%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM217-1 : 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 : n016.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 12:11:55 PM UTC 2026
% Result : Unsatisfiable 5.52s 1.74s
% Output : Refutation 5.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 14
% Syntax : Number of formulae : 36 ( 20 unt; 0 def)
% Number of atoms : 54 ( 21 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 40 ( 22 ~; 18 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 2 con; 0-3 aty)
% Number of variables : 43 ( 43 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( ~ member(X2,X0)
| ~ subclass(X0,X1)
| member(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subclass_members) ).
fof(f6,axiom,
! [X0,X1] :
( X0 != X1
| subclass(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_implies_subclass2) ).
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_set) ).
fof(f13,axiom,
! [X0,X1] : unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))) = ordered_pair(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordered_pair) ).
fof(f17,axiom,
! [X2,X0,X1] :
( ~ member(X0,cross_product(X1,X2))
| ordered_pair(first(X0),second(X0)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartesian_product4) ).
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(f28,axiom,
! [X2,X0,X1] : intersection(X0,cross_product(X1,X2)) = restrict(X0,X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',restriction1) ).
fof(f30,axiom,
! [X0,X1] :
( restrict(X0,singleton(X1),universal_class) != null_class
| ~ member(X1,domain_of(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain1) ).
fof(f67,axiom,
! [X0] :
( X0 = null_class
| member(regular(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',regularity1) ).
fof(f68,plain,
! [X0] :
( member(regular(X0),X0)
| null_class = X0 ),
inference(reorient_equations,[],[f67]) ).
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(f156,axiom,
! [X0] : subclass(rest_of(X0),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rest_of1) ).
fof(f157,axiom,
! [X2,X0,X1] :
( ~ member(ordered_pair(X0,X1),rest_of(X2))
| member(X0,domain_of(X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rest_of2) ).
fof(f176,negated_conjecture,
rest_of(null_class) != null_class,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_2_to_rest_defn_1) ).
fof(f177,plain,
null_class != rest_of(null_class),
inference(reorient_equations,[],[f176]) ).
fof(f178,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),
inference(definition_unfolding,[],[f13,f12,f12]) ).
fof(f198,plain,
! [X2,X0,X1] :
( ~ member(X0,cross_product(X1,X2))
| unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))) = X0 ),
inference(definition_unfolding,[],[f17,f178]) ).
fof(f202,plain,
! [X0,X1] :
( null_class != intersection(X0,cross_product(unordered_pair(X1,X1),universal_class))
| ~ member(X1,domain_of(X0)) ),
inference(definition_unfolding,[],[f30,f28,f12]) ).
fof(f261,plain,
! [X2,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),rest_of(X2))
| member(X0,domain_of(X2)) ),
inference(definition_unfolding,[],[f157,f178]) ).
fof(f269,plain,
! [X1] : subclass(X1,X1),
inference(equality_resolution,[],[f6]) ).
fof(f277,plain,
member(regular(rest_of(null_class)),rest_of(null_class)),
inference(unit_resulting_resolution,[],[f68,f177]) ).
fof(f280,plain,
member(regular(rest_of(null_class)),cross_product(universal_class,universal_class)),
inference(unit_resulting_resolution,[],[f1,f277,f156]) ).
fof(f281,plain,
! [X0,X1] :
( ~ member(X0,null_class)
| member(X0,X1)
| null_class = X1 ),
inference(superposition,[],[f21,f70]) ).
fof(f308,plain,
regular(rest_of(null_class)) = unordered_pair(unordered_pair(first(regular(rest_of(null_class))),first(regular(rest_of(null_class)))),unordered_pair(first(regular(rest_of(null_class))),unordered_pair(second(regular(rest_of(null_class))),second(regular(rest_of(null_class)))))),
inference(unit_resulting_resolution,[],[f198,f280]) ).
fof(f309,plain,
! [X0] :
( member(first(regular(rest_of(null_class))),domain_of(X0))
| ~ member(regular(rest_of(null_class)),rest_of(X0)) ),
inference(superposition,[],[f261,f308]) ).
fof(f361,plain,
member(first(regular(rest_of(null_class))),domain_of(null_class)),
inference(unit_resulting_resolution,[],[f309,f277]) ).
fof(f363,plain,
null_class != intersection(null_class,cross_product(unordered_pair(first(regular(rest_of(null_class))),first(regular(rest_of(null_class)))),universal_class)),
inference(unit_resulting_resolution,[],[f202,f361]) ).
fof(f440,plain,
member(regular(intersection(null_class,cross_product(unordered_pair(first(regular(rest_of(null_class))),first(regular(rest_of(null_class)))),universal_class))),intersection(null_class,cross_product(unordered_pair(first(regular(rest_of(null_class))),first(regular(rest_of(null_class)))),universal_class))),
inference(unit_resulting_resolution,[],[f68,f363]) ).
fof(f448,plain,
member(regular(intersection(null_class,cross_product(unordered_pair(first(regular(rest_of(null_class))),first(regular(rest_of(null_class)))),universal_class))),null_class),
inference(unit_resulting_resolution,[],[f21,f440]) ).
fof(f467,plain,
~ member(regular(intersection(null_class,cross_product(unordered_pair(first(regular(rest_of(null_class))),first(regular(rest_of(null_class)))),universal_class))),complement(intersection(null_class,cross_product(unordered_pair(first(regular(rest_of(null_class))),first(regular(rest_of(null_class)))),universal_class)))),
inference(unit_resulting_resolution,[],[f24,f440]) ).
fof(f579,plain,
null_class = complement(intersection(null_class,cross_product(unordered_pair(first(regular(rest_of(null_class))),first(regular(rest_of(null_class)))),universal_class))),
inference(unit_resulting_resolution,[],[f281,f467,f448]) ).
fof(f618,plain,
~ subclass(null_class,complement(intersection(null_class,cross_product(unordered_pair(first(regular(rest_of(null_class))),first(regular(rest_of(null_class)))),universal_class)))),
inference(unit_resulting_resolution,[],[f1,f467,f448]) ).
fof(f620,plain,
~ subclass(null_class,null_class),
inference(forward_demodulation,[],[f618,f579]) ).
fof(f621,plain,
$false,
inference(forward_subsumption_resolution,[],[f620,f269]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM217-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n016.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 19:17:32 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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
% 4.39/1.55 % (2938413)Input is clausal, will run a generic CNF schedule.
% 4.39/1.55 % (2938419)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3872708032:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 4.39/1.55 % (2938418)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=1699518273:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 4.39/1.55 % (2938421)lrs+10_1_sil=8000:sp=occurrence:random_seed=3863117016:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 4.39/1.55 % (2938424)dis-21_1_sil=8000:lcm=predicate:random_seed=2941886294: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)
% 4.39/1.55 % (2938420)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=355181389:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 4.39/1.55 % (2938422)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=4118973197:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 4.39/1.55 % (2938423)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2765667360:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 4.39/1.55 % (2938421)Instruction limit reached!
% 4.39/1.55 % (2938421)------------------------------
% 4.39/1.55 % (2938421)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.39/1.55 % (2938421)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.39/1.55 % (2938421)CaDiCaL version: 2.1.3
% 4.39/1.55 % (2938421)Termination reason: Instruction limit
% 4.39/1.55 % (2938421)Termination phase: Saturation
% 4.39/1.55 % (2938421)Time elapsed: 0.056 s
% 4.39/1.55 % (2938421)Peak memory usage: 89 MB
% 4.39/1.55 % (2938421)Instructions burned: 107 (million)
% 4.39/1.55 % (2938422)Instruction limit reached!
% 4.39/1.55 % (2938422)------------------------------
% 4.39/1.55 % (2938422)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.39/1.55 % (2938422)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.39/1.55 % (2938422)CaDiCaL version: 2.1.3
% 4.39/1.55 % (2938422)Termination reason: Instruction limit
% 4.39/1.55 % (2938422)Termination phase: Saturation
% 4.39/1.55 % (2938422)Time elapsed: 0.073 s
% 4.39/1.55 % (2938422)Peak memory usage: 88 MB
% 4.39/1.55 % (2938422)Instructions burned: 115 (million)
% 4.39/1.55 % (2938424)Instruction limit reached!
% 4.39/1.55 % (2938424)------------------------------
% 4.39/1.55 % (2938424)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.39/1.55 % (2938424)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.39/1.55 % (2938424)CaDiCaL version: 2.1.3
% 4.39/1.55 % (2938424)Termination reason: Instruction limit
% 4.39/1.55 % (2938424)Termination phase: Saturation
% 4.39/1.55 % (2938424)Time elapsed: 0.074 s
% 4.39/1.55 % (2938424)Peak memory usage: 89 MB
% 4.39/1.55 % (2938424)Instructions burned: 118 (million)
% 4.39/1.55 % (2938423)Instruction limit reached!
% 4.39/1.55 % (2938423)------------------------------
% 4.39/1.55 % (2938423)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.39/1.55 % (2938423)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.39/1.55 % (2938423)CaDiCaL version: 2.1.3
% 4.39/1.55 % (2938423)Termination reason: Instruction limit
% 4.39/1.55 % (2938423)Termination phase: Saturation
% 4.39/1.55 % (2938423)Time elapsed: 0.138 s
% 4.39/1.55 % (2938423)Peak memory usage: 90 MB
% 4.39/1.55 % (2938423)Instructions burned: 181 (million)
% 4.39/1.55 % (2938432)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=1299360295:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 4.39/1.55 % (2938432)Refutation not found, incomplete strategy
% 4.39/1.55 % (2938432)------------------------------
% 4.39/1.55 % (2938432)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.39/1.55 % (2938432)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.39/1.55 % (2938432)CaDiCaL version: 2.1.3
% 4.39/1.55 % (2938432)Termination reason: Refutation not found, incomplete strategy
% 4.39/1.55 % (2938432)Time elapsed: 0.002 s
% 4.39/1.55 % (2938432)Peak memory usage: 88 MB
% 4.39/1.55 % (2938432)Instructions burned: 1 (million)
% 4.39/1.55 % (2938433)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=1913872938: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)
% 5.52/1.74 % (2938434)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=974520675:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 5.52/1.74 % (2938434)Refutation not found, incomplete strategy
% 5.52/1.74 % (2938434)------------------------------
% 5.52/1.74 % (2938434)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.52/1.74 % (2938434)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.52/1.74 % (2938434)CaDiCaL version: 2.1.3
% 5.52/1.74 % (2938434)Termination reason: Refutation not found, incomplete strategy
% 5.52/1.74 % (2938434)Time elapsed: 0.004 s
% 5.52/1.74 % (2938434)Peak memory usage: 87 MB
% 5.52/1.74 % (2938434)Instructions burned: 4 (million)
% 5.52/1.74 % (2938435)lrs+10_64_to=lpo:sil=8000:random_seed=1401011751:i=126:bd=preordered_2996 on theBenchmark for (2996ds/126Mi)
% 5.52/1.74 % (2938433)Instruction limit reached!
% 5.52/1.74 % (2938433)------------------------------
% 5.52/1.74 % (2938433)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.52/1.74 % (2938433)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.52/1.74 % (2938433)CaDiCaL version: 2.1.3
% 5.52/1.74 % (2938433)Termination reason: Instruction limit
% 5.52/1.74 % (2938433)Termination phase: Saturation
% 5.52/1.74 % (2938433)Time elapsed: 0.119 s
% 5.52/1.74 % (2938433)Peak memory usage: 90 MB
% 5.52/1.74 % (2938433)Instructions burned: 190 (million)
% 5.52/1.74 % (2938419)First to succeed.
% 5.52/1.74 % (2938419)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2938413"
% 5.52/1.74 % (2938435)Instruction limit reached!
% 5.52/1.74 % (2938435)------------------------------
% 5.52/1.74 % (2938435)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.52/1.74 % (2938435)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.52/1.74 % (2938435)CaDiCaL version: 2.1.3
% 5.52/1.74 % (2938435)Termination reason: Instruction limit
% 5.52/1.74 % (2938435)Termination phase: Saturation
% 5.52/1.74 % (2938435)Time elapsed: 0.083 s
% 5.52/1.74 % (2938435)Peak memory usage: 89 MB
% 5.52/1.74 % (2938435)Instructions burned: 127 (million)
% 5.52/1.74 % (2938432)------------------------------
% 5.52/1.74 % (2938432)------------------------------
% 5.52/1.74 % (2938434)------------------------------
% 5.52/1.74 % (2938434)------------------------------
% 5.52/1.74 % (2938440)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=3224920227:avsq=on:i=194:fgj=on:bd=preordered_2994 on theBenchmark for (2994ds/194Mi)
% 5.52/1.74 % (2938419)Refutation found. Thanks to Tanya!
% 5.52/1.74 % SZS status Unsatisfiable for theBenchmark
% 5.52/1.74 % SZS output start Proof for theBenchmark
% See solution above
% 5.52/1.74 % (2938419)------------------------------
% 5.52/1.74 % (2938419)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.52/1.74 % (2938419)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.52/1.74 % (2938419)CaDiCaL version: 2.1.3
% 5.52/1.74 % (2938419)Termination reason: Refutation
% 5.52/1.74 % (2938419)Time elapsed: 0.408 s
% 5.52/1.74 % (2938419)Peak memory usage: 130 MB
% 5.52/1.74 % (2938419)Instructions burned: 1082 (million)
% 5.52/1.74 % (2938419)------------------------------
% 5.52/1.74 % (2938419)------------------------------
% 5.52/1.74 % (2938413)Success in time 0.705 s
% 5.52/1.74 % Vampire exiting
%------------------------------------------------------------------------------