),
inference(simp,[status(thm)],[47]) ).
thf(21853,plain,
! [B: $i,A: $i] :
( ~ ( g_true @ A @ B )
| ( g_both @ A @ B )
| ( ( g_false @ ( sk6 @ sk1 ) @ sk1 )
!= ( g_false @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[21850,50]) ).
thf(21854,plain,
( ~ ( g_true @ ( sk6 @ sk1 ) @ sk1 )
| ( g_both @ ( sk6 @ sk1 ) @ sk1 ) ),
inference(pattern_uni,[status(thm)],[21853:[bind(A,$thf( sk6 @ sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(458,plain,
! [C: $i,B: $i,A: $i] :
( ( g_true_only @ A @ B )
| ( g_both @ A @ B )
| ~ ( g_false_only @ C @ C )
| ( ( g_false_only @ A @ B )
!= ( g_false_only @ C @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[58,36]) ).
thf(459,plain,
! [A: $i] :
( ( g_true_only @ A @ sk1 )
| ( g_both @ A @ sk1 )
| ~ ( g_false_only @ A @ A ) ),
inference(pattern_uni,[status(thm)],[458:[bind(A,$thf( A )),bind(B,$thf( sk1 )),bind(C,$thf( A ))]]) ).
thf(809,plain,
! [C: $i,B: $i,A: $i] :
( ( g_true_only @ A @ B )
| ( g_both @ A @ B )
| ( g_true_only @ C @ sk1 )
| ( g_both @ C @ sk1 )
| ( ( g_false_only @ A @ B )
!= ( g_false_only @ C @ C ) ) ),
inference(paramod_ordered,[status(thm)],[58,459]) ).
thf(810,plain,
! [A: $i] :
( ( g_true_only @ A @ A )
| ( g_both @ A @ A )
| ( g_true_only @ A @ sk1 )
| ( g_both @ A @ sk1 ) ),
inference(pattern_uni,[status(thm)],[809:[bind(A,$thf( B )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(814,plain,
! [A: $i] :
( ( g_true_only @ A @ A )
| ( g_both @ A @ A )
| ( g_true_only @ A @ sk1 )
| ( g_both @ A @ sk1 ) ),
inference(simp,[status(thm)],[810]) ).
thf(446,plain,
! [C: $i,B: $i,A: $i] :
( ( g_true_only @ A @ B )
| ( g_both @ A @ B )
| ~ ( g_both @ C @ C )
| ( ( g_false_only @ A @ B )
!= ( g_false_only @ C @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[58,35]) ).
thf(447,plain,
! [A: $i] :
( ( g_true_only @ A @ sk1 )
| ( g_both @ A @ sk1 )
| ~ ( g_both @ A @ A ) ),
inference(pattern_uni,[status(thm)],[446:[bind(A,$thf( A )),bind(B,$thf( sk1 )),bind(C,$thf( A ))]]) ).
thf(915,plain,
! [B: $i,A: $i] :
( ( g_true_only @ A @ A )
| ( g_true_only @ A @ sk1 )
| ( g_both @ A @ sk1 )
| ( g_true_only @ B @ sk1 )
| ( g_both @ B @ sk1 )
| ( ( g_both @ A @ A )
!= ( g_both @ B @ B ) ) ),
inference(paramod_ordered,[status(thm)],[814,447]) ).
thf(916,plain,
! [A: $i] :
( ( g_true_only @ A @ A )
| ( g_true_only @ A @ sk1 )
| ( g_both @ A @ sk1 )
| ( g_true_only @ A @ sk1 )
| ( g_both @ A @ sk1 ) ),
inference(pattern_uni,[status(thm)],[915:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(932,plain,
! [A: $i] :
( ( g_true_only @ A @ A )
| ( g_true_only @ A @ sk1 )
| ( g_both @ A @ sk1 ) ),
inference(simp,[status(thm)],[916]) ).
thf(48,plain,
! [B: $i,A: $i] :
( ~ ( g_both @ A @ B )
| ( g_true @ A @ B ) ),
inference(cnf,[status(esa)],[46]) ).
thf(81,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( g_both @ A @ B )
| ~ ( g_false_only @ C @ D )
| ( ( g_true @ A @ B )
!= ( g_true @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[48,55]) ).
thf(82,plain,
! [B: $i,A: $i] :
( ~ ( g_both @ A @ B )
| ~ ( g_false_only @ A @ B ) ),
inference(pattern_uni,[status(thm)],[81:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(1504,plain,
! [C: $i,B: $i,A: $i] :
( ( g_true_only @ A @ A )
| ( g_true_only @ A @ sk1 )
| ~ ( g_false_only @ B @ C )
| ( ( g_both @ A @ sk1 )
!= ( g_both @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[932,82]) ).
thf(1505,plain,
! [A: $i] :
( ( g_true_only @ A @ A )
| ( g_true_only @ A @ sk1 )
| ~ ( g_false_only @ A @ sk1 ) ),
inference(pattern_uni,[status(thm)],[1504:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( sk1 ))]]) ).
thf(14335,plain,
! [A: $i] :
( ( g_false_only @ ( sk5 @ sk1 ) @ ( sk5 @ sk1 ) )
| ( g_true_only @ ( sk5 @ sk1 ) @ ( sk5 @ sk1 ) )
| ( g_true_only @ A @ A )
| ( g_true_only @ A @ sk1 )
| ( ( g_false_only @ ( sk6 @ sk1 ) @ sk1 )
!= ( g_false_only @ A @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[14289,1505]) ).
thf(14336,plain,
( ( g_false_only @ ( sk5 @ sk1 ) @ ( sk5 @ sk1 ) )
| ( g_true_only @ ( sk5 @ sk1 ) @ ( sk5 @ sk1 ) )
| ( g_true_only @ ( sk6 @ sk1 ) @ ( sk6 @ sk1 ) )
| ( g_true_only @ ( sk6 @ sk1 ) @ sk1 ) ),
inference(pattern_uni,[status(thm)],[14335:[bind(A,$thf( sk6 @ sk1 ))]]) ).
thf(4707,plain,
( ~ $true
| ( g_both @ ( sk5 @ sk1 ) @ sk1 )
| ( g_false_only @ ( sk6 @ sk1 ) @ sk1 ) ),
inference(rewrite,[status(thm)],[1643,4668]) ).
thf(4708,plain,
( ( g_both @ ( sk5 @ sk1 ) @ sk1 )
| ( g_false_only @ ( sk6 @ sk1 ) @ sk1 ) ),
inference(simp,[status(thm)],[4707]) ).
thf(460,plain,
! [C: $i,B: $i,A: $i] :
( ( g_true_only @ A @ B )
| ( g_both @ A @ B )
| ~ ( g_false_only @ C @ sk1 )
| ( ( g_false_only @ A @ B )
!= ( g_false_only @ C @ C ) ) ),
inference(paramod_ordered,[status(thm)],[58,36]) ).
thf(461,plain,
! [A: $i] :
( ( g_true_only @ A @ A )
| ( g_both @ A @ A )
| ~ ( g_false_only @ A @ sk1 ) ),
inference(pattern_uni,[status(thm)],[460:[bind(A,$thf( B )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(465,plain,
! [A: $i] :
( ( g_true_only @ A @ A )
| ( g_both @ A @ A )
| ~ ( g_false_only @ A @ sk1 ) ),
inference(simp,[status(thm)],[461]) ).
thf(5395,plain,
! [A: $i] :
( ( g_both @ ( sk5 @ sk1 ) @ sk1 )
| ( g_true_only @ A @ A )
| ( g_both @ A @ A )
| ( ( g_false_only @ ( sk6 @ sk1 ) @ sk1 )
!= ( g_false_only @ A @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[4708,465]) ).
thf(5396,plain,
( ( g_both @ ( sk5 @ sk1 ) @ sk1 )
| ( g_true_only @ ( sk6 @ sk1 ) @ ( sk6 @ sk1 ) )
| ( g_both @ ( sk6 @ sk1 ) @ ( sk6 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[5395:[bind(A,$thf( sk6 @ sk1 ))]]) ).
thf(7724,plain,
( ( g_both @ ( sk5 @ sk1 ) @ sk1 )
| ( g_true_only @ ( sk6 @ sk1 ) @ ( sk6 @ sk1 ) )
| ( ( g_both @ ( sk6 @ sk1 ) @ ( sk6 @ sk1 ) )
!= ( g_both @ ( sk6 @ sk1 ) @ ( sk6 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[5396,4672]) ).
thf(7725,plain,
( ( g_both @ ( sk5 @ sk1 ) @ sk1 )
| ( g_true_only @ ( sk6 @ sk1 ) @ ( sk6 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[7724:[]]) ).
thf(7897,plain,
! [A: $i] :
( ( g_true_only @ ( sk6 @ sk1 ) @ ( sk6 @ sk1 ) )
| ~ ( g_false_only @ A @ A )
| ( ( g_both @ ( sk5 @ sk1 ) @ sk1 )
!= ( g_both @ A @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[7725,34]) ).
thf(7898,plain,
( ( g_true_only @ ( sk6 @ sk1 ) @ ( sk6 @ sk1 ) )
| ~ ( g_false_only @ ( sk5 @ sk1 ) @ ( sk5 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[7897:[bind(A,$thf( sk5 @ sk1 ))]]) ).
thf(14928,plain,
( ( g_true_only @ ( sk5 @ sk1 ) @ ( sk5 @ sk1 ) )
| ( g_true_only @ ( sk6 @ sk1 ) @ ( sk6 @ sk1 ) )
| ( g_true_only @ ( sk6 @ sk1 ) @ sk1 )
| ( ( g_false_only @ ( sk5 @ sk1 ) @ ( sk5 @ sk1 ) )
!= ( g_false_only @ ( sk5 @ sk1 ) @ ( sk5 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[14336,7898]) ).
thf(14929,plain,
( ( g_true_only @ ( sk5 @ sk1 ) @ ( sk5 @ sk1 ) )
| ( g_true_only @ ( sk6 @ sk1 ) @ ( sk6 @ sk1 ) )
| ( g_true_only @ ( sk6 @ sk1 ) @ sk1 ) ),
inference(pattern_uni,[status(thm)],[14928:[]]) ).
thf(15202,plain,
! [A: $i] :
( ( g_true_only @ ( sk5 @ sk1 ) @ ( sk5 @ sk1 ) )
| ( g_true_only @ ( sk6 @ sk1 ) @ sk1 )
| ~ ( g_both @ A @ sk1 )
| ( ( g_true_only @ ( sk6 @ sk1 ) @ ( sk6 @ sk1 ) )
!= ( g_true_only @ A @ A ) ) ),
inference(paramod_ordered,[status(thm)],[14929,28]) ).
thf(15203,plain,
( ( g_true_only @ ( sk5 @ sk1 ) @ ( sk5 @ sk1 ) )
| ( g_true_only @ ( sk6 @ sk1 ) @ sk1 )
| ~ ( g_both @ ( sk6 @ sk1 ) @ sk1 ) ),
inference(pattern_uni,[status(thm)],[15202:[bind(A,$thf( sk6 @ sk1 ))]]) ).
thf(20055,plain,
( $false
| ( g_true_only @ ( sk6 @ sk1 ) @ sk1 )
| ~ ( g_both @ ( sk6 @ sk1 ) @ sk1 ) ),
inference(rewrite,[status(thm)],[15203,19449]) ).
thf(20056,plain,
( ( g_true_only @ ( sk6 @ sk1 ) @ sk1 )
| ~ ( g_both @ ( sk6 @ sk1 ) @ sk1 ) ),
inference(simp,[status(thm)],[20055]) ).
thf(43,plain,
! [B: $i,A: $i] :
( ~ ( g_true_only @ A @ B )
| ~ ( g_false @ A @ B ) ),
inference(cnf,[status(esa)],[40]) ).
thf(21855,plain,
! [B: $i,A: $i] :
( ~ ( g_true_only @ A @ B )
| ( ( g_false @ ( sk6 @ sk1 ) @ sk1 )
!= ( g_false @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[21850,43]) ).
thf(21856,plain,
~ ( g_true_only @ ( sk6 @ sk1 ) @ sk1 ),
inference(pattern_uni,[status(thm)],[21855:[bind(A,$thf( sk6 @ sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(21857,plain,
( $false
| ~ ( g_both @ ( sk6 @ sk1 ) @ sk1 ) ),
inference(rewrite,[status(thm)],[20056,21856]) ).
thf(21858,plain,
~ ( g_both @ ( sk6 @ sk1 ) @ sk1 ),
inference(simp,[status(thm)],[21857]) ).
thf(22009,plain,
( ~ ( g_true @ ( sk6 @ sk1 ) @ sk1 )
| $false ),
inference(rewrite,[status(thm)],[21854,21858]) ).
thf(22010,plain,
~ ( g_true @ ( sk6 @ sk1 ) @ sk1 ),
inference(simp,[status(thm)],[22009]) ).
thf(22011,plain,
( $false
| ( g_false_only @ ( sk6 @ sk1 ) @ sk1 ) ),
inference(rewrite,[status(thm)],[21852,22010]) ).
thf(22012,plain,
g_false_only @ ( sk6 @ sk1 ) @ sk1,
inference(simp,[status(thm)],[22011]) ).
thf(22065,plain,
! [A: $i] :
( ~ ( g_both @ A @ A )
| ( ( g_false_only @ ( sk6 @ sk1 ) @ sk1 )
!= ( g_false_only @ A @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[22012,35]) ).
thf(22066,plain,
~ ( g_both @ ( sk6 @ sk1 ) @ ( sk6 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[22065:[bind(A,$thf( sk6 @ sk1 ))]]) ).
thf(15189,plain,
! [B: $i,A: $i] :
( ( g_true_only @ ( sk5 @ sk1 ) @ ( sk5 @ sk1 ) )
| ( g_true_only @ ( sk6 @ sk1 ) @ sk1 )
| ( g_true @ A @ B )
| ( ( g_true_only @ ( sk6 @ sk1 ) @ ( sk6 @ sk1 ) )
!= ( g_true_only @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[14929,42]) ).
thf(15190,plain,
( ( g_true_only @ ( sk5 @ sk1 ) @ ( sk5 @ sk1 ) )
| ( g_true_only @ ( sk6 @ sk1 ) @ sk1 )
| ( g_true @ ( sk6 @ sk1 ) @ ( sk6 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[15189:[bind(A,$thf( sk6 @ sk1 )),bind(B,$thf( sk6 @ sk1 ))]]) ).
thf(20025,plain,
( $false
| ( g_true_only @ ( sk6 @ sk1 ) @ sk1 )
| ( g_true @ ( sk6 @ sk1 ) @ ( sk6 @ sk1 ) ) ),
inference(rewrite,[status(thm)],[15190,19449]) ).
thf(20026,plain,
( ( g_true_only @ ( sk6 @ sk1 ) @ sk1 )
| ( g_true @ ( sk6 @ sk1 ) @ ( sk6 @ sk1 ) ) ),
inference(simp,[status(thm)],[20025]) ).
thf(21859,plain,
( $false
| ( g_true @ ( sk6 @ sk1 ) @ ( sk6 @ sk1 ) ) ),
inference(rewrite,[status(thm)],[20026,21856]) ).
thf(21860,plain,
g_true @ ( sk6 @ sk1 ) @ ( sk6 @ sk1 ),
inference(simp,[status(thm)],[21859]) ).
thf(21923,plain,
! [B: $i,A: $i] :
( ~ ( g_false_only @ A @ B )
| ( ( g_true @ ( sk6 @ sk1 ) @ ( sk6 @ sk1 ) )
!= ( g_true @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[21860,55]) ).
thf(21924,plain,
~ ( g_false_only @ ( sk6 @ sk1 ) @ ( sk6 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[21923:[bind(A,$thf( sk6 @ sk1 )),bind(B,$thf( sk6 @ sk1 ))]]) ).
thf(37768,plain,
( $false
| $false
| $false
| ~ $true
| ~ $true
| $false ),
inference(rewrite,[status(thm)],[1111,22066,468,21924,19449,4668,19502]) ).
thf(37769,plain,
$false,
inference(simp,[status(thm)],[37768]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SEV515+1 : TPTP v8.2.0. Released v7.0.0.
% 0.07/0.11 % Command : run_Leo-III %s %d SAT
% 0.11/0.32 % Computer : n023.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 21 19:08:10 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.92/0.84 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.20/0.95 % [INFO] Parsing done (102ms).
% 1.20/0.95 % [INFO] Running in sequential loop mode.
% 1.61/1.15 % [INFO] nitpick registered as external prover.
% 1.61/1.16 % [INFO] Scanning for conjecture ...
% 1.73/1.22 % [INFO] Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ...
% 1.92/1.24 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 1.92/1.25 % [INFO] Problem is first-order (TPTP FOF).
% 1.92/1.25 % [INFO] Type checking passed.
% 1.92/1.25 % [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 ...
% 94.31/16.51 % [INFO] Killing All external provers ...
% 94.31/16.52 % Time passed: 16004ms (effective reasoning time: 15557ms)
% 94.31/16.52 % 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)>
% 94.31/16.52 % Axioms used in derivation (4): exhaustion_g, true_only_g, false_only_g, both_g
% 94.31/16.52 % No. of inferences in proof: 194
% 94.31/16.52 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 16004 ms resp. 15557 ms w/o parsing
% 94.43/16.64 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 94.43/16.64 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------