TSTP Solution File: SET918+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET918+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n021.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 15:13:59 EDT 2024
% Result : Theorem 0.22s 0.39s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 48 ( 10 unt; 0 def)
% Number of atoms : 258 ( 99 equ)
% Maximal formula atoms : 14 ( 5 avg)
% Number of connectives : 327 ( 117 ~; 119 |; 75 &)
% ( 12 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 132 ( 115 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f194,plain,
$false,
inference(trivial_inequality_removal,[],[f193]) ).
fof(f193,plain,
sK2 != sK2,
inference(superposition,[],[f43,f178]) ).
fof(f178,plain,
sK2 = sK3,
inference(resolution,[],[f175,f42]) ).
fof(f42,plain,
in(sK3,sK4),
inference(cnf_transformation,[],[f20]) ).
fof(f20,plain,
( sK2 != sK3
& in(sK3,sK4)
& singleton(sK2) = set_intersection2(unordered_pair(sK2,sK3),sK4) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f13,f19]) ).
fof(f19,plain,
( ? [X0,X1,X2] :
( X0 != X1
& in(X1,X2)
& singleton(X0) = set_intersection2(unordered_pair(X0,X1),X2) )
=> ( sK2 != sK3
& in(sK3,sK4)
& singleton(sK2) = set_intersection2(unordered_pair(sK2,sK3),sK4) ) ),
introduced(choice_axiom,[]) ).
fof(f13,plain,
? [X0,X1,X2] :
( X0 != X1
& in(X1,X2)
& singleton(X0) = set_intersection2(unordered_pair(X0,X1),X2) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,negated_conjecture,
~ ! [X0,X1,X2] :
~ ( X0 != X1
& in(X1,X2)
& singleton(X0) = set_intersection2(unordered_pair(X0,X1),X2) ),
inference(negated_conjecture,[],[f10]) ).
fof(f10,conjecture,
! [X0,X1,X2] :
~ ( X0 != X1
& in(X1,X2)
& singleton(X0) = set_intersection2(unordered_pair(X0,X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_zfmisc_1) ).
fof(f175,plain,
( ~ in(sK3,sK4)
| sK2 = sK3 ),
inference(resolution,[],[f172,f72]) ).
fof(f72,plain,
! [X3,X0] :
( ~ in(X3,singleton(X0))
| X0 = X3 ),
inference(equality_resolution,[],[f48]) ).
fof(f48,plain,
! [X3,X0,X1] :
( X0 = X3
| ~ in(X3,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f24]) ).
fof(f24,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ( ( sK5(X0,X1) != X0
| ~ in(sK5(X0,X1),X1) )
& ( sK5(X0,X1) = X0
| in(sK5(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f22,f23]) ).
fof(f23,plain,
! [X0,X1] :
( ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) )
=> ( ( sK5(X0,X1) != X0
| ~ in(sK5(X0,X1),X1) )
& ( sK5(X0,X1) = X0
| in(sK5(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f22,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(rectify,[],[f21]) ).
fof(f21,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| X0 != X2 )
& ( X0 = X2
| ~ in(X2,X1) ) )
| singleton(X0) != X1 ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0,X1] :
( singleton(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> X0 = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(f172,plain,
( in(sK3,singleton(sK2))
| ~ in(sK3,sK4) ),
inference(resolution,[],[f168,f104]) ).
fof(f104,plain,
! [X0,X1] : in(X0,unordered_pair(X1,X0)),
inference(resolution,[],[f73,f75]) ).
fof(f75,plain,
! [X0,X1] : sP0(X1,X0,unordered_pair(X0,X1)),
inference(equality_resolution,[],[f58]) ).
fof(f58,plain,
! [X2,X0,X1] :
( sP0(X1,X0,X2)
| unordered_pair(X0,X1) != X2 ),
inference(cnf_transformation,[],[f30]) ).
fof(f30,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) = X2
| ~ sP0(X1,X0,X2) )
& ( sP0(X1,X0,X2)
| unordered_pair(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f16]) ).
fof(f16,plain,
! [X0,X1,X2] :
( unordered_pair(X0,X1) = X2
<=> sP0(X1,X0,X2) ),
inference(definition_folding,[],[f5,f15]) ).
fof(f15,plain,
! [X1,X0,X2] :
( sP0(X1,X0,X2)
<=> ! [X3] :
( in(X3,X2)
<=> ( X1 = X3
| X0 = X3 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f5,axiom,
! [X0,X1,X2] :
( unordered_pair(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( X1 = X3
| X0 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).
fof(f73,plain,
! [X2,X1,X4] :
( ~ sP0(X4,X1,X2)
| in(X4,X2) ),
inference(equality_resolution,[],[f54]) ).
fof(f54,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| X0 != X4
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f29]) ).
fof(f29,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ( ( ( sK6(X0,X1,X2) != X0
& sK6(X0,X1,X2) != X1 )
| ~ in(sK6(X0,X1,X2),X2) )
& ( sK6(X0,X1,X2) = X0
| sK6(X0,X1,X2) = X1
| in(sK6(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( X0 != X4
& X1 != X4 ) )
& ( X0 = X4
| X1 = X4
| ~ in(X4,X2) ) )
| ~ sP0(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f27,f28]) ).
fof(f28,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ( X0 != X3
& X1 != X3 )
| ~ in(X3,X2) )
& ( X0 = X3
| X1 = X3
| in(X3,X2) ) )
=> ( ( ( sK6(X0,X1,X2) != X0
& sK6(X0,X1,X2) != X1 )
| ~ in(sK6(X0,X1,X2),X2) )
& ( sK6(X0,X1,X2) = X0
| sK6(X0,X1,X2) = X1
| in(sK6(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f27,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ? [X3] :
( ( ( X0 != X3
& X1 != X3 )
| ~ in(X3,X2) )
& ( X0 = X3
| X1 = X3
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( X0 != X4
& X1 != X4 ) )
& ( X0 = X4
| X1 = X4
| ~ in(X4,X2) ) )
| ~ sP0(X0,X1,X2) ) ),
inference(rectify,[],[f26]) ).
fof(f26,plain,
! [X1,X0,X2] :
( ( sP0(X1,X0,X2)
| ? [X3] :
( ( ( X1 != X3
& X0 != X3 )
| ~ in(X3,X2) )
& ( X1 = X3
| X0 = X3
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( X1 != X3
& X0 != X3 ) )
& ( X1 = X3
| X0 = X3
| ~ in(X3,X2) ) )
| ~ sP0(X1,X0,X2) ) ),
inference(flattening,[],[f25]) ).
fof(f25,plain,
! [X1,X0,X2] :
( ( sP0(X1,X0,X2)
| ? [X3] :
( ( ( X1 != X3
& X0 != X3 )
| ~ in(X3,X2) )
& ( X1 = X3
| X0 = X3
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( X1 != X3
& X0 != X3 ) )
& ( X1 = X3
| X0 = X3
| ~ in(X3,X2) ) )
| ~ sP0(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f15]) ).
fof(f168,plain,
! [X0] :
( ~ in(X0,unordered_pair(sK2,sK3))
| ~ in(X0,sK4)
| in(X0,singleton(sK2)) ),
inference(resolution,[],[f62,f85]) ).
fof(f85,plain,
sP1(sK4,unordered_pair(sK2,sK3),singleton(sK2)),
inference(superposition,[],[f76,f41]) ).
fof(f41,plain,
singleton(sK2) = set_intersection2(unordered_pair(sK2,sK3),sK4),
inference(cnf_transformation,[],[f20]) ).
fof(f76,plain,
! [X0,X1] : sP1(X1,X0,set_intersection2(X0,X1)),
inference(equality_resolution,[],[f66]) ).
fof(f66,plain,
! [X2,X0,X1] :
( sP1(X1,X0,X2)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f36]) ).
fof(f36,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) = X2
| ~ sP1(X1,X0,X2) )
& ( sP1(X1,X0,X2)
| set_intersection2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f18]) ).
fof(f18,plain,
! [X0,X1,X2] :
( set_intersection2(X0,X1) = X2
<=> sP1(X1,X0,X2) ),
inference(definition_folding,[],[f6,f17]) ).
fof(f17,plain,
! [X1,X0,X2] :
( sP1(X1,X0,X2)
<=> ! [X3] :
( in(X3,X2)
<=> ( 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/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f62,plain,
! [X2,X0,X1,X4] :
( ~ sP1(X0,X1,X2)
| ~ in(X4,X0)
| ~ in(X4,X1)
| in(X4,X2) ),
inference(cnf_transformation,[],[f35]) ).
fof(f35,plain,
! [X0,X1,X2] :
( ( sP1(X0,X1,X2)
| ( ( ~ in(sK7(X0,X1,X2),X0)
| ~ in(sK7(X0,X1,X2),X1)
| ~ in(sK7(X0,X1,X2),X2) )
& ( ( in(sK7(X0,X1,X2),X0)
& in(sK7(X0,X1,X2),X1) )
| in(sK7(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1) )
& ( ( in(X4,X0)
& in(X4,X1) )
| ~ in(X4,X2) ) )
| ~ sP1(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f33,f34]) ).
fof(f34,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) )
=> ( ( ~ in(sK7(X0,X1,X2),X0)
| ~ in(sK7(X0,X1,X2),X1)
| ~ in(sK7(X0,X1,X2),X2) )
& ( ( in(sK7(X0,X1,X2),X0)
& in(sK7(X0,X1,X2),X1) )
| in(sK7(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f33,plain,
! [X0,X1,X2] :
( ( sP1(X0,X1,X2)
| ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1) )
& ( ( in(X4,X0)
& in(X4,X1) )
| ~ in(X4,X2) ) )
| ~ sP1(X0,X1,X2) ) ),
inference(rectify,[],[f32]) ).
fof(f32,plain,
! [X1,X0,X2] :
( ( sP1(X1,X0,X2)
| ? [X3] :
( ( ~ in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0) )
& ( ( in(X3,X1)
& in(X3,X0) )
| ~ in(X3,X2) ) )
| ~ sP1(X1,X0,X2) ) ),
inference(flattening,[],[f31]) ).
fof(f31,plain,
! [X1,X0,X2] :
( ( sP1(X1,X0,X2)
| ? [X3] :
( ( ~ in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0) )
& ( ( in(X3,X1)
& in(X3,X0) )
| ~ in(X3,X2) ) )
| ~ sP1(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f17]) ).
fof(f43,plain,
sK2 != sK3,
inference(cnf_transformation,[],[f20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SET918+1 : TPTP v8.1.2. Released v3.2.0.
% 0.03/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.37 % Computer : n021.cluster.edu
% 0.14/0.37 % Model : x86_64 x86_64
% 0.14/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37 % Memory : 8042.1875MB
% 0.14/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37 % CPULimit : 300
% 0.14/0.37 % WCLimit : 300
% 0.14/0.37 % DateTime : Tue Apr 30 01:36:40 EDT 2024
% 0.14/0.37 % CPUTime :
% 0.22/0.37 % (17100)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.39 % (17104)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.22/0.39 % (17105)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)
% 0.22/0.39 % (17103)WARNING: value z3 for option sas not known
% 0.22/0.39 % (17107)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)
% 0.22/0.39 % (17106)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)
% 0.22/0.39 % (17103)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)
% 0.22/0.39 TRYING [1]
% 0.22/0.39 TRYING [2]
% 0.22/0.39 TRYING [3]
% 0.22/0.39 % (17101)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.22/0.39 % (17106)First to succeed.
% 0.22/0.39 % (17102)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.22/0.39 % (17103)Also succeeded, but the first one will report.
% 0.22/0.39 TRYING [4]
% 0.22/0.39 % (17106)Refutation found. Thanks to Tanya!
% 0.22/0.39 % SZS status Theorem for theBenchmark
% 0.22/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.39 % (17106)------------------------------
% 0.22/0.39 % (17106)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.22/0.39 % (17106)Termination reason: Refutation
% 0.22/0.39
% 0.22/0.39 % (17106)Memory used [KB]: 847
% 0.22/0.39 % (17106)Time elapsed: 0.007 s
% 0.22/0.39 % (17106)Instructions burned: 10 (million)
% 0.22/0.39 % (17106)------------------------------
% 0.22/0.39 % (17106)------------------------------
% 0.22/0.39 % (17100)Success in time 0.022 s
%------------------------------------------------------------------------------