TSTP Solution File: SET664+3 by SnakeForV---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SET664+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_uns --cores 0 -t %d %s
% Computer : n003.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 18:21:48 EDT 2022
% Result : Theorem 0.19s 0.52s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 11
% Syntax : Number of formulae : 50 ( 11 unt; 0 def)
% Number of atoms : 184 ( 32 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 205 ( 71 ~; 58 |; 44 &)
% ( 2 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 74 ( 59 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f280,plain,
$false,
inference(subsumption_resolution,[],[f279,f229]) ).
fof(f229,plain,
empty_set = range_of(sK10),
inference(subsumption_resolution,[],[f224,f140]) ).
fof(f140,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f34]) ).
fof(f34,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p33) ).
fof(f224,plain,
( empty_set = range_of(sK10)
| ~ ilf_type(range_of(sK10),set_type) ),
inference(resolution,[],[f193,f150]) ).
fof(f150,plain,
! [X0] :
( ~ subset(X0,empty_set)
| ~ ilf_type(X0,set_type)
| empty_set = X0 ),
inference(cnf_transformation,[],[f79]) ).
fof(f79,plain,
! [X0] :
( empty_set = X0
| ~ ilf_type(X0,set_type)
| ~ subset(X0,empty_set) ),
inference(flattening,[],[f78]) ).
fof(f78,plain,
! [X0] :
( empty_set = X0
| ~ subset(X0,empty_set)
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( subset(X0,empty_set)
=> empty_set = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
fof(f193,plain,
subset(range_of(sK10),empty_set),
inference(unit_resulting_resolution,[],[f140,f140,f167,f136]) ).
fof(f136,plain,
! [X2,X0,X1] :
( subset(range_of(X2),X1)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type) ),
inference(cnf_transformation,[],[f47]) ).
fof(f47,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ( subset(range_of(X2),X1)
& subset(domain_of(X2),X0) )
| ~ ilf_type(X2,relation_type(X0,X1)) ) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ( subset(range_of(X2),X1)
& subset(domain_of(X2),X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3) ).
fof(f167,plain,
ilf_type(sK10,relation_type(sK9,empty_set)),
inference(cnf_transformation,[],[f107]) ).
fof(f107,plain,
( ilf_type(sK8,set_type)
& ilf_type(sK9,set_type)
& ilf_type(sK10,relation_type(sK9,sK8))
& ilf_type(sK10,relation_type(sK9,empty_set))
& empty_set != sK10 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10])],[f43,f106,f105,f104]) ).
fof(f104,plain,
( ? [X0] :
( ilf_type(X0,set_type)
& ? [X1] :
( ilf_type(X1,set_type)
& ? [X2] :
( ilf_type(X2,relation_type(X1,X0))
& ilf_type(X2,relation_type(X1,empty_set))
& empty_set != X2 ) ) )
=> ( ilf_type(sK8,set_type)
& ? [X1] :
( ilf_type(X1,set_type)
& ? [X2] :
( ilf_type(X2,relation_type(X1,sK8))
& ilf_type(X2,relation_type(X1,empty_set))
& empty_set != X2 ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f105,plain,
( ? [X1] :
( ilf_type(X1,set_type)
& ? [X2] :
( ilf_type(X2,relation_type(X1,sK8))
& ilf_type(X2,relation_type(X1,empty_set))
& empty_set != X2 ) )
=> ( ilf_type(sK9,set_type)
& ? [X2] :
( ilf_type(X2,relation_type(sK9,sK8))
& ilf_type(X2,relation_type(sK9,empty_set))
& empty_set != X2 ) ) ),
introduced(choice_axiom,[]) ).
fof(f106,plain,
( ? [X2] :
( ilf_type(X2,relation_type(sK9,sK8))
& ilf_type(X2,relation_type(sK9,empty_set))
& empty_set != X2 )
=> ( ilf_type(sK10,relation_type(sK9,sK8))
& ilf_type(sK10,relation_type(sK9,empty_set))
& empty_set != sK10 ) ),
introduced(choice_axiom,[]) ).
fof(f43,plain,
? [X0] :
( ilf_type(X0,set_type)
& ? [X1] :
( ilf_type(X1,set_type)
& ? [X2] :
( ilf_type(X2,relation_type(X1,X0))
& ilf_type(X2,relation_type(X1,empty_set))
& empty_set != X2 ) ) ),
inference(flattening,[],[f42]) ).
fof(f42,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( empty_set != X2
& ilf_type(X2,relation_type(X1,empty_set))
& ilf_type(X2,relation_type(X1,X0)) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f36]) ).
fof(f36,negated_conjecture,
~ ! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X1,X0))
=> ( ilf_type(X2,relation_type(X1,empty_set))
=> empty_set = X2 ) ) ) ),
inference(negated_conjecture,[],[f35]) ).
fof(f35,conjecture,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X1,X0))
=> ( ilf_type(X2,relation_type(X1,empty_set))
=> empty_set = X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_27) ).
fof(f279,plain,
empty_set != range_of(sK10),
inference(subsumption_resolution,[],[f276,f166]) ).
fof(f166,plain,
empty_set != sK10,
inference(cnf_transformation,[],[f107]) ).
fof(f276,plain,
( empty_set = sK10
| empty_set != range_of(sK10) ),
inference(resolution,[],[f268,f162]) ).
fof(f162,plain,
! [X0] :
( ~ ilf_type(X0,binary_relation_type)
| empty_set = X0
| empty_set != range_of(X0) ),
inference(cnf_transformation,[],[f71]) ).
fof(f71,plain,
! [X0] :
( empty_set = X0
| ~ ilf_type(X0,binary_relation_type)
| ( empty_set != domain_of(X0)
& empty_set != range_of(X0) ) ),
inference(flattening,[],[f70]) ).
fof(f70,plain,
! [X0] :
( empty_set = X0
| ( empty_set != domain_of(X0)
& empty_set != range_of(X0) )
| ~ ilf_type(X0,binary_relation_type) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0] :
( ilf_type(X0,binary_relation_type)
=> ( ( empty_set = domain_of(X0)
| empty_set = range_of(X0) )
=> empty_set = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2) ).
fof(f268,plain,
ilf_type(sK10,binary_relation_type),
inference(unit_resulting_resolution,[],[f140,f260,f185]) ).
fof(f185,plain,
! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0)
| ~ ilf_type(X0,set_type) ),
inference(duplicate_literal_removal,[],[f155]) ).
fof(f155,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ~ relation_like(X0)
| ilf_type(X0,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f101]) ).
fof(f101,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ( ( ilf_type(X0,binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ relation_like(X0) )
& ( ( ilf_type(X0,set_type)
& relation_like(X0) )
| ~ ilf_type(X0,binary_relation_type) ) ) ),
inference(flattening,[],[f100]) ).
fof(f100,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ( ( ilf_type(X0,binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ relation_like(X0) )
& ( ( ilf_type(X0,set_type)
& relation_like(X0) )
| ~ ilf_type(X0,binary_relation_type) ) ) ),
inference(nnf_transformation,[],[f69]) ).
fof(f69,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ( ilf_type(X0,binary_relation_type)
<=> ( ilf_type(X0,set_type)
& relation_like(X0) ) ) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( ilf_type(X0,binary_relation_type)
<=> ( ilf_type(X0,set_type)
& relation_like(X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p13) ).
fof(f260,plain,
relation_like(sK10),
inference(subsumption_resolution,[],[f259,f140]) ).
fof(f259,plain,
( relation_like(sK10)
| ~ ilf_type(sK9,set_type) ),
inference(subsumption_resolution,[],[f256,f140]) ).
fof(f256,plain,
( ~ ilf_type(empty_set,set_type)
| relation_like(sK10)
| ~ ilf_type(sK9,set_type) ),
inference(resolution,[],[f202,f152]) ).
fof(f152,plain,
! [X2,X0,X1] :
( ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| relation_like(X2) ),
inference(cnf_transformation,[],[f64]) ).
fof(f64,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| relation_like(X2) ) ) ),
inference(ennf_transformation,[],[f29]) ).
fof(f29,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
=> relation_like(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p28) ).
fof(f202,plain,
ilf_type(sK10,subset_type(cross_product(sK9,empty_set))),
inference(subsumption_resolution,[],[f201,f140]) ).
fof(f201,plain,
( ilf_type(sK10,subset_type(cross_product(sK9,empty_set)))
| ~ ilf_type(empty_set,set_type) ),
inference(subsumption_resolution,[],[f198,f140]) ).
fof(f198,plain,
( ilf_type(sK10,subset_type(cross_product(sK9,empty_set)))
| ~ ilf_type(sK9,set_type)
| ~ ilf_type(empty_set,set_type) ),
inference(resolution,[],[f167,f121]) ).
fof(f121,plain,
! [X3,X0,X1] :
( ~ ilf_type(X3,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ilf_type(X3,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f80]) ).
fof(f80,plain,
! [X0] :
( ! [X1] :
( ( ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X2,subset_type(cross_product(X0,X1))) )
& ! [X3] :
( ilf_type(X3,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X3,relation_type(X0,X1)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(rectify,[],[f75]) ).
fof(f75,plain,
! [X0] :
( ! [X1] :
( ( ! [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)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f37]) ).
fof(f37,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,[],[f7]) ).
fof(f7,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/sandbox2/benchmark/theBenchmark.p',p6) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.12 % Problem : SET664+3 : TPTP v8.1.0. Released v2.2.0.
% 0.02/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.12/0.34 % Computer : n003.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Aug 30 14:11:07 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.49 % (1566)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)
% 0.19/0.50 % (1575)lrs+10_1:4_av=off:bs=unit_only:bsr=unit_only:ep=RS:s2a=on:sos=on:sp=frequency:to=lpo:i=16:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.19/0.50 % (1575)Instruction limit reached!
% 0.19/0.50 % (1575)------------------------------
% 0.19/0.50 % (1575)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.50 % (1574)lrs+10_1:2_br=off:nm=4:ss=included:urr=on:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.51 % (1574)Instruction limit reached!
% 0.19/0.51 % (1574)------------------------------
% 0.19/0.51 % (1574)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.51 % (1561)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 0.19/0.51 % (1574)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.51 % (1574)Termination reason: Unknown
% 0.19/0.51 % (1574)Termination phase: Saturation
% 0.19/0.51
% 0.19/0.51 % (1574)Memory used [KB]: 6012
% 0.19/0.51 % (1574)Time elapsed: 0.113 s
% 0.19/0.51 % (1574)Instructions burned: 7 (million)
% 0.19/0.51 % (1574)------------------------------
% 0.19/0.51 % (1574)------------------------------
% 0.19/0.51 % (1585)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)
% 0.19/0.51 % (1565)lrs+10_5:1_br=off:fde=none:nwc=3.0:sd=1:sgt=10:sos=on:ss=axioms:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.51 % (1566)Refutation not found, incomplete strategy% (1566)------------------------------
% 0.19/0.51 % (1566)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.51 % (1566)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.51 % (1566)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.51
% 0.19/0.51 % (1566)Memory used [KB]: 5884
% 0.19/0.51 % (1566)Time elapsed: 0.112 s
% 0.19/0.51 % (1566)Instructions burned: 2 (million)
% 0.19/0.51 % (1566)------------------------------
% 0.19/0.51 % (1566)------------------------------
% 0.19/0.51 % (1576)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)
% 0.19/0.51 % (1575)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.51 % (1575)Termination reason: Unknown
% 0.19/0.51 % (1575)Termination phase: Saturation
% 0.19/0.51
% 0.19/0.51 % (1575)Memory used [KB]: 1663
% 0.19/0.51 % (1575)Time elapsed: 0.104 s
% 0.19/0.51 % (1575)Instructions burned: 16 (million)
% 0.19/0.51 % (1575)------------------------------
% 0.19/0.51 % (1575)------------------------------
% 0.19/0.51 % (1565)Refutation not found, incomplete strategy% (1565)------------------------------
% 0.19/0.51 % (1565)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.51 % (1584)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)
% 0.19/0.52 % (1565)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.52 % (1565)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.52
% 0.19/0.52 % (1565)Memory used [KB]: 6012
% 0.19/0.52 % (1565)Time elapsed: 0.113 s
% 0.19/0.52 % (1565)Instructions burned: 5 (million)
% 0.19/0.52 % (1565)------------------------------
% 0.19/0.52 % (1565)------------------------------
% 0.19/0.52 % (1584)First to succeed.
% 0.19/0.52 % (1584)Refutation found. Thanks to Tanya!
% 0.19/0.52 % SZS status Theorem for theBenchmark
% 0.19/0.52 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.52 % (1584)------------------------------
% 0.19/0.52 % (1584)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.52 % (1584)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.52 % (1584)Termination reason: Refutation
% 0.19/0.52
% 0.19/0.52 % (1584)Memory used [KB]: 6140
% 0.19/0.52 % (1584)Time elapsed: 0.131 s
% 0.19/0.52 % (1584)Instructions burned: 9 (million)
% 0.19/0.52 % (1584)------------------------------
% 0.19/0.52 % (1584)------------------------------
% 0.19/0.52 % (1557)Success in time 0.174 s
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