TSTP Solution File: NUM412+1 by SnakeForV-SAT---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : NUM412+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 : n025.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 18:05:00 EDT 2022
% Result : Theorem 0.20s 0.53s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 50 ( 11 unt; 0 def)
% Number of atoms : 160 ( 1 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 186 ( 76 ~; 66 |; 27 &)
% ( 3 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 78 ( 67 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f429,plain,
$false,
inference(subsumption_resolution,[],[f428,f236]) ).
fof(f236,plain,
~ transfinite_sequence_of(sF19,sK12),
inference(definition_folding,[],[f202,f235]) ).
fof(f235,plain,
tseq_dom_restriction(sK11,sK13) = sF19,
introduced(function_definition,[]) ).
fof(f202,plain,
~ transfinite_sequence_of(tseq_dom_restriction(sK11,sK13),sK12),
inference(cnf_transformation,[],[f130]) ).
fof(f130,plain,
( ~ transfinite_sequence_of(tseq_dom_restriction(sK11,sK13),sK12)
& ordinal(sK13)
& transfinite_sequence_of(sK11,sK12) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11,sK12,sK13])],[f127,f129,f128]) ).
fof(f128,plain,
( ? [X0,X1] :
( ? [X2] :
( ~ transfinite_sequence_of(tseq_dom_restriction(X0,X2),X1)
& ordinal(X2) )
& transfinite_sequence_of(X0,X1) )
=> ( ? [X2] :
( ~ transfinite_sequence_of(tseq_dom_restriction(sK11,X2),sK12)
& ordinal(X2) )
& transfinite_sequence_of(sK11,sK12) ) ),
introduced(choice_axiom,[]) ).
fof(f129,plain,
( ? [X2] :
( ~ transfinite_sequence_of(tseq_dom_restriction(sK11,X2),sK12)
& ordinal(X2) )
=> ( ~ transfinite_sequence_of(tseq_dom_restriction(sK11,sK13),sK12)
& ordinal(sK13) ) ),
introduced(choice_axiom,[]) ).
fof(f127,plain,
? [X0,X1] :
( ? [X2] :
( ~ transfinite_sequence_of(tseq_dom_restriction(X0,X2),X1)
& ordinal(X2) )
& transfinite_sequence_of(X0,X1) ),
inference(rectify,[],[f71]) ).
fof(f71,plain,
? [X1,X0] :
( ? [X2] :
( ~ transfinite_sequence_of(tseq_dom_restriction(X1,X2),X0)
& ordinal(X2) )
& transfinite_sequence_of(X1,X0) ),
inference(ennf_transformation,[],[f44]) ).
fof(f44,negated_conjecture,
~ ! [X0,X1] :
( transfinite_sequence_of(X1,X0)
=> ! [X2] :
( ordinal(X2)
=> transfinite_sequence_of(tseq_dom_restriction(X1,X2),X0) ) ),
inference(negated_conjecture,[],[f43]) ).
fof(f43,conjecture,
! [X0,X1] :
( transfinite_sequence_of(X1,X0)
=> ! [X2] :
( ordinal(X2)
=> transfinite_sequence_of(tseq_dom_restriction(X1,X2),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_ordinal1) ).
fof(f428,plain,
transfinite_sequence_of(sF19,sK12),
inference(resolution,[],[f423,f200]) ).
fof(f200,plain,
transfinite_sequence_of(sK11,sK12),
inference(cnf_transformation,[],[f130]) ).
fof(f423,plain,
! [X5] :
( ~ transfinite_sequence_of(sK11,X5)
| transfinite_sequence_of(sF19,X5) ),
inference(resolution,[],[f337,f377]) ).
fof(f377,plain,
transfinite_sequence_of(sF19,relation_rng(sK11)),
inference(subsumption_resolution,[],[f376,f288]) ).
fof(f288,plain,
transfinite_sequence(sK11),
inference(resolution,[],[f160,f200]) ).
fof(f160,plain,
! [X0,X1] :
( ~ transfinite_sequence_of(X1,X0)
| transfinite_sequence(X1) ),
inference(cnf_transformation,[],[f102]) ).
fof(f102,plain,
! [X0,X1] :
( ~ transfinite_sequence_of(X1,X0)
| ( function(X1)
& transfinite_sequence(X1)
& relation(X1) ) ),
inference(rectify,[],[f70]) ).
fof(f70,plain,
! [X1,X0] :
( ~ transfinite_sequence_of(X0,X1)
| ( function(X0)
& transfinite_sequence(X0)
& relation(X0) ) ),
inference(ennf_transformation,[],[f54]) ).
fof(f54,plain,
! [X1,X0] :
( transfinite_sequence_of(X0,X1)
=> ( function(X0)
& transfinite_sequence(X0)
& relation(X0) ) ),
inference(rectify,[],[f11]) ).
fof(f11,axiom,
! [X1,X0] :
( transfinite_sequence_of(X1,X0)
=> ( function(X1)
& relation(X1)
& transfinite_sequence(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_ordinal1) ).
fof(f376,plain,
( ~ transfinite_sequence(sK11)
| transfinite_sequence_of(sF19,relation_rng(sK11)) ),
inference(subsumption_resolution,[],[f375,f201]) ).
fof(f201,plain,
ordinal(sK13),
inference(cnf_transformation,[],[f130]) ).
fof(f375,plain,
( ~ ordinal(sK13)
| ~ transfinite_sequence(sK11)
| transfinite_sequence_of(sF19,relation_rng(sK11)) ),
inference(subsumption_resolution,[],[f374,f290]) ).
fof(f290,plain,
function(sK11),
inference(resolution,[],[f161,f200]) ).
fof(f161,plain,
! [X0,X1] :
( ~ transfinite_sequence_of(X1,X0)
| function(X1) ),
inference(cnf_transformation,[],[f102]) ).
fof(f374,plain,
( ~ function(sK11)
| transfinite_sequence_of(sF19,relation_rng(sK11))
| ~ transfinite_sequence(sK11)
| ~ ordinal(sK13) ),
inference(subsumption_resolution,[],[f372,f286]) ).
fof(f286,plain,
relation(sK11),
inference(resolution,[],[f159,f200]) ).
fof(f159,plain,
! [X0,X1] :
( ~ transfinite_sequence_of(X1,X0)
| relation(X1) ),
inference(cnf_transformation,[],[f102]) ).
fof(f372,plain,
( transfinite_sequence_of(sF19,relation_rng(sK11))
| ~ relation(sK11)
| ~ ordinal(sK13)
| ~ transfinite_sequence(sK11)
| ~ function(sK11) ),
inference(superposition,[],[f171,f235]) ).
fof(f171,plain,
! [X0,X1] :
( transfinite_sequence_of(tseq_dom_restriction(X1,X0),relation_rng(X1))
| ~ function(X1)
| ~ ordinal(X0)
| ~ relation(X1)
| ~ transfinite_sequence(X1) ),
inference(cnf_transformation,[],[f111]) ).
fof(f111,plain,
! [X0,X1] :
( ~ transfinite_sequence(X1)
| ~ relation(X1)
| ~ ordinal(X0)
| transfinite_sequence_of(tseq_dom_restriction(X1,X0),relation_rng(X1))
| ~ function(X1) ),
inference(rectify,[],[f98]) ).
fof(f98,plain,
! [X1,X0] :
( ~ transfinite_sequence(X0)
| ~ relation(X0)
| ~ ordinal(X1)
| transfinite_sequence_of(tseq_dom_restriction(X0,X1),relation_rng(X0))
| ~ function(X0) ),
inference(flattening,[],[f97]) ).
fof(f97,plain,
! [X1,X0] :
( transfinite_sequence_of(tseq_dom_restriction(X0,X1),relation_rng(X0))
| ~ ordinal(X1)
| ~ relation(X0)
| ~ transfinite_sequence(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X1,X0] :
( ( ordinal(X1)
& relation(X0)
& transfinite_sequence(X0)
& function(X0) )
=> transfinite_sequence_of(tseq_dom_restriction(X0,X1),relation_rng(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_ordinal1) ).
fof(f337,plain,
! [X2,X3,X4] :
( ~ transfinite_sequence_of(X2,relation_rng(X4))
| ~ transfinite_sequence_of(X4,X3)
| transfinite_sequence_of(X2,X3) ),
inference(resolution,[],[f175,f239]) ).
fof(f239,plain,
! [X0,X1] :
( subset(relation_rng(X0),X1)
| ~ transfinite_sequence_of(X0,X1) ),
inference(subsumption_resolution,[],[f238,f161]) ).
fof(f238,plain,
! [X0,X1] :
( ~ function(X0)
| ~ transfinite_sequence_of(X0,X1)
| subset(relation_rng(X0),X1) ),
inference(subsumption_resolution,[],[f237,f159]) ).
fof(f237,plain,
! [X0,X1] :
( ~ function(X0)
| ~ transfinite_sequence_of(X0,X1)
| ~ relation(X0)
| subset(relation_rng(X0),X1) ),
inference(subsumption_resolution,[],[f173,f160]) ).
fof(f173,plain,
! [X0,X1] :
( ~ transfinite_sequence(X0)
| ~ function(X0)
| ~ relation(X0)
| subset(relation_rng(X0),X1)
| ~ transfinite_sequence_of(X0,X1) ),
inference(cnf_transformation,[],[f115]) ).
fof(f115,plain,
! [X0,X1] :
( ( ( transfinite_sequence_of(X0,X1)
| ~ subset(relation_rng(X0),X1) )
& ( subset(relation_rng(X0),X1)
| ~ transfinite_sequence_of(X0,X1) ) )
| ~ relation(X0)
| ~ function(X0)
| ~ transfinite_sequence(X0) ),
inference(rectify,[],[f114]) ).
fof(f114,plain,
! [X1,X0] :
( ( ( transfinite_sequence_of(X1,X0)
| ~ subset(relation_rng(X1),X0) )
& ( subset(relation_rng(X1),X0)
| ~ transfinite_sequence_of(X1,X0) ) )
| ~ relation(X1)
| ~ function(X1)
| ~ transfinite_sequence(X1) ),
inference(nnf_transformation,[],[f84]) ).
fof(f84,plain,
! [X1,X0] :
( ( transfinite_sequence_of(X1,X0)
<=> subset(relation_rng(X1),X0) )
| ~ relation(X1)
| ~ function(X1)
| ~ transfinite_sequence(X1) ),
inference(flattening,[],[f83]) ).
fof(f83,plain,
! [X0,X1] :
( ( transfinite_sequence_of(X1,X0)
<=> subset(relation_rng(X1),X0) )
| ~ relation(X1)
| ~ transfinite_sequence(X1)
| ~ function(X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0,X1] :
( ( relation(X1)
& transfinite_sequence(X1)
& function(X1) )
=> ( transfinite_sequence_of(X1,X0)
<=> subset(relation_rng(X1),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_ordinal1) ).
fof(f175,plain,
! [X2,X0,X1] :
( ~ subset(X0,X1)
| transfinite_sequence_of(X2,X1)
| ~ transfinite_sequence_of(X2,X0) ),
inference(cnf_transformation,[],[f116]) ).
fof(f116,plain,
! [X0,X1] :
( ! [X2] :
( ~ transfinite_sequence_of(X2,X0)
| transfinite_sequence_of(X2,X1) )
| ~ subset(X0,X1) ),
inference(rectify,[],[f88]) ).
fof(f88,plain,
! [X1,X0] :
( ! [X2] :
( ~ transfinite_sequence_of(X2,X1)
| transfinite_sequence_of(X2,X0) )
| ~ subset(X1,X0) ),
inference(ennf_transformation,[],[f55]) ).
fof(f55,plain,
! [X1,X0] :
( subset(X1,X0)
=> ! [X2] :
( transfinite_sequence_of(X2,X1)
=> transfinite_sequence_of(X2,X0) ) ),
inference(rectify,[],[f42]) ).
fof(f42,axiom,
! [X1,X0] :
( subset(X0,X1)
=> ! [X2] :
( transfinite_sequence_of(X2,X0)
=> transfinite_sequence_of(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_ordinal1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM412+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
% 0.13/0.34 % Computer : n025.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 06:38:14 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.52 % (26253)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.20/0.52 % (26261)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.20/0.52 % (26249)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)
% 0.20/0.53 % (26261)First to succeed.
% 0.20/0.53 % (26244)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 % (26248)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)
% 0.20/0.53 TRYING [1]
% 0.20/0.53 TRYING [2]
% 0.20/0.53 % (26244)Refutation not found, incomplete strategy% (26244)------------------------------
% 0.20/0.53 % (26244)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.53 % (26244)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.53 % (26244)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.53
% 0.20/0.53 % (26244)Memory used [KB]: 5500
% 0.20/0.53 % (26244)Time elapsed: 0.131 s
% 0.20/0.53 % (26244)Instructions burned: 4 (million)
% 0.20/0.53 % (26244)------------------------------
% 0.20/0.53 % (26244)------------------------------
% 0.20/0.53 % (26261)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 % (26261)------------------------------
% 0.20/0.53 % (26261)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.53 % (26261)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.53 % (26261)Termination reason: Refutation
% 0.20/0.53
% 0.20/0.53 % (26261)Memory used [KB]: 5628
% 0.20/0.53 % (26261)Time elapsed: 0.125 s
% 0.20/0.53 % (26261)Instructions burned: 9 (million)
% 0.20/0.53 % (26261)------------------------------
% 0.20/0.53 % (26261)------------------------------
% 0.20/0.53 % (26242)Success in time 0.18 s
%------------------------------------------------------------------------------