TSTP Solution File: SET600+3 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET600+3 : TPTP v8.2.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n015.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 03:19:36 EDT 2024
% Result : Theorem 0.15s 0.40s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 8
% Syntax : Number of formulae : 47 ( 10 unt; 0 def)
% Number of atoms : 150 ( 76 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 160 ( 57 ~; 63 |; 30 &)
% ( 6 <=>; 3 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 68 ( 57 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f163,plain,
$false,
inference(unit_resulting_resolution,[],[f35,f35,f97,f50]) ).
fof(f50,plain,
! [X2,X0,X1] :
( ~ member(X2,union(X0,X1))
| member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[],[f31]) ).
fof(f31,plain,
! [X0,X1,X2] :
( ( member(X2,union(X0,X1))
| ( ~ member(X2,X1)
& ~ member(X2,X0) ) )
& ( member(X2,X1)
| member(X2,X0)
| ~ member(X2,union(X0,X1)) ) ),
inference(flattening,[],[f30]) ).
fof(f30,plain,
! [X0,X1,X2] :
( ( member(X2,union(X0,X1))
| ( ~ member(X2,X1)
& ~ member(X2,X0) ) )
& ( member(X2,X1)
| member(X2,X0)
| ~ member(X2,union(X0,X1)) ) ),
inference(nnf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1,X2] :
( member(X2,union(X0,X1))
<=> ( member(X2,X1)
| member(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_defn) ).
fof(f97,plain,
member(sK4(union(empty_set,empty_set),empty_set),union(empty_set,empty_set)),
inference(unit_resulting_resolution,[],[f91,f63]) ).
fof(f63,plain,
! [X0] :
( member(sK4(X0,empty_set),X0)
| empty_set = X0 ),
inference(resolution,[],[f61,f48]) ).
fof(f48,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK4(X0,X1),X0) ),
inference(cnf_transformation,[],[f29]) ).
fof(f29,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK4(X0,X1),X1)
& member(sK4(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f27,f28]) ).
fof(f28,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) )
=> ( ~ member(sK4(X0,X1),X1)
& member(sK4(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f27,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,[],[f26]) ).
fof(f26,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,[],[f12]) ).
fof(f12,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
fof(f61,plain,
! [X0] :
( ~ subset(X0,empty_set)
| empty_set = X0 ),
inference(resolution,[],[f40,f58]) ).
fof(f58,plain,
! [X0] : subset(empty_set,X0),
inference(unit_resulting_resolution,[],[f35,f48]) ).
fof(f40,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,[],[f3]) ).
fof(f3,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).
fof(f91,plain,
empty_set != union(empty_set,empty_set),
inference(unit_resulting_resolution,[],[f80,f90,f57]) ).
fof(f57,plain,
( empty_set != union(empty_set,empty_set)
| empty_set != sK1
| empty_set != sK2 ),
inference(inner_rewriting,[],[f56]) ).
fof(f56,plain,
( empty_set != sK2
| empty_set != sK1
| empty_set != union(sK1,empty_set) ),
inference(inner_rewriting,[],[f34]) ).
fof(f34,plain,
( empty_set != sK2
| empty_set != sK1
| empty_set != union(sK1,sK2) ),
inference(cnf_transformation,[],[f18]) ).
fof(f18,plain,
( ( empty_set != sK2
| empty_set != sK1
| empty_set != union(sK1,sK2) )
& ( ( empty_set = sK2
& empty_set = sK1 )
| empty_set = union(sK1,sK2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f16,f17]) ).
fof(f17,plain,
( ? [X0,X1] :
( ( empty_set != X1
| empty_set != X0
| union(X0,X1) != empty_set )
& ( ( empty_set = X1
& empty_set = X0 )
| union(X0,X1) = empty_set ) )
=> ( ( empty_set != sK2
| empty_set != sK1
| empty_set != union(sK1,sK2) )
& ( ( empty_set = sK2
& empty_set = sK1 )
| empty_set = union(sK1,sK2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f16,plain,
? [X0,X1] :
( ( empty_set != X1
| empty_set != X0
| union(X0,X1) != empty_set )
& ( ( empty_set = X1
& empty_set = X0 )
| union(X0,X1) = empty_set ) ),
inference(flattening,[],[f15]) ).
fof(f15,plain,
? [X0,X1] :
( ( empty_set != X1
| empty_set != X0
| union(X0,X1) != empty_set )
& ( ( empty_set = X1
& empty_set = X0 )
| union(X0,X1) = empty_set ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f11,plain,
? [X0,X1] :
( union(X0,X1) = empty_set
<~> ( empty_set = X1
& empty_set = X0 ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,negated_conjecture,
~ ! [X0,X1] :
( union(X0,X1) = empty_set
<=> ( empty_set = X1
& empty_set = X0 ) ),
inference(negated_conjecture,[],[f9]) ).
fof(f9,conjecture,
! [X0,X1] :
( union(X0,X1) = empty_set
<=> ( empty_set = X1
& empty_set = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th59) ).
fof(f90,plain,
empty_set = sK1,
inference(subsumption_resolution,[],[f89,f35]) ).
fof(f89,plain,
( member(sK4(sK1,empty_set),empty_set)
| empty_set = sK1 ),
inference(duplicate_literal_removal,[],[f88]) ).
fof(f88,plain,
( member(sK4(sK1,empty_set),empty_set)
| empty_set = sK1
| empty_set = sK1 ),
inference(superposition,[],[f68,f83]) ).
fof(f83,plain,
( empty_set = union(empty_set,sK1)
| empty_set = sK1 ),
inference(superposition,[],[f82,f37]) ).
fof(f37,plain,
! [X0,X1] : union(X0,X1) = union(X1,X0),
inference(cnf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0,X1] : union(X0,X1) = union(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_union) ).
fof(f82,plain,
( empty_set = union(sK1,empty_set)
| empty_set = sK1 ),
inference(superposition,[],[f32,f80]) ).
fof(f32,plain,
( empty_set = union(sK1,sK2)
| empty_set = sK1 ),
inference(cnf_transformation,[],[f18]) ).
fof(f68,plain,
! [X0,X1] :
( member(sK4(X0,empty_set),union(X1,X0))
| empty_set = X0 ),
inference(resolution,[],[f63,f52]) ).
fof(f52,plain,
! [X2,X0,X1] :
( ~ member(X2,X1)
| member(X2,union(X0,X1)) ),
inference(cnf_transformation,[],[f31]) ).
fof(f80,plain,
empty_set = sK2,
inference(subsumption_resolution,[],[f79,f35]) ).
fof(f79,plain,
( member(sK4(sK2,empty_set),empty_set)
| empty_set = sK2 ),
inference(duplicate_literal_removal,[],[f77]) ).
fof(f77,plain,
( member(sK4(sK2,empty_set),empty_set)
| empty_set = sK2
| empty_set = sK2 ),
inference(superposition,[],[f68,f33]) ).
fof(f33,plain,
( empty_set = union(sK1,sK2)
| empty_set = sK2 ),
inference(cnf_transformation,[],[f18]) ).
fof(f35,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0] : ~ member(X0,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set_defn) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET600+3 : TPTP v8.2.0. Released v2.2.0.
% 0.12/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.37 % Computer : n015.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Mon May 20 11:31:38 EDT 2024
% 0.15/0.37 % CPUTime :
% 0.15/0.38 % (7157)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.39 % (7160)WARNING: value z3 for option sas not known
% 0.15/0.39 % (7158)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.39 % (7159)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.39 % (7164)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)
% 0.15/0.39 % (7162)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)
% 0.15/0.39 % (7161)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.39 % (7163)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)
% 0.15/0.39 % (7160)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)
% 0.15/0.40 TRYING [1]
% 0.15/0.40 TRYING [2]
% 0.15/0.40 TRYING [3]
% 0.15/0.40 TRYING [1]
% 0.15/0.40 TRYING [2]
% 0.15/0.40 TRYING [4]
% 0.15/0.40 % (7164)First to succeed.
% 0.15/0.40 % (7164)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-7157"
% 0.15/0.40 % (7163)Also succeeded, but the first one will report.
% 0.15/0.40 % (7164)Refutation found. Thanks to Tanya!
% 0.15/0.40 % SZS status Theorem for theBenchmark
% 0.15/0.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.40 % (7164)------------------------------
% 0.15/0.40 % (7164)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.40 % (7164)Termination reason: Refutation
% 0.15/0.40
% 0.15/0.40 % (7164)Memory used [KB]: 834
% 0.15/0.40 % (7164)Time elapsed: 0.007 s
% 0.15/0.40 % (7164)Instructions burned: 9 (million)
% 0.15/0.40 % (7157)Success in time 0.024 s
%------------------------------------------------------------------------------