TSTP Solution File: SET632+3 by SnakeForV---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SET632+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 18:21:41 EDT 2022
% Result : Theorem 0.20s 0.50s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 12
% Syntax : Number of formulae : 60 ( 11 unt; 0 def)
% Number of atoms : 176 ( 18 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 183 ( 67 ~; 53 |; 47 &)
% ( 9 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 93 ( 73 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f111,plain,
$false,
inference(avatar_sat_refutation,[],[f71,f77,f110]) ).
fof(f110,plain,
spl6_2,
inference(avatar_contradiction_clause,[],[f109]) ).
fof(f109,plain,
( $false
| spl6_2 ),
inference(subsumption_resolution,[],[f106,f90]) ).
fof(f90,plain,
( member(sK4(empty_set,sK2),sK0)
| spl6_2 ),
inference(resolution,[],[f58,f81]) ).
fof(f81,plain,
( member(sK4(empty_set,sK2),sK2)
| spl6_2 ),
inference(resolution,[],[f70,f42]) ).
fof(f42,plain,
! [X0,X1] :
( subset(X1,X0)
| member(sK4(X0,X1),X1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f28,plain,
! [X0,X1] :
( ( ! [X2] :
( ~ member(X2,X1)
| member(X2,X0) )
| ~ subset(X1,X0) )
& ( subset(X1,X0)
| ( member(sK4(X0,X1),X1)
& ~ member(sK4(X0,X1),X0) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f26,f27]) ).
fof(f27,plain,
! [X0,X1] :
( ? [X3] :
( member(X3,X1)
& ~ member(X3,X0) )
=> ( member(sK4(X0,X1),X1)
& ~ member(sK4(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f26,plain,
! [X0,X1] :
( ( ! [X2] :
( ~ member(X2,X1)
| member(X2,X0) )
| ~ subset(X1,X0) )
& ( subset(X1,X0)
| ? [X3] :
( member(X3,X1)
& ~ member(X3,X0) ) ) ),
inference(rectify,[],[f25]) ).
fof(f25,plain,
! [X1,X0] :
( ( ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) )
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ? [X2] :
( member(X2,X0)
& ~ member(X2,X1) ) ) ),
inference(nnf_transformation,[],[f14]) ).
fof(f14,plain,
! [X1,X0] :
( ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) )
<=> subset(X0,X1) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( ! [X2] :
( member(X2,X0)
=> member(X2,X1) )
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
fof(f70,plain,
( ~ subset(sK2,empty_set)
| spl6_2 ),
inference(avatar_component_clause,[],[f68]) ).
fof(f68,plain,
( spl6_2
<=> subset(sK2,empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_2])]) ).
fof(f58,plain,
! [X0] :
( ~ member(X0,sK2)
| member(X0,sK0) ),
inference(resolution,[],[f34,f43]) ).
fof(f43,plain,
! [X2,X0,X1] :
( ~ member(X2,X1)
| member(X2,X0)
| ~ subset(X1,X0) ),
inference(cnf_transformation,[],[f28]) ).
fof(f34,plain,
subset(sK2,sK0),
inference(cnf_transformation,[],[f20]) ).
fof(f20,plain,
( subset(sK2,sK1)
& empty_set != sK2
& subset(sK2,sK0)
& disjoint(sK1,sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f18,f19]) ).
fof(f19,plain,
( ? [X0,X1,X2] :
( subset(X2,X1)
& empty_set != X2
& subset(X2,X0)
& disjoint(X1,X0) )
=> ( subset(sK2,sK1)
& empty_set != sK2
& subset(sK2,sK0)
& disjoint(sK1,sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f18,plain,
? [X0,X1,X2] :
( subset(X2,X1)
& empty_set != X2
& subset(X2,X0)
& disjoint(X1,X0) ),
inference(rectify,[],[f17]) ).
fof(f17,plain,
? [X2,X1,X0] :
( subset(X0,X1)
& empty_set != X0
& subset(X0,X2)
& disjoint(X1,X2) ),
inference(flattening,[],[f16]) ).
fof(f16,plain,
? [X0,X2,X1] :
( empty_set != X0
& subset(X0,X2)
& disjoint(X1,X2)
& subset(X0,X1) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,negated_conjecture,
~ ! [X0,X2,X1] :
( ( subset(X0,X2)
& disjoint(X1,X2)
& subset(X0,X1) )
=> empty_set = X0 ),
inference(negated_conjecture,[],[f9]) ).
fof(f9,conjecture,
! [X0,X2,X1] :
( ( subset(X0,X2)
& disjoint(X1,X2)
& subset(X0,X1) )
=> empty_set = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th114) ).
fof(f106,plain,
( ~ member(sK4(empty_set,sK2),sK0)
| spl6_2 ),
inference(resolution,[],[f73,f98]) ).
fof(f98,plain,
( member(sK4(empty_set,sK2),sK1)
| spl6_2 ),
inference(resolution,[],[f61,f81]) ).
fof(f61,plain,
! [X0] :
( ~ member(X0,sK2)
| member(X0,sK1) ),
inference(resolution,[],[f36,f43]) ).
fof(f36,plain,
subset(sK2,sK1),
inference(cnf_transformation,[],[f20]) ).
fof(f73,plain,
! [X0] :
( ~ member(X0,sK1)
| ~ member(X0,sK0) ),
inference(resolution,[],[f55,f40]) ).
fof(f40,plain,
! [X2,X0,X1] :
( ~ member(X2,X1)
| intersect(X0,X1)
| ~ member(X2,X0) ),
inference(cnf_transformation,[],[f24]) ).
fof(f24,plain,
! [X0,X1] :
( ( intersect(X0,X1)
| ! [X2] :
( ~ member(X2,X0)
| ~ member(X2,X1) ) )
& ( ( member(sK3(X0,X1),X0)
& member(sK3(X0,X1),X1) )
| ~ intersect(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f22,f23]) ).
fof(f23,plain,
! [X0,X1] :
( ? [X3] :
( member(X3,X0)
& member(X3,X1) )
=> ( member(sK3(X0,X1),X0)
& member(sK3(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f22,plain,
! [X0,X1] :
( ( intersect(X0,X1)
| ! [X2] :
( ~ member(X2,X0)
| ~ member(X2,X1) ) )
& ( ? [X3] :
( member(X3,X0)
& member(X3,X1) )
| ~ intersect(X0,X1) ) ),
inference(rectify,[],[f21]) ).
fof(f21,plain,
! [X1,X0] :
( ( intersect(X1,X0)
| ! [X2] :
( ~ member(X2,X1)
| ~ member(X2,X0) ) )
& ( ? [X2] :
( member(X2,X1)
& member(X2,X0) )
| ~ intersect(X1,X0) ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f11,plain,
! [X1,X0] :
( intersect(X1,X0)
<=> ? [X2] :
( member(X2,X1)
& member(X2,X0) ) ),
inference(rectify,[],[f2]) ).
fof(f2,axiom,
! [X1,X0] :
( ? [X2] :
( member(X2,X1)
& member(X2,X0) )
<=> intersect(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersect_defn) ).
fof(f55,plain,
~ intersect(sK1,sK0),
inference(resolution,[],[f33,f37]) ).
fof(f37,plain,
! [X0,X1] :
( ~ intersect(X0,X1)
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f13]) ).
fof(f13,plain,
! [X0,X1] :
( ~ intersect(X0,X1)
| ~ disjoint(X0,X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,plain,
! [X0,X1] :
( disjoint(X0,X1)
=> ~ intersect(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f4]) ).
fof(f4,axiom,
! [X0,X1] :
( disjoint(X0,X1)
<=> ~ intersect(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',disjoint_defn) ).
fof(f33,plain,
disjoint(sK1,sK0),
inference(cnf_transformation,[],[f20]) ).
fof(f77,plain,
spl6_1,
inference(avatar_contradiction_clause,[],[f76]) ).
fof(f76,plain,
( $false
| spl6_1 ),
inference(subsumption_resolution,[],[f74,f44]) ).
fof(f44,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(f74,plain,
( member(sK4(sK2,empty_set),empty_set)
| spl6_1 ),
inference(resolution,[],[f66,f42]) ).
fof(f66,plain,
( ~ subset(empty_set,sK2)
| spl6_1 ),
inference(avatar_component_clause,[],[f64]) ).
fof(f64,plain,
( spl6_1
<=> subset(empty_set,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_1])]) ).
fof(f71,plain,
( ~ spl6_1
| ~ spl6_2 ),
inference(avatar_split_clause,[],[f62,f68,f64]) ).
fof(f62,plain,
( ~ subset(sK2,empty_set)
| ~ subset(empty_set,sK2) ),
inference(resolution,[],[f52,f53]) ).
fof(f53,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| sQ5_eqProxy(X0,X1)
| ~ subset(X1,X0) ),
inference(equality_proxy_replacement,[],[f47,f51]) ).
fof(f51,plain,
! [X0,X1] :
( sQ5_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(equality_proxy_definition,[new_symbols(naming,[sQ5_eqProxy])]) ).
fof(f47,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(cnf_transformation,[],[f31]) ).
fof(f31,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(rectify,[],[f30]) ).
fof(f30,plain,
! [X1,X0] :
( ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 ) ),
inference(flattening,[],[f29]) ).
fof(f29,plain,
! [X1,X0] :
( ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X1,X0] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
fof(f52,plain,
~ sQ5_eqProxy(empty_set,sK2),
inference(equality_proxy_replacement,[],[f35,f51]) ).
fof(f35,plain,
empty_set != sK2,
inference(cnf_transformation,[],[f20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET632+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_uns --cores 0 -t %d %s
% 0.12/0.34 % Computer : n025.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 14:16:30 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.20/0.48 % (2520)lrs+2_1:1_lcm=reverse:lma=on:sos=all:spb=goal_then_units:ss=included:urr=on:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.20/0.49 % (2520)Refutation not found, incomplete strategy% (2520)------------------------------
% 0.20/0.49 % (2520)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.49 % (2536)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)
% 0.20/0.50 % (2528)lrs+10_1:1_drc=off:sp=reverse_frequency:spb=goal:to=lpo:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.20/0.50 % (2515)dis+1002_1:1_aac=none:bd=off:sac=on:sos=on:spb=units:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.20/0.50 % (2528)Instruction limit reached!
% 0.20/0.50 % (2528)------------------------------
% 0.20/0.50 % (2528)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.50 % (2523)lrs+10_1:1_ep=R:lcm=predicate:lma=on:sos=all:spb=goal:ss=included:i=12:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/12Mi)
% 0.20/0.50 % (2536)Refutation not found, incomplete strategy% (2536)------------------------------
% 0.20/0.50 % (2536)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.50 % (2520)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.50 % (2520)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.50 % (2523)First to succeed.
% 0.20/0.50
% 0.20/0.50 % (2520)Memory used [KB]: 6012
% 0.20/0.50 % (2520)Time elapsed: 0.103 s
% 0.20/0.50 % (2520)Instructions burned: 9 (million)
% 0.20/0.50 % (2520)------------------------------
% 0.20/0.50 % (2520)------------------------------
% 0.20/0.50 % (2523)Refutation found. Thanks to Tanya!
% 0.20/0.50 % SZS status Theorem for theBenchmark
% 0.20/0.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.50 % (2523)------------------------------
% 0.20/0.50 % (2523)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.50 % (2523)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.50 % (2523)Termination reason: Refutation
% 0.20/0.50
% 0.20/0.50 % (2523)Memory used [KB]: 5884
% 0.20/0.50 % (2523)Time elapsed: 0.105 s
% 0.20/0.50 % (2523)Instructions burned: 2 (million)
% 0.20/0.50 % (2523)------------------------------
% 0.20/0.50 % (2523)------------------------------
% 0.20/0.50 % (2512)Success in time 0.157 s
%------------------------------------------------------------------------------