TSTP Solution File: NUM190-1 by SnakeForV-SAT---1.0
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%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : NUM190-1 : TPTP v8.1.0. Bugfixed v2.1.0.
% 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 : n004.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 18:03:39 EDT 2022
% Result : Unsatisfiable 0.19s 0.53s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 12
% Syntax : Number of formulae : 49 ( 4 unt; 0 def)
% Number of atoms : 101 ( 18 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 97 ( 45 ~; 47 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 6 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 15 ( 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f512,plain,
$false,
inference(avatar_sat_refutation,[],[f385,f438,f467,f491,f495,f500,f511]) ).
fof(f511,plain,
( ~ spl2_11
| spl2_19 ),
inference(avatar_contradiction_clause,[],[f510]) ).
fof(f510,plain,
( $false
| ~ spl2_11
| spl2_19 ),
inference(subsumption_resolution,[],[f508,f50]) ).
fof(f50,axiom,
inductive(omega),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega_is_inductive1) ).
fof(f508,plain,
( ~ inductive(omega)
| ~ spl2_11
| spl2_19 ),
inference(backward_demodulation,[],[f479,f371]) ).
fof(f371,plain,
( omega = kind_1_ordinals
| ~ spl2_11 ),
inference(avatar_component_clause,[],[f369]) ).
fof(f369,plain,
( spl2_11
<=> omega = kind_1_ordinals ),
introduced(avatar_definition,[new_symbols(naming,[spl2_11])]) ).
fof(f479,plain,
( ~ inductive(kind_1_ordinals)
| spl2_19 ),
inference(avatar_component_clause,[],[f477]) ).
fof(f477,plain,
( spl2_19
<=> inductive(kind_1_ordinals) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_19])]) ).
fof(f500,plain,
( ~ spl2_19
| spl2_16 ),
inference(avatar_split_clause,[],[f472,f450,f477]) ).
fof(f450,plain,
( spl2_16
<=> member(omega,kind_1_ordinals) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_16])]) ).
fof(f472,plain,
( ~ inductive(kind_1_ordinals)
| spl2_16 ),
inference(resolution,[],[f452,f225]) ).
fof(f225,plain,
! [X0] :
( member(omega,X0)
| ~ inductive(X0) ),
inference(definition_unfolding,[],[f47,f159]) ).
fof(f159,axiom,
null_class = omega,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_omega_is_not_null_1) ).
fof(f47,axiom,
! [X0] :
( member(null_class,X0)
| ~ inductive(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inductive1) ).
fof(f452,plain,
( ~ member(omega,kind_1_ordinals)
| spl2_16 ),
inference(avatar_component_clause,[],[f450]) ).
fof(f495,plain,
( spl2_6
| ~ spl2_9 ),
inference(avatar_split_clause,[],[f494,f352,f315]) ).
fof(f315,plain,
( spl2_6
<=> member(omega,complement(kind_1_ordinals)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_6])]) ).
fof(f352,plain,
( spl2_9
<=> omega = limit_ordinals ),
introduced(avatar_definition,[new_symbols(naming,[spl2_9])]) ).
fof(f494,plain,
( member(omega,complement(kind_1_ordinals))
| ~ spl2_9 ),
inference(subsumption_resolution,[],[f363,f50]) ).
fof(f363,plain,
( member(omega,complement(kind_1_ordinals))
| ~ inductive(omega)
| ~ spl2_9 ),
inference(superposition,[],[f306,f361]) ).
fof(f361,plain,
( omega = intersection(complement(kind_1_ordinals),ordinal_numbers)
| ~ spl2_9 ),
inference(backward_demodulation,[],[f139,f354]) ).
fof(f354,plain,
( omega = limit_ordinals
| ~ spl2_9 ),
inference(avatar_component_clause,[],[f352]) ).
fof(f139,axiom,
intersection(complement(kind_1_ordinals),ordinal_numbers) = limit_ordinals,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',limit_ordinals) ).
fof(f306,plain,
! [X3,X4] :
( ~ inductive(intersection(X3,X4))
| member(omega,X3) ),
inference(resolution,[],[f21,f225]) ).
fof(f21,axiom,
! [X0,X1,X4] :
( ~ member(X4,intersection(X0,X1))
| member(X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection1) ).
fof(f491,plain,
( spl2_11
| spl2_16 ),
inference(avatar_split_clause,[],[f471,f450,f369]) ).
fof(f471,plain,
( omega = kind_1_ordinals
| spl2_16 ),
inference(resolution,[],[f452,f423]) ).
fof(f423,plain,
! [X3] :
( member(omega,X3)
| omega = X3 ),
inference(subsumption_resolution,[],[f421,f50]) ).
fof(f421,plain,
! [X3] :
( member(omega,X3)
| ~ inductive(omega)
| omega = X3 ),
inference(superposition,[],[f306,f244]) ).
fof(f244,plain,
! [X0] :
( omega = intersection(X0,regular(X0))
| omega = X0 ),
inference(definition_unfolding,[],[f67,f159,f159]) ).
fof(f67,axiom,
! [X0] :
( null_class = X0
| null_class = intersection(X0,regular(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',regularity2) ).
fof(f467,plain,
( ~ spl2_16
| spl2_9 ),
inference(avatar_split_clause,[],[f466,f352,f450]) ).
fof(f466,plain,
( ~ member(omega,kind_1_ordinals)
| spl2_9 ),
inference(subsumption_resolution,[],[f432,f353]) ).
fof(f353,plain,
( omega != limit_ordinals
| spl2_9 ),
inference(avatar_component_clause,[],[f352]) ).
fof(f432,plain,
( ~ member(omega,kind_1_ordinals)
| omega = limit_ordinals ),
inference(resolution,[],[f423,f319]) ).
fof(f319,plain,
! [X0] :
( ~ member(X0,limit_ordinals)
| ~ member(X0,kind_1_ordinals) ),
inference(resolution,[],[f308,f24]) ).
fof(f24,axiom,
! [X0,X4] :
( ~ member(X4,complement(X0))
| ~ member(X4,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement1) ).
fof(f308,plain,
! [X0] :
( member(X0,complement(kind_1_ordinals))
| ~ member(X0,limit_ordinals) ),
inference(superposition,[],[f21,f139]) ).
fof(f438,plain,
( ~ spl2_6
| spl2_11 ),
inference(avatar_contradiction_clause,[],[f437]) ).
fof(f437,plain,
( $false
| ~ spl2_6
| spl2_11 ),
inference(subsumption_resolution,[],[f425,f370]) ).
fof(f370,plain,
( omega != kind_1_ordinals
| spl2_11 ),
inference(avatar_component_clause,[],[f369]) ).
fof(f425,plain,
( omega = kind_1_ordinals
| ~ spl2_6 ),
inference(resolution,[],[f423,f343]) ).
fof(f343,plain,
( ~ member(omega,kind_1_ordinals)
| ~ spl2_6 ),
inference(resolution,[],[f317,f24]) ).
fof(f317,plain,
( member(omega,complement(kind_1_ordinals))
| ~ spl2_6 ),
inference(avatar_component_clause,[],[f315]) ).
fof(f385,plain,
( ~ spl2_6
| ~ spl2_11 ),
inference(avatar_contradiction_clause,[],[f384]) ).
fof(f384,plain,
( $false
| ~ spl2_6
| ~ spl2_11 ),
inference(subsumption_resolution,[],[f379,f50]) ).
fof(f379,plain,
( ~ inductive(omega)
| ~ spl2_6
| ~ spl2_11 ),
inference(backward_demodulation,[],[f345,f371]) ).
fof(f345,plain,
( ~ inductive(kind_1_ordinals)
| ~ spl2_6 ),
inference(resolution,[],[f343,f225]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM190-1 : TPTP v8.1.0. Bugfixed v2.1.0.
% 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 : n004.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 06:03:49 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.19/0.48 % (29005)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)
% 0.19/0.50 % (29030)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 0.19/0.51 % (29020)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)
% 0.19/0.52 % (29017)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.19/0.52 % (29009)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 % (29028)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)
% 0.19/0.52 % (29020)First to succeed.
% 0.19/0.52 % (29011)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.19/0.52 % (29019)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)
% 0.19/0.52 % (29011)Instruction limit reached!
% 0.19/0.52 % (29011)------------------------------
% 0.19/0.52 % (29011)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.52 % (29011)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.52 % (29011)Termination reason: Unknown
% 0.19/0.52 % (29011)Termination phase: Equality resolution with deletion
% 0.19/0.52
% 0.19/0.52 % (29011)Memory used [KB]: 1023
% 0.19/0.52 % (29011)Time elapsed: 0.004 s
% 0.19/0.52 % (29011)Instructions burned: 3 (million)
% 0.19/0.52 % (29011)------------------------------
% 0.19/0.52 % (29011)------------------------------
% 0.19/0.53 % (29008)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 % (29031)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 0.19/0.53 % (29015)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.19/0.53 % (29016)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.19/0.53 % (29010)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.53 % (29004)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)
% 0.19/0.53 % (29020)Refutation found. Thanks to Tanya!
% 0.19/0.53 % SZS status Unsatisfiable for theBenchmark
% 0.19/0.53 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.53 % (29020)------------------------------
% 0.19/0.53 % (29020)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.53 % (29020)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.53 % (29020)Termination reason: Refutation
% 0.19/0.53
% 0.19/0.53 % (29020)Memory used [KB]: 5756
% 0.19/0.53 % (29020)Time elapsed: 0.130 s
% 0.19/0.53 % (29020)Instructions burned: 15 (million)
% 0.19/0.53 % (29020)------------------------------
% 0.19/0.53 % (29020)------------------------------
% 0.19/0.53 % (28998)Success in time 0.18 s
%------------------------------------------------------------------------------