TSTP Solution File: SET638+3 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET638+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 : n012.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 09:14:36 EDT 2024
% Result : Theorem 0.20s 0.38s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 42 ( 10 unt; 0 def)
% Number of atoms : 122 ( 12 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 131 ( 51 ~; 41 |; 29 &)
% ( 4 <=>; 6 =>; 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 80 ( 68 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f297,plain,
$false,
inference(resolution,[],[f295,f39]) ).
fof(f39,plain,
~ subset(sK0,sK1),
inference(cnf_transformation,[],[f22]) ).
fof(f22,plain,
( ~ subset(sK0,sK1)
& empty_set = intersection(sK0,sK2)
& subset(sK0,union(sK1,sK2)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f18,f21]) ).
fof(f21,plain,
( ? [X0,X1,X2] :
( ~ subset(X0,X1)
& empty_set = intersection(X0,X2)
& subset(X0,union(X1,X2)) )
=> ( ~ subset(sK0,sK1)
& empty_set = intersection(sK0,sK2)
& subset(sK0,union(sK1,sK2)) ) ),
introduced(choice_axiom,[]) ).
fof(f18,plain,
? [X0,X1,X2] :
( ~ subset(X0,X1)
& empty_set = intersection(X0,X2)
& subset(X0,union(X1,X2)) ),
inference(flattening,[],[f17]) ).
fof(f17,plain,
? [X0,X1,X2] :
( ~ subset(X0,X1)
& empty_set = intersection(X0,X2)
& subset(X0,union(X1,X2)) ),
inference(ennf_transformation,[],[f16]) ).
fof(f16,negated_conjecture,
~ ! [X0,X1,X2] :
( ( empty_set = intersection(X0,X2)
& subset(X0,union(X1,X2)) )
=> subset(X0,X1) ),
inference(negated_conjecture,[],[f15]) ).
fof(f15,conjecture,
! [X0,X1,X2] :
( ( empty_set = intersection(X0,X2)
& subset(X0,union(X1,X2)) )
=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th120) ).
fof(f295,plain,
subset(sK0,sK1),
inference(resolution,[],[f292,f55]) ).
fof(f55,plain,
! [X0,X1] :
( member(sK4(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f32]) ).
fof(f32,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])],[f30,f31]) ).
fof(f31,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) )
=> ( ~ member(sK4(X0,X1),X1)
& member(sK4(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f30,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,[],[f29]) ).
fof(f29,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,[],[f20]) ).
fof(f20,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
fof(f292,plain,
~ member(sK4(sK0,sK1),sK0),
inference(resolution,[],[f291,f97]) ).
fof(f97,plain,
~ member(sK4(sK0,sK1),sK1),
inference(resolution,[],[f56,f39]) ).
fof(f56,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK4(X0,X1),X1) ),
inference(cnf_transformation,[],[f32]) ).
fof(f291,plain,
! [X0] :
( member(X0,sK1)
| ~ member(X0,sK0) ),
inference(duplicate_literal_removal,[],[f289]) ).
fof(f289,plain,
! [X0] :
( ~ member(X0,sK0)
| member(X0,sK1)
| ~ member(X0,sK0) ),
inference(resolution,[],[f286,f192]) ).
fof(f192,plain,
! [X0] :
( member(X0,sK2)
| member(X0,sK1)
| ~ member(X0,sK0) ),
inference(resolution,[],[f58,f130]) ).
fof(f130,plain,
! [X0] :
( member(X0,union(sK1,sK2))
| ~ member(X0,sK0) ),
inference(superposition,[],[f62,f87]) ).
fof(f87,plain,
sK0 = intersection(sK0,union(sK1,sK2)),
inference(resolution,[],[f46,f37]) ).
fof(f37,plain,
subset(sK0,union(sK1,sK2)),
inference(cnf_transformation,[],[f22]) ).
fof(f46,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| intersection(X0,X1) = X0 ),
inference(cnf_transformation,[],[f19]) ).
fof(f19,plain,
! [X0,X1] :
( intersection(X0,X1) = X0
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0,X1] :
( subset(X0,X1)
=> intersection(X0,X1) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_intersection) ).
fof(f62,plain,
! [X2,X0,X1] :
( ~ member(X2,intersection(X0,X1))
| member(X2,X1) ),
inference(cnf_transformation,[],[f36]) ).
fof(f36,plain,
! [X0,X1,X2] :
( ( member(X2,intersection(X0,X1))
| ~ member(X2,X1)
| ~ member(X2,X0) )
& ( ( member(X2,X1)
& member(X2,X0) )
| ~ member(X2,intersection(X0,X1)) ) ),
inference(flattening,[],[f35]) ).
fof(f35,plain,
! [X0,X1,X2] :
( ( member(X2,intersection(X0,X1))
| ~ member(X2,X1)
| ~ member(X2,X0) )
& ( ( member(X2,X1)
& member(X2,X0) )
| ~ member(X2,intersection(X0,X1)) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0,X1,X2] :
( member(X2,intersection(X0,X1))
<=> ( member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_defn) ).
fof(f58,plain,
! [X2,X0,X1] :
( ~ member(X2,union(X0,X1))
| member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[],[f34]) ).
fof(f34,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,[],[f33]) ).
fof(f33,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,[],[f5]) ).
fof(f5,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(f286,plain,
! [X0] :
( ~ member(X0,sK2)
| ~ member(X0,sK0) ),
inference(resolution,[],[f278,f40]) ).
fof(f40,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] : ~ member(X0,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set_defn) ).
fof(f278,plain,
! [X0] :
( member(X0,empty_set)
| ~ member(X0,sK2)
| ~ member(X0,sK0) ),
inference(superposition,[],[f63,f38]) ).
fof(f38,plain,
empty_set = intersection(sK0,sK2),
inference(cnf_transformation,[],[f22]) ).
fof(f63,plain,
! [X2,X0,X1] :
( member(X2,intersection(X0,X1))
| ~ member(X2,X1)
| ~ member(X2,X0) ),
inference(cnf_transformation,[],[f36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET638+3 : TPTP v8.1.2. Released v2.2.0.
% 0.13/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.35 % Computer : n012.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri May 3 16:54:38 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.36 % (2515)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.37 % (2518)WARNING: value z3 for option sas not known
% 0.20/0.37 % (2516)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.20/0.37 % (2517)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.20/0.37 % (2519)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.20/0.37 % (2518)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)
% 0.20/0.37 % (2520)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)
% 0.20/0.37 % (2521)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)
% 0.20/0.37 % (2522)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)
% 0.20/0.38 TRYING [1]
% 0.20/0.38 TRYING [2]
% 0.20/0.38 TRYING [3]
% 0.20/0.38 TRYING [1]
% 0.20/0.38 TRYING [2]
% 0.20/0.38 % (2521)First to succeed.
% 0.20/0.38 % (2521)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2515"
% 0.20/0.38 % (2521)Refutation found. Thanks to Tanya!
% 0.20/0.38 % SZS status Theorem for theBenchmark
% 0.20/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.38 % (2521)------------------------------
% 0.20/0.38 % (2521)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.20/0.38 % (2521)Termination reason: Refutation
% 0.20/0.38
% 0.20/0.38 % (2521)Memory used [KB]: 857
% 0.20/0.38 % (2521)Time elapsed: 0.010 s
% 0.20/0.38 % (2521)Instructions burned: 12 (million)
% 0.20/0.38 % (2515)Success in time 0.026 s
%------------------------------------------------------------------------------