TSTP Solution File: SWC207+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWC207+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n025.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 16:10:58 EDT 2024
% Result : Theorem 0.13s 0.41s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 10
% Syntax : Number of formulae : 50 ( 14 unt; 0 def)
% Number of atoms : 291 ( 106 equ)
% Maximal formula atoms : 22 ( 5 avg)
% Number of connectives : 338 ( 97 ~; 91 |; 129 &)
% ( 2 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 82 ( 46 !; 36 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1051,plain,
$false,
inference(resolution,[],[f1041,f998]) ).
fof(f998,plain,
~ neq(nil,nil),
inference(backward_demodulation,[],[f645,f994]) ).
fof(f994,plain,
nil = sK22,
inference(resolution,[],[f993,f402]) ).
fof(f402,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax17) ).
fof(f993,plain,
( ~ ssList(nil)
| nil = sK22 ),
inference(resolution,[],[f988,f386]) ).
fof(f386,plain,
ssList(sK22),
inference(cnf_transformation,[],[f260]) ).
fof(f260,plain,
( ( ( nil = sK22
& nil = sK23 )
| sP0(sK23,sK22) )
& ~ neq(sK20,nil)
& neq(sK21,nil)
& sK20 = sK22
& sK21 = sK23
& ssList(sK23)
& ssList(sK22)
& ssList(sK21)
& ssList(sK20) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK20,sK21,sK22,sK23])],[f224,f259,f258,f257,f256]) ).
fof(f256,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( nil = X2
& nil = X3 )
| sP0(X3,X2) )
& ~ neq(X0,nil)
& neq(X1,nil)
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) )
=> ( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( nil = X2
& nil = X3 )
| sP0(X3,X2) )
& ~ neq(sK20,nil)
& neq(X1,nil)
& sK20 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(sK20) ) ),
introduced(choice_axiom,[]) ).
fof(f257,plain,
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( nil = X2
& nil = X3 )
| sP0(X3,X2) )
& ~ neq(sK20,nil)
& neq(X1,nil)
& sK20 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
=> ( ? [X2] :
( ? [X3] :
( ( ( nil = X2
& nil = X3 )
| sP0(X3,X2) )
& ~ neq(sK20,nil)
& neq(sK21,nil)
& sK20 = X2
& sK21 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(sK21) ) ),
introduced(choice_axiom,[]) ).
fof(f258,plain,
( ? [X2] :
( ? [X3] :
( ( ( nil = X2
& nil = X3 )
| sP0(X3,X2) )
& ~ neq(sK20,nil)
& neq(sK21,nil)
& sK20 = X2
& sK21 = X3
& ssList(X3) )
& ssList(X2) )
=> ( ? [X3] :
( ( ( nil = sK22
& nil = X3 )
| sP0(X3,sK22) )
& ~ neq(sK20,nil)
& neq(sK21,nil)
& sK20 = sK22
& sK21 = X3
& ssList(X3) )
& ssList(sK22) ) ),
introduced(choice_axiom,[]) ).
fof(f259,plain,
( ? [X3] :
( ( ( nil = sK22
& nil = X3 )
| sP0(X3,sK22) )
& ~ neq(sK20,nil)
& neq(sK21,nil)
& sK20 = sK22
& sK21 = X3
& ssList(X3) )
=> ( ( ( nil = sK22
& nil = sK23 )
| sP0(sK23,sK22) )
& ~ neq(sK20,nil)
& neq(sK21,nil)
& sK20 = sK22
& sK21 = sK23
& ssList(sK23) ) ),
introduced(choice_axiom,[]) ).
fof(f224,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( nil = X2
& nil = X3 )
| sP0(X3,X2) )
& ~ neq(X0,nil)
& neq(X1,nil)
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(definition_folding,[],[f99,f223]) ).
fof(f223,plain,
! [X3,X2] :
( ? [X4] :
( ! [X5] :
( ~ leq(X4,X5)
| ~ memberP(X3,X5)
| X4 = X5
| ~ ssItem(X5) )
& memberP(X3,X4)
& cons(X4,nil) = X2
& ssItem(X4) )
| ~ sP0(X3,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f99,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( nil = X2
& nil = X3 )
| ? [X4] :
( ! [X5] :
( ~ leq(X4,X5)
| ~ memberP(X3,X5)
| X4 = X5
| ~ ssItem(X5) )
& memberP(X3,X4)
& cons(X4,nil) = X2
& ssItem(X4) ) )
& ~ neq(X0,nil)
& neq(X1,nil)
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f98]) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( nil = X2
& nil = X3 )
| ? [X4] :
( ! [X5] :
( ~ leq(X4,X5)
| ~ memberP(X3,X5)
| X4 = X5
| ~ ssItem(X5) )
& memberP(X3,X4)
& cons(X4,nil) = X2
& ssItem(X4) ) )
& ~ neq(X0,nil)
& neq(X1,nil)
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( nil != X2
| nil != X3 )
& ! [X4] :
( ssItem(X4)
=> ( ? [X5] :
( leq(X4,X5)
& memberP(X3,X5)
& X4 != X5
& ssItem(X5) )
| ~ memberP(X3,X4)
| cons(X4,nil) != X2 ) ) )
| neq(X0,nil)
| ~ neq(X1,nil)
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negated_conjecture,[],[f96]) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( nil != X2
| nil != X3 )
& ! [X4] :
( ssItem(X4)
=> ( ? [X5] :
( leq(X4,X5)
& memberP(X3,X5)
& X4 != X5
& ssItem(X5) )
| ~ memberP(X3,X4)
| cons(X4,nil) != X2 ) ) )
| neq(X0,nil)
| ~ neq(X1,nil)
| X0 != X2
| X1 != X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(f988,plain,
( ~ ssList(sK22)
| ~ ssList(nil)
| nil = sK22 ),
inference(resolution,[],[f582,f645]) ).
fof(f582,plain,
! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f361]) ).
fof(f361,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f198]) ).
fof(f198,plain,
! [X0] :
( ! [X1] :
( ( neq(X0,X1)
<=> X0 != X1 )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax15) ).
fof(f645,plain,
~ neq(sK22,nil),
inference(forward_demodulation,[],[f391,f389]) ).
fof(f389,plain,
sK20 = sK22,
inference(cnf_transformation,[],[f260]) ).
fof(f391,plain,
~ neq(sK20,nil),
inference(cnf_transformation,[],[f260]) ).
fof(f1041,plain,
neq(nil,nil),
inference(backward_demodulation,[],[f646,f1038]) ).
fof(f1038,plain,
nil = sK23,
inference(resolution,[],[f1035,f402]) ).
fof(f1035,plain,
( ~ ssList(nil)
| nil = sK23 ),
inference(duplicate_literal_removal,[],[f1034]) ).
fof(f1034,plain,
( nil = sK23
| ~ ssList(nil)
| nil = sK23 ),
inference(resolution,[],[f1033,f997]) ).
fof(f997,plain,
( sP0(sK23,nil)
| nil = sK23 ),
inference(backward_demodulation,[],[f392,f994]) ).
fof(f392,plain,
( sP0(sK23,sK22)
| nil = sK23 ),
inference(cnf_transformation,[],[f260]) ).
fof(f1033,plain,
( ~ sP0(sK23,nil)
| nil = sK23
| ~ ssList(nil) ),
inference(resolution,[],[f1018,f380]) ).
fof(f380,plain,
! [X0,X1] :
( ssItem(sK19(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f255]) ).
fof(f255,plain,
! [X0,X1] :
( ( ! [X3] :
( ~ leq(sK19(X0,X1),X3)
| ~ memberP(X0,X3)
| sK19(X0,X1) = X3
| ~ ssItem(X3) )
& memberP(X0,sK19(X0,X1))
& cons(sK19(X0,X1),nil) = X1
& ssItem(sK19(X0,X1)) )
| ~ sP0(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f253,f254]) ).
fof(f254,plain,
! [X0,X1] :
( ? [X2] :
( ! [X3] :
( ~ leq(X2,X3)
| ~ memberP(X0,X3)
| X2 = X3
| ~ ssItem(X3) )
& memberP(X0,X2)
& cons(X2,nil) = X1
& ssItem(X2) )
=> ( ! [X3] :
( ~ leq(sK19(X0,X1),X3)
| ~ memberP(X0,X3)
| sK19(X0,X1) = X3
| ~ ssItem(X3) )
& memberP(X0,sK19(X0,X1))
& cons(sK19(X0,X1),nil) = X1
& ssItem(sK19(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f253,plain,
! [X0,X1] :
( ? [X2] :
( ! [X3] :
( ~ leq(X2,X3)
| ~ memberP(X0,X3)
| X2 = X3
| ~ ssItem(X3) )
& memberP(X0,X2)
& cons(X2,nil) = X1
& ssItem(X2) )
| ~ sP0(X0,X1) ),
inference(rectify,[],[f252]) ).
fof(f252,plain,
! [X3,X2] :
( ? [X4] :
( ! [X5] :
( ~ leq(X4,X5)
| ~ memberP(X3,X5)
| X4 = X5
| ~ ssItem(X5) )
& memberP(X3,X4)
& cons(X4,nil) = X2
& ssItem(X4) )
| ~ sP0(X3,X2) ),
inference(nnf_transformation,[],[f223]) ).
fof(f1018,plain,
( ~ ssItem(sK19(sK23,nil))
| ~ ssList(nil)
| nil = sK23 ),
inference(trivial_inequality_removal,[],[f1010]) ).
fof(f1010,plain,
( nil != nil
| ~ ssItem(sK19(sK23,nil))
| ~ ssList(nil)
| nil = sK23 ),
inference(backward_demodulation,[],[f752,f994]) ).
fof(f752,plain,
( nil != sK22
| ~ ssItem(sK19(sK23,nil))
| ~ ssList(nil)
| nil = sK23 ),
inference(inner_rewriting,[],[f749]) ).
fof(f749,plain,
( nil != sK22
| ~ ssItem(sK19(sK23,sK22))
| ~ ssList(nil)
| nil = sK23 ),
inference(superposition,[],[f566,f727]) ).
fof(f727,plain,
( sK22 = cons(sK19(sK23,sK22),nil)
| nil = sK23 ),
inference(resolution,[],[f381,f392]) ).
fof(f381,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| cons(sK19(X0,X1),nil) = X1 ),
inference(cnf_transformation,[],[f255]) ).
fof(f566,plain,
! [X0,X1] :
( cons(X1,X0) != X0
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f180]) ).
fof(f180,plain,
! [X0] :
( ! [X1] :
( cons(X1,X0) != X0
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f18,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> cons(X1,X0) != X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax18) ).
fof(f646,plain,
neq(sK23,nil),
inference(forward_demodulation,[],[f390,f388]) ).
fof(f388,plain,
sK21 = sK23,
inference(cnf_transformation,[],[f260]) ).
fof(f390,plain,
neq(sK21,nil),
inference(cnf_transformation,[],[f260]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SWC207+1 : TPTP v8.1.2. Released v2.4.0.
% 0.11/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.36 % Computer : n025.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8042.1875MB
% 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Tue Apr 30 04:23:11 EDT 2024
% 0.13/0.36 % CPUTime :
% 0.13/0.36 % (14830)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.38 % (14837)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)
% 0.13/0.38 % (14833)WARNING: value z3 for option sas not known
% 0.13/0.38 % (14835)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)
% 0.13/0.38 % (14834)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.38 % (14833)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)
% 0.13/0.38 % (14836)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)
% 0.13/0.38 % (14832)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.40 % (14831)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.40 TRYING [1]
% 0.13/0.40 TRYING [2]
% 0.13/0.40 % (14836)First to succeed.
% 0.13/0.41 % (14836)Refutation found. Thanks to Tanya!
% 0.13/0.41 % SZS status Theorem for theBenchmark
% 0.13/0.41 % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.41 % (14836)------------------------------
% 0.13/0.41 % (14836)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.13/0.41 % (14836)Termination reason: Refutation
% 0.13/0.41
% 0.13/0.41 % (14836)Memory used [KB]: 1583
% 0.13/0.41 % (14836)Time elapsed: 0.025 s
% 0.13/0.41 % (14836)Instructions burned: 47 (million)
% 0.13/0.41 % (14836)------------------------------
% 0.13/0.41 % (14836)------------------------------
% 0.13/0.41 % (14830)Success in time 0.042 s
%------------------------------------------------------------------------------