TSTP Solution File: LCL526+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : LCL526+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n024.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 : Sun May 5 07:46:47 EDT 2024
% Result : Theorem 10.41s 1.82s
% Output : Refutation 10.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 21
% Syntax : Number of formulae : 87 ( 43 unt; 0 def)
% Number of atoms : 152 ( 25 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 109 ( 44 ~; 35 |; 6 &)
% ( 7 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 11 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 98 ( 94 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f70179,plain,
$false,
inference(subsumption_resolution,[],[f70171,f40386]) ).
fof(f40386,plain,
! [X0,X1] : is_a_theorem(implies(strict_equiv(X0,X1),strict_implies(X0,X1))),
inference(superposition,[],[f229,f216]) ).
fof(f216,plain,
! [X0,X1] : strict_equiv(X0,X1) = and(strict_implies(X0,X1),strict_implies(X1,X0)),
inference(subsumption_resolution,[],[f189,f179]) ).
fof(f179,plain,
op_strict_equiv,
inference(cnf_transformation,[],[f87]) ).
fof(f87,axiom,
op_strict_equiv,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_op_strict_equiv) ).
fof(f189,plain,
! [X0,X1] :
( strict_equiv(X0,X1) = and(strict_implies(X0,X1),strict_implies(X1,X0))
| ~ op_strict_equiv ),
inference(cnf_transformation,[],[f131]) ).
fof(f131,plain,
( ! [X0,X1] : strict_equiv(X0,X1) = and(strict_implies(X0,X1),strict_implies(X1,X0))
| ~ op_strict_equiv ),
inference(ennf_transformation,[],[f76]) ).
fof(f76,axiom,
( op_strict_equiv
=> ! [X0,X1] : strict_equiv(X0,X1) = and(strict_implies(X0,X1),strict_implies(X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_strict_equiv) ).
fof(f229,plain,
! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)),
inference(subsumption_resolution,[],[f202,f171]) ).
fof(f171,plain,
and_1,
inference(cnf_transformation,[],[f40]) ).
fof(f40,axiom,
and_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_and_1) ).
fof(f202,plain,
! [X0,X1] :
( is_a_theorem(implies(and(X0,X1),X0))
| ~ and_1 ),
inference(cnf_transformation,[],[f143]) ).
fof(f143,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0))
| ~ and_1 ),
inference(ennf_transformation,[],[f118]) ).
fof(f118,plain,
( and_1
=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
inference(unused_predicate_definition_removal,[],[f7]) ).
fof(f7,axiom,
( and_1
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_1) ).
fof(f70171,plain,
~ is_a_theorem(implies(strict_equiv(sK0,sK1),strict_implies(sK0,sK1))),
inference(unit_resulting_resolution,[],[f221,f69101,f239]) ).
fof(f239,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(X1)
| ~ is_a_theorem(X0) ),
inference(subsumption_resolution,[],[f211,f176]) ).
fof(f176,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_modus_ponens) ).
fof(f211,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| ~ modus_ponens ),
inference(cnf_transformation,[],[f153]) ).
fof(f153,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) )
| ~ modus_ponens ),
inference(flattening,[],[f152]) ).
fof(f152,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) )
| ~ modus_ponens ),
inference(ennf_transformation,[],[f124]) ).
fof(f124,plain,
( modus_ponens
=> ! [X0,X1] :
( ( is_a_theorem(implies(X0,X1))
& is_a_theorem(X0) )
=> is_a_theorem(X1) ) ),
inference(unused_predicate_definition_removal,[],[f1]) ).
fof(f1,axiom,
( modus_ponens
<=> ! [X0,X1] :
( ( is_a_theorem(implies(X0,X1))
& is_a_theorem(X0) )
=> is_a_theorem(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',modus_ponens) ).
fof(f69101,plain,
~ is_a_theorem(strict_implies(sK0,sK1)),
inference(unit_resulting_resolution,[],[f314,f68541,f239]) ).
fof(f68541,plain,
~ is_a_theorem(implies(sK0,sK1)),
inference(unit_resulting_resolution,[],[f294,f53422,f239]) ).
fof(f53422,plain,
is_a_theorem(implies(implies(sK0,sK1),equiv(sK1,sK0))),
inference(superposition,[],[f40871,f219]) ).
fof(f219,plain,
! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)),
inference(subsumption_resolution,[],[f192,f183]) ).
fof(f183,plain,
op_equiv,
inference(cnf_transformation,[],[f86]) ).
fof(f86,axiom,
op_equiv,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_op_equiv) ).
fof(f192,plain,
! [X0,X1] :
( equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
| ~ op_equiv ),
inference(cnf_transformation,[],[f134]) ).
fof(f134,plain,
( ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
| ~ op_equiv ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,axiom,
( op_equiv
=> ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_equiv) ).
fof(f40871,plain,
! [X0] : is_a_theorem(implies(X0,and(implies(sK1,sK0),X0))),
inference(unit_resulting_resolution,[],[f40671,f521]) ).
fof(f521,plain,
! [X0,X1] :
( ~ is_a_theorem(X1)
| is_a_theorem(implies(X0,and(X1,X0))) ),
inference(resolution,[],[f239,f230]) ).
fof(f230,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))),
inference(subsumption_resolution,[],[f203,f169]) ).
fof(f169,plain,
and_3,
inference(cnf_transformation,[],[f42]) ).
fof(f42,axiom,
and_3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_and_3) ).
fof(f203,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| ~ and_3 ),
inference(cnf_transformation,[],[f144]) ).
fof(f144,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| ~ and_3 ),
inference(ennf_transformation,[],[f116]) ).
fof(f116,plain,
( and_3
=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
inference(unused_predicate_definition_removal,[],[f9]) ).
fof(f9,axiom,
( and_3
<=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_3) ).
fof(f40671,plain,
is_a_theorem(implies(sK1,sK0)),
inference(unit_resulting_resolution,[],[f314,f40415,f239]) ).
fof(f40415,plain,
is_a_theorem(strict_implies(sK1,sK0)),
inference(unit_resulting_resolution,[],[f221,f40385,f239]) ).
fof(f40385,plain,
! [X0,X1] : is_a_theorem(implies(strict_equiv(X0,X1),strict_implies(X1,X0))),
inference(superposition,[],[f228,f216]) ).
fof(f228,plain,
! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1)),
inference(subsumption_resolution,[],[f201,f170]) ).
fof(f170,plain,
and_2,
inference(cnf_transformation,[],[f41]) ).
fof(f41,axiom,
and_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_and_2) ).
fof(f201,plain,
! [X0,X1] :
( is_a_theorem(implies(and(X0,X1),X1))
| ~ and_2 ),
inference(cnf_transformation,[],[f142]) ).
fof(f142,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1))
| ~ and_2 ),
inference(ennf_transformation,[],[f117]) ).
fof(f117,plain,
( and_2
=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1)) ),
inference(unused_predicate_definition_removal,[],[f8]) ).
fof(f8,axiom,
( and_2
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_2) ).
fof(f294,plain,
~ is_a_theorem(equiv(sK1,sK0)),
inference(unit_resulting_resolution,[],[f220,f238]) ).
fof(f238,plain,
! [X0,X1] :
( ~ is_a_theorem(equiv(X0,X1))
| X0 = X1 ),
inference(subsumption_resolution,[],[f210,f163]) ).
fof(f163,plain,
substitution_of_equivalents,
inference(cnf_transformation,[],[f49]) ).
fof(f49,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',substitution_of_equivalents) ).
fof(f210,plain,
! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1))
| ~ substitution_of_equivalents ),
inference(cnf_transformation,[],[f151]) ).
fof(f151,plain,
( ! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1)) )
| ~ substitution_of_equivalents ),
inference(ennf_transformation,[],[f123]) ).
fof(f123,plain,
( substitution_of_equivalents
=> ! [X0,X1] :
( is_a_theorem(equiv(X0,X1))
=> X0 = X1 ) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f2,axiom,
( substitution_of_equivalents
<=> ! [X0,X1] :
( is_a_theorem(equiv(X0,X1))
=> X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',substitution_of_equivalents) ).
fof(f220,plain,
sK0 != sK1,
inference(subsumption_resolution,[],[f194,f158]) ).
fof(f158,plain,
~ substitution_strict_equiv,
inference(cnf_transformation,[],[f90]) ).
fof(f90,plain,
~ substitution_strict_equiv,
inference(flattening,[],[f89]) ).
fof(f89,negated_conjecture,
~ substitution_strict_equiv,
inference(negated_conjecture,[],[f88]) ).
fof(f88,conjecture,
substitution_strict_equiv,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_substitution_strict_equiv) ).
fof(f194,plain,
( substitution_strict_equiv
| sK0 != sK1 ),
inference(cnf_transformation,[],[f157]) ).
fof(f157,plain,
( substitution_strict_equiv
| ( sK0 != sK1
& is_a_theorem(strict_equiv(sK0,sK1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f135,f156]) ).
fof(f156,plain,
( ? [X0,X1] :
( X0 != X1
& is_a_theorem(strict_equiv(X0,X1)) )
=> ( sK0 != sK1
& is_a_theorem(strict_equiv(sK0,sK1)) ) ),
introduced(choice_axiom,[]) ).
fof(f135,plain,
( substitution_strict_equiv
| ? [X0,X1] :
( X0 != X1
& is_a_theorem(strict_equiv(X0,X1)) ) ),
inference(ennf_transformation,[],[f108]) ).
fof(f108,plain,
( ! [X0,X1] :
( is_a_theorem(strict_equiv(X0,X1))
=> X0 = X1 )
=> substitution_strict_equiv ),
inference(unused_predicate_definition_removal,[],[f53]) ).
fof(f53,axiom,
( substitution_strict_equiv
<=> ! [X0,X1] :
( is_a_theorem(strict_equiv(X0,X1))
=> X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',substitution_strict_equiv) ).
fof(f314,plain,
! [X0,X1] : is_a_theorem(implies(strict_implies(X0,X1),implies(X0,X1))),
inference(superposition,[],[f222,f214]) ).
fof(f214,plain,
! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1)),
inference(subsumption_resolution,[],[f187,f180]) ).
fof(f180,plain,
op_strict_implies,
inference(cnf_transformation,[],[f85]) ).
fof(f85,axiom,
op_strict_implies,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_op_strict_implies) ).
fof(f187,plain,
! [X0,X1] :
( strict_implies(X0,X1) = necessarily(implies(X0,X1))
| ~ op_strict_implies ),
inference(cnf_transformation,[],[f129]) ).
fof(f129,plain,
( ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1))
| ~ op_strict_implies ),
inference(ennf_transformation,[],[f75]) ).
fof(f75,axiom,
( op_strict_implies
=> ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_strict_implies) ).
fof(f222,plain,
! [X0] : is_a_theorem(implies(necessarily(X0),X0)),
inference(subsumption_resolution,[],[f195,f160]) ).
fof(f160,plain,
axiom_M,
inference(cnf_transformation,[],[f80]) ).
fof(f80,axiom,
axiom_M,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',km5_axiom_M) ).
fof(f195,plain,
! [X0] :
( is_a_theorem(implies(necessarily(X0),X0))
| ~ axiom_M ),
inference(cnf_transformation,[],[f136]) ).
fof(f136,plain,
( ! [X0] : is_a_theorem(implies(necessarily(X0),X0))
| ~ axiom_M ),
inference(ennf_transformation,[],[f106]) ).
fof(f106,plain,
( axiom_M
=> ! [X0] : is_a_theorem(implies(necessarily(X0),X0)) ),
inference(unused_predicate_definition_removal,[],[f55]) ).
fof(f55,axiom,
( axiom_M
<=> ! [X0] : is_a_theorem(implies(necessarily(X0),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_M) ).
fof(f221,plain,
is_a_theorem(strict_equiv(sK0,sK1)),
inference(subsumption_resolution,[],[f193,f158]) ).
fof(f193,plain,
( substitution_strict_equiv
| is_a_theorem(strict_equiv(sK0,sK1)) ),
inference(cnf_transformation,[],[f157]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : LCL526+1 : TPTP v8.1.2. Released v3.3.0.
% 0.09/0.12 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.12/0.33 % Computer : n024.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 May 3 13:37:05 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.12/0.33 % (22632)Running in auto input_syntax mode. Trying TPTP
% 0.12/0.35 % (22635)WARNING: value z3 for option sas not known
% 0.12/0.35 % (22639)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.12/0.35 % (22637)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.12/0.35 % (22638)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.12/0.35 % (22633)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.12/0.35 % (22636)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.12/0.35 % (22634)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.12/0.35 % (22635)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.12/0.35 TRYING [1]
% 0.12/0.35 TRYING [2]
% 0.12/0.36 TRYING [1]
% 0.12/0.36 TRYING [3]
% 0.12/0.36 TRYING [2]
% 0.12/0.37 TRYING [3]
% 0.12/0.37 TRYING [4]
% 0.12/0.38 TRYING [1]
% 0.12/0.38 TRYING [2]
% 0.12/0.39 TRYING [3]
% 0.17/0.41 TRYING [4]
% 0.17/0.44 TRYING [4]
% 0.17/0.44 TRYING [5]
% 0.17/0.48 TRYING [5]
% 2.05/0.62 TRYING [5]
% 2.23/0.67 TRYING [6]
% 2.78/0.72 TRYING [6]
% 5.91/1.18 TRYING [7]
% 6.84/1.33 TRYING [7]
% 8.93/1.61 TRYING [6]
% 10.13/1.81 % (22639)First to succeed.
% 10.41/1.82 % (22639)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-22632"
% 10.41/1.82 % (22639)Refutation found. Thanks to Tanya!
% 10.41/1.82 % SZS status Theorem for theBenchmark
% 10.41/1.82 % SZS output start Proof for theBenchmark
% See solution above
% 10.41/1.82 % (22639)------------------------------
% 10.41/1.82 % (22639)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 10.41/1.82 % (22639)Termination reason: Refutation
% 10.41/1.82
% 10.41/1.82 % (22639)Memory used [KB]: 24541
% 10.41/1.82 % (22639)Time elapsed: 1.463 s
% 10.41/1.82 % (22639)Instructions burned: 3044 (million)
% 10.41/1.82 % (22632)Success in time 1.477 s
%------------------------------------------------------------------------------