TSTP Solution File: SET920+1 by SnakeForV---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SET920+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_uns --cores 0 -t %d %s
% Computer : n003.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 18:22:45 EDT 2022
% Result : Theorem 0.20s 0.51s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 31 ( 5 unt; 0 def)
% Number of atoms : 185 ( 77 equ)
% Maximal formula atoms : 14 ( 5 avg)
% Number of connectives : 237 ( 83 ~; 85 |; 55 &)
% ( 8 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 97 ( 80 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f72,plain,
$false,
inference(subsumption_resolution,[],[f70,f33]) ).
fof(f33,plain,
~ in(sK1,sK0),
inference(cnf_transformation,[],[f21]) ).
fof(f21,plain,
( ~ in(sK1,sK0)
& unordered_pair(sK1,sK2) = set_intersection2(unordered_pair(sK1,sK2),sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f19,f20]) ).
fof(f20,plain,
( ? [X0,X1,X2] :
( ~ in(X1,X0)
& set_intersection2(unordered_pair(X1,X2),X0) = unordered_pair(X1,X2) )
=> ( ~ in(sK1,sK0)
& unordered_pair(sK1,sK2) = set_intersection2(unordered_pair(sK1,sK2),sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f19,plain,
? [X0,X1,X2] :
( ~ in(X1,X0)
& set_intersection2(unordered_pair(X1,X2),X0) = unordered_pair(X1,X2) ),
inference(rectify,[],[f17]) ).
fof(f17,plain,
? [X1,X2,X0] :
( ~ in(X2,X1)
& set_intersection2(unordered_pair(X2,X0),X1) = unordered_pair(X2,X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,plain,
~ ! [X1,X2,X0] :
( set_intersection2(unordered_pair(X2,X0),X1) = unordered_pair(X2,X0)
=> in(X2,X1) ),
inference(rectify,[],[f10]) ).
fof(f10,negated_conjecture,
~ ! [X1,X2,X0] :
( unordered_pair(X0,X1) = set_intersection2(unordered_pair(X0,X1),X2)
=> in(X0,X2) ),
inference(negated_conjecture,[],[f9]) ).
fof(f9,conjecture,
! [X1,X2,X0] :
( unordered_pair(X0,X1) = set_intersection2(unordered_pair(X0,X1),X2)
=> in(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_zfmisc_1) ).
fof(f70,plain,
in(sK1,sK0),
inference(resolution,[],[f60,f54]) ).
fof(f54,plain,
! [X2,X4] : in(X4,unordered_pair(X4,X2)),
inference(equality_resolution,[],[f53]) ).
fof(f53,plain,
! [X2,X1,X4] :
( in(X4,X1)
| unordered_pair(X4,X2) != X1 ),
inference(equality_resolution,[],[f43]) ).
fof(f43,plain,
! [X2,X0,X1,X4] :
( in(X4,X1)
| X0 != X4
| unordered_pair(X0,X2) != X1 ),
inference(cnf_transformation,[],[f31]) ).
fof(f31,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X2) = X1
| ( ( ( sK4(X0,X1,X2) != X0
& sK4(X0,X1,X2) != X2 )
| ~ in(sK4(X0,X1,X2),X1) )
& ( sK4(X0,X1,X2) = X0
| sK4(X0,X1,X2) = X2
| in(sK4(X0,X1,X2),X1) ) ) )
& ( ! [X4] :
( ( in(X4,X1)
| ( X0 != X4
& X2 != X4 ) )
& ( X0 = X4
| X2 = X4
| ~ in(X4,X1) ) )
| unordered_pair(X0,X2) != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f29,f30]) ).
fof(f30,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ( X0 != X3
& X2 != X3 )
| ~ in(X3,X1) )
& ( X0 = X3
| X2 = X3
| in(X3,X1) ) )
=> ( ( ( sK4(X0,X1,X2) != X0
& sK4(X0,X1,X2) != X2 )
| ~ in(sK4(X0,X1,X2),X1) )
& ( sK4(X0,X1,X2) = X0
| sK4(X0,X1,X2) = X2
| in(sK4(X0,X1,X2),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f29,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X2) = X1
| ? [X3] :
( ( ( X0 != X3
& X2 != X3 )
| ~ in(X3,X1) )
& ( X0 = X3
| X2 = X3
| in(X3,X1) ) ) )
& ( ! [X4] :
( ( in(X4,X1)
| ( X0 != X4
& X2 != X4 ) )
& ( X0 = X4
| X2 = X4
| ~ in(X4,X1) ) )
| unordered_pair(X0,X2) != X1 ) ),
inference(rectify,[],[f28]) ).
fof(f28,plain,
! [X1,X2,X0] :
( ( unordered_pair(X1,X0) = X2
| ? [X3] :
( ( ( X1 != X3
& X0 != X3 )
| ~ in(X3,X2) )
& ( X1 = X3
| X0 = X3
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( X1 != X3
& X0 != X3 ) )
& ( X1 = X3
| X0 = X3
| ~ in(X3,X2) ) )
| unordered_pair(X1,X0) != X2 ) ),
inference(flattening,[],[f27]) ).
fof(f27,plain,
! [X1,X2,X0] :
( ( unordered_pair(X1,X0) = X2
| ? [X3] :
( ( ( X1 != X3
& X0 != X3 )
| ~ in(X3,X2) )
& ( X1 = X3
| X0 = X3
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( X1 != X3
& X0 != X3 ) )
& ( X1 = X3
| X0 = X3
| ~ in(X3,X2) ) )
| unordered_pair(X1,X0) != X2 ) ),
inference(nnf_transformation,[],[f14]) ).
fof(f14,plain,
! [X1,X2,X0] :
( unordered_pair(X1,X0) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( X1 = X3
| X0 = X3 ) ) ),
inference(rectify,[],[f4]) ).
fof(f4,axiom,
! [X1,X0,X2] :
( ! [X3] :
( ( X1 = X3
| X0 = X3 )
<=> in(X3,X2) )
<=> unordered_pair(X0,X1) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
fof(f60,plain,
! [X0] :
( ~ in(X0,unordered_pair(sK1,sK2))
| in(X0,sK0) ),
inference(superposition,[],[f50,f32]) ).
fof(f32,plain,
unordered_pair(sK1,sK2) = set_intersection2(unordered_pair(sK1,sK2),sK0),
inference(cnf_transformation,[],[f21]) ).
fof(f50,plain,
! [X2,X3,X1] :
( ~ in(X3,set_intersection2(X1,X2))
| in(X3,X2) ),
inference(equality_resolution,[],[f40]) ).
fof(f40,plain,
! [X2,X3,X0,X1] :
( in(X3,X2)
| ~ in(X3,X0)
| set_intersection2(X1,X2) != X0 ),
inference(cnf_transformation,[],[f26]) ).
fof(f26,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ( ( in(X3,X2)
& in(X3,X1) )
| ~ in(X3,X0) )
& ( in(X3,X0)
| ~ in(X3,X2)
| ~ in(X3,X1) ) )
| set_intersection2(X1,X2) != X0 )
& ( set_intersection2(X1,X2) = X0
| ( ( ~ in(sK3(X0,X1,X2),X0)
| ~ in(sK3(X0,X1,X2),X2)
| ~ in(sK3(X0,X1,X2),X1) )
& ( in(sK3(X0,X1,X2),X0)
| ( in(sK3(X0,X1,X2),X2)
& in(sK3(X0,X1,X2),X1) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f24,f25]) ).
fof(f25,plain,
! [X0,X1,X2] :
( ? [X4] :
( ( ~ in(X4,X0)
| ~ in(X4,X2)
| ~ in(X4,X1) )
& ( in(X4,X0)
| ( in(X4,X2)
& in(X4,X1) ) ) )
=> ( ( ~ in(sK3(X0,X1,X2),X0)
| ~ in(sK3(X0,X1,X2),X2)
| ~ in(sK3(X0,X1,X2),X1) )
& ( in(sK3(X0,X1,X2),X0)
| ( in(sK3(X0,X1,X2),X2)
& in(sK3(X0,X1,X2),X1) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ( ( in(X3,X2)
& in(X3,X1) )
| ~ in(X3,X0) )
& ( in(X3,X0)
| ~ in(X3,X2)
| ~ in(X3,X1) ) )
| set_intersection2(X1,X2) != X0 )
& ( set_intersection2(X1,X2) = X0
| ? [X4] :
( ( ~ in(X4,X0)
| ~ in(X4,X2)
| ~ in(X4,X1) )
& ( in(X4,X0)
| ( in(X4,X2)
& in(X4,X1) ) ) ) ) ),
inference(rectify,[],[f23]) ).
fof(f23,plain,
! [X0,X2,X1] :
( ( ! [X3] :
( ( ( in(X3,X1)
& in(X3,X2) )
| ~ in(X3,X0) )
& ( in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) ) )
| set_intersection2(X2,X1) != X0 )
& ( set_intersection2(X2,X1) = X0
| ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( in(X3,X0)
| ( in(X3,X1)
& in(X3,X2) ) ) ) ) ),
inference(flattening,[],[f22]) ).
fof(f22,plain,
! [X0,X2,X1] :
( ( ! [X3] :
( ( ( in(X3,X1)
& in(X3,X2) )
| ~ in(X3,X0) )
& ( in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) ) )
| set_intersection2(X2,X1) != X0 )
& ( set_intersection2(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,[],[f13]) ).
fof(f13,plain,
! [X0,X2,X1] :
( ! [X3] :
( ( in(X3,X1)
& in(X3,X2) )
<=> in(X3,X0) )
<=> set_intersection2(X2,X1) = X0 ),
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X2,X1,X0] :
( set_intersection2(X0,X1) = X2
<=> ! [X3] :
( ( in(X3,X0)
& in(X3,X1) )
<=> in(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET920+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.35 % Computer : n003.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % 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 14:30:52 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.50 % (30187)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 0.20/0.50 % (30196)dis+10_1:1_newcnf=on:sgt=8:sos=on:ss=axioms:to=lpo:urr=on:i=49:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/49Mi)
% 0.20/0.50 % (30213)lrs+11_1:1_plsq=on:plsqc=1:plsqr=32,1:ss=included:i=95:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/95Mi)
% 0.20/0.50 % (30188)lrs+10_1:1_gsp=on:sd=1:sgt=32:sos=on:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.20/0.50 % (30204)lrs+1011_1:1_fd=preordered:fsd=on:sos=on:thsq=on:thsqc=64:thsqd=32:uwa=ground:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.20/0.50 % (30188)First to succeed.
% 0.20/0.50 % (30189)dis+1002_1:1_aac=none:bd=off:sac=on:sos=on:spb=units:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.20/0.51 % (30197)lrs+10_1:1_br=off:sos=on:ss=axioms:st=2.0:urr=on:i=33:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/33Mi)
% 0.20/0.51 % (30188)Refutation found. Thanks to Tanya!
% 0.20/0.51 % SZS status Theorem for theBenchmark
% 0.20/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.51 % (30188)------------------------------
% 0.20/0.51 % (30188)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.51 % (30188)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.51 % (30188)Termination reason: Refutation
% 0.20/0.51
% 0.20/0.51 % (30188)Memory used [KB]: 6012
% 0.20/0.51 % (30188)Time elapsed: 0.095 s
% 0.20/0.51 % (30188)Instructions burned: 2 (million)
% 0.20/0.51 % (30188)------------------------------
% 0.20/0.51 % (30188)------------------------------
% 0.20/0.51 % (30184)Success in time 0.151 s
%------------------------------------------------------------------------------