%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET186-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 12:40:27 PM UTC 2026
% Result : Unsatisfiable 7.16s 1.79s
% Output : Refutation 7.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of formulae : 30 ( 15 unt; 1 def)
% Number of atoms : 50 ( 4 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 39 ( 19 ~; 19 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 21 ( 0 sgn 21 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( ~ member(X2,X0)
| ~ subclass(X0,X1)
| member(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subclass_members) ).
fof(f2,axiom,
! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_subclass_members1) ).
fof(f3,axiom,
! [X0,X1] :
( ~ member(not_subclass_element(X0,X1),X1)
| subclass(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_subclass_members2) ).
fof(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',class_elements_are_sets) ).
fof(f21,axiom,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection1) ).
fof(f24,axiom,
! [X0,X1] :
( ~ member(X0,complement(X1))
| ~ member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement1) ).
fof(f25,axiom,
! [X0,X1] :
( member(X0,complement(X1))
| ~ member(X0,universal_class)
| member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement2) ).
fof(f26,axiom,
! [X0,X1] : complement(intersection(complement(X0),complement(X1))) = union(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union) ).
fof(f122,negated_conjecture,
union(x,y) = y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_subclass_property4_1) ).
fof(f123,plain,
y = union(x,y),
inference(reorient_equations,[],[f122]) ).
fof(f124,negated_conjecture,
~ subclass(x,y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_subclass_property4_2) ).
fof(f187,plain,
y = complement(intersection(complement(x),complement(y))),
inference(definition_unfolding,[],[f123,f26]) ).
fof(f192,plain,
member(not_subclass_element(x,y),x),
inference(resolution,[],[f124,f2]) ).
fof(f193,plain,
! [X0] :
( ~ subclass(x,X0)
| member(not_subclass_element(x,y),X0) ),
inference(resolution,[],[f192,f1]) ).
fof(f196,plain,
! [X0] :
( member(X0,intersection(complement(x),complement(y)))
| ~ member(X0,universal_class)
| member(X0,y) ),
inference(superposition,[],[f25,f187]) ).
fof(f219,plain,
member(not_subclass_element(x,y),universal_class),
inference(resolution,[],[f193,f4]) ).
fof(f279,plain,
! [X0] :
( member(X0,complement(x))
| member(X0,y)
| ~ member(X0,universal_class) ),
inference(resolution,[],[f196,f21]) ).
fof(f282,plain,
! [X0] :
( ~ member(X0,x)
| ~ member(X0,universal_class)
| member(X0,y) ),
inference(resolution,[],[f279,f24]) ).
fof(f285,plain,
( ~ member(not_subclass_element(x,y),universal_class)
| member(not_subclass_element(x,y),y) ),
inference(resolution,[],[f282,f192]) ).
fof(f317,plain,
member(not_subclass_element(x,y),y),
inference(forward_subsumption_resolution,[],[f285,f219]) ).
fof(f323,definition,
( spl0_17
<=> member(not_subclass_element(x,y),y) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f325,plain,
( member(not_subclass_element(x,y),y)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f323]) ).
fof(f327,plain,
spl0_17,
inference(avatar_split_clause,[],[f317,f323]) ).
fof(f328,plain,
( subclass(x,y)
| ~ spl0_17 ),
inference(resolution,[],[f325,f3]) ).
fof(f330,plain,
( $false
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f328,f124]) ).
fof(f331,plain,
~ spl0_17,
inference(avatar_contradiction_clause,[],[f330]) ).
cnf(s9,plain,
spl0_17,
inference(sat_conversion,[],[f327]) ).
cnf(s10,plain,
~ spl0_17,
inference(sat_conversion,[],[f331]) ).
cnf(s11,plain,
$false,
inference(rat,[],[s9,s10]) ).
fof(f332,plain,
$false,
inference(avatar_sat_refutation,[],[s11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET186-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n017.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 28 00:58:05 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.73/1.60 % (3124518)Input is clausal, will run a generic CNF schedule.
% 5.73/1.60 % (3124528)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1940243736:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 5.73/1.60 % (3124523)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=1113741457:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 5.73/1.60 % (3124524)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1030672839:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 5.73/1.60 % (3124525)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2523154120:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 5.73/1.60 % (3124526)lrs+10_1_sil=8000:sp=occurrence:random_seed=2809946516:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 5.73/1.60 % (3124527)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3543121258:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 5.73/1.60 % (3124529)dis-21_1_sil=8000:lcm=predicate:random_seed=3590757631: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)
% 5.73/1.60 % (3124526)Instruction limit reached!
% 5.73/1.60 % (3124526)------------------------------
% 5.73/1.60 % (3124526)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.73/1.60 % (3124526)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.73/1.60 % (3124526)CaDiCaL version: 2.1.3
% 5.73/1.60 % (3124526)Termination reason: Instruction limit
% 5.73/1.60 % (3124526)Termination phase: Saturation
% 5.73/1.60 % (3124526)Time elapsed: 0.066 s
% 5.73/1.60 % (3124526)Peak memory usage: 89 MB
% 5.73/1.60 % (3124526)Instructions burned: 108 (million)
% 5.73/1.60 % (3124527)Instruction limit reached!
% 5.73/1.60 % (3124527)------------------------------
% 5.73/1.60 % (3124527)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.73/1.60 % (3124527)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.73/1.60 % (3124527)CaDiCaL version: 2.1.3
% 5.73/1.60 % (3124527)Termination reason: Instruction limit
% 5.73/1.60 % (3124527)Termination phase: Saturation
% 5.73/1.60 % (3124527)Time elapsed: 0.070 s
% 5.73/1.60 % (3124527)Peak memory usage: 89 MB
% 5.73/1.60 % (3124527)Instructions burned: 115 (million)
% 5.73/1.60 % (3124529)Instruction limit reached!
% 5.73/1.60 % (3124529)------------------------------
% 5.73/1.60 % (3124529)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.73/1.60 % (3124529)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.73/1.60 % (3124529)CaDiCaL version: 2.1.3
% 5.73/1.60 % (3124529)Termination reason: Instruction limit
% 5.73/1.60 % (3124529)Termination phase: Saturation
% 5.73/1.60 % (3124529)Time elapsed: 0.070 s
% 5.73/1.60 % (3124529)Peak memory usage: 88 MB
% 5.73/1.60 % (3124529)Instructions burned: 119 (million)
% 5.73/1.60 % (3124528)Instruction limit reached!
% 5.73/1.60 % (3124528)------------------------------
% 5.73/1.60 % (3124528)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.73/1.60 % (3124528)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.73/1.60 % (3124528)CaDiCaL version: 2.1.3
% 5.73/1.60 % (3124528)Termination reason: Instruction limit
% 5.73/1.60 % (3124528)Termination phase: Saturation
% 5.73/1.60 % (3124528)Time elapsed: 0.136 s
% 5.73/1.60 % (3124528)Peak memory usage: 90 MB
% 5.73/1.60 % (3124528)Instructions burned: 180 (million)
% 5.73/1.60 % (3124537)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=742478374:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 5.73/1.60 % (3124538)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=853571195: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)
% 5.73/1.60 % (3124539)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=4059554606:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 5.73/1.60 % (3124537)Refutation not found, incomplete strategy
% 5.73/1.60 % (3124537)------------------------------
% 5.73/1.60 % (3124537)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.16/1.79 % (3124537)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.16/1.79 % (3124537)CaDiCaL version: 2.1.3
% 7.16/1.79 % (3124537)Termination reason: Refutation not found, incomplete strategy
% 7.16/1.79 % (3124537)Time elapsed: 0.003 s
% 7.16/1.79 % (3124537)Peak memory usage: 88 MB
% 7.16/1.79 % (3124537)Instructions burned: 2 (million)
% 7.16/1.79 % (3124540)lrs+10_64_to=lpo:sil=8000:random_seed=2410860068:i=126:bd=preordered_2996 on theBenchmark for (2996ds/126Mi)
% 7.16/1.79 % (3124538)Instruction limit reached!
% 7.16/1.79 % (3124538)------------------------------
% 7.16/1.79 % (3124538)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.16/1.79 % (3124538)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.16/1.79 % (3124538)CaDiCaL version: 2.1.3
% 7.16/1.79 % (3124538)Termination reason: Instruction limit
% 7.16/1.79 % (3124538)Termination phase: Saturation
% 7.16/1.79 % (3124538)Time elapsed: 0.103 s
% 7.16/1.79 % (3124538)Peak memory usage: 89 MB
% 7.16/1.79 % (3124538)Instructions burned: 191 (million)
% 7.16/1.79 % (3124540)Instruction limit reached!
% 7.16/1.79 % (3124540)------------------------------
% 7.16/1.79 % (3124540)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.16/1.79 % (3124540)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.16/1.79 % (3124540)CaDiCaL version: 2.1.3
% 7.16/1.79 % (3124540)Termination reason: Instruction limit
% 7.16/1.79 % (3124540)Termination phase: Saturation
% 7.16/1.79 % (3124540)Time elapsed: 0.043 s
% 7.16/1.79 % (3124540)Peak memory usage: 90 MB
% 7.16/1.79 % (3124540)Instructions burned: 127 (million)
% 7.16/1.79 % (3124539)Instruction limit reached!
% 7.16/1.79 % (3124539)------------------------------
% 7.16/1.79 % (3124539)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.16/1.79 % (3124539)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.16/1.79 % (3124539)CaDiCaL version: 2.1.3
% 7.16/1.79 % (3124539)Termination reason: Instruction limit
% 7.16/1.79 % (3124539)Termination phase: Saturation
% 7.16/1.79 % (3124539)Time elapsed: 0.146 s
% 7.16/1.79 % (3124539)Peak memory usage: 89 MB
% 7.16/1.79 % (3124539)Instructions burned: 219 (million)
% 7.16/1.79 % (3124546)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=3347026628:i=157:gtg=all_2994 on theBenchmark for (2994ds/157Mi)
% 7.16/1.79 % (3124545)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=1541673042:avsq=on:i=194:fgj=on:bd=preordered_2995 on theBenchmark for (2995ds/194Mi)
% 7.16/1.79 % (3124537)------------------------------
% 7.16/1.79 % (3124537)------------------------------
% 7.16/1.79 % (3124546)Instruction limit reached!
% 7.16/1.79 % (3124546)------------------------------
% 7.16/1.79 % (3124546)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.16/1.79 % (3124546)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.16/1.79 % (3124546)CaDiCaL version: 2.1.3
% 7.16/1.79 % (3124546)Termination reason: Instruction limit
% 7.16/1.79 % (3124546)Termination phase: Saturation
% 7.16/1.79 % (3124546)Time elapsed: 0.057 s
% 7.16/1.79 % (3124546)Peak memory usage: 91 MB
% 7.16/1.79 % (3124546)Instructions burned: 157 (million)
% 7.16/1.79 % (3124547)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=2093120676:i=3394:sd=4:ss=included:sgt=64_2994 on theBenchmark for (2994ds/3394Mi)
% 7.16/1.79 % (3124545)Instruction limit reached!
% 7.16/1.79 % (3124545)------------------------------
% 7.16/1.79 % (3124545)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.16/1.79 % (3124545)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.16/1.79 % (3124545)CaDiCaL version: 2.1.3
% 7.16/1.79 % (3124545)Termination reason: Instruction limit
% 7.16/1.79 % (3124545)Termination phase: Saturation
% 7.16/1.79 % (3124545)Time elapsed: 0.129 s
% 7.16/1.79 % (3124545)Peak memory usage: 89 MB
% 7.16/1.79 % (3124545)Instructions burned: 195 (million)
% 7.16/1.79 % (3124550)lrs+1011_5_to=lpo:sil=8000:tgt=full:plsq=on:prc=on:drc=off:plsqr=31,4:sp=occurrence:urr=on:nwc=0.8:s2agt=16:br=off:random_seed=4184128639:cts=off:s2a=on:i=106:fsr=off:gsp=on:ss=axioms:sgt=16:rawr=on_2993 on theBenchmark for (2993ds/106Mi)
% 7.16/1.79 % (3124551)lrs+2_4096_sil=8000:plsq=on:plsqr=12672147,131072:sos=on:spb=goal:lcm=predicate:random_seed=1510256940:i=107_2993 on theBenchmark for (2993ds/107Mi)
% 7.16/1.79 % (3124551)First to succeed.
% 7.16/1.79 % (3124551)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3124518"
% 7.16/1.79 % (3124524)Also succeeded, but the first one will report.
% 7.16/1.79 % (3124523)Also succeeded, but the first one will report.
% 7.16/1.79 % (3124525)Also succeeded, but the first one will report.
% 7.16/1.79 % (3124550)Instruction limit reached!
% 7.16/1.79 % (3124550)------------------------------
% 7.16/1.79 % (3124550)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.16/1.79 % (3124550)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.16/1.79 % (3124550)CaDiCaL version: 2.1.3
% 7.16/1.79 % (3124550)Termination reason: Instruction limit
% 7.16/1.79 % (3124550)Termination phase: Saturation
% 7.16/1.79 % (3124550)Time elapsed: 0.068 s
% 7.16/1.79 % (3124550)Peak memory usage: 90 MB
% 7.16/1.79 % (3124550)Instructions burned: 107 (million)
% 7.16/1.79 % (3124553)lrs+1011_20_sil=64000:tgt=ground:plsq=on:fde=unused:plsqc=1:plsqr=14,1:plsql=on:nwc=0.6:random_seed=1833214660:st=6:i=242:gtgl=5:kws=arity_squared:av=off:gtg=exists_sym:ss=included_2992 on theBenchmark for (2992ds/242Mi)
% 7.16/1.79 % (3124551)Refutation found. Thanks to Tanya!
% 7.16/1.79 % SZS status Unsatisfiable for theBenchmark
% 7.16/1.79 % SZS output start Proof for theBenchmark
% See solution above
% 7.16/1.79 % (3124551)------------------------------
% 7.16/1.79 % (3124551)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.16/1.79 % (3124551)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.16/1.79 % (3124551)CaDiCaL version: 2.1.3
% 7.16/1.79 % (3124551)Termination reason: Refutation
% 7.16/1.79 % (3124551)Time elapsed: 0.005 s
% 7.16/1.79 % (3124551)Peak memory usage: 89 MB
% 7.16/1.79 % (3124551)Instructions burned: 13 (million)
% 7.16/1.79 % (3124551)------------------------------
% 7.16/1.79 % (3124551)------------------------------
% 7.16/1.79 % (3124518)Success in time 0.969 s
% 7.16/1.79 % Vampire exiting
%------------------------------------------------------------------------------