%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM190-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:11:53 PM UTC 2026
% Result : Unsatisfiable 3.95s 1.47s
% Output : Refutation 3.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 36 ( 12 unt; 1 def)
% Number of atoms : 64 ( 10 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 53 ( 25 ~; 27 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 15 ( 0 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f21,axiom,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection1) ).
fof(f24,axiom,
! [X0,X1] :
( ~ member(X0,complement(X1))
| ~ member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement1) ).
fof(f25,axiom,
! [X0,X1] :
( member(X0,complement(X1))
| ~ member(X0,universal_class)
| member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement2) ).
fof(f48,axiom,
! [X0] :
( member(null_class,X0)
| ~ inductive(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inductive1) ).
fof(f51,axiom,
inductive(omega),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega_is_inductive1) ).
fof(f53,axiom,
member(omega,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega_in_universal) ).
fof(f69,axiom,
! [X0] :
( X0 = null_class
| intersection(X0,regular(X0)) = null_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',regularity2) ).
fof(f70,plain,
! [X0] :
( null_class = intersection(X0,regular(X0))
| null_class = X0 ),
inference(reorient_equations,[],[f69]) ).
fof(f176,negated_conjecture,
omega = null_class,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_omega_is_not_null_1) ).
fof(f177,plain,
null_class = omega,
inference(reorient_equations,[],[f176]) ).
fof(f184,plain,
inductive(null_class),
inference(forward_demodulation,[],[f51,f177]) ).
fof(f185,plain,
member(null_class,universal_class),
inference(forward_demodulation,[],[f53,f177]) ).
fof(f282,plain,
! [X0] :
( ~ inductive(complement(X0))
| ~ member(null_class,X0) ),
inference(resolution,[],[f24,f48]) ).
fof(f529,plain,
! [X0,X1] :
( ~ inductive(intersection(X0,X1))
| member(null_class,X0) ),
inference(resolution,[],[f21,f48]) ).
fof(f1629,definition,
( spl0_106
<=> member(null_class,complement(identity_relation)) ),
introduced(definition,[new_symbols(definition,[spl0_106])],[avatar_definition]) ).
fof(f1630,plain,
( member(null_class,complement(identity_relation))
| ~ spl0_106 ),
inference(avatar_component_clause,[],[f1629]) ).
fof(f1631,plain,
( ~ member(null_class,complement(identity_relation))
| spl0_106 ),
inference(avatar_component_clause,[],[f1629]) ).
fof(f1638,plain,
( ~ member(null_class,universal_class)
| member(null_class,identity_relation)
| spl0_106 ),
inference(resolution,[],[f1631,f25]) ).
fof(f1639,plain,
( member(null_class,identity_relation)
| spl0_106 ),
inference(forward_subsumption_resolution,[],[f1638,f185]) ).
fof(f1645,plain,
! [X0] :
( ~ inductive(null_class)
| member(null_class,X0)
| null_class = X0 ),
inference(superposition,[],[f529,f70]) ).
fof(f1669,plain,
! [X0] :
( member(null_class,X0)
| null_class = X0 ),
inference(forward_subsumption_resolution,[],[f1645,f184]) ).
fof(f1694,plain,
( null_class = complement(identity_relation)
| spl0_106 ),
inference(resolution,[],[f1669,f1631]) ).
fof(f1835,plain,
( ~ inductive(null_class)
| ~ member(null_class,identity_relation)
| spl0_106 ),
inference(superposition,[],[f282,f1694]) ).
fof(f1836,plain,
( ~ member(null_class,identity_relation)
| spl0_106 ),
inference(forward_subsumption_resolution,[],[f1835,f184]) ).
fof(f1842,plain,
( $false
| spl0_106 ),
inference(forward_subsumption_resolution,[],[f1836,f1639]) ).
fof(f1843,plain,
spl0_106,
inference(avatar_contradiction_clause,[],[f1842]) ).
fof(f1844,plain,
( ~ member(null_class,identity_relation)
| ~ spl0_106 ),
inference(resolution,[],[f1630,f24]) ).
fof(f1866,plain,
( null_class = identity_relation
| ~ spl0_106 ),
inference(resolution,[],[f1844,f1669]) ).
fof(f1890,plain,
( ~ member(null_class,null_class)
| ~ spl0_106 ),
inference(superposition,[],[f1844,f1866]) ).
fof(f1923,plain,
( ~ inductive(null_class)
| ~ spl0_106 ),
inference(resolution,[],[f1890,f48]) ).
fof(f1926,plain,
( $false
| ~ spl0_106 ),
inference(forward_subsumption_resolution,[],[f1923,f184]) ).
fof(f1927,plain,
~ spl0_106,
inference(avatar_contradiction_clause,[],[f1926]) ).
cnf(s98,plain,
spl0_106,
inference(sat_conversion,[],[f1843]) ).
cnf(s104,plain,
~ spl0_106,
inference(sat_conversion,[],[f1927]) ).
cnf(s105,plain,
$false,
inference(rat,[],[s98,s104]) ).
fof(f1928,plain,
$false,
inference(avatar_sat_refutation,[],[s105]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM190-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n017.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 19:03:57 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.95/1.47 % (2883291)Input is clausal, will run a generic CNF schedule.
% 3.95/1.47 % (2883296)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=1791340051:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.95/1.47 % (2883302)dis-21_1_sil=8000:lcm=predicate:random_seed=3426835660:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 3.95/1.47 % (2883297)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1049473600:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.95/1.47 % (2883299)lrs+10_1_sil=8000:sp=occurrence:random_seed=3656272146:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.95/1.47 % (2883300)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3714350416:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.95/1.47 % (2883298)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=4207972154:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.95/1.47 % (2883301)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4095443528:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.95/1.47 % (2883299)Refutation not found, incomplete strategy
% 3.95/1.47 % (2883299)------------------------------
% 3.95/1.47 % (2883299)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.95/1.47 % (2883299)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.95/1.47 % (2883299)CaDiCaL version: 2.1.3
% 3.95/1.47 % (2883299)Termination reason: Refutation not found, incomplete strategy
% 3.95/1.47 % (2883299)Time elapsed: 0.005 s
% 3.95/1.47 % (2883299)Peak memory usage: 88 MB
% 3.95/1.47 % (2883299)Instructions burned: 4 (million)
% 3.95/1.47 % (2883301)First to succeed.
% 3.95/1.47 % (2883301)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2883291"
% 3.95/1.47 % (2883302)Instruction limit reached!
% 3.95/1.47 % (2883302)------------------------------
% 3.95/1.47 % (2883302)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.95/1.47 % (2883302)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.95/1.47 % (2883302)CaDiCaL version: 2.1.3
% 3.95/1.47 % (2883302)Termination reason: Instruction limit
% 3.95/1.47 % (2883302)Termination phase: Saturation
% 3.95/1.47 % (2883302)Time elapsed: 0.069 s
% 3.95/1.47 % (2883302)Peak memory usage: 88 MB
% 3.95/1.47 % (2883302)Instructions burned: 117 (million)
% 3.95/1.47 % (2883300)Instruction limit reached!
% 3.95/1.47 % (2883300)------------------------------
% 3.95/1.47 % (2883300)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.95/1.47 % (2883300)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.95/1.47 % (2883300)CaDiCaL version: 2.1.3
% 3.95/1.47 % (2883300)Termination reason: Instruction limit
% 3.95/1.47 % (2883300)Termination phase: Saturation
% 3.95/1.47 % (2883300)Time elapsed: 0.075 s
% 3.95/1.47 % (2883300)Peak memory usage: 89 MB
% 3.95/1.47 % (2883300)Instructions burned: 114 (million)
% 3.95/1.47 % (2883310)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=1303991380:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.95/1.47 % (2883310)Refutation not found, incomplete strategy
% 3.95/1.47 % (2883310)------------------------------
% 3.95/1.47 % (2883310)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.95/1.47 % (2883310)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.95/1.47 % (2883310)CaDiCaL version: 2.1.3
% 3.95/1.47 % (2883310)Termination reason: Refutation not found, incomplete strategy
% 3.95/1.47 % (2883310)Time elapsed: 0.002 s
% 3.95/1.47 % (2883310)Peak memory usage: 88 MB
% 3.95/1.47 % (2883310)Instructions burned: 1 (million)
% 3.95/1.47 % (2883311)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=2008469800:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 3.95/1.47 % (2883299)------------------------------
% 3.95/1.47 % (2883299)------------------------------
% 3.95/1.47 % (2883301)Refutation found. Thanks to Tanya!
% 3.95/1.47 % SZS status Unsatisfiable for theBenchmark
% 3.95/1.47 % SZS output start Proof for theBenchmark
% See solution above
% 3.95/1.47 % (2883301)------------------------------
% 3.95/1.47 % (2883301)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.95/1.47 % (2883301)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.95/1.47 % (2883301)CaDiCaL version: 2.1.3
% 3.95/1.47 % (2883301)Termination reason: Refutation
% 3.95/1.47 % (2883301)Time elapsed: 0.055 s
% 3.95/1.47 % (2883301)Peak memory usage: 90 MB
% 3.95/1.47 % (2883301)Instructions burned: 71 (million)
% 3.95/1.47 % (2883301)------------------------------
% 3.95/1.47 % (2883301)------------------------------
% 3.95/1.47 % (2883291)Success in time 0.49 s
% 3.95/1.47 % Vampire exiting
%------------------------------------------------------------------------------