TSTP Solution File: SET914+1 by SnakeForV-SAT---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---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_sat --cores 0 -t %d %s
% Computer : n015.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 18:26:05 EDT 2022
% Result : Theorem 0.20s 0.52s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 48 ( 11 unt; 0 def)
% Number of atoms : 224 ( 85 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 275 ( 99 ~; 99 |; 62 &)
% ( 11 <=>; 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 : 127 ( 107 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f152,plain,
$false,
inference(subsumption_resolution,[],[f149,f73]) ).
fof(f73,plain,
in(sK7,sK6),
inference(cnf_transformation,[],[f48]) ).
fof(f48,plain,
( disjoint(unordered_pair(sK7,sK5),sK6)
& in(sK7,sK6) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f46,f47]) ).
fof(f47,plain,
( ? [X0,X1,X2] :
( disjoint(unordered_pair(X2,X0),X1)
& in(X2,X1) )
=> ( disjoint(unordered_pair(sK7,sK5),sK6)
& in(sK7,sK6) ) ),
introduced(choice_axiom,[]) ).
fof(f46,plain,
? [X0,X1,X2] :
( disjoint(unordered_pair(X2,X0),X1)
& in(X2,X1) ),
inference(rectify,[],[f23]) ).
fof(f23,plain,
? [X0,X2,X1] :
( disjoint(unordered_pair(X1,X0),X2)
& in(X1,X2) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,plain,
~ ! [X2,X1,X0] :
~ ( disjoint(unordered_pair(X1,X0),X2)
& in(X1,X2) ),
inference(rectify,[],[f14]) ).
fof(f14,negated_conjecture,
~ ! [X1,X0,X2] :
~ ( disjoint(unordered_pair(X0,X1),X2)
& in(X0,X2) ),
inference(negated_conjecture,[],[f13]) ).
fof(f13,conjecture,
! [X1,X0,X2] :
~ ( disjoint(unordered_pair(X0,X1),X2)
& in(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_zfmisc_1) ).
fof(f149,plain,
~ in(sK7,sK6),
inference(resolution,[],[f148,f83]) ).
fof(f83,plain,
! [X3,X0] : in(X3,unordered_pair(X0,X3)),
inference(equality_resolution,[],[f82]) ).
fof(f82,plain,
! [X2,X3,X0] :
( in(X3,X2)
| unordered_pair(X0,X3) != X2 ),
inference(equality_resolution,[],[f66]) ).
fof(f66,plain,
! [X2,X3,X0,X1] :
( in(X3,X2)
| X1 != X3
| unordered_pair(X0,X1) != X2 ),
inference(cnf_transformation,[],[f42]) ).
fof(f42,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ( X1 = X3
| X0 = X3
| ~ in(X3,X2) )
& ( in(X3,X2)
| ( X1 != X3
& X0 != X3 ) ) )
| unordered_pair(X0,X1) != X2 )
& ( unordered_pair(X0,X1) = X2
| ( ( ~ in(sK3(X0,X1,X2),X2)
| ( sK3(X0,X1,X2) != X1
& sK3(X0,X1,X2) != X0 ) )
& ( in(sK3(X0,X1,X2),X2)
| sK3(X0,X1,X2) = X1
| sK3(X0,X1,X2) = X0 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f40,f41]) ).
fof(f41,plain,
! [X0,X1,X2] :
( ? [X4] :
( ( ~ in(X4,X2)
| ( X1 != X4
& X0 != X4 ) )
& ( in(X4,X2)
| X1 = X4
| X0 = X4 ) )
=> ( ( ~ in(sK3(X0,X1,X2),X2)
| ( sK3(X0,X1,X2) != X1
& sK3(X0,X1,X2) != X0 ) )
& ( in(sK3(X0,X1,X2),X2)
| sK3(X0,X1,X2) = X1
| sK3(X0,X1,X2) = X0 ) ) ),
introduced(choice_axiom,[]) ).
fof(f40,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ( X1 = X3
| X0 = X3
| ~ in(X3,X2) )
& ( in(X3,X2)
| ( X1 != X3
& X0 != X3 ) ) )
| unordered_pair(X0,X1) != X2 )
& ( unordered_pair(X0,X1) = X2
| ? [X4] :
( ( ~ in(X4,X2)
| ( X1 != X4
& X0 != X4 ) )
& ( in(X4,X2)
| X1 = X4
| X0 = X4 ) ) ) ),
inference(rectify,[],[f39]) ).
fof(f39,plain,
! [X1,X0,X2] :
( ( ! [X3] :
( ( X0 = X3
| X1 = X3
| ~ in(X3,X2) )
& ( in(X3,X2)
| ( X0 != X3
& X1 != X3 ) ) )
| unordered_pair(X1,X0) != X2 )
& ( unordered_pair(X1,X0) = X2
| ? [X3] :
( ( ~ in(X3,X2)
| ( X0 != X3
& X1 != X3 ) )
& ( in(X3,X2)
| X0 = X3
| X1 = X3 ) ) ) ),
inference(flattening,[],[f38]) ).
fof(f38,plain,
! [X1,X0,X2] :
( ( ! [X3] :
( ( X0 = X3
| X1 = X3
| ~ in(X3,X2) )
& ( in(X3,X2)
| ( X0 != X3
& X1 != X3 ) ) )
| unordered_pair(X1,X0) != X2 )
& ( unordered_pair(X1,X0) = X2
| ? [X3] :
( ( ~ in(X3,X2)
| ( X0 != X3
& X1 != X3 ) )
& ( in(X3,X2)
| X0 = X3
| X1 = X3 ) ) ) ),
inference(nnf_transformation,[],[f20]) ).
fof(f20,plain,
! [X1,X0,X2] :
( ! [X3] :
( ( X0 = X3
| X1 = X3 )
<=> in(X3,X2) )
<=> unordered_pair(X1,X0) = X2 ),
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X1,X0,X2] :
( ! [X3] :
( ( X1 = X3
| X0 = X3 )
<=> in(X3,X2) )
<=> unordered_pair(X0,X1) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).
fof(f148,plain,
! [X8] :
( ~ in(X8,unordered_pair(sK5,sK7))
| ~ in(X8,sK6) ),
inference(subsumption_resolution,[],[f145,f77]) ).
fof(f77,plain,
! [X1] : ~ in(X1,empty_set),
inference(equality_resolution,[],[f53]) ).
fof(f53,plain,
! [X0,X1] :
( ~ in(X1,X0)
| empty_set != X0 ),
inference(cnf_transformation,[],[f31]) ).
fof(f31,plain,
! [X0] :
( ( ! [X1] : ~ in(X1,X0)
| empty_set != X0 )
& ( empty_set = X0
| in(sK1(X0),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f29,f30]) ).
fof(f30,plain,
! [X0] :
( ? [X2] : in(X2,X0)
=> in(sK1(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f29,plain,
! [X0] :
( ( ! [X1] : ~ in(X1,X0)
| empty_set != X0 )
& ( empty_set = X0
| ? [X2] : in(X2,X0) ) ),
inference(rectify,[],[f28]) ).
fof(f28,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(f145,plain,
! [X8] :
( ~ in(X8,unordered_pair(sK5,sK7))
| ~ in(X8,sK6)
| in(X8,empty_set) ),
inference(superposition,[],[f78,f102]) ).
fof(f102,plain,
empty_set = set_intersection2(unordered_pair(sK5,sK7),sK6),
inference(resolution,[],[f70,f86]) ).
fof(f86,plain,
disjoint(unordered_pair(sK5,sK7),sK6),
inference(backward_demodulation,[],[f74,f68]) ).
fof(f68,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f16]) ).
fof(f16,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(rectify,[],[f2]) ).
fof(f2,axiom,
! [X1,X0] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f74,plain,
disjoint(unordered_pair(sK7,sK5),sK6),
inference(cnf_transformation,[],[f48]) ).
fof(f70,plain,
! [X0,X1] :
( ~ disjoint(X1,X0)
| set_intersection2(X1,X0) = empty_set ),
inference(cnf_transformation,[],[f45]) ).
fof(f45,plain,
! [X0,X1] :
( ( disjoint(X1,X0)
| set_intersection2(X1,X0) != empty_set )
& ( set_intersection2(X1,X0) = empty_set
| ~ disjoint(X1,X0) ) ),
inference(nnf_transformation,[],[f22]) ).
fof(f22,plain,
! [X0,X1] :
( disjoint(X1,X0)
<=> set_intersection2(X1,X0) = empty_set ),
inference(rectify,[],[f7]) ).
fof(f7,axiom,
! [X1,X0] :
( set_intersection2(X0,X1) = empty_set
<=> disjoint(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_xboole_0) ).
fof(f78,plain,
! [X2,X1,X4] :
( in(X4,set_intersection2(X1,X2))
| ~ in(X4,X2)
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f58]) ).
fof(f58,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| ~ in(X4,X2)
| ~ in(X4,X1)
| set_intersection2(X1,X2) != X0 ),
inference(cnf_transformation,[],[f37]) ).
fof(f37,plain,
! [X0,X1,X2] :
( ( 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) ) ) )
& ( ! [X4] :
( ( in(X4,X0)
| ~ in(X4,X2)
| ~ in(X4,X1) )
& ( ( in(X4,X2)
& in(X4,X1) )
| ~ in(X4,X0) ) )
| set_intersection2(X1,X2) != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f35,f36]) ).
fof(f36,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0) )
& ( ( in(X3,X2)
& in(X3,X1) )
| in(X3,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(f35,plain,
! [X0,X1,X2] :
( ( set_intersection2(X1,X2) = X0
| ? [X3] :
( ( ~ in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0) )
& ( ( in(X3,X2)
& in(X3,X1) )
| in(X3,X0) ) ) )
& ( ! [X4] :
( ( in(X4,X0)
| ~ in(X4,X2)
| ~ in(X4,X1) )
& ( ( in(X4,X2)
& in(X4,X1) )
| ~ in(X4,X0) ) )
| set_intersection2(X1,X2) != X0 ) ),
inference(rectify,[],[f34]) ).
fof(f34,plain,
! [X1,X2,X0] :
( ( set_intersection2(X2,X0) = X1
| ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X2)
| ~ in(X3,X1) )
& ( ( in(X3,X0)
& in(X3,X2) )
| in(X3,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X2) )
| ~ in(X3,X1) ) )
| set_intersection2(X2,X0) != X1 ) ),
inference(flattening,[],[f33]) ).
fof(f33,plain,
! [X1,X2,X0] :
( ( set_intersection2(X2,X0) = X1
| ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X2)
| ~ in(X3,X1) )
& ( ( in(X3,X0)
& in(X3,X2) )
| in(X3,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X2) )
| ~ in(X3,X1) ) )
| set_intersection2(X2,X0) != X1 ) ),
inference(nnf_transformation,[],[f15]) ).
fof(f15,plain,
! [X1,X2,X0] :
( set_intersection2(X2,X0) = X1
<=> ! [X3] :
( in(X3,X1)
<=> ( in(X3,X0)
& in(X3,X2) ) ) ),
inference(rectify,[],[f6]) ).
fof(f6,axiom,
! [X1,X2,X0] :
( set_intersection2(X0,X1) = X2
<=> ! [X3] :
( ( in(X3,X0)
& in(X3,X1) )
<=> in(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SET914+1 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.14 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.35 % Computer : n015.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 30 15:10:51 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.50 % (11764)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.20/0.50 % (11772)ott+10_1:8_bsd=on:fsd=on:lcm=predicate:nwc=5.0:s2a=on:s2at=1.5:spb=goal_then_units:i=176:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/176Mi)
% 0.20/0.51 % (11772)First to succeed.
% 0.20/0.52 % (11772)Refutation found. Thanks to Tanya!
% 0.20/0.52 % SZS status Theorem for theBenchmark
% 0.20/0.52 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.52 % (11772)------------------------------
% 0.20/0.52 % (11772)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.52 % (11772)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.52 % (11772)Termination reason: Refutation
% 0.20/0.52
% 0.20/0.52 % (11772)Memory used [KB]: 5500
% 0.20/0.52 % (11772)Time elapsed: 0.086 s
% 0.20/0.52 % (11772)Instructions burned: 5 (million)
% 0.20/0.52 % (11772)------------------------------
% 0.20/0.52 % (11772)------------------------------
% 0.20/0.52 % (11751)Success in time 0.159 s
%------------------------------------------------------------------------------