TSTP Solution File: SET162+3 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET162+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 : n010.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 15:06:51 EDT 2024
% Result : Theorem 0.22s 0.39s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 36 ( 12 unt; 0 def)
% Number of atoms : 97 ( 16 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 101 ( 40 ~; 37 |; 17 &)
% ( 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 : 70 ( 65 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f360,plain,
$false,
inference(trivial_inequality_removal,[],[f359]) ).
fof(f359,plain,
sK0 != sK0,
inference(superposition,[],[f27,f282]) ).
fof(f282,plain,
! [X0] : union(X0,empty_set) = X0,
inference(resolution,[],[f259,f77]) ).
fof(f77,plain,
! [X0,X1] :
( ~ subset(union(X0,X1),X0)
| union(X0,X1) = X0 ),
inference(resolution,[],[f75,f33]) ).
fof(f33,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| X0 = X1
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f16]) ).
fof(f16,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 ) ),
inference(flattening,[],[f15]) ).
fof(f15,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/sandbox/benchmark/theBenchmark.p',equal_defn) ).
fof(f75,plain,
! [X0,X1] : subset(X0,union(X0,X1)),
inference(duplicate_literal_removal,[],[f70]) ).
fof(f70,plain,
! [X0,X1] :
( subset(X0,union(X0,X1))
| subset(X0,union(X0,X1)) ),
inference(resolution,[],[f53,f39]) ).
fof(f39,plain,
! [X0,X1] :
( member(sK2(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f24,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK2(X0,X1),X1)
& member(sK2(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f22,f23]) ).
fof(f23,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) )
=> ( ~ member(sK2(X0,X1),X1)
& member(sK2(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f22,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,[],[f21]) ).
fof(f21,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/sandbox/benchmark/theBenchmark.p',subset_defn) ).
fof(f53,plain,
! [X2,X0,X1] :
( ~ member(sK2(X0,union(X1,X2)),X1)
| subset(X0,union(X1,X2)) ),
inference(resolution,[],[f42,f40]) ).
fof(f40,plain,
! [X0,X1] :
( ~ member(sK2(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f42,plain,
! [X2,X0,X1] :
( member(X2,union(X0,X1))
| ~ member(X2,X0) ),
inference(cnf_transformation,[],[f26]) ).
fof(f26,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,[],[f25]) ).
fof(f25,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/sandbox/benchmark/theBenchmark.p',union_defn) ).
fof(f259,plain,
! [X0] : subset(union(X0,empty_set),X0),
inference(duplicate_literal_removal,[],[f246]) ).
fof(f246,plain,
! [X0] :
( subset(union(X0,empty_set),X0)
| subset(union(X0,empty_set),X0) ),
inference(resolution,[],[f141,f40]) ).
fof(f141,plain,
! [X0,X1] :
( member(sK2(union(X0,empty_set),X1),X0)
| subset(union(X0,empty_set),X1) ),
inference(resolution,[],[f65,f28]) ).
fof(f28,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0] : ~ member(X0,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set_defn) ).
fof(f65,plain,
! [X2,X0,X1] :
( member(sK2(union(X0,X1),X2),X1)
| member(sK2(union(X0,X1),X2),X0)
| subset(union(X0,X1),X2) ),
inference(resolution,[],[f41,f39]) ).
fof(f41,plain,
! [X2,X0,X1] :
( ~ member(X2,union(X0,X1))
| member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f27,plain,
sK0 != union(sK0,empty_set),
inference(cnf_transformation,[],[f14]) ).
fof(f14,plain,
sK0 != union(sK0,empty_set),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f11,f13]) ).
fof(f13,plain,
( ? [X0] : union(X0,empty_set) != X0
=> sK0 != union(sK0,empty_set) ),
introduced(choice_axiom,[]) ).
fof(f11,plain,
? [X0] : union(X0,empty_set) != X0,
inference(ennf_transformation,[],[f10]) ).
fof(f10,negated_conjecture,
~ ! [X0] : union(X0,empty_set) = X0,
inference(negated_conjecture,[],[f9]) ).
fof(f9,conjecture,
! [X0] : union(X0,empty_set) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_union_empty_set) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET162+3 : TPTP v8.1.2. Released v2.2.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35 % Computer : n010.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Tue Apr 30 01:24:05 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (27834)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38 % (27837)WARNING: value z3 for option sas not known
% 0.15/0.38 % (27838)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.38 % (27836)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.38 % (27835)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.38 % (27839)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)
% 0.15/0.38 % (27840)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)
% 0.15/0.38 % (27837)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)
% 0.15/0.38 % (27841)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)
% 0.15/0.38 TRYING [1]
% 0.15/0.38 TRYING [2]
% 0.15/0.38 TRYING [3]
% 0.22/0.38 TRYING [1]
% 0.22/0.38 TRYING [2]
% 0.22/0.38 TRYING [4]
% 0.22/0.39 TRYING [5]
% 0.22/0.39 TRYING [3]
% 0.22/0.39 TRYING [1]
% 0.22/0.39 TRYING [2]
% 0.22/0.39 TRYING [3]
% 0.22/0.39 % (27837)First to succeed.
% 0.22/0.39 TRYING [4]
% 0.22/0.39 % (27837)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 % (27837)------------------------------
% 0.22/0.39 % (27837)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.22/0.39 % (27837)Termination reason: Refutation
% 0.22/0.39
% 0.22/0.39 % (27837)Memory used [KB]: 912
% 0.22/0.39 % (27837)Time elapsed: 0.014 s
% 0.22/0.39 % (27837)Instructions burned: 17 (million)
% 0.22/0.39 % (27837)------------------------------
% 0.22/0.39 % (27837)------------------------------
% 0.22/0.39 % (27834)Success in time 0.03 s
%------------------------------------------------------------------------------