TSTP Solution File: SET351+4 by SnakeForV---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SET351+4 : TPTP v8.1.0. Released v2.2.0.
% 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 : n013.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 18:20:25 EDT 2022
% Result : Theorem 0.20s 0.51s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 49 ( 9 unt; 0 def)
% Number of atoms : 127 ( 9 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 127 ( 49 ~; 45 |; 19 &)
% ( 7 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 97 ( 88 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f101,plain,
$false,
inference(resolution,[],[f100,f41]) ).
fof(f41,plain,
~ equal_set(sum(singleton(sK2)),sK2),
inference(cnf_transformation,[],[f32]) ).
fof(f32,plain,
~ equal_set(sum(singleton(sK2)),sK2),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f20,f31]) ).
fof(f31,plain,
( ? [X0] : ~ equal_set(sum(singleton(X0)),X0)
=> ~ equal_set(sum(singleton(sK2)),sK2) ),
introduced(choice_axiom,[]) ).
fof(f20,plain,
? [X0] : ~ equal_set(sum(singleton(X0)),X0),
inference(ennf_transformation,[],[f13]) ).
fof(f13,negated_conjecture,
~ ! [X0] : equal_set(sum(singleton(X0)),X0),
inference(negated_conjecture,[],[f12]) ).
fof(f12,conjecture,
! [X0] : equal_set(sum(singleton(X0)),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI39) ).
fof(f100,plain,
! [X0] : equal_set(sum(singleton(X0)),X0),
inference(subsumption_resolution,[],[f96,f43]) ).
fof(f43,plain,
! [X1] : member(X1,singleton(X1)),
inference(equality_resolution,[],[f34]) ).
fof(f34,plain,
! [X0,X1] :
( member(X0,singleton(X1))
| X0 != X1 ),
inference(cnf_transformation,[],[f24]) ).
fof(f24,plain,
! [X0,X1] :
( ( X0 = X1
| ~ member(X0,singleton(X1)) )
& ( member(X0,singleton(X1))
| X0 != X1 ) ),
inference(rectify,[],[f23]) ).
fof(f23,plain,
! [X1,X0] :
( ( X0 = X1
| ~ member(X1,singleton(X0)) )
& ( member(X1,singleton(X0))
| X0 != X1 ) ),
inference(nnf_transformation,[],[f16]) ).
fof(f16,plain,
! [X1,X0] :
( X0 = X1
<=> member(X1,singleton(X0)) ),
inference(rectify,[],[f8]) ).
fof(f8,axiom,
! [X0,X2] :
( member(X2,singleton(X0))
<=> X0 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton) ).
fof(f96,plain,
! [X0] :
( equal_set(sum(singleton(X0)),X0)
| ~ member(X0,singleton(X0)) ),
inference(resolution,[],[f87,f73]) ).
fof(f73,plain,
! [X0] : subset(sum(singleton(X0)),X0),
inference(duplicate_literal_removal,[],[f69]) ).
fof(f69,plain,
! [X0] :
( subset(sum(singleton(X0)),X0)
| subset(sum(singleton(X0)),X0) ),
inference(resolution,[],[f62,f40]) ).
fof(f40,plain,
! [X0,X1] :
( ~ member(sK1(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f30]) ).
fof(f30,plain,
! [X0,X1] :
( subset(X0,X1)
| ( ~ member(sK1(X0,X1),X1)
& member(sK1(X0,X1),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f19,f29]) ).
fof(f29,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) )
=> ( ~ member(sK1(X0,X1),X1)
& member(sK1(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f19,plain,
! [X0,X1] :
( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) ),
inference(ennf_transformation,[],[f18]) ).
fof(f18,plain,
! [X0,X1] :
( ! [X2] :
( member(X2,X0)
=> member(X2,X1) )
=> subset(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset) ).
fof(f62,plain,
! [X3,X4] :
( member(sK1(sum(singleton(X3)),X4),X3)
| subset(sum(singleton(X3)),X4) ),
inference(resolution,[],[f60,f39]) ).
fof(f39,plain,
! [X0,X1] :
( member(sK1(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f30]) ).
fof(f60,plain,
! [X2,X3] :
( ~ member(X3,sum(singleton(X2)))
| member(X3,X2) ),
inference(duplicate_literal_removal,[],[f58]) ).
fof(f58,plain,
! [X2,X3] :
( member(X3,X2)
| ~ member(X3,sum(singleton(X2)))
| ~ member(X3,sum(singleton(X2))) ),
inference(superposition,[],[f37,f48]) ).
fof(f48,plain,
! [X0,X1] :
( sK0(singleton(X1),X0) = X1
| ~ member(X0,sum(singleton(X1))) ),
inference(resolution,[],[f38,f35]) ).
fof(f35,plain,
! [X0,X1] :
( ~ member(X0,singleton(X1))
| X0 = X1 ),
inference(cnf_transformation,[],[f24]) ).
fof(f38,plain,
! [X0,X1] :
( member(sK0(X0,X1),X0)
| ~ member(X1,sum(X0)) ),
inference(cnf_transformation,[],[f28]) ).
fof(f28,plain,
! [X0,X1] :
( ( ( member(sK0(X0,X1),X0)
& member(X1,sK0(X0,X1)) )
| ~ member(X1,sum(X0)) )
& ( member(X1,sum(X0))
| ! [X3] :
( ~ member(X3,X0)
| ~ member(X1,X3) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f26,f27]) ).
fof(f27,plain,
! [X0,X1] :
( ? [X2] :
( member(X2,X0)
& member(X1,X2) )
=> ( member(sK0(X0,X1),X0)
& member(X1,sK0(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f26,plain,
! [X0,X1] :
( ( ? [X2] :
( member(X2,X0)
& member(X1,X2) )
| ~ member(X1,sum(X0)) )
& ( member(X1,sum(X0))
| ! [X3] :
( ~ member(X3,X0)
| ~ member(X1,X3) ) ) ),
inference(rectify,[],[f25]) ).
fof(f25,plain,
! [X1,X0] :
( ( ? [X2] :
( member(X2,X1)
& member(X0,X2) )
| ~ member(X0,sum(X1)) )
& ( member(X0,sum(X1))
| ! [X2] :
( ~ member(X2,X1)
| ~ member(X0,X2) ) ) ),
inference(nnf_transformation,[],[f15]) ).
fof(f15,plain,
! [X1,X0] :
( ? [X2] :
( member(X2,X1)
& member(X0,X2) )
<=> member(X0,sum(X1)) ),
inference(rectify,[],[f10]) ).
fof(f10,axiom,
! [X2,X0] :
( ? [X4] :
( member(X2,X4)
& member(X4,X0) )
<=> member(X2,sum(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum) ).
fof(f37,plain,
! [X0,X1] :
( member(X1,sK0(X0,X1))
| ~ member(X1,sum(X0)) ),
inference(cnf_transformation,[],[f28]) ).
fof(f87,plain,
! [X2,X1] :
( ~ subset(sum(X2),X1)
| ~ member(X1,X2)
| equal_set(sum(X2),X1) ),
inference(resolution,[],[f83,f42]) ).
fof(f42,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| equal_set(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f33,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| equal_set(X0,X1) ),
inference(rectify,[],[f22]) ).
fof(f22,plain,
! [X1,X0] :
( ~ subset(X0,X1)
| ~ subset(X1,X0)
| equal_set(X1,X0) ),
inference(flattening,[],[f21]) ).
fof(f21,plain,
! [X1,X0] :
( equal_set(X1,X0)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f17]) ).
fof(f17,plain,
! [X1,X0] :
( ( subset(X1,X0)
& subset(X0,X1) )
=> equal_set(X1,X0) ),
inference(unused_predicate_definition_removal,[],[f14]) ).
fof(f14,plain,
! [X1,X0] :
( ( subset(X1,X0)
& subset(X0,X1) )
<=> equal_set(X1,X0) ),
inference(rectify,[],[f2]) ).
fof(f2,axiom,
! [X1,X0] :
( ( subset(X0,X1)
& subset(X1,X0) )
<=> equal_set(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_set) ).
fof(f83,plain,
! [X0,X1] :
( subset(X0,sum(X1))
| ~ member(X0,X1) ),
inference(duplicate_literal_removal,[],[f77]) ).
fof(f77,plain,
! [X0,X1] :
( ~ member(X0,X1)
| subset(X0,sum(X1))
| subset(X0,sum(X1)) ),
inference(resolution,[],[f51,f39]) ).
fof(f51,plain,
! [X2,X0,X1] :
( ~ member(sK1(X2,sum(X1)),X0)
| subset(X2,sum(X1))
| ~ member(X0,X1) ),
inference(resolution,[],[f36,f40]) ).
fof(f36,plain,
! [X3,X0,X1] :
( member(X1,sum(X0))
| ~ member(X3,X0)
| ~ member(X1,X3) ),
inference(cnf_transformation,[],[f28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET351+4 : TPTP v8.1.0. Released v2.2.0.
% 0.12/0.13 % 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 : n013.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 13:37:32 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.47 % (22014)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)
% 0.20/0.48 % (22014)Refutation not found, incomplete strategy% (22014)------------------------------
% 0.20/0.48 % (22014)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.48 % (22014)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.48 % (22014)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.48
% 0.20/0.48 % (22014)Memory used [KB]: 5884
% 0.20/0.48 % (22014)Time elapsed: 0.064 s
% 0.20/0.48 % (22014)Instructions burned: 2 (million)
% 0.20/0.48 % (22014)------------------------------
% 0.20/0.48 % (22014)------------------------------
% 0.20/0.48 % (22003)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)
% 0.20/0.48 % (22003)Refutation not found, incomplete strategy% (22003)------------------------------
% 0.20/0.48 % (22003)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.48 % (22003)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.48 % (22003)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.48
% 0.20/0.48 % (22003)Memory used [KB]: 5884
% 0.20/0.48 % (22003)Time elapsed: 0.073 s
% 0.20/0.48 % (22003)Instructions burned: 2 (million)
% 0.20/0.48 % (22003)------------------------------
% 0.20/0.48 % (22003)------------------------------
% 0.20/0.51 % (22009)dis+1010_1:50_awrs=decay:awrsf=128:nwc=10.0:s2pl=no:sp=frequency:ss=axioms:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.20/0.51 % (22009)First to succeed.
% 0.20/0.51 % (22009)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 % (22009)------------------------------
% 0.20/0.51 % (22009)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.51 % (22009)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.51 % (22009)Termination reason: Refutation
% 0.20/0.51
% 0.20/0.51 % (22009)Memory used [KB]: 5884
% 0.20/0.51 % (22009)Time elapsed: 0.095 s
% 0.20/0.51 % (22009)Instructions burned: 3 (million)
% 0.20/0.51 % (22009)------------------------------
% 0.20/0.51 % (22009)------------------------------
% 0.20/0.51 % (21996)Success in time 0.158 s
%------------------------------------------------------------------------------