TSTP Solution File: SET964+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET964+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n014.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 09:19:49 EDT 2024
% Result : Theorem 0.14s 0.39s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of formulae : 55 ( 5 unt; 0 def)
% Number of atoms : 166 ( 16 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 193 ( 82 ~; 71 |; 28 &)
% ( 8 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 5 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 91 ( 79 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f230,plain,
$false,
inference(avatar_sat_refutation,[],[f116,f188,f194,f204,f229]) ).
fof(f229,plain,
( spl13_3
| spl13_4
| ~ spl13_1 ),
inference(avatar_split_clause,[],[f228,f109,f186,f183]) ).
fof(f183,plain,
( spl13_3
<=> ! [X1] : ~ in(X1,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_3])]) ).
fof(f186,plain,
( spl13_4
<=> ! [X0] :
( ~ in(X0,sK2)
| in(X0,sK3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_4])]) ).
fof(f109,plain,
( spl13_1
<=> subset(cartesian_product2(sK2,sK1),cartesian_product2(sK3,sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_1])]) ).
fof(f228,plain,
( ! [X0,X1] :
( in(X0,sK3)
| ~ in(X1,sK1)
| ~ in(X0,sK2) )
| ~ spl13_1 ),
inference(resolution,[],[f208,f70]) ).
fof(f70,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) ),
inference(cnf_transformation,[],[f39]) ).
fof(f39,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) )
& ( ( in(X1,X3)
& in(X0,X2) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(flattening,[],[f38]) ).
fof(f38,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) )
& ( ( in(X1,X3)
& in(X0,X2) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<=> ( in(X1,X3)
& in(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l55_zfmisc_1) ).
fof(f208,plain,
( ! [X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(sK2,sK1))
| in(X0,sK3) )
| ~ spl13_1 ),
inference(resolution,[],[f205,f68]) ).
fof(f68,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(cnf_transformation,[],[f39]) ).
fof(f205,plain,
( ! [X0] :
( in(X0,cartesian_product2(sK3,sK1))
| ~ in(X0,cartesian_product2(sK2,sK1)) )
| ~ spl13_1 ),
inference(resolution,[],[f111,f55]) ).
fof(f55,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f30]) ).
fof(f30,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK5(X0,X1),X1)
& in(sK5(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f28,f29]) ).
fof(f29,plain,
! [X0,X1] :
( ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) )
=> ( ~ in(sK5(X0,X1),X1)
& in(sK5(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f28,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f27]) ).
fof(f27,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f18]) ).
fof(f18,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f111,plain,
( subset(cartesian_product2(sK2,sK1),cartesian_product2(sK3,sK1))
| ~ spl13_1 ),
inference(avatar_component_clause,[],[f109]) ).
fof(f204,plain,
~ spl13_4,
inference(avatar_contradiction_clause,[],[f203]) ).
fof(f203,plain,
( $false
| ~ spl13_4 ),
inference(subsumption_resolution,[],[f202,f46]) ).
fof(f46,plain,
~ subset(sK2,sK3),
inference(cnf_transformation,[],[f22]) ).
fof(f22,plain,
( ~ subset(sK2,sK3)
& ( subset(cartesian_product2(sK1,sK2),cartesian_product2(sK1,sK3))
| subset(cartesian_product2(sK2,sK1),cartesian_product2(sK3,sK1)) )
& empty_set != sK1 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f16,f21]) ).
fof(f21,plain,
( ? [X0,X1,X2] :
( ~ subset(X1,X2)
& ( subset(cartesian_product2(X0,X1),cartesian_product2(X0,X2))
| subset(cartesian_product2(X1,X0),cartesian_product2(X2,X0)) )
& empty_set != X0 )
=> ( ~ subset(sK2,sK3)
& ( subset(cartesian_product2(sK1,sK2),cartesian_product2(sK1,sK3))
| subset(cartesian_product2(sK2,sK1),cartesian_product2(sK3,sK1)) )
& empty_set != sK1 ) ),
introduced(choice_axiom,[]) ).
fof(f16,plain,
? [X0,X1,X2] :
( ~ subset(X1,X2)
& ( subset(cartesian_product2(X0,X1),cartesian_product2(X0,X2))
| subset(cartesian_product2(X1,X0),cartesian_product2(X2,X0)) )
& empty_set != X0 ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,negated_conjecture,
~ ! [X0,X1,X2] :
~ ( ~ subset(X1,X2)
& ( subset(cartesian_product2(X0,X1),cartesian_product2(X0,X2))
| subset(cartesian_product2(X1,X0),cartesian_product2(X2,X0)) )
& empty_set != X0 ),
inference(negated_conjecture,[],[f13]) ).
fof(f13,conjecture,
! [X0,X1,X2] :
~ ( ~ subset(X1,X2)
& ( subset(cartesian_product2(X0,X1),cartesian_product2(X0,X2))
| subset(cartesian_product2(X1,X0),cartesian_product2(X2,X0)) )
& empty_set != X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t117_zfmisc_1) ).
fof(f202,plain,
( subset(sK2,sK3)
| ~ spl13_4 ),
inference(duplicate_literal_removal,[],[f201]) ).
fof(f201,plain,
( subset(sK2,sK3)
| subset(sK2,sK3)
| ~ spl13_4 ),
inference(resolution,[],[f197,f56]) ).
fof(f56,plain,
! [X0,X1] :
( in(sK5(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f30]) ).
fof(f197,plain,
( ! [X0] :
( ~ in(sK5(X0,sK3),sK2)
| subset(X0,sK3) )
| ~ spl13_4 ),
inference(resolution,[],[f187,f57]) ).
fof(f57,plain,
! [X0,X1] :
( ~ in(sK5(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f30]) ).
fof(f187,plain,
( ! [X0] :
( in(X0,sK3)
| ~ in(X0,sK2) )
| ~ spl13_4 ),
inference(avatar_component_clause,[],[f186]) ).
fof(f194,plain,
~ spl13_3,
inference(avatar_contradiction_clause,[],[f193]) ).
fof(f193,plain,
( $false
| ~ spl13_3 ),
inference(subsumption_resolution,[],[f189,f44]) ).
fof(f44,plain,
empty_set != sK1,
inference(cnf_transformation,[],[f22]) ).
fof(f189,plain,
( empty_set = sK1
| ~ spl13_3 ),
inference(resolution,[],[f184,f49]) ).
fof(f49,plain,
! [X0] :
( in(sK4(X0),X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f26]) ).
fof(f26,plain,
! [X0] :
( ( empty_set = X0
| in(sK4(X0),X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f24,f25]) ).
fof(f25,plain,
! [X0] :
( ? [X1] : in(X1,X0)
=> in(sK4(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f24,plain,
! [X0] :
( ( empty_set = X0
| ? [X1] : in(X1,X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(rectify,[],[f23]) ).
fof(f23,plain,
! [X0] :
( ( empty_set = X0
| ? [X1] : in(X1,X0) )
& ( ! [X1] : ~ in(X1,X0)
| empty_set != X0 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] :
( empty_set = X0
<=> ! [X1] : ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f184,plain,
( ! [X1] : ~ in(X1,sK1)
| ~ spl13_3 ),
inference(avatar_component_clause,[],[f183]) ).
fof(f188,plain,
( spl13_3
| spl13_4
| ~ spl13_2 ),
inference(avatar_split_clause,[],[f173,f113,f186,f183]) ).
fof(f113,plain,
( spl13_2
<=> subset(cartesian_product2(sK1,sK2),cartesian_product2(sK1,sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_2])]) ).
fof(f173,plain,
( ! [X0,X1] :
( ~ in(X0,sK2)
| ~ in(X1,sK1)
| in(X0,sK3) )
| ~ spl13_2 ),
inference(resolution,[],[f70,f120]) ).
fof(f120,plain,
( ! [X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(sK1,sK2))
| in(X1,sK3) )
| ~ spl13_2 ),
inference(resolution,[],[f117,f69]) ).
fof(f69,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(cnf_transformation,[],[f39]) ).
fof(f117,plain,
( ! [X0] :
( in(X0,cartesian_product2(sK1,sK3))
| ~ in(X0,cartesian_product2(sK1,sK2)) )
| ~ spl13_2 ),
inference(resolution,[],[f115,f55]) ).
fof(f115,plain,
( subset(cartesian_product2(sK1,sK2),cartesian_product2(sK1,sK3))
| ~ spl13_2 ),
inference(avatar_component_clause,[],[f113]) ).
fof(f116,plain,
( spl13_1
| spl13_2 ),
inference(avatar_split_clause,[],[f45,f113,f109]) ).
fof(f45,plain,
( subset(cartesian_product2(sK1,sK2),cartesian_product2(sK1,sK3))
| subset(cartesian_product2(sK2,sK1),cartesian_product2(sK3,sK1)) ),
inference(cnf_transformation,[],[f22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET964+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36 % Computer : n014.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri May 3 16:35:53 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % (21828)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.38 % (21831)WARNING: value z3 for option sas not known
% 0.14/0.38 % (21832)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.38 % (21833)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)
% 0.14/0.38 % (21834)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)
% 0.14/0.38 % (21835)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)
% 0.14/0.38 % (21831)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)
% 0.14/0.38 % (21830)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.38 % (21829)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.38 TRYING [1]
% 0.14/0.38 TRYING [2]
% 0.14/0.39 TRYING [3]
% 0.14/0.39 % (21831)First to succeed.
% 0.14/0.39 % (21831)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-21828"
% 0.14/0.39 % (21831)Refutation found. Thanks to Tanya!
% 0.14/0.39 % SZS status Theorem for theBenchmark
% 0.14/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.39 % (21831)------------------------------
% 0.14/0.39 % (21831)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.39 % (21831)Termination reason: Refutation
% 0.14/0.39
% 0.14/0.39 % (21831)Memory used [KB]: 889
% 0.14/0.39 % (21831)Time elapsed: 0.010 s
% 0.14/0.39 % (21831)Instructions burned: 13 (million)
% 0.14/0.39 % (21828)Success in time 0.025 s
%------------------------------------------------------------------------------