TSTP Solution File: SEU118+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU118+1 : TPTP v8.2.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n019.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 03:53:02 EDT 2024
% Result : Theorem 0.12s 0.36s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% Syntax : Number of formulae : 46 ( 8 unt; 0 def)
% Number of atoms : 179 ( 8 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 220 ( 87 ~; 75 |; 40 &)
% ( 8 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 75 ( 65 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f261,plain,
$false,
inference(resolution,[],[f260,f101]) ).
fof(f101,plain,
element(sK3,powerset(sK2)),
inference(cnf_transformation,[],[f72]) ).
fof(f72,plain,
( ~ element(sK3,finite_subsets(sK2))
& finite(sK2)
& element(sK3,powerset(sK2)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f45,f71]) ).
fof(f71,plain,
( ? [X0,X1] :
( ~ element(X1,finite_subsets(X0))
& finite(X0)
& element(X1,powerset(X0)) )
=> ( ~ element(sK3,finite_subsets(sK2))
& finite(sK2)
& element(sK3,powerset(sK2)) ) ),
introduced(choice_axiom,[]) ).
fof(f45,plain,
? [X0,X1] :
( ~ element(X1,finite_subsets(X0))
& finite(X0)
& element(X1,powerset(X0)) ),
inference(flattening,[],[f44]) ).
fof(f44,plain,
? [X0,X1] :
( ~ element(X1,finite_subsets(X0))
& finite(X0)
& element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f28]) ).
fof(f28,negated_conjecture,
~ ! [X0,X1] :
( element(X1,powerset(X0))
=> ( finite(X0)
=> element(X1,finite_subsets(X0)) ) ),
inference(negated_conjecture,[],[f27]) ).
fof(f27,conjecture,
! [X0,X1] :
( element(X1,powerset(X0))
=> ( finite(X0)
=> element(X1,finite_subsets(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_finsub_1) ).
fof(f260,plain,
~ element(sK3,powerset(sK2)),
inference(duplicate_literal_removal,[],[f256]) ).
fof(f256,plain,
( ~ element(sK3,powerset(sK2))
| ~ element(sK3,powerset(sK2)) ),
inference(resolution,[],[f235,f102]) ).
fof(f102,plain,
finite(sK2),
inference(cnf_transformation,[],[f72]) ).
fof(f235,plain,
! [X0] :
( ~ finite(X0)
| ~ element(sK3,powerset(X0))
| ~ element(sK3,powerset(sK2)) ),
inference(resolution,[],[f233,f127]) ).
fof(f127,plain,
! [X0,X1] :
( finite(X1)
| ~ element(X1,powerset(X0))
| ~ finite(X0) ),
inference(cnf_transformation,[],[f52]) ).
fof(f52,plain,
! [X0] :
( ! [X1] :
( finite(X1)
| ~ element(X1,powerset(X0)) )
| ~ finite(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] :
( finite(X0)
=> ! [X1] :
( element(X1,powerset(X0))
=> finite(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_finset_1) ).
fof(f233,plain,
( ~ finite(sK3)
| ~ element(sK3,powerset(sK2)) ),
inference(resolution,[],[f232,f106]) ).
fof(f106,plain,
! [X0] : preboolean(finite_subsets(X0)),
inference(cnf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0] : preboolean(finite_subsets(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_finsub_1) ).
fof(f232,plain,
( ~ preboolean(finite_subsets(sK2))
| ~ finite(sK3)
| ~ element(sK3,powerset(sK2)) ),
inference(resolution,[],[f230,f150]) ).
fof(f150,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f92]) ).
fof(f92,plain,
! [X0,X1] :
( ( element(X0,powerset(X1))
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f29]) ).
fof(f29,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(f230,plain,
( ~ subset(sK3,sK2)
| ~ finite(sK3)
| ~ preboolean(finite_subsets(sK2)) ),
inference(resolution,[],[f229,f144]) ).
fof(f144,plain,
! [X0,X1] :
( sP1(X1,X0)
| ~ preboolean(X1) ),
inference(cnf_transformation,[],[f70]) ).
fof(f70,plain,
! [X0,X1] :
( sP1(X1,X0)
| ~ preboolean(X1) ),
inference(definition_folding,[],[f55,f69,f68]) ).
fof(f68,plain,
! [X0,X1] :
( sP0(X0,X1)
<=> ! [X2] :
( in(X2,X1)
<=> ( finite(X2)
& subset(X2,X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f69,plain,
! [X1,X0] :
( ( finite_subsets(X0) = X1
<=> sP0(X0,X1) )
| ~ sP1(X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f55,plain,
! [X0,X1] :
( ( finite_subsets(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ( finite(X2)
& subset(X2,X0) ) ) )
| ~ preboolean(X1) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0,X1] :
( preboolean(X1)
=> ( finite_subsets(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ( finite(X2)
& subset(X2,X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_finsub_1) ).
fof(f229,plain,
( ~ sP1(finite_subsets(sK2),sK2)
| ~ finite(sK3)
| ~ subset(sK3,sK2) ),
inference(resolution,[],[f226,f164]) ).
fof(f164,plain,
! [X1] :
( sP0(X1,finite_subsets(X1))
| ~ sP1(finite_subsets(X1),X1) ),
inference(equality_resolution,[],[f136]) ).
fof(f136,plain,
! [X0,X1] :
( sP0(X1,X0)
| finite_subsets(X1) != X0
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f86]) ).
fof(f86,plain,
! [X0,X1] :
( ( ( finite_subsets(X1) = X0
| ~ sP0(X1,X0) )
& ( sP0(X1,X0)
| finite_subsets(X1) != X0 ) )
| ~ sP1(X0,X1) ),
inference(rectify,[],[f85]) ).
fof(f85,plain,
! [X1,X0] :
( ( ( finite_subsets(X0) = X1
| ~ sP0(X0,X1) )
& ( sP0(X0,X1)
| finite_subsets(X0) != X1 ) )
| ~ sP1(X1,X0) ),
inference(nnf_transformation,[],[f69]) ).
fof(f226,plain,
! [X0] :
( ~ sP0(X0,finite_subsets(sK2))
| ~ subset(sK3,X0)
| ~ finite(sK3) ),
inference(resolution,[],[f140,f176]) ).
fof(f176,plain,
~ in(sK3,finite_subsets(sK2)),
inference(resolution,[],[f146,f103]) ).
fof(f103,plain,
~ element(sK3,finite_subsets(sK2)),
inference(cnf_transformation,[],[f72]) ).
fof(f146,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f57]) ).
fof(f57,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f25]) ).
fof(f25,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
fof(f140,plain,
! [X3,X0,X1] :
( in(X3,X1)
| ~ finite(X3)
| ~ subset(X3,X0)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f91]) ).
fof(f91,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ( ( ~ finite(sK10(X0,X1))
| ~ subset(sK10(X0,X1),X0)
| ~ in(sK10(X0,X1),X1) )
& ( ( finite(sK10(X0,X1))
& subset(sK10(X0,X1),X0) )
| in(sK10(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| ~ finite(X3)
| ~ subset(X3,X0) )
& ( ( finite(X3)
& subset(X3,X0) )
| ~ in(X3,X1) ) )
| ~ sP0(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f89,f90]) ).
fof(f90,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ finite(X2)
| ~ subset(X2,X0)
| ~ in(X2,X1) )
& ( ( finite(X2)
& subset(X2,X0) )
| in(X2,X1) ) )
=> ( ( ~ finite(sK10(X0,X1))
| ~ subset(sK10(X0,X1),X0)
| ~ in(sK10(X0,X1),X1) )
& ( ( finite(sK10(X0,X1))
& subset(sK10(X0,X1),X0) )
| in(sK10(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f89,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ? [X2] :
( ( ~ finite(X2)
| ~ subset(X2,X0)
| ~ in(X2,X1) )
& ( ( finite(X2)
& subset(X2,X0) )
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| ~ finite(X3)
| ~ subset(X3,X0) )
& ( ( finite(X3)
& subset(X3,X0) )
| ~ in(X3,X1) ) )
| ~ sP0(X0,X1) ) ),
inference(rectify,[],[f88]) ).
fof(f88,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ? [X2] :
( ( ~ finite(X2)
| ~ subset(X2,X0)
| ~ in(X2,X1) )
& ( ( finite(X2)
& subset(X2,X0) )
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ~ finite(X2)
| ~ subset(X2,X0) )
& ( ( finite(X2)
& subset(X2,X0) )
| ~ in(X2,X1) ) )
| ~ sP0(X0,X1) ) ),
inference(flattening,[],[f87]) ).
fof(f87,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ? [X2] :
( ( ~ finite(X2)
| ~ subset(X2,X0)
| ~ in(X2,X1) )
& ( ( finite(X2)
& subset(X2,X0) )
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ~ finite(X2)
| ~ subset(X2,X0) )
& ( ( finite(X2)
& subset(X2,X0) )
| ~ in(X2,X1) ) )
| ~ sP0(X0,X1) ) ),
inference(nnf_transformation,[],[f68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SEU118+1 : TPTP v8.2.0. Released v3.2.0.
% 0.06/0.13 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.12/0.33 % Computer : n019.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sun May 19 15:33:08 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.12/0.34 % (26954)Running in auto input_syntax mode. Trying TPTP
% 0.12/0.35 % (26957)WARNING: value z3 for option sas not known
% 0.12/0.35 % (26957)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)
% 0.12/0.35 % (26955)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.12/0.35 % (26956)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.12/0.35 % (26958)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.12/0.35 % (26959)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)
% 0.12/0.35 % (26961)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)
% 0.12/0.35 % (26960)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)
% 0.12/0.35 TRYING [1]
% 0.12/0.36 TRYING [2]
% 0.12/0.36 TRYING [3]
% 0.12/0.36 % (26960)First to succeed.
% 0.12/0.36 % (26960)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-26954"
% 0.12/0.36 TRYING [1]
% 0.12/0.36 TRYING [4]
% 0.12/0.36 % (26960)Refutation found. Thanks to Tanya!
% 0.12/0.36 % SZS status Theorem for theBenchmark
% 0.12/0.36 % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.36 % (26960)------------------------------
% 0.12/0.36 % (26960)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.12/0.36 % (26960)Termination reason: Refutation
% 0.12/0.36
% 0.12/0.36 % (26960)Memory used [KB]: 934
% 0.12/0.36 % (26960)Time elapsed: 0.008 s
% 0.12/0.36 % (26960)Instructions burned: 11 (million)
% 0.12/0.36 % (26954)Success in time 0.022 s
%------------------------------------------------------------------------------