TSTP Solution File: NUM412+1 by SnakeForV---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---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_uns --cores 0 -t %d %s
% Computer : n029.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 17:59:22 EDT 2022
% Result : Theorem 0.20s 0.50s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 51 ( 13 unt; 0 def)
% Number of atoms : 169 ( 6 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 190 ( 72 ~; 61 |; 34 &)
% ( 4 <=>; 19 =>; 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; 3 con; 0-2 aty)
% Number of variables : 78 ( 70 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f355,plain,
$false,
inference(subsumption_resolution,[],[f350,f333]) ).
fof(f333,plain,
transfinite_sequence_of(relation_dom_restriction(sK7,sK9),relation_rng(sK7)),
inference(forward_demodulation,[],[f316,f322]) ).
fof(f322,plain,
tseq_dom_restriction(sK7,sK9) = relation_dom_restriction(sK7,sK9),
inference(unit_resulting_resolution,[],[f191,f250,f251,f253,f203]) ).
fof(f203,plain,
! [X0,X1] :
( ~ transfinite_sequence(X1)
| tseq_dom_restriction(X1,X0) = relation_dom_restriction(X1,X0)
| ~ ordinal(X0)
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f88]) ).
fof(f88,plain,
! [X0,X1] :
( ~ ordinal(X0)
| ~ transfinite_sequence(X1)
| ~ function(X1)
| ~ relation(X1)
| tseq_dom_restriction(X1,X0) = relation_dom_restriction(X1,X0) ),
inference(flattening,[],[f87]) ).
fof(f87,plain,
! [X0,X1] :
( tseq_dom_restriction(X1,X0) = relation_dom_restriction(X1,X0)
| ~ transfinite_sequence(X1)
| ~ relation(X1)
| ~ ordinal(X0)
| ~ function(X1) ),
inference(ennf_transformation,[],[f58]) ).
fof(f58,plain,
! [X0,X1] :
( ( transfinite_sequence(X1)
& relation(X1)
& ordinal(X0)
& function(X1) )
=> tseq_dom_restriction(X1,X0) = relation_dom_restriction(X1,X0) ),
inference(rectify,[],[f37]) ).
fof(f37,axiom,
! [X1,X0] :
( ( function(X0)
& transfinite_sequence(X0)
& ordinal(X1)
& relation(X0) )
=> tseq_dom_restriction(X0,X1) = relation_dom_restriction(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_ordinal1) ).
fof(f253,plain,
transfinite_sequence(sK7),
inference(resolution,[],[f190,f155]) ).
fof(f155,plain,
! [X0,X1] :
( transfinite_sequence(X0)
| ~ transfinite_sequence_of(X0,X1) ),
inference(cnf_transformation,[],[f107]) ).
fof(f107,plain,
! [X0,X1] :
( ( transfinite_sequence(X0)
& relation(X0)
& function(X0) )
| ~ transfinite_sequence_of(X0,X1) ),
inference(rectify,[],[f81]) ).
fof(f81,plain,
! [X1,X0] :
( ( transfinite_sequence(X1)
& relation(X1)
& function(X1) )
| ~ transfinite_sequence_of(X1,X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X1,X0] :
( transfinite_sequence_of(X1,X0)
=> ( transfinite_sequence(X1)
& relation(X1)
& function(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_ordinal1) ).
fof(f190,plain,
transfinite_sequence_of(sK7,sK8),
inference(cnf_transformation,[],[f128]) ).
fof(f128,plain,
( ~ transfinite_sequence_of(tseq_dom_restriction(sK7,sK9),sK8)
& ordinal(sK9)
& transfinite_sequence_of(sK7,sK8) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9])],[f79,f127,f126]) ).
fof(f126,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(sK7,X2),sK8)
& ordinal(X2) )
& transfinite_sequence_of(sK7,sK8) ) ),
introduced(choice_axiom,[]) ).
fof(f127,plain,
( ? [X2] :
( ~ transfinite_sequence_of(tseq_dom_restriction(sK7,X2),sK8)
& ordinal(X2) )
=> ( ~ transfinite_sequence_of(tseq_dom_restriction(sK7,sK9),sK8)
& ordinal(sK9) ) ),
introduced(choice_axiom,[]) ).
fof(f79,plain,
? [X0,X1] :
( ? [X2] :
( ~ transfinite_sequence_of(tseq_dom_restriction(X0,X2),X1)
& ordinal(X2) )
& transfinite_sequence_of(X0,X1) ),
inference(ennf_transformation,[],[f52]) ).
fof(f52,plain,
~ ! [X0,X1] :
( transfinite_sequence_of(X0,X1)
=> ! [X2] :
( ordinal(X2)
=> transfinite_sequence_of(tseq_dom_restriction(X0,X2),X1) ) ),
inference(rectify,[],[f44]) ).
fof(f44,negated_conjecture,
~ ! [X1,X0] :
( transfinite_sequence_of(X1,X0)
=> ! [X2] :
( ordinal(X2)
=> transfinite_sequence_of(tseq_dom_restriction(X1,X2),X0) ) ),
inference(negated_conjecture,[],[f43]) ).
fof(f43,conjecture,
! [X1,X0] :
( transfinite_sequence_of(X1,X0)
=> ! [X2] :
( ordinal(X2)
=> transfinite_sequence_of(tseq_dom_restriction(X1,X2),X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_ordinal1) ).
fof(f251,plain,
function(sK7),
inference(unit_resulting_resolution,[],[f190,f153]) ).
fof(f153,plain,
! [X0,X1] :
( ~ transfinite_sequence_of(X0,X1)
| function(X0) ),
inference(cnf_transformation,[],[f107]) ).
fof(f250,plain,
relation(sK7),
inference(unit_resulting_resolution,[],[f190,f154]) ).
fof(f154,plain,
! [X0,X1] :
( relation(X0)
| ~ transfinite_sequence_of(X0,X1) ),
inference(cnf_transformation,[],[f107]) ).
fof(f191,plain,
ordinal(sK9),
inference(cnf_transformation,[],[f128]) ).
fof(f316,plain,
transfinite_sequence_of(tseq_dom_restriction(sK7,sK9),relation_rng(sK7)),
inference(unit_resulting_resolution,[],[f191,f251,f250,f253,f165]) ).
fof(f165,plain,
! [X0,X1] :
( ~ ordinal(X0)
| ~ function(X1)
| ~ relation(X1)
| transfinite_sequence_of(tseq_dom_restriction(X1,X0),relation_rng(X1))
| ~ transfinite_sequence(X1) ),
inference(cnf_transformation,[],[f95]) ).
fof(f95,plain,
! [X0,X1] :
( transfinite_sequence_of(tseq_dom_restriction(X1,X0),relation_rng(X1))
| ~ function(X1)
| ~ transfinite_sequence(X1)
| ~ ordinal(X0)
| ~ relation(X1) ),
inference(flattening,[],[f94]) ).
fof(f94,plain,
! [X0,X1] :
( transfinite_sequence_of(tseq_dom_restriction(X1,X0),relation_rng(X1))
| ~ ordinal(X0)
| ~ relation(X1)
| ~ transfinite_sequence(X1)
| ~ function(X1) ),
inference(ennf_transformation,[],[f59]) ).
fof(f59,plain,
! [X0,X1] :
( ( ordinal(X0)
& relation(X1)
& transfinite_sequence(X1)
& function(X1) )
=> transfinite_sequence_of(tseq_dom_restriction(X1,X0),relation_rng(X1)) ),
inference(rectify,[],[f9]) ).
fof(f9,axiom,
! [X1,X0] :
( ( function(X0)
& relation(X0)
& ordinal(X1)
& transfinite_sequence(X0) )
=> transfinite_sequence_of(tseq_dom_restriction(X0,X1),relation_rng(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_ordinal1) ).
fof(f350,plain,
~ transfinite_sequence_of(relation_dom_restriction(sK7,sK9),relation_rng(sK7)),
inference(unit_resulting_resolution,[],[f332,f260,f239]) ).
fof(f239,plain,
! [X2,X0,X1] :
( ~ transfinite_sequence_of(X2,X0)
| transfinite_sequence_of(X2,X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f148]) ).
fof(f148,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| ! [X2] :
( ~ transfinite_sequence_of(X2,X0)
| transfinite_sequence_of(X2,X1) ) ),
inference(rectify,[],[f99]) ).
fof(f99,plain,
! [X1,X0] :
( ~ subset(X1,X0)
| ! [X2] :
( ~ transfinite_sequence_of(X2,X1)
| transfinite_sequence_of(X2,X0) ) ),
inference(ennf_transformation,[],[f61]) ).
fof(f61,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/sandbox/benchmark/theBenchmark.p',t47_ordinal1) ).
fof(f260,plain,
subset(relation_rng(sK7),sK8),
inference(subsumption_resolution,[],[f259,f253]) ).
fof(f259,plain,
( subset(relation_rng(sK7),sK8)
| ~ transfinite_sequence(sK7) ),
inference(subsumption_resolution,[],[f258,f251]) ).
fof(f258,plain,
( ~ function(sK7)
| subset(relation_rng(sK7),sK8)
| ~ transfinite_sequence(sK7) ),
inference(subsumption_resolution,[],[f257,f250]) ).
fof(f257,plain,
( ~ relation(sK7)
| subset(relation_rng(sK7),sK8)
| ~ transfinite_sequence(sK7)
| ~ function(sK7) ),
inference(resolution,[],[f190,f156]) ).
fof(f156,plain,
! [X0,X1] :
( ~ transfinite_sequence(X1)
| ~ function(X1)
| ~ relation(X1)
| subset(relation_rng(X1),X0)
| ~ transfinite_sequence_of(X1,X0) ),
inference(cnf_transformation,[],[f109]) ).
fof(f109,plain,
! [X0,X1] :
( ( ( 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(rectify,[],[f108]) ).
fof(f108,plain,
! [X1,X0] :
( ( ( 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(nnf_transformation,[],[f92]) ).
fof(f92,plain,
! [X1,X0] :
( ( transfinite_sequence_of(X0,X1)
<=> subset(relation_rng(X0),X1) )
| ~ relation(X0)
| ~ function(X0)
| ~ transfinite_sequence(X0) ),
inference(flattening,[],[f91]) ).
fof(f91,plain,
! [X1,X0] :
( ( transfinite_sequence_of(X0,X1)
<=> subset(relation_rng(X0),X1) )
| ~ function(X0)
| ~ relation(X0)
| ~ transfinite_sequence(X0) ),
inference(ennf_transformation,[],[f54]) ).
fof(f54,plain,
! [X1,X0] :
( ( function(X0)
& relation(X0)
& transfinite_sequence(X0) )
=> ( transfinite_sequence_of(X0,X1)
<=> subset(relation_rng(X0),X1) ) ),
inference(rectify,[],[f8]) ).
fof(f8,axiom,
! [X1,X0] :
( ( function(X1)
& relation(X1)
& transfinite_sequence(X1) )
=> ( transfinite_sequence_of(X1,X0)
<=> subset(relation_rng(X1),X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_ordinal1) ).
fof(f332,plain,
~ transfinite_sequence_of(relation_dom_restriction(sK7,sK9),sK8),
inference(backward_demodulation,[],[f192,f322]) ).
fof(f192,plain,
~ transfinite_sequence_of(tseq_dom_restriction(sK7,sK9),sK8),
inference(cnf_transformation,[],[f128]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM412+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_uns --cores 0 -t %d %s
% 0.13/0.34 % Computer : n029.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 06:39:11 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.49 % (31889)lrs+2_1:1_lcm=reverse:lma=on:sos=all:spb=goal_then_units:ss=included:urr=on:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.20/0.49 % (31905)dis+10_1:1_av=off:sos=on:sp=reverse_arity:ss=included:st=2.0:to=lpo:urr=ec_only:i=45:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/45Mi)
% 0.20/0.49 % (31882)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 0.20/0.50 % (31890)dis+10_1:1_newcnf=on:sgt=8:sos=on:ss=axioms:to=lpo:urr=on:i=49:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/49Mi)
% 0.20/0.50 % (31889)First to succeed.
% 0.20/0.50 % (31889)Refutation found. Thanks to Tanya!
% 0.20/0.50 % SZS status Theorem for theBenchmark
% 0.20/0.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.50 % (31889)------------------------------
% 0.20/0.50 % (31889)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.50 % (31889)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.50 % (31889)Termination reason: Refutation
% 0.20/0.50
% 0.20/0.50 % (31889)Memory used [KB]: 6140
% 0.20/0.50 % (31889)Time elapsed: 0.097 s
% 0.20/0.50 % (31889)Instructions burned: 5 (million)
% 0.20/0.50 % (31889)------------------------------
% 0.20/0.50 % (31889)------------------------------
% 0.20/0.50 % (31881)Success in time 0.156 s
%------------------------------------------------------------------------------