TSTP Solution File: SEU055+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU055+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 : n013.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 15:22:03 EDT 2024
% Result : Theorem 0.21s 0.44s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 10
% Syntax : Number of formulae : 77 ( 24 unt; 0 def)
% Number of atoms : 225 ( 85 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 245 ( 97 ~; 89 |; 42 &)
% ( 7 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 5 ( 2 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 : 92 ( 83 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1399,plain,
$false,
inference(resolution,[],[f1382,f110]) ).
fof(f110,plain,
relation(sK2),
inference(cnf_transformation,[],[f75]) ).
fof(f75,plain,
( ~ one_to_one(sK2)
& ! [X1,X2] : relation_image(sK2,set_difference(X1,X2)) = set_difference(relation_image(sK2,X1),relation_image(sK2,X2))
& function(sK2)
& relation(sK2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f46,f74]) ).
fof(f74,plain,
( ? [X0] :
( ~ one_to_one(X0)
& ! [X1,X2] : relation_image(X0,set_difference(X1,X2)) = set_difference(relation_image(X0,X1),relation_image(X0,X2))
& function(X0)
& relation(X0) )
=> ( ~ one_to_one(sK2)
& ! [X2,X1] : relation_image(sK2,set_difference(X1,X2)) = set_difference(relation_image(sK2,X1),relation_image(sK2,X2))
& function(sK2)
& relation(sK2) ) ),
introduced(choice_axiom,[]) ).
fof(f46,plain,
? [X0] :
( ~ one_to_one(X0)
& ! [X1,X2] : relation_image(X0,set_difference(X1,X2)) = set_difference(relation_image(X0,X1),relation_image(X0,X2))
& function(X0)
& relation(X0) ),
inference(flattening,[],[f45]) ).
fof(f45,plain,
? [X0] :
( ~ one_to_one(X0)
& ! [X1,X2] : relation_image(X0,set_difference(X1,X2)) = set_difference(relation_image(X0,X1),relation_image(X0,X2))
& function(X0)
& relation(X0) ),
inference(ennf_transformation,[],[f29]) ).
fof(f29,negated_conjecture,
~ ! [X0] :
( ( function(X0)
& relation(X0) )
=> ( ! [X1,X2] : relation_image(X0,set_difference(X1,X2)) = set_difference(relation_image(X0,X1),relation_image(X0,X2))
=> one_to_one(X0) ) ),
inference(negated_conjecture,[],[f28]) ).
fof(f28,conjecture,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( ! [X1,X2] : relation_image(X0,set_difference(X1,X2)) = set_difference(relation_image(X0,X1),relation_image(X0,X2))
=> one_to_one(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t124_funct_1) ).
fof(f1382,plain,
~ relation(sK2),
inference(resolution,[],[f1381,f111]) ).
fof(f111,plain,
function(sK2),
inference(cnf_transformation,[],[f75]) ).
fof(f1381,plain,
( ~ function(sK2)
| ~ relation(sK2) ),
inference(resolution,[],[f1380,f201]) ).
fof(f201,plain,
( ~ sP0(sK2)
| ~ relation(sK2)
| ~ function(sK2) ),
inference(resolution,[],[f138,f200]) ).
fof(f200,plain,
( ~ sP1(sK2)
| ~ sP0(sK2) ),
inference(resolution,[],[f132,f113]) ).
fof(f113,plain,
~ one_to_one(sK2),
inference(cnf_transformation,[],[f75]) ).
fof(f132,plain,
! [X0] :
( one_to_one(X0)
| ~ sP0(X0)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f78]) ).
fof(f78,plain,
! [X0] :
( ( ( one_to_one(X0)
| ~ sP0(X0) )
& ( sP0(X0)
| ~ one_to_one(X0) ) )
| ~ sP1(X0) ),
inference(nnf_transformation,[],[f72]) ).
fof(f72,plain,
! [X0] :
( ( one_to_one(X0)
<=> sP0(X0) )
| ~ sP1(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f138,plain,
! [X0] :
( sP1(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f73]) ).
fof(f73,plain,
! [X0] :
( sP1(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(definition_folding,[],[f55,f72,f71]) ).
fof(f71,plain,
! [X0] :
( sP0(X0)
<=> ! [X1,X2] :
( X1 = X2
| apply(X0,X1) != apply(X0,X2)
| ~ in(X2,relation_dom(X0))
| ~ in(X1,relation_dom(X0)) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f55,plain,
! [X0] :
( ( one_to_one(X0)
<=> ! [X1,X2] :
( X1 = X2
| apply(X0,X1) != apply(X0,X2)
| ~ in(X2,relation_dom(X0))
| ~ in(X1,relation_dom(X0)) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f54]) ).
fof(f54,plain,
! [X0] :
( ( one_to_one(X0)
<=> ! [X1,X2] :
( X1 = X2
| apply(X0,X1) != apply(X0,X2)
| ~ in(X2,relation_dom(X0))
| ~ in(X1,relation_dom(X0)) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( one_to_one(X0)
<=> ! [X1,X2] :
( ( apply(X0,X1) = apply(X0,X2)
& in(X2,relation_dom(X0))
& in(X1,relation_dom(X0)) )
=> X1 = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_funct_1) ).
fof(f1380,plain,
sP0(sK2),
inference(trivial_inequality_removal,[],[f1378]) ).
fof(f1378,plain,
( sK4(sK2) != sK4(sK2)
| sP0(sK2) ),
inference(superposition,[],[f137,f1280]) ).
fof(f1280,plain,
sK4(sK2) = sK5(sK2),
inference(trivial_inequality_removal,[],[f1267]) ).
fof(f1267,plain,
( empty_set != empty_set
| sK4(sK2) = sK5(sK2) ),
inference(superposition,[],[f292,f1236]) ).
fof(f1236,plain,
( empty_set = singleton(apply(sK2,sK4(sK2)))
| sK4(sK2) = sK5(sK2) ),
inference(superposition,[],[f1206,f891]) ).
fof(f891,plain,
singleton(apply(sK2,sK4(sK2))) = relation_image(sK2,singleton(sK5(sK2))),
inference(resolution,[],[f889,f110]) ).
fof(f889,plain,
( ~ relation(sK2)
| singleton(apply(sK2,sK4(sK2))) = relation_image(sK2,singleton(sK5(sK2))) ),
inference(resolution,[],[f860,f111]) ).
fof(f860,plain,
( ~ function(sK2)
| singleton(apply(sK2,sK4(sK2))) = relation_image(sK2,singleton(sK5(sK2)))
| ~ relation(sK2) ),
inference(duplicate_literal_removal,[],[f859]) ).
fof(f859,plain,
( ~ relation(sK2)
| singleton(apply(sK2,sK4(sK2))) = relation_image(sK2,singleton(sK5(sK2)))
| ~ relation(sK2)
| ~ function(sK2) ),
inference(resolution,[],[f622,f201]) ).
fof(f622,plain,
( sP0(sK2)
| ~ relation(sK2)
| singleton(apply(sK2,sK4(sK2))) = relation_image(sK2,singleton(sK5(sK2))) ),
inference(forward_demodulation,[],[f620,f383]) ).
fof(f383,plain,
apply(sK2,sK4(sK2)) = apply(sK2,sK5(sK2)),
inference(resolution,[],[f381,f110]) ).
fof(f381,plain,
( ~ relation(sK2)
| apply(sK2,sK4(sK2)) = apply(sK2,sK5(sK2)) ),
inference(resolution,[],[f380,f111]) ).
fof(f380,plain,
( ~ function(sK2)
| ~ relation(sK2)
| apply(sK2,sK4(sK2)) = apply(sK2,sK5(sK2)) ),
inference(resolution,[],[f136,f201]) ).
fof(f136,plain,
! [X0] :
( sP0(X0)
| apply(X0,sK4(X0)) = apply(X0,sK5(X0)) ),
inference(cnf_transformation,[],[f82]) ).
fof(f82,plain,
! [X0] :
( ( sP0(X0)
| ( sK4(X0) != sK5(X0)
& apply(X0,sK4(X0)) = apply(X0,sK5(X0))
& in(sK5(X0),relation_dom(X0))
& in(sK4(X0),relation_dom(X0)) ) )
& ( ! [X3,X4] :
( X3 = X4
| apply(X0,X3) != apply(X0,X4)
| ~ in(X4,relation_dom(X0))
| ~ in(X3,relation_dom(X0)) )
| ~ sP0(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f80,f81]) ).
fof(f81,plain,
! [X0] :
( ? [X1,X2] :
( X1 != X2
& apply(X0,X1) = apply(X0,X2)
& in(X2,relation_dom(X0))
& in(X1,relation_dom(X0)) )
=> ( sK4(X0) != sK5(X0)
& apply(X0,sK4(X0)) = apply(X0,sK5(X0))
& in(sK5(X0),relation_dom(X0))
& in(sK4(X0),relation_dom(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f80,plain,
! [X0] :
( ( sP0(X0)
| ? [X1,X2] :
( X1 != X2
& apply(X0,X1) = apply(X0,X2)
& in(X2,relation_dom(X0))
& in(X1,relation_dom(X0)) ) )
& ( ! [X3,X4] :
( X3 = X4
| apply(X0,X3) != apply(X0,X4)
| ~ in(X4,relation_dom(X0))
| ~ in(X3,relation_dom(X0)) )
| ~ sP0(X0) ) ),
inference(rectify,[],[f79]) ).
fof(f79,plain,
! [X0] :
( ( sP0(X0)
| ? [X1,X2] :
( X1 != X2
& apply(X0,X1) = apply(X0,X2)
& in(X2,relation_dom(X0))
& in(X1,relation_dom(X0)) ) )
& ( ! [X1,X2] :
( X1 = X2
| apply(X0,X1) != apply(X0,X2)
| ~ in(X2,relation_dom(X0))
| ~ in(X1,relation_dom(X0)) )
| ~ sP0(X0) ) ),
inference(nnf_transformation,[],[f71]) ).
fof(f620,plain,
( relation_image(sK2,singleton(sK5(sK2))) = singleton(apply(sK2,sK5(sK2)))
| ~ relation(sK2)
| sP0(sK2) ),
inference(resolution,[],[f536,f135]) ).
fof(f135,plain,
! [X0] :
( in(sK5(X0),relation_dom(X0))
| sP0(X0) ),
inference(cnf_transformation,[],[f82]) ).
fof(f536,plain,
! [X0] :
( ~ in(X0,relation_dom(sK2))
| relation_image(sK2,singleton(X0)) = singleton(apply(sK2,X0))
| ~ relation(sK2) ),
inference(resolution,[],[f149,f111]) ).
fof(f149,plain,
! [X0,X1] :
( ~ function(X1)
| ~ in(X0,relation_dom(X1))
| relation_image(X1,singleton(X0)) = singleton(apply(X1,X0))
| ~ relation(X1) ),
inference(cnf_transformation,[],[f63]) ).
fof(f63,plain,
! [X0,X1] :
( relation_image(X1,singleton(X0)) = singleton(apply(X1,X0))
| ~ in(X0,relation_dom(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f62]) ).
fof(f62,plain,
! [X0,X1] :
( relation_image(X1,singleton(X0)) = singleton(apply(X1,X0))
| ~ in(X0,relation_dom(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f27]) ).
fof(f27,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ( in(X0,relation_dom(X1))
=> relation_image(X1,singleton(X0)) = singleton(apply(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t117_funct_1) ).
fof(f1206,plain,
( empty_set = relation_image(sK2,singleton(sK5(sK2)))
| sK4(sK2) = sK5(sK2) ),
inference(superposition,[],[f1199,f160]) ).
fof(f160,plain,
! [X0,X1] :
( singleton(X0) = set_difference(singleton(X0),singleton(X1))
| X0 = X1 ),
inference(cnf_transformation,[],[f93]) ).
fof(f93,plain,
! [X0,X1] :
( ( singleton(X0) = set_difference(singleton(X0),singleton(X1))
| X0 = X1 )
& ( X0 != X1
| singleton(X0) != set_difference(singleton(X0),singleton(X1)) ) ),
inference(nnf_transformation,[],[f31]) ).
fof(f31,axiom,
! [X0,X1] :
( singleton(X0) = set_difference(singleton(X0),singleton(X1))
<=> X0 != X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_zfmisc_1) ).
fof(f1199,plain,
empty_set = relation_image(sK2,set_difference(singleton(sK5(sK2)),singleton(sK4(sK2)))),
inference(forward_demodulation,[],[f1186,f299]) ).
fof(f299,plain,
empty_set = relation_image(sK2,empty_set),
inference(forward_demodulation,[],[f293,f289]) ).
fof(f289,plain,
! [X0] : empty_set = set_difference(X0,X0),
inference(resolution,[],[f158,f145]) ).
fof(f145,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f42]) ).
fof(f42,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f26]) ).
fof(f26,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f158,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| empty_set = set_difference(X0,X1) ),
inference(cnf_transformation,[],[f92]) ).
fof(f92,plain,
! [X0,X1] :
( ( empty_set = set_difference(X0,X1)
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| empty_set != set_difference(X0,X1) ) ),
inference(nnf_transformation,[],[f33]) ).
fof(f33,axiom,
! [X0,X1] :
( empty_set = set_difference(X0,X1)
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_xboole_1) ).
fof(f293,plain,
! [X0] : empty_set = relation_image(sK2,set_difference(X0,X0)),
inference(superposition,[],[f289,f112]) ).
fof(f112,plain,
! [X2,X1] : relation_image(sK2,set_difference(X1,X2)) = set_difference(relation_image(sK2,X1),relation_image(sK2,X2)),
inference(cnf_transformation,[],[f75]) ).
fof(f1186,plain,
relation_image(sK2,empty_set) = relation_image(sK2,set_difference(singleton(sK5(sK2)),singleton(sK4(sK2)))),
inference(superposition,[],[f902,f289]) ).
fof(f902,plain,
! [X0] : relation_image(sK2,set_difference(X0,singleton(sK4(sK2)))) = relation_image(sK2,set_difference(X0,singleton(sK5(sK2)))),
inference(forward_demodulation,[],[f900,f877]) ).
fof(f877,plain,
! [X0] : relation_image(sK2,set_difference(X0,singleton(sK4(sK2)))) = set_difference(relation_image(sK2,X0),singleton(apply(sK2,sK4(sK2)))),
inference(superposition,[],[f112,f869]) ).
fof(f869,plain,
relation_image(sK2,singleton(sK4(sK2))) = singleton(apply(sK2,sK4(sK2))),
inference(resolution,[],[f867,f110]) ).
fof(f867,plain,
( ~ relation(sK2)
| relation_image(sK2,singleton(sK4(sK2))) = singleton(apply(sK2,sK4(sK2))) ),
inference(resolution,[],[f858,f111]) ).
fof(f858,plain,
( ~ function(sK2)
| relation_image(sK2,singleton(sK4(sK2))) = singleton(apply(sK2,sK4(sK2)))
| ~ relation(sK2) ),
inference(duplicate_literal_removal,[],[f857]) ).
fof(f857,plain,
( ~ relation(sK2)
| relation_image(sK2,singleton(sK4(sK2))) = singleton(apply(sK2,sK4(sK2)))
| ~ relation(sK2)
| ~ function(sK2) ),
inference(resolution,[],[f619,f201]) ).
fof(f619,plain,
( sP0(sK2)
| ~ relation(sK2)
| relation_image(sK2,singleton(sK4(sK2))) = singleton(apply(sK2,sK4(sK2))) ),
inference(resolution,[],[f536,f134]) ).
fof(f134,plain,
! [X0] :
( in(sK4(X0),relation_dom(X0))
| sP0(X0) ),
inference(cnf_transformation,[],[f82]) ).
fof(f900,plain,
! [X0] : set_difference(relation_image(sK2,X0),singleton(apply(sK2,sK4(sK2)))) = relation_image(sK2,set_difference(X0,singleton(sK5(sK2)))),
inference(superposition,[],[f112,f891]) ).
fof(f292,plain,
! [X1] : empty_set != singleton(X1),
inference(backward_demodulation,[],[f183,f289]) ).
fof(f183,plain,
! [X1] : singleton(X1) != set_difference(singleton(X1),singleton(X1)),
inference(equality_resolution,[],[f159]) ).
fof(f159,plain,
! [X0,X1] :
( X0 != X1
| singleton(X0) != set_difference(singleton(X0),singleton(X1)) ),
inference(cnf_transformation,[],[f93]) ).
fof(f137,plain,
! [X0] :
( sK4(X0) != sK5(X0)
| sP0(X0) ),
inference(cnf_transformation,[],[f82]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU055+1 : TPTP v8.1.2. Released v3.2.0.
% 0.03/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36 % Computer : n013.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Mon Apr 29 20:49:04 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % (14175)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.37 % (14181)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.38 TRYING [1]
% 0.21/0.38 TRYING [2]
% 0.21/0.38 TRYING [3]
% 0.21/0.38 % (14180)WARNING: value z3 for option sas not known
% 0.21/0.38 % (14178)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.38 % (14182)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)
% 0.21/0.38 % (14180)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)
% 0.21/0.38 % (14179)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.38 % (14183)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)
% 0.21/0.38 % (14184)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)
% 0.21/0.38 TRYING [4]
% 0.21/0.39 TRYING [1]
% 0.21/0.39 TRYING [5]
% 0.21/0.39 TRYING [2]
% 0.21/0.40 TRYING [3]
% 0.21/0.41 TRYING [6]
% 0.21/0.43 % (14183)First to succeed.
% 0.21/0.44 % (14183)Refutation found. Thanks to Tanya!
% 0.21/0.44 % SZS status Theorem for theBenchmark
% 0.21/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.44 % (14183)------------------------------
% 0.21/0.44 % (14183)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.21/0.44 % (14183)Termination reason: Refutation
% 0.21/0.44
% 0.21/0.44 % (14183)Memory used [KB]: 1562
% 0.21/0.44 % (14183)Time elapsed: 0.057 s
% 0.21/0.44 % (14183)Instructions burned: 88 (million)
% 0.21/0.44 % (14183)------------------------------
% 0.21/0.44 % (14183)------------------------------
% 0.21/0.44 % (14175)Success in time 0.073 s
%------------------------------------------------------------------------------