TSTP Solution File: SEV396^5 by Leo-III---1.7.15
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.15
% Problem : SEV396^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n021.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 15:58:55 EDT 2024
% Result : Theorem 5.91s 2.40s
% Output : Refutation 5.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 1
% Syntax : Number of formulae : 57 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 274 ( 54 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 397 ( 74 ~; 83 |; 32 &; 198 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 7 con; 0-2 aty)
% Number of variables : 39 ( 23 ^ 16 !; 0 ?; 39 :)
% Comments :
%------------------------------------------------------------------------------
thf(cR_type,type,
cR: $i > $o ).
thf(cS_type,type,
cS: $i > $o ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $i ).
thf(sk6_type,type,
sk6: $i ).
thf(sk8_type,type,
sk8: $i ).
thf(1,conjecture,
( ( ! [A: $i] :
( ( cR @ A )
=> ( cS @ A ) ) )
= ( ( ^ [A: $i] :
( ( cR @ A )
& ( cS @ A ) ) )
= cR ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM31_pme) ).
thf(2,negated_conjecture,
( ( ! [A: $i] :
( ( cR @ A )
=> ( cS @ A ) ) )
!= ( ( ^ [A: $i] :
( ( cR @ A )
& ( cS @ A ) ) )
= cR ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [A: $i] :
( ( cR @ A )
=> ( cS @ A ) ) )
!= ( ( ^ [A: $i] :
( ( cR @ A )
& ( cS @ A ) ) )
= cR ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [A: $i] :
( ( cR @ A )
=> ( cS @ A ) ) )
!= ( ( ^ [A: $i] :
( ( cR @ A )
& ( cS @ A ) ) )
= cR ) ),
inference(lifteq,[status(thm)],[3]) ).
thf(5,plain,
( ~ ! [A: $i] :
( ( cR @ A )
=> ( cS @ A ) )
| ( ( ^ [A: $i] :
( ( cR @ A )
& ( cS @ A ) ) )
!= cR ) ),
inference(bool_ext,[status(thm)],[4]) ).
thf(7,plain,
( ( ( ^ [A: $i] :
( ( cR @ A )
& ( cS @ A ) ) )
!= cR )
| ~ ! [A: $i] :
( ( cR @ A )
=> ( cS @ A ) ) ),
inference(lifteq,[status(thm)],[5]) ).
thf(10,plain,
( ( cR @ sk1 )
| ( ( ^ [A: $i] :
( ( cR @ A )
& ( cS @ A ) ) )
!= cR ) ),
inference(cnf,[status(esa)],[7]) ).
thf(13,plain,
( ( ( ( cR @ sk3 )
& ( cS @ sk3 ) )
!= ( cR @ sk3 ) )
| ( cR @ sk1 ) ),
inference(func_ext,[status(esa)],[10]) ).
thf(46,plain,
( ( cR @ sk1 )
| ( ( cR @ sk3 )
& ( cS @ sk3 ) )
| ( cR @ sk3 ) ),
inference(bool_ext,[status(thm)],[13]) ).
thf(50,plain,
( ( cR @ sk3 )
| ( cR @ sk3 )
| ( cR @ sk1 ) ),
inference(cnf,[status(esa)],[46]) ).
thf(51,plain,
( ( cR @ sk3 )
| ( cR @ sk1 ) ),
inference(simp,[status(thm)],[50]) ).
thf(6,plain,
( ! [A: $i] :
( ( cR @ A )
=> ( cS @ A ) )
| ( ( ^ [A: $i] :
( ( cR @ A )
& ( cS @ A ) ) )
= cR ) ),
inference(bool_ext,[status(thm)],[4]) ).
thf(8,plain,
( ( ( ^ [A: $i] :
( ( cR @ A )
& ( cS @ A ) ) )
= cR )
| ! [A: $i] :
( ( cR @ A )
=> ( cS @ A ) ) ),
inference(lifteq,[status(thm)],[6]) ).
thf(11,plain,
! [A: $i] :
( ~ ( cR @ A )
| ( cS @ A )
| ( ( ^ [B: $i] :
( ( cR @ B )
& ( cS @ B ) ) )
= cR ) ),
inference(cnf,[status(esa)],[8]) ).
thf(56,plain,
! [A: $i] :
( ( cR @ sk1 )
| ( cS @ A )
| ( ( ^ [B: $i] :
( ( cR @ B )
& ( cS @ B ) ) )
= cR )
| ( ( cR @ sk3 )
!= ( cR @ A ) ) ),
inference(paramod_ordered,[status(thm)],[51,11]) ).
thf(57,plain,
( ( cR @ sk1 )
| ( cS @ sk3 )
| ( ( ^ [A: $i] :
( ( cR @ A )
& ( cS @ A ) ) )
= cR ) ),
inference(pattern_uni,[status(thm)],[56:[bind(A,$thf( sk3 ))]]) ).
thf(99,plain,
( ( cR @ sk1 )
| ( cS @ sk3 )
| ( ( ^ [A: $i] :
( ( cR @ A )
& ( cS @ A ) ) )
!= ( ^ [A: $i] :
( ( cR @ A )
& ( cS @ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[57,10]) ).
thf(100,plain,
( ( cR @ sk1 )
| ( cS @ sk3 ) ),
inference(pattern_uni,[status(thm)],[99:[]]) ).
thf(112,plain,
( ( cR @ sk1 )
| ( ( cS @ sk3 )
!= ( cS @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[100,13]) ).
thf(113,plain,
cR @ sk1,
inference(pattern_uni,[status(thm)],[112:[]]) ).
thf(143,plain,
! [A: $i] :
( ( cS @ A )
| ( ( ^ [B: $i] :
( ( cR @ B )
& ( cS @ B ) ) )
= cR )
| ( ( cR @ sk1 )
!= ( cR @ A ) ) ),
inference(paramod_ordered,[status(thm)],[113,11]) ).
thf(144,plain,
( ( cS @ sk1 )
| ( ( ^ [A: $i] :
( ( cR @ A )
& ( cS @ A ) ) )
= cR ) ),
inference(pattern_uni,[status(thm)],[143:[bind(A,$thf( sk1 ))]]) ).
thf(166,plain,
( ( cS @ sk1 )
| ~ ! [A: $i] :
( ( cR @ A )
=> ( cS @ A ) )
| ( ( ^ [A: $i] :
( ( cR @ A )
& ( cS @ A ) ) )
!= ( ^ [A: $i] :
( ( cR @ A )
& ( cS @ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[144,4]) ).
thf(167,plain,
( ( cS @ sk1 )
| ~ ! [A: $i] :
( ( cR @ A )
=> ( cS @ A ) ) ),
inference(pattern_uni,[status(thm)],[166:[]]) ).
thf(169,plain,
( ( cR @ sk6 )
| ( cS @ sk1 ) ),
inference(cnf,[status(esa)],[167]) ).
thf(9,plain,
( ~ ( cS @ sk1 )
| ( ( ^ [A: $i] :
( ( cR @ A )
& ( cS @ A ) ) )
!= cR ) ),
inference(cnf,[status(esa)],[7]) ).
thf(12,plain,
( ( ( ( cR @ sk2 )
& ( cS @ sk2 ) )
!= ( cR @ sk2 ) )
| ~ ( cS @ sk1 ) ),
inference(func_ext,[status(esa)],[9]) ).
thf(15,plain,
( ~ ( cS @ sk1 )
| ( ( cR @ sk2 )
& ( cS @ sk2 ) )
| ( cR @ sk2 ) ),
inference(bool_ext,[status(thm)],[12]) ).
thf(19,plain,
( ( cR @ sk2 )
| ( cR @ sk2 )
| ~ ( cS @ sk1 ) ),
inference(cnf,[status(esa)],[15]) ).
thf(20,plain,
( ( cR @ sk2 )
| ~ ( cS @ sk1 ) ),
inference(simp,[status(thm)],[19]) ).
thf(177,plain,
( ( cR @ sk6 )
| ( cR @ sk2 )
| ( ( cS @ sk1 )
!= ( cS @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[169,20]) ).
thf(178,plain,
( ( cR @ sk6 )
| ( cR @ sk2 ) ),
inference(pattern_uni,[status(thm)],[177:[]]) ).
thf(195,plain,
( ( cR @ sk2 )
| ( ( cR @ sk6 )
!= ( cR @ sk2 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[178]) ).
thf(202,plain,
( ( cR @ sk2 )
| ( sk6 != sk2 ) ),
inference(simp,[status(thm)],[195]) ).
thf(184,plain,
( ( cR @ sk6 )
| ( ( ( cR @ sk2 )
& ( cS @ sk2 ) )
!= ( cR @ sk2 ) )
| ( ( cS @ sk1 )
!= ( cS @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[169,12]) ).
thf(185,plain,
( ( cR @ sk6 )
| ( ( ( cR @ sk2 )
& ( cS @ sk2 ) )
!= ( cR @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[184:[]]) ).
thf(201,plain,
( ( cR @ sk2 )
| ( ( cR @ sk6 )
!= ( cR @ sk2 ) ) ),
inference(simp,[status(thm)],[195]) ).
thf(192,plain,
! [A: $i] :
( ( cR @ sk2 )
| ( cS @ A )
| ( ( ^ [B: $i] :
( ( cR @ B )
& ( cS @ B ) ) )
= cR )
| ( ( cR @ sk6 )
!= ( cR @ A ) ) ),
inference(paramod_ordered,[status(thm)],[178,11]) ).
thf(193,plain,
( ( cR @ sk2 )
| ( cS @ sk6 )
| ( ( ^ [A: $i] :
( ( cR @ A )
& ( cS @ A ) ) )
= cR ) ),
inference(pattern_uni,[status(thm)],[192:[bind(A,$thf( sk6 ))]]) ).
thf(181,plain,
( ( cR @ sk6 )
| ( ( ^ [A: $i] :
( ( cR @ A )
& ( cS @ A ) ) )
!= cR )
| ( ( cS @ sk1 )
!= ( cS @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[169,9]) ).
thf(182,plain,
( ( cR @ sk6 )
| ( ( ^ [A: $i] :
( ( cR @ A )
& ( cS @ A ) ) )
!= cR ) ),
inference(pattern_uni,[status(thm)],[181:[]]) ).
thf(14,plain,
( ~ ( cS @ sk1 )
| ~ ( ( cR @ sk2 )
& ( cS @ sk2 ) )
| ~ ( cR @ sk2 ) ),
inference(bool_ext,[status(thm)],[12]) ).
thf(16,plain,
( ~ ( cR @ sk2 )
| ~ ( cR @ sk2 )
| ~ ( cS @ sk2 )
| ~ ( cS @ sk1 ) ),
inference(cnf,[status(esa)],[14]) ).
thf(17,plain,
( ~ ( cR @ sk2 )
| ~ ( cS @ sk2 )
| ~ ( cS @ sk1 ) ),
inference(simp,[status(thm)],[16]) ).
thf(21,plain,
( ~ ( cR @ sk2 )
| ~ ( cS @ sk1 )
| ( ( cS @ sk2 )
!= ( cS @ sk1 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[17]) ).
thf(22,plain,
( ~ ( cR @ sk2 )
| ~ ( cS @ sk1 )
| ( ( cS @ sk2 )
!= ( cS @ sk1 ) ) ),
inference(simp,[status(thm)],[21]) ).
thf(141,plain,
( ~ ( cS @ sk1 )
| ( ( cS @ sk2 )
!= ( cS @ sk1 ) )
| ( ( cR @ sk2 )
!= ( cR @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[113,22]) ).
thf(149,plain,
( ~ ( cS @ sk1 )
| ( sk2 != sk1 )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[141]) ).
thf(152,plain,
( ~ ( cS @ sk1 )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[149]) ).
thf(179,plain,
( ( cR @ sk6 )
| ( sk2 != sk1 )
| ( ( cS @ sk1 )
!= ( cS @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[169,152]) ).
thf(180,plain,
( ( cR @ sk6 )
| ( sk2 != sk1 ) ),
inference(pattern_uni,[status(thm)],[179:[]]) ).
thf(281,plain,
( ( ( ( cR @ sk8 )
& ( cS @ sk8 ) )
!= ( cR @ sk8 ) )
| ( cR @ sk6 ) ),
inference(func_ext,[status(esa)],[182]) ).
thf(235,plain,
( ( sk6 != sk2 )
| ~ ( cS @ sk2 )
| ~ ( cS @ sk1 )
| ( ( cR @ sk2 )
!= ( cR @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[202,17]) ).
thf(236,plain,
( ( sk6 != sk2 )
| ~ ( cS @ sk2 )
| ~ ( cS @ sk1 ) ),
inference(pattern_uni,[status(thm)],[235:[]]) ).
thf(36,plain,
! [B: $i,A: $i] :
( ( ( ( cR @ B )
& ( cS @ B ) )
= ( cR @ B ) )
| ~ ( cR @ A )
| ( cS @ A ) ),
inference(func_ext,[status(esa)],[11]) ).
thf(168,plain,
( ~ ( cS @ sk6 )
| ( cS @ sk1 ) ),
inference(cnf,[status(esa)],[167]) ).
thf(430,plain,
$false,
inference(e,[status(thm)],[202,185,201,193,113,3,182,11,4,178,20,152,9,169,180,17,22,281,12,144,236,36,168]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SEV396^5 : TPTP v8.2.0. Released v4.0.0.
% 0.04/0.12 % Command : run_Leo-III %s %d THM
% 0.12/0.33 % Computer : n021.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 21 18:37:10 EDT 2024
% 0.12/0.34 % CPUTime :
% 1.07/0.93 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.27/1.06 % [INFO] Parsing done (128ms).
% 1.27/1.07 % [INFO] Running in sequential loop mode.
% 1.64/1.33 % [INFO] eprover registered as external prover.
% 1.84/1.33 % [INFO] Scanning for conjecture ...
% 1.84/1.39 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.02/1.41 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.02/1.41 % [INFO] Problem is higher-order (TPTP THF).
% 2.02/1.41 % [INFO] Type checking passed.
% 2.02/1.41 % [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 ...
% 5.91/2.39 % External prover 'e' found a proof!
% 5.91/2.40 % [INFO] Killing All external provers ...
% 5.91/2.40 % Time passed: 1867ms (effective reasoning time: 1316ms)
% 5.91/2.40 % 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)>
% 5.91/2.40 % Axioms used in derivation (0):
% 5.91/2.40 % No. of inferences in proof: 57
% 5.91/2.40 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1867 ms resp. 1316 ms w/o parsing
% 5.97/2.43 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.97/2.43 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------