TSTP Solution File: SET637+3 by SnakeForV-SAT---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : SET637+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 : n005.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 18:25:11 EDT 2022
% Result : Theorem 0.18s 0.57s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 10
% Syntax : Number of formulae : 60 ( 12 unt; 0 def)
% Number of atoms : 197 ( 36 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 210 ( 73 ~; 87 |; 34 &)
% ( 12 <=>; 3 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 111 ( 97 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f195,plain,
$false,
inference(subsumption_resolution,[],[f194,f176]) ).
fof(f176,plain,
member(sK0(sK3,sK2),sK2),
inference(resolution,[],[f172,f33]) ).
fof(f33,plain,
! [X0,X1] :
( ~ intersect(X1,X0)
| member(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f20,plain,
! [X0,X1] :
( ( intersect(X1,X0)
| ! [X2] :
( ~ member(X2,X0)
| ~ member(X2,X1) ) )
& ( ( member(sK0(X0,X1),X0)
& member(sK0(X0,X1),X1) )
| ~ intersect(X1,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f18,f19]) ).
fof(f19,plain,
! [X0,X1] :
( ? [X3] :
( member(X3,X0)
& member(X3,X1) )
=> ( member(sK0(X0,X1),X0)
& member(sK0(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f18,plain,
! [X0,X1] :
( ( intersect(X1,X0)
| ! [X2] :
( ~ member(X2,X0)
| ~ member(X2,X1) ) )
& ( ? [X3] :
( member(X3,X0)
& member(X3,X1) )
| ~ intersect(X1,X0) ) ),
inference(rectify,[],[f17]) ).
fof(f17,plain,
! [X0,X1] :
( ( intersect(X1,X0)
| ! [X2] :
( ~ member(X2,X0)
| ~ member(X2,X1) ) )
& ( ? [X2] :
( member(X2,X0)
& member(X2,X1) )
| ~ intersect(X1,X0) ) ),
inference(nnf_transformation,[],[f14]) ).
fof(f14,plain,
! [X0,X1] :
( intersect(X1,X0)
<=> ? [X2] :
( member(X2,X0)
& member(X2,X1) ) ),
inference(rectify,[],[f2]) ).
fof(f2,axiom,
! [X1,X0] :
( intersect(X0,X1)
<=> ? [X2] :
( member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersect_defn) ).
fof(f172,plain,
intersect(sK2,sK3),
inference(subsumption_resolution,[],[f165,f52]) ).
fof(f52,plain,
! [X1] : ~ not_equal(X1,X1),
inference(equality_resolution,[],[f45]) ).
fof(f45,plain,
! [X0,X1] :
( X0 != X1
| ~ not_equal(X1,X0) ),
inference(cnf_transformation,[],[f28]) ).
fof(f28,plain,
! [X0,X1] :
( ( X0 != X1
| ~ not_equal(X1,X0) )
& ( not_equal(X1,X0)
| X0 = X1 ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f12,plain,
! [X0,X1] :
( X0 != X1
<=> not_equal(X1,X0) ),
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X1,X0] :
( X0 != X1
<=> not_equal(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_equal_defn) ).
fof(f165,plain,
( intersect(sK2,sK3)
| not_equal(intersection(sK2,sK3),intersection(sK2,sK3)) ),
inference(backward_demodulation,[],[f46,f164]) ).
fof(f164,plain,
empty_set = intersection(sK2,sK3),
inference(duplicate_literal_removal,[],[f159]) ).
fof(f159,plain,
( empty_set = intersection(sK2,sK3)
| empty_set = intersection(sK2,sK3) ),
inference(resolution,[],[f148,f49]) ).
fof(f49,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(f148,plain,
! [X0] :
( member(sK1(intersection(sK2,sK3),X0),X0)
| empty_set = intersection(sK2,sK3)
| intersection(sK2,sK3) = X0 ),
inference(forward_demodulation,[],[f147,f36]) ).
fof(f36,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/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(f147,plain,
! [X0] :
( intersection(sK2,sK3) = X0
| member(sK1(intersection(sK3,sK2),X0),X0)
| empty_set = intersection(sK2,sK3) ),
inference(forward_demodulation,[],[f145,f36]) ).
fof(f145,plain,
! [X0] :
( empty_set = intersection(sK2,sK3)
| intersection(sK3,sK2) = X0
| member(sK1(intersection(sK3,sK2),X0),X0) ),
inference(duplicate_literal_removal,[],[f139]) ).
fof(f139,plain,
! [X0] :
( member(sK1(intersection(sK3,sK2),X0),X0)
| intersection(sK3,sK2) = X0
| intersection(sK3,sK2) = X0
| member(sK1(intersection(sK3,sK2),X0),X0)
| empty_set = intersection(sK2,sK3) ),
inference(resolution,[],[f131,f69]) ).
fof(f69,plain,
! [X2,X3,X1] :
( member(sK1(intersection(X1,X2),X3),X2)
| member(sK1(intersection(X1,X2),X3),X3)
| intersection(X1,X2) = X3 ),
inference(resolution,[],[f39,f43]) ).
fof(f43,plain,
! [X2,X0,X1] :
( ~ member(X2,intersection(X0,X1))
| member(X2,X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f27,plain,
! [X0,X1,X2] :
( ( ( member(X2,X1)
& member(X2,X0) )
| ~ member(X2,intersection(X0,X1)) )
& ( member(X2,intersection(X0,X1))
| ~ member(X2,X1)
| ~ member(X2,X0) ) ),
inference(rectify,[],[f26]) ).
fof(f26,plain,
! [X2,X0,X1] :
( ( ( member(X1,X0)
& member(X1,X2) )
| ~ member(X1,intersection(X2,X0)) )
& ( member(X1,intersection(X2,X0))
| ~ member(X1,X0)
| ~ member(X1,X2) ) ),
inference(flattening,[],[f25]) ).
fof(f25,plain,
! [X2,X0,X1] :
( ( ( member(X1,X0)
& member(X1,X2) )
| ~ member(X1,intersection(X2,X0)) )
& ( member(X1,intersection(X2,X0))
| ~ member(X1,X0)
| ~ member(X1,X2) ) ),
inference(nnf_transformation,[],[f13]) ).
fof(f13,plain,
! [X2,X0,X1] :
( ( member(X1,X0)
& member(X1,X2) )
<=> member(X1,intersection(X2,X0)) ),
inference(rectify,[],[f1]) ).
fof(f1,axiom,
! [X1,X2,X0] :
( ( member(X2,X0)
& member(X2,X1) )
<=> member(X2,intersection(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_defn) ).
fof(f39,plain,
! [X0,X1] :
( member(sK1(X0,X1),X0)
| member(sK1(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f24]) ).
fof(f24,plain,
! [X0,X1] :
( ( X0 = X1
| ( ( ~ member(sK1(X0,X1),X0)
| ~ member(sK1(X0,X1),X1) )
& ( member(sK1(X0,X1),X0)
| member(sK1(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,[sK1])],[f22,f23]) ).
fof(f23,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ member(X2,X0)
| ~ member(X2,X1) )
& ( member(X2,X0)
| member(X2,X1) ) )
=> ( ( ~ member(sK1(X0,X1),X0)
| ~ member(sK1(X0,X1),X1) )
& ( member(sK1(X0,X1),X0)
| member(sK1(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f22,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,[],[f21]) ).
fof(f21,plain,
! [X1,X0] :
( ( X0 = X1
| ? [X2] :
( ( ~ member(X2,X1)
| ~ member(X2,X0) )
& ( member(X2,X1)
| member(X2,X0) ) ) )
& ( ! [X2] :
( ( member(X2,X0)
| ~ member(X2,X1) )
& ( member(X2,X1)
| ~ member(X2,X0) ) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f11,plain,
! [X1,X0] :
( X0 = X1
<=> ! [X2] :
( member(X2,X0)
<=> member(X2,X1) ) ),
inference(rectify,[],[f4]) ).
fof(f4,axiom,
! [X1,X0] :
( ! [X2] :
( member(X2,X0)
<=> member(X2,X1) )
<=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_member_defn) ).
fof(f131,plain,
! [X0,X1] :
( ~ member(sK1(intersection(sK3,X0),X1),sK2)
| member(sK1(intersection(sK3,X0),X1),X1)
| empty_set = intersection(sK2,sK3)
| intersection(sK3,X0) = X1 ),
inference(superposition,[],[f114,f36]) ).
fof(f114,plain,
! [X19,X20] :
( ~ member(sK1(intersection(X19,sK3),X20),sK2)
| intersection(X19,sK3) = X20
| empty_set = intersection(sK2,sK3)
| member(sK1(intersection(X19,sK3),X20),X20) ),
inference(resolution,[],[f69,f60]) ).
fof(f60,plain,
! [X0] :
( ~ member(X0,sK3)
| empty_set = intersection(sK2,sK3)
| ~ member(X0,sK2) ),
inference(resolution,[],[f35,f54]) ).
fof(f54,plain,
( ~ intersect(sK2,sK3)
| empty_set = intersection(sK2,sK3) ),
inference(resolution,[],[f44,f47]) ).
fof(f47,plain,
( ~ not_equal(intersection(sK2,sK3),empty_set)
| ~ intersect(sK2,sK3) ),
inference(cnf_transformation,[],[f31]) ).
fof(f31,plain,
( ( ~ not_equal(intersection(sK2,sK3),empty_set)
| ~ intersect(sK2,sK3) )
& ( not_equal(intersection(sK2,sK3),empty_set)
| intersect(sK2,sK3) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f29,f30]) ).
fof(f30,plain,
( ? [X0,X1] :
( ( ~ not_equal(intersection(X0,X1),empty_set)
| ~ intersect(X0,X1) )
& ( not_equal(intersection(X0,X1),empty_set)
| intersect(X0,X1) ) )
=> ( ( ~ not_equal(intersection(sK2,sK3),empty_set)
| ~ intersect(sK2,sK3) )
& ( not_equal(intersection(sK2,sK3),empty_set)
| intersect(sK2,sK3) ) ) ),
introduced(choice_axiom,[]) ).
fof(f29,plain,
? [X0,X1] :
( ( ~ not_equal(intersection(X0,X1),empty_set)
| ~ intersect(X0,X1) )
& ( not_equal(intersection(X0,X1),empty_set)
| intersect(X0,X1) ) ),
inference(nnf_transformation,[],[f16]) ).
fof(f16,plain,
? [X0,X1] :
( intersect(X0,X1)
<~> not_equal(intersection(X0,X1),empty_set) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,negated_conjecture,
~ ! [X1,X0] :
( intersect(X0,X1)
<=> not_equal(intersection(X0,X1),empty_set) ),
inference(negated_conjecture,[],[f9]) ).
fof(f9,conjecture,
! [X1,X0] :
( intersect(X0,X1)
<=> not_equal(intersection(X0,X1),empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th119) ).
fof(f44,plain,
! [X0,X1] :
( not_equal(X1,X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f28]) ).
fof(f35,plain,
! [X2,X0,X1] :
( intersect(X1,X0)
| ~ member(X2,X1)
| ~ member(X2,X0) ),
inference(cnf_transformation,[],[f20]) ).
fof(f46,plain,
( not_equal(intersection(sK2,sK3),empty_set)
| intersect(sK2,sK3) ),
inference(cnf_transformation,[],[f31]) ).
fof(f194,plain,
~ member(sK0(sK3,sK2),sK2),
inference(resolution,[],[f178,f175]) ).
fof(f175,plain,
member(sK0(sK3,sK2),sK3),
inference(resolution,[],[f172,f34]) ).
fof(f34,plain,
! [X0,X1] :
( ~ intersect(X1,X0)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f20]) ).
fof(f178,plain,
! [X0] :
( ~ member(X0,sK3)
| ~ member(X0,sK2) ),
inference(resolution,[],[f167,f41]) ).
fof(f41,plain,
! [X2,X0,X1] :
( member(X2,intersection(X0,X1))
| ~ member(X2,X1)
| ~ member(X2,X0) ),
inference(cnf_transformation,[],[f27]) ).
fof(f167,plain,
! [X0] : ~ member(X0,intersection(sK2,sK3)),
inference(backward_demodulation,[],[f49,f164]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET637+3 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.12/0.34 % Computer : n005.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 14:08:48 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.18/0.51 % (23090)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 (3000ds/191324Mi)
% 0.18/0.52 TRYING [1]
% 0.18/0.53 % (23113)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 (3000ds/467Mi)
% 0.18/0.53 TRYING [2]
% 0.18/0.53 TRYING [3]
% 0.18/0.54 % (23105)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/75Mi)
% 0.18/0.54 TRYING [4]
% 0.18/0.54 TRYING [5]
% 0.18/0.55 % (23091)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/50Mi)
% 0.18/0.55 % (23098)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/2Mi)
% 0.18/0.55 % (23112)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 (3000ds/498Mi)
% 0.18/0.55 % (23107)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/59Mi)
% 0.18/0.56 % (23098)Instruction limit reached!
% 0.18/0.56 % (23098)------------------------------
% 0.18/0.56 % (23098)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.56 % (23098)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.56 % (23098)Termination reason: Unknown
% 0.18/0.56 % (23098)Termination phase: Saturation
% 0.18/0.56
% 0.18/0.56 % (23098)Memory used [KB]: 5373
% 0.18/0.56 % (23098)Time elapsed: 0.006 s
% 0.18/0.56 % (23098)Instructions burned: 2 (million)
% 0.18/0.56 % (23098)------------------------------
% 0.18/0.56 % (23098)------------------------------
% 0.18/0.56 % (23091)Refutation not found, incomplete strategy% (23091)------------------------------
% 0.18/0.56 % (23091)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.56 % (23091)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.56 % (23091)Termination reason: Refutation not found, incomplete strategy
% 0.18/0.56
% 0.18/0.56 % (23091)Memory used [KB]: 5373
% 0.18/0.56 % (23091)Time elapsed: 0.111 s
% 0.18/0.56 % (23091)Instructions burned: 2 (million)
% 0.18/0.56 % (23091)------------------------------
% 0.18/0.56 % (23091)------------------------------
% 0.18/0.56 % (23100)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/50Mi)
% 0.18/0.56 % (23115)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/500Mi)
% 0.18/0.57 TRYING [1]
% 0.18/0.57 % (23112)First to succeed.
% 0.18/0.57 % (23092)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/37Mi)
% 0.18/0.57 % (23112)Refutation found. Thanks to Tanya!
% 0.18/0.57 % SZS status Theorem for theBenchmark
% 0.18/0.57 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.57 % (23112)------------------------------
% 0.18/0.57 % (23112)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.57 % (23112)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.57 % (23112)Termination reason: Refutation
% 0.18/0.57
% 0.18/0.57 % (23112)Memory used [KB]: 1023
% 0.18/0.57 % (23112)Time elapsed: 0.147 s
% 0.18/0.57 % (23112)Instructions burned: 9 (million)
% 0.18/0.57 % (23112)------------------------------
% 0.18/0.57 % (23112)------------------------------
% 0.18/0.57 % (23089)Success in time 0.227 s
%------------------------------------------------------------------------------