TSTP Solution File: SET906+1 by SnakeForV---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SET906+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 : n008.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 18:22:42 EDT 2022
% Result : Theorem 0.19s 0.52s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 41 ( 9 unt; 0 def)
% Number of atoms : 206 ( 71 equ)
% Maximal formula atoms : 14 ( 5 avg)
% Number of connectives : 253 ( 88 ~; 92 |; 53 &)
% ( 10 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 119 ( 102 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f141,plain,
$false,
inference(subsumption_resolution,[],[f139,f60]) ).
fof(f60,plain,
~ in(sK2,sK4),
inference(cnf_transformation,[],[f40]) ).
fof(f40,plain,
( ~ in(sK2,sK4)
& subset(set_union2(unordered_pair(sK2,sK3),sK4),sK4) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f38,f39]) ).
fof(f39,plain,
( ? [X0,X1,X2] :
( ~ in(X0,X2)
& subset(set_union2(unordered_pair(X0,X1),X2),X2) )
=> ( ~ in(sK2,sK4)
& subset(set_union2(unordered_pair(sK2,sK3),sK4),sK4) ) ),
introduced(choice_axiom,[]) ).
fof(f38,plain,
? [X0,X1,X2] :
( ~ in(X0,X2)
& subset(set_union2(unordered_pair(X0,X1),X2),X2) ),
inference(rectify,[],[f23]) ).
fof(f23,plain,
? [X1,X2,X0] :
( ~ in(X1,X0)
& subset(set_union2(unordered_pair(X1,X2),X0),X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,plain,
~ ! [X1,X0,X2] :
( subset(set_union2(unordered_pair(X1,X2),X0),X0)
=> in(X1,X0) ),
inference(rectify,[],[f14]) ).
fof(f14,negated_conjecture,
~ ! [X2,X0,X1] :
( subset(set_union2(unordered_pair(X0,X1),X2),X2)
=> in(X0,X2) ),
inference(negated_conjecture,[],[f13]) ).
fof(f13,conjecture,
! [X2,X0,X1] :
( subset(set_union2(unordered_pair(X0,X1),X2),X2)
=> in(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_zfmisc_1) ).
fof(f139,plain,
in(sK2,sK4),
inference(resolution,[],[f138,f67]) ).
fof(f67,plain,
! [X2,X3] : in(X3,unordered_pair(X3,X2)),
inference(equality_resolution,[],[f66]) ).
fof(f66,plain,
! [X2,X3,X1] :
( in(X3,X1)
| unordered_pair(X3,X2) != X1 ),
inference(equality_resolution,[],[f57]) ).
fof(f57,plain,
! [X2,X3,X0,X1] :
( in(X3,X1)
| X0 != X3
| unordered_pair(X0,X2) != X1 ),
inference(cnf_transformation,[],[f37]) ).
fof(f37,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ( X0 = X3
| X2 = X3
| ~ in(X3,X1) )
& ( in(X3,X1)
| ( X0 != X3
& X2 != X3 ) ) )
| unordered_pair(X0,X2) != X1 )
& ( unordered_pair(X0,X2) = X1
| ( ( ~ in(sK1(X0,X1,X2),X1)
| ( sK1(X0,X1,X2) != X0
& sK1(X0,X1,X2) != X2 ) )
& ( in(sK1(X0,X1,X2),X1)
| sK1(X0,X1,X2) = X0
| sK1(X0,X1,X2) = X2 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f35,f36]) ).
fof(f36,plain,
! [X0,X1,X2] :
( ? [X4] :
( ( ~ in(X4,X1)
| ( X0 != X4
& X2 != X4 ) )
& ( in(X4,X1)
| X0 = X4
| X2 = X4 ) )
=> ( ( ~ in(sK1(X0,X1,X2),X1)
| ( sK1(X0,X1,X2) != X0
& sK1(X0,X1,X2) != X2 ) )
& ( in(sK1(X0,X1,X2),X1)
| sK1(X0,X1,X2) = X0
| sK1(X0,X1,X2) = X2 ) ) ),
introduced(choice_axiom,[]) ).
fof(f35,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ( X0 = X3
| X2 = X3
| ~ in(X3,X1) )
& ( in(X3,X1)
| ( X0 != X3
& X2 != X3 ) ) )
| unordered_pair(X0,X2) != X1 )
& ( unordered_pair(X0,X2) = X1
| ? [X4] :
( ( ~ in(X4,X1)
| ( X0 != X4
& X2 != X4 ) )
& ( in(X4,X1)
| X0 = X4
| X2 = X4 ) ) ) ),
inference(rectify,[],[f34]) ).
fof(f34,plain,
! [X2,X1,X0] :
( ( ! [X3] :
( ( X2 = X3
| X0 = X3
| ~ in(X3,X1) )
& ( in(X3,X1)
| ( X2 != X3
& X0 != X3 ) ) )
| unordered_pair(X2,X0) != X1 )
& ( unordered_pair(X2,X0) = X1
| ? [X3] :
( ( ~ in(X3,X1)
| ( X2 != X3
& X0 != X3 ) )
& ( in(X3,X1)
| X2 = X3
| X0 = X3 ) ) ) ),
inference(flattening,[],[f33]) ).
fof(f33,plain,
! [X2,X1,X0] :
( ( ! [X3] :
( ( X2 = X3
| X0 = X3
| ~ in(X3,X1) )
& ( in(X3,X1)
| ( X2 != X3
& X0 != X3 ) ) )
| unordered_pair(X2,X0) != X1 )
& ( unordered_pair(X2,X0) = X1
| ? [X3] :
( ( ~ in(X3,X1)
| ( X2 != X3
& X0 != X3 ) )
& ( in(X3,X1)
| X2 = X3
| X0 = X3 ) ) ) ),
inference(nnf_transformation,[],[f19]) ).
fof(f19,plain,
! [X2,X1,X0] :
( ! [X3] :
( ( X2 = X3
| X0 = X3 )
<=> in(X3,X1) )
<=> unordered_pair(X2,X0) = X1 ),
inference(rectify,[],[f4]) ).
fof(f4,axiom,
! [X1,X2,X0] :
( ! [X3] :
( in(X3,X2)
<=> ( X1 = X3
| X0 = X3 ) )
<=> unordered_pair(X0,X1) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
fof(f138,plain,
! [X1] :
( ~ in(X1,unordered_pair(sK2,sK3))
| in(X1,sK4) ),
inference(resolution,[],[f135,f63]) ).
fof(f63,plain,
! [X2,X0,X4] :
( in(X4,set_union2(X0,X2))
| ~ in(X4,X2) ),
inference(equality_resolution,[],[f45]) ).
fof(f45,plain,
! [X2,X0,X1,X4] :
( in(X4,X1)
| ~ in(X4,X2)
| set_union2(X0,X2) != X1 ),
inference(cnf_transformation,[],[f31]) ).
fof(f31,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X2) = X1
| ( ( ~ in(sK0(X0,X1,X2),X1)
| ( ~ in(sK0(X0,X1,X2),X2)
& ~ in(sK0(X0,X1,X2),X0) ) )
& ( in(sK0(X0,X1,X2),X1)
| in(sK0(X0,X1,X2),X2)
| in(sK0(X0,X1,X2),X0) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| in(X4,X0)
| ~ in(X4,X1) )
& ( in(X4,X1)
| ( ~ in(X4,X2)
& ~ in(X4,X0) ) ) )
| set_union2(X0,X2) != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f29,f30]) ).
fof(f30,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ in(X3,X1)
| ( ~ in(X3,X2)
& ~ in(X3,X0) ) )
& ( in(X3,X1)
| in(X3,X2)
| in(X3,X0) ) )
=> ( ( ~ in(sK0(X0,X1,X2),X1)
| ( ~ in(sK0(X0,X1,X2),X2)
& ~ in(sK0(X0,X1,X2),X0) ) )
& ( in(sK0(X0,X1,X2),X1)
| in(sK0(X0,X1,X2),X2)
| in(sK0(X0,X1,X2),X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f29,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X2) = X1
| ? [X3] :
( ( ~ in(X3,X1)
| ( ~ in(X3,X2)
& ~ in(X3,X0) ) )
& ( in(X3,X1)
| in(X3,X2)
| in(X3,X0) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| in(X4,X0)
| ~ in(X4,X1) )
& ( in(X4,X1)
| ( ~ in(X4,X2)
& ~ in(X4,X0) ) ) )
| set_union2(X0,X2) != X1 ) ),
inference(rectify,[],[f28]) ).
fof(f28,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X2) = X1
| ? [X3] :
( ( ~ in(X3,X1)
| ( ~ in(X3,X2)
& ~ in(X3,X0) ) )
& ( in(X3,X1)
| in(X3,X2)
| in(X3,X0) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| in(X3,X0)
| ~ in(X3,X1) )
& ( in(X3,X1)
| ( ~ in(X3,X2)
& ~ in(X3,X0) ) ) )
| set_union2(X0,X2) != X1 ) ),
inference(flattening,[],[f27]) ).
fof(f27,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X2) = X1
| ? [X3] :
( ( ~ in(X3,X1)
| ( ~ in(X3,X2)
& ~ in(X3,X0) ) )
& ( in(X3,X1)
| in(X3,X2)
| in(X3,X0) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| in(X3,X0)
| ~ in(X3,X1) )
& ( in(X3,X1)
| ( ~ in(X3,X2)
& ~ in(X3,X0) ) ) )
| set_union2(X0,X2) != X1 ) ),
inference(nnf_transformation,[],[f16]) ).
fof(f16,plain,
! [X0,X1,X2] :
( set_union2(X0,X2) = X1
<=> ! [X3] :
( ( in(X3,X2)
| in(X3,X0) )
<=> in(X3,X1) ) ),
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X0,X2,X1] :
( ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
| in(X3,X0) ) )
<=> set_union2(X0,X1) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f135,plain,
! [X0] :
( ~ in(X0,set_union2(sK4,unordered_pair(sK2,sK3)))
| in(X0,sK4) ),
inference(resolution,[],[f52,f70]) ).
fof(f70,plain,
subset(set_union2(sK4,unordered_pair(sK2,sK3)),sK4),
inference(backward_demodulation,[],[f59,f43]) ).
fof(f43,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f26]) ).
fof(f26,plain,
! [X0,X1] : 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(f59,plain,
subset(set_union2(unordered_pair(sK2,sK3),sK4),sK4),
inference(cnf_transformation,[],[f40]) ).
fof(f52,plain,
! [X2,X0,X1] :
( ~ subset(X1,X0)
| ~ in(X2,X1)
| in(X2,X0) ),
inference(cnf_transformation,[],[f24]) ).
fof(f24,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ! [X2] :
( ~ in(X2,X1)
| in(X2,X0) ) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,plain,
! [X0,X1] :
( subset(X1,X0)
=> ! [X2] :
( in(X2,X1)
=> in(X2,X0) ) ),
inference(unused_predicate_definition_removal,[],[f17]) ).
fof(f17,plain,
! [X0,X1] :
( ! [X2] :
( in(X2,X1)
=> in(X2,X0) )
<=> subset(X1,X0) ),
inference(rectify,[],[f6]) ).
fof(f6,axiom,
! [X1,X0] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET906+1 : TPTP v8.1.0. Released v3.2.0.
% 0.04/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.34 % Computer : n008.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 14:32:40 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.50 % (14686)lrs+10_1:2_br=off:nm=4:ss=included:urr=on:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.51 % (14685)lrs+10_1:1_ep=R:lcm=predicate:lma=on:sos=all:spb=goal:ss=included:i=12:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/12Mi)
% 0.19/0.51 % (14686)Instruction limit reached!
% 0.19/0.51 % (14686)------------------------------
% 0.19/0.51 % (14686)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.51 % (14679)lrs+10_1:1024_nm=0:nwc=5.0:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.19/0.51 % (14679)First to succeed.
% 0.19/0.51 % (14686)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.51 % (14686)Termination reason: Unknown
% 0.19/0.51 % (14686)Termination phase: Saturation
% 0.19/0.51
% 0.19/0.51 % (14686)Memory used [KB]: 6012
% 0.19/0.51 % (14686)Time elapsed: 0.113 s
% 0.19/0.51 % (14686)Instructions burned: 7 (million)
% 0.19/0.51 % (14686)------------------------------
% 0.19/0.51 % (14686)------------------------------
% 0.19/0.52 % (14679)Refutation found. Thanks to Tanya!
% 0.19/0.52 % SZS status Theorem for theBenchmark
% 0.19/0.52 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.52 % (14679)------------------------------
% 0.19/0.52 % (14679)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.52 % (14679)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.52 % (14679)Termination reason: Refutation
% 0.19/0.52
% 0.19/0.52 % (14679)Memory used [KB]: 6012
% 0.19/0.52 % (14679)Time elapsed: 0.114 s
% 0.19/0.52 % (14679)Instructions burned: 4 (million)
% 0.19/0.52 % (14679)------------------------------
% 0.19/0.52 % (14679)------------------------------
% 0.19/0.52 % (14674)Success in time 0.17 s
%------------------------------------------------------------------------------