TSTP Solution File: SET979+1 by SnakeForV---1.0
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%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SET979+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 : 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 18:22:56 EDT 2022
% Result : Theorem 0.20s 0.56s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 20 ( 8 unt; 0 def)
% Number of atoms : 34 ( 33 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 31 ( 17 ~; 7 |; 6 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 41 ( 32 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f35,plain,
$false,
inference(subsumption_resolution,[],[f34,f30]) ).
fof(f30,plain,
! [X2,X0,X1] : set_union2(cartesian_product2(X1,X0),cartesian_product2(X2,X0)) = cartesian_product2(set_union2(X1,X2),X0),
inference(cnf_transformation,[],[f24]) ).
fof(f24,plain,
! [X0,X1,X2] :
( cartesian_product2(X0,set_union2(X1,X2)) = set_union2(cartesian_product2(X0,X1),cartesian_product2(X0,X2))
& set_union2(cartesian_product2(X1,X0),cartesian_product2(X2,X0)) = cartesian_product2(set_union2(X1,X2),X0) ),
inference(rectify,[],[f15]) ).
fof(f15,plain,
! [X1,X2,X0] :
( cartesian_product2(X1,set_union2(X2,X0)) = set_union2(cartesian_product2(X1,X2),cartesian_product2(X1,X0))
& set_union2(cartesian_product2(X2,X1),cartesian_product2(X0,X1)) = cartesian_product2(set_union2(X2,X0),X1) ),
inference(rectify,[],[f8]) ).
fof(f8,axiom,
! [X1,X2,X0] :
( cartesian_product2(set_union2(X0,X1),X2) = set_union2(cartesian_product2(X0,X2),cartesian_product2(X1,X2))
& cartesian_product2(X2,set_union2(X0,X1)) = set_union2(cartesian_product2(X2,X0),cartesian_product2(X2,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t120_zfmisc_1) ).
fof(f34,plain,
cartesian_product2(set_union2(singleton(sK2),singleton(sK1)),sK0) != set_union2(cartesian_product2(singleton(sK2),sK0),cartesian_product2(singleton(sK1),sK0)),
inference(subsumption_resolution,[],[f32,f31]) ).
fof(f31,plain,
! [X2,X0,X1] : cartesian_product2(X0,set_union2(X1,X2)) = set_union2(cartesian_product2(X0,X1),cartesian_product2(X0,X2)),
inference(cnf_transformation,[],[f24]) ).
fof(f32,plain,
( set_union2(cartesian_product2(sK0,singleton(sK2)),cartesian_product2(sK0,singleton(sK1))) != cartesian_product2(sK0,set_union2(singleton(sK2),singleton(sK1)))
| cartesian_product2(set_union2(singleton(sK2),singleton(sK1)),sK0) != set_union2(cartesian_product2(singleton(sK2),sK0),cartesian_product2(singleton(sK1),sK0)) ),
inference(definition_unfolding,[],[f27,f26,f26]) ).
fof(f26,plain,
! [X0,X1] : unordered_pair(X0,X1) = set_union2(singleton(X0),singleton(X1)),
inference(cnf_transformation,[],[f19]) ).
fof(f19,plain,
! [X0,X1] : unordered_pair(X0,X1) = set_union2(singleton(X0),singleton(X1)),
inference(rectify,[],[f14]) ).
fof(f14,plain,
! [X1,X0] : unordered_pair(X1,X0) = set_union2(singleton(X1),singleton(X0)),
inference(rectify,[],[f11]) ).
fof(f11,axiom,
! [X1,X0] : unordered_pair(X0,X1) = set_union2(singleton(X0),singleton(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_enumset1) ).
fof(f27,plain,
( cartesian_product2(unordered_pair(sK2,sK1),sK0) != set_union2(cartesian_product2(singleton(sK2),sK0),cartesian_product2(singleton(sK1),sK0))
| set_union2(cartesian_product2(sK0,singleton(sK2)),cartesian_product2(sK0,singleton(sK1))) != cartesian_product2(sK0,unordered_pair(sK2,sK1)) ),
inference(cnf_transformation,[],[f22]) ).
fof(f22,plain,
( cartesian_product2(unordered_pair(sK2,sK1),sK0) != set_union2(cartesian_product2(singleton(sK2),sK0),cartesian_product2(singleton(sK1),sK0))
| set_union2(cartesian_product2(sK0,singleton(sK2)),cartesian_product2(sK0,singleton(sK1))) != cartesian_product2(sK0,unordered_pair(sK2,sK1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f20,f21]) ).
fof(f21,plain,
( ? [X0,X1,X2] :
( cartesian_product2(unordered_pair(X2,X1),X0) != set_union2(cartesian_product2(singleton(X2),X0),cartesian_product2(singleton(X1),X0))
| cartesian_product2(X0,unordered_pair(X2,X1)) != set_union2(cartesian_product2(X0,singleton(X2)),cartesian_product2(X0,singleton(X1))) )
=> ( cartesian_product2(unordered_pair(sK2,sK1),sK0) != set_union2(cartesian_product2(singleton(sK2),sK0),cartesian_product2(singleton(sK1),sK0))
| set_union2(cartesian_product2(sK0,singleton(sK2)),cartesian_product2(sK0,singleton(sK1))) != cartesian_product2(sK0,unordered_pair(sK2,sK1)) ) ),
introduced(choice_axiom,[]) ).
fof(f20,plain,
? [X0,X1,X2] :
( cartesian_product2(unordered_pair(X2,X1),X0) != set_union2(cartesian_product2(singleton(X2),X0),cartesian_product2(singleton(X1),X0))
| cartesian_product2(X0,unordered_pair(X2,X1)) != set_union2(cartesian_product2(X0,singleton(X2)),cartesian_product2(X0,singleton(X1))) ),
inference(rectify,[],[f17]) ).
fof(f17,plain,
? [X1,X2,X0] :
( set_union2(cartesian_product2(singleton(X0),X1),cartesian_product2(singleton(X2),X1)) != cartesian_product2(unordered_pair(X0,X2),X1)
| set_union2(cartesian_product2(X1,singleton(X0)),cartesian_product2(X1,singleton(X2))) != cartesian_product2(X1,unordered_pair(X0,X2)) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,plain,
~ ! [X1,X2,X0] :
( set_union2(cartesian_product2(singleton(X0),X1),cartesian_product2(singleton(X2),X1)) = cartesian_product2(unordered_pair(X0,X2),X1)
& set_union2(cartesian_product2(X1,singleton(X0)),cartesian_product2(X1,singleton(X2))) = cartesian_product2(X1,unordered_pair(X0,X2)) ),
inference(rectify,[],[f10]) ).
fof(f10,negated_conjecture,
~ ! [X0,X2,X1] :
( cartesian_product2(X2,unordered_pair(X0,X1)) = set_union2(cartesian_product2(X2,singleton(X0)),cartesian_product2(X2,singleton(X1)))
& cartesian_product2(unordered_pair(X0,X1),X2) = set_union2(cartesian_product2(singleton(X0),X2),cartesian_product2(singleton(X1),X2)) ),
inference(negated_conjecture,[],[f9]) ).
fof(f9,conjecture,
! [X0,X2,X1] :
( cartesian_product2(X2,unordered_pair(X0,X1)) = set_union2(cartesian_product2(X2,singleton(X0)),cartesian_product2(X2,singleton(X1)))
& cartesian_product2(unordered_pair(X0,X1),X2) = set_union2(cartesian_product2(singleton(X0),X2),cartesian_product2(singleton(X1),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t132_zfmisc_1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET979+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.14 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.35 % 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 14:44:51 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.53 % (1673)lrs+10_1:1024_nm=0:nwc=5.0:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.20/0.54 % (1670)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)
% 0.20/0.55 % (1673)First to succeed.
% 0.20/0.56 % (1691)dis+1010_2:3_fs=off:fsr=off:nm=0:nwc=5.0:s2a=on:s2agt=32:i=82:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/82Mi)
% 0.20/0.56 % (1673)Refutation found. Thanks to Tanya!
% 0.20/0.56 % SZS status Theorem for theBenchmark
% 0.20/0.56 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.56 % (1673)------------------------------
% 0.20/0.56 % (1673)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.56 % (1673)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.56 % (1673)Termination reason: Refutation
% 0.20/0.56
% 0.20/0.56 % (1673)Memory used [KB]: 5884
% 0.20/0.56 % (1673)Time elapsed: 0.006 s
% 0.20/0.56 % (1673)Instructions burned: 2 (million)
% 0.20/0.56 % (1673)------------------------------
% 0.20/0.56 % (1673)------------------------------
% 0.20/0.56 % (1668)Success in time 0.202 s
%------------------------------------------------------------------------------