%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM156-1 : 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 : n009.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 12:11:50 PM UTC 2026
% Result : Unsatisfiable 5.54s 1.76s
% Output : Refutation 5.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 17
% Syntax : Number of formulae : 32 ( 24 unt; 0 def)
% Number of atoms : 42 ( 12 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 24 ( 14 ~; 10 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 6 con; 0-3 aty)
% Number of variables : 35 ( 35 !; 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(f9,axiom,
! [X0,X1] :
( ~ member(X0,universal_class)
| member(X0,unordered_pair(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair2) ).
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_set) ).
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(f28,axiom,
! [X2,X0,X1] : intersection(X0,cross_product(X1,X2)) = restrict(X0,X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',restriction1) ).
fof(f29,axiom,
! [X2,X0,X1] : intersection(cross_product(X0,X1),X2) = restrict(X2,X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',restriction2) ).
fof(f39,axiom,
! [X0] : domain_of(flip(cross_product(X0,universal_class))) = inverse(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse) ).
fof(f40,axiom,
! [X0] : domain_of(inverse(X0)) = range_of(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',range_of) ).
fof(f43,axiom,
! [X0,X1] : range_of(restrict(X0,X1,universal_class)) = image(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',image) ).
fof(f48,axiom,
! [X0] :
( ~ inductive(X0)
| member(null_class,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inductive1) ).
fof(f51,axiom,
inductive(omega),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega_is_inductive1) ).
fof(f154,axiom,
union(singleton(null_class),image(successor_relation,ordinal_numbers)) = kind_1_ordinals,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kind_1_ordinals) ).
fof(f176,negated_conjecture,
~ member(null_class,kind_1_ordinals),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_null_class_is_kind_1_1) ).
fof(f178,plain,
! [X0] : range_of(X0) = domain_of(domain_of(flip(cross_product(X0,universal_class)))),
inference(definition_unfolding,[],[f40,f39]) ).
fof(f181,plain,
! [X0,X1] : image(X0,X1) = domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(X1,universal_class)),universal_class)))),
inference(definition_unfolding,[],[f43,f178,f28]) ).
fof(f200,plain,
! [X2,X0,X1] : intersection(cross_product(X0,X1),X2) = intersection(X2,cross_product(X0,X1)),
inference(definition_unfolding,[],[f29,f28]) ).
fof(f259,plain,
kind_1_ordinals = complement(intersection(complement(unordered_pair(null_class,null_class)),complement(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(ordinal_numbers,universal_class)),universal_class))))))),
inference(definition_unfolding,[],[f154,f26,f12,f181]) ).
fof(f274,plain,
~ member(null_class,complement(intersection(complement(unordered_pair(null_class,null_class)),complement(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(ordinal_numbers,universal_class)),universal_class)))))))),
inference(backward_demodulation,[],[f176,f259]) ).
fof(f276,plain,
~ member(null_class,complement(intersection(complement(unordered_pair(null_class,null_class)),complement(domain_of(domain_of(flip(cross_product(intersection(cross_product(ordinal_numbers,universal_class),successor_relation),universal_class)))))))),
inference(forward_demodulation,[],[f274,f200]) ).
fof(f287,plain,
member(null_class,omega),
inference(resolution,[],[f48,f51]) ).
fof(f652,plain,
! [X0] :
( ~ subclass(omega,X0)
| member(null_class,X0) ),
inference(resolution,[],[f287,f1]) ).
fof(f659,plain,
member(null_class,universal_class),
inference(resolution,[],[f652,f4]) ).
fof(f663,plain,
! [X0] : member(null_class,unordered_pair(null_class,X0)),
inference(resolution,[],[f659,f9]) ).
fof(f844,plain,
( ~ member(null_class,universal_class)
| member(null_class,intersection(complement(unordered_pair(null_class,null_class)),complement(domain_of(domain_of(flip(cross_product(intersection(cross_product(ordinal_numbers,universal_class),successor_relation),universal_class))))))) ),
inference(resolution,[],[f276,f25]) ).
fof(f845,plain,
member(null_class,intersection(complement(unordered_pair(null_class,null_class)),complement(domain_of(domain_of(flip(cross_product(intersection(cross_product(ordinal_numbers,universal_class),successor_relation),universal_class))))))),
inference(forward_subsumption_resolution,[],[f844,f659]) ).
fof(f847,plain,
member(null_class,complement(unordered_pair(null_class,null_class))),
inference(resolution,[],[f845,f21]) ).
fof(f849,plain,
~ member(null_class,unordered_pair(null_class,null_class)),
inference(resolution,[],[f847,f24]) ).
fof(f851,plain,
$false,
inference(forward_subsumption_resolution,[],[f849,f663]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM156-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.38 % Computer : n009.cluster.edu
% 0.09/0.38 % Model : x86_64 x86_64
% 0.09/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.38 % Memory : 8046.5625MB
% 0.09/0.38 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Sun Sep 27 19:01:31 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.42 Running first-order theorem proving
% 0.09/0.42 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
% 4.20/1.57 % (2336699)Input is clausal, will run a generic CNF schedule.
% 4.20/1.57 % (2336705)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=667196567:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 4.20/1.57 % (2336710)dis-21_1_sil=8000:lcm=predicate:random_seed=3498646377: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)
% 4.20/1.57 % (2336709)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2468689785:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 4.20/1.57 % (2336707)lrs+10_1_sil=8000:sp=occurrence:random_seed=971558354:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 4.20/1.57 % (2336704)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=4270267579:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 4.20/1.57 % (2336708)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=557513452:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 4.20/1.57 % (2336706)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3861130465:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 4.20/1.57 % (2336710)Instruction limit reached!
% 4.20/1.57 % (2336710)------------------------------
% 4.20/1.57 % (2336710)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.20/1.57 % (2336710)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.20/1.57 % (2336710)CaDiCaL version: 2.1.3
% 4.20/1.57 % (2336710)Termination reason: Instruction limit
% 4.20/1.57 % (2336710)Termination phase: Saturation
% 4.20/1.57 % (2336710)Time elapsed: 0.066 s
% 4.20/1.57 % (2336710)Peak memory usage: 89 MB
% 4.20/1.57 % (2336710)Instructions burned: 118 (million)
% 4.20/1.57 % (2336708)Instruction limit reached!
% 4.20/1.57 % (2336708)------------------------------
% 4.20/1.57 % (2336708)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.20/1.57 % (2336708)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.20/1.57 % (2336708)CaDiCaL version: 2.1.3
% 4.20/1.57 % (2336708)Termination reason: Instruction limit
% 4.20/1.57 % (2336708)Termination phase: Saturation
% 4.20/1.57 % (2336708)Time elapsed: 0.073 s
% 4.20/1.57 % (2336708)Peak memory usage: 89 MB
% 4.20/1.57 % (2336708)Instructions burned: 116 (million)
% 4.20/1.57 % (2336707)Instruction limit reached!
% 4.20/1.57 % (2336707)------------------------------
% 4.20/1.57 % (2336707)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.20/1.57 % (2336707)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.20/1.57 % (2336707)CaDiCaL version: 2.1.3
% 4.20/1.57 % (2336707)Termination reason: Instruction limit
% 4.20/1.57 % (2336707)Termination phase: Saturation
% 4.20/1.57 % (2336707)Time elapsed: 0.074 s
% 4.20/1.57 % (2336707)Peak memory usage: 90 MB
% 4.20/1.57 % (2336707)Instructions burned: 108 (million)
% 4.20/1.57 % (2336709)Instruction limit reached!
% 4.20/1.57 % (2336709)------------------------------
% 4.20/1.57 % (2336709)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.20/1.57 % (2336709)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.20/1.57 % (2336709)CaDiCaL version: 2.1.3
% 4.20/1.57 % (2336709)Termination reason: Instruction limit
% 4.20/1.57 % (2336709)Termination phase: Saturation
% 4.20/1.57 % (2336709)Time elapsed: 0.131 s
% 4.20/1.57 % (2336709)Peak memory usage: 90 MB
% 4.20/1.57 % (2336709)Instructions burned: 181 (million)
% 4.20/1.57 % (2336718)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=3490114602:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 4.20/1.57 % (2336718)Refutation not found, incomplete strategy
% 4.20/1.57 % (2336718)------------------------------
% 4.20/1.57 % (2336718)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.20/1.57 % (2336718)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.20/1.57 % (2336718)CaDiCaL version: 2.1.3
% 4.20/1.57 % (2336718)Termination reason: Refutation not found, incomplete strategy
% 4.20/1.57 % (2336718)Time elapsed: 0.003 s
% 4.20/1.57 % (2336718)Peak memory usage: 88 MB
% 4.20/1.57 % (2336718)Instructions burned: 3 (million)
% 4.20/1.57 % (2336719)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=4271174566: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)
% 5.54/1.76 % (2336720)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=898664428:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 5.54/1.76 % (2336721)lrs+10_64_to=lpo:sil=8000:random_seed=1344412622:i=126:bd=preordered_2997 on theBenchmark for (2997ds/126Mi)
% 5.54/1.76 % (2336721)First to succeed.
% 5.54/1.76 % (2336721)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2336699"
% 5.54/1.76 % (2336719)Instruction limit reached!
% 5.54/1.76 % (2336719)------------------------------
% 5.54/1.76 % (2336719)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.54/1.76 % (2336719)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.54/1.76 % (2336719)CaDiCaL version: 2.1.3
% 5.54/1.76 % (2336719)Termination reason: Instruction limit
% 5.54/1.76 % (2336719)Termination phase: Saturation
% 5.54/1.76 % (2336719)Time elapsed: 0.121 s
% 5.54/1.76 % (2336719)Peak memory usage: 90 MB
% 5.54/1.76 % (2336719)Instructions burned: 189 (million)
% 5.54/1.76 % (2336720)Instruction limit reached!
% 5.54/1.76 % (2336720)------------------------------
% 5.54/1.76 % (2336720)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.54/1.76 % (2336720)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.54/1.76 % (2336720)CaDiCaL version: 2.1.3
% 5.54/1.76 % (2336720)Termination reason: Instruction limit
% 5.54/1.76 % (2336720)Termination phase: Saturation
% 5.54/1.76 % (2336720)Time elapsed: 0.137 s
% 5.54/1.76 % (2336720)Peak memory usage: 89 MB
% 5.54/1.76 % (2336720)Instructions burned: 220 (million)
% 5.54/1.76 % (2336718)------------------------------
% 5.54/1.76 % (2336718)------------------------------
% 5.54/1.76 % (2336705)Also succeeded, but the first one will report.
% 5.54/1.76 % (2336726)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=3816536058:avsq=on:i=194:fgj=on:bd=preordered_2995 on theBenchmark for (2995ds/194Mi)
% 5.54/1.76 % (2336727)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=1059581486:i=157:gtg=all_2995 on theBenchmark for (2995ds/157Mi)
% 5.54/1.76 % (2336721)Refutation found. Thanks to Tanya!
% 5.54/1.76 % SZS status Unsatisfiable for theBenchmark
% 5.54/1.76 % SZS output start Proof for theBenchmark
% See solution above
% 5.54/1.76 % (2336721)------------------------------
% 5.54/1.76 % (2336721)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.54/1.76 % (2336721)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.54/1.76 % (2336721)CaDiCaL version: 2.1.3
% 5.54/1.76 % (2336721)Termination reason: Refutation
% 5.54/1.76 % (2336721)Time elapsed: 0.030 s
% 5.54/1.76 % (2336721)Peak memory usage: 89 MB
% 5.54/1.76 % (2336721)Instructions burned: 47 (million)
% 5.54/1.76 % (2336721)------------------------------
% 5.54/1.76 % (2336721)------------------------------
% 5.54/1.76 % (2336699)Success in time 0.712 s
% 5.54/1.76 % Vampire exiting
%------------------------------------------------------------------------------