TSTP Solution File: SEU154+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU154+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 : n029.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 15:22:38 EDT 2024
% Result : Theorem 0.22s 0.50s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 16
% Syntax : Number of formulae : 77 ( 26 unt; 0 def)
% Number of atoms : 244 ( 45 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 277 ( 110 ~; 94 |; 50 &)
% ( 15 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 158 ( 145 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6153,plain,
$false,
inference(subsumption_resolution,[],[f6129,f1046]) ).
fof(f1046,plain,
! [X0] : ~ in(sK3,set_intersection2(sK4,X0)),
inference(forward_demodulation,[],[f987,f238]) ).
fof(f238,plain,
sK3 = sK5(singleton(sK3),sK4),
inference(unit_resulting_resolution,[],[f184,f94,f74]) ).
fof(f74,plain,
! [X3,X0,X1] :
( ~ sP0(X0,X1)
| ~ in(X3,X1)
| X0 = X3 ),
inference(cnf_transformation,[],[f43]) ).
fof(f43,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ( ( sK6(X0,X1) != X0
| ~ in(sK6(X0,X1),X1) )
& ( sK6(X0,X1) = X0
| in(sK6(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| ~ sP0(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f41,f42]) ).
fof(f42,plain,
! [X0,X1] :
( ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) )
=> ( ( sK6(X0,X1) != X0
| ~ in(sK6(X0,X1),X1) )
& ( sK6(X0,X1) = X0
| in(sK6(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f41,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| ~ sP0(X0,X1) ) ),
inference(rectify,[],[f40]) ).
fof(f40,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| X0 != X2 )
& ( X0 = X2
| ~ in(X2,X1) ) )
| ~ sP0(X0,X1) ) ),
inference(nnf_transformation,[],[f26]) ).
fof(f26,plain,
! [X0,X1] :
( sP0(X0,X1)
<=> ! [X2] :
( in(X2,X1)
<=> X0 = X2 ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f94,plain,
! [X0] : sP0(X0,singleton(X0)),
inference(equality_resolution,[],[f78]) ).
fof(f78,plain,
! [X0,X1] :
( sP0(X0,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f44]) ).
fof(f44,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ~ sP0(X0,X1) )
& ( sP0(X0,X1)
| singleton(X0) != X1 ) ),
inference(nnf_transformation,[],[f27]) ).
fof(f27,plain,
! [X0,X1] :
( singleton(X0) = X1
<=> sP0(X0,X1) ),
inference(definition_folding,[],[f4,f26]) ).
fof(f4,axiom,
! [X0,X1] :
( singleton(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> X0 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(f184,plain,
in(sK5(singleton(sK3),sK4),singleton(sK3)),
inference(unit_resulting_resolution,[],[f170,f72]) ).
fof(f72,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sK5(X0,X1),X0) ),
inference(cnf_transformation,[],[f39]) ).
fof(f39,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK5(X0,X1),X1)
& in(sK5(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f37,f38]) ).
fof(f38,plain,
! [X0,X1] :
( ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) )
=> ( ~ in(sK5(X0,X1),X1)
& in(sK5(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f37,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f36]) ).
fof(f36,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f25]) ).
fof(f25,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f170,plain,
~ subset(singleton(sK3),sK4),
inference(unit_resulting_resolution,[],[f57,f100,f71]) ).
fof(f71,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f39]) ).
fof(f100,plain,
! [X0] : in(X0,singleton(X0)),
inference(unit_resulting_resolution,[],[f94,f93]) ).
fof(f93,plain,
! [X3,X1] :
( ~ sP0(X3,X1)
| in(X3,X1) ),
inference(equality_resolution,[],[f75]) ).
fof(f75,plain,
! [X3,X0,X1] :
( in(X3,X1)
| X0 != X3
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f43]) ).
fof(f57,plain,
~ in(sK3,sK4),
inference(cnf_transformation,[],[f32]) ).
fof(f32,plain,
( ~ disjoint(singleton(sK3),sK4)
& ~ in(sK3,sK4) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f22,f31]) ).
fof(f31,plain,
( ? [X0,X1] :
( ~ disjoint(singleton(X0),X1)
& ~ in(X0,X1) )
=> ( ~ disjoint(singleton(sK3),sK4)
& ~ in(sK3,sK4) ) ),
introduced(choice_axiom,[]) ).
fof(f22,plain,
? [X0,X1] :
( ~ disjoint(singleton(X0),X1)
& ~ in(X0,X1) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,negated_conjecture,
~ ! [X0,X1] :
( ~ in(X0,X1)
=> disjoint(singleton(X0),X1) ),
inference(negated_conjecture,[],[f13]) ).
fof(f13,conjecture,
! [X0,X1] :
( ~ in(X0,X1)
=> disjoint(singleton(X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l28_zfmisc_1) ).
fof(f987,plain,
! [X0] : ~ in(sK5(singleton(sK3),sK4),set_intersection2(sK4,X0)),
inference(unit_resulting_resolution,[],[f202,f107,f80]) ).
fof(f80,plain,
! [X2,X0,X1,X4] :
( ~ sP2(X0,X1,X2)
| ~ in(X4,X2)
| sP1(X1,X4,X0) ),
inference(cnf_transformation,[],[f48]) ).
fof(f48,plain,
! [X0,X1,X2] :
( ( sP2(X0,X1,X2)
| ( ( ~ sP1(X1,sK7(X0,X1,X2),X0)
| ~ in(sK7(X0,X1,X2),X2) )
& ( sP1(X1,sK7(X0,X1,X2),X0)
| in(sK7(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ sP1(X1,X4,X0) )
& ( sP1(X1,X4,X0)
| ~ in(X4,X2) ) )
| ~ sP2(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f46,f47]) ).
fof(f47,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ sP1(X1,X3,X0)
| ~ in(X3,X2) )
& ( sP1(X1,X3,X0)
| in(X3,X2) ) )
=> ( ( ~ sP1(X1,sK7(X0,X1,X2),X0)
| ~ in(sK7(X0,X1,X2),X2) )
& ( sP1(X1,sK7(X0,X1,X2),X0)
| in(sK7(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f46,plain,
! [X0,X1,X2] :
( ( sP2(X0,X1,X2)
| ? [X3] :
( ( ~ sP1(X1,X3,X0)
| ~ in(X3,X2) )
& ( sP1(X1,X3,X0)
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ sP1(X1,X4,X0) )
& ( sP1(X1,X4,X0)
| ~ in(X4,X2) ) )
| ~ sP2(X0,X1,X2) ) ),
inference(rectify,[],[f45]) ).
fof(f45,plain,
! [X0,X1,X2] :
( ( sP2(X0,X1,X2)
| ? [X3] :
( ( ~ sP1(X1,X3,X0)
| ~ in(X3,X2) )
& ( sP1(X1,X3,X0)
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ sP1(X1,X3,X0) )
& ( sP1(X1,X3,X0)
| ~ in(X3,X2) ) )
| ~ sP2(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f29]) ).
fof(f29,plain,
! [X0,X1,X2] :
( sP2(X0,X1,X2)
<=> ! [X3] :
( in(X3,X2)
<=> sP1(X1,X3,X0) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f107,plain,
! [X0,X1] : sP2(X0,X1,set_intersection2(X1,X0)),
inference(superposition,[],[f95,f63]) ).
fof(f63,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f95,plain,
! [X0,X1] : sP2(X0,X1,set_intersection2(X0,X1)),
inference(equality_resolution,[],[f87]) ).
fof(f87,plain,
! [X2,X0,X1] :
( sP2(X0,X1,X2)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f52]) ).
fof(f52,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) = X2
| ~ sP2(X0,X1,X2) )
& ( sP2(X0,X1,X2)
| set_intersection2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f30]) ).
fof(f30,plain,
! [X0,X1,X2] :
( set_intersection2(X0,X1) = X2
<=> sP2(X0,X1,X2) ),
inference(definition_folding,[],[f6,f29,f28]) ).
fof(f28,plain,
! [X1,X3,X0] :
( sP1(X1,X3,X0)
<=> ( in(X3,X1)
& in(X3,X0) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f6,axiom,
! [X0,X1,X2] :
( set_intersection2(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f202,plain,
! [X0] : ~ sP1(sK4,sK5(singleton(sK3),sK4),X0),
inference(unit_resulting_resolution,[],[f183,f85]) ).
fof(f85,plain,
! [X2,X0,X1] :
( ~ sP1(X0,X1,X2)
| in(X1,X0) ),
inference(cnf_transformation,[],[f51]) ).
fof(f51,plain,
! [X0,X1,X2] :
( ( sP1(X0,X1,X2)
| ~ in(X1,X0)
| ~ in(X1,X2) )
& ( ( in(X1,X0)
& in(X1,X2) )
| ~ sP1(X0,X1,X2) ) ),
inference(rectify,[],[f50]) ).
fof(f50,plain,
! [X1,X3,X0] :
( ( sP1(X1,X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X0) )
& ( ( in(X3,X1)
& in(X3,X0) )
| ~ sP1(X1,X3,X0) ) ),
inference(flattening,[],[f49]) ).
fof(f49,plain,
! [X1,X3,X0] :
( ( sP1(X1,X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X0) )
& ( ( in(X3,X1)
& in(X3,X0) )
| ~ sP1(X1,X3,X0) ) ),
inference(nnf_transformation,[],[f28]) ).
fof(f183,plain,
~ in(sK5(singleton(sK3),sK4),sK4),
inference(unit_resulting_resolution,[],[f170,f73]) ).
fof(f73,plain,
! [X0,X1] :
( ~ in(sK5(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f39]) ).
fof(f6129,plain,
in(sK3,set_intersection2(sK4,singleton(sK3))),
inference(superposition,[],[f151,f6096]) ).
fof(f6096,plain,
sK3 = sK5(set_intersection2(sK4,singleton(sK3)),empty_set),
inference(unit_resulting_resolution,[],[f94,f4870,f74]) ).
fof(f4870,plain,
in(sK5(set_intersection2(sK4,singleton(sK3)),empty_set),singleton(sK3)),
inference(unit_resulting_resolution,[],[f946,f85]) ).
fof(f946,plain,
sP1(singleton(sK3),sK5(set_intersection2(sK4,singleton(sK3)),empty_set),sK4),
inference(unit_resulting_resolution,[],[f151,f95,f80]) ).
fof(f151,plain,
in(sK5(set_intersection2(sK4,singleton(sK3)),empty_set),set_intersection2(sK4,singleton(sK3))),
inference(unit_resulting_resolution,[],[f145,f72]) ).
fof(f145,plain,
~ subset(set_intersection2(sK4,singleton(sK3)),empty_set),
inference(unit_resulting_resolution,[],[f119,f60,f68]) ).
fof(f68,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| X0 = X1
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f34]) ).
fof(f34,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 ) ),
inference(flattening,[],[f33]) ).
fof(f33,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(f60,plain,
! [X0] : subset(empty_set,X0),
inference(cnf_transformation,[],[f19]) ).
fof(f19,axiom,
! [X0] : subset(empty_set,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
fof(f119,plain,
empty_set != set_intersection2(sK4,singleton(sK3)),
inference(unit_resulting_resolution,[],[f97,f70]) ).
fof(f70,plain,
! [X0,X1] :
( set_intersection2(X0,X1) != empty_set
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f35]) ).
fof(f35,plain,
! [X0,X1] :
( ( disjoint(X0,X1)
| set_intersection2(X0,X1) != empty_set )
& ( set_intersection2(X0,X1) = empty_set
| ~ disjoint(X0,X1) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0,X1] :
( disjoint(X0,X1)
<=> set_intersection2(X0,X1) = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_xboole_0) ).
fof(f97,plain,
~ disjoint(sK4,singleton(sK3)),
inference(unit_resulting_resolution,[],[f58,f65]) ).
fof(f65,plain,
! [X0,X1] :
( ~ disjoint(X0,X1)
| disjoint(X1,X0) ),
inference(cnf_transformation,[],[f24]) ).
fof(f24,plain,
! [X0,X1] :
( disjoint(X1,X0)
| ~ disjoint(X0,X1) ),
inference(ennf_transformation,[],[f18]) ).
fof(f18,axiom,
! [X0,X1] :
( disjoint(X0,X1)
=> disjoint(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
fof(f58,plain,
~ disjoint(singleton(sK3),sK4),
inference(cnf_transformation,[],[f32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.13 % Problem : SEU154+1 : TPTP v8.1.2. Released v3.3.0.
% 0.14/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n029.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Mon Apr 29 20:52:50 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.37 % (24990)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38 % (24994)WARNING: value z3 for option sas not known
% 0.15/0.38 % (24994)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)
% 0.15/0.38 % (24992)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.38 % (24996)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)
% 0.15/0.38 % (24997)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)
% 0.15/0.38 % (24993)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.38 % (24998)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)
% 0.15/0.39 % (24995)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.39 TRYING [1]
% 0.15/0.39 TRYING [2]
% 0.15/0.39 TRYING [3]
% 0.15/0.39 TRYING [1]
% 0.15/0.39 TRYING [2]
% 0.15/0.39 TRYING [4]
% 0.15/0.40 TRYING [5]
% 0.15/0.41 TRYING [3]
% 0.15/0.43 TRYING [6]
% 0.22/0.45 TRYING [4]
% 0.22/0.47 TRYING [7]
% 0.22/0.50 % (24998)First to succeed.
% 0.22/0.50 % (24998)Refutation found. Thanks to Tanya!
% 0.22/0.50 % SZS status Theorem for theBenchmark
% 0.22/0.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.50 % (24998)------------------------------
% 0.22/0.50 % (24998)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.22/0.50 % (24998)Termination reason: Refutation
% 0.22/0.50
% 0.22/0.50 % (24998)Memory used [KB]: 1832
% 0.22/0.50 % (24998)Time elapsed: 0.114 s
% 0.22/0.50 % (24998)Instructions burned: 199 (million)
% 0.22/0.50 % (24998)------------------------------
% 0.22/0.50 % (24998)------------------------------
% 0.22/0.50 % (24990)Success in time 0.131 s
%------------------------------------------------------------------------------