TSTP Solution File: SEV037^5 by Leo-III-SAT---1.7.15
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.15
% Problem : SEV037^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d SAT
% Computer : n025.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 15:59:21 EDT 2024
% Result : Theorem 16.71s 3.70s
% Output : Refutation 16.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 1
% Syntax : Number of formulae : 85 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 321 ( 50 equ; 0 cnn)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 1351 ( 118 ~; 124 |; 36 &; 981 @)
% ( 0 <=>; 92 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 7 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 120 ( 120 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 7 con; 0-3 aty)
% Number of variables : 373 ( 72 ^ 301 !; 0 ?; 373 :)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(b_type,type,
b: $tType ).
thf(sk1_type,type,
sk1: a > a > $o ).
thf(sk2_type,type,
sk2: a > a > $o ).
thf(sk3_type,type,
sk3: a > b > b > $o ).
thf(sk4_type,type,
sk4: $o ).
thf(sk5_type,type,
sk5: a > b ).
thf(sk6_type,type,
sk6: a > b ).
thf(sk7_type,type,
sk7: a ).
thf(sk8_type,type,
sk8: a ).
thf(sk9_type,type,
sk9: a > b ).
thf(sk10_type,type,
sk10: a > b ).
thf(sk11_type,type,
sk11: a > b ).
thf(sk12_type,type,
sk12: a ).
thf(sk13_type,type,
sk13: a ).
thf(1,conjecture,
! [A: a > a > $o,B: a > a > $o,C: a > b > b > $o] :
( ( ! [D: a,E: a] :
( ( A @ D @ E )
=> ( A @ E @ D ) )
& ! [D: a,E: a,F: a] :
( ( ( A @ D @ E )
& ( A @ E @ F ) )
=> ( A @ D @ F ) )
& ( A = B ) )
=> ( ! [D: a,E: a] :
( ( A @ D @ E )
=> ( ! [F: b,G: b] :
( ( C @ D @ F @ G )
=> ( C @ D @ G @ F ) )
& ! [F: b,G: b,H: b] :
( ( ( C @ D @ F @ G )
& ( C @ D @ G @ H ) )
=> ( C @ D @ F @ H ) )
& ( ( C @ D )
= ( C @ E ) ) ) )
=> ( ! [D: a > b,E: a > b] :
( ! [F: a,G: a] :
( ( A @ F @ G )
=> ( C @ F @ ( D @ F ) @ ( E @ G ) ) )
=> ! [F: a,G: a] :
( ( A @ F @ G )
=> ( C @ F @ ( E @ F ) @ ( D @ G ) ) ) )
& ! [D: a > b,E: a > b,F: a > b] :
( ( ! [G: a,H: a] :
( ( A @ G @ H )
=> ( C @ G @ ( D @ G ) @ ( E @ H ) ) )
& ! [G: a,H: a] :
( ( A @ G @ H )
=> ( C @ G @ ( E @ G ) @ ( F @ H ) ) ) )
=> ! [G: a,H: a] :
( ( A @ G @ H )
=> ( C @ G @ ( D @ G ) @ ( F @ H ) ) ) )
& ( ( ^ [D: a > b,E: a > b] :
! [F: a,G: a] :
( ( A @ F @ G )
=> ( C @ F @ ( D @ F ) @ ( E @ G ) ) ) )
= ( ^ [D: a > b,E: a > b] :
! [F: a,G: a] :
( ( B @ F @ G )
=> ( C @ F @ ( D @ F ) @ ( E @ G ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM516_pme) ).
thf(2,negated_conjecture,
~ ! [A: a > a > $o,B: a > a > $o,C: a > b > b > $o] :
( ( ! [D: a,E: a] :
( ( A @ D @ E )
=> ( A @ E @ D ) )
& ! [D: a,E: a,F: a] :
( ( ( A @ D @ E )
& ( A @ E @ F ) )
=> ( A @ D @ F ) )
& ( A = B ) )
=> ( ! [D: a,E: a] :
( ( A @ D @ E )
=> ( ! [F: b,G: b] :
( ( C @ D @ F @ G )
=> ( C @ D @ G @ F ) )
& ! [F: b,G: b,H: b] :
( ( ( C @ D @ F @ G )
& ( C @ D @ G @ H ) )
=> ( C @ D @ F @ H ) )
& ( ( C @ D )
= ( C @ E ) ) ) )
=> ( ! [D: a > b,E: a > b] :
( ! [F: a,G: a] :
( ( A @ F @ G )
=> ( C @ F @ ( D @ F ) @ ( E @ G ) ) )
=> ! [F: a,G: a] :
( ( A @ F @ G )
=> ( C @ F @ ( E @ F ) @ ( D @ G ) ) ) )
& ! [D: a > b,E: a > b,F: a > b] :
( ( ! [G: a,H: a] :
( ( A @ G @ H )
=> ( C @ G @ ( D @ G ) @ ( E @ H ) ) )
& ! [G: a,H: a] :
( ( A @ G @ H )
=> ( C @ G @ ( E @ G ) @ ( F @ H ) ) ) )
=> ! [G: a,H: a] :
( ( A @ G @ H )
=> ( C @ G @ ( D @ G ) @ ( F @ H ) ) ) )
& ( ( ^ [D: a > b,E: a > b] :
! [F: a,G: a] :
( ( A @ F @ G )
=> ( C @ F @ ( D @ F ) @ ( E @ G ) ) ) )
= ( ^ [D: a > b,E: a > b] :
! [F: a,G: a] :
( ( B @ F @ G )
=> ( C @ F @ ( D @ F ) @ ( E @ G ) ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: a > a > $o,B: a > a > $o,C: a > b > b > $o] :
( ( ! [D: a,E: a] :
( ( A @ D @ E )
=> ( A @ E @ D ) )
& ! [D: a,E: a,F: a] :
( ( ( A @ D @ E )
& ( A @ E @ F ) )
=> ( A @ D @ F ) )
& ( A = B ) )
=> ( ! [D: a,E: a] :
( ( A @ D @ E )
=> ( ! [F: b,G: b] :
( ( C @ D @ F @ G )
=> ( C @ D @ G @ F ) )
& ! [F: b,G: b,H: b] :
( ( ( C @ D @ F @ G )
& ( C @ D @ G @ H ) )
=> ( C @ D @ F @ H ) )
& ( ( C @ D )
= ( C @ E ) ) ) )
=> ( ! [D: a > b,E: a > b] :
( ! [F: a,G: a] :
( ( A @ F @ G )
=> ( C @ F @ ( D @ F ) @ ( E @ G ) ) )
=> ! [F: a,G: a] :
( ( A @ F @ G )
=> ( C @ F @ ( E @ F ) @ ( D @ G ) ) ) )
& ! [D: a > b,E: a > b,F: a > b] :
( ( ! [G: a,H: a] :
( ( A @ G @ H )
=> ( C @ G @ ( D @ G ) @ ( E @ H ) ) )
& ! [G: a,H: a] :
( ( A @ G @ H )
=> ( C @ G @ ( E @ G ) @ ( F @ H ) ) ) )
=> ! [G: a,H: a] :
( ( A @ G @ H )
=> ( C @ G @ ( D @ G ) @ ( F @ H ) ) ) )
& ( ( ^ [D: a > b,E: a > b] :
! [F: a,G: a] :
( ( A @ F @ G )
=> ( C @ F @ ( D @ F ) @ ( E @ G ) ) ) )
= ( ^ [D: a > b,E: a > b] :
! [F: a,G: a] :
( ( B @ F @ G )
=> ( C @ F @ ( D @ F ) @ ( E @ G ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
~ ! [A: a > a > $o,B: a > a > $o] :
( ( ! [C: a,D: a] :
( ( A @ C @ D )
=> ( A @ D @ C ) )
& ! [C: a,D: a,E: a] :
( ( ( A @ C @ D )
& ( A @ D @ E ) )
=> ( A @ C @ E ) )
& ( A = B ) )
=> ! [C: a > b > b > $o] :
( ! [D: a,E: a] :
( ( A @ D @ E )
=> ( ! [F: b,G: b] :
( ( C @ D @ F @ G )
=> ( C @ D @ G @ F ) )
& ! [F: b,G: b,H: b] :
( ( ( C @ D @ F @ G )
& ( C @ D @ G @ H ) )
=> ( C @ D @ F @ H ) )
& ( ( C @ D )
= ( C @ E ) ) ) )
=> ( ! [D: a > b,E: a > b] :
( ! [F: a,G: a] :
( ( A @ F @ G )
=> ( C @ F @ ( D @ F ) @ ( E @ G ) ) )
=> ! [F: a,G: a] :
( ( A @ F @ G )
=> ( C @ F @ ( E @ F ) @ ( D @ G ) ) ) )
& ! [D: a > b,E: a > b,F: a > b] :
( ( ! [G: a,H: a] :
( ( A @ G @ H )
=> ( C @ G @ ( D @ G ) @ ( E @ H ) ) )
& ! [G: a,H: a] :
( ( A @ G @ H )
=> ( C @ G @ ( E @ G ) @ ( F @ H ) ) ) )
=> ! [G: a,H: a] :
( ( A @ G @ H )
=> ( C @ G @ ( D @ G ) @ ( F @ H ) ) ) )
& ( ( ^ [D: a > b,E: a > b] :
! [F: a,G: a] :
( ( A @ F @ G )
=> ( C @ F @ ( D @ F ) @ ( E @ G ) ) ) )
= ( ^ [D: a > b,E: a > b] :
! [F: a,G: a] :
( ( B @ F @ G )
=> ( C @ F @ ( D @ F ) @ ( E @ G ) ) ) ) ) ) ) ),
inference(miniscope,[status(thm)],[3]) ).
thf(6,plain,
( sk4
| ( sk1 @ sk12 @ sk13 )
| ( ( ^ [A: a > b,B: a > b] :
! [C: a,D: a] :
( ( sk1 @ C @ D )
=> ( sk3 @ C @ ( A @ C ) @ ( B @ D ) ) ) )
!= ( ^ [A: a > b,B: a > b] :
! [C: a,D: a] :
( ( sk2 @ C @ D )
=> ( sk3 @ C @ ( A @ C ) @ ( B @ D ) ) ) ) ) ),
inference(cnf,[status(esa)],[4]) ).
thf(20,plain,
( ( ( ^ [A: a > b,B: a > b] :
! [C: a,D: a] :
( ( sk2 @ C @ D )
=> ( sk3 @ C @ ( A @ C ) @ ( B @ D ) ) ) )
!= ( ^ [A: a > b,B: a > b] :
! [C: a,D: a] :
( ( sk1 @ C @ D )
=> ( sk3 @ C @ ( A @ C ) @ ( B @ D ) ) ) ) )
| sk4
| ( sk1 @ sk12 @ sk13 ) ),
inference(lifteq,[status(thm)],[6]) ).
thf(10,plain,
sk1 = sk2,
inference(cnf,[status(esa)],[4]) ).
thf(18,plain,
sk2 = sk1,
inference(lifteq,[status(thm)],[10]) ).
thf(32,plain,
! [B: a,A: a] :
( ( sk2 @ A @ B )
= ( sk1 @ A @ B ) ),
inference(func_ext,[status(esa)],[18]) ).
thf(54,plain,
( ( ( ^ [A: a > b,B: a > b] :
! [C: a,D: a] :
( ( sk1 @ C @ D )
=> ( sk3 @ C @ ( A @ C ) @ ( B @ D ) ) ) )
!= ( ^ [A: a > b,B: a > b] :
! [C: a,D: a] :
( ( sk1 @ C @ D )
=> ( sk3 @ C @ ( A @ C ) @ ( B @ D ) ) ) ) )
| sk4
| ( sk1 @ sk12 @ sk13 ) ),
inference(rewrite,[status(thm)],[20,32]) ).
thf(55,plain,
( sk4
| ( sk1 @ sk12 @ sk13 ) ),
inference(simp,[status(thm)],[54]) ).
thf(7,plain,
! [B: a,A: a] :
( sk4
| ~ ( sk1 @ A @ B )
| ( sk3 @ A @ ( sk10 @ A ) @ ( sk11 @ B ) )
| ( ( ^ [C: a > b,D: a > b] :
! [E: a,F: a] :
( ( sk1 @ E @ F )
=> ( sk3 @ E @ ( C @ E ) @ ( D @ F ) ) ) )
!= ( ^ [C: a > b,D: a > b] :
! [E: a,F: a] :
( ( sk2 @ E @ F )
=> ( sk3 @ E @ ( C @ E ) @ ( D @ F ) ) ) ) ) ),
inference(cnf,[status(esa)],[4]) ).
thf(25,plain,
! [B: a,A: a] :
( ( ( ^ [C: a > b,D: a > b] :
! [E: a,F: a] :
( ( sk2 @ E @ F )
=> ( sk3 @ E @ ( C @ E ) @ ( D @ F ) ) ) )
!= ( ^ [C: a > b,D: a > b] :
! [E: a,F: a] :
( ( sk1 @ E @ F )
=> ( sk3 @ E @ ( C @ E ) @ ( D @ F ) ) ) ) )
| sk4
| ~ ( sk1 @ A @ B )
| ( sk3 @ A @ ( sk10 @ A ) @ ( sk11 @ B ) ) ),
inference(lifteq,[status(thm)],[7]) ).
thf(26,plain,
! [B: a,A: a] :
( ( ( ^ [C: a > b,D: a > b] :
! [E: a,F: a] :
( ( sk2 @ E @ F )
=> ( sk3 @ E @ ( C @ E ) @ ( D @ F ) ) ) )
!= ( ^ [C: a > b,D: a > b] :
! [E: a,F: a] :
( ( sk1 @ E @ F )
=> ( sk3 @ E @ ( C @ E ) @ ( D @ F ) ) ) ) )
| sk4
| ~ ( sk1 @ A @ B )
| ( sk3 @ A @ ( sk10 @ A ) @ ( sk11 @ B ) ) ),
inference(simp,[status(thm)],[25]) ).
thf(248,plain,
! [B: a,A: a] :
( ( ( ^ [C: a > b,D: a > b] :
! [E: a,F: a] :
( ( sk1 @ E @ F )
=> ( sk3 @ E @ ( C @ E ) @ ( D @ F ) ) ) )
!= ( ^ [C: a > b,D: a > b] :
! [E: a,F: a] :
( ( sk1 @ E @ F )
=> ( sk3 @ E @ ( C @ E ) @ ( D @ F ) ) ) ) )
| sk4
| ~ ( sk1 @ A @ B )
| ( sk3 @ A @ ( sk10 @ A ) @ ( sk11 @ B ) ) ),
inference(rewrite,[status(thm)],[26,32]) ).
thf(249,plain,
! [B: a,A: a] :
( sk4
| ~ ( sk1 @ A @ B )
| ( sk3 @ A @ ( sk10 @ A ) @ ( sk11 @ B ) ) ),
inference(simp,[status(thm)],[248]) ).
thf(265,plain,
! [B: a,A: a] :
( sk4
| ( sk3 @ A @ ( sk10 @ A ) @ ( sk11 @ B ) )
| ( ( sk1 @ sk12 @ sk13 )
!= ( sk1 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[55,249]) ).
thf(266,plain,
( sk4
| ( sk3 @ sk12 @ ( sk10 @ sk12 ) @ ( sk11 @ sk13 ) ) ),
inference(pattern_uni,[status(thm)],[265:[bind(A,$thf( sk12 )),bind(B,$thf( sk13 ))]]) ).
thf(5,plain,
( ( sk1 @ sk7 @ sk8 )
| ~ sk4 ),
inference(cnf,[status(esa)],[4]) ).
thf(17,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ( sk1 @ B @ A ) ),
inference(cnf,[status(esa)],[4]) ).
thf(59,plain,
! [B: a,A: a] :
( ~ sk4
| ( sk1 @ B @ A )
| ( ( sk1 @ sk7 @ sk8 )
!= ( sk1 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[5,17]) ).
thf(60,plain,
( ~ sk4
| ( sk1 @ sk8 @ sk7 ) ),
inference(pattern_uni,[status(thm)],[59:[bind(A,$thf( sk7 )),bind(B,$thf( sk8 ))]]) ).
thf(12,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ( ( sk3 @ A )
= ( sk3 @ B ) ) ),
inference(cnf,[status(esa)],[4]) ).
thf(23,plain,
! [B: a,A: a] :
( ( ( sk3 @ A )
= ( sk3 @ B ) )
| ~ ( sk1 @ A @ B ) ),
inference(lifteq,[status(thm)],[12]) ).
thf(24,plain,
! [B: a,A: a] :
( ( ( sk3 @ A )
= ( sk3 @ B ) )
| ~ ( sk1 @ A @ B ) ),
inference(simp,[status(thm)],[23]) ).
thf(124,plain,
! [B: a,A: a] :
( ~ sk4
| ( ( sk3 @ A )
= ( sk3 @ B ) )
| ( ( sk1 @ sk8 @ sk7 )
!= ( sk1 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[60,24]) ).
thf(125,plain,
( ~ sk4
| ( ( sk3 @ sk8 )
= ( sk3 @ sk7 ) ) ),
inference(pattern_uni,[status(thm)],[124:[bind(A,$thf( sk8 )),bind(B,$thf( sk7 ))]]) ).
thf(173,plain,
! [B: b,A: b] :
( ( ( sk3 @ sk8 @ A @ B )
= ( sk3 @ sk7 @ A @ B ) )
| ~ sk4 ),
inference(func_ext,[status(esa)],[125]) ).
thf(14,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ( sk3 @ A @ ( sk5 @ A ) @ ( sk6 @ B ) )
| ~ sk4 ),
inference(cnf,[status(esa)],[4]) ).
thf(19,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ( sk3 @ A @ ( sk5 @ A ) @ ( sk6 @ B ) )
| ~ sk4 ),
inference(simp,[status(thm)],[14]) ).
thf(75,plain,
! [B: a,A: a] :
( ~ sk4
| ( sk3 @ A @ ( sk5 @ A ) @ ( sk6 @ B ) )
| ( ( sk1 @ sk8 @ sk7 )
!= ( sk1 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[60,19]) ).
thf(76,plain,
( ~ sk4
| ( sk3 @ sk8 @ ( sk5 @ sk8 ) @ ( sk6 @ sk7 ) ) ),
inference(pattern_uni,[status(thm)],[75:[bind(A,$thf( sk8 )),bind(B,$thf( sk7 ))]]) ).
thf(315,plain,
! [B: b,A: b] :
( ~ sk4
| ( sk3 @ sk7 @ A @ B )
| ( ( sk3 @ sk8 @ A @ B )
!= ( sk3 @ sk8 @ ( sk5 @ sk8 ) @ ( sk6 @ sk7 ) ) ) ),
inference(paramod_ordered,[status(thm)],[173,76]) ).
thf(316,plain,
( ~ sk4
| ( sk3 @ sk7 @ ( sk5 @ sk8 ) @ ( sk6 @ sk7 ) ) ),
inference(pattern_uni,[status(thm)],[315:[bind(A,$thf( sk5 @ sk8 )),bind(B,$thf( sk6 @ sk7 ))]]) ).
thf(9,plain,
! [D: b,C: b,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk3 @ A @ C @ D )
| ( sk3 @ A @ D @ C ) ),
inference(cnf,[status(esa)],[4]) ).
thf(21,plain,
! [D: b,C: b,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk3 @ A @ C @ D )
| ( sk3 @ A @ D @ C ) ),
inference(simp,[status(thm)],[9]) ).
thf(15,plain,
( ~ ( sk3 @ sk7 @ ( sk6 @ sk7 ) @ ( sk5 @ sk8 ) )
| ~ sk4 ),
inference(cnf,[status(esa)],[4]) ).
thf(150,plain,
! [D: b,C: b,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk3 @ A @ C @ D )
| ~ sk4
| ( ( sk3 @ A @ D @ C )
!= ( sk3 @ sk7 @ ( sk6 @ sk7 ) @ ( sk5 @ sk8 ) ) ) ),
inference(paramod_ordered,[status(thm)],[21,15]) ).
thf(151,plain,
! [A: a] :
( ~ ( sk1 @ sk7 @ A )
| ~ ( sk3 @ sk7 @ ( sk5 @ sk8 ) @ ( sk6 @ sk7 ) )
| ~ sk4 ),
inference(pattern_uni,[status(thm)],[150:[bind(A,$thf( sk7 )),bind(B,$thf( B )),bind(C,$thf( sk5 @ sk8 )),bind(D,$thf( sk6 @ sk7 ))]]) ).
thf(167,plain,
! [A: a] :
( ~ ( sk1 @ sk7 @ A )
| ~ ( sk3 @ sk7 @ ( sk5 @ sk8 ) @ ( sk6 @ sk7 ) )
| ~ sk4 ),
inference(simp,[status(thm)],[151]) ).
thf(497,plain,
! [A: a] :
( ~ sk4
| ~ ( sk3 @ sk7 @ ( sk5 @ sk8 ) @ ( sk6 @ sk7 ) )
| ( ( sk1 @ sk7 @ sk8 )
!= ( sk1 @ sk7 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[5,167]) ).
thf(498,plain,
( ~ sk4
| ~ ( sk3 @ sk7 @ ( sk5 @ sk8 ) @ ( sk6 @ sk7 ) ) ),
inference(pattern_uni,[status(thm)],[497:[bind(A,$thf( sk8 ))]]) ).
thf(523,plain,
( ~ sk4
| ( ( sk3 @ sk7 @ ( sk5 @ sk8 ) @ ( sk6 @ sk7 ) )
!= ( sk3 @ sk7 @ ( sk5 @ sk8 ) @ ( sk6 @ sk7 ) ) ) ),
inference(paramod_ordered,[status(thm)],[316,498]) ).
thf(524,plain,
~ sk4,
inference(pattern_uni,[status(thm)],[523:[]]) ).
thf(553,plain,
( $false
| ( sk3 @ sk12 @ ( sk10 @ sk12 ) @ ( sk11 @ sk13 ) ) ),
inference(rewrite,[status(thm)],[266,524]) ).
thf(554,plain,
sk3 @ sk12 @ ( sk10 @ sk12 ) @ ( sk11 @ sk13 ),
inference(simp,[status(thm)],[553]) ).
thf(13,plain,
! [E: b,D: b,C: b,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk3 @ A @ C @ D )
| ~ ( sk3 @ A @ D @ E )
| ( sk3 @ A @ C @ E ) ),
inference(cnf,[status(esa)],[4]) ).
thf(22,plain,
! [E: b,D: b,C: b,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk3 @ A @ C @ D )
| ~ ( sk3 @ A @ D @ E )
| ( sk3 @ A @ C @ E ) ),
inference(simp,[status(thm)],[13]) ).
thf(56,plain,
! [E: b,D: b,C: b,B: a,A: a] :
( sk4
| ~ ( sk3 @ A @ C @ D )
| ~ ( sk3 @ A @ D @ E )
| ( sk3 @ A @ C @ E )
| ( ( sk1 @ sk12 @ sk13 )
!= ( sk1 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[55,22]) ).
thf(57,plain,
! [C: b,B: b,A: b] :
( sk4
| ~ ( sk3 @ sk12 @ A @ B )
| ~ ( sk3 @ sk12 @ B @ C )
| ( sk3 @ sk12 @ A @ C ) ),
inference(pattern_uni,[status(thm)],[56:[bind(A,$thf( sk12 )),bind(B,$thf( sk13 ))]]) ).
thf(58,plain,
! [C: b,B: b,A: b] :
( sk4
| ~ ( sk3 @ sk12 @ A @ B )
| ~ ( sk3 @ sk12 @ B @ C )
| ( sk3 @ sk12 @ A @ C ) ),
inference(simp,[status(thm)],[57]) ).
thf(1356,plain,
! [C: b,B: b,A: b] :
( $false
| ~ ( sk3 @ sk12 @ A @ B )
| ~ ( sk3 @ sk12 @ B @ C )
| ( sk3 @ sk12 @ A @ C ) ),
inference(rewrite,[status(thm)],[58,524]) ).
thf(1357,plain,
! [C: b,B: b,A: b] :
( ~ ( sk3 @ sk12 @ A @ B )
| ~ ( sk3 @ sk12 @ B @ C )
| ( sk3 @ sk12 @ A @ C ) ),
inference(simp,[status(thm)],[1356]) ).
thf(16,plain,
( sk4
| ~ ( sk3 @ sk12 @ ( sk9 @ sk12 ) @ ( sk11 @ sk13 ) )
| ( ( ^ [A: a > b,B: a > b] :
! [C: a,D: a] :
( ( sk1 @ C @ D )
=> ( sk3 @ C @ ( A @ C ) @ ( B @ D ) ) ) )
!= ( ^ [A: a > b,B: a > b] :
! [C: a,D: a] :
( ( sk2 @ C @ D )
=> ( sk3 @ C @ ( A @ C ) @ ( B @ D ) ) ) ) ) ),
inference(cnf,[status(esa)],[4]) ).
thf(27,plain,
( ( ( ^ [A: a > b,B: a > b] :
! [C: a,D: a] :
( ( sk2 @ C @ D )
=> ( sk3 @ C @ ( A @ C ) @ ( B @ D ) ) ) )
!= ( ^ [A: a > b,B: a > b] :
! [C: a,D: a] :
( ( sk1 @ C @ D )
=> ( sk3 @ C @ ( A @ C ) @ ( B @ D ) ) ) ) )
| sk4
| ~ ( sk3 @ sk12 @ ( sk9 @ sk12 ) @ ( sk11 @ sk13 ) ) ),
inference(lifteq,[status(thm)],[16]) ).
thf(410,plain,
( ( ( ^ [A: a > b,B: a > b] :
! [C: a,D: a] :
( ( sk1 @ C @ D )
=> ( sk3 @ C @ ( A @ C ) @ ( B @ D ) ) ) )
!= ( ^ [A: a > b,B: a > b] :
! [C: a,D: a] :
( ( sk1 @ C @ D )
=> ( sk3 @ C @ ( A @ C ) @ ( B @ D ) ) ) ) )
| sk4
| ~ ( sk3 @ sk12 @ ( sk9 @ sk12 ) @ ( sk11 @ sk13 ) ) ),
inference(rewrite,[status(thm)],[27,32]) ).
thf(411,plain,
( sk4
| ~ ( sk3 @ sk12 @ ( sk9 @ sk12 ) @ ( sk11 @ sk13 ) ) ),
inference(simp,[status(thm)],[410]) ).
thf(549,plain,
( $false
| ~ ( sk3 @ sk12 @ ( sk9 @ sk12 ) @ ( sk11 @ sk13 ) ) ),
inference(rewrite,[status(thm)],[411,524]) ).
thf(550,plain,
~ ( sk3 @ sk12 @ ( sk9 @ sk12 ) @ ( sk11 @ sk13 ) ),
inference(simp,[status(thm)],[549]) ).
thf(1358,plain,
! [C: b,B: b,A: b] :
( ~ ( sk3 @ sk12 @ A @ B )
| ~ ( sk3 @ sk12 @ B @ C )
| ( ( sk3 @ sk12 @ A @ C )
!= ( sk3 @ sk12 @ ( sk9 @ sk12 ) @ ( sk11 @ sk13 ) ) ) ),
inference(paramod_ordered,[status(thm)],[1357,550]) ).
thf(1359,plain,
! [A: b] :
( ~ ( sk3 @ sk12 @ ( sk9 @ sk12 ) @ A )
| ~ ( sk3 @ sk12 @ A @ ( sk11 @ sk13 ) ) ),
inference(pattern_uni,[status(thm)],[1358:[bind(A,$thf( sk9 @ sk12 )),bind(B,$thf( B )),bind(C,$thf( sk11 @ sk13 ))]]) ).
thf(1443,plain,
! [A: b] :
( ~ ( sk3 @ sk12 @ ( sk9 @ sk12 ) @ A )
| ~ ( sk3 @ sk12 @ A @ ( sk11 @ sk13 ) ) ),
inference(simp,[status(thm)],[1359]) ).
thf(2428,plain,
! [A: b] :
( ~ ( sk3 @ sk12 @ ( sk9 @ sk12 ) @ A )
| ( ( sk3 @ sk12 @ ( sk10 @ sk12 ) @ ( sk11 @ sk13 ) )
!= ( sk3 @ sk12 @ A @ ( sk11 @ sk13 ) ) ) ),
inference(paramod_ordered,[status(thm)],[554,1443]) ).
thf(2429,plain,
~ ( sk3 @ sk12 @ ( sk9 @ sk12 ) @ ( sk10 @ sk12 ) ),
inference(pattern_uni,[status(thm)],[2428:[bind(A,$thf( sk10 @ sk12 ))]]) ).
thf(565,plain,
( $false
| ( sk1 @ sk12 @ sk13 ) ),
inference(rewrite,[status(thm)],[55,524]) ).
thf(566,plain,
sk1 @ sk12 @ sk13,
inference(simp,[status(thm)],[565]) ).
thf(63,plain,
! [B: a,A: a] :
( sk4
| ( sk1 @ B @ A )
| ( ( sk1 @ sk12 @ sk13 )
!= ( sk1 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[55,17]) ).
thf(64,plain,
( sk4
| ( sk1 @ sk13 @ sk12 ) ),
inference(pattern_uni,[status(thm)],[63:[bind(A,$thf( sk12 )),bind(B,$thf( sk13 ))]]) ).
thf(561,plain,
( $false
| ( sk1 @ sk13 @ sk12 ) ),
inference(rewrite,[status(thm)],[64,524]) ).
thf(562,plain,
sk1 @ sk13 @ sk12,
inference(simp,[status(thm)],[561]) ).
thf(8,plain,
! [C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk1 @ B @ C )
| ( sk1 @ A @ C ) ),
inference(cnf,[status(esa)],[4]) ).
thf(30,plain,
! [C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ~ ( sk1 @ B @ C )
| ( sk1 @ A @ C ) ),
inference(simp,[status(thm)],[8]) ).
thf(658,plain,
! [C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ( sk1 @ A @ C )
| ( ( sk1 @ sk13 @ sk12 )
!= ( sk1 @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[562,30]) ).
thf(659,plain,
! [A: a] :
( ~ ( sk1 @ A @ sk13 )
| ( sk1 @ A @ sk12 ) ),
inference(pattern_uni,[status(thm)],[658:[bind(A,$thf( A )),bind(B,$thf( sk13 )),bind(C,$thf( sk12 ))]]) ).
thf(1252,plain,
! [A: a] :
( ( sk1 @ A @ sk12 )
| ( ( sk1 @ sk12 @ sk13 )
!= ( sk1 @ A @ sk13 ) ) ),
inference(paramod_ordered,[status(thm)],[566,659]) ).
thf(1253,plain,
sk1 @ sk12 @ sk12,
inference(pattern_uni,[status(thm)],[1252:[bind(A,$thf( sk12 ))]]) ).
thf(11,plain,
! [B: a,A: a] :
( sk4
| ~ ( sk1 @ A @ B )
| ( sk3 @ A @ ( sk9 @ A ) @ ( sk10 @ B ) )
| ( ( ^ [C: a > b,D: a > b] :
! [E: a,F: a] :
( ( sk1 @ E @ F )
=> ( sk3 @ E @ ( C @ E ) @ ( D @ F ) ) ) )
!= ( ^ [C: a > b,D: a > b] :
! [E: a,F: a] :
( ( sk2 @ E @ F )
=> ( sk3 @ E @ ( C @ E ) @ ( D @ F ) ) ) ) ) ),
inference(cnf,[status(esa)],[4]) ).
thf(28,plain,
! [B: a,A: a] :
( ( ( ^ [C: a > b,D: a > b] :
! [E: a,F: a] :
( ( sk2 @ E @ F )
=> ( sk3 @ E @ ( C @ E ) @ ( D @ F ) ) ) )
!= ( ^ [C: a > b,D: a > b] :
! [E: a,F: a] :
( ( sk1 @ E @ F )
=> ( sk3 @ E @ ( C @ E ) @ ( D @ F ) ) ) ) )
| sk4
| ~ ( sk1 @ A @ B )
| ( sk3 @ A @ ( sk9 @ A ) @ ( sk10 @ B ) ) ),
inference(lifteq,[status(thm)],[11]) ).
thf(29,plain,
! [B: a,A: a] :
( ( ( ^ [C: a > b,D: a > b] :
! [E: a,F: a] :
( ( sk2 @ E @ F )
=> ( sk3 @ E @ ( C @ E ) @ ( D @ F ) ) ) )
!= ( ^ [C: a > b,D: a > b] :
! [E: a,F: a] :
( ( sk1 @ E @ F )
=> ( sk3 @ E @ ( C @ E ) @ ( D @ F ) ) ) ) )
| sk4
| ~ ( sk1 @ A @ B )
| ( sk3 @ A @ ( sk9 @ A ) @ ( sk10 @ B ) ) ),
inference(simp,[status(thm)],[28]) ).
thf(568,plain,
! [B: a,A: a] :
( ( ( ^ [C: a > b,D: a > b] :
! [E: a,F: a] :
( ( sk1 @ E @ F )
=> ( sk3 @ E @ ( C @ E ) @ ( D @ F ) ) ) )
!= ( ^ [C: a > b,D: a > b] :
! [E: a,F: a] :
( ( sk1 @ E @ F )
=> ( sk3 @ E @ ( C @ E ) @ ( D @ F ) ) ) ) )
| $false
| ~ ( sk1 @ A @ B )
| ( sk3 @ A @ ( sk9 @ A ) @ ( sk10 @ B ) ) ),
inference(rewrite,[status(thm)],[29,32,524]) ).
thf(569,plain,
! [B: a,A: a] :
( ~ ( sk1 @ A @ B )
| ( sk3 @ A @ ( sk9 @ A ) @ ( sk10 @ B ) ) ),
inference(simp,[status(thm)],[568]) ).
thf(1270,plain,
! [B: a,A: a] :
( ( sk3 @ A @ ( sk9 @ A ) @ ( sk10 @ B ) )
| ( ( sk1 @ sk12 @ sk12 )
!= ( sk1 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1253,569]) ).
thf(1271,plain,
sk3 @ sk12 @ ( sk9 @ sk12 ) @ ( sk10 @ sk12 ),
inference(pattern_uni,[status(thm)],[1270:[bind(A,$thf( sk12 )),bind(B,$thf( sk12 ))]]) ).
thf(2514,plain,
~ $true,
inference(rewrite,[status(thm)],[2429,1271]) ).
thf(2515,plain,
$false,
inference(simp,[status(thm)],[2514]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEV037^5 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.12 % Command : run_Leo-III %s %d SAT
% 0.12/0.32 % Computer : n025.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Fri Jun 21 19:43:40 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.96/0.86 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.17/0.97 % [INFO] Parsing done (110ms).
% 1.17/0.98 % [INFO] Running in sequential loop mode.
% 1.66/1.18 % [INFO] nitpick registered as external prover.
% 1.66/1.18 % [INFO] Scanning for conjecture ...
% 1.88/1.26 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.97/1.28 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.97/1.28 % [INFO] Problem is higher-order (TPTP THF).
% 1.97/1.29 % [INFO] Type checking passed.
% 1.97/1.29 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 16.71/3.69 % [INFO] Killing All external provers ...
% 16.71/3.69 % Time passed: 3169ms (effective reasoning time: 2706ms)
% 16.71/3.69 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 16.71/3.69 % Axioms used in derivation (0):
% 16.71/3.69 % No. of inferences in proof: 85
% 16.71/3.70 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3169 ms resp. 2706 ms w/o parsing
% 16.75/3.80 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 16.75/3.80 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------