TSTP Solution File: NUM409+1 by SnakeForV-SAT---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : NUM409+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 : n024.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 1.62s 0.58s
% Output : Refutation 1.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 49 ( 17 unt; 0 def)
% Number of atoms : 135 ( 7 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 139 ( 53 ~; 47 |; 27 &)
% ( 6 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-1 aty)
% Number of variables : 37 ( 35 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f355,plain,
$false,
inference(resolution,[],[f351,f222]) ).
fof(f222,plain,
~ transfinite_sequence_of(empty_set,sK12),
inference(cnf_transformation,[],[f134]) ).
fof(f134,plain,
~ transfinite_sequence_of(empty_set,sK12),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f84,f133]) ).
fof(f133,plain,
( ? [X0] : ~ transfinite_sequence_of(empty_set,X0)
=> ~ transfinite_sequence_of(empty_set,sK12) ),
introduced(choice_axiom,[]) ).
fof(f84,plain,
? [X0] : ~ transfinite_sequence_of(empty_set,X0),
inference(ennf_transformation,[],[f46]) ).
fof(f46,negated_conjecture,
~ ! [X0] : transfinite_sequence_of(empty_set,X0),
inference(negated_conjecture,[],[f45]) ).
fof(f45,conjecture,
! [X0] : transfinite_sequence_of(empty_set,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_ordinal1) ).
fof(f351,plain,
! [X3] : transfinite_sequence_of(empty_set,X3),
inference(subsumption_resolution,[],[f350,f193]) ).
fof(f193,plain,
! [X0] : subset(empty_set,X0),
inference(cnf_transformation,[],[f43]) ).
fof(f43,axiom,
! [X0] : subset(empty_set,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
fof(f350,plain,
! [X3] :
( ~ subset(empty_set,X3)
| transfinite_sequence_of(empty_set,X3) ),
inference(forward_demodulation,[],[f349,f275]) ).
fof(f275,plain,
empty_set = relation_rng(empty_set),
inference(resolution,[],[f263,f202]) ).
fof(f202,plain,
empty(empty_set),
inference(cnf_transformation,[],[f17]) ).
fof(f17,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f263,plain,
! [X0] :
( ~ empty(X0)
| empty_set = relation_rng(X0) ),
inference(resolution,[],[f171,f167]) ).
fof(f167,plain,
! [X0] :
( ~ empty(X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f86]) ).
fof(f86,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(ennf_transformation,[],[f50]) ).
fof(f50,axiom,
! [X0] :
( empty(X0)
=> empty_set = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(f171,plain,
! [X0] :
( empty(relation_rng(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f77]) ).
fof(f77,plain,
! [X0] :
( ( empty(relation_rng(X0))
& relation(relation_rng(X0)) )
| ~ empty(X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f25,axiom,
! [X0] :
( empty(X0)
=> ( empty(relation_rng(X0))
& relation(relation_rng(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc8_relat_1) ).
fof(f349,plain,
! [X3] :
( ~ subset(relation_rng(empty_set),X3)
| transfinite_sequence_of(empty_set,X3) ),
inference(subsumption_resolution,[],[f348,f188]) ).
fof(f188,plain,
relation(empty_set),
inference(cnf_transformation,[],[f66]) ).
fof(f66,plain,
( ordinal(empty_set)
& epsilon_transitive(empty_set)
& empty(empty_set)
& relation(empty_set)
& epsilon_connected(empty_set)
& function(empty_set) ),
inference(pure_predicate_removal,[],[f64]) ).
fof(f64,plain,
( function(empty_set)
& epsilon_transitive(empty_set)
& empty(empty_set)
& ordinal(empty_set)
& epsilon_connected(empty_set)
& one_to_one(empty_set)
& relation(empty_set) ),
inference(pure_predicate_removal,[],[f19]) ).
fof(f19,axiom,
( function(empty_set)
& epsilon_transitive(empty_set)
& empty(empty_set)
& ordinal(empty_set)
& epsilon_connected(empty_set)
& one_to_one(empty_set)
& relation(empty_set)
& relation_empty_yielding(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_ordinal1) ).
fof(f348,plain,
! [X3] :
( ~ relation(empty_set)
| ~ subset(relation_rng(empty_set),X3)
| transfinite_sequence_of(empty_set,X3) ),
inference(subsumption_resolution,[],[f343,f186]) ).
fof(f186,plain,
function(empty_set),
inference(cnf_transformation,[],[f66]) ).
fof(f343,plain,
! [X3] :
( transfinite_sequence_of(empty_set,X3)
| ~ function(empty_set)
| ~ relation(empty_set)
| ~ subset(relation_rng(empty_set),X3) ),
inference(resolution,[],[f217,f302]) ).
fof(f302,plain,
transfinite_sequence(empty_set),
inference(subsumption_resolution,[],[f301,f188]) ).
fof(f301,plain,
( transfinite_sequence(empty_set)
| ~ relation(empty_set) ),
inference(subsumption_resolution,[],[f300,f186]) ).
fof(f300,plain,
( ~ function(empty_set)
| ~ relation(empty_set)
| transfinite_sequence(empty_set) ),
inference(subsumption_resolution,[],[f299,f191]) ).
fof(f191,plain,
ordinal(empty_set),
inference(cnf_transformation,[],[f66]) ).
fof(f299,plain,
( transfinite_sequence(empty_set)
| ~ ordinal(empty_set)
| ~ function(empty_set)
| ~ relation(empty_set) ),
inference(superposition,[],[f172,f280]) ).
fof(f280,plain,
empty_set = relation_dom(empty_set),
inference(resolution,[],[f264,f202]) ).
fof(f264,plain,
! [X0] :
( ~ empty(X0)
| relation_dom(X0) = empty_set ),
inference(resolution,[],[f201,f167]) ).
fof(f201,plain,
! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f81,plain,
! [X0] :
( ( empty(relation_dom(X0))
& relation(relation_dom(X0)) )
| ~ empty(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f24,axiom,
! [X0] :
( empty(X0)
=> ( empty(relation_dom(X0))
& relation(relation_dom(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_relat_1) ).
fof(f172,plain,
! [X0] :
( ~ ordinal(relation_dom(X0))
| ~ function(X0)
| ~ relation(X0)
| transfinite_sequence(X0) ),
inference(cnf_transformation,[],[f111]) ).
fof(f111,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ( ( ordinal(relation_dom(X0))
| ~ transfinite_sequence(X0) )
& ( transfinite_sequence(X0)
| ~ ordinal(relation_dom(X0)) ) ) ),
inference(nnf_transformation,[],[f89]) ).
fof(f89,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| ( ordinal(relation_dom(X0))
<=> transfinite_sequence(X0) ) ),
inference(flattening,[],[f88]) ).
fof(f88,plain,
! [X0] :
( ( ordinal(relation_dom(X0))
<=> transfinite_sequence(X0) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ( ordinal(relation_dom(X0))
<=> transfinite_sequence(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_ordinal1) ).
fof(f217,plain,
! [X0,X1] :
( ~ transfinite_sequence(X1)
| ~ function(X1)
| ~ subset(relation_rng(X1),X0)
| transfinite_sequence_of(X1,X0)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f132]) ).
fof(f132,plain,
! [X0,X1] :
( ~ function(X1)
| ~ transfinite_sequence(X1)
| ( ( transfinite_sequence_of(X1,X0)
| ~ subset(relation_rng(X1),X0) )
& ( subset(relation_rng(X1),X0)
| ~ transfinite_sequence_of(X1,X0) ) )
| ~ relation(X1) ),
inference(nnf_transformation,[],[f80]) ).
fof(f80,plain,
! [X0,X1] :
( ~ function(X1)
| ~ transfinite_sequence(X1)
| ( transfinite_sequence_of(X1,X0)
<=> subset(relation_rng(X1),X0) )
| ~ relation(X1) ),
inference(flattening,[],[f79]) ).
fof(f79,plain,
! [X1,X0] :
( ( transfinite_sequence_of(X1,X0)
<=> subset(relation_rng(X1),X0) )
| ~ transfinite_sequence(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X1,X0] :
( ( transfinite_sequence(X1)
& relation(X1)
& function(X1) )
=> ( transfinite_sequence_of(X1,X0)
<=> subset(relation_rng(X1),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_ordinal1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : NUM409+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.14 % 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 : n024.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 06:31:04 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.55 % (3137)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.20/0.55 % (3136)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)
% 1.33/0.56 % (3138)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 1.33/0.56 % (3153)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)
% 1.33/0.56 % (3146)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)
% 1.33/0.56 % (3152)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)
% 1.33/0.56 % (3138)Instruction limit reached!
% 1.33/0.56 % (3138)------------------------------
% 1.33/0.56 % (3138)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.33/0.56 % (3138)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.33/0.56 % (3138)Termination reason: Unknown
% 1.33/0.56 % (3138)Termination phase: Preprocessing 2
% 1.33/0.56
% 1.33/0.56 % (3138)Memory used [KB]: 895
% 1.33/0.56 % (3138)Time elapsed: 0.004 s
% 1.33/0.56 % (3138)Instructions burned: 2 (million)
% 1.33/0.56 % (3138)------------------------------
% 1.33/0.56 % (3138)------------------------------
% 1.33/0.57 % (3145)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/75Mi)
% 1.33/0.57 % (3144)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)
% 1.33/0.57 % (3154)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 1.33/0.57 % (3145)First to succeed.
% 1.33/0.57 TRYING [1]
% 1.62/0.57 % (3137)Instruction limit reached!
% 1.62/0.57 % (3137)------------------------------
% 1.62/0.57 % (3137)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.62/0.57 % (3137)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.62/0.57 % (3137)Termination reason: Unknown
% 1.62/0.57 % (3137)Termination phase: Saturation
% 1.62/0.57
% 1.62/0.57 % (3137)Memory used [KB]: 5628
% 1.62/0.57 % (3137)Time elapsed: 0.147 s
% 1.62/0.57 % (3137)Instructions burned: 8 (million)
% 1.62/0.57 % (3137)------------------------------
% 1.62/0.57 % (3137)------------------------------
% 1.62/0.57 TRYING [2]
% 1.62/0.58 TRYING [3]
% 1.62/0.58 % (3135)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)
% 1.62/0.58 % (3154)Also succeeded, but the first one will report.
% 1.62/0.58 % (3132)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)
% 1.62/0.58 % (3145)Refutation found. Thanks to Tanya!
% 1.62/0.58 % SZS status Theorem for theBenchmark
% 1.62/0.58 % SZS output start Proof for theBenchmark
% See solution above
% 1.62/0.58 % (3145)------------------------------
% 1.62/0.58 % (3145)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.62/0.58 % (3145)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.62/0.58 % (3145)Termination reason: Refutation
% 1.62/0.58
% 1.62/0.58 % (3145)Memory used [KB]: 1151
% 1.62/0.58 % (3145)Time elapsed: 0.142 s
% 1.62/0.58 % (3145)Instructions burned: 8 (million)
% 1.62/0.58 % (3145)------------------------------
% 1.62/0.58 % (3145)------------------------------
% 1.62/0.58 % (3129)Success in time 0.218 s
%------------------------------------------------------------------------------