TSTP Solution File: SET950+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET950+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 : n016.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 15:14:05 EDT 2024
% Result : Theorem 0.15s 0.52s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 49 ( 7 unt; 0 def)
% Number of atoms : 198 ( 39 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 235 ( 86 ~; 78 |; 56 &)
% ( 8 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-3 aty)
% Number of variables : 144 ( 113 !; 31 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f401,plain,
$false,
inference(avatar_sat_refutation,[],[f388,f392,f400]) ).
fof(f400,plain,
spl12_2,
inference(avatar_contradiction_clause,[],[f399]) ).
fof(f399,plain,
( $false
| spl12_2 ),
inference(subsumption_resolution,[],[f398,f33]) ).
fof(f33,plain,
in(sK4,sK1),
inference(cnf_transformation,[],[f20]) ).
fof(f20,plain,
( ! [X4,X5] :
( ordered_pair(X4,X5) != sK4
| ~ in(X5,sK3)
| ~ in(X4,sK2) )
& in(sK4,sK1)
& subset(sK1,cartesian_product2(sK2,sK3)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4])],[f14,f19]) ).
fof(f19,plain,
( ? [X0,X1,X2,X3] :
( ! [X4,X5] :
( ordered_pair(X4,X5) != X3
| ~ in(X5,X2)
| ~ in(X4,X1) )
& in(X3,X0)
& subset(X0,cartesian_product2(X1,X2)) )
=> ( ! [X5,X4] :
( ordered_pair(X4,X5) != sK4
| ~ in(X5,sK3)
| ~ in(X4,sK2) )
& in(sK4,sK1)
& subset(sK1,cartesian_product2(sK2,sK3)) ) ),
introduced(choice_axiom,[]) ).
fof(f14,plain,
? [X0,X1,X2,X3] :
( ! [X4,X5] :
( ordered_pair(X4,X5) != X3
| ~ in(X5,X2)
| ~ in(X4,X1) )
& in(X3,X0)
& subset(X0,cartesian_product2(X1,X2)) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,negated_conjecture,
~ ! [X0,X1,X2,X3] :
~ ( ! [X4,X5] :
~ ( ordered_pair(X4,X5) = X3
& in(X5,X2)
& in(X4,X1) )
& in(X3,X0)
& subset(X0,cartesian_product2(X1,X2)) ),
inference(negated_conjecture,[],[f10]) ).
fof(f10,conjecture,
! [X0,X1,X2,X3] :
~ ( ! [X4,X5] :
~ ( ordered_pair(X4,X5) = X3
& in(X5,X2)
& in(X4,X1) )
& in(X3,X0)
& subset(X0,cartesian_product2(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t103_zfmisc_1) ).
fof(f398,plain,
( ~ in(sK4,sK1)
| spl12_2 ),
inference(resolution,[],[f394,f56]) ).
fof(f56,plain,
! [X0] :
( in(X0,cartesian_product2(sK2,sK3))
| ~ in(X0,sK1) ),
inference(resolution,[],[f40,f32]) ).
fof(f32,plain,
subset(sK1,cartesian_product2(sK2,sK3)),
inference(cnf_transformation,[],[f20]) ).
fof(f40,plain,
! [X2,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X2,X0)
| in(X2,X1) ),
inference(cnf_transformation,[],[f16]) ).
fof(f16,plain,
! [X0,X1] :
( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,plain,
! [X0,X1] :
( subset(X0,X1)
=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
inference(unused_predicate_definition_removal,[],[f4]) ).
fof(f4,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f394,plain,
( ~ in(sK4,cartesian_product2(sK2,sK3))
| spl12_2 ),
inference(resolution,[],[f387,f95]) ).
fof(f95,plain,
! [X2,X0,X1] :
( in(sK9(X2,X1,X0),X2)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(resolution,[],[f42,f54]) ).
fof(f54,plain,
! [X0,X1] : sP0(X1,X0,cartesian_product2(X0,X1)),
inference(equality_resolution,[],[f49]) ).
fof(f49,plain,
! [X2,X0,X1] :
( sP0(X1,X0,X2)
| cartesian_product2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f27]) ).
fof(f27,plain,
! [X0,X1,X2] :
( ( cartesian_product2(X0,X1) = X2
| ~ sP0(X1,X0,X2) )
& ( sP0(X1,X0,X2)
| cartesian_product2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f18]) ).
fof(f18,plain,
! [X0,X1,X2] :
( cartesian_product2(X0,X1) = X2
<=> sP0(X1,X0,X2) ),
inference(definition_folding,[],[f3,f17]) ).
fof(f17,plain,
! [X1,X0,X2] :
( sP0(X1,X0,X2)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4,X5] :
( ordered_pair(X4,X5) = X3
& in(X5,X1)
& in(X4,X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f3,axiom,
! [X0,X1,X2] :
( cartesian_product2(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4,X5] :
( ordered_pair(X4,X5) = X3
& in(X5,X1)
& in(X4,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_zfmisc_1) ).
fof(f42,plain,
! [X2,X0,X1,X8] :
( ~ sP0(X0,X1,X2)
| ~ in(X8,X2)
| in(sK9(X0,X1,X8),X0) ),
inference(cnf_transformation,[],[f26]) ).
fof(f26,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ( ( ! [X4,X5] :
( ordered_pair(X4,X5) != sK5(X0,X1,X2)
| ~ in(X5,X0)
| ~ in(X4,X1) )
| ~ in(sK5(X0,X1,X2),X2) )
& ( ( sK5(X0,X1,X2) = ordered_pair(sK6(X0,X1,X2),sK7(X0,X1,X2))
& in(sK7(X0,X1,X2),X0)
& in(sK6(X0,X1,X2),X1) )
| in(sK5(X0,X1,X2),X2) ) ) )
& ( ! [X8] :
( ( in(X8,X2)
| ! [X9,X10] :
( ordered_pair(X9,X10) != X8
| ~ in(X10,X0)
| ~ in(X9,X1) ) )
& ( ( ordered_pair(sK8(X0,X1,X8),sK9(X0,X1,X8)) = X8
& in(sK9(X0,X1,X8),X0)
& in(sK8(X0,X1,X8),X1) )
| ~ in(X8,X2) ) )
| ~ sP0(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7,sK8,sK9])],[f22,f25,f24,f23]) ).
fof(f23,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ! [X4,X5] :
( ordered_pair(X4,X5) != X3
| ~ in(X5,X0)
| ~ in(X4,X1) )
| ~ in(X3,X2) )
& ( ? [X6,X7] :
( ordered_pair(X6,X7) = X3
& in(X7,X0)
& in(X6,X1) )
| in(X3,X2) ) )
=> ( ( ! [X5,X4] :
( ordered_pair(X4,X5) != sK5(X0,X1,X2)
| ~ in(X5,X0)
| ~ in(X4,X1) )
| ~ in(sK5(X0,X1,X2),X2) )
& ( ? [X7,X6] :
( ordered_pair(X6,X7) = sK5(X0,X1,X2)
& in(X7,X0)
& in(X6,X1) )
| in(sK5(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ? [X7,X6] :
( ordered_pair(X6,X7) = sK5(X0,X1,X2)
& in(X7,X0)
& in(X6,X1) )
=> ( sK5(X0,X1,X2) = ordered_pair(sK6(X0,X1,X2),sK7(X0,X1,X2))
& in(sK7(X0,X1,X2),X0)
& in(sK6(X0,X1,X2),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f25,plain,
! [X0,X1,X8] :
( ? [X11,X12] :
( ordered_pair(X11,X12) = X8
& in(X12,X0)
& in(X11,X1) )
=> ( ordered_pair(sK8(X0,X1,X8),sK9(X0,X1,X8)) = X8
& in(sK9(X0,X1,X8),X0)
& in(sK8(X0,X1,X8),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ? [X3] :
( ( ! [X4,X5] :
( ordered_pair(X4,X5) != X3
| ~ in(X5,X0)
| ~ in(X4,X1) )
| ~ in(X3,X2) )
& ( ? [X6,X7] :
( ordered_pair(X6,X7) = X3
& in(X7,X0)
& in(X6,X1) )
| in(X3,X2) ) ) )
& ( ! [X8] :
( ( in(X8,X2)
| ! [X9,X10] :
( ordered_pair(X9,X10) != X8
| ~ in(X10,X0)
| ~ in(X9,X1) ) )
& ( ? [X11,X12] :
( ordered_pair(X11,X12) = X8
& in(X12,X0)
& in(X11,X1) )
| ~ in(X8,X2) ) )
| ~ sP0(X0,X1,X2) ) ),
inference(rectify,[],[f21]) ).
fof(f21,plain,
! [X1,X0,X2] :
( ( sP0(X1,X0,X2)
| ? [X3] :
( ( ! [X4,X5] :
( ordered_pair(X4,X5) != X3
| ~ in(X5,X1)
| ~ in(X4,X0) )
| ~ in(X3,X2) )
& ( ? [X4,X5] :
( ordered_pair(X4,X5) = X3
& in(X5,X1)
& in(X4,X0) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ! [X4,X5] :
( ordered_pair(X4,X5) != X3
| ~ in(X5,X1)
| ~ in(X4,X0) ) )
& ( ? [X4,X5] :
( ordered_pair(X4,X5) = X3
& in(X5,X1)
& in(X4,X0) )
| ~ in(X3,X2) ) )
| ~ sP0(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f17]) ).
fof(f387,plain,
( ~ in(sK9(sK3,sK2,sK4),sK3)
| spl12_2 ),
inference(avatar_component_clause,[],[f385]) ).
fof(f385,plain,
( spl12_2
<=> in(sK9(sK3,sK2,sK4),sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_2])]) ).
fof(f392,plain,
spl12_1,
inference(avatar_contradiction_clause,[],[f391]) ).
fof(f391,plain,
( $false
| spl12_1 ),
inference(subsumption_resolution,[],[f390,f33]) ).
fof(f390,plain,
( ~ in(sK4,sK1)
| spl12_1 ),
inference(resolution,[],[f389,f56]) ).
fof(f389,plain,
( ~ in(sK4,cartesian_product2(sK2,sK3))
| spl12_1 ),
inference(resolution,[],[f383,f93]) ).
fof(f93,plain,
! [X2,X0,X1] :
( in(sK8(X2,X1,X0),X1)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(resolution,[],[f41,f54]) ).
fof(f41,plain,
! [X2,X0,X1,X8] :
( ~ sP0(X0,X1,X2)
| ~ in(X8,X2)
| in(sK8(X0,X1,X8),X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f383,plain,
( ~ in(sK8(sK3,sK2,sK4),sK2)
| spl12_1 ),
inference(avatar_component_clause,[],[f381]) ).
fof(f381,plain,
( spl12_1
<=> in(sK8(sK3,sK2,sK4),sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_1])]) ).
fof(f388,plain,
( ~ spl12_1
| ~ spl12_2 ),
inference(avatar_split_clause,[],[f371,f385,f381]) ).
fof(f371,plain,
( ~ in(sK9(sK3,sK2,sK4),sK3)
| ~ in(sK8(sK3,sK2,sK4),sK2) ),
inference(trivial_inequality_removal,[],[f359]) ).
fof(f359,plain,
( sK4 != sK4
| ~ in(sK9(sK3,sK2,sK4),sK3)
| ~ in(sK8(sK3,sK2,sK4),sK2) ),
inference(superposition,[],[f34,f352]) ).
fof(f352,plain,
sK4 = ordered_pair(sK8(sK3,sK2,sK4),sK9(sK3,sK2,sK4)),
inference(resolution,[],[f344,f33]) ).
fof(f344,plain,
! [X0] :
( ~ in(X0,sK1)
| ordered_pair(sK8(sK3,sK2,X0),sK9(sK3,sK2,X0)) = X0 ),
inference(resolution,[],[f343,f56]) ).
fof(f343,plain,
! [X2,X0,X1] :
( ~ in(X0,cartesian_product2(X1,X2))
| ordered_pair(sK8(X2,X1,X0),sK9(X2,X1,X0)) = X0 ),
inference(resolution,[],[f43,f54]) ).
fof(f43,plain,
! [X2,X0,X1,X8] :
( ~ sP0(X0,X1,X2)
| ~ in(X8,X2)
| ordered_pair(sK8(X0,X1,X8),sK9(X0,X1,X8)) = X8 ),
inference(cnf_transformation,[],[f26]) ).
fof(f34,plain,
! [X4,X5] :
( ordered_pair(X4,X5) != sK4
| ~ in(X5,sK3)
| ~ in(X4,sK2) ),
inference(cnf_transformation,[],[f20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.26 % Problem : SET950+1 : TPTP v8.1.2. Released v3.2.0.
% 0.13/0.28 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.48 % Computer : n016.cluster.edu
% 0.15/0.48 % Model : x86_64 x86_64
% 0.15/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.48 % Memory : 8042.1875MB
% 0.15/0.48 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.49 % CPULimit : 300
% 0.15/0.49 % WCLimit : 300
% 0.15/0.49 % DateTime : Tue Apr 30 01:50:26 EDT 2024
% 0.15/0.49 % CPUTime :
% 0.15/0.49 % (16128)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.50 % (16131)WARNING: value z3 for option sas not known
% 0.15/0.50 % (16131)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)
% 0.15/0.51 % (16129)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.51 % (16130)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.51 % (16132)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.51 % (16133)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)
% 0.15/0.51 % (16134)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)
% 0.15/0.51 % (16135)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)
% 0.15/0.51 TRYING [1]
% 0.15/0.51 TRYING [2]
% 0.15/0.52 TRYING [1]
% 0.15/0.52 TRYING [3]
% 0.15/0.52 TRYING [1]
% 0.15/0.52 TRYING [2]
% 0.15/0.52 TRYING [2]
% 0.15/0.52 % (16131)First to succeed.
% 0.15/0.52 % (16135)Also succeeded, but the first one will report.
% 0.15/0.52 % (16131)Refutation found. Thanks to Tanya!
% 0.15/0.52 % SZS status Theorem for theBenchmark
% 0.15/0.52 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.52 % (16131)------------------------------
% 0.15/0.52 % (16131)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.15/0.52 % (16131)Termination reason: Refutation
% 0.15/0.52
% 0.15/0.52 % (16131)Memory used [KB]: 983
% 0.15/0.52 % (16131)Time elapsed: 0.017 s
% 0.15/0.52 % (16131)Instructions burned: 32 (million)
% 0.15/0.52 % (16131)------------------------------
% 0.15/0.52 % (16131)------------------------------
% 0.15/0.52 % (16128)Success in time 0.019 s
%------------------------------------------------------------------------------