TSTP Solution File: SET945+1 by Vampire-SAT---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET945+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 : n019.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 : Sun May 5 09:19:46 EDT 2024
% Result : Theorem 0.14s 0.38s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 14
% Syntax : Number of formulae : 67 ( 19 unt; 0 def)
% Number of atoms : 233 ( 12 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 269 ( 103 ~; 91 |; 54 &)
% ( 12 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-3 aty)
% Number of variables : 163 ( 144 !; 19 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1014,plain,
$false,
inference(subsumption_resolution,[],[f1012,f247]) ).
fof(f247,plain,
in(sK6(union(sK4),sK5),sK8(sK4,sK6(union(sK4),sK5))),
inference(unit_resulting_resolution,[],[f230,f61]) ).
fof(f61,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| in(X1,sK8(X0,X1)) ),
inference(cnf_transformation,[],[f35]) ).
fof(f35,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ! [X2] :
( ~ in(X2,X0)
| ~ in(X1,X2) ) )
& ( ( in(sK8(X0,X1),X0)
& in(X1,sK8(X0,X1)) )
| ~ sP0(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f33,f34]) ).
fof(f34,plain,
! [X0,X1] :
( ? [X3] :
( in(X3,X0)
& in(X1,X3) )
=> ( in(sK8(X0,X1),X0)
& in(X1,sK8(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f33,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ! [X2] :
( ~ in(X2,X0)
| ~ in(X1,X2) ) )
& ( ? [X3] :
( in(X3,X0)
& in(X1,X3) )
| ~ sP0(X0,X1) ) ),
inference(rectify,[],[f32]) ).
fof(f32,plain,
! [X0,X2] :
( ( sP0(X0,X2)
| ! [X3] :
( ~ in(X3,X0)
| ~ in(X2,X3) ) )
& ( ? [X3] :
( in(X3,X0)
& in(X2,X3) )
| ~ sP0(X0,X2) ) ),
inference(nnf_transformation,[],[f18]) ).
fof(f18,plain,
! [X0,X2] :
( sP0(X0,X2)
<=> ? [X3] :
( in(X3,X0)
& in(X2,X3) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f230,plain,
sP0(sK4,sK6(union(sK4),sK5)),
inference(unit_resulting_resolution,[],[f77,f209,f57]) ).
fof(f57,plain,
! [X3,X0,X1] :
( ~ sP1(X0,X1)
| ~ in(X3,X1)
| sP0(X0,X3) ),
inference(cnf_transformation,[],[f31]) ).
fof(f31,plain,
! [X0,X1] :
( ( sP1(X0,X1)
| ( ( ~ sP0(X0,sK7(X0,X1))
| ~ in(sK7(X0,X1),X1) )
& ( sP0(X0,sK7(X0,X1))
| in(sK7(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| ~ sP0(X0,X3) )
& ( sP0(X0,X3)
| ~ in(X3,X1) ) )
| ~ sP1(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f29,f30]) ).
fof(f30,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ sP0(X0,X2)
| ~ in(X2,X1) )
& ( sP0(X0,X2)
| in(X2,X1) ) )
=> ( ( ~ sP0(X0,sK7(X0,X1))
| ~ in(sK7(X0,X1),X1) )
& ( sP0(X0,sK7(X0,X1))
| in(sK7(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f29,plain,
! [X0,X1] :
( ( sP1(X0,X1)
| ? [X2] :
( ( ~ sP0(X0,X2)
| ~ in(X2,X1) )
& ( sP0(X0,X2)
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| ~ sP0(X0,X3) )
& ( sP0(X0,X3)
| ~ in(X3,X1) ) )
| ~ sP1(X0,X1) ) ),
inference(rectify,[],[f28]) ).
fof(f28,plain,
! [X0,X1] :
( ( sP1(X0,X1)
| ? [X2] :
( ( ~ sP0(X0,X2)
| ~ in(X2,X1) )
& ( sP0(X0,X2)
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ~ sP0(X0,X2) )
& ( sP0(X0,X2)
| ~ in(X2,X1) ) )
| ~ sP1(X0,X1) ) ),
inference(nnf_transformation,[],[f19]) ).
fof(f19,plain,
! [X0,X1] :
( sP1(X0,X1)
<=> ! [X2] :
( in(X2,X1)
<=> sP0(X0,X2) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f209,plain,
in(sK6(union(sK4),sK5),union(sK4)),
inference(unit_resulting_resolution,[],[f140,f71]) ).
fof(f71,plain,
! [X2,X0,X1] :
( ~ sP2(X0,X1,X2)
| in(X1,X0) ),
inference(cnf_transformation,[],[f43]) ).
fof(f43,plain,
! [X0,X1,X2] :
( ( sP2(X0,X1,X2)
| ~ in(X1,X0)
| ~ in(X1,X2) )
& ( ( in(X1,X0)
& in(X1,X2) )
| ~ sP2(X0,X1,X2) ) ),
inference(rectify,[],[f42]) ).
fof(f42,plain,
! [X1,X3,X0] :
( ( sP2(X1,X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X0) )
& ( ( in(X3,X1)
& in(X3,X0) )
| ~ sP2(X1,X3,X0) ) ),
inference(flattening,[],[f41]) ).
fof(f41,plain,
! [X1,X3,X0] :
( ( sP2(X1,X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X0) )
& ( ( in(X3,X1)
& in(X3,X0) )
| ~ sP2(X1,X3,X0) ) ),
inference(nnf_transformation,[],[f21]) ).
fof(f21,plain,
! [X1,X3,X0] :
( sP2(X1,X3,X0)
<=> ( in(X3,X1)
& in(X3,X0) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f140,plain,
sP2(union(sK4),sK6(union(sK4),sK5),sK5),
inference(unit_resulting_resolution,[],[f106,f78,f66]) ).
fof(f66,plain,
! [X2,X0,X1,X4] :
( ~ sP3(X0,X1,X2)
| ~ in(X4,X2)
| sP2(X1,X4,X0) ),
inference(cnf_transformation,[],[f40]) ).
fof(f40,plain,
! [X0,X1,X2] :
( ( sP3(X0,X1,X2)
| ( ( ~ sP2(X1,sK9(X0,X1,X2),X0)
| ~ in(sK9(X0,X1,X2),X2) )
& ( sP2(X1,sK9(X0,X1,X2),X0)
| in(sK9(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ sP2(X1,X4,X0) )
& ( sP2(X1,X4,X0)
| ~ in(X4,X2) ) )
| ~ sP3(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f38,f39]) ).
fof(f39,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ sP2(X1,X3,X0)
| ~ in(X3,X2) )
& ( sP2(X1,X3,X0)
| in(X3,X2) ) )
=> ( ( ~ sP2(X1,sK9(X0,X1,X2),X0)
| ~ in(sK9(X0,X1,X2),X2) )
& ( sP2(X1,sK9(X0,X1,X2),X0)
| in(sK9(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f38,plain,
! [X0,X1,X2] :
( ( sP3(X0,X1,X2)
| ? [X3] :
( ( ~ sP2(X1,X3,X0)
| ~ in(X3,X2) )
& ( sP2(X1,X3,X0)
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ sP2(X1,X4,X0) )
& ( sP2(X1,X4,X0)
| ~ in(X4,X2) ) )
| ~ sP3(X0,X1,X2) ) ),
inference(rectify,[],[f37]) ).
fof(f37,plain,
! [X0,X1,X2] :
( ( sP3(X0,X1,X2)
| ? [X3] :
( ( ~ sP2(X1,X3,X0)
| ~ in(X3,X2) )
& ( sP2(X1,X3,X0)
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ sP2(X1,X3,X0) )
& ( sP2(X1,X3,X0)
| ~ in(X3,X2) ) )
| ~ sP3(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f22]) ).
fof(f22,plain,
! [X0,X1,X2] :
( sP3(X0,X1,X2)
<=> ! [X3] :
( in(X3,X2)
<=> sP2(X1,X3,X0) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f78,plain,
! [X0,X1] : sP3(X0,X1,set_intersection2(X0,X1)),
inference(equality_resolution,[],[f73]) ).
fof(f73,plain,
! [X2,X0,X1] :
( sP3(X0,X1,X2)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f44]) ).
fof(f44,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) = X2
| ~ sP3(X0,X1,X2) )
& ( sP3(X0,X1,X2)
| set_intersection2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f23]) ).
fof(f23,plain,
! [X0,X1,X2] :
( set_intersection2(X0,X1) = X2
<=> sP3(X0,X1,X2) ),
inference(definition_folding,[],[f3,f22,f21]) ).
fof(f3,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(f106,plain,
in(sK6(union(sK4),sK5),set_intersection2(sK5,union(sK4))),
inference(forward_demodulation,[],[f100,f52]) ).
fof(f52,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/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f100,plain,
in(sK6(union(sK4),sK5),set_intersection2(union(sK4),sK5)),
inference(unit_resulting_resolution,[],[f50,f53]) ).
fof(f53,plain,
! [X0,X1] :
( disjoint(X0,X1)
| in(sK6(X0,X1),set_intersection2(X0,X1)) ),
inference(cnf_transformation,[],[f27]) ).
fof(f27,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| ! [X2] : ~ in(X2,set_intersection2(X0,X1)) )
& ( in(sK6(X0,X1),set_intersection2(X0,X1))
| disjoint(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f15,f26]) ).
fof(f26,plain,
! [X0,X1] :
( ? [X3] : in(X3,set_intersection2(X0,X1))
=> in(sK6(X0,X1),set_intersection2(X0,X1)) ),
introduced(choice_axiom,[]) ).
fof(f15,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| ! [X2] : ~ in(X2,set_intersection2(X0,X1)) )
& ( ? [X3] : in(X3,set_intersection2(X0,X1))
| disjoint(X0,X1) ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,plain,
! [X0,X1] :
( ~ ( disjoint(X0,X1)
& ? [X2] : in(X2,set_intersection2(X0,X1)) )
& ~ ( ! [X3] : ~ in(X3,set_intersection2(X0,X1))
& ~ disjoint(X0,X1) ) ),
inference(rectify,[],[f9]) ).
fof(f9,axiom,
! [X0,X1] :
( ~ ( disjoint(X0,X1)
& ? [X2] : in(X2,set_intersection2(X0,X1)) )
& ~ ( ! [X2] : ~ in(X2,set_intersection2(X0,X1))
& ~ disjoint(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_xboole_0) ).
fof(f50,plain,
~ disjoint(union(sK4),sK5),
inference(cnf_transformation,[],[f25]) ).
fof(f25,plain,
( ~ disjoint(union(sK4),sK5)
& ! [X2] :
( disjoint(X2,sK5)
| ~ in(X2,sK4) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f14,f24]) ).
fof(f24,plain,
( ? [X0,X1] :
( ~ disjoint(union(X0),X1)
& ! [X2] :
( disjoint(X2,X1)
| ~ in(X2,X0) ) )
=> ( ~ disjoint(union(sK4),sK5)
& ! [X2] :
( disjoint(X2,sK5)
| ~ in(X2,sK4) ) ) ),
introduced(choice_axiom,[]) ).
fof(f14,plain,
? [X0,X1] :
( ~ disjoint(union(X0),X1)
& ! [X2] :
( disjoint(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,negated_conjecture,
~ ! [X0,X1] :
( ! [X2] :
( in(X2,X0)
=> disjoint(X2,X1) )
=> disjoint(union(X0),X1) ),
inference(negated_conjecture,[],[f10]) ).
fof(f10,conjecture,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
=> disjoint(X2,X1) )
=> disjoint(union(X0),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t98_zfmisc_1) ).
fof(f77,plain,
! [X0] : sP1(X0,union(X0)),
inference(equality_resolution,[],[f64]) ).
fof(f64,plain,
! [X0,X1] :
( sP1(X0,X1)
| union(X0) != X1 ),
inference(cnf_transformation,[],[f36]) ).
fof(f36,plain,
! [X0,X1] :
( ( union(X0) = X1
| ~ sP1(X0,X1) )
& ( sP1(X0,X1)
| union(X0) != X1 ) ),
inference(nnf_transformation,[],[f20]) ).
fof(f20,plain,
! [X0,X1] :
( union(X0) = X1
<=> sP1(X0,X1) ),
inference(definition_folding,[],[f4,f19,f18]) ).
fof(f4,axiom,
! [X0,X1] :
( union(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X3,X0)
& in(X2,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_tarski) ).
fof(f1012,plain,
~ in(sK6(union(sK4),sK5),sK8(sK4,sK6(union(sK4),sK5))),
inference(unit_resulting_resolution,[],[f210,f987,f72]) ).
fof(f72,plain,
! [X2,X0,X1] :
( ~ in(X1,X0)
| sP2(X0,X1,X2)
| ~ in(X1,X2) ),
inference(cnf_transformation,[],[f43]) ).
fof(f987,plain,
! [X0] : ~ sP2(sK8(sK4,sK6(union(sK4),sK5)),X0,sK5),
inference(unit_resulting_resolution,[],[f78,f471,f67]) ).
fof(f67,plain,
! [X2,X0,X1,X4] :
( ~ sP3(X0,X1,X2)
| ~ sP2(X1,X4,X0)
| in(X4,X2) ),
inference(cnf_transformation,[],[f40]) ).
fof(f471,plain,
! [X0] : ~ in(X0,set_intersection2(sK5,sK8(sK4,sK6(union(sK4),sK5)))),
inference(forward_demodulation,[],[f467,f52]) ).
fof(f467,plain,
! [X0] : ~ in(X0,set_intersection2(sK8(sK4,sK6(union(sK4),sK5)),sK5)),
inference(unit_resulting_resolution,[],[f411,f54]) ).
fof(f54,plain,
! [X2,X0,X1] :
( ~ disjoint(X0,X1)
| ~ in(X2,set_intersection2(X0,X1)) ),
inference(cnf_transformation,[],[f27]) ).
fof(f411,plain,
disjoint(sK8(sK4,sK6(union(sK4),sK5)),sK5),
inference(unit_resulting_resolution,[],[f246,f49]) ).
fof(f49,plain,
! [X2] :
( ~ in(X2,sK4)
| disjoint(X2,sK5) ),
inference(cnf_transformation,[],[f25]) ).
fof(f246,plain,
in(sK8(sK4,sK6(union(sK4),sK5)),sK4),
inference(unit_resulting_resolution,[],[f230,f62]) ).
fof(f62,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| in(sK8(X0,X1),X0) ),
inference(cnf_transformation,[],[f35]) ).
fof(f210,plain,
in(sK6(union(sK4),sK5),sK5),
inference(unit_resulting_resolution,[],[f140,f70]) ).
fof(f70,plain,
! [X2,X0,X1] :
( ~ sP2(X0,X1,X2)
| in(X1,X2) ),
inference(cnf_transformation,[],[f43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET945+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.34 % Computer : n019.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Fri May 3 16:29:08 EDT 2024
% 0.14/0.34 % CPUTime :
% 0.14/0.35 % (3298)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.36 % (3303)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)
% 0.14/0.36 % (3301)WARNING: value z3 for option sas not known
% 0.14/0.36 % (3299)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.36 % (3302)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.36 % (3304)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)
% 0.14/0.36 % (3301)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)
% 0.14/0.36 % (3305)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)
% 0.14/0.36 % (3300)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.37 TRYING [1]
% 0.14/0.37 TRYING [2]
% 0.14/0.37 TRYING [3]
% 0.14/0.37 TRYING [1]
% 0.14/0.37 TRYING [2]
% 0.14/0.37 TRYING [4]
% 0.14/0.38 % (3305)First to succeed.
% 0.14/0.38 % (3305)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3298"
% 0.14/0.38 TRYING [3]
% 0.14/0.38 % (3305)Refutation found. Thanks to Tanya!
% 0.14/0.38 % SZS status Theorem for theBenchmark
% 0.14/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.38 % (3305)------------------------------
% 0.14/0.38 % (3305)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.38 % (3305)Termination reason: Refutation
% 0.14/0.38
% 0.14/0.38 % (3305)Memory used [KB]: 937
% 0.14/0.38 % (3305)Time elapsed: 0.020 s
% 0.14/0.38 % (3305)Instructions burned: 31 (million)
% 0.14/0.38 % (3298)Success in time 0.036 s
%------------------------------------------------------------------------------