TSTP Solution File: SET908+1 by SnakeForV-SAT---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : SET908+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 : n018.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 18:26:04 EDT 2022
% Result : Theorem 0.20s 0.53s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 34 ( 10 unt; 0 def)
% Number of atoms : 159 ( 54 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 199 ( 74 ~; 76 |; 38 &)
% ( 7 <=>; 4 =>; 0 <=; 0 <~>)
% 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 : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 88 ( 72 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f113,plain,
$false,
inference(resolution,[],[f106,f71]) ).
fof(f71,plain,
! [X2] : in(X2,singleton(X2)),
inference(equality_resolution,[],[f70]) ).
fof(f70,plain,
! [X2,X0] :
( in(X2,X0)
| singleton(X2) != X0 ),
inference(equality_resolution,[],[f56]) ).
fof(f56,plain,
! [X2,X0,X1] :
( in(X2,X0)
| X1 != X2
| singleton(X1) != X0 ),
inference(cnf_transformation,[],[f37]) ).
fof(f37,plain,
! [X0,X1] :
( ( ! [X2] :
( ( X1 = X2
| ~ in(X2,X0) )
& ( in(X2,X0)
| X1 != X2 ) )
| singleton(X1) != X0 )
& ( singleton(X1) = X0
| ( ( ~ in(sK3(X0,X1),X0)
| sK3(X0,X1) != X1 )
& ( in(sK3(X0,X1),X0)
| sK3(X0,X1) = X1 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f35,f36]) ).
fof(f36,plain,
! [X0,X1] :
( ? [X3] :
( ( ~ in(X3,X0)
| X1 != X3 )
& ( in(X3,X0)
| X1 = X3 ) )
=> ( ( ~ in(sK3(X0,X1),X0)
| sK3(X0,X1) != X1 )
& ( in(sK3(X0,X1),X0)
| sK3(X0,X1) = X1 ) ) ),
introduced(choice_axiom,[]) ).
fof(f35,plain,
! [X0,X1] :
( ( ! [X2] :
( ( X1 = X2
| ~ in(X2,X0) )
& ( in(X2,X0)
| X1 != X2 ) )
| singleton(X1) != X0 )
& ( singleton(X1) = X0
| ? [X3] :
( ( ~ in(X3,X0)
| X1 != X3 )
& ( in(X3,X0)
| X1 = X3 ) ) ) ),
inference(rectify,[],[f34]) ).
fof(f34,plain,
! [X1,X0] :
( ( ! [X2] :
( ( X0 = X2
| ~ in(X2,X1) )
& ( in(X2,X1)
| X0 != X2 ) )
| singleton(X0) != X1 )
& ( singleton(X0) = X1
| ? [X2] :
( ( ~ in(X2,X1)
| X0 != X2 )
& ( in(X2,X1)
| X0 = X2 ) ) ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X1,X0] :
( ! [X2] :
( X0 = X2
<=> in(X2,X1) )
<=> singleton(X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(f106,plain,
! [X8] : ~ in(X8,singleton(sK1)),
inference(subsumption_resolution,[],[f104,f68]) ).
fof(f68,plain,
! [X1] : ~ in(X1,empty_set),
inference(equality_resolution,[],[f50]) ).
fof(f50,plain,
! [X0,X1] :
( ~ in(X1,X0)
| empty_set != X0 ),
inference(cnf_transformation,[],[f30]) ).
fof(f30,plain,
! [X0] :
( ( ! [X1] : ~ in(X1,X0)
| empty_set != X0 )
& ( empty_set = X0
| in(sK2(X0),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f28,f29]) ).
fof(f29,plain,
! [X0] :
( ? [X2] : in(X2,X0)
=> in(sK2(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f28,plain,
! [X0] :
( ( ! [X1] : ~ in(X1,X0)
| empty_set != X0 )
& ( empty_set = X0
| ? [X2] : in(X2,X0) ) ),
inference(rectify,[],[f27]) ).
fof(f27,plain,
! [X0] :
( ( ! [X1] : ~ in(X1,X0)
| empty_set != X0 )
& ( empty_set = X0
| ? [X1] : in(X1,X0) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] :
( ! [X1] : ~ in(X1,X0)
<=> empty_set = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f104,plain,
! [X8] :
( ~ in(X8,singleton(sK1))
| in(X8,empty_set) ),
inference(superposition,[],[f73,f48]) ).
fof(f48,plain,
empty_set = set_union2(singleton(sK1),sK0),
inference(cnf_transformation,[],[f26]) ).
fof(f26,plain,
empty_set = set_union2(singleton(sK1),sK0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f24,f25]) ).
fof(f25,plain,
( ? [X0,X1] : empty_set = set_union2(singleton(X1),X0)
=> empty_set = set_union2(singleton(sK1),sK0) ),
introduced(choice_axiom,[]) ).
fof(f24,plain,
? [X0,X1] : empty_set = set_union2(singleton(X1),X0),
inference(rectify,[],[f20]) ).
fof(f20,plain,
? [X1,X0] : empty_set = set_union2(singleton(X0),X1),
inference(ennf_transformation,[],[f13]) ).
fof(f13,negated_conjecture,
~ ! [X1,X0] : empty_set != set_union2(singleton(X0),X1),
inference(negated_conjecture,[],[f12]) ).
fof(f12,conjecture,
! [X1,X0] : empty_set != set_union2(singleton(X0),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_zfmisc_1) ).
fof(f73,plain,
! [X2,X1,X4] :
( in(X4,set_union2(X1,X2))
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f62]) ).
fof(f62,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| ~ in(X4,X1)
| set_union2(X1,X2) != X0 ),
inference(cnf_transformation,[],[f46]) ).
fof(f46,plain,
! [X0,X1,X2] :
( ( set_union2(X1,X2) = X0
| ( ( ~ in(sK6(X0,X1,X2),X0)
| ( ~ in(sK6(X0,X1,X2),X1)
& ~ in(sK6(X0,X1,X2),X2) ) )
& ( in(sK6(X0,X1,X2),X0)
| in(sK6(X0,X1,X2),X1)
| in(sK6(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X1)
| in(X4,X2)
| ~ in(X4,X0) )
& ( in(X4,X0)
| ( ~ in(X4,X1)
& ~ in(X4,X2) ) ) )
| set_union2(X1,X2) != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f44,f45]) ).
fof(f45,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ in(X3,X0)
| ( ~ in(X3,X1)
& ~ in(X3,X2) ) )
& ( in(X3,X0)
| in(X3,X1)
| in(X3,X2) ) )
=> ( ( ~ in(sK6(X0,X1,X2),X0)
| ( ~ in(sK6(X0,X1,X2),X1)
& ~ in(sK6(X0,X1,X2),X2) ) )
& ( in(sK6(X0,X1,X2),X0)
| in(sK6(X0,X1,X2),X1)
| in(sK6(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f44,plain,
! [X0,X1,X2] :
( ( set_union2(X1,X2) = X0
| ? [X3] :
( ( ~ in(X3,X0)
| ( ~ in(X3,X1)
& ~ in(X3,X2) ) )
& ( in(X3,X0)
| in(X3,X1)
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X1)
| in(X4,X2)
| ~ in(X4,X0) )
& ( in(X4,X0)
| ( ~ in(X4,X1)
& ~ in(X4,X2) ) ) )
| set_union2(X1,X2) != X0 ) ),
inference(rectify,[],[f43]) ).
fof(f43,plain,
! [X0,X2,X1] :
( ( set_union2(X2,X1) = 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(X2,X1) != X0 ) ),
inference(flattening,[],[f42]) ).
fof(f42,plain,
! [X0,X2,X1] :
( ( set_union2(X2,X1) = 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(X2,X1) != X0 ) ),
inference(nnf_transformation,[],[f16]) ).
fof(f16,plain,
! [X0,X2,X1] :
( set_union2(X2,X1) = X0
<=> ! [X3] :
( ( in(X3,X2)
| in(X3,X1) )
<=> in(X3,X0) ) ),
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X2,X1,X0] :
( set_union2(X0,X1) = X2
<=> ! [X3] :
( ( in(X3,X1)
| in(X3,X0) )
<=> in(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET908+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12 % 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 : n018.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 14:33:10 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.51 % (24201)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.20/0.52 % (24192)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.20/0.52 % (24189)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.52 % (24185)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)
% 0.20/0.52 % (24201)First to succeed.
% 0.20/0.52 % (24188)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)
% 0.20/0.52 % (24190)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/48Mi)
% 0.20/0.53 % (24213)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 0.20/0.53 % (24201)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 % (24201)------------------------------
% 0.20/0.53 % (24201)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.53 % (24201)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.53 % (24201)Termination reason: Refutation
% 0.20/0.53
% 0.20/0.53 % (24201)Memory used [KB]: 5500
% 0.20/0.53 % (24201)Time elapsed: 0.116 s
% 0.20/0.53 % (24201)Instructions burned: 4 (million)
% 0.20/0.53 % (24201)------------------------------
% 0.20/0.53 % (24201)------------------------------
% 0.20/0.53 % (24184)Success in time 0.184 s
%------------------------------------------------------------------------------