TSTP Solution File: SET941+1 by Vampire-SAT---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET941+1 : TPTP v8.2.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n004.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 May 21 03:24:53 EDT 2024
% Result : Theorem 0.15s 0.38s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 40 ( 4 unt; 0 def)
% Number of atoms : 162 ( 5 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 191 ( 69 ~; 67 |; 38 &)
% ( 7 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 108 ( 88 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f78,plain,
$false,
inference(subsumption_resolution,[],[f77,f33]) ).
fof(f33,plain,
~ subset(union(sK1),sK2),
inference(cnf_transformation,[],[f16]) ).
fof(f16,plain,
( ~ subset(union(sK1),sK2)
& ! [X2] :
( subset(X2,sK2)
| ~ in(X2,sK1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f10,f15]) ).
fof(f15,plain,
( ? [X0,X1] :
( ~ subset(union(X0),X1)
& ! [X2] :
( subset(X2,X1)
| ~ in(X2,X0) ) )
=> ( ~ subset(union(sK1),sK2)
& ! [X2] :
( subset(X2,sK2)
| ~ in(X2,sK1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f10,plain,
? [X0,X1] :
( ~ subset(union(X0),X1)
& ! [X2] :
( subset(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,negated_conjecture,
~ ! [X0,X1] :
( ! [X2] :
( in(X2,X0)
=> subset(X2,X1) )
=> subset(union(X0),X1) ),
inference(negated_conjecture,[],[f7]) ).
fof(f7,conjecture,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
=> subset(X2,X1) )
=> subset(union(X0),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t94_zfmisc_1) ).
fof(f77,plain,
subset(union(sK1),sK2),
inference(duplicate_literal_removal,[],[f75]) ).
fof(f75,plain,
( subset(union(sK1),sK2)
| subset(union(sK1),sK2) ),
inference(resolution,[],[f73,f38]) ).
fof(f38,plain,
! [X0,X1] :
( ~ in(sK3(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f20,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK3(X0,X1),X1)
& in(sK3(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f18,f19]) ).
fof(f19,plain,
! [X0,X1] :
( ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) )
=> ( ~ in(sK3(X0,X1),X1)
& in(sK3(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f18,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,[],[f17]) ).
fof(f17,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,[],[f12]) ).
fof(f12,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f73,plain,
! [X0] :
( in(sK3(union(sK1),X0),sK2)
| subset(union(sK1),X0) ),
inference(resolution,[],[f72,f37]) ).
fof(f37,plain,
! [X0,X1] :
( in(sK3(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f72,plain,
! [X0] :
( ~ in(X0,union(sK1))
| in(X0,sK2) ),
inference(duplicate_literal_removal,[],[f70]) ).
fof(f70,plain,
! [X0] :
( in(X0,sK2)
| ~ in(X0,union(sK1))
| ~ in(X0,union(sK1)) ),
inference(resolution,[],[f65,f57]) ).
fof(f57,plain,
! [X0,X1] :
( in(X0,sK6(X1,X0))
| ~ in(X0,union(X1)) ),
inference(resolution,[],[f39,f49]) ).
fof(f49,plain,
! [X0] : sP0(X0,union(X0)),
inference(equality_resolution,[],[f45]) ).
fof(f45,plain,
! [X0,X1] :
( sP0(X0,X1)
| union(X0) != X1 ),
inference(cnf_transformation,[],[f27]) ).
fof(f27,plain,
! [X0,X1] :
( ( union(X0) = X1
| ~ sP0(X0,X1) )
& ( sP0(X0,X1)
| union(X0) != X1 ) ),
inference(nnf_transformation,[],[f14]) ).
fof(f14,plain,
! [X0,X1] :
( union(X0) = X1
<=> sP0(X0,X1) ),
inference(definition_folding,[],[f3,f13]) ).
fof(f13,plain,
! [X0,X1] :
( sP0(X0,X1)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X3,X0)
& in(X2,X3) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f3,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(f39,plain,
! [X0,X1,X5] :
( ~ sP0(X0,X1)
| ~ in(X5,X1)
| in(X5,sK6(X0,X5)) ),
inference(cnf_transformation,[],[f26]) ).
fof(f26,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ( ( ! [X3] :
( ~ in(X3,X0)
| ~ in(sK4(X0,X1),X3) )
| ~ in(sK4(X0,X1),X1) )
& ( ( in(sK5(X0,X1),X0)
& in(sK4(X0,X1),sK5(X0,X1)) )
| in(sK4(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( ~ in(X6,X0)
| ~ in(X5,X6) ) )
& ( ( in(sK6(X0,X5),X0)
& in(X5,sK6(X0,X5)) )
| ~ in(X5,X1) ) )
| ~ sP0(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f22,f25,f24,f23]) ).
fof(f23,plain,
! [X0,X1] :
( ? [X2] :
( ( ! [X3] :
( ~ in(X3,X0)
| ~ in(X2,X3) )
| ~ in(X2,X1) )
& ( ? [X4] :
( in(X4,X0)
& in(X2,X4) )
| in(X2,X1) ) )
=> ( ( ! [X3] :
( ~ in(X3,X0)
| ~ in(sK4(X0,X1),X3) )
| ~ in(sK4(X0,X1),X1) )
& ( ? [X4] :
( in(X4,X0)
& in(sK4(X0,X1),X4) )
| in(sK4(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f24,plain,
! [X0,X1] :
( ? [X4] :
( in(X4,X0)
& in(sK4(X0,X1),X4) )
=> ( in(sK5(X0,X1),X0)
& in(sK4(X0,X1),sK5(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f25,plain,
! [X0,X5] :
( ? [X7] :
( in(X7,X0)
& in(X5,X7) )
=> ( in(sK6(X0,X5),X0)
& in(X5,sK6(X0,X5)) ) ),
introduced(choice_axiom,[]) ).
fof(f22,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ? [X2] :
( ( ! [X3] :
( ~ in(X3,X0)
| ~ in(X2,X3) )
| ~ in(X2,X1) )
& ( ? [X4] :
( in(X4,X0)
& in(X2,X4) )
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( ~ in(X6,X0)
| ~ in(X5,X6) ) )
& ( ? [X7] :
( in(X7,X0)
& in(X5,X7) )
| ~ in(X5,X1) ) )
| ~ sP0(X0,X1) ) ),
inference(rectify,[],[f21]) ).
fof(f21,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ? [X2] :
( ( ! [X3] :
( ~ in(X3,X0)
| ~ in(X2,X3) )
| ~ in(X2,X1) )
& ( ? [X3] :
( in(X3,X0)
& in(X2,X3) )
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] :
( ~ in(X3,X0)
| ~ in(X2,X3) ) )
& ( ? [X3] :
( in(X3,X0)
& in(X2,X3) )
| ~ in(X2,X1) ) )
| ~ sP0(X0,X1) ) ),
inference(nnf_transformation,[],[f13]) ).
fof(f65,plain,
! [X0,X1] :
( ~ in(X1,sK6(sK1,X0))
| in(X1,sK2)
| ~ in(X0,union(sK1)) ),
inference(resolution,[],[f61,f56]) ).
fof(f56,plain,
! [X0,X1] :
( ~ in(X1,sK1)
| in(X0,sK2)
| ~ in(X0,X1) ),
inference(resolution,[],[f36,f32]) ).
fof(f32,plain,
! [X2] :
( subset(X2,sK2)
| ~ in(X2,sK1) ),
inference(cnf_transformation,[],[f16]) ).
fof(f36,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f61,plain,
! [X0,X1] :
( in(sK6(X1,X0),X1)
| ~ in(X0,union(X1)) ),
inference(resolution,[],[f40,f49]) ).
fof(f40,plain,
! [X0,X1,X5] :
( ~ sP0(X0,X1)
| ~ in(X5,X1)
| in(sK6(X0,X5),X0) ),
inference(cnf_transformation,[],[f26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET941+1 : TPTP v8.2.0. Released v3.2.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35 % Computer : n004.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Mon May 20 11:16:23 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.15/0.35 % (21032)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.37 % (21035)WARNING: value z3 for option sas not known
% 0.15/0.37 % (21033)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.37 % (21036)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.37 % (21035)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)
% 0.15/0.37 % (21038)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)
% 0.15/0.37 % (21037)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)
% 0.15/0.37 TRYING [1]
% 0.15/0.37 TRYING [2]
% 0.15/0.37 TRYING [3]
% 0.15/0.37 % (21035)First to succeed.
% 0.15/0.38 TRYING [1]
% 0.15/0.38 % (21035)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-21032"
% 0.15/0.38 TRYING [2]
% 0.15/0.38 % (21035)Refutation found. Thanks to Tanya!
% 0.15/0.38 % SZS status Theorem for theBenchmark
% 0.15/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.38 % (21035)------------------------------
% 0.15/0.38 % (21035)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.38 % (21035)Termination reason: Refutation
% 0.15/0.38
% 0.15/0.38 % (21035)Memory used [KB]: 829
% 0.15/0.38 % (21035)Time elapsed: 0.006 s
% 0.15/0.38 % (21035)Instructions burned: 6 (million)
% 0.15/0.38 % (21032)Success in time 0.004 s
%------------------------------------------------------------------------------