TSTP Solution File: SET914+1 by SnakeForV---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SET914+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 : n005.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 18:22:44 EDT 2022
% Result : Theorem 0.19s 0.47s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 43 ( 7 unt; 0 def)
% Number of atoms : 218 ( 81 equ)
% Maximal formula atoms : 14 ( 5 avg)
% Number of connectives : 274 ( 99 ~; 99 |; 62 &)
% ( 10 <=>; 4 =>; 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 : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 119 ( 99 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f106,plain,
$false,
inference(subsumption_resolution,[],[f89,f56]) ).
fof(f56,plain,
in(sK2,sK4),
inference(cnf_transformation,[],[f35]) ).
fof(f35,plain,
( in(sK2,sK4)
& disjoint(unordered_pair(sK2,sK3),sK4) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f33,f34]) ).
fof(f34,plain,
( ? [X0,X1,X2] :
( in(X0,X2)
& disjoint(unordered_pair(X0,X1),X2) )
=> ( in(sK2,sK4)
& disjoint(unordered_pair(sK2,sK3),sK4) ) ),
introduced(choice_axiom,[]) ).
fof(f33,plain,
? [X0,X1,X2] :
( in(X0,X2)
& disjoint(unordered_pair(X0,X1),X2) ),
inference(rectify,[],[f22]) ).
fof(f22,plain,
? [X0,X2,X1] :
( in(X0,X1)
& disjoint(unordered_pair(X0,X2),X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,plain,
~ ! [X2,X0,X1] :
~ ( in(X0,X1)
& disjoint(unordered_pair(X0,X2),X1) ),
inference(rectify,[],[f14]) ).
fof(f14,negated_conjecture,
~ ! [X0,X2,X1] :
~ ( in(X0,X2)
& disjoint(unordered_pair(X0,X1),X2) ),
inference(negated_conjecture,[],[f13]) ).
fof(f13,conjecture,
! [X0,X2,X1] :
~ ( in(X0,X2)
& disjoint(unordered_pair(X0,X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_zfmisc_1) ).
fof(f89,plain,
~ in(sK2,sK4),
inference(resolution,[],[f83,f67]) ).
fof(f67,plain,
! [X3,X1] : in(X3,unordered_pair(X3,X1)),
inference(equality_resolution,[],[f66]) ).
fof(f66,plain,
! [X3,X0,X1] :
( in(X3,X0)
| unordered_pair(X3,X1) != X0 ),
inference(equality_resolution,[],[f47]) ).
fof(f47,plain,
! [X2,X3,X0,X1] :
( in(X3,X0)
| X2 != X3
| unordered_pair(X2,X1) != X0 ),
inference(cnf_transformation,[],[f27]) ).
fof(f27,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ( in(X3,X0)
| ( X1 != X3
& X2 != X3 ) )
& ( X1 = X3
| X2 = X3
| ~ in(X3,X0) ) )
| unordered_pair(X2,X1) != X0 )
& ( unordered_pair(X2,X1) = X0
| ( ( ( sK0(X0,X1,X2) != X1
& sK0(X0,X1,X2) != X2 )
| ~ in(sK0(X0,X1,X2),X0) )
& ( sK0(X0,X1,X2) = X1
| sK0(X0,X1,X2) = X2
| in(sK0(X0,X1,X2),X0) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f25,f26]) ).
fof(f26,plain,
! [X0,X1,X2] :
( ? [X4] :
( ( ( X1 != X4
& X2 != X4 )
| ~ in(X4,X0) )
& ( X1 = X4
| X2 = X4
| in(X4,X0) ) )
=> ( ( ( sK0(X0,X1,X2) != X1
& sK0(X0,X1,X2) != X2 )
| ~ in(sK0(X0,X1,X2),X0) )
& ( sK0(X0,X1,X2) = X1
| sK0(X0,X1,X2) = X2
| in(sK0(X0,X1,X2),X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f25,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ( in(X3,X0)
| ( X1 != X3
& X2 != X3 ) )
& ( X1 = X3
| X2 = X3
| ~ in(X3,X0) ) )
| unordered_pair(X2,X1) != X0 )
& ( unordered_pair(X2,X1) = X0
| ? [X4] :
( ( ( X1 != X4
& X2 != X4 )
| ~ in(X4,X0) )
& ( X1 = X4
| X2 = X4
| in(X4,X0) ) ) ) ),
inference(rectify,[],[f24]) ).
fof(f24,plain,
! [X1,X2,X0] :
( ( ! [X3] :
( ( in(X3,X1)
| ( X2 != X3
& X0 != X3 ) )
& ( X2 = X3
| X0 = X3
| ~ in(X3,X1) ) )
| unordered_pair(X0,X2) != X1 )
& ( unordered_pair(X0,X2) = X1
| ? [X3] :
( ( ( X2 != X3
& X0 != X3 )
| ~ in(X3,X1) )
& ( X2 = X3
| X0 = X3
| in(X3,X1) ) ) ) ),
inference(flattening,[],[f23]) ).
fof(f23,plain,
! [X1,X2,X0] :
( ( ! [X3] :
( ( in(X3,X1)
| ( X2 != X3
& X0 != X3 ) )
& ( X2 = X3
| X0 = X3
| ~ in(X3,X1) ) )
| unordered_pair(X0,X2) != X1 )
& ( unordered_pair(X0,X2) = X1
| ? [X3] :
( ( ( X2 != X3
& X0 != X3 )
| ~ in(X3,X1) )
& ( X2 = X3
| X0 = X3
| in(X3,X1) ) ) ) ),
inference(nnf_transformation,[],[f16]) ).
fof(f16,plain,
! [X1,X2,X0] :
( ! [X3] :
( in(X3,X1)
<=> ( X2 = X3
| X0 = X3 ) )
<=> unordered_pair(X0,X2) = X1 ),
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X0,X2,X1] :
( ! [X3] :
( ( X1 = X3
| X0 = X3 )
<=> in(X3,X2) )
<=> unordered_pair(X0,X1) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).
fof(f83,plain,
! [X0] :
( ~ in(X0,unordered_pair(sK2,sK3))
| ~ in(X0,sK4) ),
inference(subsumption_resolution,[],[f78,f72]) ).
fof(f72,plain,
! [X1] : ~ in(X1,empty_set),
inference(equality_resolution,[],[f62]) ).
fof(f62,plain,
! [X0,X1] :
( ~ in(X1,X0)
| empty_set != X0 ),
inference(cnf_transformation,[],[f41]) ).
fof(f41,plain,
! [X0] :
( ( ! [X1] : ~ in(X1,X0)
| empty_set != X0 )
& ( empty_set = X0
| in(sK5(X0),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f39,f40]) ).
fof(f40,plain,
! [X0] :
( ? [X2] : in(X2,X0)
=> in(sK5(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f39,plain,
! [X0] :
( ( ! [X1] : ~ in(X1,X0)
| empty_set != X0 )
& ( empty_set = X0
| ? [X2] : in(X2,X0) ) ),
inference(rectify,[],[f38]) ).
fof(f38,plain,
! [X0] :
( ( ! [X1] : ~ in(X1,X0)
| empty_set != X0 )
& ( empty_set = X0
| ? [X1] : in(X1,X0) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] :
( ! [X1] : ~ in(X1,X0)
<=> empty_set = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f78,plain,
! [X0] :
( ~ in(X0,sK4)
| ~ in(X0,unordered_pair(sK2,sK3))
| in(X0,empty_set) ),
inference(superposition,[],[f71,f74]) ).
fof(f74,plain,
empty_set = set_intersection2(unordered_pair(sK2,sK3),sK4),
inference(resolution,[],[f55,f58]) ).
fof(f58,plain,
! [X0,X1] :
( ~ disjoint(X0,X1)
| set_intersection2(X0,X1) = empty_set ),
inference(cnf_transformation,[],[f37]) ).
fof(f37,plain,
! [X0,X1] :
( ( disjoint(X0,X1)
| set_intersection2(X0,X1) != empty_set )
& ( set_intersection2(X0,X1) = empty_set
| ~ disjoint(X0,X1) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0,X1] :
( disjoint(X0,X1)
<=> set_intersection2(X0,X1) = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_xboole_0) ).
fof(f55,plain,
disjoint(unordered_pair(sK2,sK3),sK4),
inference(cnf_transformation,[],[f35]) ).
fof(f71,plain,
! [X2,X1,X4] :
( in(X4,set_intersection2(X1,X2))
| ~ in(X4,X2)
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f49]) ).
fof(f49,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| ~ in(X4,X2)
| ~ in(X4,X1)
| set_intersection2(X1,X2) != X0 ),
inference(cnf_transformation,[],[f32]) ).
fof(f32,plain,
! [X0,X1,X2] :
( ( set_intersection2(X1,X2) = X0
| ( ( ~ in(sK1(X0,X1,X2),X0)
| ~ in(sK1(X0,X1,X2),X2)
| ~ in(sK1(X0,X1,X2),X1) )
& ( in(sK1(X0,X1,X2),X0)
| ( in(sK1(X0,X1,X2),X2)
& in(sK1(X0,X1,X2),X1) ) ) ) )
& ( ! [X4] :
( ( ( in(X4,X2)
& in(X4,X1) )
| ~ in(X4,X0) )
& ( in(X4,X0)
| ~ in(X4,X2)
| ~ in(X4,X1) ) )
| set_intersection2(X1,X2) != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f30,f31]) ).
fof(f31,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X2)
| ~ in(X3,X1) )
& ( in(X3,X0)
| ( in(X3,X2)
& in(X3,X1) ) ) )
=> ( ( ~ in(sK1(X0,X1,X2),X0)
| ~ in(sK1(X0,X1,X2),X2)
| ~ in(sK1(X0,X1,X2),X1) )
& ( in(sK1(X0,X1,X2),X0)
| ( in(sK1(X0,X1,X2),X2)
& in(sK1(X0,X1,X2),X1) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f30,plain,
! [X0,X1,X2] :
( ( set_intersection2(X1,X2) = X0
| ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X2)
| ~ in(X3,X1) )
& ( in(X3,X0)
| ( in(X3,X2)
& in(X3,X1) ) ) ) )
& ( ! [X4] :
( ( ( in(X4,X2)
& in(X4,X1) )
| ~ in(X4,X0) )
& ( in(X4,X0)
| ~ in(X4,X2)
| ~ in(X4,X1) ) )
| set_intersection2(X1,X2) != X0 ) ),
inference(rectify,[],[f29]) ).
fof(f29,plain,
! [X1,X2,X0] :
( ( set_intersection2(X2,X0) = X1
| ? [X3] :
( ( ~ in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( in(X3,X1)
| ( in(X3,X0)
& in(X3,X2) ) ) ) )
& ( ! [X3] :
( ( ( in(X3,X0)
& in(X3,X2) )
| ~ in(X3,X1) )
& ( in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) ) )
| set_intersection2(X2,X0) != X1 ) ),
inference(flattening,[],[f28]) ).
fof(f28,plain,
! [X1,X2,X0] :
( ( set_intersection2(X2,X0) = X1
| ? [X3] :
( ( ~ in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( in(X3,X1)
| ( in(X3,X0)
& in(X3,X2) ) ) ) )
& ( ! [X3] :
( ( ( in(X3,X0)
& in(X3,X2) )
| ~ in(X3,X1) )
& ( in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) ) )
| set_intersection2(X2,X0) != X1 ) ),
inference(nnf_transformation,[],[f17]) ).
fof(f17,plain,
! [X1,X2,X0] :
( set_intersection2(X2,X0) = X1
<=> ! [X3] :
( ( in(X3,X0)
& in(X3,X2) )
<=> in(X3,X1) ) ),
inference(rectify,[],[f6]) ).
fof(f6,axiom,
! [X1,X2,X0] :
( set_intersection2(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X0)
& in(X3,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET914+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % 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 : n005.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 16:08:18 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.44 % (12953)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)
% 0.19/0.47 % (12953)First to succeed.
% 0.19/0.47 % (12953)Refutation found. Thanks to Tanya!
% 0.19/0.47 % SZS status Theorem for theBenchmark
% 0.19/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.48 % (12953)------------------------------
% 0.19/0.48 % (12953)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.48 % (12953)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.48 % (12953)Termination reason: Refutation
% 0.19/0.48
% 0.19/0.48 % (12953)Memory used [KB]: 6012
% 0.19/0.48 % (12953)Time elapsed: 0.088 s
% 0.19/0.48 % (12953)Instructions burned: 3 (million)
% 0.19/0.48 % (12953)------------------------------
% 0.19/0.48 % (12953)------------------------------
% 0.19/0.48 % (12950)Success in time 0.128 s
%------------------------------------------------------------------------------