TSTP Solution File: SET909+1 by SnakeForV-SAT---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : SET909+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 : n023.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 0.47s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 42 ( 16 unt; 0 def)
% Number of atoms : 200 ( 90 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 249 ( 91 ~; 94 |; 51 &)
% ( 9 <=>; 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 : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 121 ( 101 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f122,plain,
$false,
inference(resolution,[],[f116,f79]) ).
fof(f79,plain,
! [X0,X4] : in(X4,unordered_pair(X0,X4)),
inference(equality_resolution,[],[f78]) ).
fof(f78,plain,
! [X0,X1,X4] :
( in(X4,X1)
| unordered_pair(X0,X4) != X1 ),
inference(equality_resolution,[],[f61]) ).
fof(f61,plain,
! [X2,X0,X1,X4] :
( in(X4,X1)
| X2 != X4
| unordered_pair(X0,X2) != X1 ),
inference(cnf_transformation,[],[f41]) ).
fof(f41,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X2) = X1
| ( ( ~ in(sK5(X0,X1,X2),X1)
| ( sK5(X0,X1,X2) != X2
& sK5(X0,X1,X2) != X0 ) )
& ( in(sK5(X0,X1,X2),X1)
| sK5(X0,X1,X2) = X2
| sK5(X0,X1,X2) = X0 ) ) )
& ( ! [X4] :
( ( X2 = X4
| X0 = X4
| ~ in(X4,X1) )
& ( in(X4,X1)
| ( X2 != X4
& X0 != X4 ) ) )
| unordered_pair(X0,X2) != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f39,f40]) ).
fof(f40,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ in(X3,X1)
| ( X2 != X3
& X0 != X3 ) )
& ( in(X3,X1)
| X2 = X3
| X0 = X3 ) )
=> ( ( ~ in(sK5(X0,X1,X2),X1)
| ( sK5(X0,X1,X2) != X2
& sK5(X0,X1,X2) != X0 ) )
& ( in(sK5(X0,X1,X2),X1)
| sK5(X0,X1,X2) = X2
| sK5(X0,X1,X2) = X0 ) ) ),
introduced(choice_axiom,[]) ).
fof(f39,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X2) = X1
| ? [X3] :
( ( ~ in(X3,X1)
| ( X2 != X3
& X0 != X3 ) )
& ( in(X3,X1)
| X2 = X3
| X0 = X3 ) ) )
& ( ! [X4] :
( ( X2 = X4
| X0 = X4
| ~ in(X4,X1) )
& ( in(X4,X1)
| ( X2 != X4
& X0 != X4 ) ) )
| unordered_pair(X0,X2) != X1 ) ),
inference(rectify,[],[f38]) ).
fof(f38,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X2) = X1
| ? [X3] :
( ( ~ in(X3,X1)
| ( X2 != X3
& X0 != X3 ) )
& ( in(X3,X1)
| X2 = X3
| X0 = X3 ) ) )
& ( ! [X3] :
( ( X2 = X3
| X0 = X3
| ~ in(X3,X1) )
& ( in(X3,X1)
| ( X2 != X3
& X0 != X3 ) ) )
| unordered_pair(X0,X2) != X1 ) ),
inference(flattening,[],[f37]) ).
fof(f37,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X2) = X1
| ? [X3] :
( ( ~ in(X3,X1)
| ( X2 != X3
& X0 != X3 ) )
& ( in(X3,X1)
| X2 = X3
| X0 = X3 ) ) )
& ( ! [X3] :
( ( X2 = X3
| X0 = X3
| ~ in(X3,X1) )
& ( in(X3,X1)
| ( X2 != X3
& X0 != X3 ) ) )
| unordered_pair(X0,X2) != X1 ) ),
inference(nnf_transformation,[],[f19]) ).
fof(f19,plain,
! [X0,X1,X2] :
( unordered_pair(X0,X2) = X1
<=> ! [X3] :
( ( X2 = X3
| X0 = X3 )
<=> in(X3,X1) ) ),
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X0,X2,X1] :
( unordered_pair(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( X0 = X3
| X1 = X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
fof(f116,plain,
! [X9] : ~ in(X9,unordered_pair(sK2,sK3)),
inference(subsumption_resolution,[],[f114,f76]) ).
fof(f76,plain,
! [X2] : ~ in(X2,empty_set),
inference(equality_resolution,[],[f52]) ).
fof(f52,plain,
! [X2,X0] :
( ~ in(X2,X0)
| empty_set != X0 ),
inference(cnf_transformation,[],[f29]) ).
fof(f29,plain,
! [X0] :
( ( empty_set = X0
| in(sK0(X0),X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f27,f28]) ).
fof(f28,plain,
! [X0] :
( ? [X1] : in(X1,X0)
=> in(sK0(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f27,plain,
! [X0] :
( ( empty_set = X0
| ? [X1] : in(X1,X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(rectify,[],[f26]) ).
fof(f26,plain,
! [X0] :
( ( empty_set = X0
| ? [X1] : in(X1,X0) )
& ( ! [X1] : ~ in(X1,X0)
| empty_set != X0 ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] :
( empty_set = X0
<=> ! [X1] : ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f114,plain,
! [X9] :
( ~ in(X9,unordered_pair(sK2,sK3))
| in(X9,empty_set) ),
inference(superposition,[],[f83,f99]) ).
fof(f99,plain,
empty_set = set_union2(sK1,unordered_pair(sK2,sK3)),
inference(superposition,[],[f67,f55]) ).
fof(f55,plain,
empty_set = set_union2(unordered_pair(sK2,sK3),sK1),
inference(cnf_transformation,[],[f33]) ).
fof(f33,plain,
empty_set = set_union2(unordered_pair(sK2,sK3),sK1),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f31,f32]) ).
fof(f32,plain,
( ? [X0,X1,X2] : empty_set = set_union2(unordered_pair(X1,X2),X0)
=> empty_set = set_union2(unordered_pair(sK2,sK3),sK1) ),
introduced(choice_axiom,[]) ).
fof(f31,plain,
? [X0,X1,X2] : empty_set = set_union2(unordered_pair(X1,X2),X0),
inference(rectify,[],[f25]) ).
fof(f25,plain,
? [X1,X0,X2] : empty_set = set_union2(unordered_pair(X0,X2),X1),
inference(ennf_transformation,[],[f16]) ).
fof(f16,plain,
~ ! [X0,X2,X1] : empty_set != set_union2(unordered_pair(X0,X2),X1),
inference(rectify,[],[f14]) ).
fof(f14,negated_conjecture,
~ ! [X0,X2,X1] : empty_set != set_union2(unordered_pair(X0,X1),X2),
inference(negated_conjecture,[],[f13]) ).
fof(f13,conjecture,
! [X0,X2,X1] : empty_set != set_union2(unordered_pair(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_zfmisc_1) ).
fof(f67,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f44]) ).
fof(f44,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(rectify,[],[f17]) ).
fof(f17,plain,
! [X1,X0] : set_union2(X0,X1) = set_union2(X1,X0),
inference(rectify,[],[f3]) ).
fof(f3,axiom,
! [X1,X0] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f83,plain,
! [X2,X3,X0] :
( in(X3,set_union2(X2,X0))
| ~ in(X3,X0) ),
inference(equality_resolution,[],[f73]) ).
fof(f73,plain,
! [X2,X3,X0,X1] :
( in(X3,X1)
| ~ in(X3,X0)
| set_union2(X2,X0) != X1 ),
inference(cnf_transformation,[],[f50]) ).
fof(f50,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ( in(X3,X0)
| in(X3,X2)
| ~ in(X3,X1) )
& ( in(X3,X1)
| ( ~ in(X3,X0)
& ~ in(X3,X2) ) ) )
| set_union2(X2,X0) != X1 )
& ( set_union2(X2,X0) = X1
| ( ( ~ in(sK7(X0,X1,X2),X1)
| ( ~ in(sK7(X0,X1,X2),X0)
& ~ in(sK7(X0,X1,X2),X2) ) )
& ( in(sK7(X0,X1,X2),X1)
| in(sK7(X0,X1,X2),X0)
| in(sK7(X0,X1,X2),X2) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f48,f49]) ).
fof(f49,plain,
! [X0,X1,X2] :
( ? [X4] :
( ( ~ in(X4,X1)
| ( ~ in(X4,X0)
& ~ in(X4,X2) ) )
& ( in(X4,X1)
| in(X4,X0)
| in(X4,X2) ) )
=> ( ( ~ in(sK7(X0,X1,X2),X1)
| ( ~ in(sK7(X0,X1,X2),X0)
& ~ in(sK7(X0,X1,X2),X2) ) )
& ( in(sK7(X0,X1,X2),X1)
| in(sK7(X0,X1,X2),X0)
| in(sK7(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f48,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ( in(X3,X0)
| in(X3,X2)
| ~ in(X3,X1) )
& ( in(X3,X1)
| ( ~ in(X3,X0)
& ~ in(X3,X2) ) ) )
| set_union2(X2,X0) != X1 )
& ( set_union2(X2,X0) = X1
| ? [X4] :
( ( ~ in(X4,X1)
| ( ~ in(X4,X0)
& ~ in(X4,X2) ) )
& ( in(X4,X1)
| in(X4,X0)
| in(X4,X2) ) ) ) ),
inference(rectify,[],[f47]) ).
fof(f47,plain,
! [X1,X0,X2] :
( ( ! [X3] :
( ( in(X3,X1)
| in(X3,X2)
| ~ in(X3,X0) )
& ( in(X3,X0)
| ( ~ in(X3,X1)
& ~ in(X3,X2) ) ) )
| set_union2(X2,X1) != X0 )
& ( set_union2(X2,X1) = X0
| ? [X3] :
( ( ~ in(X3,X0)
| ( ~ in(X3,X1)
& ~ in(X3,X2) ) )
& ( in(X3,X0)
| in(X3,X1)
| in(X3,X2) ) ) ) ),
inference(flattening,[],[f46]) ).
fof(f46,plain,
! [X1,X0,X2] :
( ( ! [X3] :
( ( in(X3,X1)
| in(X3,X2)
| ~ in(X3,X0) )
& ( in(X3,X0)
| ( ~ in(X3,X1)
& ~ in(X3,X2) ) ) )
| set_union2(X2,X1) != X0 )
& ( set_union2(X2,X1) = X0
| ? [X3] :
( ( ~ in(X3,X0)
| ( ~ in(X3,X1)
& ~ in(X3,X2) ) )
& ( in(X3,X0)
| in(X3,X1)
| in(X3,X2) ) ) ) ),
inference(nnf_transformation,[],[f20]) ).
fof(f20,plain,
! [X1,X0,X2] :
( ! [X3] :
( ( in(X3,X1)
| in(X3,X2) )
<=> in(X3,X0) )
<=> set_union2(X2,X1) = X0 ),
inference(rectify,[],[f6]) ).
fof(f6,axiom,
! [X2,X1,X0] :
( set_union2(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X0)
| in(X3,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET909+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 : n023.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
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 30 15:02:05 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.46 % (10313)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)
% 0.20/0.46 % (10305)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.20/0.47 % (10313)First to succeed.
% 0.20/0.47 % (10313)Refutation found. Thanks to Tanya!
% 0.20/0.47 % SZS status Theorem for theBenchmark
% 0.20/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.47 % (10313)------------------------------
% 0.20/0.47 % (10313)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.47 % (10313)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.47 % (10313)Termination reason: Refutation
% 0.20/0.47
% 0.20/0.47 % (10313)Memory used [KB]: 1023
% 0.20/0.47 % (10313)Time elapsed: 0.009 s
% 0.20/0.47 % (10313)Instructions burned: 4 (million)
% 0.20/0.47 % (10313)------------------------------
% 0.20/0.47 % (10313)------------------------------
% 0.20/0.47 % (10290)Success in time 0.117 s
%------------------------------------------------------------------------------