TSTP Solution File: SET934+1 by Vampire-SAT---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET934+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 : n005.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 09:19:44 EDT 2024
% Result : Theorem 82.70s 12.16s
% Output : Refutation 82.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 14
% Syntax : Number of formulae : 63 ( 23 unt; 0 def)
% Number of atoms : 209 ( 12 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 239 ( 93 ~; 88 |; 39 &)
% ( 13 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 147 ( 134 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f267499,plain,
$false,
inference(subsumption_resolution,[],[f267103,f79878]) ).
fof(f79878,plain,
sP1(powerset(sK3),sK5(set_union2(powerset(sK3),powerset(sK4)),powerset(set_union2(sK3,sK4))),powerset(sK4)),
inference(unit_resulting_resolution,[],[f112,f5006,f71]) ).
fof(f71,plain,
! [X2,X0,X1,X4] :
( ~ sP2(X0,X1,X2)
| ~ in(X4,X2)
| sP1(X1,X4,X0) ),
inference(cnf_transformation,[],[f44]) ).
fof(f44,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])],[f42,f43]) ).
fof(f43,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(f42,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,[],[f41]) ).
fof(f41,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,[],[f28]) ).
fof(f28,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(f5006,plain,
in(sK5(set_union2(powerset(sK3),powerset(sK4)),powerset(set_union2(sK3,sK4))),set_union2(powerset(sK3),powerset(sK4))),
inference(unit_resulting_resolution,[],[f53,f62]) ).
fof(f62,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sK5(X0,X1),X0) ),
inference(cnf_transformation,[],[f35]) ).
fof(f35,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])],[f33,f34]) ).
fof(f34,plain,
! [X0,X1] :
( ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) )
=> ( ~ in(sK5(X0,X1),X1)
& in(sK5(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f33,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,[],[f32]) ).
fof(f32,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,[],[f22]) ).
fof(f22,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(f53,plain,
~ subset(set_union2(powerset(sK3),powerset(sK4)),powerset(set_union2(sK3,sK4))),
inference(cnf_transformation,[],[f31]) ).
fof(f31,plain,
~ subset(set_union2(powerset(sK3),powerset(sK4)),powerset(set_union2(sK3,sK4))),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f18,f30]) ).
fof(f30,plain,
( ? [X0,X1] : ~ subset(set_union2(powerset(X0),powerset(X1)),powerset(set_union2(X0,X1)))
=> ~ subset(set_union2(powerset(sK3),powerset(sK4)),powerset(set_union2(sK3,sK4))) ),
introduced(choice_axiom,[]) ).
fof(f18,plain,
? [X0,X1] : ~ subset(set_union2(powerset(X0),powerset(X1)),powerset(set_union2(X0,X1))),
inference(ennf_transformation,[],[f15]) ).
fof(f15,negated_conjecture,
~ ! [X0,X1] : subset(set_union2(powerset(X0),powerset(X1)),powerset(set_union2(X0,X1))),
inference(negated_conjecture,[],[f14]) ).
fof(f14,conjecture,
! [X0,X1] : subset(set_union2(powerset(X0),powerset(X1)),powerset(set_union2(X0,X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t81_zfmisc_1) ).
fof(f112,plain,
! [X0,X1] : sP2(X0,X1,set_union2(X1,X0)),
inference(superposition,[],[f83,f57]) ).
fof(f57,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f83,plain,
! [X0,X1] : sP2(X0,X1,set_union2(X0,X1)),
inference(equality_resolution,[],[f78]) ).
fof(f78,plain,
! [X2,X0,X1] :
( sP2(X0,X1,X2)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f48]) ).
fof(f48,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) = X2
| ~ sP2(X0,X1,X2) )
& ( sP2(X0,X1,X2)
| set_union2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f29]) ).
fof(f29,plain,
! [X0,X1,X2] :
( set_union2(X0,X1) = X2
<=> sP2(X0,X1,X2) ),
inference(definition_folding,[],[f4,f28,f27]) ).
fof(f27,plain,
! [X1,X3,X0] :
( sP1(X1,X3,X0)
<=> ( in(X3,X1)
| in(X3,X0) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f4,axiom,
! [X0,X1,X2] :
( set_union2(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
| in(X3,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f267103,plain,
~ sP1(powerset(sK3),sK5(set_union2(powerset(sK3),powerset(sK4)),powerset(set_union2(sK3,sK4))),powerset(sK4)),
inference(unit_resulting_resolution,[],[f251842,f252027,f75]) ).
fof(f75,plain,
! [X2,X0,X1] :
( ~ sP1(X0,X1,X2)
| in(X1,X2)
| in(X1,X0) ),
inference(cnf_transformation,[],[f47]) ).
fof(f47,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,[],[f46]) ).
fof(f46,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,[],[f45]) ).
fof(f45,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,[],[f27]) ).
fof(f252027,plain,
~ in(sK5(set_union2(powerset(sK3),powerset(sK4)),powerset(set_union2(sK3,sK4))),powerset(sK4)),
inference(unit_resulting_resolution,[],[f251622,f240]) ).
fof(f240,plain,
! [X0,X1] :
( ~ in(X0,powerset(X1))
| subset(X0,X1) ),
inference(resolution,[],[f64,f82]) ).
fof(f82,plain,
! [X0] : sP0(X0,powerset(X0)),
inference(equality_resolution,[],[f68]) ).
fof(f68,plain,
! [X0,X1] :
( sP0(X0,X1)
| powerset(X0) != X1 ),
inference(cnf_transformation,[],[f40]) ).
fof(f40,plain,
! [X0,X1] :
( ( powerset(X0) = X1
| ~ sP0(X0,X1) )
& ( sP0(X0,X1)
| powerset(X0) != X1 ) ),
inference(nnf_transformation,[],[f26]) ).
fof(f26,plain,
! [X0,X1] :
( powerset(X0) = X1
<=> sP0(X0,X1) ),
inference(definition_folding,[],[f3,f25]) ).
fof(f25,plain,
! [X0,X1] :
( sP0(X0,X1)
<=> ! [X2] :
( in(X2,X1)
<=> subset(X2,X0) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f3,axiom,
! [X0,X1] :
( powerset(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> subset(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_zfmisc_1) ).
fof(f64,plain,
! [X3,X0,X1] :
( ~ sP0(X0,X1)
| ~ in(X3,X1)
| subset(X3,X0) ),
inference(cnf_transformation,[],[f39]) ).
fof(f39,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ( ( ~ subset(sK6(X0,X1),X0)
| ~ in(sK6(X0,X1),X1) )
& ( subset(sK6(X0,X1),X0)
| in(sK6(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| ~ subset(X3,X0) )
& ( subset(X3,X0)
| ~ in(X3,X1) ) )
| ~ sP0(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f37,f38]) ).
fof(f38,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ subset(X2,X0)
| ~ in(X2,X1) )
& ( subset(X2,X0)
| in(X2,X1) ) )
=> ( ( ~ subset(sK6(X0,X1),X0)
| ~ in(sK6(X0,X1),X1) )
& ( subset(sK6(X0,X1),X0)
| in(sK6(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f37,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ? [X2] :
( ( ~ subset(X2,X0)
| ~ in(X2,X1) )
& ( subset(X2,X0)
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| ~ subset(X3,X0) )
& ( subset(X3,X0)
| ~ in(X3,X1) ) )
| ~ sP0(X0,X1) ) ),
inference(rectify,[],[f36]) ).
fof(f36,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ? [X2] :
( ( ~ subset(X2,X0)
| ~ in(X2,X1) )
& ( subset(X2,X0)
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ~ subset(X2,X0) )
& ( subset(X2,X0)
| ~ in(X2,X1) ) )
| ~ sP0(X0,X1) ) ),
inference(nnf_transformation,[],[f25]) ).
fof(f251622,plain,
~ subset(sK5(set_union2(powerset(sK3),powerset(sK4)),powerset(set_union2(sK3,sK4))),sK4),
inference(unit_resulting_resolution,[],[f115,f56333,f70]) ).
fof(f70,plain,
! [X2,X0,X1] :
( ~ subset(X1,X2)
| subset(X0,X2)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f24,plain,
! [X0,X1,X2] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(flattening,[],[f23]) ).
fof(f23,plain,
! [X0,X1,X2] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0,X1,X2] :
( ( subset(X1,X2)
& subset(X0,X1) )
=> subset(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).
fof(f56333,plain,
~ subset(sK5(set_union2(powerset(sK3),powerset(sK4)),powerset(set_union2(sK3,sK4))),set_union2(sK3,sK4)),
inference(unit_resulting_resolution,[],[f82,f5005,f65]) ).
fof(f65,plain,
! [X3,X0,X1] :
( ~ sP0(X0,X1)
| ~ subset(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f39]) ).
fof(f5005,plain,
~ in(sK5(set_union2(powerset(sK3),powerset(sK4)),powerset(set_union2(sK3,sK4))),powerset(set_union2(sK3,sK4))),
inference(unit_resulting_resolution,[],[f53,f63]) ).
fof(f63,plain,
! [X0,X1] :
( ~ in(sK5(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f35]) ).
fof(f115,plain,
! [X0,X1] : subset(X0,set_union2(X1,X0)),
inference(superposition,[],[f56,f57]) ).
fof(f56,plain,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
inference(cnf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_xboole_1) ).
fof(f251842,plain,
~ in(sK5(set_union2(powerset(sK3),powerset(sK4)),powerset(set_union2(sK3,sK4))),powerset(sK3)),
inference(unit_resulting_resolution,[],[f251621,f240]) ).
fof(f251621,plain,
~ subset(sK5(set_union2(powerset(sK3),powerset(sK4)),powerset(set_union2(sK3,sK4))),sK3),
inference(unit_resulting_resolution,[],[f56,f56333,f70]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SET934+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.11 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.10/0.31 % Computer : n005.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Fri May 3 17:06:23 EDT 2024
% 0.16/0.31 % CPUTime :
% 0.16/0.32 % (21521)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.33 % (21524)WARNING: value z3 for option sas not known
% 0.16/0.33 % (21524)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)
% 0.16/0.33 % (21528)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)
% 0.16/0.33 % (21523)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.16/0.33 % (21525)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.16/0.33 % (21522)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.16/0.33 % (21526)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 % (21527)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)
% 0.16/0.33 TRYING [1]
% 0.16/0.33 TRYING [2]
% 0.16/0.33 TRYING [3]
% 0.16/0.34 TRYING [1]
% 0.16/0.34 TRYING [2]
% 0.16/0.34 TRYING [4]
% 0.16/0.35 TRYING [3]
% 0.16/0.35 TRYING [5]
% 0.16/0.38 TRYING [6]
% 0.16/0.39 TRYING [4]
% 0.16/0.44 TRYING [7]
% 0.16/0.49 TRYING [5]
% 0.16/0.57 TRYING [8]
% 2.98/0.77 TRYING [6]
% 3.87/0.87 TRYING [9]
% 7.79/1.43 TRYING [1]
% 7.79/1.43 TRYING [2]
% 7.79/1.43 TRYING [3]
% 7.79/1.44 TRYING [4]
% 7.79/1.45 TRYING [5]
% 8.22/1.49 TRYING [6]
% 8.22/1.50 TRYING [10]
% 8.22/1.56 TRYING [7]
% 9.86/1.72 TRYING [8]
% 9.86/1.73 TRYING [7]
% 11.97/2.08 TRYING [9]
% 18.86/3.08 TRYING [10]
% 19.55/3.11 TRYING [11]
% 37.88/5.75 TRYING [8]
% 39.42/6.00 TRYING [11]
% 52.08/7.78 TRYING [12]
% 77.80/11.45 TRYING [12]
% 82.70/12.14 % (21528)First to succeed.
% 82.70/12.14 % (21528)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-21521"
% 82.70/12.16 % (21528)Refutation found. Thanks to Tanya!
% 82.70/12.16 % SZS status Theorem for theBenchmark
% 82.70/12.16 % SZS output start Proof for theBenchmark
% See solution above
% 82.70/12.16 % (21528)------------------------------
% 82.70/12.16 % (21528)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 82.70/12.16 % (21528)Termination reason: Refutation
% 82.70/12.16
% 82.70/12.16 % (21528)Memory used [KB]: 110347
% 82.70/12.16 % (21528)Time elapsed: 11.811 s
% 82.70/12.16 % (21528)Instructions burned: 33403 (million)
% 82.70/12.16 % (21521)Success in time 11.732 s
%------------------------------------------------------------------------------