TSTP Solution File: SET600+3 by SnakeForV---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---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_uns --cores 0 -t %d %s
% Computer : n002.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 18:21:33 EDT 2022
% Result : Theorem 0.20s 0.49s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 58 ( 3 unt; 0 def)
% Number of atoms : 204 ( 66 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 240 ( 94 ~; 104 |; 30 &)
% ( 9 <=>; 2 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 63 ( 52 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f228,plain,
$false,
inference(avatar_sat_refutation,[],[f66,f71,f72,f96,f210,f226]) ).
fof(f226,plain,
( ~ spl4_1
| ~ spl4_2
| spl4_3 ),
inference(avatar_contradiction_clause,[],[f225]) ).
fof(f225,plain,
( $false
| ~ spl4_1
| ~ spl4_2
| spl4_3 ),
inference(subsumption_resolution,[],[f216,f177]) ).
fof(f177,plain,
( ! [X1] : ~ member(X1,sK0)
| ~ spl4_1 ),
inference(subsumption_resolution,[],[f174,f38]) ).
fof(f38,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0] : ~ member(X0,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set_defn) ).
fof(f174,plain,
( ! [X1] :
( member(X1,empty_set)
| ~ member(X1,sK0) )
| ~ spl4_1 ),
inference(superposition,[],[f46,f61]) ).
fof(f61,plain,
( empty_set = union(sK0,sK1)
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f59]) ).
fof(f59,plain,
( spl4_1
<=> empty_set = union(sK0,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_1])]) ).
fof(f46,plain,
! [X2,X0,X1] :
( member(X2,union(X0,X1))
| ~ member(X2,X0) ),
inference(cnf_transformation,[],[f27]) ).
fof(f27,plain,
! [X0,X1,X2] :
( ( member(X2,union(X0,X1))
| ( ~ member(X2,X0)
& ~ member(X2,X1) ) )
& ( member(X2,X0)
| member(X2,X1)
| ~ member(X2,union(X0,X1)) ) ),
inference(rectify,[],[f26]) ).
fof(f26,plain,
! [X2,X1,X0] :
( ( member(X0,union(X2,X1))
| ( ~ member(X0,X2)
& ~ member(X0,X1) ) )
& ( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X2,X1)) ) ),
inference(flattening,[],[f25]) ).
fof(f25,plain,
! [X2,X1,X0] :
( ( member(X0,union(X2,X1))
| ( ~ member(X0,X2)
& ~ member(X0,X1) ) )
& ( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X2,X1)) ) ),
inference(nnf_transformation,[],[f13]) ).
fof(f13,plain,
! [X2,X1,X0] :
( member(X0,union(X2,X1))
<=> ( member(X0,X2)
| member(X0,X1) ) ),
inference(rectify,[],[f1]) ).
fof(f1,axiom,
! [X2,X1,X0] :
( ( member(X2,X0)
| member(X2,X1) )
<=> member(X2,union(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_defn) ).
fof(f216,plain,
( member(sK2(sK1,sK0),sK0)
| ~ spl4_2
| spl4_3 ),
inference(backward_demodulation,[],[f165,f65]) ).
fof(f65,plain,
( empty_set = sK1
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f63]) ).
fof(f63,plain,
( spl4_2
<=> empty_set = sK1 ),
introduced(avatar_definition,[new_symbols(naming,[spl4_2])]) ).
fof(f165,plain,
( member(sK2(empty_set,sK0),sK0)
| spl4_3 ),
inference(unit_resulting_resolution,[],[f70,f38,f41]) ).
fof(f41,plain,
! [X0,X1] :
( member(sK2(X0,X1),X0)
| X0 = X1
| member(sK2(X0,X1),X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f23,plain,
! [X0,X1] :
( ( X0 = X1
| ( ( ~ member(sK2(X0,X1),X0)
| ~ member(sK2(X0,X1),X1) )
& ( member(sK2(X0,X1),X0)
| member(sK2(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( member(X3,X1)
| ~ member(X3,X0) )
& ( member(X3,X0)
| ~ member(X3,X1) ) )
| X0 != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f21,f22]) ).
fof(f22,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ member(X2,X0)
| ~ member(X2,X1) )
& ( member(X2,X0)
| member(X2,X1) ) )
=> ( ( ~ member(sK2(X0,X1),X0)
| ~ member(sK2(X0,X1),X1) )
& ( member(sK2(X0,X1),X0)
| member(sK2(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f21,plain,
! [X0,X1] :
( ( X0 = X1
| ? [X2] :
( ( ~ member(X2,X0)
| ~ member(X2,X1) )
& ( member(X2,X0)
| member(X2,X1) ) ) )
& ( ! [X3] :
( ( member(X3,X1)
| ~ member(X3,X0) )
& ( member(X3,X0)
| ~ member(X3,X1) ) )
| X0 != X1 ) ),
inference(rectify,[],[f20]) ).
fof(f20,plain,
! [X0,X1] :
( ( X0 = X1
| ? [X2] :
( ( ~ member(X2,X0)
| ~ member(X2,X1) )
& ( member(X2,X0)
| member(X2,X1) ) ) )
& ( ! [X2] :
( ( member(X2,X1)
| ~ member(X2,X0) )
& ( member(X2,X0)
| ~ member(X2,X1) ) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0,X1] :
( X0 = X1
<=> ! [X2] :
( member(X2,X1)
<=> member(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_member_defn) ).
fof(f70,plain,
( empty_set != sK0
| spl4_3 ),
inference(avatar_component_clause,[],[f68]) ).
fof(f68,plain,
( spl4_3
<=> empty_set = sK0 ),
introduced(avatar_definition,[new_symbols(naming,[spl4_3])]) ).
fof(f210,plain,
( ~ spl4_1
| spl4_2 ),
inference(avatar_contradiction_clause,[],[f209]) ).
fof(f209,plain,
( $false
| ~ spl4_1
| spl4_2 ),
inference(subsumption_resolution,[],[f190,f38]) ).
fof(f190,plain,
( member(sK2(sK1,empty_set),empty_set)
| ~ spl4_1
| spl4_2 ),
inference(unit_resulting_resolution,[],[f64,f176,f41]) ).
fof(f176,plain,
( ! [X0] : ~ member(X0,sK1)
| ~ spl4_1 ),
inference(subsumption_resolution,[],[f173,f38]) ).
fof(f173,plain,
( ! [X0] :
( member(X0,empty_set)
| ~ member(X0,sK1) )
| ~ spl4_1 ),
inference(superposition,[],[f45,f61]) ).
fof(f45,plain,
! [X2,X0,X1] :
( ~ member(X2,X1)
| member(X2,union(X0,X1)) ),
inference(cnf_transformation,[],[f27]) ).
fof(f64,plain,
( empty_set != sK1
| spl4_2 ),
inference(avatar_component_clause,[],[f63]) ).
fof(f96,plain,
( spl4_1
| ~ spl4_2
| ~ spl4_3 ),
inference(avatar_contradiction_clause,[],[f95]) ).
fof(f95,plain,
( $false
| spl4_1
| ~ spl4_2
| ~ spl4_3 ),
inference(subsumption_resolution,[],[f91,f81]) ).
fof(f81,plain,
( ! [X0] : ~ member(X0,union(sK0,sK0))
| ~ spl4_3 ),
inference(unit_resulting_resolution,[],[f73,f73,f44]) ).
fof(f44,plain,
! [X2,X0,X1] :
( ~ member(X2,union(X0,X1))
| member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f73,plain,
( ! [X0] : ~ member(X0,sK0)
| ~ spl4_3 ),
inference(backward_demodulation,[],[f38,f69]) ).
fof(f69,plain,
( empty_set = sK0
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f68]) ).
fof(f91,plain,
( member(sK2(sK0,union(sK0,sK0)),union(sK0,sK0))
| spl4_1
| ~ spl4_2
| ~ spl4_3 ),
inference(unit_resulting_resolution,[],[f73,f76,f41]) ).
fof(f76,plain,
( sK0 != union(sK0,sK0)
| spl4_1
| ~ spl4_2
| ~ spl4_3 ),
inference(backward_demodulation,[],[f74,f75]) ).
fof(f75,plain,
( sK0 = sK1
| ~ spl4_2
| ~ spl4_3 ),
inference(forward_demodulation,[],[f65,f69]) ).
fof(f74,plain,
( sK0 != union(sK0,sK1)
| spl4_1
| ~ spl4_3 ),
inference(forward_demodulation,[],[f60,f69]) ).
fof(f60,plain,
( empty_set != union(sK0,sK1)
| spl4_1 ),
inference(avatar_component_clause,[],[f59]) ).
fof(f72,plain,
( spl4_3
| spl4_1 ),
inference(avatar_split_clause,[],[f35,f59,f68]) ).
fof(f35,plain,
( empty_set = union(sK0,sK1)
| empty_set = sK0 ),
inference(cnf_transformation,[],[f19]) ).
fof(f19,plain,
( ( empty_set != union(sK0,sK1)
| empty_set != sK1
| empty_set != sK0 )
& ( empty_set = union(sK0,sK1)
| ( empty_set = sK1
& empty_set = sK0 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f17,f18]) ).
fof(f18,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(sK0,sK1)
| empty_set != sK1
| empty_set != sK0 )
& ( empty_set = union(sK0,sK1)
| ( empty_set = sK1
& empty_set = sK0 ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f17,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(flattening,[],[f16]) ).
fof(f16,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(nnf_transformation,[],[f14]) ).
fof(f14,plain,
? [X0,X1] :
( ( empty_set = X1
& empty_set = X0 )
<~> union(X0,X1) = empty_set ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,negated_conjecture,
~ ! [X1,X0] :
( union(X0,X1) = empty_set
<=> ( empty_set = X1
& empty_set = X0 ) ),
inference(negated_conjecture,[],[f9]) ).
fof(f9,conjecture,
! [X1,X0] :
( union(X0,X1) = empty_set
<=> ( empty_set = X1
& empty_set = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th59) ).
fof(f71,plain,
( ~ spl4_1
| ~ spl4_3
| ~ spl4_2 ),
inference(avatar_split_clause,[],[f37,f63,f68,f59]) ).
fof(f37,plain,
( empty_set != sK1
| empty_set != sK0
| empty_set != union(sK0,sK1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f66,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f36,f63,f59]) ).
fof(f36,plain,
( empty_set = sK1
| empty_set = union(sK0,sK1) ),
inference(cnf_transformation,[],[f19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET600+3 : TPTP v8.1.0. Released v2.2.0.
% 0.06/0.12 % 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 : n002.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 14:16:14 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.20/0.44 % (14051)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)
% 0.20/0.45 % (14043)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)
% 0.20/0.47 % (14051)Refutation not found, incomplete strategy% (14051)------------------------------
% 0.20/0.47 % (14051)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.47 % (14051)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.47 % (14051)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.47
% 0.20/0.47 % (14051)Memory used [KB]: 1535
% 0.20/0.47 % (14051)Time elapsed: 0.065 s
% 0.20/0.47 % (14051)Instructions burned: 7 (million)
% 0.20/0.47 % (14051)------------------------------
% 0.20/0.47 % (14051)------------------------------
% 0.20/0.47 % (14043)Instruction limit reached!
% 0.20/0.47 % (14043)------------------------------
% 0.20/0.47 % (14043)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.48 % (14035)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)
% 0.20/0.48 % (14043)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.48 % (14043)Termination reason: Unknown
% 0.20/0.48 % (14043)Termination phase: Saturation
% 0.20/0.48
% 0.20/0.48 % (14043)Memory used [KB]: 6012
% 0.20/0.48 % (14043)Time elapsed: 0.058 s
% 0.20/0.48 % (14043)Instructions burned: 7 (million)
% 0.20/0.48 % (14043)------------------------------
% 0.20/0.48 % (14043)------------------------------
% 0.20/0.48 % (14035)First to succeed.
% 0.20/0.49 % (14035)Refutation found. Thanks to Tanya!
% 0.20/0.49 % SZS status Theorem for theBenchmark
% 0.20/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.49 % (14035)------------------------------
% 0.20/0.49 % (14035)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.49 % (14035)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.49 % (14035)Termination reason: Refutation
% 0.20/0.49
% 0.20/0.49 % (14035)Memory used [KB]: 6012
% 0.20/0.49 % (14035)Time elapsed: 0.070 s
% 0.20/0.49 % (14035)Instructions burned: 5 (million)
% 0.20/0.49 % (14035)------------------------------
% 0.20/0.49 % (14035)------------------------------
% 0.20/0.49 % (14025)Success in time 0.145 s
%------------------------------------------------------------------------------