TSTP Solution File: LCL539+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : LCL539+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 : n022.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 Apr 30 13:44:07 EDT 2024
% Result : Theorem 6.98s 1.34s
% Output : Refutation 6.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 19
% Syntax : Number of formulae : 79 ( 39 unt; 0 def)
% Number of atoms : 140 ( 21 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 103 ( 42 ~; 32 |; 6 &)
% ( 7 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 10 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 87 ( 83 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f78529,plain,
$false,
inference(subsumption_resolution,[],[f78470,f45234]) ).
fof(f45234,plain,
! [X0,X1] : is_a_theorem(implies(strict_equiv(X0,X1),strict_implies(X1,X0))),
inference(superposition,[],[f235,f221]) ).
fof(f221,plain,
! [X0,X1] : strict_equiv(X0,X1) = and(strict_implies(X0,X1),strict_implies(X1,X0)),
inference(subsumption_resolution,[],[f193,f182]) ).
fof(f182,plain,
op_strict_equiv,
inference(cnf_transformation,[],[f88]) ).
fof(f88,axiom,
op_strict_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_op_strict_equiv) ).
fof(f193,plain,
! [X0,X1] :
( strict_equiv(X0,X1) = and(strict_implies(X0,X1),strict_implies(X1,X0))
| ~ op_strict_equiv ),
inference(cnf_transformation,[],[f133]) ).
fof(f133,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/sandbox/benchmark/theBenchmark.p',op_strict_equiv) ).
fof(f235,plain,
! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1)),
inference(subsumption_resolution,[],[f207,f174]) ).
fof(f174,plain,
and_2,
inference(cnf_transformation,[],[f41]) ).
fof(f41,axiom,
and_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_and_2) ).
fof(f207,plain,
! [X0,X1] :
( is_a_theorem(implies(and(X0,X1),X1))
| ~ and_2 ),
inference(cnf_transformation,[],[f146]) ).
fof(f146,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1))
| ~ and_2 ),
inference(ennf_transformation,[],[f119]) ).
fof(f119,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/sandbox/benchmark/theBenchmark.p',and_2) ).
fof(f78470,plain,
~ is_a_theorem(implies(strict_equiv(sK0,sK1),strict_implies(sK1,sK0))),
inference(unit_resulting_resolution,[],[f226,f77201,f245]) ).
fof(f245,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(X1)
| ~ is_a_theorem(X0) ),
inference(subsumption_resolution,[],[f216,f180]) ).
fof(f180,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_modus_ponens) ).
fof(f216,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| ~ modus_ponens ),
inference(cnf_transformation,[],[f156]) ).
fof(f156,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) )
| ~ modus_ponens ),
inference(flattening,[],[f155]) ).
fof(f155,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) )
| ~ modus_ponens ),
inference(ennf_transformation,[],[f126]) ).
fof(f126,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/sandbox/benchmark/theBenchmark.p',modus_ponens) ).
fof(f77201,plain,
~ is_a_theorem(strict_implies(sK1,sK0)),
inference(unit_resulting_resolution,[],[f330,f76567,f245]) ).
fof(f76567,plain,
~ is_a_theorem(implies(sK1,sK0)),
inference(unit_resulting_resolution,[],[f52453,f243,f245]) ).
fof(f243,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))),
inference(subsumption_resolution,[],[f214,f168]) ).
fof(f168,plain,
equivalence_3,
inference(cnf_transformation,[],[f48]) ).
fof(f48,axiom,
equivalence_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_equivalence_3) ).
fof(f214,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1))))
| ~ equivalence_3 ),
inference(cnf_transformation,[],[f153]) ).
fof(f153,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1))))
| ~ equivalence_3 ),
inference(ennf_transformation,[],[f112]) ).
fof(f112,plain,
( equivalence_3
=> ! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))) ),
inference(unused_predicate_definition_removal,[],[f15]) ).
fof(f15,axiom,
( equivalence_3
<=> ! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equivalence_3) ).
fof(f52453,plain,
~ is_a_theorem(implies(implies(sK0,sK1),equiv(sK1,sK0))),
inference(unit_resulting_resolution,[],[f306,f52356,f245]) ).
fof(f52356,plain,
is_a_theorem(implies(sK0,sK1)),
inference(unit_resulting_resolution,[],[f330,f52112,f245]) ).
fof(f52112,plain,
is_a_theorem(strict_implies(sK0,sK1)),
inference(unit_resulting_resolution,[],[f226,f45233,f245]) ).
fof(f45233,plain,
! [X0,X1] : is_a_theorem(implies(strict_equiv(X0,X1),strict_implies(X0,X1))),
inference(superposition,[],[f234,f221]) ).
fof(f234,plain,
! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)),
inference(subsumption_resolution,[],[f206,f175]) ).
fof(f175,plain,
and_1,
inference(cnf_transformation,[],[f40]) ).
fof(f40,axiom,
and_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_and_1) ).
fof(f206,plain,
! [X0,X1] :
( is_a_theorem(implies(and(X0,X1),X0))
| ~ and_1 ),
inference(cnf_transformation,[],[f145]) ).
fof(f145,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0))
| ~ and_1 ),
inference(ennf_transformation,[],[f120]) ).
fof(f120,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/sandbox/benchmark/theBenchmark.p',and_1) ).
fof(f306,plain,
~ is_a_theorem(equiv(sK1,sK0)),
inference(unit_resulting_resolution,[],[f225,f244]) ).
fof(f244,plain,
! [X0,X1] :
( ~ is_a_theorem(equiv(X0,X1))
| X0 = X1 ),
inference(subsumption_resolution,[],[f215,f167]) ).
fof(f167,plain,
substitution_of_equivalents,
inference(cnf_transformation,[],[f49]) ).
fof(f49,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',substitution_of_equivalents) ).
fof(f215,plain,
! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1))
| ~ substitution_of_equivalents ),
inference(cnf_transformation,[],[f154]) ).
fof(f154,plain,
( ! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1)) )
| ~ substitution_of_equivalents ),
inference(ennf_transformation,[],[f125]) ).
fof(f125,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/sandbox/benchmark/theBenchmark.p',substitution_of_equivalents) ).
fof(f225,plain,
sK0 != sK1,
inference(subsumption_resolution,[],[f198,f161]) ).
fof(f161,plain,
~ substitution_strict_equiv,
inference(cnf_transformation,[],[f91]) ).
fof(f91,plain,
~ substitution_strict_equiv,
inference(flattening,[],[f90]) ).
fof(f90,negated_conjecture,
~ substitution_strict_equiv,
inference(negated_conjecture,[],[f89]) ).
fof(f89,conjecture,
substitution_strict_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_substitution_strict_equiv) ).
fof(f198,plain,
( substitution_strict_equiv
| sK0 != sK1 ),
inference(cnf_transformation,[],[f160]) ).
fof(f160,plain,
( substitution_strict_equiv
| ( sK0 != sK1
& is_a_theorem(strict_equiv(sK0,sK1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f137,f159]) ).
fof(f159,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(f137,plain,
( substitution_strict_equiv
| ? [X0,X1] :
( X0 != X1
& is_a_theorem(strict_equiv(X0,X1)) ) ),
inference(ennf_transformation,[],[f110]) ).
fof(f110,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/sandbox/benchmark/theBenchmark.p',substitution_strict_equiv) ).
fof(f330,plain,
! [X0,X1] : is_a_theorem(implies(strict_implies(X0,X1),implies(X0,X1))),
inference(superposition,[],[f227,f219]) ).
fof(f219,plain,
! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1)),
inference(subsumption_resolution,[],[f191,f184]) ).
fof(f184,plain,
op_strict_implies,
inference(cnf_transformation,[],[f86]) ).
fof(f86,axiom,
op_strict_implies,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_op_strict_implies) ).
fof(f191,plain,
! [X0,X1] :
( strict_implies(X0,X1) = necessarily(implies(X0,X1))
| ~ op_strict_implies ),
inference(cnf_transformation,[],[f131]) ).
fof(f131,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/sandbox/benchmark/theBenchmark.p',op_strict_implies) ).
fof(f227,plain,
! [X0] : is_a_theorem(implies(necessarily(X0),X0)),
inference(subsumption_resolution,[],[f199,f164]) ).
fof(f164,plain,
axiom_M,
inference(cnf_transformation,[],[f80]) ).
fof(f80,axiom,
axiom_M,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',km4b_axiom_M) ).
fof(f199,plain,
! [X0] :
( is_a_theorem(implies(necessarily(X0),X0))
| ~ axiom_M ),
inference(cnf_transformation,[],[f138]) ).
fof(f138,plain,
( ! [X0] : is_a_theorem(implies(necessarily(X0),X0))
| ~ axiom_M ),
inference(ennf_transformation,[],[f108]) ).
fof(f108,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/sandbox/benchmark/theBenchmark.p',axiom_M) ).
fof(f226,plain,
is_a_theorem(strict_equiv(sK0,sK1)),
inference(subsumption_resolution,[],[f197,f161]) ).
fof(f197,plain,
( substitution_strict_equiv
| is_a_theorem(strict_equiv(sK0,sK1)) ),
inference(cnf_transformation,[],[f160]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL539+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35 % Computer : n022.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 : Mon Apr 29 22:49:29 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (29682)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.37 % (29686)WARNING: value z3 for option sas not known
% 0.15/0.38 % (29687)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.38 % (29684)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.38 % (29688)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)
% 0.21/0.38 % (29686)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)
% 0.21/0.38 % (29689)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)
% 0.21/0.38 % (29690)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)
% 0.21/0.38 % (29685)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.38 TRYING [1]
% 0.21/0.38 TRYING [2]
% 0.21/0.39 TRYING [1]
% 0.21/0.39 TRYING [3]
% 0.21/0.39 TRYING [2]
% 0.21/0.41 TRYING [3]
% 0.21/0.41 TRYING [4]
% 0.21/0.42 TRYING [1]
% 0.21/0.42 TRYING [2]
% 0.21/0.42 TRYING [3]
% 0.21/0.45 TRYING [4]
% 0.21/0.48 TRYING [4]
% 0.21/0.48 TRYING [5]
% 0.21/0.51 TRYING [5]
% 1.40/0.62 TRYING [5]
% 2.00/0.65 TRYING [6]
% 2.00/0.67 TRYING [6]
% 4.47/1.00 TRYING [7]
% 4.47/1.03 TRYING [7]
% 6.19/1.25 TRYING [6]
% 6.48/1.33 % (29690)First to succeed.
% 6.98/1.34 % (29690)Refutation found. Thanks to Tanya!
% 6.98/1.34 % SZS status Theorem for theBenchmark
% 6.98/1.34 % SZS output start Proof for theBenchmark
% See solution above
% 6.98/1.34 % (29690)------------------------------
% 6.98/1.34 % (29690)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 6.98/1.34 % (29690)Termination reason: Refutation
% 6.98/1.34
% 6.98/1.34 % (29690)Memory used [KB]: 28031
% 6.98/1.34 % (29690)Time elapsed: 0.962 s
% 6.98/1.34 % (29690)Instructions burned: 3247 (million)
% 6.98/1.34 % (29690)------------------------------
% 6.98/1.34 % (29690)------------------------------
% 6.98/1.34 % (29682)Success in time 0.974 s
%------------------------------------------------------------------------------