TSTP Solution File: SET628+3 by SnakeForV-SAT---1.0
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%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : SET628+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 : n015.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 18:25:09 EDT 2022
% Result : Theorem 0.20s 0.50s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 52 ( 5 unt; 0 def)
% Number of atoms : 168 ( 23 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 182 ( 66 ~; 76 |; 26 &)
% ( 10 <=>; 3 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 68 ( 58 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f116,plain,
$false,
inference(avatar_sat_refutation,[],[f50,f51,f107,f115]) ).
fof(f115,plain,
( ~ spl3_1
| spl3_2 ),
inference(avatar_contradiction_clause,[],[f114]) ).
fof(f114,plain,
( $false
| ~ spl3_1
| spl3_2 ),
inference(subsumption_resolution,[],[f112,f53]) ).
fof(f53,plain,
! [X0] : ~ intersect(empty_set,X0),
inference(resolution,[],[f35,f38]) ).
fof(f38,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(f35,plain,
! [X0,X1] :
( member(sK2(X0,X1),X0)
| ~ intersect(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f25,plain,
! [X0,X1] :
( ( intersect(X0,X1)
| ! [X2] :
( ~ member(X2,X1)
| ~ member(X2,X0) ) )
& ( ( member(sK2(X0,X1),X1)
& member(sK2(X0,X1),X0) )
| ~ intersect(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f23,f24]) ).
fof(f24,plain,
! [X0,X1] :
( ? [X3] :
( member(X3,X1)
& member(X3,X0) )
=> ( member(sK2(X0,X1),X1)
& member(sK2(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f23,plain,
! [X0,X1] :
( ( intersect(X0,X1)
| ! [X2] :
( ~ member(X2,X1)
| ~ member(X2,X0) ) )
& ( ? [X3] :
( member(X3,X1)
& member(X3,X0) )
| ~ intersect(X0,X1) ) ),
inference(rectify,[],[f22]) ).
fof(f22,plain,
! [X0,X1] :
( ( intersect(X0,X1)
| ! [X2] :
( ~ member(X2,X1)
| ~ member(X2,X0) ) )
& ( ? [X2] :
( member(X2,X1)
& member(X2,X0) )
| ~ intersect(X0,X1) ) ),
inference(nnf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( intersect(X0,X1)
<=> ? [X2] :
( member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersect_defn) ).
fof(f112,plain,
( intersect(empty_set,empty_set)
| ~ spl3_1
| spl3_2 ),
inference(backward_demodulation,[],[f45,f111]) ).
fof(f111,plain,
( empty_set = sK0
| spl3_2 ),
inference(resolution,[],[f48,f27]) ).
fof(f27,plain,
! [X0,X1] :
( not_equal(X1,X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f14]) ).
fof(f14,plain,
! [X0,X1] :
( ( not_equal(X1,X0)
| X0 = X1 )
& ( X0 != X1
| ~ not_equal(X1,X0) ) ),
inference(rectify,[],[f13]) ).
fof(f13,plain,
! [X1,X0] :
( ( not_equal(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ not_equal(X0,X1) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X1,X0] :
( not_equal(X0,X1)
<=> X0 != X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_equal_defn) ).
fof(f48,plain,
( ~ not_equal(sK0,empty_set)
| spl3_2 ),
inference(avatar_component_clause,[],[f47]) ).
fof(f47,plain,
( spl3_2
<=> not_equal(sK0,empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).
fof(f45,plain,
( intersect(sK0,sK0)
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f43]) ).
fof(f43,plain,
( spl3_1
<=> intersect(sK0,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).
fof(f107,plain,
( spl3_1
| ~ spl3_2 ),
inference(avatar_contradiction_clause,[],[f106]) ).
fof(f106,plain,
( $false
| spl3_1
| ~ spl3_2 ),
inference(subsumption_resolution,[],[f105,f39]) ).
fof(f39,plain,
! [X1] : ~ not_equal(X1,X1),
inference(equality_resolution,[],[f26]) ).
fof(f26,plain,
! [X0,X1] :
( X0 != X1
| ~ not_equal(X1,X0) ),
inference(cnf_transformation,[],[f14]) ).
fof(f105,plain,
( not_equal(empty_set,empty_set)
| spl3_1
| ~ spl3_2 ),
inference(backward_demodulation,[],[f49,f98]) ).
fof(f98,plain,
( empty_set = sK0
| spl3_1 ),
inference(resolution,[],[f89,f44]) ).
fof(f44,plain,
( ~ intersect(sK0,sK0)
| spl3_1 ),
inference(avatar_component_clause,[],[f43]) ).
fof(f89,plain,
! [X0] :
( intersect(X0,X0)
| empty_set = X0 ),
inference(duplicate_literal_removal,[],[f82]) ).
fof(f82,plain,
! [X0] :
( intersect(X0,X0)
| empty_set = X0
| empty_set = X0 ),
inference(resolution,[],[f72,f61]) ).
fof(f61,plain,
! [X0] :
( member(sK1(X0,empty_set),X0)
| empty_set = X0 ),
inference(resolution,[],[f31,f38]) ).
fof(f31,plain,
! [X0,X1] :
( member(sK1(X0,X1),X1)
| member(sK1(X0,X1),X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f21]) ).
fof(f21,plain,
! [X0,X1] :
( ( ! [X2] :
( ( member(X2,X0)
| ~ member(X2,X1) )
& ( member(X2,X1)
| ~ member(X2,X0) ) )
| X0 != X1 )
& ( X0 = X1
| ( ( ~ member(sK1(X0,X1),X1)
| ~ member(sK1(X0,X1),X0) )
& ( member(sK1(X0,X1),X1)
| member(sK1(X0,X1),X0) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f19,f20]) ).
fof(f20,plain,
! [X0,X1] :
( ? [X3] :
( ( ~ member(X3,X1)
| ~ member(X3,X0) )
& ( member(X3,X1)
| member(X3,X0) ) )
=> ( ( ~ member(sK1(X0,X1),X1)
| ~ member(sK1(X0,X1),X0) )
& ( member(sK1(X0,X1),X1)
| member(sK1(X0,X1),X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f19,plain,
! [X0,X1] :
( ( ! [X2] :
( ( member(X2,X0)
| ~ member(X2,X1) )
& ( member(X2,X1)
| ~ member(X2,X0) ) )
| X0 != X1 )
& ( X0 = X1
| ? [X3] :
( ( ~ member(X3,X1)
| ~ member(X3,X0) )
& ( member(X3,X1)
| member(X3,X0) ) ) ) ),
inference(rectify,[],[f18]) ).
fof(f18,plain,
! [X1,X0] :
( ( ! [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,[],[f9]) ).
fof(f9,plain,
! [X1,X0] :
( ! [X2] :
( member(X2,X1)
<=> member(X2,X0) )
<=> X0 = X1 ),
inference(rectify,[],[f3]) ).
fof(f3,axiom,
! [X1,X0] :
( ! [X2] :
( member(X2,X0)
<=> member(X2,X1) )
<=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_member_defn) ).
fof(f72,plain,
! [X0,X1] :
( ~ member(sK1(X0,empty_set),X1)
| empty_set = X0
| intersect(X1,X0) ),
inference(resolution,[],[f61,f37]) ).
fof(f37,plain,
! [X2,X0,X1] :
( ~ member(X2,X1)
| intersect(X0,X1)
| ~ member(X2,X0) ),
inference(cnf_transformation,[],[f25]) ).
fof(f49,plain,
( not_equal(sK0,empty_set)
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f47]) ).
fof(f51,plain,
( ~ spl3_2
| ~ spl3_1 ),
inference(avatar_split_clause,[],[f30,f43,f47]) ).
fof(f30,plain,
( ~ intersect(sK0,sK0)
| ~ not_equal(sK0,empty_set) ),
inference(cnf_transformation,[],[f17]) ).
fof(f17,plain,
( ( ~ intersect(sK0,sK0)
| ~ not_equal(sK0,empty_set) )
& ( intersect(sK0,sK0)
| not_equal(sK0,empty_set) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f15,f16]) ).
fof(f16,plain,
( ? [X0] :
( ( ~ intersect(X0,X0)
| ~ not_equal(X0,empty_set) )
& ( intersect(X0,X0)
| not_equal(X0,empty_set) ) )
=> ( ( ~ intersect(sK0,sK0)
| ~ not_equal(sK0,empty_set) )
& ( intersect(sK0,sK0)
| not_equal(sK0,empty_set) ) ) ),
introduced(choice_axiom,[]) ).
fof(f15,plain,
? [X0] :
( ( ~ intersect(X0,X0)
| ~ not_equal(X0,empty_set) )
& ( intersect(X0,X0)
| not_equal(X0,empty_set) ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f11,plain,
? [X0] :
( not_equal(X0,empty_set)
<~> intersect(X0,X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,negated_conjecture,
~ ! [X0] :
( intersect(X0,X0)
<=> not_equal(X0,empty_set) ),
inference(negated_conjecture,[],[f7]) ).
fof(f7,conjecture,
! [X0] :
( intersect(X0,X0)
<=> not_equal(X0,empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th110) ).
fof(f50,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f29,f47,f43]) ).
fof(f29,plain,
( not_equal(sK0,empty_set)
| intersect(sK0,sK0) ),
inference(cnf_transformation,[],[f17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET628+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
% 0.14/0.34 % Computer : n015.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 14:18:21 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.20/0.49 % (9165)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/138Mi)
% 0.20/0.49 % (9165)First to succeed.
% 0.20/0.50 % (9173)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 (3000ds/355Mi)
% 0.20/0.50 % (9165)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 % (9165)------------------------------
% 0.20/0.50 % (9165)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.50 % (9165)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.50 % (9165)Termination reason: Refutation
% 0.20/0.50
% 0.20/0.50 % (9165)Memory used [KB]: 5373
% 0.20/0.50 % (9165)Time elapsed: 0.092 s
% 0.20/0.50 % (9165)Instructions burned: 2 (million)
% 0.20/0.50 % (9165)------------------------------
% 0.20/0.50 % (9165)------------------------------
% 0.20/0.50 % (9143)Success in time 0.15 s
%------------------------------------------------------------------------------