TSTP Solution File: SET950+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% 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 : n011.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 0.22s 0.39s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 37 ( 9 unt; 0 def)
% Number of atoms : 151 ( 24 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 178 ( 64 ~; 56 |; 45 &)
% ( 7 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 123 ( 102 !; 21 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f569,plain,
$false,
inference(unit_resulting_resolution,[],[f102,f112,f50]) ).
fof(f50,plain,
! [X2,X0,X1] :
( ~ sP0(X0,X1,X2)
| ordered_pair(sK7(X0,X1,X2),sK8(X0,X1,X2)) = X0 ),
inference(cnf_transformation,[],[f29]) ).
fof(f29,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ! [X3,X4] :
( ordered_pair(X3,X4) != X0
| ~ in(X4,X1)
| ~ in(X3,X2) ) )
& ( ( ordered_pair(sK7(X0,X1,X2),sK8(X0,X1,X2)) = X0
& in(sK8(X0,X1,X2),X1)
& in(sK7(X0,X1,X2),X2) )
| ~ sP0(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8])],[f27,f28]) ).
fof(f28,plain,
! [X0,X1,X2] :
( ? [X5,X6] :
( ordered_pair(X5,X6) = X0
& in(X6,X1)
& in(X5,X2) )
=> ( ordered_pair(sK7(X0,X1,X2),sK8(X0,X1,X2)) = X0
& in(sK8(X0,X1,X2),X1)
& in(sK7(X0,X1,X2),X2) ) ),
introduced(choice_axiom,[]) ).
fof(f27,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ! [X3,X4] :
( ordered_pair(X3,X4) != X0
| ~ in(X4,X1)
| ~ in(X3,X2) ) )
& ( ? [X5,X6] :
( ordered_pair(X5,X6) = X0
& in(X6,X1)
& in(X5,X2) )
| ~ sP0(X0,X1,X2) ) ),
inference(rectify,[],[f26]) ).
fof(f26,plain,
! [X3,X1,X0] :
( ( sP0(X3,X1,X0)
| ! [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) )
| ~ sP0(X3,X1,X0) ) ),
inference(nnf_transformation,[],[f17]) ).
fof(f17,plain,
! [X3,X1,X0] :
( sP0(X3,X1,X0)
<=> ? [X4,X5] :
( ordered_pair(X4,X5) = X3
& in(X5,X1)
& in(X4,X0) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f112,plain,
sK5 != ordered_pair(sK7(sK5,sK4,sK3),sK8(sK5,sK4,sK3)),
inference(unit_resulting_resolution,[],[f104,f105,f37]) ).
fof(f37,plain,
! [X4,X5] :
( ~ in(X5,sK4)
| ordered_pair(X4,X5) != sK5
| ~ in(X4,sK3) ),
inference(cnf_transformation,[],[f21]) ).
fof(f21,plain,
( ! [X4,X5] :
( ordered_pair(X4,X5) != sK5
| ~ in(X5,sK4)
| ~ in(X4,sK3) )
& in(sK5,sK2)
& subset(sK2,cartesian_product2(sK3,sK4)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5])],[f14,f20]) ).
fof(f20,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) != sK5
| ~ in(X5,sK4)
| ~ in(X4,sK3) )
& in(sK5,sK2)
& subset(sK2,cartesian_product2(sK3,sK4)) ) ),
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/sandbox/benchmark/theBenchmark.p',t103_zfmisc_1) ).
fof(f105,plain,
in(sK7(sK5,sK4,sK3),sK3),
inference(unit_resulting_resolution,[],[f102,f48]) ).
fof(f48,plain,
! [X2,X0,X1] :
( ~ sP0(X0,X1,X2)
| in(sK7(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f29]) ).
fof(f104,plain,
in(sK8(sK5,sK4,sK3),sK4),
inference(unit_resulting_resolution,[],[f102,f49]) ).
fof(f49,plain,
! [X2,X0,X1] :
( ~ sP0(X0,X1,X2)
| in(sK8(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f29]) ).
fof(f102,plain,
sP0(sK5,sK4,sK3),
inference(unit_resulting_resolution,[],[f61,f57,f44]) ).
fof(f44,plain,
! [X2,X0,X1,X4] :
( ~ sP1(X0,X1,X2)
| ~ in(X4,X2)
| sP0(X4,X1,X0) ),
inference(cnf_transformation,[],[f25]) ).
fof(f25,plain,
! [X0,X1,X2] :
( ( sP1(X0,X1,X2)
| ( ( ~ sP0(sK6(X0,X1,X2),X1,X0)
| ~ in(sK6(X0,X1,X2),X2) )
& ( sP0(sK6(X0,X1,X2),X1,X0)
| in(sK6(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ sP0(X4,X1,X0) )
& ( sP0(X4,X1,X0)
| ~ in(X4,X2) ) )
| ~ sP1(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f23,f24]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ sP0(X3,X1,X0)
| ~ in(X3,X2) )
& ( sP0(X3,X1,X0)
| in(X3,X2) ) )
=> ( ( ~ sP0(sK6(X0,X1,X2),X1,X0)
| ~ in(sK6(X0,X1,X2),X2) )
& ( sP0(sK6(X0,X1,X2),X1,X0)
| in(sK6(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f23,plain,
! [X0,X1,X2] :
( ( sP1(X0,X1,X2)
| ? [X3] :
( ( ~ sP0(X3,X1,X0)
| ~ in(X3,X2) )
& ( sP0(X3,X1,X0)
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ sP0(X4,X1,X0) )
& ( sP0(X4,X1,X0)
| ~ in(X4,X2) ) )
| ~ sP1(X0,X1,X2) ) ),
inference(rectify,[],[f22]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ( sP1(X0,X1,X2)
| ? [X3] :
( ( ~ sP0(X3,X1,X0)
| ~ in(X3,X2) )
& ( sP0(X3,X1,X0)
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ sP0(X3,X1,X0) )
& ( sP0(X3,X1,X0)
| ~ in(X3,X2) ) )
| ~ sP1(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f18]) ).
fof(f18,plain,
! [X0,X1,X2] :
( sP1(X0,X1,X2)
<=> ! [X3] :
( in(X3,X2)
<=> sP0(X3,X1,X0) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f57,plain,
! [X0,X1] : sP1(X0,X1,cartesian_product2(X0,X1)),
inference(equality_resolution,[],[f52]) ).
fof(f52,plain,
! [X2,X0,X1] :
( sP1(X0,X1,X2)
| cartesian_product2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f30]) ).
fof(f30,plain,
! [X0,X1,X2] :
( ( cartesian_product2(X0,X1) = X2
| ~ sP1(X0,X1,X2) )
& ( sP1(X0,X1,X2)
| cartesian_product2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f19]) ).
fof(f19,plain,
! [X0,X1,X2] :
( cartesian_product2(X0,X1) = X2
<=> sP1(X0,X1,X2) ),
inference(definition_folding,[],[f3,f18,f17]) ).
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/sandbox/benchmark/theBenchmark.p',d2_zfmisc_1) ).
fof(f61,plain,
in(sK5,cartesian_product2(sK3,sK4)),
inference(unit_resulting_resolution,[],[f36,f35,f43]) ).
fof(f43,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/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f35,plain,
subset(sK2,cartesian_product2(sK3,sK4)),
inference(cnf_transformation,[],[f21]) ).
fof(f36,plain,
in(sK5,sK2),
inference(cnf_transformation,[],[f21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET950+1 : TPTP v8.1.2. Released v3.2.0.
% 0.04/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n011.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri May 3 16:29:56 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % (20257)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.37 % (20262)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)
% 0.22/0.37 % (20260)WARNING: value z3 for option sas not known
% 0.22/0.38 % (20258)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.22/0.38 % (20259)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.22/0.38 % (20261)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.22/0.38 % (20260)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)
% 0.22/0.38 % (20263)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)
% 0.22/0.38 % (20264)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)
% 0.22/0.38 TRYING [1]
% 0.22/0.38 TRYING [2]
% 0.22/0.39 TRYING [1]
% 0.22/0.39 TRYING [3]
% 0.22/0.39 TRYING [1]
% 0.22/0.39 TRYING [2]
% 0.22/0.39 TRYING [2]
% 0.22/0.39 % (20264)First to succeed.
% 0.22/0.39 TRYING [3]
% 0.22/0.39 % (20264)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-20257"
% 0.22/0.39 % (20264)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 % (20264)------------------------------
% 0.22/0.39 % (20264)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.22/0.39 % (20264)Termination reason: Refutation
% 0.22/0.39
% 0.22/0.39 % (20264)Memory used [KB]: 954
% 0.22/0.39 % (20264)Time elapsed: 0.015 s
% 0.22/0.39 % (20264)Instructions burned: 24 (million)
% 0.22/0.39 % (20257)Success in time 0.032 s
%------------------------------------------------------------------------------