TSTP Solution File: SET603+3 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET603+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n027.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 09:14:26 EDT 2024
% Result : Theorem 0.14s 0.38s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 36 ( 12 unt; 0 def)
% Number of atoms : 98 ( 16 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 103 ( 41 ~; 37 |; 18 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 71 ( 66 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f372,plain,
$false,
inference(trivial_inequality_removal,[],[f371]) ).
fof(f371,plain,
sK0 != sK0,
inference(superposition,[],[f31,f331]) ).
fof(f331,plain,
! [X0] : difference(X0,empty_set) = X0,
inference(resolution,[],[f319,f83]) ).
fof(f83,plain,
! [X0,X1] :
( ~ subset(X0,difference(X0,X1))
| difference(X0,X1) = X0 ),
inference(resolution,[],[f71,f38]) ).
fof(f38,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| X0 = X1
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f20,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 ) ),
inference(flattening,[],[f19]) ).
fof(f19,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
fof(f71,plain,
! [X0,X1] : subset(difference(X0,X1),X0),
inference(duplicate_literal_removal,[],[f67]) ).
fof(f67,plain,
! [X0,X1] :
( subset(difference(X0,X1),X0)
| subset(difference(X0,X1),X0) ),
inference(resolution,[],[f56,f45]) ).
fof(f45,plain,
! [X0,X1] :
( ~ member(sK3(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f28,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK3(X0,X1),X1)
& member(sK3(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f26,f27]) ).
fof(f27,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) )
=> ( ~ member(sK3(X0,X1),X1)
& member(sK3(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f26,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f25]) ).
fof(f25,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f13]) ).
fof(f13,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
fof(f56,plain,
! [X2,X0,X1] :
( member(sK3(difference(X0,X1),X2),X0)
| subset(difference(X0,X1),X2) ),
inference(resolution,[],[f46,f44]) ).
fof(f44,plain,
! [X0,X1] :
( member(sK3(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f46,plain,
! [X2,X0,X1] :
( ~ member(X2,difference(X0,X1))
| member(X2,X0) ),
inference(cnf_transformation,[],[f30]) ).
fof(f30,plain,
! [X0,X1,X2] :
( ( member(X2,difference(X0,X1))
| member(X2,X1)
| ~ member(X2,X0) )
& ( ( ~ member(X2,X1)
& member(X2,X0) )
| ~ member(X2,difference(X0,X1)) ) ),
inference(flattening,[],[f29]) ).
fof(f29,plain,
! [X0,X1,X2] :
( ( member(X2,difference(X0,X1))
| member(X2,X1)
| ~ member(X2,X0) )
& ( ( ~ member(X2,X1)
& member(X2,X0) )
| ~ member(X2,difference(X0,X1)) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0,X1,X2] :
( member(X2,difference(X0,X1))
<=> ( ~ member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_defn) ).
fof(f319,plain,
! [X0] : subset(X0,difference(X0,empty_set)),
inference(resolution,[],[f313,f32]) ).
fof(f32,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] : ~ member(X0,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set_defn) ).
fof(f313,plain,
! [X0,X1] :
( member(sK3(X0,difference(X0,X1)),X1)
| subset(X0,difference(X0,X1)) ),
inference(duplicate_literal_removal,[],[f304]) ).
fof(f304,plain,
! [X0,X1] :
( member(sK3(X0,difference(X0,X1)),X1)
| subset(X0,difference(X0,X1))
| subset(X0,difference(X0,X1)) ),
inference(resolution,[],[f66,f44]) ).
fof(f66,plain,
! [X2,X0,X1] :
( ~ member(sK3(X0,difference(X1,X2)),X1)
| member(sK3(X0,difference(X1,X2)),X2)
| subset(X0,difference(X1,X2)) ),
inference(resolution,[],[f48,f45]) ).
fof(f48,plain,
! [X2,X0,X1] :
( member(X2,difference(X0,X1))
| member(X2,X1)
| ~ member(X2,X0) ),
inference(cnf_transformation,[],[f30]) ).
fof(f31,plain,
sK0 != difference(sK0,empty_set),
inference(cnf_transformation,[],[f15]) ).
fof(f15,plain,
sK0 != difference(sK0,empty_set),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f11,f14]) ).
fof(f14,plain,
( ? [X0] : difference(X0,empty_set) != X0
=> sK0 != difference(sK0,empty_set) ),
introduced(choice_axiom,[]) ).
fof(f11,plain,
? [X0] : difference(X0,empty_set) != X0,
inference(ennf_transformation,[],[f10]) ).
fof(f10,negated_conjecture,
~ ! [X0] : difference(X0,empty_set) = X0,
inference(negated_conjecture,[],[f9]) ).
fof(f9,conjecture,
! [X0] : difference(X0,empty_set) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th74) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET603+3 : TPTP v8.1.2. Released v2.2.0.
% 0.12/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n027.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 16:43:08 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.36 % (5613)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37 % (5616)WARNING: value z3 for option sas not known
% 0.14/0.37 % (5616)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)
% 0.14/0.37 % (5614)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.37 % (5615)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.37 % (5617)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.37 % (5619)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)
% 0.14/0.37 % (5620)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)
% 0.14/0.37 % (5618)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)
% 0.14/0.38 TRYING [1]
% 0.14/0.38 TRYING [2]
% 0.14/0.38 TRYING [3]
% 0.14/0.38 TRYING [1]
% 0.14/0.38 % (5616)First to succeed.
% 0.14/0.38 TRYING [2]
% 0.14/0.38 % (5616)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-5613"
% 0.14/0.38 % (5616)Refutation found. Thanks to Tanya!
% 0.14/0.38 % SZS status Theorem for theBenchmark
% 0.14/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.38 % (5616)------------------------------
% 0.14/0.38 % (5616)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.38 % (5616)Termination reason: Refutation
% 0.14/0.38
% 0.14/0.38 % (5616)Memory used [KB]: 863
% 0.14/0.38 % (5616)Time elapsed: 0.009 s
% 0.14/0.38 % (5616)Instructions burned: 13 (million)
% 0.14/0.38 % (5613)Success in time 0.022 s
%------------------------------------------------------------------------------