TSTP Solution File: SET643+3 by SnakeForV-SAT---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : SET643+3 : TPTP v8.1.0. Released v2.2.0.
% 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 : n028.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 18:25:12 EDT 2022
% Result : Theorem 0.20s 0.50s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of formulae : 58 ( 7 unt; 0 def)
% Number of atoms : 239 ( 0 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 294 ( 113 ~; 107 |; 38 &)
% ( 10 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-2 aty)
% Number of variables : 127 ( 115 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f227,plain,
$false,
inference(subsumption_resolution,[],[f115,f219]) ).
fof(f219,plain,
! [X3,X4] : ilf_type(cross_product(X3,X4),relation_type(X3,X4)),
inference(resolution,[],[f217,f186]) ).
fof(f186,plain,
! [X0] : ilf_type(X0,subset_type(X0)),
inference(resolution,[],[f183,f158]) ).
fof(f158,plain,
! [X0] : member(X0,power_set(X0)),
inference(duplicate_literal_removal,[],[f156]) ).
fof(f156,plain,
! [X0] :
( member(X0,power_set(X0))
| member(X0,power_set(X0)) ),
inference(resolution,[],[f155,f153]) ).
fof(f153,plain,
! [X0,X1] :
( ~ member(sK0(X0,X1),X1)
| member(X0,power_set(X1)) ),
inference(subsumption_resolution,[],[f152,f92]) ).
fof(f92,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f19]) ).
fof(f19,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p19) ).
fof(f152,plain,
! [X0,X1] :
( ~ member(sK0(X0,X1),X1)
| ~ ilf_type(X0,set_type)
| member(X0,power_set(X1)) ),
inference(subsumption_resolution,[],[f86,f92]) ).
fof(f86,plain,
! [X0,X1] :
( ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| member(X0,power_set(X1))
| ~ member(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f52]) ).
fof(f52,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,power_set(X1))
| ( member(sK0(X0,X1),X0)
& ~ member(sK0(X0,X1),X1)
& ilf_type(sK0(X0,X1),set_type) ) )
& ( ! [X3] :
( ~ member(X3,X0)
| member(X3,X1)
| ~ ilf_type(X3,set_type) )
| ~ member(X0,power_set(X1)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f50,f51]) ).
fof(f51,plain,
! [X0,X1] :
( ? [X2] :
( member(X2,X0)
& ~ member(X2,X1)
& ilf_type(X2,set_type) )
=> ( member(sK0(X0,X1),X0)
& ~ member(sK0(X0,X1),X1)
& ilf_type(sK0(X0,X1),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f50,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,power_set(X1))
| ? [X2] :
( member(X2,X0)
& ~ member(X2,X1)
& ilf_type(X2,set_type) ) )
& ( ! [X3] :
( ~ member(X3,X0)
| member(X3,X1)
| ~ ilf_type(X3,set_type) )
| ~ member(X0,power_set(X1)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(rectify,[],[f49]) ).
fof(f49,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,power_set(X1))
| ? [X2] :
( member(X2,X0)
& ~ member(X2,X1)
& ilf_type(X2,set_type) ) )
& ( ! [X2] :
( ~ member(X2,X0)
| member(X2,X1)
| ~ ilf_type(X2,set_type) )
| ~ member(X0,power_set(X1)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f33]) ).
fof(f33,plain,
! [X0] :
( ! [X1] :
( ( member(X0,power_set(X1))
<=> ! [X2] :
( ~ member(X2,X0)
| member(X2,X1)
| ~ ilf_type(X2,set_type) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f32]) ).
fof(f32,plain,
! [X0] :
( ! [X1] :
( ( member(X0,power_set(X1))
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( member(X0,power_set(X1))
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ( member(X2,X0)
=> member(X2,X1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p11) ).
fof(f155,plain,
! [X0,X1] :
( member(sK0(X0,X1),X0)
| member(X0,power_set(X1)) ),
inference(subsumption_resolution,[],[f154,f92]) ).
fof(f154,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| ~ ilf_type(X0,set_type)
| member(sK0(X0,X1),X0) ),
inference(subsumption_resolution,[],[f87,f92]) ).
fof(f87,plain,
! [X0,X1] :
( member(sK0(X0,X1),X0)
| member(X0,power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f52]) ).
fof(f183,plain,
! [X3,X4] :
( ~ member(X3,power_set(X4))
| ilf_type(X3,subset_type(X4)) ),
inference(resolution,[],[f180,f170]) ).
fof(f170,plain,
! [X0,X1] :
( ilf_type(X0,member_type(X1))
| ~ member(X0,X1) ),
inference(subsumption_resolution,[],[f169,f137]) ).
fof(f137,plain,
! [X2,X0] :
( ~ member(X2,X0)
| ~ empty(X0) ),
inference(subsumption_resolution,[],[f136,f92]) ).
fof(f136,plain,
! [X2,X0] :
( ~ member(X2,X0)
| ~ ilf_type(X0,set_type)
| ~ empty(X0) ),
inference(subsumption_resolution,[],[f88,f92]) ).
fof(f88,plain,
! [X2,X0] :
( ~ empty(X0)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f56]) ).
fof(f56,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ( ( empty(X0)
| ( member(sK1(X0),X0)
& ilf_type(sK1(X0),set_type) ) )
& ( ! [X2] :
( ~ member(X2,X0)
| ~ ilf_type(X2,set_type) )
| ~ empty(X0) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f54,f55]) ).
fof(f55,plain,
! [X0] :
( ? [X1] :
( member(X1,X0)
& ilf_type(X1,set_type) )
=> ( member(sK1(X0),X0)
& ilf_type(sK1(X0),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f54,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ( ( empty(X0)
| ? [X1] :
( member(X1,X0)
& ilf_type(X1,set_type) ) )
& ( ! [X2] :
( ~ member(X2,X0)
| ~ ilf_type(X2,set_type) )
| ~ empty(X0) ) ) ),
inference(rectify,[],[f53]) ).
fof(f53,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ( ( empty(X0)
| ? [X1] :
( member(X1,X0)
& ilf_type(X1,set_type) ) )
& ( ! [X1] :
( ~ member(X1,X0)
| ~ ilf_type(X1,set_type) )
| ~ empty(X0) ) ) ),
inference(nnf_transformation,[],[f34]) ).
fof(f34,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ( empty(X0)
<=> ! [X1] :
( ~ member(X1,X0)
| ~ ilf_type(X1,set_type) ) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( ! [X1] :
( ilf_type(X1,set_type)
=> ~ member(X1,X0) )
<=> empty(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p15) ).
fof(f169,plain,
! [X0,X1] :
( empty(X1)
| ~ member(X0,X1)
| ilf_type(X0,member_type(X1)) ),
inference(subsumption_resolution,[],[f168,f92]) ).
fof(f168,plain,
! [X0,X1] :
( ilf_type(X0,member_type(X1))
| ~ member(X0,X1)
| ~ ilf_type(X1,set_type)
| empty(X1) ),
inference(subsumption_resolution,[],[f99,f92]) ).
fof(f99,plain,
! [X0,X1] :
( empty(X1)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ member(X0,X1)
| ilf_type(X0,member_type(X1)) ),
inference(cnf_transformation,[],[f61]) ).
fof(f61,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( empty(X1)
| ~ ilf_type(X1,set_type)
| ( ( ilf_type(X0,member_type(X1))
| ~ member(X0,X1) )
& ( member(X0,X1)
| ~ ilf_type(X0,member_type(X1)) ) ) ) ),
inference(nnf_transformation,[],[f39]) ).
fof(f39,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( empty(X1)
| ~ ilf_type(X1,set_type)
| ( ilf_type(X0,member_type(X1))
<=> member(X0,X1) ) ) ),
inference(flattening,[],[f38]) ).
fof(f38,plain,
! [X0] :
( ! [X1] :
( ( ilf_type(X0,member_type(X1))
<=> member(X0,X1) )
| ~ ilf_type(X1,set_type)
| empty(X1) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ( ilf_type(X1,set_type)
& ~ empty(X1) )
=> ( ilf_type(X0,member_type(X1))
<=> member(X0,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p13) ).
fof(f180,plain,
! [X0,X1] :
( ~ ilf_type(X1,member_type(power_set(X0)))
| ilf_type(X1,subset_type(X0)) ),
inference(subsumption_resolution,[],[f179,f92]) ).
fof(f179,plain,
! [X0,X1] :
( ilf_type(X1,subset_type(X0))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,member_type(power_set(X0))) ),
inference(subsumption_resolution,[],[f105,f92]) ).
fof(f105,plain,
! [X0,X1] :
( ~ ilf_type(X1,set_type)
| ~ ilf_type(X1,member_type(power_set(X0)))
| ~ ilf_type(X0,set_type)
| ilf_type(X1,subset_type(X0)) ),
inference(cnf_transformation,[],[f66]) ).
fof(f66,plain,
! [X0] :
( ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ( ilf_type(X1,subset_type(X0))
| ~ ilf_type(X1,member_type(power_set(X0))) )
& ( ilf_type(X1,member_type(power_set(X0)))
| ~ ilf_type(X1,subset_type(X0)) ) ) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f35]) ).
fof(f35,plain,
! [X0] :
( ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ilf_type(X1,subset_type(X0))
<=> ilf_type(X1,member_type(power_set(X0))) ) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ilf_type(X1,subset_type(X0))
<=> ilf_type(X1,member_type(power_set(X0))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p7) ).
fof(f217,plain,
! [X2,X0,X1] :
( ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| ilf_type(X2,relation_type(X0,X1)) ),
inference(subsumption_resolution,[],[f216,f92]) ).
fof(f216,plain,
! [X2,X0,X1] :
( ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X1,set_type) ),
inference(subsumption_resolution,[],[f118,f92]) ).
fof(f118,plain,
! [X2,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type) ),
inference(cnf_transformation,[],[f78]) ).
fof(f78,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ( ! [X2] :
( ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| ilf_type(X2,relation_type(X0,X1)) )
& ! [X3] :
( ilf_type(X3,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X3,relation_type(X0,X1)) ) )
| ~ ilf_type(X1,set_type) ) ),
inference(rectify,[],[f29]) ).
fof(f29,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ( ! [X3] :
( ~ ilf_type(X3,subset_type(cross_product(X0,X1)))
| ilf_type(X3,relation_type(X0,X1)) )
& ! [X2] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X2,relation_type(X0,X1)) ) )
| ~ ilf_type(X1,set_type) ) ),
inference(ennf_transformation,[],[f22]) ).
fof(f22,plain,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ! [X3] :
( ilf_type(X3,subset_type(cross_product(X0,X1)))
=> ilf_type(X3,relation_type(X0,X1)) )
& ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ilf_type(X2,subset_type(cross_product(X0,X1))) ) ) ) ),
inference(rectify,[],[f4]) ).
fof(f4,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ! [X3] :
( ilf_type(X3,relation_type(X0,X1))
=> ilf_type(X3,subset_type(cross_product(X0,X1))) )
& ! [X2] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
=> ilf_type(X2,relation_type(X0,X1)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p4) ).
fof(f115,plain,
~ ilf_type(cross_product(sK9,sK10),relation_type(sK9,sK10)),
inference(cnf_transformation,[],[f77]) ).
fof(f77,plain,
( ilf_type(sK9,set_type)
& ~ ilf_type(cross_product(sK9,sK10),relation_type(sK9,sK10))
& ilf_type(sK10,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10])],[f46,f76,f75]) ).
fof(f75,plain,
( ? [X0] :
( ilf_type(X0,set_type)
& ? [X1] :
( ~ ilf_type(cross_product(X0,X1),relation_type(X0,X1))
& ilf_type(X1,set_type) ) )
=> ( ilf_type(sK9,set_type)
& ? [X1] :
( ~ ilf_type(cross_product(sK9,X1),relation_type(sK9,X1))
& ilf_type(X1,set_type) ) ) ),
introduced(choice_axiom,[]) ).
fof(f76,plain,
( ? [X1] :
( ~ ilf_type(cross_product(sK9,X1),relation_type(sK9,X1))
& ilf_type(X1,set_type) )
=> ( ~ ilf_type(cross_product(sK9,sK10),relation_type(sK9,sK10))
& ilf_type(sK10,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f46,plain,
? [X0] :
( ilf_type(X0,set_type)
& ? [X1] :
( ~ ilf_type(cross_product(X0,X1),relation_type(X0,X1))
& ilf_type(X1,set_type) ) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,negated_conjecture,
~ ! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ilf_type(cross_product(X0,X1),relation_type(X0,X1)) ) ),
inference(negated_conjecture,[],[f20]) ).
fof(f20,conjecture,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ilf_type(cross_product(X0,X1),relation_type(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_5) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET643+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.34 % Computer : n028.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 14:18:33 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.47 % (16378)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.48 % (16386)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.20/0.48 % (16378)Instruction limit reached!
% 0.20/0.48 % (16378)------------------------------
% 0.20/0.48 % (16378)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.48 % (16378)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.48 % (16378)Termination reason: Unknown
% 0.20/0.48 % (16378)Termination phase: shuffling
% 0.20/0.48
% 0.20/0.48 % (16378)Memory used [KB]: 895
% 0.20/0.48 % (16378)Time elapsed: 0.004 s
% 0.20/0.48 % (16378)Instructions burned: 2 (million)
% 0.20/0.48 % (16378)------------------------------
% 0.20/0.48 % (16378)------------------------------
% 0.20/0.49 % (16386)First to succeed.
% 0.20/0.50 % (16386)Refutation found. Thanks to Tanya!
% 0.20/0.50 % SZS status Theorem for theBenchmark
% 0.20/0.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.50 % (16386)------------------------------
% 0.20/0.50 % (16386)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.50 % (16386)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.50 % (16386)Termination reason: Refutation
% 0.20/0.50
% 0.20/0.50 % (16386)Memory used [KB]: 5500
% 0.20/0.50 % (16386)Time elapsed: 0.072 s
% 0.20/0.50 % (16386)Instructions burned: 8 (million)
% 0.20/0.50 % (16386)------------------------------
% 0.20/0.50 % (16386)------------------------------
% 0.20/0.50 % (16369)Success in time 0.145 s
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