TSTP Solution File: NUM390+1 by SnakeForV-SAT---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : NUM390+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 : n006.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 18:04:58 EDT 2022
% Result : Theorem 0.20s 0.53s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 14
% Syntax : Number of formulae : 70 ( 17 unt; 3 typ; 0 def)
% Number of atoms : 207 ( 12 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 219 ( 79 ~; 62 |; 56 &)
% ( 3 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 4 ( 0 usr; 3 ari)
% Number of type conns : 6 ( 3 >; 3 *; 0 +; 0 <<)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 98 ( 80 !; 18 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(pred_def_15,type,
sQ17_eqProxy: ( $int * $int ) > $o ).
tff(pred_def_16,type,
sQ18_eqProxy: ( $rat * $rat ) > $o ).
tff(pred_def_17,type,
sQ19_eqProxy: ( $real * $real ) > $o ).
fof(f428,plain,
$false,
inference(subsumption_resolution,[],[f409,f222]) ).
fof(f222,plain,
subset(sK4,sK5),
inference(literal_reordering,[],[f144]) ).
fof(f144,plain,
subset(sK4,sK5),
inference(cnf_transformation,[],[f94]) ).
fof(f94,plain,
( ordinal(sK6)
& ~ in(sK4,sK6)
& in(sK5,sK6)
& subset(sK4,sK5)
& ordinal(sK5)
& epsilon_transitive(sK4) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f69,f93,f92,f91]) ).
fof(f91,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ordinal(X2)
& ~ in(X0,X2)
& in(X1,X2)
& subset(X0,X1) )
& ordinal(X1) )
& epsilon_transitive(X0) )
=> ( ? [X1] :
( ? [X2] :
( ordinal(X2)
& ~ in(sK4,X2)
& in(X1,X2)
& subset(sK4,X1) )
& ordinal(X1) )
& epsilon_transitive(sK4) ) ),
introduced(choice_axiom,[]) ).
fof(f92,plain,
( ? [X1] :
( ? [X2] :
( ordinal(X2)
& ~ in(sK4,X2)
& in(X1,X2)
& subset(sK4,X1) )
& ordinal(X1) )
=> ( ? [X2] :
( ordinal(X2)
& ~ in(sK4,X2)
& in(sK5,X2)
& subset(sK4,sK5) )
& ordinal(sK5) ) ),
introduced(choice_axiom,[]) ).
fof(f93,plain,
( ? [X2] :
( ordinal(X2)
& ~ in(sK4,X2)
& in(sK5,X2)
& subset(sK4,sK5) )
=> ( ordinal(sK6)
& ~ in(sK4,sK6)
& in(sK5,sK6)
& subset(sK4,sK5) ) ),
introduced(choice_axiom,[]) ).
fof(f69,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ordinal(X2)
& ~ in(X0,X2)
& in(X1,X2)
& subset(X0,X1) )
& ordinal(X1) )
& epsilon_transitive(X0) ),
inference(flattening,[],[f68]) ).
fof(f68,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ~ in(X0,X2)
& in(X1,X2)
& subset(X0,X1)
& ordinal(X2) )
& ordinal(X1) )
& epsilon_transitive(X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,negated_conjecture,
~ ! [X0] :
( epsilon_transitive(X0)
=> ! [X1] :
( ordinal(X1)
=> ! [X2] :
( ordinal(X2)
=> ( ( in(X1,X2)
& subset(X0,X1) )
=> in(X0,X2) ) ) ) ),
inference(negated_conjecture,[],[f30]) ).
fof(f30,conjecture,
! [X0] :
( epsilon_transitive(X0)
=> ! [X1] :
( ordinal(X1)
=> ! [X2] :
( ordinal(X2)
=> ( ( in(X1,X2)
& subset(X0,X1) )
=> in(X0,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_ordinal1) ).
fof(f409,plain,
~ subset(sK4,sK5),
inference(backward_demodulation,[],[f292,f403]) ).
fof(f403,plain,
sK4 = sK6,
inference(subsumption_resolution,[],[f402,f218]) ).
fof(f218,plain,
ordinal(sK6),
inference(literal_reordering,[],[f147]) ).
fof(f147,plain,
ordinal(sK6),
inference(cnf_transformation,[],[f94]) ).
fof(f402,plain,
( sK4 = sK6
| ~ ordinal(sK6) ),
inference(subsumption_resolution,[],[f401,f191]) ).
fof(f191,plain,
epsilon_transitive(sK4),
inference(literal_reordering,[],[f142]) ).
fof(f142,plain,
epsilon_transitive(sK4),
inference(cnf_transformation,[],[f94]) ).
fof(f401,plain,
( ~ epsilon_transitive(sK4)
| sK4 = sK6
| ~ ordinal(sK6) ),
inference(subsumption_resolution,[],[f399,f207]) ).
fof(f207,plain,
~ in(sK4,sK6),
inference(literal_reordering,[],[f146]) ).
fof(f146,plain,
~ in(sK4,sK6),
inference(cnf_transformation,[],[f94]) ).
fof(f399,plain,
( in(sK4,sK6)
| ~ epsilon_transitive(sK4)
| ~ ordinal(sK6)
| sK4 = sK6 ),
inference(resolution,[],[f339,f219]) ).
fof(f219,plain,
! [X0,X1] :
( ~ proper_subset(X0,X1)
| ~ epsilon_transitive(X0)
| in(X0,X1)
| ~ ordinal(X1) ),
inference(literal_reordering,[],[f182]) ).
fof(f182,plain,
! [X0,X1] :
( ~ proper_subset(X0,X1)
| ~ epsilon_transitive(X0)
| in(X0,X1)
| ~ ordinal(X1) ),
inference(cnf_transformation,[],[f72]) ).
fof(f72,plain,
! [X0] :
( ~ epsilon_transitive(X0)
| ! [X1] :
( ~ ordinal(X1)
| ~ proper_subset(X0,X1)
| in(X0,X1) ) ),
inference(flattening,[],[f71]) ).
fof(f71,plain,
! [X0] :
( ! [X1] :
( in(X0,X1)
| ~ proper_subset(X0,X1)
| ~ ordinal(X1) )
| ~ epsilon_transitive(X0) ),
inference(ennf_transformation,[],[f29]) ).
fof(f29,axiom,
! [X0] :
( epsilon_transitive(X0)
=> ! [X1] :
( ordinal(X1)
=> ( proper_subset(X0,X1)
=> in(X0,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_ordinal1) ).
fof(f339,plain,
( proper_subset(sK4,sK6)
| sK4 = sK6 ),
inference(resolution,[],[f331,f225]) ).
fof(f225,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| X0 = X1
| proper_subset(X1,X0) ),
inference(literal_reordering,[],[f177]) ).
fof(f177,plain,
! [X0,X1] :
( proper_subset(X1,X0)
| X0 = X1
| ~ subset(X1,X0) ),
inference(cnf_transformation,[],[f117]) ).
fof(f117,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| proper_subset(X1,X0)
| X0 = X1 ),
inference(rectify,[],[f59]) ).
fof(f59,plain,
! [X1,X0] :
( ~ subset(X0,X1)
| proper_subset(X0,X1)
| X0 = X1 ),
inference(flattening,[],[f58]) ).
fof(f58,plain,
! [X1,X0] :
( proper_subset(X0,X1)
| X0 = X1
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f48]) ).
fof(f48,plain,
! [X1,X0] :
( ( X0 != X1
& subset(X0,X1) )
=> proper_subset(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f9]) ).
fof(f9,axiom,
! [X1,X0] :
( ( X0 != X1
& subset(X0,X1) )
<=> proper_subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_xboole_0) ).
fof(f331,plain,
subset(sK4,sK6),
inference(resolution,[],[f315,f310]) ).
fof(f310,plain,
subset(sK5,sK6),
inference(subsumption_resolution,[],[f309,f281]) ).
fof(f281,plain,
epsilon_transitive(sK6),
inference(resolution,[],[f228,f218]) ).
fof(f228,plain,
! [X0] :
( ~ ordinal(X0)
| epsilon_transitive(X0) ),
inference(literal_reordering,[],[f132]) ).
fof(f132,plain,
! [X0] :
( ~ ordinal(X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f70]) ).
fof(f70,plain,
! [X0] :
( ( epsilon_transitive(X0)
& epsilon_connected(X0) )
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] :
( ordinal(X0)
=> ( epsilon_transitive(X0)
& epsilon_connected(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_ordinal1) ).
fof(f309,plain,
( ~ epsilon_transitive(sK6)
| subset(sK5,sK6) ),
inference(resolution,[],[f237,f239]) ).
fof(f239,plain,
in(sK5,sK6),
inference(literal_reordering,[],[f145]) ).
fof(f145,plain,
in(sK5,sK6),
inference(cnf_transformation,[],[f94]) ).
fof(f237,plain,
! [X2,X0] :
( ~ in(X2,X0)
| ~ epsilon_transitive(X0)
| subset(X2,X0) ),
inference(literal_reordering,[],[f178]) ).
fof(f178,plain,
! [X2,X0] :
( ~ epsilon_transitive(X0)
| subset(X2,X0)
| ~ in(X2,X0) ),
inference(cnf_transformation,[],[f121]) ).
fof(f121,plain,
! [X0] :
( ( epsilon_transitive(X0)
| ( ~ subset(sK15(X0),X0)
& in(sK15(X0),X0) ) )
& ( ! [X2] :
( subset(X2,X0)
| ~ in(X2,X0) )
| ~ epsilon_transitive(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15])],[f119,f120]) ).
fof(f120,plain,
! [X0] :
( ? [X1] :
( ~ subset(X1,X0)
& in(X1,X0) )
=> ( ~ subset(sK15(X0),X0)
& in(sK15(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f119,plain,
! [X0] :
( ( epsilon_transitive(X0)
| ? [X1] :
( ~ subset(X1,X0)
& in(X1,X0) ) )
& ( ! [X2] :
( subset(X2,X0)
| ~ in(X2,X0) )
| ~ epsilon_transitive(X0) ) ),
inference(rectify,[],[f118]) ).
fof(f118,plain,
! [X0] :
( ( epsilon_transitive(X0)
| ? [X1] :
( ~ subset(X1,X0)
& in(X1,X0) ) )
& ( ! [X1] :
( subset(X1,X0)
| ~ in(X1,X0) )
| ~ epsilon_transitive(X0) ) ),
inference(nnf_transformation,[],[f65]) ).
fof(f65,plain,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( subset(X1,X0)
| ~ in(X1,X0) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( in(X1,X0)
=> subset(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_ordinal1) ).
fof(f315,plain,
! [X0] :
( ~ subset(sK5,X0)
| subset(sK4,X0) ),
inference(resolution,[],[f240,f222]) ).
fof(f240,plain,
! [X2,X0,X1] :
( ~ subset(X2,X0)
| ~ subset(X0,X1)
| subset(X2,X1) ),
inference(literal_reordering,[],[f176]) ).
fof(f176,plain,
! [X2,X0,X1] :
( ~ subset(X2,X0)
| ~ subset(X0,X1)
| subset(X2,X1) ),
inference(cnf_transformation,[],[f116]) ).
fof(f116,plain,
! [X0,X1,X2] :
( subset(X2,X1)
| ~ subset(X0,X1)
| ~ subset(X2,X0) ),
inference(rectify,[],[f78]) ).
fof(f78,plain,
! [X1,X2,X0] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(flattening,[],[f77]) ).
fof(f77,plain,
! [X1,X0,X2] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f28]) ).
fof(f28,axiom,
! [X1,X0,X2] :
( ( subset(X1,X2)
& subset(X0,X1) )
=> subset(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_xboole_1) ).
fof(f292,plain,
~ subset(sK6,sK5),
inference(resolution,[],[f227,f239]) ).
fof(f227,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ subset(X1,X0) ),
inference(literal_reordering,[],[f181]) ).
fof(f181,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f122]) ).
fof(f122,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ subset(X1,X0) ),
inference(rectify,[],[f63]) ).
fof(f63,plain,
! [X1,X0] :
( ~ in(X1,X0)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f42]) ).
fof(f42,plain,
! [X0,X1] :
~ ( subset(X0,X1)
& in(X1,X0) ),
inference(rectify,[],[f38]) ).
fof(f38,axiom,
! [X1,X0] :
~ ( subset(X1,X0)
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_ordinal1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM390+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % 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 : n006.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 06:27:25 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.20/0.50 % (25343)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)
% 0.20/0.50 % (25335)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)
% 0.20/0.51 % (25327)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)
% 0.20/0.51 TRYING [1]
% 0.20/0.51 TRYING [2]
% 0.20/0.52 TRYING [3]
% 0.20/0.52 TRYING [4]
% 0.20/0.52 % (25335)First to succeed.
% 0.20/0.52 % (25329)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.52 TRYING [5]
% 0.20/0.52 % (25323)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)
% 0.20/0.53 % (25322)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)
% 0.20/0.53 % (25345)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 0.20/0.53 % (25335)Refutation found. Thanks to Tanya!
% 0.20/0.53 % SZS status Theorem for theBenchmark
% 0.20/0.53 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.53 % (25335)------------------------------
% 0.20/0.53 % (25335)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.53 % (25335)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.53 % (25335)Termination reason: Refutation
% 0.20/0.53
% 0.20/0.53 % (25335)Memory used [KB]: 6012
% 0.20/0.53 % (25335)Time elapsed: 0.016 s
% 0.20/0.53 % (25335)Instructions burned: 10 (million)
% 0.20/0.53 % (25335)------------------------------
% 0.20/0.53 % (25335)------------------------------
% 0.20/0.53 % (25320)Success in time 0.177 s
%------------------------------------------------------------------------------