%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM042-1 : 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 : n026.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 12:11:38 PM UTC 2026
% Result : Unsatisfiable 4.93s 1.66s
% Output : Refutation 4.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 12
% Syntax : Number of formulae : 22 ( 16 unt; 0 def)
% Number of atoms : 29 ( 7 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 19 ( 12 ~; 7 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 11 ( 3 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-3 aty)
% Number of variables : 28 ( 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subclass_members) ).
fof(f2,axiom,
! [X0,X1] :
( member(not_subclass_element(X0,X1),X0)
| subclass(X0,X1) ),
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(f21,axiom,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection1) ).
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(f122,axiom,
! [X0] : union(X0,inverse(X0)) = symmetrization_of(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetrization) ).
fof(f124,axiom,
! [X0,X1] :
( ~ subclass(restrict(X0,X1,X1),complement(identity_relation))
| irreflexive(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',irreflexive2) ).
fof(f176,negated_conjecture,
subclass(x,complement(identity_relation)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_irreflexive_class_property4_1) ).
fof(f177,negated_conjecture,
~ irreflexive(x,domain_of(symmetrization_of(x))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_irreflexive_class_property4_2) ).
fof(f191,plain,
! [X0] : symmetrization_of(X0) = complement(intersection(complement(X0),complement(domain_of(flip(cross_product(X0,universal_class)))))),
inference(definition_unfolding,[],[f122,f26,f39]) ).
fof(f195,plain,
~ irreflexive(x,domain_of(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class)))))))),
inference(definition_unfolding,[],[f177,f191]) ).
fof(f196,plain,
! [X0,X1] :
( ~ subclass(intersection(cross_product(X1,X1),X0),complement(identity_relation))
| irreflexive(X0,X1) ),
inference(definition_unfolding,[],[f124,f29]) ).
fof(f226,plain,
! [X2,X0,X1] : intersection(X0,cross_product(X1,X2)) = intersection(cross_product(X1,X2),X0),
inference(definition_unfolding,[],[f28,f29]) ).
fof(f269,plain,
~ subclass(intersection(cross_product(domain_of(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class))))))),domain_of(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class)))))))),x),complement(identity_relation)),
inference(unit_resulting_resolution,[],[f196,f195]) ).
fof(f270,plain,
~ subclass(intersection(x,cross_product(domain_of(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class))))))),domain_of(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class))))))))),complement(identity_relation)),
inference(forward_demodulation,[],[f269,f226]) ).
fof(f271,plain,
member(not_subclass_element(intersection(x,cross_product(domain_of(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class))))))),domain_of(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class))))))))),complement(identity_relation)),intersection(x,cross_product(domain_of(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class))))))),domain_of(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class)))))))))),
inference(unit_resulting_resolution,[],[f2,f270]) ).
fof(f272,plain,
~ member(not_subclass_element(intersection(x,cross_product(domain_of(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class))))))),domain_of(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class))))))))),complement(identity_relation)),complement(identity_relation)),
inference(unit_resulting_resolution,[],[f3,f270]) ).
fof(f275,plain,
~ member(not_subclass_element(intersection(x,cross_product(domain_of(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class))))))),domain_of(complement(intersection(complement(x),complement(domain_of(flip(cross_product(x,universal_class))))))))),complement(identity_relation)),x),
inference(unit_resulting_resolution,[],[f1,f176,f272]) ).
fof(f289,plain,
$false,
inference(unit_resulting_resolution,[],[f21,f275,f271]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM042-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n026.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 18:45:12 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 4.93/1.66 % (3139610)Input is clausal, will run a generic CNF schedule.
% 4.93/1.66 % (3139615)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=4125560145:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 4.93/1.66 % (3139620)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1002232546:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 4.93/1.66 % (3139621)dis-21_1_sil=8000:lcm=predicate:random_seed=2640262421: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)
% 4.93/1.66 % (3139617)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=957684789:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 4.93/1.66 % (3139616)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1678251680:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 4.93/1.66 % (3139618)lrs+10_1_sil=8000:sp=occurrence:random_seed=3736734893:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 4.93/1.66 % (3139619)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1020651026:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 4.93/1.66 % (3139621)Instruction limit reached!
% 4.93/1.66 % (3139621)------------------------------
% 4.93/1.66 % (3139621)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.93/1.66 % (3139621)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.93/1.66 % (3139621)CaDiCaL version: 2.1.3
% 4.93/1.66 % (3139621)Termination reason: Instruction limit
% 4.93/1.66 % (3139621)Termination phase: Saturation
% 4.93/1.66 % (3139621)Time elapsed: 0.054 s
% 4.93/1.66 % (3139621)Peak memory usage: 89 MB
% 4.93/1.66 % (3139621)Instructions burned: 118 (million)
% 4.93/1.66 % (3139619)Instruction limit reached!
% 4.93/1.66 % (3139619)------------------------------
% 4.93/1.66 % (3139619)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.93/1.66 % (3139619)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.93/1.66 % (3139619)CaDiCaL version: 2.1.3
% 4.93/1.66 % (3139619)Termination reason: Instruction limit
% 4.93/1.66 % (3139619)Termination phase: Saturation
% 4.93/1.66 % (3139619)Time elapsed: 0.069 s
% 4.93/1.66 % (3139619)Peak memory usage: 89 MB
% 4.93/1.66 % (3139619)Instructions burned: 115 (million)
% 4.93/1.66 % (3139618)Instruction limit reached!
% 4.93/1.66 % (3139618)------------------------------
% 4.93/1.66 % (3139618)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.93/1.66 % (3139618)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.93/1.66 % (3139618)CaDiCaL version: 2.1.3
% 4.93/1.66 % (3139618)Termination reason: Instruction limit
% 4.93/1.66 % (3139618)Termination phase: Saturation
% 4.93/1.66 % (3139618)Time elapsed: 0.070 s
% 4.93/1.66 % (3139618)Peak memory usage: 89 MB
% 4.93/1.66 % (3139618)Instructions burned: 107 (million)
% 4.93/1.66 % (3139620)Instruction limit reached!
% 4.93/1.66 % (3139620)------------------------------
% 4.93/1.66 % (3139620)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.93/1.66 % (3139620)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.93/1.66 % (3139620)CaDiCaL version: 2.1.3
% 4.93/1.66 % (3139620)Termination reason: Instruction limit
% 4.93/1.66 % (3139620)Termination phase: Saturation
% 4.93/1.66 % (3139620)Time elapsed: 0.142 s
% 4.93/1.66 % (3139620)Peak memory usage: 90 MB
% 4.93/1.66 % (3139620)Instructions burned: 180 (million)
% 4.93/1.66 % (3139629)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=362453709:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 4.93/1.66 % (3139629)Refutation not found, incomplete strategy
% 4.93/1.66 % (3139629)------------------------------
% 4.93/1.66 % (3139629)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.93/1.66 % (3139629)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.93/1.66 % (3139629)CaDiCaL version: 2.1.3
% 4.93/1.66 % (3139629)Termination reason: Refutation not found, incomplete strategy
% 4.93/1.66 % (3139629)Time elapsed: 0.004 s
% 4.93/1.66 % (3139629)Peak memory usage: 88 MB
% 4.93/1.66 % (3139629)Instructions burned: 4 (million)
% 4.93/1.66 % (3139631)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=54566967:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 4.93/1.66 % (3139630)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=4010189180: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)
% 4.93/1.66 % (3139631)Refutation not found, incomplete strategy
% 4.93/1.66 % (3139631)------------------------------
% 4.93/1.66 % (3139631)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.93/1.66 % (3139631)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.93/1.66 % (3139631)CaDiCaL version: 2.1.3
% 4.93/1.66 % (3139631)Termination reason: Refutation not found, incomplete strategy
% 4.93/1.66 % (3139631)Time elapsed: 0.004 s
% 4.93/1.66 % (3139631)Peak memory usage: 88 MB
% 4.93/1.66 % (3139631)Instructions burned: 5 (million)
% 4.93/1.66 % (3139630)First to succeed.
% 4.93/1.66 % (3139630)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3139610"
% 4.93/1.66 % (3139632)lrs+10_64_to=lpo:sil=8000:random_seed=1646792994:i=126:bd=preordered_2997 on theBenchmark for (2997ds/126Mi)
% 4.93/1.66 % (3139632)Instruction limit reached!
% 4.93/1.66 % (3139632)------------------------------
% 4.93/1.66 % (3139632)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.93/1.66 % (3139632)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.93/1.66 % (3139632)CaDiCaL version: 2.1.3
% 4.93/1.66 % (3139632)Termination reason: Instruction limit
% 4.93/1.66 % (3139632)Termination phase: Saturation
% 4.93/1.66 % (3139632)Time elapsed: 0.081 s
% 4.93/1.66 % (3139632)Peak memory usage: 89 MB
% 4.93/1.66 % (3139632)Instructions burned: 127 (million)
% 4.93/1.66 % (3139629)------------------------------
% 4.93/1.66 % (3139629)------------------------------
% 4.93/1.66 % (3139631)------------------------------
% 4.93/1.66 % (3139631)------------------------------
% 4.93/1.66 % (3139630)Refutation found. Thanks to Tanya!
% 4.93/1.66 % SZS status Unsatisfiable for theBenchmark
% 4.93/1.66 % SZS output start Proof for theBenchmark
% See solution above
% 4.93/1.66 % (3139630)------------------------------
% 4.93/1.66 % (3139630)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.93/1.66 % (3139630)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.93/1.66 % (3139630)CaDiCaL version: 2.1.3
% 4.93/1.66 % (3139630)Termination reason: Refutation
% 4.93/1.66 % (3139630)Time elapsed: 0.016 s
% 4.93/1.66 % (3139630)Peak memory usage: 89 MB
% 4.93/1.66 % (3139630)Instructions burned: 27 (million)
% 4.93/1.66 % (3139630)------------------------------
% 4.93/1.66 % (3139630)------------------------------
% 4.93/1.66 % (3139610)Success in time 0.619 s
% 4.93/1.66 % Vampire exiting
%------------------------------------------------------------------------------