%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : REL008-3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 12:33:40 PM UTC 2026
% Result : Unsatisfiable 2.50s 0.95s
% Output : Refutation 2.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 17 ( 17 unt; 1 def)
% Number of atoms : 17 ( 8 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 15 ( 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [X2,X0,X1] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_distributivity_7) ).
fof(f10,axiom,
! [X0] : converse(converse(X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_idempotence_8) ).
fof(f11,axiom,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_additivity_9) ).
fof(f12,axiom,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_multiplicativity_10) ).
fof(f23,negated_conjecture,
composition(sk1,join(sk2,sk3)) != join(composition(sk1,sk2),composition(sk1,sk3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_17) ).
fof(f28,definition,
~ sP0(composition(sk1,join(sk2,sk3))),
introduced(definition,[new_symbols(definition,[sP0])],[inequality_splitting_name_introduction]) ).
fof(f29,plain,
sP0(join(composition(sk1,sk2),composition(sk1,sk3))),
inference(inequality_splitting,[],[f23,f28]) ).
fof(f33,plain,
! [X0,X1] : converse(join(X1,converse(X0))) = join(converse(X1),X0),
inference(superposition,[],[f11,f10]) ).
fof(f48,plain,
! [X0,X1] : composition(X1,X0) = converse(composition(converse(X0),converse(X1))),
inference(superposition,[],[f10,f12]) ).
fof(f94,plain,
! [X2,X0,X1] : composition(join(X2,converse(X1)),converse(X0)) = join(composition(X2,converse(X0)),converse(composition(X0,X1))),
inference(superposition,[],[f9,f12]) ).
fof(f634,plain,
sP0(join(converse(composition(converse(sk2),converse(sk1))),composition(sk1,sk3))),
inference(superposition,[],[f29,f48]) ).
fof(f661,plain,
sP0(converse(join(composition(converse(sk2),converse(sk1)),converse(composition(sk1,sk3))))),
inference(forward_demodulation,[],[f634,f33]) ).
fof(f691,plain,
sP0(converse(composition(join(converse(sk2),converse(sk3)),converse(sk1)))),
inference(forward_demodulation,[],[f661,f94]) ).
fof(f700,plain,
sP0(converse(composition(converse(join(sk2,converse(converse(sk3)))),converse(sk1)))),
inference(forward_demodulation,[],[f691,f33]) ).
fof(f702,plain,
sP0(converse(composition(converse(join(sk2,sk3)),converse(sk1)))),
inference(forward_demodulation,[],[f700,f10]) ).
fof(f708,plain,
sP0(composition(sk1,join(sk2,sk3))),
inference(superposition,[],[f702,f48]) ).
fof(f715,plain,
$false,
inference(forward_subsumption_resolution,[],[f708,f28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : REL008-3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Sun Sep 27 22:50:22 UTC 2026
% 0.03/0.31 % CPUTime :
% 0.03/0.31 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.33 Running first-order theorem proving
% 0.07/0.33 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
% 2.50/0.95 % (2838437)Detected a unit-equality problem, will run specialized UEQ schedule.
% 2.50/0.95 % (2838443)lrs+11_1_ncem=casc2026/models/loop6.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=2610191259:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 2.50/0.95 % (2838442)lrs+1002_1_ncem=casc2026/models/loop7.pt:sil=128000:tgt=ground:npcc=on:drc=off:sp=reverse_frequency:spb=goal:acc=on:s2agt=16:kmz=on:sac=on:random_seed=1921544727:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 2.50/0.95 % (2838446)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=274900149:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 2.50/0.95 % (2838448)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=301360969:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 2.50/0.95 % (2838445)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=323352721:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 2.50/0.95 % (2838447)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=698975589:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 2.50/0.95 % (2838444)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=747235459:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 2.50/0.95 % (2838445)First to succeed.
% 2.50/0.95 % (2838445)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2838437"
% 2.50/0.95 % (2838446)Instruction limit reached!
% 2.50/0.95 % (2838446)------------------------------
% 2.50/0.95 % (2838446)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.50/0.95 % (2838446)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.50/0.95 % (2838446)CaDiCaL version: 2.1.3
% 2.50/0.95 % (2838446)Termination reason: Instruction limit
% 2.50/0.95 % (2838446)Termination phase: Saturation
% 2.50/0.95 % (2838446)Time elapsed: 0.056 s
% 2.50/0.95 % (2838446)Peak memory usage: 89 MB
% 2.50/0.95 % (2838446)Instructions burned: 182 (million)
% 2.50/0.95 % (2838447)Instruction limit reached!
% 2.50/0.95 % (2838447)------------------------------
% 2.50/0.95 % (2838447)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.50/0.95 % (2838447)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.50/0.95 % (2838447)CaDiCaL version: 2.1.3
% 2.50/0.95 % (2838447)Termination reason: Instruction limit
% 2.50/0.95 % (2838447)Termination phase: Saturation
% 2.50/0.95 % (2838447)Time elapsed: 0.089 s
% 2.50/0.95 % (2838447)Peak memory usage: 90 MB
% 2.50/0.95 % (2838447)Instructions burned: 260 (million)
% 2.50/0.95 % (2838456)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=1907102493:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2998 on theBenchmark for (2998ds/2051Mi)
% 2.50/0.95 % (2838445)Refutation found. Thanks to Tanya!
% 2.50/0.95 % SZS status Unsatisfiable for theBenchmark
% 2.50/0.95 % SZS output start Proof for theBenchmark
% See solution above
% 2.50/0.95 % (2838445)------------------------------
% 2.50/0.95 % (2838445)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.50/0.95 % (2838445)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.50/0.95 % (2838445)CaDiCaL version: 2.1.3
% 2.50/0.95 % (2838445)Termination reason: Refutation
% 2.50/0.95 % (2838445)Time elapsed: 0.019 s
% 2.50/0.95 % (2838445)Peak memory usage: 88 MB
% 2.50/0.95 % (2838445)Instructions burned: 57 (million)
% 2.50/0.95 % (2838445)------------------------------
% 2.50/0.95 % (2838445)------------------------------
% 2.50/0.95 % (2838437)Success in time 0.324 s
% 2.50/0.95 % Vampire exiting
%------------------------------------------------------------------------------