TSTP Solution File: NUM386+1 by SnakeForV-SAT---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : NUM386+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% Computer : n013.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 : Wed Aug 31 18:04:57 EDT 2022
% Result : Theorem 0.20s 0.53s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 49 ( 8 unt; 0 def)
% Number of atoms : 223 ( 70 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 276 ( 102 ~; 115 |; 47 &)
% ( 8 <=>; 3 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 95 ( 78 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f281,plain,
$false,
inference(subsumption_resolution,[],[f277,f164]) ).
fof(f164,plain,
! [X2] : in(X2,singleton(X2)),
inference(equality_resolution,[],[f163]) ).
fof(f163,plain,
! [X2,X1] :
( in(X2,X1)
| singleton(X2) != X1 ),
inference(equality_resolution,[],[f138]) ).
fof(f138,plain,
! [X2,X0,X1] :
( in(X2,X1)
| X0 != X2
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f89]) ).
fof(f89,plain,
! [X0,X1] :
( ( ! [X2] :
( ( X0 = X2
| ~ in(X2,X1) )
& ( in(X2,X1)
| X0 != X2 ) )
| singleton(X0) != X1 )
& ( singleton(X0) = X1
| ( ( ~ in(sK9(X0,X1),X1)
| sK9(X0,X1) != X0 )
& ( in(sK9(X0,X1),X1)
| sK9(X0,X1) = X0 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f87,f88]) ).
fof(f88,plain,
! [X0,X1] :
( ? [X3] :
( ( ~ in(X3,X1)
| X0 != X3 )
& ( in(X3,X1)
| X0 = X3 ) )
=> ( ( ~ in(sK9(X0,X1),X1)
| sK9(X0,X1) != X0 )
& ( in(sK9(X0,X1),X1)
| sK9(X0,X1) = X0 ) ) ),
introduced(choice_axiom,[]) ).
fof(f87,plain,
! [X0,X1] :
( ( ! [X2] :
( ( X0 = X2
| ~ in(X2,X1) )
& ( in(X2,X1)
| X0 != X2 ) )
| singleton(X0) != X1 )
& ( singleton(X0) = X1
| ? [X3] :
( ( ~ in(X3,X1)
| X0 != X3 )
& ( in(X3,X1)
| X0 = X3 ) ) ) ),
inference(rectify,[],[f86]) ).
fof(f86,plain,
! [X1,X0] :
( ( ! [X2] :
( ( X1 = X2
| ~ in(X2,X0) )
& ( in(X2,X0)
| X1 != X2 ) )
| singleton(X1) != X0 )
& ( singleton(X1) = X0
| ? [X2] :
( ( ~ in(X2,X0)
| X1 != X2 )
& ( in(X2,X0)
| X1 = X2 ) ) ) ),
inference(nnf_transformation,[],[f38]) ).
fof(f38,plain,
! [X1,X0] :
( ! [X2] :
( X1 = X2
<=> in(X2,X0) )
<=> singleton(X1) = X0 ),
inference(rectify,[],[f7]) ).
fof(f7,axiom,
! [X1,X0] :
( ! [X2] :
( in(X2,X1)
<=> X0 = X2 )
<=> singleton(X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(f277,plain,
~ in(sK0,singleton(sK0)),
inference(backward_demodulation,[],[f257,f269]) ).
fof(f269,plain,
sK0 = sK1,
inference(subsumption_resolution,[],[f268,f257]) ).
fof(f268,plain,
( sK0 = sK1
| in(sK1,singleton(sK0)) ),
inference(subsumption_resolution,[],[f267,f239]) ).
fof(f239,plain,
~ in(sK1,sK0),
inference(duplicate_literal_removal,[],[f232]) ).
fof(f232,plain,
( ~ in(sK1,sK0)
| ~ in(sK1,sK0) ),
inference(resolution,[],[f166,f159]) ).
fof(f159,plain,
( ~ in(sK1,set_union2(sK0,singleton(sK0)))
| ~ in(sK1,sK0) ),
inference(definition_unfolding,[],[f104,f133]) ).
fof(f133,plain,
! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
inference(cnf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_ordinal1) ).
fof(f104,plain,
( ~ in(sK1,sK0)
| ~ in(sK1,succ(sK0)) ),
inference(cnf_transformation,[],[f65]) ).
fof(f65,plain,
( ( ( sK0 != sK1
& ~ in(sK1,sK0) )
| ~ in(sK1,succ(sK0)) )
& ( sK0 = sK1
| in(sK1,sK0)
| in(sK1,succ(sK0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f63,f64]) ).
fof(f64,plain,
( ? [X0,X1] :
( ( ( X0 != X1
& ~ in(X1,X0) )
| ~ in(X1,succ(X0)) )
& ( X0 = X1
| in(X1,X0)
| in(X1,succ(X0)) ) )
=> ( ( ( sK0 != sK1
& ~ in(sK1,sK0) )
| ~ in(sK1,succ(sK0)) )
& ( sK0 = sK1
| in(sK1,sK0)
| in(sK1,succ(sK0)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f63,plain,
? [X0,X1] :
( ( ( X0 != X1
& ~ in(X1,X0) )
| ~ in(X1,succ(X0)) )
& ( X0 = X1
| in(X1,X0)
| in(X1,succ(X0)) ) ),
inference(rectify,[],[f62]) ).
fof(f62,plain,
? [X1,X0] :
( ( ( X0 != X1
& ~ in(X0,X1) )
| ~ in(X0,succ(X1)) )
& ( X0 = X1
| in(X0,X1)
| in(X0,succ(X1)) ) ),
inference(flattening,[],[f61]) ).
fof(f61,plain,
? [X1,X0] :
( ( ( X0 != X1
& ~ in(X0,X1) )
| ~ in(X0,succ(X1)) )
& ( X0 = X1
| in(X0,X1)
| in(X0,succ(X1)) ) ),
inference(nnf_transformation,[],[f48]) ).
fof(f48,plain,
? [X1,X0] :
( in(X0,succ(X1))
<~> ( X0 = X1
| in(X0,X1) ) ),
inference(ennf_transformation,[],[f29]) ).
fof(f29,negated_conjecture,
~ ! [X0,X1] :
( in(X0,succ(X1))
<=> ( X0 = X1
| in(X0,X1) ) ),
inference(negated_conjecture,[],[f28]) ).
fof(f28,conjecture,
! [X0,X1] :
( in(X0,succ(X1))
<=> ( X0 = X1
| in(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_ordinal1) ).
fof(f166,plain,
! [X3,X0,X1] :
( in(X3,set_union2(X1,X0))
| ~ in(X3,X1) ),
inference(equality_resolution,[],[f151]) ).
fof(f151,plain,
! [X2,X3,X0,X1] :
( in(X3,X2)
| ~ in(X3,X1)
| set_union2(X1,X0) != X2 ),
inference(cnf_transformation,[],[f100]) ).
fof(f100,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ( in(X3,X1)
| in(X3,X0)
| ~ in(X3,X2) )
& ( in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) ) )
| set_union2(X1,X0) != X2 )
& ( set_union2(X1,X0) = X2
| ( ( ~ in(sK13(X0,X1,X2),X2)
| ( ~ in(sK13(X0,X1,X2),X1)
& ~ in(sK13(X0,X1,X2),X0) ) )
& ( in(sK13(X0,X1,X2),X2)
| in(sK13(X0,X1,X2),X1)
| in(sK13(X0,X1,X2),X0) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f98,f99]) ).
fof(f99,plain,
! [X0,X1,X2] :
( ? [X4] :
( ( ~ in(X4,X2)
| ( ~ in(X4,X1)
& ~ in(X4,X0) ) )
& ( in(X4,X2)
| in(X4,X1)
| in(X4,X0) ) )
=> ( ( ~ in(sK13(X0,X1,X2),X2)
| ( ~ in(sK13(X0,X1,X2),X1)
& ~ in(sK13(X0,X1,X2),X0) ) )
& ( in(sK13(X0,X1,X2),X2)
| in(sK13(X0,X1,X2),X1)
| in(sK13(X0,X1,X2),X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f98,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ( in(X3,X1)
| in(X3,X0)
| ~ in(X3,X2) )
& ( in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) ) )
| set_union2(X1,X0) != X2 )
& ( set_union2(X1,X0) = X2
| ? [X4] :
( ( ~ in(X4,X2)
| ( ~ in(X4,X1)
& ~ in(X4,X0) ) )
& ( in(X4,X2)
| in(X4,X1)
| in(X4,X0) ) ) ) ),
inference(rectify,[],[f97]) ).
fof(f97,plain,
! [X1,X0,X2] :
( ( ! [X3] :
( ( in(X3,X0)
| in(X3,X1)
| ~ in(X3,X2) )
& ( in(X3,X2)
| ( ~ in(X3,X0)
& ~ in(X3,X1) ) ) )
| set_union2(X0,X1) != X2 )
& ( set_union2(X0,X1) = X2
| ? [X3] :
( ( ~ in(X3,X2)
| ( ~ in(X3,X0)
& ~ in(X3,X1) ) )
& ( in(X3,X2)
| in(X3,X0)
| in(X3,X1) ) ) ) ),
inference(flattening,[],[f96]) ).
fof(f96,plain,
! [X1,X0,X2] :
( ( ! [X3] :
( ( in(X3,X0)
| in(X3,X1)
| ~ in(X3,X2) )
& ( in(X3,X2)
| ( ~ in(X3,X0)
& ~ in(X3,X1) ) ) )
| set_union2(X0,X1) != X2 )
& ( set_union2(X0,X1) = X2
| ? [X3] :
( ( ~ in(X3,X2)
| ( ~ in(X3,X0)
& ~ in(X3,X1) ) )
& ( in(X3,X2)
| in(X3,X0)
| in(X3,X1) ) ) ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X1,X0,X2] :
( ! [X3] :
( ( in(X3,X0)
| in(X3,X1) )
<=> in(X3,X2) )
<=> set_union2(X0,X1) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f267,plain,
( sK0 = sK1
| in(sK1,sK0)
| in(sK1,singleton(sK0)) ),
inference(duplicate_literal_removal,[],[f258]) ).
fof(f258,plain,
( in(sK1,sK0)
| in(sK1,singleton(sK0))
| in(sK1,sK0)
| sK0 = sK1 ),
inference(resolution,[],[f165,f160]) ).
fof(f160,plain,
( in(sK1,set_union2(sK0,singleton(sK0)))
| in(sK1,sK0)
| sK0 = sK1 ),
inference(definition_unfolding,[],[f103,f133]) ).
fof(f103,plain,
( sK0 = sK1
| in(sK1,sK0)
| in(sK1,succ(sK0)) ),
inference(cnf_transformation,[],[f65]) ).
fof(f165,plain,
! [X3,X0,X1] :
( ~ in(X3,set_union2(X1,X0))
| in(X3,X1)
| in(X3,X0) ),
inference(equality_resolution,[],[f152]) ).
fof(f152,plain,
! [X2,X3,X0,X1] :
( in(X3,X1)
| in(X3,X0)
| ~ in(X3,X2)
| set_union2(X1,X0) != X2 ),
inference(cnf_transformation,[],[f100]) ).
fof(f257,plain,
~ in(sK1,singleton(sK0)),
inference(subsumption_resolution,[],[f251,f162]) ).
fof(f162,plain,
! [X2,X0] :
( ~ in(X2,singleton(X0))
| X0 = X2 ),
inference(equality_resolution,[],[f139]) ).
fof(f139,plain,
! [X2,X0,X1] :
( X0 = X2
| ~ in(X2,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f89]) ).
fof(f251,plain,
( sK0 != sK1
| ~ in(sK1,singleton(sK0)) ),
inference(resolution,[],[f167,f158]) ).
fof(f158,plain,
( ~ in(sK1,set_union2(sK0,singleton(sK0)))
| sK0 != sK1 ),
inference(definition_unfolding,[],[f105,f133]) ).
fof(f105,plain,
( sK0 != sK1
| ~ in(sK1,succ(sK0)) ),
inference(cnf_transformation,[],[f65]) ).
fof(f167,plain,
! [X3,X0,X1] :
( in(X3,set_union2(X1,X0))
| ~ in(X3,X0) ),
inference(equality_resolution,[],[f150]) ).
fof(f150,plain,
! [X2,X3,X0,X1] :
( in(X3,X2)
| ~ in(X3,X0)
| set_union2(X1,X0) != X2 ),
inference(cnf_transformation,[],[f100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM386+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.34 % Computer : n013.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 30 06:35:17 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.50 % (27844)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 0.20/0.51 % (27845)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/498Mi)
% 0.20/0.51 % (27836)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.20/0.51 % (27822)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=191324:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/191324Mi)
% 0.20/0.51 % (27834)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.20/0.52 % (27845)First to succeed.
% 0.20/0.53 % (27825)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.53 % (27845)Refutation found. Thanks to Tanya!
% 0.20/0.53 % SZS status Theorem for theBenchmark
% 0.20/0.53 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.53 % (27845)------------------------------
% 0.20/0.53 % (27845)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.53 % (27845)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.53 % (27845)Termination reason: Refutation
% 0.20/0.53
% 0.20/0.53 % (27845)Memory used [KB]: 1023
% 0.20/0.53 % (27845)Time elapsed: 0.110 s
% 0.20/0.53 % (27845)Instructions burned: 7 (million)
% 0.20/0.53 % (27845)------------------------------
% 0.20/0.53 % (27845)------------------------------
% 0.20/0.53 % (27820)Success in time 0.173 s
%------------------------------------------------------------------------------