%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET454-6 : 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 : n005.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 12:40:59 PM UTC 2026
% Result : Unsatisfiable 6.17s 1.83s
% Output : Refutation 6.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 18 ( 14 unt; 0 def)
% Number of atoms : 22 ( 7 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 9 ( 5 ~; 4 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 13 ( 3 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-2 aty)
% Number of variables : 11 ( 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(f21,axiom,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection1) ).
fof(f22,axiom,
! [X2,X0,X1] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection2) ).
fof(f39,axiom,
! [X0] : domain_of(flip(cross_product(X0,universal_class))) = inverse(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse) ).
fof(f78,axiom,
intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation))))) = subset_relation,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_relation) ).
fof(f79,axiom,
intersection(inverse(subset_relation),subset_relation) = identity_relation,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_relation) ).
fof(f80,plain,
identity_relation = intersection(inverse(subset_relation),subset_relation),
inference(reorient_equations,[],[f79]) ).
fof(f122,negated_conjecture,
~ subclass(identity_relation,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_identity_alternate_defn1_1) ).
fof(f165,plain,
subset_relation = intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),
inference(definition_unfolding,[],[f78,f39]) ).
fof(f166,plain,
identity_relation = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation),
inference(definition_unfolding,[],[f80,f39]) ).
fof(f189,plain,
identity_relation = intersection(domain_of(flip(cross_product(intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),universal_class))),intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),
inference(backward_demodulation,[],[f166,f165]) ).
fof(f195,plain,
~ subclass(intersection(domain_of(flip(cross_product(intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),universal_class))),intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),cross_product(universal_class,universal_class)),
inference(backward_demodulation,[],[f122,f189]) ).
fof(f200,plain,
member(not_subclass_element(intersection(domain_of(flip(cross_product(intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),universal_class))),intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),cross_product(universal_class,universal_class)),intersection(domain_of(flip(cross_product(intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),universal_class))),intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))))),
inference(resolution,[],[f2,f195]) ).
fof(f235,plain,
member(not_subclass_element(intersection(domain_of(flip(cross_product(intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),universal_class))),intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),cross_product(universal_class,universal_class)),intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),
inference(resolution,[],[f200,f22]) ).
fof(f238,plain,
member(not_subclass_element(intersection(domain_of(flip(cross_product(intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),universal_class))),intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),cross_product(universal_class,universal_class)),cross_product(universal_class,universal_class)),
inference(resolution,[],[f235,f21]) ).
fof(f239,plain,
subclass(intersection(domain_of(flip(cross_product(intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),universal_class))),intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),cross_product(universal_class,universal_class)),
inference(resolution,[],[f238,f3]) ).
fof(f240,plain,
$false,
inference(forward_subsumption_resolution,[],[f239,f195]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET454-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n005.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 : Mon Sep 28 01:51:32 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.13/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 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
% 5.19/1.64 % (358128)Input is clausal, will run a generic CNF schedule.
% 5.19/1.64 % (358136)lrs+10_1_sil=8000:sp=occurrence:random_seed=2687245816:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 5.19/1.64 % (358136)Refutation not found, incomplete strategy
% 5.19/1.64 % (358136)------------------------------
% 5.19/1.64 % (358136)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.19/1.64 % (358136)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.19/1.64 % (358136)CaDiCaL version: 2.1.3
% 5.19/1.64 % (358136)Termination reason: Refutation not found, incomplete strategy
% 5.19/1.64 % (358136)Time elapsed: 0.001 s
% 5.19/1.64 % (358136)Peak memory usage: 88 MB
% 5.19/1.64 % (358136)Instructions burned: 1 (million)
% 5.19/1.64 % (358134)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1171145180:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 5.19/1.64 % (358138)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=883821886:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 5.19/1.64 % (358137)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1022571124:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 5.19/1.64 % (358133)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=2415792540:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 5.19/1.64 % (358137)Refutation not found, incomplete strategy
% 5.19/1.64 % (358137)------------------------------
% 5.19/1.64 % (358137)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.19/1.64 % (358135)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=943296217:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 5.19/1.64 % (358137)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.19/1.64 % (358137)CaDiCaL version: 2.1.3
% 5.19/1.64 % (358137)Termination reason: Refutation not found, incomplete strategy
% 5.19/1.64 % (358137)Time elapsed: 0.003 s
% 5.19/1.64 % (358137)Peak memory usage: 88 MB
% 5.19/1.64 % (358137)Instructions burned: 3 (million)
% 5.19/1.64 % (358139)dis-21_1_sil=8000:lcm=predicate:random_seed=1817939407: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)
% 5.19/1.64 % (358139)Instruction limit reached!
% 5.19/1.64 % (358139)------------------------------
% 5.19/1.64 % (358139)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.19/1.64 % (358139)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.19/1.64 % (358139)CaDiCaL version: 2.1.3
% 5.19/1.64 % (358139)Termination reason: Instruction limit
% 5.19/1.64 % (358139)Termination phase: Saturation
% 5.19/1.64 % (358139)Time elapsed: 0.071 s
% 5.19/1.64 % (358139)Peak memory usage: 89 MB
% 5.19/1.64 % (358139)Instructions burned: 118 (million)
% 5.19/1.64 % (358136)------------------------------
% 5.19/1.64 % (358136)------------------------------
% 5.19/1.64 % (358138)Instruction limit reached!
% 5.19/1.64 % (358138)------------------------------
% 5.19/1.64 % (358138)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.19/1.64 % (358138)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.19/1.64 % (358138)CaDiCaL version: 2.1.3
% 5.19/1.64 % (358138)Termination reason: Instruction limit
% 5.19/1.64 % (358138)Termination phase: Saturation
% 5.19/1.64 % (358138)Time elapsed: 0.140 s
% 5.19/1.64 % (358138)Peak memory usage: 90 MB
% 5.19/1.64 % (358138)Instructions burned: 180 (million)
% 5.19/1.64 % (358147)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=344588983:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 5.19/1.64 % (358147)Refutation not found, incomplete strategy
% 5.19/1.64 % (358147)------------------------------
% 5.19/1.64 % (358147)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.19/1.64 % (358147)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.19/1.64 % (358147)CaDiCaL version: 2.1.3
% 5.19/1.64 % (358147)Termination reason: Refutation not found, incomplete strategy
% 5.19/1.64 % (358147)Time elapsed: 0.003 s
% 5.19/1.64 % (358147)Peak memory usage: 88 MB
% 5.19/1.64 % (358147)Instructions burned: 3 (million)
% 6.17/1.83 % (358148)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=580571513: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)
% 6.17/1.83 % (358137)------------------------------
% 6.17/1.83 % (358137)------------------------------
% 6.17/1.83 % (358149)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=4009605200:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 6.17/1.83 % (358149)Refutation not found, incomplete strategy
% 6.17/1.83 % (358149)------------------------------
% 6.17/1.83 % (358149)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.17/1.83 % (358149)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.17/1.83 % (358149)CaDiCaL version: 2.1.3
% 6.17/1.83 % (358149)Termination reason: Refutation not found, incomplete strategy
% 6.17/1.83 % (358149)Time elapsed: 0.003 s
% 6.17/1.83 % (358149)Peak memory usage: 88 MB
% 6.17/1.83 % (358149)Instructions burned: 3 (million)
% 6.17/1.83 % (358148)Instruction limit reached!
% 6.17/1.83 % (358148)------------------------------
% 6.17/1.83 % (358148)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.17/1.83 % (358148)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.17/1.83 % (358148)CaDiCaL version: 2.1.3
% 6.17/1.83 % (358148)Termination reason: Instruction limit
% 6.17/1.83 % (358148)Termination phase: Saturation
% 6.17/1.83 % (358148)Time elapsed: 0.059 s
% 6.17/1.83 % (358148)Peak memory usage: 91 MB
% 6.17/1.83 % (358148)Instructions burned: 189 (million)
% 6.17/1.83 % (358152)lrs+10_64_to=lpo:sil=8000:random_seed=477663251:i=126:bd=preordered_2996 on theBenchmark for (2996ds/126Mi)
% 6.17/1.83 % (358152)First to succeed.
% 6.17/1.83 % (358152)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-358128"
% 6.17/1.83 % (358154)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=3478094179:avsq=on:i=194:fgj=on:bd=preordered_2995 on theBenchmark for (2995ds/194Mi)
% 6.17/1.83 % (358154)Instruction limit reached!
% 6.17/1.83 % (358154)------------------------------
% 6.17/1.83 % (358154)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.17/1.83 % (358154)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.17/1.83 % (358154)CaDiCaL version: 2.1.3
% 6.17/1.83 % (358154)Termination reason: Instruction limit
% 6.17/1.83 % (358154)Termination phase: Saturation
% 6.17/1.83 % (358154)Time elapsed: 0.067 s
% 6.17/1.83 % (358154)Peak memory usage: 90 MB
% 6.17/1.83 % (358154)Instructions burned: 194 (million)
% 6.17/1.83 % (358147)------------------------------
% 6.17/1.83 % (358147)------------------------------
% 6.17/1.83 % (358149)------------------------------
% 6.17/1.83 % (358149)------------------------------
% 6.17/1.83 % (358157)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=827216957:i=157:gtg=all_2993 on theBenchmark for (2993ds/157Mi)
% 6.17/1.83 % (358157)Instruction limit reached!
% 6.17/1.83 % (358157)------------------------------
% 6.17/1.83 % (358157)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.17/1.83 % (358157)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.17/1.83 % (358157)CaDiCaL version: 2.1.3
% 6.17/1.83 % (358157)Termination reason: Instruction limit
% 6.17/1.83 % (358157)Termination phase: Saturation
% 6.17/1.83 % (358157)Time elapsed: 0.057 s
% 6.17/1.83 % (358157)Peak memory usage: 91 MB
% 6.17/1.83 % (358157)Instructions burned: 158 (million)
% 6.17/1.83 % (358158)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=2924576673:i=3394:sd=4:ss=included:sgt=64_2993 on theBenchmark for (2993ds/3394Mi)
% 6.17/1.83 % (358152)Refutation found. Thanks to Tanya!
% 6.17/1.83 % SZS status Unsatisfiable for theBenchmark
% 6.17/1.83 % SZS output start Proof for theBenchmark
% See solution above
% 6.17/1.83 % (358152)------------------------------
% 6.17/1.83 % (358152)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.17/1.83 % (358152)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.17/1.83 % (358152)CaDiCaL version: 2.1.3
% 6.17/1.83 % (358152)Termination reason: Refutation
% 6.17/1.83 % (358152)Time elapsed: 0.012 s
% 6.17/1.83 % (358152)Peak memory usage: 89 MB
% 6.17/1.83 % (358152)Instructions burned: 19 (million)
% 6.17/1.83 % (358152)------------------------------
% 6.17/1.83 % (358152)------------------------------
% 6.17/1.83 % (358128)Success in time 0.792 s
% 6.17/1.83 % Vampire exiting
%------------------------------------------------------------------------------