TSTP Solution File: SEV191^5 by Leo-III-SAT---1.7.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SEV191^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 04:11:05 EDT 2024
% Result : Theorem 8.97s 2.70s
% Output : Refutation 8.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 17
% Syntax : Number of formulae : 81 ( 10 unt; 16 typ; 0 def)
% Number of atoms : 221 ( 118 equ; 0 cnn)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 578 ( 98 ~; 108 |; 54 &; 304 @)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 38 ( 38 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 14 con; 0-3 aty)
% Number of variables : 131 ( 0 ^ 83 !; 48 ?; 131 :)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(cP_type,type,
cP: a > a > a ).
thf(c0_type,type,
c0: a ).
thf(sk1_type,type,
sk1: a > a > a > $o ).
thf(sk2_type,type,
sk2: a > a > a > $o ).
thf(sk3_type,type,
sk3: a ).
thf(sk4_type,type,
sk4: a ).
thf(sk5_type,type,
sk5: a ).
thf(sk6_type,type,
sk6: $o ).
thf(sk7_type,type,
sk7: $o ).
thf(sk8_type,type,
sk8: a ).
thf(sk9_type,type,
sk9: a ).
thf(sk10_type,type,
sk10: a ).
thf(sk11_type,type,
sk11: a ).
thf(sk12_type,type,
sk12: a ).
thf(sk13_type,type,
sk13: a ).
thf(1,conjecture,
( ! [A: a > a > a > $o] :
( $true
=> $true )
& ! [A: a > a > a > $o,B: a > a > a > $o] :
( ( $true
& $true
& ! [C: a,D: a,E: a] :
( ( A @ C @ D @ E )
=> ( B @ C @ D @ E ) ) )
=> ! [C: a,D: a,E: a] :
( ( ( ( C = c0 )
& ( D = E ) )
| ( ( D = c0 )
& ( C = E ) )
| ? [F: a,G: a,H: a,I: a,J: a,K: a] :
( ( C
= ( cP @ F @ G ) )
& ( D
= ( cP @ H @ I ) )
& ( E
= ( cP @ J @ K ) )
& ( A @ F @ H @ J )
& ( A @ G @ I @ K ) ) )
=> ( ( ( C = c0 )
& ( D = E ) )
| ( ( D = c0 )
& ( C = E ) )
| ? [F: a,G: a,H: a,I: a,J: a,K: a] :
( ( C
= ( cP @ F @ G ) )
& ( D
= ( cP @ H @ I ) )
& ( E
= ( cP @ J @ K ) )
& ( B @ F @ H @ J )
& ( B @ G @ I @ K ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cS_JOINFN_MONOTONE_pme) ).
thf(2,negated_conjecture,
~ ( ! [A: a > a > a > $o] :
( $true
=> $true )
& ! [A: a > a > a > $o,B: a > a > a > $o] :
( ( $true
& $true
& ! [C: a,D: a,E: a] :
( ( A @ C @ D @ E )
=> ( B @ C @ D @ E ) ) )
=> ! [C: a,D: a,E: a] :
( ( ( ( C = c0 )
& ( D = E ) )
| ( ( D = c0 )
& ( C = E ) )
| ? [F: a,G: a,H: a,I: a,J: a,K: a] :
( ( C
= ( cP @ F @ G ) )
& ( D
= ( cP @ H @ I ) )
& ( E
= ( cP @ J @ K ) )
& ( A @ F @ H @ J )
& ( A @ G @ I @ K ) ) )
=> ( ( ( C = c0 )
& ( D = E ) )
| ( ( D = c0 )
& ( C = E ) )
| ? [F: a,G: a,H: a,I: a,J: a,K: a] :
( ( C
= ( cP @ F @ G ) )
& ( D
= ( cP @ H @ I ) )
& ( E
= ( cP @ J @ K ) )
& ( B @ F @ H @ J )
& ( B @ G @ I @ K ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: a > a > a > $o,B: a > a > a > $o] :
( ! [C: a,D: a,E: a] :
( ( A @ C @ D @ E )
=> ( B @ C @ D @ E ) )
=> ! [C: a,D: a,E: a] :
( ( ( ( C = c0 )
& ( D = E ) )
| ( ( D = c0 )
& ( C = E ) )
| ? [F: a,G: a,H: a,I: a,J: a,K: a] :
( ( C
= ( cP @ F @ G ) )
& ( D
= ( cP @ H @ I ) )
& ( E
= ( cP @ J @ K ) )
& ( A @ F @ H @ J )
& ( A @ G @ I @ K ) ) )
=> ( ( ( C = c0 )
& ( D = E ) )
| ( ( D = c0 )
& ( C = E ) )
| ? [F: a,G: a,H: a,I: a,J: a,K: a] :
( ( C
= ( cP @ F @ G ) )
& ( D
= ( cP @ H @ I ) )
& ( E
= ( cP @ J @ K ) )
& ( B @ F @ H @ J )
& ( B @ G @ I @ K ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
~ ! [A: a > a > a > $o,B: a > a > a > $o] :
( ! [C: a,D: a,E: a] :
( ( A @ C @ D @ E )
=> ( B @ C @ D @ E ) )
=> ! [C: a,D: a,E: a] :
( ( ( ( C = c0 )
& ( D = E ) )
| ( ( D = c0 )
& ( C = E ) )
| ? [F: a,G: a] :
( ( C
= ( cP @ F @ G ) )
& ? [H: a,I: a] :
( ( D
= ( cP @ H @ I ) )
& ? [J: a,K: a] :
( ( E
= ( cP @ J @ K ) )
& ( A @ F @ H @ J )
& ( A @ G @ I @ K ) ) ) ) )
=> ( ( ( C = c0 )
& ( D = E ) )
| ( ( D = c0 )
& ( C = E ) )
| ? [F: a,G: a] :
( ( C
= ( cP @ F @ G ) )
& ? [H: a,I: a] :
( ( D
= ( cP @ H @ I ) )
& ? [J: a,K: a] :
( ( E
= ( cP @ J @ K ) )
& ( B @ F @ H @ J )
& ( B @ G @ I @ K ) ) ) ) ) ) ),
inference(miniscope,[status(thm)],[3]) ).
thf(12,plain,
( ~ sk6
| ~ sk7
| ( sk4
= ( cP @ sk10 @ sk11 ) ) ),
inference(cnf,[status(esa)],[4]) ).
thf(25,plain,
( ( ( cP @ sk10 @ sk11 )
= sk4 )
| ~ sk6
| ~ sk7 ),
inference(lifteq,[status(thm)],[12]) ).
thf(8,plain,
( ~ sk6
| ( sk4 = c0 )
| sk7 ),
inference(cnf,[status(esa)],[4]) ).
thf(28,plain,
( ( sk4 = c0 )
| ~ sk6
| sk7 ),
inference(lifteq,[status(thm)],[8]) ).
thf(11,plain,
( ( sk4 = sk5 )
| sk6 ),
inference(cnf,[status(esa)],[4]) ).
thf(27,plain,
( ( sk5 = sk4 )
| sk6 ),
inference(lifteq,[status(thm)],[11]) ).
thf(17,plain,
( ( sk3 = c0 )
| sk6 ),
inference(cnf,[status(esa)],[4]) ).
thf(24,plain,
( ( sk3 = c0 )
| sk6 ),
inference(lifteq,[status(thm)],[17]) ).
thf(13,plain,
( ( sk3 != c0 )
| ( sk4 != sk5 ) ),
inference(cnf,[status(esa)],[4]) ).
thf(23,plain,
( ( sk3 != c0 )
| ( sk5 != sk4 ) ),
inference(lifteq,[status(thm)],[13]) ).
thf(31,plain,
( sk6
| ( sk5 != sk4 )
| ( sk3 != sk3 ) ),
inference(paramod_ordered,[status(thm)],[24,23]) ).
thf(32,plain,
( sk6
| ( sk5 != sk4 ) ),
inference(pattern_uni,[status(thm)],[31:[]]) ).
thf(54,plain,
( sk6
| ( sk5 != sk5 ) ),
inference(paramod_ordered,[status(thm)],[27,32]) ).
thf(55,plain,
sk6,
inference(pattern_uni,[status(thm)],[54:[]]) ).
thf(83,plain,
( ( sk4 = c0 )
| ~ $true
| sk7 ),
inference(rewrite,[status(thm)],[28,55]) ).
thf(84,plain,
( ( sk4 = c0 )
| sk7 ),
inference(simp,[status(thm)],[83]) ).
thf(5,plain,
( ~ sk6
| ( sk3 = sk5 )
| sk7 ),
inference(cnf,[status(esa)],[4]) ).
thf(18,plain,
( ( sk5 = sk3 )
| ~ sk6
| sk7 ),
inference(lifteq,[status(thm)],[5]) ).
thf(56,plain,
( ( sk5 = sk3 )
| ~ $true
| sk7 ),
inference(rewrite,[status(thm)],[18,55]) ).
thf(57,plain,
( ( sk5 = sk3 )
| sk7 ),
inference(simp,[status(thm)],[56]) ).
thf(6,plain,
( ( sk4 != c0 )
| ( sk3 != sk5 ) ),
inference(cnf,[status(esa)],[4]) ).
thf(22,plain,
( ( sk4 != c0 )
| ( sk5 != sk3 ) ),
inference(lifteq,[status(thm)],[6]) ).
thf(61,plain,
( sk7
| ( sk4 != c0 )
| ( sk5 != sk5 ) ),
inference(paramod_ordered,[status(thm)],[57,22]) ).
thf(62,plain,
( sk7
| ( sk4 != c0 ) ),
inference(pattern_uni,[status(thm)],[61:[]]) ).
thf(85,plain,
( sk7
| ( sk4 != sk4 ) ),
inference(paramod_ordered,[status(thm)],[84,62]) ).
thf(86,plain,
sk7,
inference(pattern_uni,[status(thm)],[85:[]]) ).
thf(164,plain,
( ( ( cP @ sk10 @ sk11 )
= sk4 )
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[25,86,55]) ).
thf(165,plain,
( ( cP @ sk10 @ sk11 )
= sk4 ),
inference(simp,[status(thm)],[164]) ).
thf(16,plain,
( ~ sk6
| ~ sk7
| ( sk5
= ( cP @ sk12 @ sk13 ) ) ),
inference(cnf,[status(esa)],[4]) ).
thf(26,plain,
( ( ( cP @ sk12 @ sk13 )
= sk5 )
| ~ sk6
| ~ sk7 ),
inference(lifteq,[status(thm)],[16]) ).
thf(199,plain,
( ( ( cP @ sk12 @ sk13 )
= sk5 )
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[26,86,55]) ).
thf(200,plain,
( ( cP @ sk12 @ sk13 )
= sk5 ),
inference(simp,[status(thm)],[199]) ).
thf(10,plain,
( ~ sk6
| ~ sk7
| ( sk3
= ( cP @ sk8 @ sk9 ) ) ),
inference(cnf,[status(esa)],[4]) ).
thf(19,plain,
( ( ( cP @ sk8 @ sk9 )
= sk3 )
| ~ sk6
| ~ sk7 ),
inference(lifteq,[status(thm)],[10]) ).
thf(104,plain,
( ( ( cP @ sk8 @ sk9 )
= sk3 )
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[19,86,55]) ).
thf(105,plain,
( ( cP @ sk8 @ sk9 )
= sk3 ),
inference(simp,[status(thm)],[104]) ).
thf(14,plain,
! [F: a,E: a,D: a,C: a,B: a,A: a] :
( ( sk3
!= ( cP @ A @ B ) )
| ( sk4
!= ( cP @ C @ D ) )
| ( sk5
!= ( cP @ E @ F ) )
| ~ ( sk2 @ A @ C @ E )
| ~ ( sk2 @ B @ D @ F ) ),
inference(cnf,[status(esa)],[4]) ).
thf(20,plain,
! [F: a,E: a,D: a,C: a,B: a,A: a] :
( ( ( cP @ A @ B )
!= sk3 )
| ( ( cP @ C @ D )
!= sk4 )
| ( ( cP @ E @ F )
!= sk5 )
| ~ ( sk2 @ A @ C @ E )
| ~ ( sk2 @ B @ D @ F ) ),
inference(lifteq,[status(thm)],[14]) ).
thf(21,plain,
! [F: a,E: a,D: a,C: a,B: a,A: a] :
( ( ( cP @ A @ B )
!= sk3 )
| ( ( cP @ C @ D )
!= sk4 )
| ( ( cP @ E @ F )
!= sk5 )
| ~ ( sk2 @ A @ C @ E )
| ~ ( sk2 @ B @ D @ F ) ),
inference(simp,[status(thm)],[20]) ).
thf(109,plain,
! [F: a,E: a,D: a,C: a,B: a,A: a] :
( ( ( cP @ C @ D )
!= sk4 )
| ( ( cP @ E @ F )
!= sk5 )
| ~ ( sk2 @ A @ C @ E )
| ~ ( sk2 @ B @ D @ F )
| ( ( cP @ sk8 @ sk9 )
!= ( cP @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[105,21]) ).
thf(110,plain,
! [D: a,C: a,B: a,A: a] :
( ( ( cP @ A @ B )
!= sk4 )
| ( ( cP @ C @ D )
!= sk5 )
| ~ ( sk2 @ sk8 @ A @ C )
| ~ ( sk2 @ sk9 @ B @ D ) ),
inference(pattern_uni,[status(thm)],[109:[bind(A,$thf( sk8 )),bind(B,$thf( sk9 ))]]) ).
thf(122,plain,
! [D: a,C: a,B: a,A: a] :
( ( ( cP @ A @ B )
!= sk4 )
| ( ( cP @ C @ D )
!= sk5 )
| ~ ( sk2 @ sk8 @ A @ C )
| ~ ( sk2 @ sk9 @ B @ D ) ),
inference(simp,[status(thm)],[110]) ).
thf(660,plain,
! [D: a,C: a,B: a,A: a] :
( ( ( cP @ A @ B )
!= sk4 )
| ~ ( sk2 @ sk8 @ A @ C )
| ~ ( sk2 @ sk9 @ B @ D )
| ( ( cP @ sk12 @ sk13 )
!= ( cP @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[200,122]) ).
thf(661,plain,
! [B: a,A: a] :
( ( ( cP @ A @ B )
!= sk4 )
| ~ ( sk2 @ sk8 @ A @ sk12 )
| ~ ( sk2 @ sk9 @ B @ sk13 ) ),
inference(pattern_uni,[status(thm)],[660:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk12 )),bind(D,$thf( sk13 ))]]) ).
thf(685,plain,
! [B: a,A: a] :
( ~ ( sk2 @ sk8 @ A @ sk12 )
| ~ ( sk2 @ sk9 @ B @ sk13 )
| ( ( cP @ sk10 @ sk11 )
!= ( cP @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[165,661]) ).
thf(686,plain,
( ~ ( sk2 @ sk8 @ sk10 @ sk12 )
| ~ ( sk2 @ sk9 @ sk11 @ sk13 ) ),
inference(pattern_uni,[status(thm)],[685:[bind(A,$thf( sk10 )),bind(B,$thf( sk11 ))]]) ).
thf(9,plain,
( ~ sk6
| ~ sk7
| ( sk1 @ sk9 @ sk11 @ sk13 ) ),
inference(cnf,[status(esa)],[4]) ).
thf(95,plain,
( ~ $true
| ~ $true
| ( sk1 @ sk9 @ sk11 @ sk13 ) ),
inference(rewrite,[status(thm)],[9,86,55]) ).
thf(96,plain,
sk1 @ sk9 @ sk11 @ sk13,
inference(simp,[status(thm)],[95]) ).
thf(15,plain,
! [C: a,B: a,A: a] :
( ~ ( sk1 @ A @ B @ C )
| ( sk2 @ A @ B @ C ) ),
inference(cnf,[status(esa)],[4]) ).
thf(129,plain,
! [C: a,B: a,A: a] :
( ( sk2 @ A @ B @ C )
| ( ( sk1 @ sk9 @ sk11 @ sk13 )
!= ( sk1 @ A @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[96,15]) ).
thf(130,plain,
sk2 @ sk9 @ sk11 @ sk13,
inference(pattern_uni,[status(thm)],[129:[bind(A,$thf( sk9 )),bind(B,$thf( sk11 )),bind(C,$thf( sk13 ))]]) ).
thf(7,plain,
( ~ sk6
| ~ sk7
| ( sk1 @ sk8 @ sk10 @ sk12 ) ),
inference(cnf,[status(esa)],[4]) ).
thf(58,plain,
( ~ $true
| ~ sk7
| ( sk1 @ sk8 @ sk10 @ sk12 ) ),
inference(rewrite,[status(thm)],[7,55]) ).
thf(59,plain,
( ~ sk7
| ( sk1 @ sk8 @ sk10 @ sk12 ) ),
inference(simp,[status(thm)],[58]) ).
thf(93,plain,
( ~ $true
| ( sk1 @ sk8 @ sk10 @ sk12 ) ),
inference(rewrite,[status(thm)],[59,86]) ).
thf(94,plain,
sk1 @ sk8 @ sk10 @ sk12,
inference(simp,[status(thm)],[93]) ).
thf(131,plain,
! [C: a,B: a,A: a] :
( ( sk2 @ A @ B @ C )
| ( ( sk1 @ sk8 @ sk10 @ sk12 )
!= ( sk1 @ A @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[94,15]) ).
thf(132,plain,
sk2 @ sk8 @ sk10 @ sk12,
inference(pattern_uni,[status(thm)],[131:[bind(A,$thf( sk8 )),bind(B,$thf( sk10 )),bind(C,$thf( sk12 ))]]) ).
thf(704,plain,
( ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[686,130,132]) ).
thf(705,plain,
$false,
inference(simp,[status(thm)],[704]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEV191^5 : TPTP v8.2.0. Released v4.0.0.
% 0.13/0.15 % Command : run_Leo-III %s %d
% 0.14/0.36 % Computer : n019.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sun May 19 18:59:54 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.99/0.91 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.31/1.03 % [INFO] Parsing done (121ms).
% 1.31/1.04 % [INFO] Running in sequential loop mode.
% 1.75/1.24 % [INFO] nitpick registered as external prover.
% 1.75/1.25 % [INFO] Scanning for conjecture ...
% 1.75/1.32 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.06/1.35 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.06/1.35 % [INFO] Problem is higher-order (TPTP THF).
% 2.06/1.36 % [INFO] Type checking passed.
% 2.06/1.36 % [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 ...
% 8.97/2.69 % [INFO] Killing All external provers ...
% 8.97/2.70 % Time passed: 2168ms (effective reasoning time: 1656ms)
% 8.97/2.70 % 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)>
% 8.97/2.70 % Axioms used in derivation (0):
% 8.97/2.70 % No. of inferences in proof: 65
% 8.97/2.70 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2168 ms resp. 1656 ms w/o parsing
% 8.97/2.74 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 8.97/2.74 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------