TSTP Solution File: SET600+3 by SnakeForV-SAT---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : SET600+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 : n024.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 18:25:02 EDT 2022
% Result : Theorem 0.20s 0.52s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 11
% Syntax : Number of formulae : 75 ( 5 unt; 0 def)
% Number of atoms : 239 ( 83 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 272 ( 108 ~; 110 |; 37 &)
% ( 12 <=>; 4 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 93 ( 80 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f147,plain,
$false,
inference(avatar_sat_refutation,[],[f72,f77,f78,f121,f134,f146]) ).
fof(f146,plain,
( ~ spl5_1
| spl5_3 ),
inference(avatar_contradiction_clause,[],[f145]) ).
fof(f145,plain,
( $false
| ~ spl5_1
| spl5_3 ),
inference(subsumption_resolution,[],[f144,f75]) ).
fof(f75,plain,
( empty_set != sK3
| spl5_3 ),
inference(avatar_component_clause,[],[f74]) ).
fof(f74,plain,
( spl5_3
<=> empty_set = sK3 ),
introduced(avatar_definition,[new_symbols(naming,[spl5_3])]) ).
fof(f144,plain,
( empty_set = sK3
| ~ spl5_1 ),
inference(resolution,[],[f141,f99]) ).
fof(f99,plain,
! [X1] :
( ~ subset(X1,empty_set)
| empty_set = X1 ),
inference(resolution,[],[f38,f96]) ).
fof(f96,plain,
! [X1] : subset(empty_set,X1),
inference(resolution,[],[f49,f51]) ).
fof(f51,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0] : ~ member(X0,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set_defn) ).
fof(f49,plain,
! [X0,X1] :
( member(sK1(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f31]) ).
fof(f31,plain,
! [X0,X1] :
( ( ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) )
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ( member(sK1(X0,X1),X0)
& ~ member(sK1(X0,X1),X1) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f29,f30]) ).
fof(f30,plain,
! [X0,X1] :
( ? [X3] :
( member(X3,X0)
& ~ member(X3,X1) )
=> ( member(sK1(X0,X1),X0)
& ~ member(sK1(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f29,plain,
! [X0,X1] :
( ( ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) )
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ? [X3] :
( member(X3,X0)
& ~ member(X3,X1) ) ) ),
inference(rectify,[],[f28]) ).
fof(f28,plain,
! [X1,X0] :
( ( ! [X2] :
( ~ member(X2,X1)
| member(X2,X0) )
| ~ subset(X1,X0) )
& ( subset(X1,X0)
| ? [X2] :
( member(X2,X1)
& ~ member(X2,X0) ) ) ),
inference(nnf_transformation,[],[f16]) ).
fof(f16,plain,
! [X1,X0] :
( ! [X2] :
( ~ member(X2,X1)
| member(X2,X0) )
<=> subset(X1,X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,plain,
! [X0,X1] :
( subset(X1,X0)
<=> ! [X2] :
( member(X2,X1)
=> member(X2,X0) ) ),
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X1,X0] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
fof(f38,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| X0 = X1
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f20,plain,
! [X0,X1] :
( ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 )
& ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f19]) ).
fof(f19,plain,
! [X1,X0] :
( ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 )
& ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) ) ),
inference(flattening,[],[f18]) ).
fof(f18,plain,
! [X1,X0] :
( ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 )
& ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X1,X0] :
( ( subset(X0,X1)
& subset(X1,X0) )
<=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
fof(f141,plain,
( ! [X0] : subset(sK3,X0)
| ~ spl5_1 ),
inference(resolution,[],[f136,f49]) ).
fof(f136,plain,
( ! [X0] : ~ member(X0,sK3)
| ~ spl5_1 ),
inference(subsumption_resolution,[],[f135,f51]) ).
fof(f135,plain,
( ! [X0] :
( ~ member(X0,sK3)
| member(X0,empty_set) )
| ~ spl5_1 ),
inference(forward_demodulation,[],[f83,f67]) ).
fof(f67,plain,
( empty_set = sF4
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f65]) ).
fof(f65,plain,
( spl5_1
<=> empty_set = sF4 ),
introduced(avatar_definition,[new_symbols(naming,[spl5_1])]) ).
fof(f83,plain,
! [X0] :
( ~ member(X0,sK3)
| member(X0,sF4) ),
inference(superposition,[],[f45,f60]) ).
fof(f60,plain,
union(sK2,sK3) = sF4,
introduced(function_definition,[]) ).
fof(f45,plain,
! [X2,X0,X1] :
( member(X2,union(X1,X0))
| ~ member(X2,X0) ),
inference(cnf_transformation,[],[f27]) ).
fof(f27,plain,
! [X0,X1,X2] :
( ( member(X2,X1)
| member(X2,X0)
| ~ member(X2,union(X1,X0)) )
& ( member(X2,union(X1,X0))
| ( ~ member(X2,X1)
& ~ member(X2,X0) ) ) ),
inference(rectify,[],[f26]) ).
fof(f26,plain,
! [X2,X0,X1] :
( ( member(X1,X0)
| member(X1,X2)
| ~ member(X1,union(X0,X2)) )
& ( member(X1,union(X0,X2))
| ( ~ member(X1,X0)
& ~ member(X1,X2) ) ) ),
inference(flattening,[],[f25]) ).
fof(f25,plain,
! [X2,X0,X1] :
( ( member(X1,X0)
| member(X1,X2)
| ~ member(X1,union(X0,X2)) )
& ( member(X1,union(X0,X2))
| ( ~ member(X1,X0)
& ~ member(X1,X2) ) ) ),
inference(nnf_transformation,[],[f14]) ).
fof(f14,plain,
! [X2,X0,X1] :
( ( member(X1,X0)
| member(X1,X2) )
<=> member(X1,union(X0,X2)) ),
inference(rectify,[],[f1]) ).
fof(f1,axiom,
! [X0,X2,X1] :
( ( member(X2,X1)
| member(X2,X0) )
<=> member(X2,union(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_defn) ).
fof(f134,plain,
( spl5_2
| ~ spl5_1 ),
inference(avatar_split_clause,[],[f129,f65,f69]) ).
fof(f69,plain,
( spl5_2
<=> empty_set = sK2 ),
introduced(avatar_definition,[new_symbols(naming,[spl5_2])]) ).
fof(f129,plain,
( empty_set = sK2
| ~ spl5_1 ),
inference(resolution,[],[f126,f99]) ).
fof(f126,plain,
( ! [X0] : subset(sK2,X0)
| ~ spl5_1 ),
inference(resolution,[],[f125,f49]) ).
fof(f125,plain,
( ! [X0] : ~ member(X0,sK2)
| ~ spl5_1 ),
inference(subsumption_resolution,[],[f124,f51]) ).
fof(f124,plain,
( ! [X0] :
( member(X0,empty_set)
| ~ member(X0,sK2) )
| ~ spl5_1 ),
inference(forward_demodulation,[],[f88,f67]) ).
fof(f88,plain,
! [X0] :
( member(X0,sF4)
| ~ member(X0,sK2) ),
inference(superposition,[],[f46,f60]) ).
fof(f46,plain,
! [X2,X0,X1] :
( member(X2,union(X1,X0))
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f121,plain,
( spl5_1
| ~ spl5_2
| ~ spl5_3 ),
inference(avatar_contradiction_clause,[],[f120]) ).
fof(f120,plain,
( $false
| spl5_1
| ~ spl5_2
| ~ spl5_3 ),
inference(subsumption_resolution,[],[f119,f66]) ).
fof(f66,plain,
( empty_set != sF4
| spl5_1 ),
inference(avatar_component_clause,[],[f65]) ).
fof(f119,plain,
( empty_set = sF4
| ~ spl5_2
| ~ spl5_3 ),
inference(resolution,[],[f116,f99]) ).
fof(f116,plain,
( ! [X0] : subset(sF4,X0)
| ~ spl5_2
| ~ spl5_3 ),
inference(resolution,[],[f115,f49]) ).
fof(f115,plain,
( ! [X0] : ~ member(X0,sF4)
| ~ spl5_2
| ~ spl5_3 ),
inference(subsumption_resolution,[],[f114,f51]) ).
fof(f114,plain,
( ! [X0] :
( member(X0,empty_set)
| ~ member(X0,sF4) )
| ~ spl5_2
| ~ spl5_3 ),
inference(forward_demodulation,[],[f113,f76]) ).
fof(f76,plain,
( empty_set = sK3
| ~ spl5_3 ),
inference(avatar_component_clause,[],[f74]) ).
fof(f113,plain,
( ! [X0] :
( member(X0,sK3)
| ~ member(X0,sF4) )
| ~ spl5_2 ),
inference(subsumption_resolution,[],[f112,f51]) ).
fof(f112,plain,
( ! [X0] :
( member(X0,empty_set)
| ~ member(X0,sF4)
| member(X0,sK3) )
| ~ spl5_2 ),
inference(forward_demodulation,[],[f107,f71]) ).
fof(f71,plain,
( empty_set = sK2
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f69]) ).
fof(f107,plain,
! [X0] :
( member(X0,sK2)
| member(X0,sK3)
| ~ member(X0,sF4) ),
inference(superposition,[],[f47,f60]) ).
fof(f47,plain,
! [X2,X0,X1] :
( ~ member(X2,union(X1,X0))
| member(X2,X1)
| member(X2,X0) ),
inference(cnf_transformation,[],[f27]) ).
fof(f78,plain,
( ~ spl5_3
| ~ spl5_2
| ~ spl5_1 ),
inference(avatar_split_clause,[],[f61,f65,f69,f74]) ).
fof(f61,plain,
( empty_set != sF4
| empty_set != sK2
| empty_set != sK3 ),
inference(definition_folding,[],[f54,f60]) ).
fof(f54,plain,
( empty_set != union(sK2,sK3)
| empty_set != sK3
| empty_set != sK2 ),
inference(cnf_transformation,[],[f36]) ).
fof(f36,plain,
( ( empty_set != union(sK2,sK3)
| empty_set != sK3
| empty_set != sK2 )
& ( empty_set = union(sK2,sK3)
| ( empty_set = sK3
& empty_set = sK2 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f34,f35]) ).
fof(f35,plain,
( ? [X0,X1] :
( ( union(X0,X1) != empty_set
| empty_set != X1
| empty_set != X0 )
& ( union(X0,X1) = empty_set
| ( empty_set = X1
& empty_set = X0 ) ) )
=> ( ( empty_set != union(sK2,sK3)
| empty_set != sK3
| empty_set != sK2 )
& ( empty_set = union(sK2,sK3)
| ( empty_set = sK3
& empty_set = sK2 ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f34,plain,
? [X0,X1] :
( ( union(X0,X1) != empty_set
| empty_set != X1
| empty_set != X0 )
& ( union(X0,X1) = empty_set
| ( empty_set = X1
& empty_set = X0 ) ) ),
inference(rectify,[],[f33]) ).
fof(f33,plain,
? [X1,X0] :
( ( empty_set != union(X1,X0)
| empty_set != X0
| empty_set != X1 )
& ( empty_set = union(X1,X0)
| ( empty_set = X0
& empty_set = X1 ) ) ),
inference(flattening,[],[f32]) ).
fof(f32,plain,
? [X1,X0] :
( ( empty_set != union(X1,X0)
| empty_set != X0
| empty_set != X1 )
& ( empty_set = union(X1,X0)
| ( empty_set = X0
& empty_set = X1 ) ) ),
inference(nnf_transformation,[],[f17]) ).
fof(f17,plain,
? [X1,X0] :
( ( empty_set = X0
& empty_set = X1 )
<~> empty_set = union(X1,X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,plain,
~ ! [X1,X0] :
( empty_set = union(X1,X0)
<=> ( empty_set = X0
& empty_set = X1 ) ),
inference(rectify,[],[f10]) ).
fof(f10,negated_conjecture,
~ ! [X1,X0] :
( ( empty_set = X1
& empty_set = X0 )
<=> union(X0,X1) = empty_set ),
inference(negated_conjecture,[],[f9]) ).
fof(f9,conjecture,
! [X1,X0] :
( ( empty_set = X1
& empty_set = X0 )
<=> union(X0,X1) = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th59) ).
fof(f77,plain,
( spl5_3
| spl5_1 ),
inference(avatar_split_clause,[],[f62,f65,f74]) ).
fof(f62,plain,
( empty_set = sF4
| empty_set = sK3 ),
inference(definition_folding,[],[f53,f60]) ).
fof(f53,plain,
( empty_set = union(sK2,sK3)
| empty_set = sK3 ),
inference(cnf_transformation,[],[f36]) ).
fof(f72,plain,
( spl5_1
| spl5_2 ),
inference(avatar_split_clause,[],[f63,f69,f65]) ).
fof(f63,plain,
( empty_set = sK2
| empty_set = sF4 ),
inference(definition_folding,[],[f52,f60]) ).
fof(f52,plain,
( empty_set = union(sK2,sK3)
| empty_set = sK2 ),
inference(cnf_transformation,[],[f36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET600+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
% 0.14/0.34 % Computer : n024.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Aug 30 14:06:19 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.20/0.47 % (7808)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)
% 0.20/0.48 TRYING [1]
% 0.20/0.49 TRYING [2]
% 0.20/0.49 TRYING [3]
% 0.20/0.49 TRYING [4]
% 0.20/0.49 TRYING [5]
% 0.20/0.50 % (7832)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 0.20/0.50 % (7824)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)
% 0.20/0.50 % (7821)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.20/0.50 % (7812)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.50 % (7821)First to succeed.
% 0.20/0.50 % (7816)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.50 % (7820)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 % (7816)Instruction limit reached!
% 0.20/0.51 % (7816)------------------------------
% 0.20/0.51 % (7816)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.51 % (7816)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.51 % (7816)Termination reason: Unknown
% 0.20/0.51 % (7816)Termination phase: Saturation
% 0.20/0.51
% 0.20/0.51 % (7816)Memory used [KB]: 5373
% 0.20/0.51 % (7816)Time elapsed: 0.123 s
% 0.20/0.51 % (7816)Instructions burned: 3 (million)
% 0.20/0.51 % (7816)------------------------------
% 0.20/0.51 % (7816)------------------------------
% 0.20/0.51 % (7830)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)
% 0.20/0.51 % (7831)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)
% 0.20/0.51 % (7814)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)
% 0.20/0.51 TRYING [6]
% 0.20/0.52 % (7821)Refutation found. Thanks to Tanya!
% 0.20/0.52 % SZS status Theorem for theBenchmark
% 0.20/0.52 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.52 % (7821)------------------------------
% 0.20/0.52 % (7821)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.52 % (7821)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.52 % (7821)Termination reason: Refutation
% 0.20/0.52
% 0.20/0.52 % (7821)Memory used [KB]: 5500
% 0.20/0.52 % (7821)Time elapsed: 0.097 s
% 0.20/0.52 % (7821)Instructions burned: 4 (million)
% 0.20/0.52 % (7821)------------------------------
% 0.20/0.52 % (7821)------------------------------
% 0.20/0.52 % (7807)Success in time 0.165 s
%------------------------------------------------------------------------------