TSTP Solution File: SEV293^5 by Leo-III---1.7.15
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---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 THM
% Computer : n026.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 15:58:43 EDT 2024
% Result : Theorem 8.72s 2.92s
% Output : Refutation 8.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 2
% Syntax : Number of formulae : 76 ( 11 unt; 0 typ; 1 def)
% Number of atoms : 365 ( 203 equ; 45 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 512 ( 157 ~; 105 |; 38 &; 212 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 14 usr; 12 con; 0-2 aty)
% Number of variables : 64 ( 12 ^ 16 !; 36 ?; 64 :)
% Comments :
%------------------------------------------------------------------------------
thf(cONE_type,type,
cONE: ( $i > $o ) > $o ).
thf(cONE_def,definition,
( cONE
= ( cSUCC @ cZERO ) ) ).
thf(sk1_type,type,
sk1: $i > $o ).
thf(sk2_type,type,
sk2: $i > $o ).
thf(sk3_type,type,
sk3: $i ).
thf(sk4_type,type,
sk4: $i > $i ).
thf(sk5_type,type,
sk5: $i ).
thf(sk6_type,type,
sk6: $i > $i ).
thf(sk7_type,type,
sk7: $i ).
thf(sk10_type,type,
sk10: $i ).
thf(sk11_type,type,
sk11: $i ).
thf(sk12_type,type,
sk12: $i ).
thf(sk13_type,type,
sk13: $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(116,plain,
( ( sk2 @ sk3 )
| ? [A: $i] :
( ( A != sk3 )
& ( sk2 @ A ) )
| ( sk2 != sk2 ) ),
inference(paramod_ordered,[status(thm)],[27,112]) ).
thf(117,plain,
( ( sk2 @ sk3 )
| ? [A: $i] :
( ( A != sk3 )
& ( sk2 @ A ) ) ),
inference(pattern_uni,[status(thm)],[116:[]]) ).
thf(122,plain,
( ( sk2 @ sk10 )
| ( sk2 @ sk3 ) ),
inference(cnf,[status(esa)],[117]) ).
thf(134,plain,
( ( sk2 @ sk3 )
| ( ( sk2 @ sk10 )
!= ( sk2 @ sk3 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[122]) ).
thf(138,plain,
( ( sk2 @ sk3 )
| ( ( sk2 @ sk10 )
!= ( sk2 @ sk3 ) ) ),
inference(simp,[status(thm)],[134]) ).
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(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(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(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(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(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(6,plain,
( ( ? [A: $i] :
( ( sk1 @ A )
& ~ ? [B: $i] :
( ( B != A )
& ( sk1 @ B ) ) ) )
!= ( ? [A: $i] :
( sk1
= ( (=) @ $i @ A ) ) ) ),
inference(func_ext,[status(esa)],[4]) ).
thf(123,plain,
( ( sk10 != sk3 )
| ( sk2 @ sk3 ) ),
inference(cnf,[status(esa)],[117]) ).
thf(124,plain,
( ( sk10 != sk3 )
| ( sk2 @ sk3 ) ),
inference(lifteq,[status(thm)],[123]) ).
thf(9,plain,
( ~ ? [A: $i] :
( ( sk1 @ A )
& ~ ? [B: $i] :
( ( B != A )
& ( sk1 @ B ) ) )
| ~ ? [A: $i] :
( sk1
= ( (=) @ $i @ A ) ) ),
inference(bool_ext,[status(thm)],[6]) ).
thf(11,plain,
! [B: $i,A: $i] :
( ( sk1
!= ( (=) @ $i @ B ) )
| ~ ( sk1 @ A )
| ( ( sk4 @ A )
!= A ) ),
inference(cnf,[status(esa)],[9]) ).
thf(13,plain,
! [B: $i,A: $i] :
( ( sk1
!= ( (=) @ $i @ B ) )
| ( ( sk4 @ A )
!= A )
| ~ ( sk1 @ A ) ),
inference(lifteq,[status(thm)],[11]) ).
thf(10,plain,
( ? [A: $i] :
( ( sk1 @ A )
& ~ ? [B: $i] :
( ( B != A )
& ( sk1 @ B ) ) )
| ? [A: $i] :
( sk1
= ( (=) @ $i @ A ) ) ),
inference(bool_ext,[status(thm)],[6]) ).
thf(15,plain,
! [A: $i] :
( ( sk1
= ( (=) @ $i @ ( sk6 @ A ) ) )
| ( A = sk5 )
| ~ ( sk1 @ A ) ),
inference(cnf,[status(esa)],[10]) ).
thf(17,plain,
! [A: $i] :
( ( sk1
= ( (=) @ $i @ ( sk6 @ A ) ) )
| ( A = sk5 )
| ~ ( sk1 @ A ) ),
inference(lifteq,[status(thm)],[15]) ).
thf(19,plain,
( ~ ( ( sk2 @ sk3 )
& ~ ? [A: $i] :
( ( A != sk3 )
& ( sk2 @ A ) ) )
| ( sk2
!= ( (=) @ $i @ sk3 ) ) ),
inference(bool_ext,[status(thm)],[7]) ).
thf(21,plain,
( ( sk2
!= ( (=) @ $i @ sk3 ) )
| ~ ( ( sk2 @ sk3 )
& ~ ? [A: $i] :
( ( A != sk3 )
& ( sk2 @ A ) ) ) ),
inference(lifteq,[status(thm)],[19]) ).
thf(23,plain,
( ~ ( sk2 @ sk3 )
| ( sk7 != sk3 )
| ( sk2
!= ( (=) @ $i @ sk3 ) ) ),
inference(cnf,[status(esa)],[21]) ).
thf(25,plain,
( ( sk7 != sk3 )
| ~ ( sk2 @ sk3 )
| ( sk2
!= ( (=) @ $i @ sk3 ) ) ),
inference(lifteq,[status(thm)],[23]) ).
thf(158,plain,
( ( sk10 != sk3 )
| ( sk7 != sk3 )
| ( sk2
!= ( (=) @ $i @ sk3 ) )
| ( ( sk2 @ sk3 )
!= ( sk2 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[124,25]) ).
thf(159,plain,
( ( sk10 != sk3 )
| ( sk7 != sk3 )
| ( sk2
!= ( (=) @ $i @ sk3 ) ) ),
inference(pattern_uni,[status(thm)],[158:[]]) ).
thf(16,plain,
! [A: $i] :
( ( sk1
= ( (=) @ $i @ ( sk6 @ A ) ) )
| ( sk1 @ sk5 ) ),
inference(cnf,[status(esa)],[10]) ).
thf(18,plain,
! [A: $i] :
( ( sk1
= ( (=) @ $i @ ( sk6 @ A ) ) )
| ( sk1 @ sk5 ) ),
inference(lifteq,[status(thm)],[16]) ).
thf(8,plain,
( ( ^ [A: $i] :
( ( sk1 @ A )
& ~ ? [B: $i] :
( ( B != A )
& ( sk1 @ B ) ) ) )
!= ( ^ [A: $i] :
( sk1
= ( (=) @ $i @ A ) ) ) ),
inference(simp,[status(thm)],[6]) ).
thf(184,plain,
( ( sk2 @ sk3 )
| ( sk2 @ sk11 )
| ( sk2 != sk2 ) ),
inference(paramod_ordered,[status(thm)],[27,125]) ).
thf(185,plain,
( ( sk2 @ sk3 )
| ( sk2 @ sk11 ) ),
inference(pattern_uni,[status(thm)],[184:[]]) ).
thf(198,plain,
( ( sk2 @ sk3 )
| ( ( sk2 @ sk11 )
!= ( sk2 @ sk3 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[185]) ).
thf(202,plain,
( ( sk2 @ sk3 )
| ( ( sk2 @ sk11 )
!= ( sk2 @ sk3 ) ) ),
inference(simp,[status(thm)],[198]) ).
thf(24,plain,
( ~ ( sk2 @ sk3 )
| ( sk2 @ sk7 )
| ( sk2
!= ( (=) @ $i @ sk3 ) ) ),
inference(cnf,[status(esa)],[21]) ).
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(418,plain,
( ( sk10 != sk3 )
| ( sk13 != sk3 )
| ( sk2 @ sk11 )
| ( ( sk2 @ sk13 )
!= ( sk2 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[124,370]) ).
thf(433,plain,
( ( sk2 @ sk11 )
| ( sk10 != sk3 )
| ( sk13 != sk3 )
| ( sk13 != sk3 ) ),
inference(simp,[status(thm)],[418]) ).
thf(436,plain,
( ( sk2 @ sk11 )
| ( sk10 != sk3 )
| ( sk13 != sk3 ) ),
inference(simp,[status(thm)],[433]) ).
thf(12,plain,
! [B: $i,A: $i] :
( ( sk1
!= ( (=) @ $i @ B ) )
| ~ ( sk1 @ A )
| ( sk1 @ ( sk4 @ A ) ) ),
inference(cnf,[status(esa)],[9]) ).
thf(14,plain,
! [B: $i,A: $i] :
( ( sk1
!= ( (=) @ $i @ B ) )
| ~ ( sk1 @ A )
| ( sk1 @ ( sk4 @ A ) ) ),
inference(lifteq,[status(thm)],[12]) ).
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(402,plain,
( ( sk13 = sk3 )
| ( sk2 @ sk11 )
| ( ( sk2 @ sk13 )
!= ( sk2 @ sk11 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[376]) ).
thf(407,plain,
( ( sk13 = sk3 )
| ( sk2 @ sk11 )
| ( sk13 != sk11 ) ),
inference(simp,[status(thm)],[402]) ).
thf(799,plain,
$false,
inference(e,[status(thm)],[138,142,376,243,6,124,13,17,27,159,7,140,3,112,18,231,8,183,4,122,5,202,185,24,436,25,14,125,28,407,370,127]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SEV293^5 : TPTP v8.2.0. Bugfixed v6.2.0.
% 0.08/0.13 % Command : run_Leo-III %s %d THM
% 0.12/0.34 % Computer : n026.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 21 18:37:55 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.96/0.87 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.17/0.98 % [INFO] Parsing done (115ms).
% 1.29/0.99 % [INFO] Running in sequential loop mode.
% 1.62/1.23 % [INFO] eprover registered as external prover.
% 1.62/1.23 % [INFO] Scanning for conjecture ...
% 1.88/1.30 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.88/1.32 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.88/1.32 % [INFO] Problem is higher-order (TPTP THF).
% 1.88/1.32 % [INFO] Type checking passed.
% 1.88/1.32 % [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 ...
% 8.72/2.92 % External prover 'e' found a proof!
% 8.72/2.92 % [INFO] Killing All external provers ...
% 8.72/2.92 % Time passed: 2374ms (effective reasoning time: 1925ms)
% 8.72/2.92 % 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)>
% 8.72/2.92 % Axioms used in derivation (0):
% 8.72/2.92 % No. of inferences in proof: 75
% 8.72/2.92 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2374 ms resp. 1925 ms w/o parsing
% 8.74/2.98 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 8.74/2.98 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------