TSTP Solution File: SET663+3 by SnakeForV-SAT---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : SET663+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 : n005.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 18:25:16 EDT 2022
% Result : Theorem 0.20s 0.53s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 15
% Syntax : Number of formulae : 67 ( 10 unt; 0 def)
% Number of atoms : 200 ( 30 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 223 ( 90 ~; 86 |; 16 &)
% ( 8 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 7 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 69 ( 63 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f380,plain,
$false,
inference(avatar_sat_refutation,[],[f201,f203,f235,f257,f364,f372,f379]) ).
fof(f379,plain,
~ spl17_11,
inference(avatar_contradiction_clause,[],[f378]) ).
fof(f378,plain,
( $false
| ~ spl17_11 ),
inference(trivial_inequality_removal,[],[f373]) ).
fof(f373,plain,
( empty_set != empty_set
| ~ spl17_11 ),
inference(superposition,[],[f103,f252]) ).
fof(f252,plain,
( empty_set = sK9
| ~ spl17_11 ),
inference(avatar_component_clause,[],[f250]) ).
fof(f250,plain,
( spl17_11
<=> empty_set = sK9 ),
introduced(avatar_definition,[new_symbols(naming,[spl17_11])]) ).
fof(f103,plain,
empty_set != sK9,
inference(cnf_transformation,[],[f57]) ).
fof(f57,plain,
? [X0] :
( ilf_type(X0,set_type)
& ? [X1] :
( ilf_type(X1,set_type)
& ? [X2] :
( ilf_type(X2,relation_type(X0,X1))
& ilf_type(X2,relation_type(empty_set,X1))
& empty_set != X2 ) ) ),
inference(flattening,[],[f56]) ).
fof(f56,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( empty_set != X2
& ilf_type(X2,relation_type(empty_set,X1))
& ilf_type(X2,relation_type(X0,X1)) )
& 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(X0,X1))
=> ( ilf_type(X2,relation_type(empty_set,X1))
=> 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(X0,X1))
=> ( ilf_type(X2,relation_type(empty_set,X1))
=> empty_set = X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_26) ).
fof(f372,plain,
( spl17_12
| ~ spl17_20 ),
inference(avatar_contradiction_clause,[],[f371]) ).
fof(f371,plain,
( $false
| spl17_12
| ~ spl17_20 ),
inference(resolution,[],[f369,f258]) ).
fof(f258,plain,
( ~ relation_like(sK9)
| spl17_12 ),
inference(resolution,[],[f256,f152]) ).
fof(f152,plain,
! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0) ),
inference(resolution,[],[f132,f113]) ).
fof(f113,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(f132,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ~ relation_like(X0)
| ilf_type(X0,binary_relation_type) ),
inference(cnf_transformation,[],[f67]) ).
fof(f67,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ( ( ilf_type(X0,set_type)
& relation_like(X0) )
<=> ilf_type(X0,binary_relation_type) ) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( ( ilf_type(X0,set_type)
& relation_like(X0) )
<=> ilf_type(X0,binary_relation_type) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p13) ).
fof(f256,plain,
( ~ ilf_type(sK9,binary_relation_type)
| spl17_12 ),
inference(avatar_component_clause,[],[f254]) ).
fof(f254,plain,
( spl17_12
<=> ilf_type(sK9,binary_relation_type) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_12])]) ).
fof(f369,plain,
( relation_like(sK9)
| ~ spl17_20 ),
inference(resolution,[],[f363,f146]) ).
fof(f146,plain,
ilf_type(sK9,sF16),
inference(definition_folding,[],[f104,f145]) ).
fof(f145,plain,
sF16 = relation_type(empty_set,sK8),
introduced(function_definition,[]) ).
fof(f104,plain,
ilf_type(sK9,relation_type(empty_set,sK8)),
inference(cnf_transformation,[],[f57]) ).
fof(f363,plain,
( ! [X1] :
( ~ ilf_type(X1,sF16)
| relation_like(X1) )
| ~ spl17_20 ),
inference(avatar_component_clause,[],[f362]) ).
fof(f362,plain,
( spl17_20
<=> ! [X1] :
( ~ ilf_type(X1,sF16)
| relation_like(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_20])]) ).
fof(f364,plain,
( ~ spl17_5
| ~ spl17_4
| spl17_20 ),
inference(avatar_split_clause,[],[f359,f362,f183,f187]) ).
fof(f187,plain,
( spl17_5
<=> ilf_type(sK8,set_type) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_5])]) ).
fof(f183,plain,
( spl17_4
<=> ilf_type(empty_set,set_type) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_4])]) ).
fof(f359,plain,
! [X1] :
( ~ ilf_type(X1,sF16)
| ~ ilf_type(empty_set,set_type)
| relation_like(X1)
| ~ ilf_type(sK8,set_type) ),
inference(superposition,[],[f356,f145]) ).
fof(f356,plain,
! [X2,X0,X1] :
( ~ ilf_type(X2,relation_type(X0,X1))
| relation_like(X2)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(duplicate_literal_removal,[],[f355]) ).
fof(f355,plain,
! [X2,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| relation_like(X2) ),
inference(resolution,[],[f123,f114]) ).
fof(f114,plain,
! [X2,X0,X1] :
( ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| relation_like(X2) ),
inference(cnf_transformation,[],[f63]) ).
fof(f63,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( relation_like(X2)
| ~ ilf_type(X2,subset_type(cross_product(X0,X1))) ) ) ),
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(f123,plain,
! [X3,X0,X1] :
( ilf_type(X3,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,relation_type(X0,X1)) ),
inference(cnf_transformation,[],[f40]) ).
fof(f40,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [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) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ! [X2] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
=> ilf_type(X2,relation_type(X0,X1)) )
& ! [X3] :
( ilf_type(X3,relation_type(X0,X1))
=> ilf_type(X3,subset_type(cross_product(X0,X1))) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p6) ).
fof(f257,plain,
( spl17_11
| ~ spl17_12
| ~ spl17_9 ),
inference(avatar_split_clause,[],[f248,f233,f254,f250]) ).
fof(f233,plain,
( spl17_9
<=> ! [X1] :
( subset(domain_of(X1),empty_set)
| ~ ilf_type(X1,sF16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_9])]) ).
fof(f248,plain,
( ~ ilf_type(sK9,binary_relation_type)
| empty_set = sK9
| ~ spl17_9 ),
inference(trivial_inequality_removal,[],[f247]) ).
fof(f247,plain,
( empty_set != empty_set
| empty_set = sK9
| ~ ilf_type(sK9,binary_relation_type)
| ~ spl17_9 ),
inference(superposition,[],[f136,f242]) ).
fof(f242,plain,
( empty_set = domain_of(sK9)
| ~ spl17_9 ),
inference(resolution,[],[f241,f146]) ).
fof(f241,plain,
( ! [X0] :
( ~ ilf_type(X0,sF16)
| empty_set = domain_of(X0) )
| ~ spl17_9 ),
inference(resolution,[],[f240,f113]) ).
fof(f240,plain,
( ! [X0] :
( ~ ilf_type(domain_of(X0),set_type)
| ~ ilf_type(X0,sF16)
| empty_set = domain_of(X0) )
| ~ spl17_9 ),
inference(resolution,[],[f234,f122]) ).
fof(f122,plain,
! [X0] :
( ~ subset(X0,empty_set)
| ~ ilf_type(X0,set_type)
| empty_set = X0 ),
inference(cnf_transformation,[],[f66]) ).
fof(f66,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| empty_set = X0
| ~ subset(X0,empty_set) ),
inference(flattening,[],[f65]) ).
fof(f65,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(f234,plain,
( ! [X1] :
( subset(domain_of(X1),empty_set)
| ~ ilf_type(X1,sF16) )
| ~ spl17_9 ),
inference(avatar_component_clause,[],[f233]) ).
fof(f136,plain,
! [X0] :
( empty_set != domain_of(X0)
| ~ ilf_type(X0,binary_relation_type)
| empty_set = X0 ),
inference(cnf_transformation,[],[f42]) ).
fof(f42,plain,
! [X0] :
( empty_set = X0
| ( empty_set != domain_of(X0)
& empty_set != range_of(X0) )
| ~ ilf_type(X0,binary_relation_type) ),
inference(flattening,[],[f41]) ).
fof(f41,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(f235,plain,
( spl17_9
| ~ spl17_4
| ~ spl17_5 ),
inference(avatar_split_clause,[],[f230,f187,f183,f233]) ).
fof(f230,plain,
! [X1] :
( ~ ilf_type(sK8,set_type)
| ~ ilf_type(empty_set,set_type)
| subset(domain_of(X1),empty_set)
| ~ ilf_type(X1,sF16) ),
inference(superposition,[],[f101,f145]) ).
fof(f101,plain,
! [X2,X0,X1] :
( ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X0,set_type)
| subset(domain_of(X2),X0)
| ~ ilf_type(X1,set_type) ),
inference(cnf_transformation,[],[f60]) ).
fof(f60,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(f203,plain,
spl17_4,
inference(avatar_contradiction_clause,[],[f202]) ).
fof(f202,plain,
( $false
| spl17_4 ),
inference(resolution,[],[f185,f113]) ).
fof(f185,plain,
( ~ ilf_type(empty_set,set_type)
| spl17_4 ),
inference(avatar_component_clause,[],[f183]) ).
fof(f201,plain,
spl17_5,
inference(avatar_contradiction_clause,[],[f200]) ).
fof(f200,plain,
( $false
| spl17_5 ),
inference(resolution,[],[f189,f113]) ).
fof(f189,plain,
( ~ ilf_type(sK8,set_type)
| spl17_5 ),
inference(avatar_component_clause,[],[f187]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET663+3 : TPTP v8.1.0. Released v2.2.0.
% 0.12/0.13 % 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 : n005.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 14:10:33 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.50 % (29646)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.50 % (29649)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.50 % (29648)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/48Mi)
% 0.20/0.51 % (29669)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.20/0.51 % (29656)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.20/0.51 % (29667)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 0.20/0.51 TRYING [1]
% 0.20/0.51 TRYING [2]
% 0.20/0.51 % (29655)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.20/0.51 % (29654)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.20/0.52 % (29663)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)
% 0.20/0.52 % (29673)ott+10_7:2_awrs=decay:awrsf=8:bd=preordered:drc=off:fd=preordered:fde=unused:fsr=off:slsq=on:slsqc=2:slsqr=5,8:sp=const_min:spb=units:to=lpo:i=355:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/355Mi)
% 0.20/0.52 % (29654)First to succeed.
% 0.20/0.52 % (29647)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.52 % (29665)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/498Mi)
% 0.20/0.52 % (29657)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.20/0.52 % (29659)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)
% 0.20/0.53 % (29654)Refutation found. Thanks to Tanya!
% 0.20/0.53 % SZS status Theorem for theBenchmark
% 0.20/0.53 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.53 % (29654)------------------------------
% 0.20/0.53 % (29654)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.53 % (29654)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.53 % (29654)Termination reason: Refutation
% 0.20/0.53
% 0.20/0.53 % (29654)Memory used [KB]: 5628
% 0.20/0.53 % (29654)Time elapsed: 0.120 s
% 0.20/0.53 % (29654)Instructions burned: 10 (million)
% 0.20/0.53 % (29654)------------------------------
% 0.20/0.53 % (29654)------------------------------
% 0.20/0.53 % (29642)Success in time 0.173 s
%------------------------------------------------------------------------------