TSTP Solution File: SET945+1 by SnakeForV---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SET945+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 18:22:49 EDT 2022
% Result : Theorem 0.18s 0.47s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% Syntax : Number of formulae : 51 ( 3 unt; 0 def)
% Number of atoms : 243 ( 23 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 310 ( 118 ~; 110 |; 64 &)
% ( 8 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-3 aty)
% Number of variables : 159 ( 133 !; 26 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f354,plain,
$false,
inference(subsumption_resolution,[],[f353,f43]) ).
fof(f43,plain,
~ disjoint(union(sK0),sK1),
inference(cnf_transformation,[],[f24]) ).
fof(f24,plain,
( ~ disjoint(union(sK0),sK1)
& ! [X2] :
( ~ in(X2,sK0)
| disjoint(X2,sK1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f21,f23]) ).
fof(f23,plain,
( ? [X0,X1] :
( ~ disjoint(union(X0),X1)
& ! [X2] :
( ~ in(X2,X0)
| disjoint(X2,X1) ) )
=> ( ~ disjoint(union(sK0),sK1)
& ! [X2] :
( ~ in(X2,sK0)
| disjoint(X2,sK1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f21,plain,
? [X0,X1] :
( ~ disjoint(union(X0),X1)
& ! [X2] :
( ~ in(X2,X0)
| disjoint(X2,X1) ) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,negated_conjecture,
~ ! [X1,X0] :
( ! [X2] :
( in(X2,X0)
=> disjoint(X2,X1) )
=> disjoint(union(X0),X1) ),
inference(negated_conjecture,[],[f10]) ).
fof(f10,conjecture,
! [X1,X0] :
( ! [X2] :
( in(X2,X0)
=> disjoint(X2,X1) )
=> disjoint(union(X0),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t98_zfmisc_1) ).
fof(f353,plain,
disjoint(union(sK0),sK1),
inference(duplicate_literal_removal,[],[f352]) ).
fof(f352,plain,
( disjoint(union(sK0),sK1)
| disjoint(union(sK0),sK1) ),
inference(resolution,[],[f347,f106]) ).
fof(f106,plain,
! [X4,X5] :
( in(sK6(X4,X5),X5)
| disjoint(X4,X5) ),
inference(resolution,[],[f60,f63]) ).
fof(f63,plain,
! [X2,X3,X1] :
( ~ in(X3,set_intersection2(X1,X2))
| in(X3,X2) ),
inference(equality_resolution,[],[f49]) ).
fof(f49,plain,
! [X2,X3,X0,X1] :
( in(X3,X2)
| ~ in(X3,X0)
| set_intersection2(X1,X2) != X0 ),
inference(cnf_transformation,[],[f30]) ).
fof(f30,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ( in(X3,X0)
| ~ in(X3,X2)
| ~ in(X3,X1) )
& ( ( in(X3,X2)
& in(X3,X1) )
| ~ in(X3,X0) ) )
| set_intersection2(X1,X2) != X0 )
& ( set_intersection2(X1,X2) = X0
| ( ( ~ in(sK2(X0,X1,X2),X2)
| ~ in(sK2(X0,X1,X2),X1)
| ~ in(sK2(X0,X1,X2),X0) )
& ( ( in(sK2(X0,X1,X2),X2)
& in(sK2(X0,X1,X2),X1) )
| in(sK2(X0,X1,X2),X0) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f28,f29]) ).
fof(f29,plain,
! [X0,X1,X2] :
( ? [X4] :
( ( ~ in(X4,X2)
| ~ in(X4,X1)
| ~ in(X4,X0) )
& ( ( in(X4,X2)
& in(X4,X1) )
| in(X4,X0) ) )
=> ( ( ~ in(sK2(X0,X1,X2),X2)
| ~ in(sK2(X0,X1,X2),X1)
| ~ in(sK2(X0,X1,X2),X0) )
& ( ( in(sK2(X0,X1,X2),X2)
& in(sK2(X0,X1,X2),X1) )
| in(sK2(X0,X1,X2),X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f28,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ( in(X3,X0)
| ~ in(X3,X2)
| ~ in(X3,X1) )
& ( ( in(X3,X2)
& in(X3,X1) )
| ~ in(X3,X0) ) )
| set_intersection2(X1,X2) != X0 )
& ( set_intersection2(X1,X2) = X0
| ? [X4] :
( ( ~ in(X4,X2)
| ~ in(X4,X1)
| ~ in(X4,X0) )
& ( ( in(X4,X2)
& in(X4,X1) )
| in(X4,X0) ) ) ) ),
inference(rectify,[],[f27]) ).
fof(f27,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ( in(X3,X0)
| ~ in(X3,X2)
| ~ in(X3,X1) )
& ( ( in(X3,X2)
& in(X3,X1) )
| ~ in(X3,X0) ) )
| set_intersection2(X1,X2) != X0 )
& ( set_intersection2(X1,X2) = X0
| ? [X3] :
( ( ~ in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0) )
& ( ( in(X3,X2)
& in(X3,X1) )
| in(X3,X0) ) ) ) ),
inference(flattening,[],[f26]) ).
fof(f26,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ( in(X3,X0)
| ~ in(X3,X2)
| ~ in(X3,X1) )
& ( ( in(X3,X2)
& in(X3,X1) )
| ~ in(X3,X0) ) )
| set_intersection2(X1,X2) != X0 )
& ( set_intersection2(X1,X2) = X0
| ? [X3] :
( ( ~ in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0) )
& ( ( in(X3,X2)
& in(X3,X1) )
| in(X3,X0) ) ) ) ),
inference(nnf_transformation,[],[f16]) ).
fof(f16,plain,
! [X0,X1,X2] :
( ! [X3] :
( in(X3,X0)
<=> ( in(X3,X2)
& in(X3,X1) ) )
<=> set_intersection2(X1,X2) = X0 ),
inference(rectify,[],[f3]) ).
fof(f3,axiom,
! [X2,X0,X1] :
( ! [X3] :
( in(X3,X2)
<=> ( in(X3,X0)
& in(X3,X1) ) )
<=> set_intersection2(X0,X1) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f60,plain,
! [X0,X1] :
( in(sK6(X0,X1),set_intersection2(X0,X1))
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f40]) ).
fof(f40,plain,
! [X0,X1] :
( ( disjoint(X0,X1)
| in(sK6(X0,X1),set_intersection2(X0,X1)) )
& ( ! [X3] : ~ in(X3,set_intersection2(X0,X1))
| ~ disjoint(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f38,f39]) ).
fof(f39,plain,
! [X0,X1] :
( ? [X2] : in(X2,set_intersection2(X0,X1))
=> in(sK6(X0,X1),set_intersection2(X0,X1)) ),
introduced(choice_axiom,[]) ).
fof(f38,plain,
! [X0,X1] :
( ( disjoint(X0,X1)
| ? [X2] : in(X2,set_intersection2(X0,X1)) )
& ( ! [X3] : ~ in(X3,set_intersection2(X0,X1))
| ~ disjoint(X0,X1) ) ),
inference(rectify,[],[f19]) ).
fof(f19,plain,
! [X0,X1] :
( ( disjoint(X0,X1)
| ? [X3] : in(X3,set_intersection2(X0,X1)) )
& ( ! [X2] : ~ in(X2,set_intersection2(X0,X1))
| ~ disjoint(X0,X1) ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,plain,
! [X1,X0] :
( ~ ( ~ disjoint(X0,X1)
& ! [X3] : ~ in(X3,set_intersection2(X0,X1)) )
& ~ ( disjoint(X0,X1)
& ? [X2] : in(X2,set_intersection2(X0,X1)) ) ),
inference(rectify,[],[f9]) ).
fof(f9,axiom,
! [X0,X1] :
( ~ ( disjoint(X0,X1)
& ? [X2] : in(X2,set_intersection2(X0,X1)) )
& ~ ( ! [X2] : ~ in(X2,set_intersection2(X0,X1))
& ~ disjoint(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_xboole_0) ).
fof(f347,plain,
! [X3] :
( ~ in(sK6(union(sK0),X3),sK1)
| disjoint(union(sK0),X3) ),
inference(resolution,[],[f344,f105]) ).
fof(f105,plain,
! [X2,X3] :
( in(sK6(X2,X3),X2)
| disjoint(X2,X3) ),
inference(resolution,[],[f60,f64]) ).
fof(f64,plain,
! [X2,X3,X1] :
( ~ in(X3,set_intersection2(X1,X2))
| in(X3,X1) ),
inference(equality_resolution,[],[f48]) ).
fof(f48,plain,
! [X2,X3,X0,X1] :
( in(X3,X1)
| ~ in(X3,X0)
| set_intersection2(X1,X2) != X0 ),
inference(cnf_transformation,[],[f30]) ).
fof(f344,plain,
! [X2] :
( ~ in(X2,union(sK0))
| ~ in(X2,sK1) ),
inference(duplicate_literal_removal,[],[f341]) ).
fof(f341,plain,
! [X2] :
( ~ in(X2,union(sK0))
| ~ in(X2,sK1)
| ~ in(X2,union(sK0)) ),
inference(resolution,[],[f331,f66]) ).
fof(f66,plain,
! [X2,X1] :
( in(X2,sK3(X1,X2))
| ~ in(X2,union(X1)) ),
inference(equality_resolution,[],[f57]) ).
fof(f57,plain,
! [X2,X0,X1] :
( in(X2,sK3(X1,X2))
| ~ in(X2,X0)
| union(X1) != X0 ),
inference(cnf_transformation,[],[f37]) ).
fof(f37,plain,
! [X0,X1] :
( ( ! [X2] :
( ( ( in(sK3(X1,X2),X1)
& in(X2,sK3(X1,X2)) )
| ~ in(X2,X0) )
& ( in(X2,X0)
| ! [X4] :
( ~ in(X4,X1)
| ~ in(X2,X4) ) ) )
| union(X1) != X0 )
& ( union(X1) = X0
| ( ( ~ in(sK4(X0,X1),X0)
| ! [X6] :
( ~ in(X6,X1)
| ~ in(sK4(X0,X1),X6) ) )
& ( in(sK4(X0,X1),X0)
| ( in(sK5(X0,X1),X1)
& in(sK4(X0,X1),sK5(X0,X1)) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f33,f36,f35,f34]) ).
fof(f34,plain,
! [X1,X2] :
( ? [X3] :
( in(X3,X1)
& in(X2,X3) )
=> ( in(sK3(X1,X2),X1)
& in(X2,sK3(X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f35,plain,
! [X0,X1] :
( ? [X5] :
( ( ~ in(X5,X0)
| ! [X6] :
( ~ in(X6,X1)
| ~ in(X5,X6) ) )
& ( in(X5,X0)
| ? [X7] :
( in(X7,X1)
& in(X5,X7) ) ) )
=> ( ( ~ in(sK4(X0,X1),X0)
| ! [X6] :
( ~ in(X6,X1)
| ~ in(sK4(X0,X1),X6) ) )
& ( in(sK4(X0,X1),X0)
| ? [X7] :
( in(X7,X1)
& in(sK4(X0,X1),X7) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f36,plain,
! [X0,X1] :
( ? [X7] :
( in(X7,X1)
& in(sK4(X0,X1),X7) )
=> ( in(sK5(X0,X1),X1)
& in(sK4(X0,X1),sK5(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f33,plain,
! [X0,X1] :
( ( ! [X2] :
( ( ? [X3] :
( in(X3,X1)
& in(X2,X3) )
| ~ in(X2,X0) )
& ( in(X2,X0)
| ! [X4] :
( ~ in(X4,X1)
| ~ in(X2,X4) ) ) )
| union(X1) != X0 )
& ( union(X1) = X0
| ? [X5] :
( ( ~ in(X5,X0)
| ! [X6] :
( ~ in(X6,X1)
| ~ in(X5,X6) ) )
& ( in(X5,X0)
| ? [X7] :
( in(X7,X1)
& in(X5,X7) ) ) ) ) ),
inference(rectify,[],[f32]) ).
fof(f32,plain,
! [X0,X1] :
( ( ! [X2] :
( ( ? [X3] :
( in(X3,X1)
& in(X2,X3) )
| ~ in(X2,X0) )
& ( in(X2,X0)
| ! [X3] :
( ~ in(X3,X1)
| ~ in(X2,X3) ) ) )
| union(X1) != X0 )
& ( union(X1) = X0
| ? [X2] :
( ( ~ in(X2,X0)
| ! [X3] :
( ~ in(X3,X1)
| ~ in(X2,X3) ) )
& ( in(X2,X0)
| ? [X3] :
( in(X3,X1)
& in(X2,X3) ) ) ) ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f12,plain,
! [X0,X1] :
( ! [X2] :
( ? [X3] :
( in(X3,X1)
& in(X2,X3) )
<=> in(X2,X0) )
<=> union(X1) = X0 ),
inference(rectify,[],[f4]) ).
fof(f4,axiom,
! [X1,X0] :
( union(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X3,X0)
& in(X2,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_tarski) ).
fof(f331,plain,
! [X78,X79] :
( ~ in(X78,sK3(sK0,X79))
| ~ in(X79,union(sK0))
| ~ in(X78,sK1) ),
inference(resolution,[],[f300,f80]) ).
fof(f80,plain,
! [X0] :
( disjoint(sK3(sK0,X0),sK1)
| ~ in(X0,union(sK0)) ),
inference(resolution,[],[f65,f42]) ).
fof(f42,plain,
! [X2] :
( ~ in(X2,sK0)
| disjoint(X2,sK1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f65,plain,
! [X2,X1] :
( in(sK3(X1,X2),X1)
| ~ in(X2,union(X1)) ),
inference(equality_resolution,[],[f58]) ).
fof(f58,plain,
! [X2,X0,X1] :
( in(sK3(X1,X2),X1)
| ~ in(X2,X0)
| union(X1) != X0 ),
inference(cnf_transformation,[],[f37]) ).
fof(f300,plain,
! [X10,X11,X9] :
( ~ disjoint(X11,X10)
| ~ in(X9,X10)
| ~ in(X9,X11) ),
inference(resolution,[],[f62,f59]) ).
fof(f59,plain,
! [X3,X0,X1] :
( ~ in(X3,set_intersection2(X0,X1))
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f40]) ).
fof(f62,plain,
! [X2,X3,X1] :
( in(X3,set_intersection2(X1,X2))
| ~ in(X3,X2)
| ~ in(X3,X1) ),
inference(equality_resolution,[],[f50]) ).
fof(f50,plain,
! [X2,X3,X0,X1] :
( in(X3,X0)
| ~ in(X3,X2)
| ~ in(X3,X1)
| set_intersection2(X1,X2) != X0 ),
inference(cnf_transformation,[],[f30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SET945+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.12 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Aug 30 14:35:25 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.43 % (23445)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)
% 0.18/0.45 % (23451)lrs+10_1:4_av=off:bs=unit_only:bsr=unit_only:ep=RS:s2a=on:sos=on:sp=frequency:to=lpo:i=16:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.18/0.46 % (23445)First to succeed.
% 0.18/0.46 % (23459)dis+1010_1:1_bs=on:ep=RS:erd=off:newcnf=on:nwc=10.0:s2a=on:sgt=32:ss=axioms:i=30:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/30Mi)
% 0.18/0.47 % (23445)Refutation found. Thanks to Tanya!
% 0.18/0.47 % SZS status Theorem for theBenchmark
% 0.18/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.47 % (23445)------------------------------
% 0.18/0.47 % (23445)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.47 % (23445)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.47 % (23445)Termination reason: Refutation
% 0.18/0.47
% 0.18/0.47 % (23445)Memory used [KB]: 6012
% 0.18/0.47 % (23445)Time elapsed: 0.093 s
% 0.18/0.47 % (23445)Instructions burned: 15 (million)
% 0.18/0.47 % (23445)------------------------------
% 0.18/0.47 % (23445)------------------------------
% 0.18/0.47 % (23438)Success in time 0.134 s
%------------------------------------------------------------------------------