TSTP Solution File: COM018+4 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : COM018+4 : TPTP v8.1.2. Released v4.0.0.
% 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 : Tue Apr 30 10:47:05 EDT 2024
% Result : Theorem 0.16s 0.33s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 13
% Syntax : Number of formulae : 36 ( 7 unt; 0 def)
% Number of atoms : 305 ( 21 equ)
% Maximal formula atoms : 30 ( 8 avg)
% Number of connectives : 353 ( 84 ~; 110 |; 147 &)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 8 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 93 ( 54 !; 39 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f308,plain,
$false,
inference(resolution,[],[f307,f182]) ).
fof(f182,plain,
aElement0(xw),
inference(cnf_transformation,[],[f93]) ).
fof(f93,plain,
( sdtmndtasgtdt0(xv,xR,xw)
& ( ( sdtmndtplgtdt0(xv,xR,xw)
& ( ( sdtmndtplgtdt0(sK20,xR,xw)
& aReductOfIn0(sK20,xv,xR)
& aElement0(sK20) )
| aReductOfIn0(xw,xv,xR) ) )
| xv = xw )
& sdtmndtasgtdt0(xu,xR,xw)
& ( ( sdtmndtplgtdt0(xu,xR,xw)
& ( ( sdtmndtplgtdt0(sK21,xR,xw)
& aReductOfIn0(sK21,xu,xR)
& aElement0(sK21) )
| aReductOfIn0(xw,xu,xR) ) )
| xu = xw )
& aElement0(xw) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK20,sK21])],[f26,f92,f91]) ).
fof(f91,plain,
( ? [X0] :
( sdtmndtplgtdt0(X0,xR,xw)
& aReductOfIn0(X0,xv,xR)
& aElement0(X0) )
=> ( sdtmndtplgtdt0(sK20,xR,xw)
& aReductOfIn0(sK20,xv,xR)
& aElement0(sK20) ) ),
introduced(choice_axiom,[]) ).
fof(f92,plain,
( ? [X1] :
( sdtmndtplgtdt0(X1,xR,xw)
& aReductOfIn0(X1,xu,xR)
& aElement0(X1) )
=> ( sdtmndtplgtdt0(sK21,xR,xw)
& aReductOfIn0(sK21,xu,xR)
& aElement0(sK21) ) ),
introduced(choice_axiom,[]) ).
fof(f26,plain,
( sdtmndtasgtdt0(xv,xR,xw)
& ( ( sdtmndtplgtdt0(xv,xR,xw)
& ( ? [X0] :
( sdtmndtplgtdt0(X0,xR,xw)
& aReductOfIn0(X0,xv,xR)
& aElement0(X0) )
| aReductOfIn0(xw,xv,xR) ) )
| xv = xw )
& sdtmndtasgtdt0(xu,xR,xw)
& ( ( sdtmndtplgtdt0(xu,xR,xw)
& ( ? [X1] :
( sdtmndtplgtdt0(X1,xR,xw)
& aReductOfIn0(X1,xu,xR)
& aElement0(X1) )
| aReductOfIn0(xw,xu,xR) ) )
| xu = xw )
& aElement0(xw) ),
inference(rectify,[],[f22]) ).
fof(f22,axiom,
( sdtmndtasgtdt0(xv,xR,xw)
& ( ( sdtmndtplgtdt0(xv,xR,xw)
& ( ? [X0] :
( sdtmndtplgtdt0(X0,xR,xw)
& aReductOfIn0(X0,xv,xR)
& aElement0(X0) )
| aReductOfIn0(xw,xv,xR) ) )
| xv = xw )
& sdtmndtasgtdt0(xu,xR,xw)
& ( ( sdtmndtplgtdt0(xu,xR,xw)
& ( ? [X0] :
( sdtmndtplgtdt0(X0,xR,xw)
& aReductOfIn0(X0,xu,xR)
& aElement0(X0) )
| aReductOfIn0(xw,xu,xR) ) )
| xu = xw )
& aElement0(xw) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__799) ).
fof(f307,plain,
~ aElement0(xw),
inference(resolution,[],[f305,f164]) ).
fof(f164,plain,
aRewritingSystem0(xR),
inference(cnf_transformation,[],[f15]) ).
fof(f15,axiom,
aRewritingSystem0(xR),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__656) ).
fof(f305,plain,
( ~ aRewritingSystem0(xR)
| ~ aElement0(xw) ),
inference(resolution,[],[f302,f219]) ).
fof(f219,plain,
isTerminating0(xR),
inference(cnf_transformation,[],[f64]) ).
fof(f64,plain,
( isTerminating0(xR)
& ! [X0,X1] :
( iLess0(X1,X0)
| ( ~ sdtmndtplgtdt0(X0,xR,X1)
& ! [X2] :
( ~ sdtmndtplgtdt0(X2,xR,X1)
| ~ aReductOfIn0(X2,X0,xR)
| ~ aElement0(X2) )
& ~ aReductOfIn0(X1,X0,xR) )
| ~ aElement0(X1)
| ~ aElement0(X0) )
& isLocallyConfluent0(xR)
& ! [X3,X4,X5] :
( sP3(X5,X4)
| ~ aReductOfIn0(X5,X3,xR)
| ~ aReductOfIn0(X4,X3,xR)
| ~ aElement0(X5)
| ~ aElement0(X4)
| ~ aElement0(X3) ) ),
inference(definition_folding,[],[f36,f63,f62,f61]) ).
fof(f61,plain,
! [X6,X4] :
( ( sdtmndtplgtdt0(X4,xR,X6)
& ( ? [X8] :
( sdtmndtplgtdt0(X8,xR,X6)
& aReductOfIn0(X8,X4,xR)
& aElement0(X8) )
| aReductOfIn0(X6,X4,xR) ) )
| X4 = X6
| ~ sP1(X6,X4) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f62,plain,
! [X6,X5] :
( ( sdtmndtplgtdt0(X5,xR,X6)
& ( ? [X7] :
( sdtmndtplgtdt0(X7,xR,X6)
& aReductOfIn0(X7,X5,xR)
& aElement0(X7) )
| aReductOfIn0(X6,X5,xR) ) )
| X5 = X6
| ~ sP2(X6,X5) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f63,plain,
! [X5,X4] :
( ? [X6] :
( sdtmndtasgtdt0(X5,xR,X6)
& sP2(X6,X5)
& sdtmndtasgtdt0(X4,xR,X6)
& sP1(X6,X4)
& aElement0(X6) )
| ~ sP3(X5,X4) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f36,plain,
( isTerminating0(xR)
& ! [X0,X1] :
( iLess0(X1,X0)
| ( ~ sdtmndtplgtdt0(X0,xR,X1)
& ! [X2] :
( ~ sdtmndtplgtdt0(X2,xR,X1)
| ~ aReductOfIn0(X2,X0,xR)
| ~ aElement0(X2) )
& ~ aReductOfIn0(X1,X0,xR) )
| ~ aElement0(X1)
| ~ aElement0(X0) )
& isLocallyConfluent0(xR)
& ! [X3,X4,X5] :
( ? [X6] :
( sdtmndtasgtdt0(X5,xR,X6)
& ( ( sdtmndtplgtdt0(X5,xR,X6)
& ( ? [X7] :
( sdtmndtplgtdt0(X7,xR,X6)
& aReductOfIn0(X7,X5,xR)
& aElement0(X7) )
| aReductOfIn0(X6,X5,xR) ) )
| X5 = X6 )
& sdtmndtasgtdt0(X4,xR,X6)
& ( ( sdtmndtplgtdt0(X4,xR,X6)
& ( ? [X8] :
( sdtmndtplgtdt0(X8,xR,X6)
& aReductOfIn0(X8,X4,xR)
& aElement0(X8) )
| aReductOfIn0(X6,X4,xR) ) )
| X4 = X6 )
& aElement0(X6) )
| ~ aReductOfIn0(X5,X3,xR)
| ~ aReductOfIn0(X4,X3,xR)
| ~ aElement0(X5)
| ~ aElement0(X4)
| ~ aElement0(X3) ) ),
inference(flattening,[],[f35]) ).
fof(f35,plain,
( isTerminating0(xR)
& ! [X0,X1] :
( iLess0(X1,X0)
| ( ~ sdtmndtplgtdt0(X0,xR,X1)
& ! [X2] :
( ~ sdtmndtplgtdt0(X2,xR,X1)
| ~ aReductOfIn0(X2,X0,xR)
| ~ aElement0(X2) )
& ~ aReductOfIn0(X1,X0,xR) )
| ~ aElement0(X1)
| ~ aElement0(X0) )
& isLocallyConfluent0(xR)
& ! [X3,X4,X5] :
( ? [X6] :
( sdtmndtasgtdt0(X5,xR,X6)
& ( ( sdtmndtplgtdt0(X5,xR,X6)
& ( ? [X7] :
( sdtmndtplgtdt0(X7,xR,X6)
& aReductOfIn0(X7,X5,xR)
& aElement0(X7) )
| aReductOfIn0(X6,X5,xR) ) )
| X5 = X6 )
& sdtmndtasgtdt0(X4,xR,X6)
& ( ( sdtmndtplgtdt0(X4,xR,X6)
& ( ? [X8] :
( sdtmndtplgtdt0(X8,xR,X6)
& aReductOfIn0(X8,X4,xR)
& aElement0(X8) )
| aReductOfIn0(X6,X4,xR) ) )
| X4 = X6 )
& aElement0(X6) )
| ~ aReductOfIn0(X5,X3,xR)
| ~ aReductOfIn0(X4,X3,xR)
| ~ aElement0(X5)
| ~ aElement0(X4)
| ~ aElement0(X3) ) ),
inference(ennf_transformation,[],[f28]) ).
fof(f28,plain,
( isTerminating0(xR)
& ! [X0,X1] :
( ( aElement0(X1)
& aElement0(X0) )
=> ( ( sdtmndtplgtdt0(X0,xR,X1)
| ? [X2] :
( sdtmndtplgtdt0(X2,xR,X1)
& aReductOfIn0(X2,X0,xR)
& aElement0(X2) )
| aReductOfIn0(X1,X0,xR) )
=> iLess0(X1,X0) ) )
& isLocallyConfluent0(xR)
& ! [X3,X4,X5] :
( ( aReductOfIn0(X5,X3,xR)
& aReductOfIn0(X4,X3,xR)
& aElement0(X5)
& aElement0(X4)
& aElement0(X3) )
=> ? [X6] :
( sdtmndtasgtdt0(X5,xR,X6)
& ( ( sdtmndtplgtdt0(X5,xR,X6)
& ( ? [X7] :
( sdtmndtplgtdt0(X7,xR,X6)
& aReductOfIn0(X7,X5,xR)
& aElement0(X7) )
| aReductOfIn0(X6,X5,xR) ) )
| X5 = X6 )
& sdtmndtasgtdt0(X4,xR,X6)
& ( ( sdtmndtplgtdt0(X4,xR,X6)
& ( ? [X8] :
( sdtmndtplgtdt0(X8,xR,X6)
& aReductOfIn0(X8,X4,xR)
& aElement0(X8) )
| aReductOfIn0(X6,X4,xR) ) )
| X4 = X6 )
& aElement0(X6) ) ) ),
inference(rectify,[],[f16]) ).
fof(f16,axiom,
( isTerminating0(xR)
& ! [X0,X1] :
( ( aElement0(X1)
& aElement0(X0) )
=> ( ( sdtmndtplgtdt0(X0,xR,X1)
| ? [X2] :
( sdtmndtplgtdt0(X2,xR,X1)
& aReductOfIn0(X2,X0,xR)
& aElement0(X2) )
| aReductOfIn0(X1,X0,xR) )
=> iLess0(X1,X0) ) )
& isLocallyConfluent0(xR)
& ! [X0,X1,X2] :
( ( aReductOfIn0(X2,X0,xR)
& aReductOfIn0(X1,X0,xR)
& aElement0(X2)
& aElement0(X1)
& aElement0(X0) )
=> ? [X3] :
( sdtmndtasgtdt0(X2,xR,X3)
& ( ( sdtmndtplgtdt0(X2,xR,X3)
& ( ? [X4] :
( sdtmndtplgtdt0(X4,xR,X3)
& aReductOfIn0(X4,X2,xR)
& aElement0(X4) )
| aReductOfIn0(X3,X2,xR) ) )
| X2 = X3 )
& sdtmndtasgtdt0(X1,xR,X3)
& ( ( sdtmndtplgtdt0(X1,xR,X3)
& ( ? [X4] :
( sdtmndtplgtdt0(X4,xR,X3)
& aReductOfIn0(X4,X1,xR)
& aElement0(X4) )
| aReductOfIn0(X3,X1,xR) ) )
| X1 = X3 )
& aElement0(X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__656_01) ).
fof(f302,plain,
( ~ isTerminating0(xR)
| ~ aElement0(xw)
| ~ aRewritingSystem0(xR) ),
inference(resolution,[],[f276,f163]) ).
fof(f163,plain,
! [X0] : ~ aNormalFormOfIn0(X0,xw,xR),
inference(cnf_transformation,[],[f86]) ).
fof(f86,plain,
! [X0] :
( ~ aNormalFormOfIn0(X0,xw,xR)
& ( aReductOfIn0(sK17(X0),X0,xR)
| sP0(X0)
| ~ aElement0(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK17])],[f60,f85]) ).
fof(f85,plain,
! [X0] :
( ? [X1] : aReductOfIn0(X1,X0,xR)
=> aReductOfIn0(sK17(X0),X0,xR) ),
introduced(choice_axiom,[]) ).
fof(f60,plain,
! [X0] :
( ~ aNormalFormOfIn0(X0,xw,xR)
& ( ? [X1] : aReductOfIn0(X1,X0,xR)
| sP0(X0)
| ~ aElement0(X0) ) ),
inference(definition_folding,[],[f34,f59]) ).
fof(f59,plain,
! [X0] :
( ( ~ sdtmndtasgtdt0(xw,xR,X0)
& ~ sdtmndtplgtdt0(xw,xR,X0)
& ! [X2] :
( ~ sdtmndtplgtdt0(X2,xR,X0)
| ~ aReductOfIn0(X2,xw,xR)
| ~ aElement0(X2) )
& ~ aReductOfIn0(X0,xw,xR)
& xw != X0 )
| ~ sP0(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f34,plain,
! [X0] :
( ~ aNormalFormOfIn0(X0,xw,xR)
& ( ? [X1] : aReductOfIn0(X1,X0,xR)
| ( ~ sdtmndtasgtdt0(xw,xR,X0)
& ~ sdtmndtplgtdt0(xw,xR,X0)
& ! [X2] :
( ~ sdtmndtplgtdt0(X2,xR,X0)
| ~ aReductOfIn0(X2,xw,xR)
| ~ aElement0(X2) )
& ~ aReductOfIn0(X0,xw,xR)
& xw != X0 )
| ~ aElement0(X0) ) ),
inference(ennf_transformation,[],[f25]) ).
fof(f25,plain,
~ ? [X0] :
( aNormalFormOfIn0(X0,xw,xR)
| ( ~ ? [X1] : aReductOfIn0(X1,X0,xR)
& ( sdtmndtasgtdt0(xw,xR,X0)
| sdtmndtplgtdt0(xw,xR,X0)
| ? [X2] :
( sdtmndtplgtdt0(X2,xR,X0)
& aReductOfIn0(X2,xw,xR)
& aElement0(X2) )
| aReductOfIn0(X0,xw,xR)
| xw = X0 )
& aElement0(X0) ) ),
inference(rectify,[],[f24]) ).
fof(f24,negated_conjecture,
~ ? [X0] :
( aNormalFormOfIn0(X0,xw,xR)
| ( ~ ? [X1] : aReductOfIn0(X1,X0,xR)
& ( sdtmndtasgtdt0(xw,xR,X0)
| sdtmndtplgtdt0(xw,xR,X0)
| ? [X1] :
( sdtmndtplgtdt0(X1,xR,X0)
& aReductOfIn0(X1,xw,xR)
& aElement0(X1) )
| aReductOfIn0(X0,xw,xR)
| xw = X0 )
& aElement0(X0) ) ),
inference(negated_conjecture,[],[f23]) ).
fof(f23,conjecture,
? [X0] :
( aNormalFormOfIn0(X0,xw,xR)
| ( ~ ? [X1] : aReductOfIn0(X1,X0,xR)
& ( sdtmndtasgtdt0(xw,xR,X0)
| sdtmndtplgtdt0(xw,xR,X0)
| ? [X1] :
( sdtmndtplgtdt0(X1,xR,X0)
& aReductOfIn0(X1,xw,xR)
& aElement0(X1) )
| aReductOfIn0(X0,xw,xR)
| xw = X0 )
& aElement0(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f276,plain,
! [X0,X1] :
( aNormalFormOfIn0(sK40(X0,X1),X1,X0)
| ~ aElement0(X1)
| ~ isTerminating0(X0)
| ~ aRewritingSystem0(X0) ),
inference(cnf_transformation,[],[f143]) ).
fof(f143,plain,
! [X0] :
( ! [X1] :
( aNormalFormOfIn0(sK40(X0,X1),X1,X0)
| ~ aElement0(X1) )
| ~ isTerminating0(X0)
| ~ aRewritingSystem0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK40])],[f46,f142]) ).
fof(f142,plain,
! [X0,X1] :
( ? [X2] : aNormalFormOfIn0(X2,X1,X0)
=> aNormalFormOfIn0(sK40(X0,X1),X1,X0) ),
introduced(choice_axiom,[]) ).
fof(f46,plain,
! [X0] :
( ! [X1] :
( ? [X2] : aNormalFormOfIn0(X2,X1,X0)
| ~ aElement0(X1) )
| ~ isTerminating0(X0)
| ~ aRewritingSystem0(X0) ),
inference(flattening,[],[f45]) ).
fof(f45,plain,
! [X0] :
( ! [X1] :
( ? [X2] : aNormalFormOfIn0(X2,X1,X0)
| ~ aElement0(X1) )
| ~ isTerminating0(X0)
| ~ aRewritingSystem0(X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,axiom,
! [X0] :
( ( isTerminating0(X0)
& aRewritingSystem0(X0) )
=> ! [X1] :
( aElement0(X1)
=> ? [X2] : aNormalFormOfIn0(X2,X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mTermNF) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : COM018+4 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.10 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.10/0.30 % Computer : n024.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Tue Apr 30 05:05:06 EDT 2024
% 0.10/0.30 % CPUTime :
% 0.10/0.31 % (14635)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.32 % (14638)WARNING: value z3 for option sas not known
% 0.16/0.32 % (14639)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.16/0.32 % (14636)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.16/0.32 % (14638)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)
% 0.16/0.32 % (14641)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)
% 0.16/0.32 % (14637)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.16/0.32 % (14642)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)
% 0.16/0.32 % (14640)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)
% 0.16/0.33 % (14641)First to succeed.
% 0.16/0.33 % (14641)Refutation found. Thanks to Tanya!
% 0.16/0.33 % SZS status Theorem for theBenchmark
% 0.16/0.33 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.33 % (14641)------------------------------
% 0.16/0.33 % (14641)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.16/0.33 % (14641)Termination reason: Refutation
% 0.16/0.33
% 0.16/0.33 % (14641)Memory used [KB]: 1010
% 0.16/0.33 % (14641)Time elapsed: 0.008 s
% 0.16/0.33 % (14641)Instructions burned: 14 (million)
% 0.16/0.33 % (14641)------------------------------
% 0.16/0.33 % (14641)------------------------------
% 0.16/0.33 % (14635)Success in time 0.024 s
%------------------------------------------------------------------------------