TSTP Solution File: SEV031^5 by Leo-III-SAT---1.7.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SEV031^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n016.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 04:10:47 EDT 2024
% Result : Theorem 11.57s 3.16s
% Output : Refutation 11.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 16
% Syntax : Number of formulae : 80 ( 8 unt; 15 typ; 0 def)
% Number of atoms : 188 ( 10 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 617 ( 91 ~; 106 |; 18 &; 366 @)
% ( 0 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 88 ( 88 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 7 con; 0-3 aty)
% Number of variables : 108 ( 0 ^ 108 !; 0 ?; 108 :)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(b_type,type,
b: $tType ).
thf(sk1_type,type,
sk1: a > $o ).
thf(sk2_type,type,
sk2: a > ( a > b ) > ( a > b ) > $o ).
thf(sk3_type,type,
sk3: $o ).
thf(sk4_type,type,
sk4: a > b ).
thf(sk5_type,type,
sk5: a ).
thf(sk6_type,type,
sk6: $o ).
thf(sk7_type,type,
sk7: a > b ).
thf(sk8_type,type,
sk8: a > b ).
thf(sk9_type,type,
sk9: a ).
thf(sk10_type,type,
sk10: a > b ).
thf(sk11_type,type,
sk11: a > b ).
thf(sk12_type,type,
sk12: a > b ).
thf(sk13_type,type,
sk13: a ).
thf(1,conjecture,
! [A: a > $o,B: a > ( a > b ) > ( a > b ) > $o] :
( ! [C: a] :
( ( A @ C )
=> ( ! [D: a > b] : ( B @ C @ D @ D )
& ! [D: a > b,E: a > b] :
( ( B @ C @ D @ E )
=> ( B @ C @ E @ D ) )
& ! [D: a > b,E: a > b,F: a > b] :
( ( ( B @ C @ D @ E )
& ( B @ C @ E @ F ) )
=> ( B @ C @ D @ F ) ) ) )
=> ( ! [C: a > b,D: a] :
( ( A @ D )
=> ( B @ D @ C @ C ) )
& ! [C: a > b,D: a > b] :
( ! [E: a] :
( ( A @ E )
=> ( B @ E @ C @ D ) )
=> ! [E: a] :
( ( A @ E )
=> ( B @ E @ D @ C ) ) )
& ! [C: a > b,D: a > b,E: a > b] :
( ( ! [F: a] :
( ( A @ F )
=> ( B @ F @ C @ D ) )
& ! [F: a] :
( ( A @ F )
=> ( B @ F @ D @ E ) ) )
=> ! [F: a] :
( ( A @ F )
=> ( B @ F @ C @ E ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM512_pme) ).
thf(2,negated_conjecture,
~ ! [A: a > $o,B: a > ( a > b ) > ( a > b ) > $o] :
( ! [C: a] :
( ( A @ C )
=> ( ! [D: a > b] : ( B @ C @ D @ D )
& ! [D: a > b,E: a > b] :
( ( B @ C @ D @ E )
=> ( B @ C @ E @ D ) )
& ! [D: a > b,E: a > b,F: a > b] :
( ( ( B @ C @ D @ E )
& ( B @ C @ E @ F ) )
=> ( B @ C @ D @ F ) ) ) )
=> ( ! [C: a > b,D: a] :
( ( A @ D )
=> ( B @ D @ C @ C ) )
& ! [C: a > b,D: a > b] :
( ! [E: a] :
( ( A @ E )
=> ( B @ E @ C @ D ) )
=> ! [E: a] :
( ( A @ E )
=> ( B @ E @ D @ C ) ) )
& ! [C: a > b,D: a > b,E: a > b] :
( ( ! [F: a] :
( ( A @ F )
=> ( B @ F @ C @ D ) )
& ! [F: a] :
( ( A @ F )
=> ( B @ F @ D @ E ) ) )
=> ! [F: a] :
( ( A @ F )
=> ( B @ F @ C @ E ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: a > $o,B: a > ( a > b ) > ( a > b ) > $o] :
( ! [C: a] :
( ( A @ C )
=> ( ! [D: a > b] : ( B @ C @ D @ D )
& ! [D: a > b,E: a > b] :
( ( B @ C @ D @ E )
=> ( B @ C @ E @ D ) )
& ! [D: a > b,E: a > b,F: a > b] :
( ( ( B @ C @ D @ E )
& ( B @ C @ E @ F ) )
=> ( B @ C @ D @ F ) ) ) )
=> ( ! [C: a > b,D: a] :
( ( A @ D )
=> ( B @ D @ C @ C ) )
& ! [C: a > b,D: a > b] :
( ! [E: a] :
( ( A @ E )
=> ( B @ E @ C @ D ) )
=> ! [E: a] :
( ( A @ E )
=> ( B @ E @ D @ C ) ) )
& ! [C: a > b,D: a > b,E: a > b] :
( ( ! [F: a] :
( ( A @ F )
=> ( B @ F @ C @ D ) )
& ! [F: a] :
( ( A @ F )
=> ( B @ F @ D @ E ) ) )
=> ! [F: a] :
( ( A @ F )
=> ( B @ F @ C @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(12,plain,
( sk3
| sk6
| ( sk1 @ sk13 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(4,plain,
( ( sk1 @ sk5 )
| ~ sk3 ),
inference(cnf,[status(esa)],[3]) ).
thf(15,plain,
! [B: a > b,A: a] :
( ~ ( sk1 @ A )
| ( sk2 @ A @ B @ B ) ),
inference(cnf,[status(esa)],[3]) ).
thf(7,plain,
( ~ ( sk2 @ sk5 @ sk4 @ sk4 )
| ~ sk3 ),
inference(cnf,[status(esa)],[3]) ).
thf(23,plain,
! [B: a > b,A: a] :
( ~ ( sk1 @ A )
| ~ sk3
| ( ( sk2 @ A @ B @ B )
!= ( sk2 @ sk5 @ sk4 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[15,7]) ).
thf(24,plain,
( ~ ( sk1 @ sk5 )
| ~ sk3 ),
inference(pattern_uni,[status(thm)],[23:[bind(A,$thf( sk5 )),bind(B,$thf( sk4 ))]]) ).
thf(26,plain,
( ~ sk3
| ( ( sk1 @ sk5 )
!= ( sk1 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[4,24]) ).
thf(27,plain,
~ sk3,
inference(pattern_uni,[status(thm)],[26:[]]) ).
thf(41,plain,
( $false
| sk6
| ( sk1 @ sk13 ) ),
inference(rewrite,[status(thm)],[12,27]) ).
thf(42,plain,
( sk6
| ( sk1 @ sk13 ) ),
inference(simp,[status(thm)],[41]) ).
thf(9,plain,
! [A: a] :
( sk3
| sk6
| ~ ( sk1 @ A )
| ( sk2 @ A @ sk11 @ sk12 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(19,plain,
! [A: a] :
( sk3
| sk6
| ~ ( sk1 @ A )
| ( sk2 @ A @ sk11 @ sk12 ) ),
inference(simp,[status(thm)],[9]) ).
thf(88,plain,
! [A: a] :
( $false
| sk6
| ~ ( sk1 @ A )
| ( sk2 @ A @ sk11 @ sk12 ) ),
inference(rewrite,[status(thm)],[19,27]) ).
thf(89,plain,
! [A: a] :
( sk6
| ~ ( sk1 @ A )
| ( sk2 @ A @ sk11 @ sk12 ) ),
inference(simp,[status(thm)],[88]) ).
thf(90,plain,
! [A: a] :
( sk6
| ( sk2 @ A @ sk11 @ sk12 )
| ( ( sk1 @ sk13 )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[42,89]) ).
thf(91,plain,
( sk6
| ( sk2 @ sk13 @ sk11 @ sk12 ) ),
inference(pattern_uni,[status(thm)],[90:[bind(A,$thf( sk13 ))]]) ).
thf(13,plain,
( sk3
| ( sk1 @ sk9 )
| ~ sk6 ),
inference(cnf,[status(esa)],[3]) ).
thf(49,plain,
( $false
| ( sk1 @ sk9 )
| ~ sk6 ),
inference(rewrite,[status(thm)],[13,27]) ).
thf(50,plain,
( ( sk1 @ sk9 )
| ~ sk6 ),
inference(simp,[status(thm)],[49]) ).
thf(10,plain,
! [A: a] :
( sk3
| ~ ( sk1 @ A )
| ( sk2 @ A @ sk7 @ sk8 )
| ~ sk6 ),
inference(cnf,[status(esa)],[3]) ).
thf(17,plain,
! [A: a] :
( sk3
| ~ ( sk1 @ A )
| ( sk2 @ A @ sk7 @ sk8 )
| ~ sk6 ),
inference(simp,[status(thm)],[10]) ).
thf(189,plain,
! [A: a] :
( $false
| ~ ( sk1 @ A )
| ( sk2 @ A @ sk7 @ sk8 )
| ~ sk6 ),
inference(rewrite,[status(thm)],[17,27]) ).
thf(190,plain,
! [A: a] :
( ~ ( sk1 @ A )
| ( sk2 @ A @ sk7 @ sk8 )
| ~ sk6 ),
inference(simp,[status(thm)],[189]) ).
thf(198,plain,
! [A: a] :
( ~ sk6
| ( sk2 @ A @ sk7 @ sk8 )
| ( ( sk1 @ sk9 )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[50,190]) ).
thf(199,plain,
( ~ sk6
| ( sk2 @ sk9 @ sk7 @ sk8 ) ),
inference(pattern_uni,[status(thm)],[198:[bind(A,$thf( sk9 ))]]) ).
thf(5,plain,
! [C: a > b,B: a > b,A: a] :
( ~ ( sk1 @ A )
| ~ ( sk2 @ A @ B @ C )
| ( sk2 @ A @ C @ B ) ),
inference(cnf,[status(esa)],[3]) ).
thf(16,plain,
! [C: a > b,B: a > b,A: a] :
( ~ ( sk1 @ A )
| ~ ( sk2 @ A @ B @ C )
| ( sk2 @ A @ C @ B ) ),
inference(simp,[status(thm)],[5]) ).
thf(11,plain,
( sk3
| ~ ( sk2 @ sk9 @ sk8 @ sk7 )
| ~ sk6 ),
inference(cnf,[status(esa)],[3]) ).
thf(57,plain,
( $false
| ~ ( sk2 @ sk9 @ sk8 @ sk7 )
| ~ sk6 ),
inference(rewrite,[status(thm)],[11,27]) ).
thf(58,plain,
( ~ ( sk2 @ sk9 @ sk8 @ sk7 )
| ~ sk6 ),
inference(simp,[status(thm)],[57]) ).
thf(123,plain,
! [C: a > b,B: a > b,A: a] :
( ~ ( sk1 @ A )
| ~ ( sk2 @ A @ B @ C )
| ~ sk6
| ( ( sk2 @ A @ C @ B )
!= ( sk2 @ sk9 @ sk8 @ sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[16,58]) ).
thf(124,plain,
( ~ ( sk1 @ sk9 )
| ~ ( sk2 @ sk9 @ sk7 @ sk8 )
| ~ sk6 ),
inference(pattern_uni,[status(thm)],[123:[bind(A,$thf( sk9 )),bind(B,$thf( sk7 )),bind(C,$thf( sk8 ))]]) ).
thf(235,plain,
( ~ sk6
| ~ ( sk1 @ sk9 )
| ( ( sk2 @ sk9 @ sk7 @ sk8 )
!= ( sk2 @ sk9 @ sk7 @ sk8 ) ) ),
inference(paramod_ordered,[status(thm)],[199,124]) ).
thf(236,plain,
( ~ sk6
| ~ ( sk1 @ sk9 ) ),
inference(pattern_uni,[status(thm)],[235:[]]) ).
thf(262,plain,
( ~ sk6
| ( ( sk1 @ sk9 )
!= ( sk1 @ sk9 ) ) ),
inference(paramod_ordered,[status(thm)],[50,236]) ).
thf(263,plain,
~ sk6,
inference(pattern_uni,[status(thm)],[262:[]]) ).
thf(286,plain,
( $false
| ( sk2 @ sk13 @ sk11 @ sk12 ) ),
inference(rewrite,[status(thm)],[91,263]) ).
thf(287,plain,
sk2 @ sk13 @ sk11 @ sk12,
inference(simp,[status(thm)],[286]) ).
thf(6,plain,
! [D: a > b,C: a > b,B: a > b,A: a] :
( ~ ( sk1 @ A )
| ~ ( sk2 @ A @ B @ C )
| ~ ( sk2 @ A @ C @ D )
| ( sk2 @ A @ B @ D ) ),
inference(cnf,[status(esa)],[3]) ).
thf(18,plain,
! [D: a > b,C: a > b,B: a > b,A: a] :
( ~ ( sk1 @ A )
| ~ ( sk2 @ A @ B @ C )
| ~ ( sk2 @ A @ C @ D )
| ( sk2 @ A @ B @ D ) ),
inference(simp,[status(thm)],[6]) ).
thf(14,plain,
( sk3
| sk6
| ~ ( sk2 @ sk13 @ sk10 @ sk12 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(65,plain,
( $false
| sk6
| ~ ( sk2 @ sk13 @ sk10 @ sk12 ) ),
inference(rewrite,[status(thm)],[14,27]) ).
thf(66,plain,
( sk6
| ~ ( sk2 @ sk13 @ sk10 @ sk12 ) ),
inference(simp,[status(thm)],[65]) ).
thf(67,plain,
! [D: a > b,C: a > b,B: a > b,A: a] :
( ~ ( sk1 @ A )
| ~ ( sk2 @ A @ B @ C )
| ~ ( sk2 @ A @ C @ D )
| sk6
| ( ( sk2 @ A @ B @ D )
!= ( sk2 @ sk13 @ sk10 @ sk12 ) ) ),
inference(paramod_ordered,[status(thm)],[18,66]) ).
thf(68,plain,
! [A: a > b] :
( ~ ( sk1 @ sk13 )
| ~ ( sk2 @ sk13 @ sk10 @ A )
| ~ ( sk2 @ sk13 @ A @ sk12 )
| sk6 ),
inference(pattern_uni,[status(thm)],[67:[bind(A,$thf( sk13 )),bind(B,$thf( sk10 )),bind(C,$thf( C )),bind(D,$thf( sk12 ))]]) ).
thf(71,plain,
! [A: a > b] :
( ~ ( sk1 @ sk13 )
| ~ ( sk2 @ sk13 @ sk10 @ A )
| ~ ( sk2 @ sk13 @ A @ sk12 )
| sk6 ),
inference(simp,[status(thm)],[68]) ).
thf(266,plain,
( $false
| ( sk1 @ sk13 ) ),
inference(rewrite,[status(thm)],[42,263]) ).
thf(267,plain,
sk1 @ sk13,
inference(simp,[status(thm)],[266]) ).
thf(918,plain,
! [A: a > b] :
( ~ $true
| ~ ( sk2 @ sk13 @ sk10 @ A )
| ~ ( sk2 @ sk13 @ A @ sk12 )
| $false ),
inference(rewrite,[status(thm)],[71,263,267]) ).
thf(919,plain,
! [A: a > b] :
( ~ ( sk2 @ sk13 @ sk10 @ A )
| ~ ( sk2 @ sk13 @ A @ sk12 ) ),
inference(simp,[status(thm)],[918]) ).
thf(925,plain,
! [A: a > b] :
( ~ ( sk2 @ sk13 @ sk10 @ A )
| ( ( sk2 @ sk13 @ sk11 @ sk12 )
!= ( sk2 @ sk13 @ A @ sk12 ) ) ),
inference(paramod_ordered,[status(thm)],[287,919]) ).
thf(926,plain,
~ ( sk2 @ sk13 @ sk10 @ sk11 ),
inference(pattern_uni,[status(thm)],[925:[bind(A,$thf( sk11 ))]]) ).
thf(8,plain,
! [A: a] :
( sk3
| sk6
| ~ ( sk1 @ A )
| ( sk2 @ A @ sk10 @ sk11 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(20,plain,
! [A: a] :
( sk3
| sk6
| ~ ( sk1 @ A )
| ( sk2 @ A @ sk10 @ sk11 ) ),
inference(simp,[status(thm)],[8]) ).
thf(158,plain,
! [A: a] :
( $false
| sk6
| ~ ( sk1 @ A )
| ( sk2 @ A @ sk10 @ sk11 ) ),
inference(rewrite,[status(thm)],[20,27]) ).
thf(159,plain,
! [A: a] :
( sk6
| ~ ( sk1 @ A )
| ( sk2 @ A @ sk10 @ sk11 ) ),
inference(simp,[status(thm)],[158]) ).
thf(160,plain,
! [A: a] :
( sk6
| ( sk2 @ A @ sk10 @ sk11 )
| ( ( sk1 @ sk13 )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[42,159]) ).
thf(161,plain,
( sk6
| ( sk2 @ sk13 @ sk10 @ sk11 ) ),
inference(pattern_uni,[status(thm)],[160:[bind(A,$thf( sk13 ))]]) ).
thf(272,plain,
( $false
| ( sk2 @ sk13 @ sk10 @ sk11 ) ),
inference(rewrite,[status(thm)],[161,263]) ).
thf(273,plain,
sk2 @ sk13 @ sk10 @ sk11,
inference(simp,[status(thm)],[272]) ).
thf(1005,plain,
~ $true,
inference(rewrite,[status(thm)],[926,273]) ).
thf(1006,plain,
$false,
inference(simp,[status(thm)],[1005]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SEV031^5 : TPTP v8.2.0. Released v4.0.0.
% 0.08/0.17 % Command : run_Leo-III %s %d
% 0.16/0.38 % Computer : n016.cluster.edu
% 0.16/0.38 % Model : x86_64 x86_64
% 0.16/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.38 % Memory : 8042.1875MB
% 0.16/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.38 % CPULimit : 300
% 0.16/0.38 % WCLimit : 300
% 0.16/0.38 % DateTime : Sun May 19 19:06:39 EDT 2024
% 0.16/0.38 % CPUTime :
% 0.87/0.80 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.94/0.91 % [INFO] Parsing done (113ms).
% 1.16/0.92 % [INFO] Running in sequential loop mode.
% 1.53/1.15 % [INFO] nitpick registered as external prover.
% 1.53/1.15 % [INFO] Scanning for conjecture ...
% 1.79/1.23 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.79/1.25 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.79/1.26 % [INFO] Problem is higher-order (TPTP THF).
% 1.79/1.26 % [INFO] Type checking passed.
% 1.79/1.26 % [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 ...
% 11.57/3.12 % [INFO] Killing All external provers ...
% 11.57/3.14 % Time passed: 2655ms (effective reasoning time: 2215ms)
% 11.57/3.15 % 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)>
% 11.57/3.16 % Axioms used in derivation (0):
% 11.57/3.16 % No. of inferences in proof: 65
% 11.57/3.16 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2655 ms resp. 2215 ms w/o parsing
% 11.57/3.22 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 11.57/3.22 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------