TSTP Solution File: SEU126+1 by SnakeForV-SAT---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : SEU126+1 : TPTP v8.1.0. Released v3.3.0.
% 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 : 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 : Wed Aug 31 18:32:01 EDT 2022
% Result : Theorem 0.21s 0.48s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 51 ( 8 unt; 0 def)
% Number of atoms : 196 ( 33 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 226 ( 81 ~; 83 |; 45 &)
% ( 9 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 105 ( 92 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f258,plain,
$false,
inference(subsumption_resolution,[],[f257,f239]) ).
fof(f239,plain,
~ subset(sK3,sF6),
inference(subsumption_resolution,[],[f237,f91]) ).
fof(f91,plain,
sK3 != sF6,
inference(definition_folding,[],[f74,f90]) ).
fof(f90,plain,
sF6 = set_union2(sK2,sK3),
introduced(function_definition,[]) ).
fof(f74,plain,
sK3 != set_union2(sK2,sK3),
inference(cnf_transformation,[],[f49]) ).
fof(f49,plain,
( subset(sK2,sK3)
& sK3 != set_union2(sK2,sK3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f47,f48]) ).
fof(f48,plain,
( ? [X0,X1] :
( subset(X0,X1)
& set_union2(X0,X1) != X1 )
=> ( subset(sK2,sK3)
& sK3 != set_union2(sK2,sK3) ) ),
introduced(choice_axiom,[]) ).
fof(f47,plain,
? [X0,X1] :
( subset(X0,X1)
& set_union2(X0,X1) != X1 ),
inference(rectify,[],[f32]) ).
fof(f32,plain,
? [X1,X0] :
( subset(X1,X0)
& set_union2(X1,X0) != X0 ),
inference(ennf_transformation,[],[f29]) ).
fof(f29,plain,
~ ! [X0,X1] :
( subset(X1,X0)
=> set_union2(X1,X0) = X0 ),
inference(rectify,[],[f16]) ).
fof(f16,negated_conjecture,
~ ! [X1,X0] :
( subset(X0,X1)
=> set_union2(X0,X1) = X1 ),
inference(negated_conjecture,[],[f15]) ).
fof(f15,conjecture,
! [X1,X0] :
( subset(X0,X1)
=> set_union2(X0,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_xboole_1) ).
fof(f237,plain,
( sK3 = sF6
| ~ subset(sK3,sF6) ),
inference(resolution,[],[f236,f61]) ).
fof(f61,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| X0 = X1
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f44]) ).
fof(f44,plain,
! [X0,X1] :
( ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 )
& ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f43]) ).
fof(f43,plain,
! [X1,X0] :
( ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 )
& ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) ) ),
inference(flattening,[],[f42]) ).
fof(f42,plain,
! [X1,X0] :
( ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 )
& ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) ) ),
inference(nnf_transformation,[],[f22]) ).
fof(f22,plain,
! [X1,X0] :
( ( subset(X0,X1)
& subset(X1,X0) )
<=> X0 = X1 ),
inference(rectify,[],[f3]) ).
fof(f3,axiom,
! [X1,X0] :
( ( subset(X0,X1)
& subset(X1,X0) )
<=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(f236,plain,
subset(sF6,sK3),
inference(duplicate_literal_removal,[],[f233]) ).
fof(f233,plain,
( subset(sF6,sK3)
| subset(sF6,sK3) ),
inference(resolution,[],[f223,f59]) ).
fof(f59,plain,
! [X0,X1] :
( ~ in(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f41]) ).
fof(f41,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( in(sK0(X0,X1),X0)
& ~ in(sK0(X0,X1),X1) ) )
& ( ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f39,f40]) ).
fof(f40,plain,
! [X0,X1] :
( ? [X2] :
( in(X2,X0)
& ~ in(X2,X1) )
=> ( in(sK0(X0,X1),X0)
& ~ in(sK0(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f39,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( in(X2,X0)
& ~ in(X2,X1) ) )
& ( ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f38]) ).
fof(f38,plain,
! [X1,X0] :
( ( subset(X1,X0)
| ? [X2] :
( in(X2,X1)
& ~ in(X2,X0) ) )
& ( ! [X2] :
( ~ in(X2,X1)
| in(X2,X0) )
| ~ subset(X1,X0) ) ),
inference(nnf_transformation,[],[f30]) ).
fof(f30,plain,
! [X1,X0] :
( subset(X1,X0)
<=> ! [X2] :
( ~ in(X2,X1)
| in(X2,X0) ) ),
inference(ennf_transformation,[],[f27]) ).
fof(f27,plain,
! [X0,X1] :
( ! [X2] :
( in(X2,X1)
=> in(X2,X0) )
<=> subset(X1,X0) ),
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X1,X0] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f223,plain,
! [X0] :
( in(sK0(sF6,X0),sK3)
| subset(sF6,X0) ),
inference(resolution,[],[f222,f60]) ).
fof(f60,plain,
! [X0,X1] :
( in(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f41]) ).
fof(f222,plain,
! [X10] :
( ~ in(X10,sF6)
| in(X10,sK3) ),
inference(subsumption_resolution,[],[f219,f171]) ).
fof(f171,plain,
! [X0] :
( ~ in(X0,sK2)
| in(X0,sK3) ),
inference(resolution,[],[f58,f75]) ).
fof(f75,plain,
subset(sK2,sK3),
inference(cnf_transformation,[],[f49]) ).
fof(f58,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| in(X3,X1)
| ~ in(X3,X0) ),
inference(cnf_transformation,[],[f41]) ).
fof(f219,plain,
! [X10] :
( in(X10,sK3)
| in(X10,sK2)
| ~ in(X10,sF6) ),
inference(superposition,[],[f87,f90]) ).
fof(f87,plain,
! [X2,X0,X4] :
( ~ in(X4,set_union2(X2,X0))
| in(X4,X2)
| in(X4,X0) ),
inference(equality_resolution,[],[f79]) ).
fof(f79,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| in(X4,X2)
| ~ in(X4,X1)
| set_union2(X2,X0) != X1 ),
inference(cnf_transformation,[],[f54]) ).
fof(f54,plain,
! [X0,X1,X2] :
( ( set_union2(X2,X0) = X1
| ( ( ~ in(sK4(X0,X1,X2),X1)
| ( ~ in(sK4(X0,X1,X2),X0)
& ~ in(sK4(X0,X1,X2),X2) ) )
& ( in(sK4(X0,X1,X2),X1)
| in(sK4(X0,X1,X2),X0)
| in(sK4(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X0)
| in(X4,X2)
| ~ in(X4,X1) )
& ( in(X4,X1)
| ( ~ in(X4,X0)
& ~ in(X4,X2) ) ) )
| set_union2(X2,X0) != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f52,f53]) ).
fof(f53,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ in(X3,X1)
| ( ~ in(X3,X0)
& ~ in(X3,X2) ) )
& ( in(X3,X1)
| in(X3,X0)
| in(X3,X2) ) )
=> ( ( ~ in(sK4(X0,X1,X2),X1)
| ( ~ in(sK4(X0,X1,X2),X0)
& ~ in(sK4(X0,X1,X2),X2) ) )
& ( in(sK4(X0,X1,X2),X1)
| in(sK4(X0,X1,X2),X0)
| in(sK4(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f52,plain,
! [X0,X1,X2] :
( ( set_union2(X2,X0) = X1
| ? [X3] :
( ( ~ in(X3,X1)
| ( ~ in(X3,X0)
& ~ in(X3,X2) ) )
& ( in(X3,X1)
| in(X3,X0)
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X0)
| in(X4,X2)
| ~ in(X4,X1) )
& ( in(X4,X1)
| ( ~ in(X4,X0)
& ~ in(X4,X2) ) ) )
| set_union2(X2,X0) != X1 ) ),
inference(rectify,[],[f51]) ).
fof(f51,plain,
! [X2,X0,X1] :
( ( set_union2(X1,X2) = X0
| ? [X3] :
( ( ~ in(X3,X0)
| ( ~ in(X3,X2)
& ~ in(X3,X1) ) )
& ( in(X3,X0)
| in(X3,X2)
| in(X3,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| in(X3,X1)
| ~ in(X3,X0) )
& ( in(X3,X0)
| ( ~ in(X3,X2)
& ~ in(X3,X1) ) ) )
| set_union2(X1,X2) != X0 ) ),
inference(flattening,[],[f50]) ).
fof(f50,plain,
! [X2,X0,X1] :
( ( set_union2(X1,X2) = X0
| ? [X3] :
( ( ~ in(X3,X0)
| ( ~ in(X3,X2)
& ~ in(X3,X1) ) )
& ( in(X3,X0)
| in(X3,X2)
| in(X3,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| in(X3,X1)
| ~ in(X3,X0) )
& ( in(X3,X0)
| ( ~ in(X3,X2)
& ~ in(X3,X1) ) ) )
| set_union2(X1,X2) != X0 ) ),
inference(nnf_transformation,[],[f28]) ).
fof(f28,plain,
! [X2,X0,X1] :
( set_union2(X1,X2) = X0
<=> ! [X3] :
( ( in(X3,X2)
| in(X3,X1) )
<=> in(X3,X0) ) ),
inference(rectify,[],[f4]) ).
fof(f4,axiom,
! [X2,X0,X1] :
( ! [X3] :
( ( in(X3,X1)
| in(X3,X0) )
<=> in(X3,X2) )
<=> set_union2(X0,X1) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f257,plain,
subset(sK3,sF6),
inference(duplicate_literal_removal,[],[f254]) ).
fof(f254,plain,
( subset(sK3,sF6)
| subset(sK3,sF6) ),
inference(resolution,[],[f141,f59]) ).
fof(f141,plain,
! [X0] :
( in(sK0(sK3,X0),sF6)
| subset(sK3,X0) ),
inference(resolution,[],[f138,f60]) ).
fof(f138,plain,
! [X10] :
( ~ in(X10,sK3)
| in(X10,sF6) ),
inference(superposition,[],[f88,f90]) ).
fof(f88,plain,
! [X2,X0,X4] :
( in(X4,set_union2(X2,X0))
| ~ in(X4,X0) ),
inference(equality_resolution,[],[f78]) ).
fof(f78,plain,
! [X2,X0,X1,X4] :
( in(X4,X1)
| ~ in(X4,X0)
| set_union2(X2,X0) != X1 ),
inference(cnf_transformation,[],[f54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SEU126+1 : TPTP v8.1.0. Released v3.3.0.
% 0.08/0.14 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.15/0.36 % Computer : n014.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Tue Aug 30 14:41:18 EDT 2022
% 0.15/0.36 % CPUTime :
% 0.21/0.45 % (7886)ott-1_1:6_av=off:cond=on:fsr=off:nwc=3.0:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.21/0.46 % (7902)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 0.21/0.48 % (7902)First to succeed.
% 0.21/0.48 % (7902)Refutation found. Thanks to Tanya!
% 0.21/0.48 % SZS status Theorem for theBenchmark
% 0.21/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.48 % (7902)------------------------------
% 0.21/0.48 % (7902)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.48 % (7902)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.48 % (7902)Termination reason: Refutation
% 0.21/0.48
% 0.21/0.48 % (7902)Memory used [KB]: 5500
% 0.21/0.48 % (7902)Time elapsed: 0.067 s
% 0.21/0.48 % (7902)Instructions burned: 7 (million)
% 0.21/0.48 % (7902)------------------------------
% 0.21/0.48 % (7902)------------------------------
% 0.21/0.48 % (7876)Success in time 0.11 s
%------------------------------------------------------------------------------