%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM066-1 : 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 : n018.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 12:11:41 PM UTC 2026
% Result : Unsatisfiable 3.68s 1.49s
% Output : Refutation 3.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of formulae : 35 ( 12 unt; 2 def)
% Number of atoms : 85 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 111 ( 61 ~; 48 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 36 ( 0 sgn 36 !; 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(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',class_elements_are_sets) ).
fof(f16,axiom,
! [X2,X3,X0,X1] :
( member(ordered_pair(X0,X2),cross_product(X1,X3))
| ~ member(X2,X3)
| ~ member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartesian_product3) ).
fof(f20,axiom,
! [X0,X1] :
( ~ member(ordered_pair(X0,X1),cross_product(universal_class,universal_class))
| ~ member(X0,X1)
| member(ordered_pair(X0,X1),element_relation) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_relation3) ).
fof(f137,axiom,
! [X2,X3,X0,X1] :
( ~ well_ordering(X0,X1)
| ~ subclass(X2,X1)
| ~ member(X3,X2)
| member(least(X0,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_ordering3) ).
fof(f140,axiom,
! [X2,X3,X0,X1] :
( ~ member(ordered_pair(X3,least(X0,X2)),X0)
| ~ subclass(X2,X1)
| ~ member(X3,X2)
| ~ well_ordering(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_ordering5) ).
fof(f176,negated_conjecture,
well_ordering(element_relation,y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_to_well_ordering_property1_1) ).
fof(f177,negated_conjecture,
subclass(u,y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_to_well_ordering_property1_2) ).
fof(f178,negated_conjecture,
member(v,u),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_to_well_ordering_property1_3) ).
fof(f179,negated_conjecture,
member(v,least(element_relation,u)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_to_well_ordering_property1_4) ).
fof(f230,plain,
! [X0,X1] :
( ~ member(X1,X0)
| ~ subclass(X0,y)
| member(least(element_relation,X0),X0) ),
inference(resolution,[],[f137,f176]) ).
fof(f232,plain,
! [X0,X1] :
( member(ordered_pair(X0,X1),element_relation)
| ~ member(X0,X1)
| ~ member(X1,universal_class)
| ~ member(X0,universal_class) ),
inference(resolution,[],[f20,f16]) ).
fof(f239,plain,
( ~ subclass(u,y)
| member(least(element_relation,u),u) ),
inference(resolution,[],[f230,f178]) ).
fof(f241,plain,
member(least(element_relation,u),u),
inference(forward_subsumption_resolution,[],[f239,f177]) ).
fof(f265,plain,
! [X0] :
( member(least(element_relation,u),X0)
| ~ subclass(u,X0) ),
inference(resolution,[],[f241,f1]) ).
fof(f272,plain,
! [X2,X0,X1] :
( ~ member(least(element_relation,X1),universal_class)
| ~ member(X0,least(element_relation,X1))
| ~ member(X0,universal_class)
| ~ subclass(X1,X2)
| ~ member(X0,X1)
| ~ well_ordering(element_relation,X2) ),
inference(resolution,[],[f232,f140]) ).
fof(f461,plain,
! [X0,X1] :
( ~ member(X0,least(element_relation,u))
| ~ member(X0,universal_class)
| ~ subclass(u,X1)
| ~ member(X0,u)
| ~ well_ordering(element_relation,X1)
| ~ subclass(u,universal_class) ),
inference(resolution,[],[f272,f265]) ).
fof(f469,plain,
! [X0,X1] :
( ~ member(X0,least(element_relation,u))
| ~ subclass(u,X1)
| ~ member(X0,u)
| ~ well_ordering(element_relation,X1)
| ~ subclass(u,universal_class) ),
inference(forward_subsumption_resolution,[],[f461,f1]) ).
fof(f472,plain,
! [X0,X1] :
( ~ member(X0,least(element_relation,u))
| ~ subclass(u,X1)
| ~ member(X0,u)
| ~ well_ordering(element_relation,X1) ),
inference(forward_subsumption_resolution,[],[f469,f4]) ).
fof(f481,definition,
( spl0_27
<=> ! [X1] :
( ~ subclass(u,X1)
| ~ well_ordering(element_relation,X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_27])],[avatar_definition]) ).
fof(f482,plain,
( ! [X1] :
( ~ well_ordering(element_relation,X1)
| ~ subclass(u,X1) )
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f481]) ).
fof(f484,definition,
( spl0_28
<=> ! [X0] :
( ~ member(X0,least(element_relation,u))
| ~ member(X0,u) ) ),
introduced(definition,[new_symbols(definition,[spl0_28])],[avatar_definition]) ).
fof(f485,plain,
( ! [X0] :
( ~ member(X0,least(element_relation,u))
| ~ member(X0,u) )
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f484]) ).
fof(f486,plain,
( spl0_27
| spl0_28 ),
inference(avatar_split_clause,[],[f472,f484,f481]) ).
fof(f597,plain,
( ~ subclass(u,y)
| ~ spl0_27 ),
inference(resolution,[],[f482,f176]) ).
fof(f598,plain,
( $false
| ~ spl0_27 ),
inference(forward_subsumption_resolution,[],[f597,f177]) ).
fof(f599,plain,
~ spl0_27,
inference(avatar_contradiction_clause,[],[f598]) ).
fof(f1188,plain,
( ~ member(v,u)
| ~ spl0_28 ),
inference(resolution,[],[f485,f179]) ).
fof(f1190,plain,
( $false
| ~ spl0_28 ),
inference(forward_subsumption_resolution,[],[f1188,f178]) ).
fof(f1191,plain,
~ spl0_28,
inference(avatar_contradiction_clause,[],[f1190]) ).
cnf(s17,plain,
( spl0_27
| spl0_28 ),
inference(sat_conversion,[],[f486]) ).
cnf(s26,plain,
~ spl0_27,
inference(sat_conversion,[],[f599]) ).
cnf(s59,plain,
~ spl0_28,
inference(sat_conversion,[],[f1191]) ).
cnf(s66,plain,
$false,
inference(rat,[],[s17,s59,s26]) ).
fof(f1211,plain,
$false,
inference(avatar_sat_refutation,[],[s66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM066-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n018.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 18:50:39 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 3.68/1.49 % (2666309)Input is clausal, will run a generic CNF schedule.
% 3.68/1.49 % (2666318)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2814955113:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.68/1.49 % (2666317)lrs+10_1_sil=8000:sp=occurrence:random_seed=2791440834:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.68/1.49 % (2666314)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=261414781:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.68/1.49 % (2666315)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=945163373:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.68/1.49 % (2666316)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2368585264:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.68/1.49 % (2666318)Instruction limit reached!
% 3.68/1.49 % (2666318)------------------------------
% 3.68/1.49 % (2666318)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.68/1.49 % (2666318)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.68/1.49 % (2666318)CaDiCaL version: 2.1.3
% 3.68/1.49 % (2666318)Termination reason: Instruction limit
% 3.68/1.49 % (2666318)Termination phase: Saturation
% 3.68/1.49 % (2666318)Time elapsed: 0.039 s
% 3.68/1.49 % (2666318)Peak memory usage: 89 MB
% 3.68/1.49 % (2666318)Instructions burned: 117 (million)
% 3.68/1.49 % (2666320)dis-21_1_sil=8000:lcm=predicate:random_seed=2872314413: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)
% 3.68/1.49 % (2666319)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1375885194:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.68/1.49 % (2666317)First to succeed.
% 3.68/1.49 % (2666317)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2666309"
% 3.68/1.49 % (2666320)Instruction limit reached!
% 3.68/1.49 % (2666320)------------------------------
% 3.68/1.49 % (2666320)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.68/1.49 % (2666320)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.68/1.49 % (2666320)CaDiCaL version: 2.1.3
% 3.68/1.49 % (2666320)Termination reason: Instruction limit
% 3.68/1.49 % (2666320)Termination phase: Saturation
% 3.68/1.49 % (2666320)Time elapsed: 0.069 s
% 3.68/1.49 % (2666320)Peak memory usage: 89 MB
% 3.68/1.49 % (2666320)Instructions burned: 118 (million)
% 3.68/1.49 % (2666319)Instruction limit reached!
% 3.68/1.49 % (2666319)------------------------------
% 3.68/1.49 % (2666319)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.68/1.49 % (2666319)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.68/1.49 % (2666319)CaDiCaL version: 2.1.3
% 3.68/1.49 % (2666319)Termination reason: Instruction limit
% 3.68/1.49 % (2666319)Termination phase: Saturation
% 3.68/1.49 % (2666319)Time elapsed: 0.073 s
% 3.68/1.49 % (2666319)Peak memory usage: 90 MB
% 3.68/1.49 % (2666319)Instructions burned: 180 (million)
% 3.68/1.49 % (2666328)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=3734719809:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 3.68/1.49 % (2666328)Refutation not found, incomplete strategy
% 3.68/1.49 % (2666328)------------------------------
% 3.68/1.49 % (2666328)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.68/1.49 % (2666328)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.68/1.49 % (2666328)CaDiCaL version: 2.1.3
% 3.68/1.49 % (2666328)Termination reason: Refutation not found, incomplete strategy
% 3.68/1.49 % (2666328)Time elapsed: 0.004 s
% 3.68/1.49 % (2666328)Peak memory usage: 88 MB
% 3.68/1.49 % (2666328)Instructions burned: 4 (million)
% 3.68/1.49 % (2666330)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=1085756104:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 3.68/1.49 % (2666330)Refutation not found, incomplete strategy
% 3.68/1.49 % (2666330)------------------------------
% 3.68/1.49 % (2666330)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.68/1.49 % (2666330)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.68/1.49 % (2666330)CaDiCaL version: 2.1.3
% 3.68/1.49 % (2666330)Termination reason: Refutation not found, incomplete strategy
% 3.68/1.49 % (2666330)Time elapsed: 0.002 s
% 3.68/1.49 % (2666330)Peak memory usage: 88 MB
% 3.68/1.49 % (2666330)Instructions burned: 4 (million)
% 3.68/1.49 % (2666329)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=563500882: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)
% 3.68/1.49 % (2666329)Also succeeded, but the first one will report.
% 3.68/1.49 % (2666317)Refutation found. Thanks to Tanya!
% 3.68/1.49 % SZS status Unsatisfiable for theBenchmark
% 3.68/1.49 % SZS output start Proof for theBenchmark
% See solution above
% 3.68/1.49 % (2666317)------------------------------
% 3.68/1.49 % (2666317)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.68/1.49 % (2666317)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.68/1.49 % (2666317)CaDiCaL version: 2.1.3
% 3.68/1.49 % (2666317)Termination reason: Refutation
% 3.68/1.49 % (2666317)Time elapsed: 0.027 s
% 3.68/1.49 % (2666317)Peak memory usage: 89 MB
% 3.68/1.49 % (2666317)Instructions burned: 37 (million)
% 3.68/1.49 % (2666317)------------------------------
% 3.68/1.49 % (2666317)------------------------------
% 3.68/1.49 % (2666309)Success in time 0.446 s
% 3.68/1.49 % Vampire exiting
%------------------------------------------------------------------------------