TSTP Solution File: SET956+1 by SnakeForV---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SET956+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 : n023.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 18:22:51 EDT 2022
% Result : Theorem 0.20s 0.51s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 39 ( 12 unt; 0 def)
% Number of atoms : 124 ( 9 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 131 ( 46 ~; 30 |; 41 &)
% ( 3 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 4 ( 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 : 120 ( 95 !; 25 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f105,plain,
$false,
inference(subsumption_resolution,[],[f104,f56]) ).
fof(f56,plain,
in(sK8(sK2,sK3),sK3),
inference(unit_resulting_resolution,[],[f42,f53]) ).
fof(f53,plain,
! [X0,X1] :
( in(sK8(X0,X1),X1)
| subset(X1,X0) ),
inference(cnf_transformation,[],[f39]) ).
fof(f39,plain,
! [X0,X1] :
( ( ! [X2] :
( ~ in(X2,X1)
| in(X2,X0) )
| ~ subset(X1,X0) )
& ( subset(X1,X0)
| ( in(sK8(X0,X1),X1)
& ~ in(sK8(X0,X1),X0) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f37,f38]) ).
fof(f38,plain,
! [X0,X1] :
( ? [X3] :
( in(X3,X1)
& ~ in(X3,X0) )
=> ( in(sK8(X0,X1),X1)
& ~ in(sK8(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f37,plain,
! [X0,X1] :
( ( ! [X2] :
( ~ in(X2,X1)
| in(X2,X0) )
| ~ subset(X1,X0) )
& ( subset(X1,X0)
| ? [X3] :
( in(X3,X1)
& ~ in(X3,X0) ) ) ),
inference(rectify,[],[f36]) ).
fof(f36,plain,
! [X0,X1] :
( ( ! [X2] :
( ~ in(X2,X1)
| in(X2,X0) )
| ~ subset(X1,X0) )
& ( subset(X1,X0)
| ? [X2] :
( in(X2,X1)
& ~ in(X2,X0) ) ) ),
inference(nnf_transformation,[],[f22]) ).
fof(f22,plain,
! [X0,X1] :
( ! [X2] :
( ~ in(X2,X1)
| in(X2,X0) )
<=> subset(X1,X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,plain,
! [X1,X0] :
( ! [X2] :
( in(X2,X1)
=> in(X2,X0) )
<=> subset(X1,X0) ),
inference(rectify,[],[f3]) ).
fof(f3,axiom,
! [X1,X0] :
( ! [X2] :
( in(X2,X0)
=> in(X2,X1) )
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f42,plain,
~ subset(sK3,sK2),
inference(cnf_transformation,[],[f27]) ).
fof(f27,plain,
( ! [X4,X5] :
( in(ordered_pair(X4,X5),sK2)
| ~ in(ordered_pair(X4,X5),sK3) )
& ~ subset(sK3,sK2)
& subset(sK3,cartesian_product2(sK4,sK1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4])],[f25,f26]) ).
fof(f26,plain,
( ? [X0,X1,X2,X3] :
( ! [X4,X5] :
( in(ordered_pair(X4,X5),X1)
| ~ in(ordered_pair(X4,X5),X2) )
& ~ subset(X2,X1)
& subset(X2,cartesian_product2(X3,X0)) )
=> ( ! [X5,X4] :
( in(ordered_pair(X4,X5),sK2)
| ~ in(ordered_pair(X4,X5),sK3) )
& ~ subset(sK3,sK2)
& subset(sK3,cartesian_product2(sK4,sK1)) ) ),
introduced(choice_axiom,[]) ).
fof(f25,plain,
? [X0,X1,X2,X3] :
( ! [X4,X5] :
( in(ordered_pair(X4,X5),X1)
| ~ in(ordered_pair(X4,X5),X2) )
& ~ subset(X2,X1)
& subset(X2,cartesian_product2(X3,X0)) ),
inference(rectify,[],[f21]) ).
fof(f21,plain,
? [X3,X2,X1,X0] :
( ! [X4,X5] :
( in(ordered_pair(X4,X5),X2)
| ~ in(ordered_pair(X4,X5),X1) )
& ~ subset(X1,X2)
& subset(X1,cartesian_product2(X0,X3)) ),
inference(flattening,[],[f20]) ).
fof(f20,plain,
? [X2,X1,X0,X3] :
( ~ subset(X1,X2)
& ! [X4,X5] :
( in(ordered_pair(X4,X5),X2)
| ~ in(ordered_pair(X4,X5),X1) )
& subset(X1,cartesian_product2(X0,X3)) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,plain,
~ ! [X2,X1,X0,X3] :
( ( ! [X5,X4] :
( in(ordered_pair(X4,X5),X1)
=> in(ordered_pair(X4,X5),X2) )
& subset(X1,cartesian_product2(X0,X3)) )
=> subset(X1,X2) ),
inference(rectify,[],[f11]) ).
fof(f11,negated_conjecture,
~ ! [X1,X0,X3,X2] :
( ( ! [X4,X5] :
( in(ordered_pair(X4,X5),X0)
=> in(ordered_pair(X4,X5),X3) )
& subset(X0,cartesian_product2(X1,X2)) )
=> subset(X0,X3) ),
inference(negated_conjecture,[],[f10]) ).
fof(f10,conjecture,
! [X1,X0,X3,X2] :
( ( ! [X4,X5] :
( in(ordered_pair(X4,X5),X0)
=> in(ordered_pair(X4,X5),X3) )
& subset(X0,cartesian_product2(X1,X2)) )
=> subset(X0,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t109_zfmisc_1) ).
fof(f104,plain,
~ in(sK8(sK2,sK3),sK3),
inference(subsumption_resolution,[],[f102,f55]) ).
fof(f55,plain,
~ in(sK8(sK2,sK3),sK2),
inference(unit_resulting_resolution,[],[f42,f52]) ).
fof(f52,plain,
! [X0,X1] :
( ~ in(sK8(X0,X1),X0)
| subset(X1,X0) ),
inference(cnf_transformation,[],[f39]) ).
fof(f102,plain,
( in(sK8(sK2,sK3),sK2)
| ~ in(sK8(sK2,sK3),sK3) ),
inference(superposition,[],[f43,f91]) ).
fof(f91,plain,
sK8(sK2,sK3) = ordered_pair(sK5(sK4,sK1,sK8(sK2,sK3)),sK6(sK4,sK1,sK8(sK2,sK3))),
inference(unit_resulting_resolution,[],[f63,f49,f47]) ).
fof(f47,plain,
! [X2,X3,X0,X1] :
( ~ subset(X3,cartesian_product2(X0,X1))
| ~ in(X2,X3)
| ordered_pair(sK5(X0,X1,X2),sK6(X0,X1,X2)) = X2 ),
inference(cnf_transformation,[],[f32]) ).
fof(f32,plain,
! [X0,X1,X2,X3] :
( ~ in(X2,X3)
| ~ subset(X3,cartesian_product2(X0,X1))
| ( in(sK5(X0,X1,X2),X0)
& ordered_pair(sK5(X0,X1,X2),sK6(X0,X1,X2)) = X2
& in(sK6(X0,X1,X2),X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6])],[f30,f31]) ).
fof(f31,plain,
! [X0,X1,X2] :
( ? [X4,X5] :
( in(X4,X0)
& ordered_pair(X4,X5) = X2
& in(X5,X1) )
=> ( in(sK5(X0,X1,X2),X0)
& ordered_pair(sK5(X0,X1,X2),sK6(X0,X1,X2)) = X2
& in(sK6(X0,X1,X2),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f30,plain,
! [X0,X1,X2,X3] :
( ~ in(X2,X3)
| ~ subset(X3,cartesian_product2(X0,X1))
| ? [X4,X5] :
( in(X4,X0)
& ordered_pair(X4,X5) = X2
& in(X5,X1) ) ),
inference(rectify,[],[f18]) ).
fof(f18,plain,
! [X1,X3,X2,X0] :
( ~ in(X2,X0)
| ~ subset(X0,cartesian_product2(X1,X3))
| ? [X5,X4] :
( in(X5,X1)
& ordered_pair(X5,X4) = X2
& in(X4,X3) ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,plain,
! [X0,X3,X2,X1] :
~ ( ! [X4,X5] :
~ ( in(X5,X1)
& ordered_pair(X5,X4) = X2
& in(X4,X3) )
& in(X2,X0)
& subset(X0,cartesian_product2(X1,X3)) ),
inference(rectify,[],[f9]) ).
fof(f9,axiom,
! [X0,X1,X3,X2] :
~ ( subset(X0,cartesian_product2(X1,X2))
& ! [X5,X4] :
~ ( in(X5,X2)
& ordered_pair(X4,X5) = X3
& in(X4,X1) )
& in(X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t103_zfmisc_1) ).
fof(f49,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f33]) ).
fof(f33,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f16]) ).
fof(f16,plain,
! [X1] : subset(X1,X1),
inference(rectify,[],[f8]) ).
fof(f8,axiom,
! [X1,X0] : subset(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f63,plain,
in(sK8(sK2,sK3),cartesian_product2(sK4,sK1)),
inference(unit_resulting_resolution,[],[f56,f41,f54]) ).
fof(f54,plain,
! [X2,X0,X1] :
( ~ subset(X1,X0)
| in(X2,X0)
| ~ in(X2,X1) ),
inference(cnf_transformation,[],[f39]) ).
fof(f41,plain,
subset(sK3,cartesian_product2(sK4,sK1)),
inference(cnf_transformation,[],[f27]) ).
fof(f43,plain,
! [X4,X5] :
( ~ in(ordered_pair(X4,X5),sK3)
| in(ordered_pair(X4,X5),sK2) ),
inference(cnf_transformation,[],[f27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET956+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 : n023.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 14:53:35 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.49 % (17367)lrs+10_1:32_br=off:nm=16:sd=2:ss=axioms:st=2.0:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.50 % (17375)ott+21_1:1_erd=off:s2a=on:sac=on:sd=1:sgt=64:sos=on:ss=included:st=3.0:to=lpo:urr=on:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.20/0.50 % (17367)First to succeed.
% 0.20/0.51 % (17367)Refutation found. Thanks to Tanya!
% 0.20/0.51 % SZS status Theorem for theBenchmark
% 0.20/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.51 % (17367)------------------------------
% 0.20/0.51 % (17367)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.51 % (17367)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.51 % (17367)Termination reason: Refutation
% 0.20/0.51
% 0.20/0.51 % (17367)Memory used [KB]: 6012
% 0.20/0.51 % (17367)Time elapsed: 0.084 s
% 0.20/0.51 % (17367)Instructions burned: 4 (million)
% 0.20/0.51 % (17367)------------------------------
% 0.20/0.51 % (17367)------------------------------
% 0.20/0.51 % (17353)Success in time 0.155 s
%------------------------------------------------------------------------------