TSTP Solution File: NUM385+1 by SnakeForV-SAT---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : NUM385+1 : TPTP v8.1.0. Released v3.2.0.
% 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 18:04:57 EDT 2022
% Result : Theorem 0.19s 0.53s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 45 ( 15 unt; 0 def)
% Number of atoms : 175 ( 59 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 209 ( 79 ~; 77 |; 40 &)
% ( 6 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 86 ( 73 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f289,plain,
$false,
inference(subsumption_resolution,[],[f288,f278]) ).
fof(f278,plain,
in(sK1,sK0),
inference(subsumption_resolution,[],[f269,f215]) ).
fof(f215,plain,
~ in(sK1,singleton(sK0)),
inference(extensionality_resolution,[],[f170,f109]) ).
fof(f109,plain,
sK1 != sK0,
inference(cnf_transformation,[],[f70]) ).
fof(f70,plain,
( sK1 != sK0
& succ(sK0) = succ(sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f68,f69]) ).
fof(f69,plain,
( ? [X0,X1] :
( X0 != X1
& succ(X0) = succ(X1) )
=> ( sK1 != sK0
& succ(sK0) = succ(sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f68,plain,
? [X0,X1] :
( X0 != X1
& succ(X0) = succ(X1) ),
inference(rectify,[],[f65]) ).
fof(f65,plain,
? [X1,X0] :
( X0 != X1
& succ(X0) = succ(X1) ),
inference(ennf_transformation,[],[f40]) ).
fof(f40,plain,
~ ! [X1,X0] :
( succ(X0) = succ(X1)
=> X0 = X1 ),
inference(rectify,[],[f30]) ).
fof(f30,negated_conjecture,
~ ! [X1,X0] :
( succ(X0) = succ(X1)
=> X0 = X1 ),
inference(negated_conjecture,[],[f29]) ).
fof(f29,conjecture,
! [X1,X0] :
( succ(X0) = succ(X1)
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_ordinal1) ).
fof(f170,plain,
! [X2,X1] :
( ~ in(X2,singleton(X1))
| X1 = X2 ),
inference(equality_resolution,[],[f144]) ).
fof(f144,plain,
! [X2,X0,X1] :
( X1 = X2
| ~ in(X2,X0)
| singleton(X1) != X0 ),
inference(cnf_transformation,[],[f94]) ).
fof(f94,plain,
! [X0,X1] :
( ( ! [X2] :
( ( in(X2,X0)
| X1 != X2 )
& ( X1 = X2
| ~ in(X2,X0) ) )
| singleton(X1) != X0 )
& ( singleton(X1) = X0
| ( ( sK9(X0,X1) != X1
| ~ in(sK9(X0,X1),X0) )
& ( sK9(X0,X1) = X1
| in(sK9(X0,X1),X0) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f92,f93]) ).
fof(f93,plain,
! [X0,X1] :
( ? [X3] :
( ( X1 != X3
| ~ in(X3,X0) )
& ( X1 = X3
| in(X3,X0) ) )
=> ( ( sK9(X0,X1) != X1
| ~ in(sK9(X0,X1),X0) )
& ( sK9(X0,X1) = X1
| in(sK9(X0,X1),X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f92,plain,
! [X0,X1] :
( ( ! [X2] :
( ( in(X2,X0)
| X1 != X2 )
& ( X1 = X2
| ~ in(X2,X0) ) )
| singleton(X1) != X0 )
& ( singleton(X1) = X0
| ? [X3] :
( ( X1 != X3
| ~ in(X3,X0) )
& ( X1 = X3
| in(X3,X0) ) ) ) ),
inference(rectify,[],[f91]) ).
fof(f91,plain,
! [X1,X0] :
( ( ! [X2] :
( ( in(X2,X1)
| X0 != X2 )
& ( X0 = X2
| ~ in(X2,X1) ) )
| singleton(X0) != X1 )
& ( singleton(X0) = X1
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) ) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X1,X0] :
( ! [X2] :
( in(X2,X1)
<=> X0 = X2 )
<=> singleton(X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(f269,plain,
( in(sK1,sK0)
| in(sK1,singleton(sK0)) ),
inference(resolution,[],[f167,f193]) ).
fof(f193,plain,
in(sK1,set_union2(sK0,singleton(sK0))),
inference(superposition,[],[f164,f162]) ).
fof(f162,plain,
set_union2(sK0,singleton(sK0)) = set_union2(sK1,singleton(sK1)),
inference(definition_unfolding,[],[f108,f114,f114]) ).
fof(f114,plain,
! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
inference(cnf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_ordinal1) ).
fof(f108,plain,
succ(sK0) = succ(sK1),
inference(cnf_transformation,[],[f70]) ).
fof(f164,plain,
! [X0] : in(X0,set_union2(X0,singleton(X0))),
inference(definition_unfolding,[],[f161,f114]) ).
fof(f161,plain,
! [X0] : in(X0,succ(X0)),
inference(cnf_transformation,[],[f28]) ).
fof(f28,axiom,
! [X0] : in(X0,succ(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_ordinal1) ).
fof(f167,plain,
! [X3,X0,X1] :
( ~ in(X3,set_union2(X0,X1))
| in(X3,X0)
| in(X3,X1) ),
inference(equality_resolution,[],[f129]) ).
fof(f129,plain,
! [X2,X3,X0,X1] :
( in(X3,X1)
| in(X3,X0)
| ~ in(X3,X2)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f82]) ).
fof(f82,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ( in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) )
& ( in(X3,X1)
| in(X3,X0)
| ~ in(X3,X2) ) )
| set_union2(X0,X1) != X2 )
& ( set_union2(X0,X1) = X2
| ( ( ( ~ in(sK5(X0,X1,X2),X1)
& ~ in(sK5(X0,X1,X2),X0) )
| ~ in(sK5(X0,X1,X2),X2) )
& ( in(sK5(X0,X1,X2),X1)
| in(sK5(X0,X1,X2),X0)
| in(sK5(X0,X1,X2),X2) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f80,f81]) ).
fof(f81,plain,
! [X0,X1,X2] :
( ? [X4] :
( ( ( ~ in(X4,X1)
& ~ in(X4,X0) )
| ~ in(X4,X2) )
& ( in(X4,X1)
| in(X4,X0)
| in(X4,X2) ) )
=> ( ( ( ~ in(sK5(X0,X1,X2),X1)
& ~ in(sK5(X0,X1,X2),X0) )
| ~ in(sK5(X0,X1,X2),X2) )
& ( in(sK5(X0,X1,X2),X1)
| in(sK5(X0,X1,X2),X0)
| in(sK5(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f80,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ( in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) )
& ( in(X3,X1)
| in(X3,X0)
| ~ in(X3,X2) ) )
| set_union2(X0,X1) != X2 )
& ( set_union2(X0,X1) = X2
| ? [X4] :
( ( ( ~ in(X4,X1)
& ~ in(X4,X0) )
| ~ in(X4,X2) )
& ( in(X4,X1)
| in(X4,X0)
| in(X4,X2) ) ) ) ),
inference(rectify,[],[f79]) ).
fof(f79,plain,
! [X2,X0,X1] :
( ( ! [X3] :
( ( in(X3,X1)
| ( ~ in(X3,X0)
& ~ in(X3,X2) ) )
& ( in(X3,X0)
| in(X3,X2)
| ~ in(X3,X1) ) )
| set_union2(X2,X0) != X1 )
& ( set_union2(X2,X0) = X1
| ? [X3] :
( ( ( ~ in(X3,X0)
& ~ in(X3,X2) )
| ~ in(X3,X1) )
& ( in(X3,X0)
| in(X3,X2)
| in(X3,X1) ) ) ) ),
inference(flattening,[],[f78]) ).
fof(f78,plain,
! [X2,X0,X1] :
( ( ! [X3] :
( ( in(X3,X1)
| ( ~ in(X3,X0)
& ~ in(X3,X2) ) )
& ( in(X3,X0)
| in(X3,X2)
| ~ in(X3,X1) ) )
| set_union2(X2,X0) != X1 )
& ( set_union2(X2,X0) = X1
| ? [X3] :
( ( ( ~ in(X3,X0)
& ~ in(X3,X2) )
| ~ in(X3,X1) )
& ( in(X3,X0)
| in(X3,X2)
| in(X3,X1) ) ) ) ),
inference(nnf_transformation,[],[f44]) ).
fof(f44,plain,
! [X2,X0,X1] :
( ! [X3] :
( in(X3,X1)
<=> ( in(X3,X0)
| in(X3,X2) ) )
<=> set_union2(X2,X0) = X1 ),
inference(rectify,[],[f8]) ).
fof(f8,axiom,
! [X1,X2,X0] :
( set_union2(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X0)
| in(X3,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f288,plain,
~ in(sK1,sK0),
inference(resolution,[],[f285,f133]) ).
fof(f133,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ in(X1,X0) ),
inference(cnf_transformation,[],[f84]) ).
fof(f84,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ in(X1,X0) ),
inference(rectify,[],[f66]) ).
fof(f66,plain,
! [X1,X0] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X1,X0] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f285,plain,
in(sK0,sK1),
inference(subsumption_resolution,[],[f284,f164]) ).
fof(f284,plain,
( ~ in(sK0,set_union2(sK0,singleton(sK0)))
| in(sK0,sK1) ),
inference(resolution,[],[f271,f214]) ).
fof(f214,plain,
~ in(sK0,singleton(sK1)),
inference(extensionality_resolution,[],[f170,f109]) ).
fof(f271,plain,
! [X0] :
( in(X0,singleton(sK1))
| in(X0,sK1)
| ~ in(X0,set_union2(sK0,singleton(sK0))) ),
inference(superposition,[],[f167,f162]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM385+1 : TPTP v8.1.0. Released v3.2.0.
% 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
% 0.13/0.34 % Computer : n005.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 30 06:39:48 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.50 % (10364)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.19/0.51 % (10363)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.19/0.51 % (10352)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.19/0.51 % (10370)ott+4_1:1_av=off:bd=off:nwc=5.0:rp=on:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.19/0.51 % (10352)Refutation not found, incomplete strategy% (10352)------------------------------
% 0.19/0.51 % (10352)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.52 % (10374)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)
% 0.19/0.52 % (10352)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.52 % (10357)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)
% 0.19/0.52 % (10374)First to succeed.
% 0.19/0.52 % (10352)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.52
% 0.19/0.52 % (10352)Memory used [KB]: 5500
% 0.19/0.52 % (10352)Time elapsed: 0.117 s
% 0.19/0.52 % (10352)Instructions burned: 6 (million)
% 0.19/0.52 % (10352)------------------------------
% 0.19/0.52 % (10352)------------------------------
% 0.19/0.52 % (10353)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)
% 0.19/0.52 % (10365)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)
% 0.19/0.52 % (10375)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)
% 0.19/0.53 % (10372)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 0.19/0.53 TRYING [1]
% 0.19/0.53 TRYING [2]
% 0.19/0.53 % (10356)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/48Mi)
% 0.19/0.53 % (10355)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.53 % (10353)Also succeeded, but the first one will report.
% 0.19/0.53 % (10374)Refutation found. Thanks to Tanya!
% 0.19/0.53 % SZS status Theorem for theBenchmark
% 0.19/0.53 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.53 % (10374)------------------------------
% 0.19/0.53 % (10374)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.53 % (10374)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.53 % (10374)Termination reason: Refutation
% 0.19/0.53
% 0.19/0.53 % (10374)Memory used [KB]: 1023
% 0.19/0.53 % (10374)Time elapsed: 0.122 s
% 0.19/0.53 % (10374)Instructions burned: 8 (million)
% 0.19/0.53 % (10374)------------------------------
% 0.19/0.53 % (10374)------------------------------
% 0.19/0.53 % (10348)Success in time 0.179 s
%------------------------------------------------------------------------------