TSTP Solution File: SET890+1 by SnakeForV---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SET890+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 : n001.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 18:22:40 EDT 2022
% Result : Theorem 0.19s 0.52s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 12
% Syntax : Number of formulae : 56 ( 10 unt; 0 def)
% Number of atoms : 219 ( 58 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 258 ( 95 ~; 95 |; 49 &)
% ( 9 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 1 con; 0-2 aty)
% Number of variables : 139 ( 119 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f174,plain,
$false,
inference(trivial_inequality_removal,[],[f162]) ).
fof(f162,plain,
sK4 != sK4,
inference(superposition,[],[f51,f155]) ).
fof(f155,plain,
! [X0] : union(singleton(X0)) = X0,
inference(subsumption_resolution,[],[f151,f66]) ).
fof(f66,plain,
! [X2] : in(X2,singleton(X2)),
inference(equality_resolution,[],[f65]) ).
fof(f65,plain,
! [X2,X0] :
( in(X2,X0)
| singleton(X2) != X0 ),
inference(equality_resolution,[],[f57]) ).
fof(f57,plain,
! [X2,X0,X1] :
( in(X2,X0)
| X1 != X2
| singleton(X1) != X0 ),
inference(cnf_transformation,[],[f38]) ).
fof(f38,plain,
! [X0,X1] :
( ( ! [X2] :
( ( X1 = X2
| ~ in(X2,X0) )
& ( in(X2,X0)
| X1 != X2 ) )
| singleton(X1) != X0 )
& ( singleton(X1) = X0
| ( ( ~ in(sK5(X0,X1),X0)
| sK5(X0,X1) != X1 )
& ( in(sK5(X0,X1),X0)
| sK5(X0,X1) = X1 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f36,f37]) ).
fof(f37,plain,
! [X0,X1] :
( ? [X3] :
( ( ~ in(X3,X0)
| X1 != X3 )
& ( in(X3,X0)
| X1 = X3 ) )
=> ( ( ~ in(sK5(X0,X1),X0)
| sK5(X0,X1) != X1 )
& ( in(sK5(X0,X1),X0)
| sK5(X0,X1) = X1 ) ) ),
introduced(choice_axiom,[]) ).
fof(f36,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,[],[f35]) ).
fof(f35,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(f151,plain,
! [X0] :
( ~ in(X0,singleton(X0))
| union(singleton(X0)) = X0 ),
inference(resolution,[],[f150,f76]) ).
fof(f76,plain,
! [X2,X1] :
( ~ subset(union(X1),X2)
| union(X1) = X2
| ~ in(X2,X1) ),
inference(resolution,[],[f44,f52]) ).
fof(f52,plain,
! [X0,X1] :
( subset(X1,union(X0))
| ~ in(X1,X0) ),
inference(cnf_transformation,[],[f18]) ).
fof(f18,plain,
! [X0,X1] :
( ~ in(X1,X0)
| subset(X1,union(X0)) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,plain,
! [X0,X1] :
( in(X1,X0)
=> subset(X1,union(X0)) ),
inference(rectify,[],[f6]) ).
fof(f6,axiom,
! [X1,X0] :
( in(X0,X1)
=> subset(X0,union(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l50_zfmisc_1) ).
fof(f44,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f26]) ).
fof(f26,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(flattening,[],[f25]) ).
fof(f25,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f12,plain,
! [X0,X1] :
( X0 = X1
<=> ( subset(X0,X1)
& subset(X1,X0) ) ),
inference(rectify,[],[f2]) ).
fof(f2,axiom,
! [X1,X0] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(f150,plain,
! [X0] : subset(union(singleton(X0)),X0),
inference(duplicate_literal_removal,[],[f142]) ).
fof(f142,plain,
! [X0] :
( subset(union(singleton(X0)),X0)
| subset(union(singleton(X0)),X0) ),
inference(resolution,[],[f122,f40]) ).
fof(f40,plain,
! [X0,X1] :
( ~ in(sK0(X0,X1),X0)
| subset(X1,X0) ),
inference(cnf_transformation,[],[f24]) ).
fof(f24,plain,
! [X0,X1] :
( ( ! [X2] :
( in(X2,X0)
| ~ in(X2,X1) )
| ~ subset(X1,X0) )
& ( subset(X1,X0)
| ( ~ in(sK0(X0,X1),X0)
& in(sK0(X0,X1),X1) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f22,f23]) ).
fof(f23,plain,
! [X0,X1] :
( ? [X3] :
( ~ in(X3,X0)
& in(X3,X1) )
=> ( ~ in(sK0(X0,X1),X0)
& in(sK0(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f22,plain,
! [X0,X1] :
( ( ! [X2] :
( in(X2,X0)
| ~ in(X2,X1) )
| ~ subset(X1,X0) )
& ( subset(X1,X0)
| ? [X3] :
( ~ in(X3,X0)
& in(X3,X1) ) ) ),
inference(rectify,[],[f21]) ).
fof(f21,plain,
! [X0,X1] :
( ( ! [X2] :
( in(X2,X0)
| ~ in(X2,X1) )
| ~ subset(X1,X0) )
& ( subset(X1,X0)
| ? [X2] :
( ~ in(X2,X0)
& in(X2,X1) ) ) ),
inference(nnf_transformation,[],[f17]) ).
fof(f17,plain,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
| ~ in(X2,X1) )
<=> subset(X1,X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,plain,
! [X1,X0] :
( subset(X1,X0)
<=> ! [X2] :
( in(X2,X1)
=> in(X2,X0) ) ),
inference(rectify,[],[f4]) ).
fof(f4,axiom,
! [X1,X0] :
( ! [X2] :
( in(X2,X0)
=> in(X2,X1) )
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f122,plain,
! [X3,X4] :
( in(sK0(X3,union(singleton(X4))),X4)
| subset(union(singleton(X4)),X3) ),
inference(resolution,[],[f118,f39]) ).
fof(f39,plain,
! [X0,X1] :
( in(sK0(X0,X1),X1)
| subset(X1,X0) ),
inference(cnf_transformation,[],[f24]) ).
fof(f118,plain,
! [X6,X7] :
( ~ in(X7,union(singleton(X6)))
| in(X7,X6) ),
inference(duplicate_literal_removal,[],[f116]) ).
fof(f116,plain,
! [X6,X7] :
( ~ in(X7,union(singleton(X6)))
| ~ in(X7,union(singleton(X6)))
| in(X7,X6) ),
inference(superposition,[],[f61,f79]) ).
fof(f79,plain,
! [X2,X3] :
( sK3(singleton(X3),X2) = X3
| ~ in(X2,union(singleton(X3))) ),
inference(resolution,[],[f62,f64]) ).
fof(f64,plain,
! [X2,X1] :
( ~ in(X2,singleton(X1))
| X1 = X2 ),
inference(equality_resolution,[],[f58]) ).
fof(f58,plain,
! [X2,X0,X1] :
( X1 = X2
| ~ in(X2,X0)
| singleton(X1) != X0 ),
inference(cnf_transformation,[],[f38]) ).
fof(f62,plain,
! [X1,X5] :
( in(sK3(X1,X5),X1)
| ~ in(X5,union(X1)) ),
inference(equality_resolution,[],[f46]) ).
fof(f46,plain,
! [X0,X1,X5] :
( in(sK3(X1,X5),X1)
| ~ in(X5,X0)
| union(X1) != X0 ),
inference(cnf_transformation,[],[f32]) ).
fof(f32,plain,
! [X0,X1] :
( ( union(X1) = X0
| ( ( ~ in(sK1(X0,X1),X0)
| ! [X3] :
( ~ in(sK1(X0,X1),X3)
| ~ in(X3,X1) ) )
& ( in(sK1(X0,X1),X0)
| ( in(sK1(X0,X1),sK2(X0,X1))
& in(sK2(X0,X1),X1) ) ) ) )
& ( ! [X5] :
( ( ( in(X5,sK3(X1,X5))
& in(sK3(X1,X5),X1) )
| ~ in(X5,X0) )
& ( in(X5,X0)
| ! [X7] :
( ~ in(X5,X7)
| ~ in(X7,X1) ) ) )
| union(X1) != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f28,f31,f30,f29]) ).
fof(f29,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ in(X2,X0)
| ! [X3] :
( ~ in(X2,X3)
| ~ in(X3,X1) ) )
& ( in(X2,X0)
| ? [X4] :
( in(X2,X4)
& in(X4,X1) ) ) )
=> ( ( ~ in(sK1(X0,X1),X0)
| ! [X3] :
( ~ in(sK1(X0,X1),X3)
| ~ in(X3,X1) ) )
& ( in(sK1(X0,X1),X0)
| ? [X4] :
( in(sK1(X0,X1),X4)
& in(X4,X1) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f30,plain,
! [X0,X1] :
( ? [X4] :
( in(sK1(X0,X1),X4)
& in(X4,X1) )
=> ( in(sK1(X0,X1),sK2(X0,X1))
& in(sK2(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f31,plain,
! [X1,X5] :
( ? [X6] :
( in(X5,X6)
& in(X6,X1) )
=> ( in(X5,sK3(X1,X5))
& in(sK3(X1,X5),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f28,plain,
! [X0,X1] :
( ( union(X1) = X0
| ? [X2] :
( ( ~ in(X2,X0)
| ! [X3] :
( ~ in(X2,X3)
| ~ in(X3,X1) ) )
& ( in(X2,X0)
| ? [X4] :
( in(X2,X4)
& in(X4,X1) ) ) ) )
& ( ! [X5] :
( ( ? [X6] :
( in(X5,X6)
& in(X6,X1) )
| ~ in(X5,X0) )
& ( in(X5,X0)
| ! [X7] :
( ~ in(X5,X7)
| ~ in(X7,X1) ) ) )
| union(X1) != X0 ) ),
inference(rectify,[],[f27]) ).
fof(f27,plain,
! [X1,X0] :
( ( union(X0) = X1
| ? [X2] :
( ( ~ in(X2,X1)
| ! [X3] :
( ~ in(X2,X3)
| ~ in(X3,X0) ) )
& ( in(X2,X1)
| ? [X3] :
( in(X2,X3)
& in(X3,X0) ) ) ) )
& ( ! [X2] :
( ( ? [X3] :
( in(X2,X3)
& in(X3,X0) )
| ~ in(X2,X1) )
& ( in(X2,X1)
| ! [X3] :
( ~ in(X2,X3)
| ~ in(X3,X0) ) ) )
| union(X0) != X1 ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X1,X0] :
( union(X0) = X1
<=> ! [X2] :
( ? [X3] :
( in(X2,X3)
& in(X3,X0) )
<=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_tarski) ).
fof(f61,plain,
! [X1,X5] :
( in(X5,sK3(X1,X5))
| ~ in(X5,union(X1)) ),
inference(equality_resolution,[],[f47]) ).
fof(f47,plain,
! [X0,X1,X5] :
( in(X5,sK3(X1,X5))
| ~ in(X5,X0)
| union(X1) != X0 ),
inference(cnf_transformation,[],[f32]) ).
fof(f51,plain,
sK4 != union(singleton(sK4)),
inference(cnf_transformation,[],[f34]) ).
fof(f34,plain,
sK4 != union(singleton(sK4)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f19,f33]) ).
fof(f33,plain,
( ? [X0] : union(singleton(X0)) != X0
=> sK4 != union(singleton(sK4)) ),
introduced(choice_axiom,[]) ).
fof(f19,plain,
? [X0] : union(singleton(X0)) != X0,
inference(ennf_transformation,[],[f11]) ).
fof(f11,negated_conjecture,
~ ! [X0] : union(singleton(X0)) = X0,
inference(negated_conjecture,[],[f10]) ).
fof(f10,conjecture,
! [X0] : union(singleton(X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t31_zfmisc_1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET890+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
% 0.13/0.34 % Computer : n001.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 14:50:01 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.50 % (15625)lrs+10_1:1_ins=3:sp=reverse_frequency:spb=goal:to=lpo:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.19/0.51 % (15617)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)
% 0.19/0.51 % (15625)Instruction limit reached!
% 0.19/0.51 % (15625)------------------------------
% 0.19/0.51 % (15625)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.51 % (15625)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.51 % (15625)Termination reason: Unknown
% 0.19/0.51 % (15625)Termination phase: Saturation
% 0.19/0.51
% 0.19/0.51 % (15625)Memory used [KB]: 5884
% 0.19/0.51 % (15625)Time elapsed: 0.065 s
% 0.19/0.51 % (15625)Instructions burned: 3 (million)
% 0.19/0.51 % (15625)------------------------------
% 0.19/0.51 % (15625)------------------------------
% 0.19/0.51 % (15635)dis+21_1:1_ep=RS:nwc=10.0:s2a=on:s2at=1.5:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.19/0.52 % (15617)First to succeed.
% 0.19/0.52 % (15617)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 % (15617)------------------------------
% 0.19/0.52 % (15617)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.52 % (15617)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.52 % (15617)Termination reason: Refutation
% 0.19/0.52
% 0.19/0.52 % (15617)Memory used [KB]: 6012
% 0.19/0.52 % (15617)Time elapsed: 0.075 s
% 0.19/0.52 % (15617)Instructions burned: 7 (million)
% 0.19/0.52 % (15617)------------------------------
% 0.19/0.52 % (15617)------------------------------
% 0.19/0.52 % (15610)Success in time 0.168 s
%------------------------------------------------------------------------------