TSTP Solution File: SEV293^5 by Leo-III-SAT---1.7.15
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.15
% Problem : SEV293^5 : TPTP v8.2.0. Bugfixed v6.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d SAT
% Computer : n032.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 15:59:56 EDT 2024
% Result : Theorem 13.62s 3.18s
% Output : Refutation 13.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 2
% Syntax : Number of formulae : 75 ( 17 unt; 0 typ; 1 def)
% Number of atoms : 329 ( 205 equ; 44 cnn)
% Maximal formula atoms : 5 ( 4 avg)
% Number of connectives : 400 ( 114 ~; 92 |; 26 &; 168 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 9 con; 0-2 aty)
% Number of variables : 42 ( 10 ^ 8 !; 24 ?; 42 :)
% Comments :
%------------------------------------------------------------------------------
thf(cONE_type,type,
cONE: ( $i > $o ) > $o ).
thf(cONE_def,definition,
( cONE
= ( cSUCC @ cZERO ) ) ).
thf(sk2_type,type,
sk2: $i > $o ).
thf(sk3_type,type,
sk3: $i ).
thf(sk11_type,type,
sk11: $i ).
thf(sk12_type,type,
sk12: $i ).
thf(sk13_type,type,
sk13: $i ).
thf(sk20_type,type,
sk20: $i ).
thf(1,conjecture,
( cONE
= ( ^ [A: $i > $o] :
? [B: $i] :
( A
= ( (=) @ $i @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cX6101_pme) ).
thf(2,negated_conjecture,
( cONE
!= ( ^ [A: $i > $o] :
? [B: $i] :
( A
= ( (=) @ $i @ B ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ^ [A: $i > $o] :
? [B: $i] :
( ( A @ B )
& ~ ? [C: $i] :
( ( C != B )
& ( A @ C ) ) ) )
!= ( ^ [A: $i > $o] :
? [B: $i] :
( A
= ( (=) @ $i @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
( ( ^ [A: $i > $o] :
? [B: $i] :
( ( A @ B )
& ~ ? [C: $i] :
( ( C != B )
& ( A @ C ) ) ) )
!= ( ^ [A: $i > $o] :
? [B: $i] :
( A
= ( (=) @ $i @ B ) ) ) ),
inference(lifteq,[status(thm)],[3]) ).
thf(5,plain,
( ( ^ [A: $i > $o,B: $i] :
( ( A @ B )
& ~ ? [C: $i] :
( ( C != B )
& ( A @ C ) ) ) )
!= ( ^ [A: $i > $o,B: $i] :
( A
= ( (=) @ $i @ B ) ) ) ),
inference(simp,[status(thm)],[4]) ).
thf(7,plain,
( ( ( sk2 @ sk3 )
& ~ ? [A: $i] :
( ( A != sk3 )
& ( sk2 @ A ) ) )
!= ( sk2
= ( (=) @ $i @ sk3 ) ) ),
inference(func_ext,[status(esa)],[5]) ).
thf(20,plain,
( ( ( sk2 @ sk3 )
& ~ ? [A: $i] :
( ( A != sk3 )
& ( sk2 @ A ) ) )
| ( sk2
= ( (=) @ $i @ sk3 ) ) ),
inference(bool_ext,[status(thm)],[7]) ).
thf(22,plain,
( ( sk2
= ( (=) @ $i @ sk3 ) )
| ( ( sk2 @ sk3 )
& ~ ? [A: $i] :
( ( A != sk3 )
& ( sk2 @ A ) ) ) ),
inference(lifteq,[status(thm)],[20]) ).
thf(27,plain,
( ( sk2 @ sk3 )
| ( sk2
= ( (=) @ $i @ sk3 ) ) ),
inference(cnf,[status(esa)],[22]) ).
thf(33,plain,
( ( sk2
= ( (=) @ $i @ sk3 ) )
| ( ( ~ ? [A: $i] :
( ( A != sk3 )
& ( sk2 @ A ) ) )
!= ( sk2
= ( (=) @ $i @ sk3 ) ) )
| ( ( sk2 @ sk3 )
!= ( sk2 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[27,7]) ).
thf(34,plain,
( ( sk2
= ( (=) @ $i @ sk3 ) )
| ( ( ~ ? [A: $i] :
( ( A != sk3 )
& ( sk2 @ A ) ) )
!= ( sk2
= ( (=) @ $i @ sk3 ) ) ) ),
inference(pattern_uni,[status(thm)],[33:[]]) ).
thf(54,plain,
! [A: $i] :
( ( ( sk2 @ A )
= ( sk3 = A ) )
| ( ( ~ ? [B: $i] :
( ( B != sk3 )
& ( sk2 @ B ) ) )
!= ( sk2
= ( (=) @ $i @ sk3 ) ) ) ),
inference(func_ext,[status(esa)],[34]) ).
thf(78,plain,
! [A: $i] :
( ( ( ~ ? [B: $i] :
( ( B != sk3 )
& ( sk2 @ B ) ) )
!= ( sk2
= ( (=) @ $i @ sk3 ) ) )
| ( ( ( sk3 = A )
& ~ ? [B: $i] :
( ( B != sk3 )
& ( sk2 @ B ) ) )
!= ( sk2
= ( (=) @ $i @ sk3 ) ) )
| ( ( sk2 @ A )
!= ( sk2 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[54,7]) ).
thf(79,plain,
( ( ( ~ ? [A: $i] :
( ( A != sk3 )
& ( sk2 @ A ) ) )
!= ( sk2
= ( (=) @ $i @ sk3 ) ) )
| ( ( ( sk3 = sk3 )
& ~ ? [A: $i] :
( ( A != sk3 )
& ( sk2 @ A ) ) )
!= ( sk2
= ( (=) @ $i @ sk3 ) ) ) ),
inference(pattern_uni,[status(thm)],[78:[bind(A,$thf( sk3 ))]]) ).
thf(112,plain,
( ( ~ ? [A: $i] :
( ( A != sk3 )
& ( sk2 @ A ) ) )
!= ( sk2
= ( (=) @ $i @ sk3 ) ) ),
inference(simp,[status(thm)],[79]) ).
thf(114,plain,
( ~ ~ ? [A: $i] :
( ( A != sk3 )
& ( sk2 @ A ) )
| ( sk2
!= ( (=) @ $i @ sk3 ) ) ),
inference(bool_ext,[status(thm)],[112]) ).
thf(119,plain,
( ( sk2
!= ( (=) @ $i @ sk3 ) )
| ~ ~ ? [A: $i] :
( ( A != sk3 )
& ( sk2 @ A ) ) ),
inference(lifteq,[status(thm)],[114]) ).
thf(125,plain,
( ( sk2 @ sk11 )
| ( sk2
!= ( (=) @ $i @ sk3 ) ) ),
inference(cnf,[status(esa)],[119]) ).
thf(183,plain,
( ( ( sk2 @ sk13 )
!= ( sk3 = sk13 ) )
| ( sk2 @ sk11 ) ),
inference(func_ext,[status(esa)],[125]) ).
thf(358,plain,
( ( sk2 @ sk11 )
| ( sk2 @ sk13 )
| ( sk3 = sk13 ) ),
inference(bool_ext,[status(thm)],[183]) ).
thf(376,plain,
( ( sk13 = sk3 )
| ( sk2 @ sk11 )
| ( sk2 @ sk13 ) ),
inference(lifteq,[status(thm)],[358]) ).
thf(26,plain,
! [A: $i] :
( ( A = sk3 )
| ~ ( sk2 @ A )
| ( sk2
= ( (=) @ $i @ sk3 ) ) ),
inference(cnf,[status(esa)],[22]) ).
thf(28,plain,
! [A: $i] :
( ( A = sk3 )
| ~ ( sk2 @ A )
| ( sk2
= ( (=) @ $i @ sk3 ) ) ),
inference(lifteq,[status(thm)],[26]) ).
thf(453,plain,
! [A: $i] :
( ( sk13 = sk3 )
| ( sk2 @ sk11 )
| ( A = sk3 )
| ( sk2
= ( (=) @ $i @ sk3 ) )
| ( ( sk2 @ sk13 )
!= ( sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[376,28]) ).
thf(454,plain,
( ( sk13 = sk3 )
| ( sk2 @ sk11 )
| ( sk13 = sk3 )
| ( sk2
= ( (=) @ $i @ sk3 ) ) ),
inference(pattern_uni,[status(thm)],[453:[bind(A,$thf( sk13 ))]]) ).
thf(573,plain,
( ( sk13 = sk3 )
| ( sk2 @ sk11 )
| ( sk2
= ( (=) @ $i @ sk3 ) ) ),
inference(simp,[status(thm)],[454]) ).
thf(1074,plain,
( ( sk13 = sk3 )
| ( sk2 @ sk11 )
| ( sk2 != sk2 ) ),
inference(paramod_ordered,[status(thm)],[573,125]) ).
thf(1075,plain,
( ( sk13 = sk3 )
| ( sk2 @ sk11 ) ),
inference(pattern_uni,[status(thm)],[1074:[]]) ).
thf(357,plain,
( ( sk2 @ sk11 )
| ~ ( sk2 @ sk13 )
| ( sk3 != sk13 ) ),
inference(bool_ext,[status(thm)],[183]) ).
thf(370,plain,
( ( sk13 != sk3 )
| ( sk2 @ sk11 )
| ~ ( sk2 @ sk13 ) ),
inference(lifteq,[status(thm)],[357]) ).
thf(423,plain,
( ( sk2
= ( (=) @ $i @ sk3 ) )
| ( sk13 != sk3 )
| ( sk2 @ sk11 )
| ( ( sk2 @ sk13 )
!= ( sk2 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[27,370]) ).
thf(431,plain,
( ( sk2
= ( (=) @ $i @ sk3 ) )
| ( sk2 @ sk11 )
| ( sk13 != sk3 )
| ( sk13 != sk3 ) ),
inference(simp,[status(thm)],[423]) ).
thf(438,plain,
( ( sk2
= ( (=) @ $i @ sk3 ) )
| ( sk2 @ sk11 )
| ( sk13 != sk3 ) ),
inference(simp,[status(thm)],[431]) ).
thf(856,plain,
( ( sk2 @ sk11 )
| ( sk13 != sk3 )
| ( sk2 != sk2 ) ),
inference(paramod_ordered,[status(thm)],[438,125]) ).
thf(857,plain,
( ( sk2 @ sk11 )
| ( sk13 != sk3 ) ),
inference(pattern_uni,[status(thm)],[856:[]]) ).
thf(1102,plain,
( ( sk2 @ sk11 )
| ( sk13 != sk13 ) ),
inference(paramod_ordered,[status(thm)],[1075,857]) ).
thf(1103,plain,
sk2 @ sk11,
inference(pattern_uni,[status(thm)],[1102:[]]) ).
thf(1132,plain,
! [A: $i] :
( ( A = sk3 )
| ( sk2
= ( (=) @ $i @ sk3 ) )
| ( ( sk2 @ sk11 )
!= ( sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1103,28]) ).
thf(1133,plain,
( ( sk11 = sk3 )
| ( sk2
= ( (=) @ $i @ sk3 ) ) ),
inference(pattern_uni,[status(thm)],[1132:[bind(A,$thf( sk11 ))]]) ).
thf(1202,plain,
( ( sk11 = sk3 )
| ? [A: $i] :
( ( A != sk3 )
& ( sk2 @ A ) )
| ( sk2 != sk2 ) ),
inference(paramod_ordered,[status(thm)],[1133,112]) ).
thf(1203,plain,
( ( sk11 = sk3 )
| ? [A: $i] :
( ( A != sk3 )
& ( sk2 @ A ) ) ),
inference(pattern_uni,[status(thm)],[1202:[]]) ).
thf(1222,plain,
( ( sk2 @ sk20 )
| ( sk11 = sk3 ) ),
inference(cnf,[status(esa)],[1203]) ).
thf(126,plain,
( ( sk11 != sk3 )
| ( sk2
!= ( (=) @ $i @ sk3 ) ) ),
inference(cnf,[status(esa)],[119]) ).
thf(127,plain,
( ( sk11 != sk3 )
| ( sk2
!= ( (=) @ $i @ sk3 ) ) ),
inference(lifteq,[status(thm)],[126]) ).
thf(140,plain,
( ( ( sk2 @ sk12 )
!= ( sk3 = sk12 ) )
| ( sk11 != sk3 ) ),
inference(func_ext,[status(esa)],[127]) ).
thf(144,plain,
( ( sk11 != sk3 )
| ( sk2 @ sk12 )
| ( sk3 = sk12 ) ),
inference(bool_ext,[status(thm)],[140]) ).
thf(149,plain,
( ( sk12 = sk3 )
| ( sk11 != sk3 )
| ( sk2 @ sk12 ) ),
inference(lifteq,[status(thm)],[144]) ).
thf(141,plain,
( ( sk2 @ sk3 )
| ( sk11 != sk3 )
| ( sk2 != sk2 ) ),
inference(paramod_ordered,[status(thm)],[27,127]) ).
thf(142,plain,
( ( sk2 @ sk3 )
| ( sk11 != sk3 ) ),
inference(pattern_uni,[status(thm)],[141:[]]) ).
thf(143,plain,
( ( sk11 != sk3 )
| ~ ( sk2 @ sk12 )
| ( sk3 != sk12 ) ),
inference(bool_ext,[status(thm)],[140]) ).
thf(151,plain,
( ( sk12 != sk3 )
| ( sk11 != sk3 )
| ~ ( sk2 @ sk12 ) ),
inference(lifteq,[status(thm)],[143]) ).
thf(217,plain,
( ( sk11 != sk3 )
| ( sk12 != sk3 )
| ( ( sk2 @ sk12 )
!= ( sk2 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[142,151]) ).
thf(224,plain,
( ( sk11 != sk3 )
| ( sk12 != sk3 )
| ( sk12 != sk3 ) ),
inference(simp,[status(thm)],[217]) ).
thf(231,plain,
( ( sk11 != sk3 )
| ( sk12 != sk3 ) ),
inference(simp,[status(thm)],[224]) ).
thf(242,plain,
( ( sk11 != sk3 )
| ( sk2 @ sk12 )
| ( sk12 != sk12 ) ),
inference(paramod_ordered,[status(thm)],[149,231]) ).
thf(243,plain,
( ( sk11 != sk3 )
| ( sk2 @ sk12 ) ),
inference(pattern_uni,[status(thm)],[242:[]]) ).
thf(1216,plain,
( ( sk2
= ( (=) @ $i @ sk3 ) )
| ( sk2 @ sk12 )
| ( sk11 != sk11 ) ),
inference(paramod_ordered,[status(thm)],[1133,243]) ).
thf(1217,plain,
( ( sk2
= ( (=) @ $i @ sk3 ) )
| ( sk2 @ sk12 ) ),
inference(pattern_uni,[status(thm)],[1216:[]]) ).
thf(1442,plain,
! [A: $i] :
( ( sk2
= ( (=) @ $i @ sk3 ) )
| ( A = sk3 )
| ( ( sk2 @ sk12 )
!= ( sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1217,28]) ).
thf(1443,plain,
( ( sk2
= ( (=) @ $i @ sk3 ) )
| ( sk12 = sk3 ) ),
inference(pattern_uni,[status(thm)],[1442:[bind(A,$thf( sk12 ))]]) ).
thf(1208,plain,
( ( sk2
= ( (=) @ $i @ sk3 ) )
| ( sk12 != sk3 )
| ( sk11 != sk11 ) ),
inference(paramod_ordered,[status(thm)],[1133,231]) ).
thf(1209,plain,
( ( sk2
= ( (=) @ $i @ sk3 ) )
| ( sk12 != sk3 ) ),
inference(pattern_uni,[status(thm)],[1208:[]]) ).
thf(1714,plain,
( ( sk2
= ( (=) @ $i @ sk3 ) )
| ( sk12 != sk12 ) ),
inference(paramod_ordered,[status(thm)],[1443,1209]) ).
thf(1715,plain,
( sk2
= ( (=) @ $i @ sk3 ) ),
inference(pattern_uni,[status(thm)],[1714:[]]) ).
thf(1729,plain,
( ( sk11 != sk3 )
| ( ( (=) @ $i @ sk3 )
!= ( (=) @ $i @ sk3 ) ) ),
inference(rewrite,[status(thm)],[127,1715]) ).
thf(1730,plain,
sk11 != sk3,
inference(simp,[status(thm)],[1729]) ).
thf(1748,plain,
sk2 @ sk20,
inference(simplifyReflect,[status(thm)],[1222,1730]) ).
thf(1741,plain,
! [A: $i] :
( ( sk2 @ A )
= ( sk3 = A ) ),
inference(func_ext,[status(esa)],[1715]) ).
thf(1837,plain,
sk3 = sk20,
inference(rewrite,[status(thm)],[1748,1741]) ).
thf(1846,plain,
sk20 = sk3,
inference(lifteq,[status(thm)],[1837]) ).
thf(1223,plain,
( ( sk20 != sk3 )
| ( sk11 = sk3 ) ),
inference(cnf,[status(esa)],[1203]) ).
thf(1224,plain,
( ( sk20 != sk3 )
| ( sk11 = sk3 ) ),
inference(lifteq,[status(thm)],[1223]) ).
thf(1749,plain,
sk20 != sk3,
inference(simplifyReflect,[status(thm)],[1224,1730]) ).
thf(1857,plain,
$false,
inference(simplifyReflect,[status(thm)],[1846,1749]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09 % Problem : SEV293^5 : TPTP v8.2.0. Bugfixed v6.2.0.
% 0.02/0.09 % Command : run_Leo-III %s %d SAT
% 0.09/0.29 % Computer : n032.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Fri Jun 21 18:37:55 EDT 2024
% 0.09/0.30 % CPUTime :
% 0.70/0.76 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.01/0.86 % [INFO] Parsing done (100ms).
% 1.01/0.87 % [INFO] Running in sequential loop mode.
% 1.24/1.07 % [INFO] nitpick registered as external prover.
% 1.24/1.07 % [INFO] Scanning for conjecture ...
% 1.39/1.13 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.39/1.14 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.39/1.15 % [INFO] Problem is higher-order (TPTP THF).
% 1.39/1.15 % [INFO] Type checking passed.
% 1.39/1.15 % [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 ...
% 13.62/3.18 % [INFO] Killing All external provers ...
% 13.62/3.18 % Time passed: 2723ms (effective reasoning time: 2310ms)
% 13.62/3.18 % 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)>
% 13.62/3.18 % Axioms used in derivation (0):
% 13.62/3.18 % No. of inferences in proof: 74
% 13.62/3.18 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2723 ms resp. 2310 ms w/o parsing
% 13.62/3.24 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 13.62/3.24 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------