TSTP Solution File: SET162+3 by SnakeForV-SAT---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : SET162+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 : n004.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 18:24:00 EDT 2022
% Result : Theorem 0.20s 0.51s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 44 ( 13 unt; 0 def)
% Number of atoms : 123 ( 19 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 128 ( 49 ~; 46 |; 22 &)
% ( 7 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 71 ( 66 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f169,plain,
$false,
inference(subsumption_resolution,[],[f168,f82]) ).
fof(f82,plain,
~ subset(sF3,sK0),
inference(subsumption_resolution,[],[f81,f56]) ).
fof(f56,plain,
sK0 != sF3,
inference(definition_folding,[],[f35,f55]) ).
fof(f55,plain,
union(sK0,empty_set) = sF3,
introduced(function_definition,[]) ).
fof(f35,plain,
union(sK0,empty_set) != sK0,
inference(cnf_transformation,[],[f19]) ).
fof(f19,plain,
union(sK0,empty_set) != sK0,
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f16,f18]) ).
fof(f18,plain,
( ? [X0] : union(X0,empty_set) != X0
=> union(sK0,empty_set) != sK0 ),
introduced(choice_axiom,[]) ).
fof(f16,plain,
? [X0] : union(X0,empty_set) != X0,
inference(ennf_transformation,[],[f10]) ).
fof(f10,negated_conjecture,
~ ! [X0] : union(X0,empty_set) = X0,
inference(negated_conjecture,[],[f9]) ).
fof(f9,conjecture,
! [X0] : union(X0,empty_set) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_union_empty_set) ).
fof(f81,plain,
( sK0 = sF3
| ~ subset(sF3,sK0) ),
inference(resolution,[],[f80,f45]) ).
fof(f45,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f29]) ).
fof(f29,plain,
! [X0,X1] :
( ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 )
& ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f28]) ).
fof(f28,plain,
! [X1,X0] :
( ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 )
& ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) ) ),
inference(flattening,[],[f27]) ).
fof(f27,plain,
! [X1,X0] :
( ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 )
& ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) ) ),
inference(nnf_transformation,[],[f14]) ).
fof(f14,plain,
! [X1,X0] :
( ( subset(X0,X1)
& subset(X1,X0) )
<=> X0 = X1 ),
inference(rectify,[],[f3]) ).
fof(f3,axiom,
! [X1,X0] :
( ( subset(X0,X1)
& subset(X1,X0) )
<=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
fof(f80,plain,
subset(sK0,sF3),
inference(duplicate_literal_removal,[],[f79]) ).
fof(f79,plain,
( subset(sK0,sF3)
| subset(sK0,sF3) ),
inference(resolution,[],[f70,f50]) ).
fof(f50,plain,
! [X0,X1] :
( ~ member(sK2(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f33,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK2(X0,X1),X1)
& member(sK2(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f31,f32]) ).
fof(f32,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) )
=> ( ~ member(sK2(X0,X1),X1)
& member(sK2(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f31,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f30]) ).
fof(f30,plain,
! [X1,X0] :
( ( subset(X1,X0)
| ? [X2] :
( ~ member(X2,X0)
& member(X2,X1) ) )
& ( ! [X2] :
( member(X2,X0)
| ~ member(X2,X1) )
| ~ subset(X1,X0) ) ),
inference(nnf_transformation,[],[f17]) ).
fof(f17,plain,
! [X1,X0] :
( subset(X1,X0)
<=> ! [X2] :
( member(X2,X0)
| ~ member(X2,X1) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,plain,
! [X0,X1] :
( ! [X2] :
( member(X2,X1)
=> member(X2,X0) )
<=> subset(X1,X0) ),
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X1,X0] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
fof(f70,plain,
! [X1] :
( member(sK2(sK0,X1),sF3)
| subset(sK0,X1) ),
inference(resolution,[],[f49,f61]) ).
fof(f61,plain,
! [X0] :
( ~ member(X0,sK0)
| member(X0,sF3) ),
inference(superposition,[],[f43,f55]) ).
fof(f43,plain,
! [X2,X0,X1] :
( member(X1,union(X2,X0))
| ~ member(X1,X2) ),
inference(cnf_transformation,[],[f26]) ).
fof(f26,plain,
! [X0,X1,X2] :
( ( member(X1,union(X2,X0))
| ( ~ member(X1,X0)
& ~ member(X1,X2) ) )
& ( member(X1,X0)
| member(X1,X2)
| ~ member(X1,union(X2,X0)) ) ),
inference(rectify,[],[f25]) ).
fof(f25,plain,
! [X0,X2,X1] :
( ( member(X2,union(X1,X0))
| ( ~ member(X2,X0)
& ~ member(X2,X1) ) )
& ( member(X2,X0)
| member(X2,X1)
| ~ member(X2,union(X1,X0)) ) ),
inference(flattening,[],[f24]) ).
fof(f24,plain,
! [X0,X2,X1] :
( ( member(X2,union(X1,X0))
| ( ~ member(X2,X0)
& ~ member(X2,X1) ) )
& ( member(X2,X0)
| member(X2,X1)
| ~ member(X2,union(X1,X0)) ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f11,plain,
! [X0,X2,X1] :
( member(X2,union(X1,X0))
<=> ( member(X2,X0)
| member(X2,X1) ) ),
inference(rectify,[],[f1]) ).
fof(f1,axiom,
! [X1,X0,X2] :
( ( member(X2,X0)
| member(X2,X1) )
<=> member(X2,union(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_defn) ).
fof(f49,plain,
! [X0,X1] :
( member(sK2(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f168,plain,
subset(sF3,sK0),
inference(duplicate_literal_removal,[],[f166]) ).
fof(f166,plain,
( subset(sF3,sK0)
| subset(sF3,sK0) ),
inference(resolution,[],[f102,f50]) ).
fof(f102,plain,
! [X1] :
( member(sK2(sF3,X1),sK0)
| subset(sF3,X1) ),
inference(resolution,[],[f93,f49]) ).
fof(f93,plain,
! [X0] :
( ~ member(X0,sF3)
| member(X0,sK0) ),
inference(subsumption_resolution,[],[f89,f36]) ).
fof(f36,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(f89,plain,
! [X0] :
( member(X0,empty_set)
| ~ member(X0,sF3)
| member(X0,sK0) ),
inference(superposition,[],[f42,f55]) ).
fof(f42,plain,
! [X2,X0,X1] :
( ~ member(X1,union(X2,X0))
| member(X1,X2)
| member(X1,X0) ),
inference(cnf_transformation,[],[f26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET162+3 : TPTP v8.1.0. Released v2.2.0.
% 0.13/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.35 % Computer : n004.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 30 13:20:49 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.47 % (4280)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 (2999ds/191324Mi)
% 0.20/0.47 TRYING [1]
% 0.20/0.47 TRYING [2]
% 0.20/0.47 TRYING [3]
% 0.20/0.47 TRYING [4]
% 0.20/0.48 % (4296)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.20/0.49 % (4294)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.20/0.49 TRYING [5]
% 0.20/0.49 % (4288)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.49 % (4288)Instruction limit reached!
% 0.20/0.49 % (4288)------------------------------
% 0.20/0.49 % (4288)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.49 % (4288)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.49 % (4288)Termination reason: Unknown
% 0.20/0.49 % (4288)Termination phase: Clausification
% 0.20/0.49
% 0.20/0.49 % (4288)Memory used [KB]: 895
% 0.20/0.49 % (4288)Time elapsed: 0.002 s
% 0.20/0.49 % (4288)Instructions burned: 2 (million)
% 0.20/0.49 % (4288)------------------------------
% 0.20/0.49 % (4288)------------------------------
% 0.20/0.50 % (4286)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.50 % (4282)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 (2999ds/37Mi)
% 0.20/0.50 TRYING [6]
% 0.20/0.50 % (4307)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 0.20/0.51 % (4304)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 (2999ds/467Mi)
% 0.20/0.51 % (4303)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 (2999ds/498Mi)
% 0.20/0.51 % (4283)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.51 % (4307)First to succeed.
% 0.20/0.51 % (4284)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.51 % (4307)Refutation found. Thanks to Tanya!
% 0.20/0.51 % SZS status Theorem for theBenchmark
% 0.20/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.51 % (4307)------------------------------
% 0.20/0.51 % (4307)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.51 % (4307)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.51 % (4307)Termination reason: Refutation
% 0.20/0.51
% 0.20/0.51 % (4307)Memory used [KB]: 5500
% 0.20/0.51 % (4307)Time elapsed: 0.121 s
% 0.20/0.51 % (4307)Instructions burned: 4 (million)
% 0.20/0.51 % (4307)------------------------------
% 0.20/0.51 % (4307)------------------------------
% 0.20/0.51 % (4277)Success in time 0.159 s
%------------------------------------------------------------------------------