TSTP Solution File: SET628+3 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET628+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 : n023.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 09:14:33 EDT 2024
% Result : Theorem 0.19s 0.37s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 39 ( 8 unt; 0 def)
% Number of atoms : 132 ( 21 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 149 ( 56 ~; 58 |; 25 &)
% ( 6 <=>; 3 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 62 ( 52 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f76,plain,
$false,
inference(resolution,[],[f75,f66]) ).
fof(f66,plain,
! [X0] : ~ intersect(sK0,X0),
inference(backward_demodulation,[],[f43,f62]) ).
fof(f62,plain,
empty_set = sK0,
inference(duplicate_literal_removal,[],[f59]) ).
fof(f59,plain,
( empty_set = sK0
| empty_set = sK0 ),
inference(resolution,[],[f58,f25]) ).
fof(f25,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) ).
fof(f58,plain,
! [X0] :
( member(sK1(X0,sK0),X0)
| sK0 = X0
| empty_set = sK0 ),
inference(resolution,[],[f29,f50]) ).
fof(f50,plain,
! [X0] :
( ~ member(X0,sK0)
| empty_set = sK0 ),
inference(duplicate_literal_removal,[],[f47]) ).
fof(f47,plain,
! [X0] :
( ~ member(X0,sK0)
| ~ member(X0,sK0)
| empty_set = sK0 ),
inference(resolution,[],[f35,f41]) ).
fof(f41,plain,
( ~ intersect(sK0,sK0)
| empty_set = sK0 ),
inference(resolution,[],[f32,f24]) ).
fof(f24,plain,
( ~ not_equal(sK0,empty_set)
| ~ intersect(sK0,sK0) ),
inference(cnf_transformation,[],[f13]) ).
fof(f13,plain,
( ( ~ not_equal(sK0,empty_set)
| ~ intersect(sK0,sK0) )
& ( not_equal(sK0,empty_set)
| intersect(sK0,sK0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f11,f12]) ).
fof(f12,plain,
( ? [X0] :
( ( ~ not_equal(X0,empty_set)
| ~ intersect(X0,X0) )
& ( not_equal(X0,empty_set)
| intersect(X0,X0) ) )
=> ( ( ~ not_equal(sK0,empty_set)
| ~ intersect(sK0,sK0) )
& ( not_equal(sK0,empty_set)
| intersect(sK0,sK0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f11,plain,
? [X0] :
( ( ~ not_equal(X0,empty_set)
| ~ intersect(X0,X0) )
& ( not_equal(X0,empty_set)
| intersect(X0,X0) ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f9,plain,
? [X0] :
( intersect(X0,X0)
<~> not_equal(X0,empty_set) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,negated_conjecture,
~ ! [X0] :
( intersect(X0,X0)
<=> not_equal(X0,empty_set) ),
inference(negated_conjecture,[],[f7]) ).
fof(f7,conjecture,
! [X0] :
( intersect(X0,X0)
<=> not_equal(X0,empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th110) ).
fof(f32,plain,
! [X0,X1] :
( not_equal(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f18]) ).
fof(f18,plain,
! [X0,X1] :
( ( not_equal(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ not_equal(X0,X1) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0,X1] :
( not_equal(X0,X1)
<=> X0 != X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_equal_defn) ).
fof(f35,plain,
! [X2,X0,X1] :
( intersect(X0,X1)
| ~ member(X2,X1)
| ~ member(X2,X0) ),
inference(cnf_transformation,[],[f22]) ).
fof(f22,plain,
! [X0,X1] :
( ( intersect(X0,X1)
| ! [X2] :
( ~ member(X2,X1)
| ~ member(X2,X0) ) )
& ( ( member(sK2(X0,X1),X1)
& member(sK2(X0,X1),X0) )
| ~ intersect(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f20,f21]) ).
fof(f21,plain,
! [X0,X1] :
( ? [X3] :
( member(X3,X1)
& member(X3,X0) )
=> ( member(sK2(X0,X1),X1)
& member(sK2(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f20,plain,
! [X0,X1] :
( ( intersect(X0,X1)
| ! [X2] :
( ~ member(X2,X1)
| ~ member(X2,X0) ) )
& ( ? [X3] :
( member(X3,X1)
& member(X3,X0) )
| ~ intersect(X0,X1) ) ),
inference(rectify,[],[f19]) ).
fof(f19,plain,
! [X0,X1] :
( ( intersect(X0,X1)
| ! [X2] :
( ~ member(X2,X1)
| ~ member(X2,X0) ) )
& ( ? [X2] :
( member(X2,X1)
& member(X2,X0) )
| ~ intersect(X0,X1) ) ),
inference(nnf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( intersect(X0,X1)
<=> ? [X2] :
( member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersect_defn) ).
fof(f29,plain,
! [X0,X1] :
( member(sK1(X0,X1),X1)
| X0 = X1
| member(sK1(X0,X1),X0) ),
inference(cnf_transformation,[],[f17]) ).
fof(f17,plain,
! [X0,X1] :
( ( X0 = X1
| ( ( ~ member(sK1(X0,X1),X1)
| ~ member(sK1(X0,X1),X0) )
& ( member(sK1(X0,X1),X1)
| member(sK1(X0,X1),X0) ) ) )
& ( ! [X3] :
( ( member(X3,X0)
| ~ member(X3,X1) )
& ( member(X3,X1)
| ~ member(X3,X0) ) )
| X0 != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f15,f16]) ).
fof(f16,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ member(X2,X1)
| ~ member(X2,X0) )
& ( member(X2,X1)
| member(X2,X0) ) )
=> ( ( ~ member(sK1(X0,X1),X1)
| ~ member(sK1(X0,X1),X0) )
& ( member(sK1(X0,X1),X1)
| member(sK1(X0,X1),X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f15,plain,
! [X0,X1] :
( ( X0 = X1
| ? [X2] :
( ( ~ member(X2,X1)
| ~ member(X2,X0) )
& ( member(X2,X1)
| member(X2,X0) ) ) )
& ( ! [X3] :
( ( member(X3,X0)
| ~ member(X3,X1) )
& ( member(X3,X1)
| ~ member(X3,X0) ) )
| X0 != X1 ) ),
inference(rectify,[],[f14]) ).
fof(f14,plain,
! [X0,X1] :
( ( X0 = X1
| ? [X2] :
( ( ~ member(X2,X1)
| ~ member(X2,X0) )
& ( member(X2,X1)
| member(X2,X0) ) ) )
& ( ! [X2] :
( ( member(X2,X0)
| ~ member(X2,X1) )
& ( member(X2,X1)
| ~ member(X2,X0) ) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0,X1] :
( X0 = X1
<=> ! [X2] :
( member(X2,X0)
<=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_member_defn) ).
fof(f43,plain,
! [X0] : ~ intersect(empty_set,X0),
inference(resolution,[],[f33,f25]) ).
fof(f33,plain,
! [X0,X1] :
( member(sK2(X0,X1),X0)
| ~ intersect(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f75,plain,
intersect(sK0,sK0),
inference(resolution,[],[f63,f38]) ).
fof(f38,plain,
! [X1] : ~ not_equal(X1,X1),
inference(equality_resolution,[],[f31]) ).
fof(f31,plain,
! [X0,X1] :
( X0 != X1
| ~ not_equal(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f63,plain,
( not_equal(sK0,sK0)
| intersect(sK0,sK0) ),
inference(backward_demodulation,[],[f23,f62]) ).
fof(f23,plain,
( not_equal(sK0,empty_set)
| intersect(sK0,sK0) ),
inference(cnf_transformation,[],[f13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SET628+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
% 0.14/0.34 % Computer : n023.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Fri May 3 16:57:08 EDT 2024
% 0.14/0.34 % CPUTime :
% 0.14/0.35 % (24336)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.36 % (24341)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.19/0.36 TRYING [1]
% 0.19/0.36 TRYING [2]
% 0.19/0.36 TRYING [3]
% 0.19/0.36 % (24340)WARNING: value z3 for option sas not known
% 0.19/0.36 TRYING [4]
% 0.19/0.36 % (24339)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.19/0.37 % (24338)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.19/0.37 % (24340)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)
% 0.19/0.37 TRYING [5]
% 0.19/0.37 % (24343)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)
% 0.19/0.37 % (24344)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)
% 0.19/0.37 % (24342)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)
% 0.19/0.37 TRYING [1]
% 0.19/0.37 % (24343)First to succeed.
% 0.19/0.37 % (24344)Also succeeded, but the first one will report.
% 0.19/0.37 TRYING [6]
% 0.19/0.37 TRYING [2]
% 0.19/0.37 % (24343)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-24336"
% 0.19/0.37 TRYING [1]
% 0.19/0.37 TRYING [2]
% 0.19/0.37 % (24340)Also succeeded, but the first one will report.
% 0.19/0.37 % (24343)Refutation found. Thanks to Tanya!
% 0.19/0.37 % SZS status Theorem for theBenchmark
% 0.19/0.37 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.37 % (24343)------------------------------
% 0.19/0.37 % (24343)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.19/0.37 % (24343)Termination reason: Refutation
% 0.19/0.37
% 0.19/0.37 % (24343)Memory used [KB]: 768
% 0.19/0.37 % (24343)Time elapsed: 0.005 s
% 0.19/0.37 % (24343)Instructions burned: 4 (million)
% 0.19/0.37 % (24336)Success in time 0.021 s
%------------------------------------------------------------------------------