TSTP Solution File: SET587+3 by SnakeForV-SAT---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : SET587+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 : n018.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 18:24:59 EDT 2022
% Result : Theorem 0.20s 0.55s
% Output : Refutation 1.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 64 ( 5 unt; 0 def)
% Number of atoms : 186 ( 30 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 203 ( 81 ~; 82 |; 26 &)
% ( 10 <=>; 3 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 85 ( 76 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f124,plain,
$false,
inference(avatar_sat_refutation,[],[f71,f72,f98,f123]) ).
fof(f123,plain,
( ~ spl6_1
| spl6_2 ),
inference(avatar_contradiction_clause,[],[f122]) ).
fof(f122,plain,
( $false
| ~ spl6_1
| spl6_2 ),
inference(subsumption_resolution,[],[f121,f70]) ).
fof(f70,plain,
( empty_set != sF5
| spl6_2 ),
inference(avatar_component_clause,[],[f68]) ).
fof(f68,plain,
( spl6_2
<=> empty_set = sF5 ),
introduced(avatar_definition,[new_symbols(naming,[spl6_2])]) ).
fof(f121,plain,
( empty_set = sF5
| ~ spl6_1 ),
inference(resolution,[],[f118,f85]) ).
fof(f85,plain,
! [X1] :
( ~ subset(X1,empty_set)
| empty_set = X1 ),
inference(resolution,[],[f49,f77]) ).
fof(f77,plain,
! [X0] : subset(empty_set,X0),
inference(resolution,[],[f42,f55]) ).
fof(f55,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] : ~ member(X0,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set_defn) ).
fof(f42,plain,
! [X0,X1] :
( member(sK1(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f26,plain,
! [X0,X1] :
( ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) )
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ( ~ member(sK1(X0,X1),X1)
& member(sK1(X0,X1),X0) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f24,f25]) ).
fof(f25,plain,
! [X0,X1] :
( ? [X3] :
( ~ member(X3,X1)
& member(X3,X0) )
=> ( ~ member(sK1(X0,X1),X1)
& member(sK1(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f24,plain,
! [X0,X1] :
( ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) )
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ? [X3] :
( ~ member(X3,X1)
& member(X3,X0) ) ) ),
inference(rectify,[],[f23]) ).
fof(f23,plain,
! [X0,X1] :
( ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) )
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) ) ),
inference(nnf_transformation,[],[f15]) ).
fof(f15,plain,
! [X0,X1] :
( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) )
<=> subset(X0,X1) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X1,X0] :
( ! [X2] :
( member(X2,X0)
=> member(X2,X1) )
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
fof(f49,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| X0 = X1
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f32]) ).
fof(f32,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 ) ),
inference(rectify,[],[f31]) ).
fof(f31,plain,
! [X1,X0] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(flattening,[],[f30]) ).
fof(f30,plain,
! [X1,X0] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f11,plain,
! [X1,X0] :
( X0 = X1
<=> ( subset(X0,X1)
& subset(X1,X0) ) ),
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X1,X0] :
( X0 = X1
<=> ( subset(X0,X1)
& subset(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
fof(f118,plain,
( ! [X0] : subset(sF5,X0)
| ~ spl6_1 ),
inference(subsumption_resolution,[],[f116,f112]) ).
fof(f112,plain,
! [X0] :
( ~ member(sK1(sF5,X0),sK3)
| subset(sF5,X0) ),
inference(resolution,[],[f75,f42]) ).
fof(f75,plain,
! [X0] :
( ~ member(X0,sF5)
| ~ member(X0,sK3) ),
inference(superposition,[],[f38,f60]) ).
fof(f60,plain,
difference(sK2,sK3) = sF5,
introduced(function_definition,[]) ).
fof(f38,plain,
! [X2,X0,X1] :
( ~ member(X1,difference(X2,X0))
| ~ member(X1,X0) ),
inference(cnf_transformation,[],[f18]) ).
fof(f18,plain,
! [X0,X1,X2] :
( ( member(X1,difference(X2,X0))
| member(X1,X0)
| ~ member(X1,X2) )
& ( ( ~ member(X1,X0)
& member(X1,X2) )
| ~ member(X1,difference(X2,X0)) ) ),
inference(flattening,[],[f17]) ).
fof(f17,plain,
! [X0,X1,X2] :
( ( member(X1,difference(X2,X0))
| member(X1,X0)
| ~ member(X1,X2) )
& ( ( ~ member(X1,X0)
& member(X1,X2) )
| ~ member(X1,difference(X2,X0)) ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f12,plain,
! [X0,X1,X2] :
( member(X1,difference(X2,X0))
<=> ( ~ member(X1,X0)
& member(X1,X2) ) ),
inference(rectify,[],[f2]) ).
fof(f2,axiom,
! [X1,X2,X0] :
( member(X2,difference(X0,X1))
<=> ( ~ member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_defn) ).
fof(f116,plain,
( ! [X0] :
( subset(sF5,X0)
| member(sK1(sF5,X0),sK3) )
| ~ spl6_1 ),
inference(resolution,[],[f111,f100]) ).
fof(f100,plain,
( ! [X0] :
( ~ member(X0,sK2)
| member(X0,sK3) )
| ~ spl6_1 ),
inference(resolution,[],[f65,f44]) ).
fof(f44,plain,
! [X2,X0,X1] :
( ~ subset(X0,X1)
| member(X2,X1)
| ~ member(X2,X0) ),
inference(cnf_transformation,[],[f26]) ).
fof(f65,plain,
( subset(sK2,sK3)
| ~ spl6_1 ),
inference(avatar_component_clause,[],[f64]) ).
fof(f64,plain,
( spl6_1
<=> subset(sK2,sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_1])]) ).
fof(f111,plain,
! [X0] :
( member(sK1(sF5,X0),sK2)
| subset(sF5,X0) ),
inference(resolution,[],[f73,f42]) ).
fof(f73,plain,
! [X0] :
( ~ member(X0,sF5)
| member(X0,sK2) ),
inference(superposition,[],[f37,f60]) ).
fof(f37,plain,
! [X2,X0,X1] :
( ~ member(X1,difference(X2,X0))
| member(X1,X2) ),
inference(cnf_transformation,[],[f18]) ).
fof(f98,plain,
( spl6_1
| ~ spl6_2 ),
inference(avatar_contradiction_clause,[],[f97]) ).
fof(f97,plain,
( $false
| spl6_1
| ~ spl6_2 ),
inference(subsumption_resolution,[],[f96,f66]) ).
fof(f66,plain,
( ~ subset(sK2,sK3)
| spl6_1 ),
inference(avatar_component_clause,[],[f64]) ).
fof(f96,plain,
( subset(sK2,sK3)
| ~ spl6_2 ),
inference(duplicate_literal_removal,[],[f95]) ).
fof(f95,plain,
( subset(sK2,sK3)
| subset(sK2,sK3)
| ~ spl6_2 ),
inference(resolution,[],[f94,f43]) ).
fof(f43,plain,
! [X0,X1] :
( ~ member(sK1(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f94,plain,
( ! [X0] :
( member(sK1(sK2,X0),sK3)
| subset(sK2,X0) )
| ~ spl6_2 ),
inference(resolution,[],[f93,f42]) ).
fof(f93,plain,
( ! [X0] :
( ~ member(X0,sK2)
| member(X0,sK3) )
| ~ spl6_2 ),
inference(subsumption_resolution,[],[f92,f55]) ).
fof(f92,plain,
( ! [X0] :
( member(X0,sK3)
| member(X0,empty_set)
| ~ member(X0,sK2) )
| ~ spl6_2 ),
inference(forward_demodulation,[],[f91,f69]) ).
fof(f69,plain,
( empty_set = sF5
| ~ spl6_2 ),
inference(avatar_component_clause,[],[f68]) ).
fof(f91,plain,
! [X0] :
( member(X0,sF5)
| member(X0,sK3)
| ~ member(X0,sK2) ),
inference(superposition,[],[f39,f60]) ).
fof(f39,plain,
! [X2,X0,X1] :
( member(X1,difference(X2,X0))
| member(X1,X0)
| ~ member(X1,X2) ),
inference(cnf_transformation,[],[f18]) ).
fof(f72,plain,
( spl6_1
| spl6_2 ),
inference(avatar_split_clause,[],[f62,f68,f64]) ).
fof(f62,plain,
( empty_set = sF5
| subset(sK2,sK3) ),
inference(definition_folding,[],[f45,f60]) ).
fof(f45,plain,
( subset(sK2,sK3)
| empty_set = difference(sK2,sK3) ),
inference(cnf_transformation,[],[f29]) ).
fof(f29,plain,
( ( ~ subset(sK2,sK3)
| empty_set != difference(sK2,sK3) )
& ( subset(sK2,sK3)
| empty_set = difference(sK2,sK3) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f27,f28]) ).
fof(f28,plain,
( ? [X0,X1] :
( ( ~ subset(X0,X1)
| difference(X0,X1) != empty_set )
& ( subset(X0,X1)
| difference(X0,X1) = empty_set ) )
=> ( ( ~ subset(sK2,sK3)
| empty_set != difference(sK2,sK3) )
& ( subset(sK2,sK3)
| empty_set = difference(sK2,sK3) ) ) ),
introduced(choice_axiom,[]) ).
fof(f27,plain,
? [X0,X1] :
( ( ~ subset(X0,X1)
| difference(X0,X1) != empty_set )
& ( subset(X0,X1)
| difference(X0,X1) = empty_set ) ),
inference(nnf_transformation,[],[f16]) ).
fof(f16,plain,
? [X0,X1] :
( difference(X0,X1) = empty_set
<~> subset(X0,X1) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,negated_conjecture,
~ ! [X1,X0] :
( difference(X0,X1) = empty_set
<=> subset(X0,X1) ),
inference(negated_conjecture,[],[f9]) ).
fof(f9,conjecture,
! [X1,X0] :
( difference(X0,X1) = empty_set
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_difference_empty_set) ).
fof(f71,plain,
( ~ spl6_1
| ~ spl6_2 ),
inference(avatar_split_clause,[],[f61,f68,f64]) ).
fof(f61,plain,
( empty_set != sF5
| ~ subset(sK2,sK3) ),
inference(definition_folding,[],[f46,f60]) ).
fof(f46,plain,
( ~ subset(sK2,sK3)
| empty_set != difference(sK2,sK3) ),
inference(cnf_transformation,[],[f29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET587+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.35 % Computer : n018.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 14:06:55 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.49 % (31508)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.20/0.51 % (31528)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 0.20/0.51 % (31508)Refutation not found, incomplete strategy% (31508)------------------------------
% 0.20/0.51 % (31508)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.51 % (31508)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.51 % (31508)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.51
% 0.20/0.51 % (31508)Memory used [KB]: 5373
% 0.20/0.51 % (31508)Time elapsed: 0.104 s
% 0.20/0.51 % (31508)Instructions burned: 2 (million)
% 0.20/0.51 % (31508)------------------------------
% 0.20/0.51 % (31508)------------------------------
% 0.20/0.52 % (31515)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.52 % (31515)Instruction limit reached!
% 0.20/0.52 % (31515)------------------------------
% 0.20/0.52 % (31515)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.52 % (31515)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.52 % (31515)Termination reason: Unknown
% 0.20/0.52 % (31515)Termination phase: Saturation
% 0.20/0.52
% 0.20/0.52 % (31515)Memory used [KB]: 5373
% 0.20/0.52 % (31515)Time elapsed: 0.110 s
% 0.20/0.52 % (31515)Instructions burned: 3 (million)
% 0.20/0.52 % (31515)------------------------------
% 0.20/0.52 % (31515)------------------------------
% 0.20/0.52 % (31534)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=177:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/177Mi)
% 0.20/0.53 % (31509)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.20/0.53 % (31521)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)
% 0.20/0.53 % (31525)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.20/0.53 % (31510)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)
% 0.20/0.53 % (31511)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.53 % (31529)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)
% 0.20/0.53 % (31512)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)
% 0.20/0.54 % (31507)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=191324:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/191324Mi)
% 0.20/0.54 TRYING [1]
% 0.20/0.54 TRYING [2]
% 0.20/0.54 TRYING [3]
% 0.20/0.54 % (31523)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)
% 0.20/0.54 % (31519)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.20/0.54 TRYING [4]
% 0.20/0.54 % (31524)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 0.20/0.54 % (31526)ott+4_1:1_av=off:bd=off:nwc=5.0:rp=on:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.20/0.54 TRYING [1]
% 0.20/0.54 % (31530)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/467Mi)
% 0.20/0.54 TRYING [2]
% 0.20/0.54 % (31514)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.20/0.54 TRYING [3]
% 0.20/0.54 % (31513)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)
% 0.20/0.54 % (31519)First to succeed.
% 0.20/0.54 % (31517)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.20/0.54 % (31535)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 0.20/0.54 % (31518)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)
% 0.20/0.55 % (31536)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)
% 0.20/0.55 % (31516)ott-1_1:6_av=off:cond=on:fsr=off:nwc=3.0:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.55 % (31531)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 0.20/0.55 % (31519)Refutation found. Thanks to Tanya!
% 0.20/0.55 % SZS status Theorem for theBenchmark
% 0.20/0.55 % SZS output start Proof for theBenchmark
% See solution above
% 1.52/0.55 % (31519)------------------------------
% 1.52/0.55 % (31519)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.52/0.55 % (31519)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.52/0.55 % (31519)Termination reason: Refutation
% 1.52/0.55
% 1.52/0.55 % (31519)Memory used [KB]: 5500
% 1.52/0.55 % (31519)Time elapsed: 0.126 s
% 1.52/0.55 % (31519)Instructions burned: 4 (million)
% 1.52/0.55 % (31519)------------------------------
% 1.52/0.55 % (31519)------------------------------
% 1.52/0.55 % (31506)Success in time 0.191 s
%------------------------------------------------------------------------------