TSTP Solution File: SEV222^5 by Leo-III-SAT---1.7.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SEV222^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n009.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 04:11:08 EDT 2024
% Result : Theorem 33.95s 6.06s
% Output : Refutation 34.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 8
% Syntax : Number of formulae : 68 ( 16 unt; 7 typ; 0 def)
% Number of atoms : 238 ( 34 equ; 0 cnn)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 413 ( 61 ~; 119 |; 7 &; 212 @)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 51 ( 51 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 73 ( 15 ^ 51 !; 7 ?; 73 :)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(cZ_type,type,
cZ: a > $o ).
thf(cW_type,type,
cW: ( a > $o ) > $o ).
thf(sk1_type,type,
sk1: a ).
thf(sk2_type,type,
sk2: a > $o ).
thf(sk3_type,type,
sk3: a > $o ).
thf(sk4_type,type,
sk4: a > $o ).
thf(1,conjecture,
! [A: a] :
( ( ! [B: a > $o] :
( ( cW @ B )
=> ( B @ A ) )
| ( cZ @ A ) )
= ( ! [B: a > $o] :
( ? [C: a > $o] :
( ( cW @ C )
& ( B
= ( ^ [D: a] :
( ( cZ @ D )
| ( C @ D ) ) ) ) )
=> ( B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM60_pme) ).
thf(2,negated_conjecture,
~ ! [A: a] :
( ( ! [B: a > $o] :
( ( cW @ B )
=> ( B @ A ) )
| ( cZ @ A ) )
= ( ! [B: a > $o] :
( ? [C: a > $o] :
( ( cW @ C )
& ( B
= ( ^ [D: a] :
( ( cZ @ D )
| ( C @ D ) ) ) ) )
=> ( B @ A ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: a] :
( ( ! [B: a > $o] :
( ( cW @ B )
=> ( B @ A ) )
| ( cZ @ A ) )
= ( ! [B: a > $o] :
( ? [C: a > $o] :
( ( cW @ C )
& ( B
= ( ^ [D: a] :
( ( cZ @ D )
| ( C @ D ) ) ) ) )
=> ( B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [A: a > $o] :
( ( cW @ A )
=> ( A @ sk1 ) )
| ( cZ @ sk1 ) )
!= ( ! [A: a > $o] :
( ? [B: a > $o] :
( ( cW @ B )
& ( A
= ( ^ [C: a] :
( ( cZ @ C )
| ( B @ C ) ) ) ) )
=> ( A @ sk1 ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
( ( ! [A: a > $o] :
( ( cW @ A )
=> ( A @ sk1 ) )
| ( cZ @ sk1 ) )
!= ( ! [A: a > $o] :
( ? [B: a > $o] :
( ( cW @ B )
& ( A
= ( ^ [C: a] :
( ( cZ @ C )
| ( B @ C ) ) ) ) )
=> ( A @ sk1 ) ) ) ),
inference(lifteq,[status(thm)],[4]) ).
thf(6,plain,
( ~ ( ! [A: a > $o] :
( ( cW @ A )
=> ( A @ sk1 ) )
| ( cZ @ sk1 ) )
| ~ ! [A: a > $o] :
( ? [B: a > $o] :
( ( cW @ B )
& ( A
= ( ^ [C: a] :
( ( cZ @ C )
| ( B @ C ) ) ) ) )
=> ( A @ sk1 ) ) ),
inference(bool_ext,[status(thm)],[5]) ).
thf(11,plain,
( ( cW @ sk4 )
| ~ ( sk2 @ sk1 ) ),
inference(cnf,[status(esa)],[6]) ).
thf(16,plain,
( ( cW @ sk4 )
| ( cW @ sk2 ) ),
inference(cnf,[status(esa)],[6]) ).
thf(7,plain,
( ! [A: a > $o] :
( ( cW @ A )
=> ( A @ sk1 ) )
| ( cZ @ sk1 )
| ! [A: a > $o] :
( ? [B: a > $o] :
( ( cW @ B )
& ( A
= ( ^ [C: a] :
( ( cZ @ C )
| ( B @ C ) ) ) ) )
=> ( A @ sk1 ) ) ),
inference(bool_ext,[status(thm)],[5]) ).
thf(20,plain,
! [C: a > $o,B: a > $o,A: a > $o] :
( ~ ( cW @ C )
| ( B
!= ( ^ [D: a] :
( ( cZ @ D )
| ( C @ D ) ) ) )
| ( B @ sk1 )
| ~ ( cW @ A )
| ( A @ sk1 )
| ( cZ @ sk1 ) ),
inference(cnf,[status(esa)],[7]) ).
thf(21,plain,
! [C: a > $o,B: a > $o,A: a > $o] :
( ( B
!= ( ^ [D: a] :
( ( cZ @ D )
| ( C @ D ) ) ) )
| ~ ( cW @ C )
| ( B @ sk1 )
| ~ ( cW @ A )
| ( A @ sk1 )
| ( cZ @ sk1 ) ),
inference(lifteq,[status(thm)],[20]) ).
thf(22,plain,
! [B: a > $o,A: a > $o] :
( ~ ( cW @ B )
| ( cZ @ sk1 )
| ( B @ sk1 )
| ~ ( cW @ A )
| ( A @ sk1 )
| ( cZ @ sk1 ) ),
inference(simp,[status(thm)],[21]) ).
thf(23,plain,
! [B: a > $o,A: a > $o] :
( ( cZ @ sk1 )
| ( A @ sk1 )
| ~ ( cW @ A )
| ( cZ @ sk1 )
| ( B @ sk1 )
| ~ ( cW @ B ) ),
inference(cnf,[status(esa)],[22]) ).
thf(24,plain,
! [B: a > $o,A: a > $o] :
( ( cZ @ sk1 )
| ( A @ sk1 )
| ~ ( cW @ A )
| ( B @ sk1 )
| ~ ( cW @ B ) ),
inference(simp,[status(thm)],[23]) ).
thf(137,plain,
! [B: a > $o,A: a > $o] :
( ( cW @ sk2 )
| ( cZ @ sk1 )
| ( A @ sk1 )
| ~ ( cW @ A )
| ( B @ sk1 )
| ( ( cW @ sk4 )
!= ( cW @ B ) ) ),
inference(paramod_ordered,[status(thm)],[16,24]) ).
thf(138,plain,
! [A: a > $o] :
( ( cW @ sk2 )
| ( cZ @ sk1 )
| ( A @ sk1 )
| ~ ( cW @ A )
| ( sk4 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[137:[bind(A,$thf( A )),bind(B,$thf( sk4 ))]]) ).
thf(748,plain,
! [A: a > $o] :
( ( cW @ sk2 )
| ( cZ @ sk1 )
| ( A @ sk1 )
| ( sk4 @ sk1 )
| ( ( cW @ sk4 )
!= ( cW @ A ) ) ),
inference(paramod_ordered,[status(thm)],[16,138]) ).
thf(749,plain,
( ( cW @ sk2 )
| ( cZ @ sk1 )
| ( sk4 @ sk1 )
| ( sk4 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[748:[bind(A,$thf( sk4 ))]]) ).
thf(1060,plain,
( ( cW @ sk2 )
| ( cZ @ sk1 )
| ( sk4 @ sk1 ) ),
inference(simp,[status(thm)],[749]) ).
thf(14,plain,
( ( sk3
= ( ^ [A: a] :
( ( cZ @ A )
| ( sk4 @ A ) ) ) )
| ~ ( cZ @ sk1 ) ),
inference(cnf,[status(esa)],[6]) ).
thf(17,plain,
( ( ( ^ [A: a] :
( ( cZ @ A )
| ( sk4 @ A ) ) )
= sk3 )
| ~ ( cZ @ sk1 ) ),
inference(lifteq,[status(thm)],[14]) ).
thf(29,plain,
! [A: a] :
( ( ( ( cZ @ A )
| ( sk4 @ A ) )
= ( sk3 @ A ) )
| ~ ( cZ @ sk1 ) ),
inference(func_ext,[status(esa)],[17]) ).
thf(53,plain,
! [A: a] :
( ~ ( cZ @ sk1 )
| ~ ( ( cZ @ A )
| ( sk4 @ A ) )
| ( sk3 @ A ) ),
inference(bool_ext,[status(thm)],[29]) ).
thf(58,plain,
! [A: a] :
( ( sk3 @ A )
| ~ ( cZ @ A )
| ~ ( cZ @ sk1 ) ),
inference(cnf,[status(esa)],[53]) ).
thf(8,plain,
( ~ ( sk3 @ sk1 )
| ~ ( cZ @ sk1 ) ),
inference(cnf,[status(esa)],[6]) ).
thf(1092,plain,
! [A: a] :
( ~ ( cZ @ A )
| ~ ( cZ @ sk1 )
| ( ( sk3 @ A )
!= ( sk3 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[58,8]) ).
thf(1093,plain,
( ~ ( cZ @ sk1 )
| ~ ( cZ @ sk1 ) ),
inference(pattern_uni,[status(thm)],[1092:[bind(A,$thf( sk1 ))]]) ).
thf(1105,plain,
~ ( cZ @ sk1 ),
inference(simp,[status(thm)],[1093]) ).
thf(1367,plain,
( ( cW @ sk2 )
| $false
| ( sk4 @ sk1 ) ),
inference(rewrite,[status(thm)],[1060,1105]) ).
thf(1368,plain,
( ( cW @ sk2 )
| ( sk4 @ sk1 ) ),
inference(simp,[status(thm)],[1367]) ).
thf(13,plain,
( ( sk3
= ( ^ [A: a] :
( ( cZ @ A )
| ( sk4 @ A ) ) ) )
| ( cW @ sk2 ) ),
inference(cnf,[status(esa)],[6]) ).
thf(19,plain,
( ( ( ^ [A: a] :
( ( cZ @ A )
| ( sk4 @ A ) ) )
= sk3 )
| ( cW @ sk2 ) ),
inference(lifteq,[status(thm)],[13]) ).
thf(35,plain,
! [A: a] :
( ( ( ( cZ @ A )
| ( sk4 @ A ) )
= ( sk3 @ A ) )
| ( cW @ sk2 ) ),
inference(func_ext,[status(esa)],[19]) ).
thf(1370,plain,
! [A: a] :
( ( cW @ sk2 )
| ( sk3 @ A )
| ( ( sk4 @ sk1 )
!= ( sk4 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1368,35]) ).
thf(1371,plain,
( ( cW @ sk2 )
| ( sk3 @ sk1 ) ),
inference(pattern_uni,[status(thm)],[1370:[bind(A,$thf( sk1 ))]]) ).
thf(10,plain,
( ~ ( sk3 @ sk1 )
| ( cW @ sk2 ) ),
inference(cnf,[status(esa)],[6]) ).
thf(1381,plain,
( ( cW @ sk2 )
| ( ( sk3 @ sk1 )
!= ( sk3 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[1371,10]) ).
thf(1382,plain,
cW @ sk2,
inference(pattern_uni,[status(thm)],[1381:[]]) ).
thf(206,plain,
! [B: a > $o,A: a > $o] :
( ( cZ @ sk1 )
| ( A @ sk1 )
| ~ ( cW @ A )
| ( B @ sk1 )
| ( ( cW @ B )
!= ( cW @ A ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[24]) ).
thf(273,plain,
! [A: a > $o] :
( ( cZ @ sk1 )
| ( A @ sk1 )
| ~ ( cW @ A )
| ( A @ sk1 ) ),
inference(pattern_uni,[status(thm)],[206:[bind(A,$thf( B ))]]) ).
thf(329,plain,
! [A: a > $o] :
( ( cZ @ sk1 )
| ( A @ sk1 )
| ~ ( cW @ A ) ),
inference(simp,[status(thm)],[273]) ).
thf(1894,plain,
! [A: a > $o] :
( $false
| ( A @ sk1 )
| ~ ( cW @ A ) ),
inference(rewrite,[status(thm)],[329,1105]) ).
thf(1895,plain,
! [A: a > $o] :
( ( A @ sk1 )
| ~ ( cW @ A ) ),
inference(simp,[status(thm)],[1894]) ).
thf(1937,plain,
! [A: a > $o] :
( ( A @ sk1 )
| ( ( cW @ sk2 )
!= ( cW @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1382,1895]) ).
thf(1938,plain,
sk2 @ sk1,
inference(pattern_uni,[status(thm)],[1937:[bind(A,$thf( sk2 ))]]) ).
thf(2313,plain,
( ( cW @ sk4 )
| ~ $true ),
inference(rewrite,[status(thm)],[11,1938]) ).
thf(2314,plain,
cW @ sk4,
inference(simp,[status(thm)],[2313]) ).
thf(2401,plain,
! [A: a > $o] :
( ( A @ sk1 )
| ( ( cW @ sk4 )
!= ( cW @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2314,1895]) ).
thf(2402,plain,
sk4 @ sk1,
inference(pattern_uni,[status(thm)],[2401:[bind(A,$thf( sk4 ))]]) ).
thf(9,plain,
( ( sk3
= ( ^ [A: a] :
( ( cZ @ A )
| ( sk4 @ A ) ) ) )
| ~ ( sk2 @ sk1 ) ),
inference(cnf,[status(esa)],[6]) ).
thf(18,plain,
( ( ( ^ [A: a] :
( ( cZ @ A )
| ( sk4 @ A ) ) )
= sk3 )
| ~ ( sk2 @ sk1 ) ),
inference(lifteq,[status(thm)],[9]) ).
thf(30,plain,
! [A: a] :
( ( ( ( cZ @ A )
| ( sk4 @ A ) )
= ( sk3 @ A ) )
| ~ ( sk2 @ sk1 ) ),
inference(func_ext,[status(esa)],[18]) ).
thf(2315,plain,
! [A: a] :
( ( ( ( cZ @ A )
| ( sk4 @ A ) )
= ( sk3 @ A ) )
| ~ $true ),
inference(rewrite,[status(thm)],[30,1938]) ).
thf(2316,plain,
! [A: a] :
( ( ( cZ @ A )
| ( sk4 @ A ) )
= ( sk3 @ A ) ),
inference(simp,[status(thm)],[2315]) ).
thf(3464,plain,
! [A: a] :
( ( sk3 @ A )
| ( ( sk4 @ sk1 )
!= ( sk4 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2402,2316]) ).
thf(3465,plain,
sk3 @ sk1,
inference(pattern_uni,[status(thm)],[3464:[bind(A,$thf( sk1 ))]]) ).
thf(12,plain,
( ~ ( sk3 @ sk1 )
| ~ ( sk2 @ sk1 ) ),
inference(cnf,[status(esa)],[6]) ).
thf(2309,plain,
( ~ ( sk3 @ sk1 )
| ~ $true ),
inference(rewrite,[status(thm)],[12,1938]) ).
thf(2310,plain,
~ ( sk3 @ sk1 ),
inference(simp,[status(thm)],[2309]) ).
thf(3492,plain,
$false,
inference(rewrite,[status(thm)],[3465,2310]) ).
thf(3493,plain,
$false,
inference(simp,[status(thm)],[3492]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.12 % Problem : SEV222^5 : TPTP v8.2.0. Released v4.0.0.
% 0.12/0.15 % Command : run_Leo-III %s %d
% 0.15/0.35 % Computer : n009.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Sun May 19 18:38:38 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.82/0.85 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.18/0.95 % [INFO] Parsing done (105ms).
% 1.18/0.96 % [INFO] Running in sequential loop mode.
% 1.62/1.18 % [INFO] nitpick registered as external prover.
% 1.62/1.18 % [INFO] Scanning for conjecture ...
% 1.77/1.24 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.77/1.26 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.77/1.26 % [INFO] Problem is higher-order (TPTP THF).
% 1.77/1.26 % [INFO] Type checking passed.
% 1.77/1.27 % [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 ...
% 33.95/6.05 % [INFO] Killing All external provers ...
% 33.95/6.06 % Time passed: 5539ms (effective reasoning time: 5089ms)
% 33.95/6.06 % 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)>
% 33.95/6.06 % Axioms used in derivation (0):
% 33.95/6.06 % No. of inferences in proof: 61
% 33.95/6.06 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 5539 ms resp. 5089 ms w/o parsing
% 34.05/6.13 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 34.05/6.13 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------