TSTP Solution File: SET636+3 by SnakeForV---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SET636+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 : n025.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 18:21:42 EDT 2022
% Result : Theorem 0.21s 0.52s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of formulae : 67 ( 5 unt; 0 def)
% Number of atoms : 216 ( 30 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 243 ( 94 ~; 100 |; 35 &)
% ( 10 <=>; 3 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 98 ( 83 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f235,plain,
$false,
inference(avatar_sat_refutation,[],[f76,f79,f182,f234]) ).
fof(f234,plain,
( spl5_1
| ~ spl5_2 ),
inference(avatar_contradiction_clause,[],[f233]) ).
fof(f233,plain,
( $false
| spl5_1
| ~ spl5_2 ),
inference(subsumption_resolution,[],[f219,f207]) ).
fof(f207,plain,
( member(sK2(sK1,sK0),sK0)
| spl5_1 ),
inference(resolution,[],[f184,f52]) ).
fof(f52,plain,
! [X0,X1] :
( ~ intersect(X0,X1)
| member(sK2(X0,X1),X1) ),
inference(cnf_transformation,[],[f29]) ).
fof(f29,plain,
! [X0,X1] :
( ( ( member(sK2(X0,X1),X1)
& member(sK2(X0,X1),X0) )
| ~ intersect(X0,X1) )
& ( intersect(X0,X1)
| ! [X3] :
( ~ member(X3,X1)
| ~ member(X3,X0) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f27,f28]) ).
fof(f28,plain,
! [X0,X1] :
( ? [X2] :
( member(X2,X1)
& member(X2,X0) )
=> ( member(sK2(X0,X1),X1)
& member(sK2(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f27,plain,
! [X0,X1] :
( ( ? [X2] :
( member(X2,X1)
& member(X2,X0) )
| ~ intersect(X0,X1) )
& ( intersect(X0,X1)
| ! [X3] :
( ~ member(X3,X1)
| ~ member(X3,X0) ) ) ),
inference(rectify,[],[f26]) ).
fof(f26,plain,
! [X0,X1] :
( ( ? [X2] :
( member(X2,X1)
& member(X2,X0) )
| ~ intersect(X0,X1) )
& ( intersect(X0,X1)
| ! [X2] :
( ~ member(X2,X1)
| ~ member(X2,X0) ) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0,X1] :
( ? [X2] :
( member(X2,X1)
& member(X2,X0) )
<=> intersect(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersect_defn) ).
fof(f184,plain,
( intersect(sK1,sK0)
| spl5_1 ),
inference(resolution,[],[f71,f62]) ).
fof(f62,plain,
! [X0,X1] :
( disjoint(X1,X0)
| intersect(X1,X0) ),
inference(cnf_transformation,[],[f39]) ).
fof(f39,plain,
! [X0,X1] :
( ( disjoint(X1,X0)
| intersect(X1,X0) )
& ( ~ intersect(X1,X0)
| ~ disjoint(X1,X0) ) ),
inference(rectify,[],[f38]) ).
fof(f38,plain,
! [X1,X0] :
( ( disjoint(X0,X1)
| intersect(X0,X1) )
& ( ~ intersect(X0,X1)
| ~ disjoint(X0,X1) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X1,X0] :
( disjoint(X0,X1)
<=> ~ intersect(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',disjoint_defn) ).
fof(f71,plain,
( ~ disjoint(sK1,sK0)
| spl5_1 ),
inference(avatar_component_clause,[],[f69]) ).
fof(f69,plain,
( spl5_1
<=> disjoint(sK1,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_1])]) ).
fof(f219,plain,
( ~ member(sK2(sK1,sK0),sK0)
| spl5_1
| ~ spl5_2 ),
inference(unit_resulting_resolution,[],[f205,f196]) ).
fof(f196,plain,
( ! [X2] :
( ~ member(X2,sK1)
| ~ member(X2,sK0) )
| ~ spl5_2 ),
inference(subsumption_resolution,[],[f193,f43]) ).
fof(f43,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] : ~ member(X0,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set_defn) ).
fof(f193,plain,
( ! [X2] :
( ~ member(X2,sK0)
| ~ member(X2,sK1)
| member(X2,empty_set) )
| ~ spl5_2 ),
inference(superposition,[],[f46,f74]) ).
fof(f74,plain,
( empty_set = intersection(sK0,sK1)
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f73]) ).
fof(f73,plain,
( spl5_2
<=> empty_set = intersection(sK0,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_2])]) ).
fof(f46,plain,
! [X2,X0,X1] :
( member(X0,intersection(X2,X1))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f21]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ( member(X0,intersection(X2,X1))
| ~ member(X0,X2)
| ~ member(X0,X1) )
& ( ( member(X0,X2)
& member(X0,X1) )
| ~ member(X0,intersection(X2,X1)) ) ),
inference(rectify,[],[f20]) ).
fof(f20,plain,
! [X2,X0,X1] :
( ( member(X2,intersection(X1,X0))
| ~ member(X2,X1)
| ~ member(X2,X0) )
& ( ( member(X2,X1)
& member(X2,X0) )
| ~ member(X2,intersection(X1,X0)) ) ),
inference(flattening,[],[f19]) ).
fof(f19,plain,
! [X2,X0,X1] :
( ( member(X2,intersection(X1,X0))
| ~ member(X2,X1)
| ~ member(X2,X0) )
& ( ( member(X2,X1)
& member(X2,X0) )
| ~ member(X2,intersection(X1,X0)) ) ),
inference(nnf_transformation,[],[f14]) ).
fof(f14,plain,
! [X2,X0,X1] :
( member(X2,intersection(X1,X0))
<=> ( member(X2,X1)
& member(X2,X0) ) ),
inference(rectify,[],[f1]) ).
fof(f1,axiom,
! [X1,X0,X2] :
( ( member(X2,X0)
& member(X2,X1) )
<=> member(X2,intersection(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_defn) ).
fof(f205,plain,
( member(sK2(sK1,sK0),sK1)
| spl5_1 ),
inference(resolution,[],[f184,f51]) ).
fof(f51,plain,
! [X0,X1] :
( ~ intersect(X0,X1)
| member(sK2(X0,X1),X0) ),
inference(cnf_transformation,[],[f29]) ).
fof(f182,plain,
( ~ spl5_1
| spl5_2 ),
inference(avatar_contradiction_clause,[],[f181]) ).
fof(f181,plain,
( $false
| ~ spl5_1
| spl5_2 ),
inference(subsumption_resolution,[],[f171,f107]) ).
fof(f107,plain,
( member(sK3(empty_set,intersection(sK0,sK1)),sK0)
| spl5_2 ),
inference(resolution,[],[f82,f45]) ).
fof(f45,plain,
! [X2,X0,X1] :
( ~ member(X0,intersection(X2,X1))
| member(X0,X2) ),
inference(cnf_transformation,[],[f21]) ).
fof(f82,plain,
( member(sK3(empty_set,intersection(sK0,sK1)),intersection(sK0,sK1))
| spl5_2 ),
inference(unit_resulting_resolution,[],[f43,f75,f54]) ).
fof(f54,plain,
! [X0,X1] :
( member(sK3(X0,X1),X0)
| member(sK3(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f33]) ).
fof(f33,plain,
! [X0,X1] :
( ( ! [X2] :
( ( member(X2,X1)
| ~ member(X2,X0) )
& ( member(X2,X0)
| ~ member(X2,X1) ) )
| X0 != X1 )
& ( X0 = X1
| ( ( ~ member(sK3(X0,X1),X0)
| ~ member(sK3(X0,X1),X1) )
& ( member(sK3(X0,X1),X0)
| member(sK3(X0,X1),X1) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f31,f32]) ).
fof(f32,plain,
! [X0,X1] :
( ? [X3] :
( ( ~ member(X3,X0)
| ~ member(X3,X1) )
& ( member(X3,X0)
| member(X3,X1) ) )
=> ( ( ~ member(sK3(X0,X1),X0)
| ~ member(sK3(X0,X1),X1) )
& ( member(sK3(X0,X1),X0)
| member(sK3(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f31,plain,
! [X0,X1] :
( ( ! [X2] :
( ( member(X2,X1)
| ~ member(X2,X0) )
& ( member(X2,X0)
| ~ member(X2,X1) ) )
| X0 != X1 )
& ( X0 = X1
| ? [X3] :
( ( ~ member(X3,X0)
| ~ member(X3,X1) )
& ( member(X3,X0)
| member(X3,X1) ) ) ) ),
inference(rectify,[],[f30]) ).
fof(f30,plain,
! [X0,X1] :
( ( ! [X2] :
( ( member(X2,X1)
| ~ member(X2,X0) )
& ( member(X2,X0)
| ~ member(X2,X1) ) )
| X0 != X1 )
& ( X0 = X1
| ? [X2] :
( ( ~ member(X2,X0)
| ~ member(X2,X1) )
& ( member(X2,X0)
| member(X2,X1) ) ) ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0,X1] :
( ! [X2] :
( member(X2,X1)
<=> member(X2,X0) )
<=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_member_defn) ).
fof(f75,plain,
( empty_set != intersection(sK0,sK1)
| spl5_2 ),
inference(avatar_component_clause,[],[f73]) ).
fof(f171,plain,
( ~ member(sK3(empty_set,intersection(sK0,sK1)),sK0)
| ~ spl5_1
| spl5_2 ),
inference(resolution,[],[f106,f86]) ).
fof(f86,plain,
( ! [X0] :
( ~ member(X0,sK1)
| ~ member(X0,sK0) )
| ~ spl5_1 ),
inference(resolution,[],[f81,f50]) ).
fof(f50,plain,
! [X3,X0,X1] :
( intersect(X0,X1)
| ~ member(X3,X0)
| ~ member(X3,X1) ),
inference(cnf_transformation,[],[f29]) ).
fof(f81,plain,
( ~ intersect(sK1,sK0)
| ~ spl5_1 ),
inference(resolution,[],[f70,f61]) ).
fof(f61,plain,
! [X0,X1] :
( ~ disjoint(X1,X0)
| ~ intersect(X1,X0) ),
inference(cnf_transformation,[],[f39]) ).
fof(f70,plain,
( disjoint(sK1,sK0)
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f69]) ).
fof(f106,plain,
( member(sK3(empty_set,intersection(sK0,sK1)),sK1)
| spl5_2 ),
inference(resolution,[],[f82,f44]) ).
fof(f44,plain,
! [X2,X0,X1] :
( ~ member(X0,intersection(X2,X1))
| member(X0,X1) ),
inference(cnf_transformation,[],[f21]) ).
fof(f79,plain,
( spl5_2
| spl5_1 ),
inference(avatar_split_clause,[],[f67,f69,f73]) ).
fof(f67,plain,
( disjoint(sK1,sK0)
| empty_set = intersection(sK0,sK1) ),
inference(forward_demodulation,[],[f47,f42]) ).
fof(f42,plain,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(f47,plain,
( empty_set = intersection(sK1,sK0)
| disjoint(sK1,sK0) ),
inference(cnf_transformation,[],[f25]) ).
fof(f25,plain,
( ( ~ disjoint(sK1,sK0)
| empty_set != intersection(sK1,sK0) )
& ( disjoint(sK1,sK0)
| empty_set = intersection(sK1,sK0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f23,f24]) ).
fof(f24,plain,
( ? [X0,X1] :
( ( ~ disjoint(X1,X0)
| empty_set != intersection(X1,X0) )
& ( disjoint(X1,X0)
| empty_set = intersection(X1,X0) ) )
=> ( ( ~ disjoint(sK1,sK0)
| empty_set != intersection(sK1,sK0) )
& ( disjoint(sK1,sK0)
| empty_set = intersection(sK1,sK0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f23,plain,
? [X0,X1] :
( ( ~ disjoint(X1,X0)
| empty_set != intersection(X1,X0) )
& ( disjoint(X1,X0)
| empty_set = intersection(X1,X0) ) ),
inference(rectify,[],[f22]) ).
fof(f22,plain,
? [X1,X0] :
( ( ~ disjoint(X0,X1)
| intersection(X0,X1) != empty_set )
& ( disjoint(X0,X1)
| intersection(X0,X1) = empty_set ) ),
inference(nnf_transformation,[],[f16]) ).
fof(f16,plain,
? [X1,X0] :
( intersection(X0,X1) = empty_set
<~> disjoint(X0,X1) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,negated_conjecture,
~ ! [X0,X1] :
( intersection(X0,X1) = empty_set
<=> disjoint(X0,X1) ),
inference(negated_conjecture,[],[f12]) ).
fof(f12,conjecture,
! [X0,X1] :
( intersection(X0,X1) = empty_set
<=> disjoint(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th118) ).
fof(f76,plain,
( ~ spl5_1
| ~ spl5_2 ),
inference(avatar_split_clause,[],[f66,f73,f69]) ).
fof(f66,plain,
( empty_set != intersection(sK0,sK1)
| ~ disjoint(sK1,sK0) ),
inference(forward_demodulation,[],[f48,f42]) ).
fof(f48,plain,
( ~ disjoint(sK1,sK0)
| empty_set != intersection(sK1,sK0) ),
inference(cnf_transformation,[],[f25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET636+3 : TPTP v8.1.0. Released v2.2.0.
% 0.04/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.14/0.34 % Computer : n025.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 14:18:00 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.21/0.50 % (7755)dis+21_1:1_av=off:sos=on:sp=frequency:ss=included:to=lpo:i=15:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.21/0.50 % (7763)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)
% 0.21/0.51 % (7756)dis+1010_1:50_awrs=decay:awrsf=128:nwc=10.0:s2pl=no:sp=frequency:ss=axioms:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.21/0.51 % (7755)Refutation not found, incomplete strategy% (7755)------------------------------
% 0.21/0.51 % (7755)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.51 % (7755)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.51 % (7755)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.51
% 0.21/0.51 % (7755)Memory used [KB]: 1407
% 0.21/0.51 % (7755)Time elapsed: 0.106 s
% 0.21/0.51 % (7755)Instructions burned: 2 (million)
% 0.21/0.51 % (7755)------------------------------
% 0.21/0.51 % (7755)------------------------------
% 0.21/0.51 % (7771)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)
% 0.21/0.51 % (7767)fmb+10_1:1_nm=2:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.21/0.51 % (7750)lrs+10_1:1_gsp=on:sd=1:sgt=32:sos=on:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.21/0.52 % (7771)First to succeed.
% 0.21/0.52 % (7768)ott+1010_1:1_sd=2:sos=on:sp=occurrence:ss=axioms:urr=on:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.21/0.52 % (7750)Refutation not found, incomplete strategy% (7750)------------------------------
% 0.21/0.52 % (7750)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.52 % (7750)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.52 % (7750)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.52
% 0.21/0.52 % (7750)Memory used [KB]: 5884
% 0.21/0.52 % (7750)Time elapsed: 0.112 s
% 0.21/0.52 % (7750)Instructions burned: 2 (million)
% 0.21/0.52 % (7750)------------------------------
% 0.21/0.52 % (7750)------------------------------
% 0.21/0.52 % (7773)dis+10_1:1_av=off:sos=on:sp=reverse_arity:ss=included:st=2.0:to=lpo:urr=ec_only:i=45:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/45Mi)
% 0.21/0.52 % (7759)lrs+10_1:1_br=off:sos=on:ss=axioms:st=2.0:urr=on:i=33:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/33Mi)
% 0.21/0.52 % (7771)Refutation found. Thanks to Tanya!
% 0.21/0.52 % SZS status Theorem for theBenchmark
% 0.21/0.52 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.52 % (7771)------------------------------
% 0.21/0.52 % (7771)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.52 % (7771)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.52 % (7771)Termination reason: Refutation
% 0.21/0.52
% 0.21/0.52 % (7771)Memory used [KB]: 6012
% 0.21/0.52 % (7771)Time elapsed: 0.113 s
% 0.21/0.52 % (7771)Instructions burned: 6 (million)
% 0.21/0.52 % (7771)------------------------------
% 0.21/0.52 % (7771)------------------------------
% 0.21/0.52 % (7746)Success in time 0.165 s
%------------------------------------------------------------------------------