TSTP Solution File: SET997+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET997+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 : n021.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 03:25:03 EDT 2024
% Result : Theorem 0.16s 0.41s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of formulae : 52 ( 13 unt; 0 def)
% Number of atoms : 206 ( 31 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 235 ( 81 ~; 70 |; 61 &)
% ( 12 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-2 aty)
% Number of variables : 114 ( 90 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5226,plain,
$false,
inference(subsumption_resolution,[],[f5225,f3215]) ).
fof(f3215,plain,
~ sP0(sK11(sK3,relation_rng(sK4)),sK4),
inference(unit_resulting_resolution,[],[f937,f356,f125]) ).
fof(f125,plain,
! [X3,X0,X1] :
( ~ sP1(X0,X1)
| ~ sP0(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f74]) ).
fof(f74,plain,
! [X0,X1] :
( ( sP1(X0,X1)
| ( ( ~ sP0(sK7(X0,X1),X0)
| ~ in(sK7(X0,X1),X1) )
& ( sP0(sK7(X0,X1),X0)
| in(sK7(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| ~ sP0(X3,X0) )
& ( sP0(X3,X0)
| ~ in(X3,X1) ) )
| ~ sP1(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f72,f73]) ).
fof(f73,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ sP0(X2,X0)
| ~ in(X2,X1) )
& ( sP0(X2,X0)
| in(X2,X1) ) )
=> ( ( ~ sP0(sK7(X0,X1),X0)
| ~ in(sK7(X0,X1),X1) )
& ( sP0(sK7(X0,X1),X0)
| in(sK7(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f72,plain,
! [X0,X1] :
( ( sP1(X0,X1)
| ? [X2] :
( ( ~ sP0(X2,X0)
| ~ in(X2,X1) )
& ( sP0(X2,X0)
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| ~ sP0(X3,X0) )
& ( sP0(X3,X0)
| ~ in(X3,X1) ) )
| ~ sP1(X0,X1) ) ),
inference(rectify,[],[f71]) ).
fof(f71,plain,
! [X0,X1] :
( ( sP1(X0,X1)
| ? [X2] :
( ( ~ sP0(X2,X0)
| ~ in(X2,X1) )
& ( sP0(X2,X0)
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ~ sP0(X2,X0) )
& ( sP0(X2,X0)
| ~ in(X2,X1) ) )
| ~ sP1(X0,X1) ) ),
inference(nnf_transformation,[],[f62]) ).
fof(f62,plain,
! [X0,X1] :
( sP1(X0,X1)
<=> ! [X2] :
( in(X2,X1)
<=> sP0(X2,X0) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f356,plain,
sP1(sK4,relation_rng(sK4)),
inference(unit_resulting_resolution,[],[f326,f157]) ).
fof(f157,plain,
! [X0] :
( ~ sP2(X0)
| sP1(X0,relation_rng(X0)) ),
inference(equality_resolution,[],[f122]) ).
fof(f122,plain,
! [X0,X1] :
( sP1(X0,X1)
| relation_rng(X0) != X1
| ~ sP2(X0) ),
inference(cnf_transformation,[],[f70]) ).
fof(f70,plain,
! [X0] :
( ! [X1] :
( ( relation_rng(X0) = X1
| ~ sP1(X0,X1) )
& ( sP1(X0,X1)
| relation_rng(X0) != X1 ) )
| ~ sP2(X0) ),
inference(nnf_transformation,[],[f63]) ).
fof(f63,plain,
! [X0] :
( ! [X1] :
( relation_rng(X0) = X1
<=> sP1(X0,X1) )
| ~ sP2(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f326,plain,
sP2(sK4),
inference(unit_resulting_resolution,[],[f101,f100,f131]) ).
fof(f131,plain,
! [X0] :
( ~ relation(X0)
| ~ function(X0)
| sP2(X0) ),
inference(cnf_transformation,[],[f64]) ).
fof(f64,plain,
! [X0] :
( sP2(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(definition_folding,[],[f50,f63,f62,f61]) ).
fof(f61,plain,
! [X2,X0] :
( sP0(X2,X0)
<=> ? [X3] :
( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f50,plain,
! [X0] :
( ! [X1] :
( relation_rng(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) ) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f49]) ).
fof(f49,plain,
! [X0] :
( ! [X1] :
( relation_rng(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) ) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ! [X1] :
( relation_rng(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_funct_1) ).
fof(f100,plain,
relation(sK4),
inference(cnf_transformation,[],[f67]) ).
fof(f67,plain,
( ~ subset(sK3,relation_rng(sK4))
& ! [X2] :
( ( apply(sK4,sK5(X2)) = X2
& in(sK5(X2),relation_dom(sK4)) )
| ~ in(X2,sK3) )
& function(sK4)
& relation(sK4) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f38,f66,f65]) ).
fof(f65,plain,
( ? [X0,X1] :
( ~ subset(X0,relation_rng(X1))
& ! [X2] :
( ? [X3] :
( apply(X1,X3) = X2
& in(X3,relation_dom(X1)) )
| ~ in(X2,X0) )
& function(X1)
& relation(X1) )
=> ( ~ subset(sK3,relation_rng(sK4))
& ! [X2] :
( ? [X3] :
( apply(sK4,X3) = X2
& in(X3,relation_dom(sK4)) )
| ~ in(X2,sK3) )
& function(sK4)
& relation(sK4) ) ),
introduced(choice_axiom,[]) ).
fof(f66,plain,
! [X2] :
( ? [X3] :
( apply(sK4,X3) = X2
& in(X3,relation_dom(sK4)) )
=> ( apply(sK4,sK5(X2)) = X2
& in(sK5(X2),relation_dom(sK4)) ) ),
introduced(choice_axiom,[]) ).
fof(f38,plain,
? [X0,X1] :
( ~ subset(X0,relation_rng(X1))
& ! [X2] :
( ? [X3] :
( apply(X1,X3) = X2
& in(X3,relation_dom(X1)) )
| ~ in(X2,X0) )
& function(X1)
& relation(X1) ),
inference(flattening,[],[f37]) ).
fof(f37,plain,
? [X0,X1] :
( ~ subset(X0,relation_rng(X1))
& ! [X2] :
( ? [X3] :
( apply(X1,X3) = X2
& in(X3,relation_dom(X1)) )
| ~ in(X2,X0) )
& function(X1)
& relation(X1) ),
inference(ennf_transformation,[],[f25]) ).
fof(f25,negated_conjecture,
~ ! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ( ! [X2] :
~ ( ! [X3] :
~ ( apply(X1,X3) = X2
& in(X3,relation_dom(X1)) )
& in(X2,X0) )
=> subset(X0,relation_rng(X1)) ) ),
inference(negated_conjecture,[],[f24]) ).
fof(f24,conjecture,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ( ! [X2] :
~ ( ! [X3] :
~ ( apply(X1,X3) = X2
& in(X3,relation_dom(X1)) )
& in(X2,X0) )
=> subset(X0,relation_rng(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_funct_1) ).
fof(f101,plain,
function(sK4),
inference(cnf_transformation,[],[f67]) ).
fof(f937,plain,
~ in(sK11(sK3,relation_rng(sK4)),relation_rng(sK4)),
inference(unit_resulting_resolution,[],[f104,f141]) ).
fof(f141,plain,
! [X0,X1] :
( ~ in(sK11(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f86]) ).
fof(f86,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK11(X0,X1),X1)
& in(sK11(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f84,f85]) ).
fof(f85,plain,
! [X0,X1] :
( ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) )
=> ( ~ in(sK11(X0,X1),X1)
& in(sK11(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f84,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,[],[f83]) ).
fof(f83,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,[],[f55]) ).
fof(f55,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[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(f104,plain,
~ subset(sK3,relation_rng(sK4)),
inference(cnf_transformation,[],[f67]) ).
fof(f5225,plain,
sP0(sK11(sK3,relation_rng(sK4)),sK4),
inference(forward_demodulation,[],[f5207,f2081]) ).
fof(f2081,plain,
sK11(sK3,relation_rng(sK4)) = apply(sK4,sK5(sK11(sK3,relation_rng(sK4)))),
inference(unit_resulting_resolution,[],[f706,f103]) ).
fof(f103,plain,
! [X2] :
( ~ in(X2,sK3)
| apply(sK4,sK5(X2)) = X2 ),
inference(cnf_transformation,[],[f67]) ).
fof(f706,plain,
in(sK11(sK3,relation_rng(sK4)),sK3),
inference(unit_resulting_resolution,[],[f104,f140]) ).
fof(f140,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sK11(X0,X1),X0) ),
inference(cnf_transformation,[],[f86]) ).
fof(f5207,plain,
sP0(apply(sK4,sK5(sK11(sK3,relation_rng(sK4)))),sK4),
inference(unit_resulting_resolution,[],[f723,f158]) ).
fof(f158,plain,
! [X2,X1] :
( ~ in(X2,relation_dom(X1))
| sP0(apply(X1,X2),X1) ),
inference(equality_resolution,[],[f130]) ).
fof(f130,plain,
! [X2,X0,X1] :
( sP0(X0,X1)
| apply(X1,X2) != X0
| ~ in(X2,relation_dom(X1)) ),
inference(cnf_transformation,[],[f78]) ).
fof(f78,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ! [X2] :
( apply(X1,X2) != X0
| ~ in(X2,relation_dom(X1)) ) )
& ( ( apply(X1,sK8(X0,X1)) = X0
& in(sK8(X0,X1),relation_dom(X1)) )
| ~ sP0(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f76,f77]) ).
fof(f77,plain,
! [X0,X1] :
( ? [X3] :
( apply(X1,X3) = X0
& in(X3,relation_dom(X1)) )
=> ( apply(X1,sK8(X0,X1)) = X0
& in(sK8(X0,X1),relation_dom(X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f76,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ! [X2] :
( apply(X1,X2) != X0
| ~ in(X2,relation_dom(X1)) ) )
& ( ? [X3] :
( apply(X1,X3) = X0
& in(X3,relation_dom(X1)) )
| ~ sP0(X0,X1) ) ),
inference(rectify,[],[f75]) ).
fof(f75,plain,
! [X2,X0] :
( ( sP0(X2,X0)
| ! [X3] :
( apply(X0,X3) != X2
| ~ in(X3,relation_dom(X0)) ) )
& ( ? [X3] :
( apply(X0,X3) = X2
& in(X3,relation_dom(X0)) )
| ~ sP0(X2,X0) ) ),
inference(nnf_transformation,[],[f61]) ).
fof(f723,plain,
in(sK5(sK11(sK3,relation_rng(sK4))),relation_dom(sK4)),
inference(unit_resulting_resolution,[],[f706,f102]) ).
fof(f102,plain,
! [X2] :
( ~ in(X2,sK3)
| in(sK5(X2),relation_dom(sK4)) ),
inference(cnf_transformation,[],[f67]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.10 % Problem : SET997+1 : TPTP v8.2.0. Released v3.2.0.
% 0.07/0.11 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.10/0.31 % Computer : n021.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 : Mon May 20 11:16:07 EDT 2024
% 0.10/0.31 % CPUTime :
% 0.10/0.32 % (20791)Running in auto input_syntax mode. Trying TPTP
% 0.10/0.33 % (20793)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.10/0.33 % (20794)WARNING: value z3 for option sas not known
% 0.10/0.33 % (20792)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.10/0.33 % (20797)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)
% 0.10/0.33 % (20795)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.10/0.33 % (20794)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)
% 0.10/0.33 % (20796)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)
% 0.10/0.33 TRYING [1]
% 0.10/0.33 TRYING [2]
% 0.10/0.34 TRYING [3]
% 0.10/0.34 TRYING [1]
% 0.10/0.34 % (20798)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)
% 0.10/0.34 TRYING [2]
% 0.10/0.34 TRYING [4]
% 0.10/0.35 TRYING [5]
% 0.10/0.35 TRYING [3]
% 0.10/0.37 TRYING [4]
% 0.10/0.37 TRYING [6]
% 0.16/0.40 % (20798)First to succeed.
% 0.16/0.40 TRYING [5]
% 0.16/0.41 % (20798)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-20791"
% 0.16/0.41 % (20798)Refutation found. Thanks to Tanya!
% 0.16/0.41 % SZS status Theorem for theBenchmark
% 0.16/0.41 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.41 % (20798)------------------------------
% 0.16/0.41 % (20798)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.16/0.41 % (20798)Termination reason: Refutation
% 0.16/0.41
% 0.16/0.41 % (20798)Memory used [KB]: 2068
% 0.16/0.41 % (20798)Time elapsed: 0.069 s
% 0.16/0.41 % (20798)Instructions burned: 148 (million)
% 0.16/0.41 % (20791)Success in time 0.079 s
%------------------------------------------------------------------------------