%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP023-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 10:12:08 AM UTC 2026
% Result : Unsatisfiable 2.52s 1.32s
% Output : Refutation 2.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 10 ( 10 unt; 1 def)
% Number of atoms : 10 ( 6 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 3 ( 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f5,axiom,
! [X0] : multiply(X0,identity) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_identity) ).
fof(f8,negated_conjecture,
inverse(identity) != identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_inverse_of_id_is_id) ).
fof(f9,plain,
identity != inverse(identity),
inference(reorient_equations,[],[f8]) ).
fof(f10,definition,
~ sP0(inverse(identity)),
introduced(definition,[new_symbols(definition,[sP0])],[inequality_splitting_name_introduction]) ).
fof(f11,plain,
sP0(identity),
inference(inequality_splitting,[],[f9,f10]) ).
fof(f18,plain,
identity = inverse(identity),
inference(superposition,[],[f5,f3]) ).
fof(f19,plain,
~ sP0(identity),
inference(backward_demodulation,[],[f10,f18]) ).
fof(f21,plain,
$false,
inference(forward_subsumption_resolution,[],[f19,f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP023-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.39 % Computer : n009.cluster.edu
% 0.10/0.39 % Model : x86_64 x86_64
% 0.10/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.39 % Memory : 8046.5625MB
% 0.10/0.39 % OS : Linux 6.8.0-71-generic
% 0.10/0.39 % CPULimit : 300
% 0.10/0.39 % WCLimit : 300
% 0.10/0.39 % DateTime : Sun Sep 27 09:14:15 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.43 Running first-order theorem proving
% 0.10/0.43 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
% 2.52/1.32 % (1755194)Detected a unit-equality problem, will run specialized UEQ schedule.
% 2.52/1.32 % (1755263)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=1825756351:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 2.52/1.32 % (1755263)First to succeed.
% 2.52/1.32 % (1755263)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1755194"
% 2.52/1.32 % (1755260)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=4199758540:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 2.52/1.32 % (1755264)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=2164704198:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 2.52/1.32 % (1755261)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=2471248543:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 2.52/1.32 % (1755266)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=3502900543:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 2.52/1.32 % (1755262)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=4032110683:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 2.52/1.32 % (1755266)Also succeeded, but the first one will report.
% 2.52/1.32 % (1755264)Also succeeded, but the first one will report.
% 2.52/1.32 % (1755265)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2920134706:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 2.52/1.32 % (1755265)Also succeeded, but the first one will report.
% 2.52/1.32 % (1755263)Refutation found. Thanks to Tanya!
% 2.52/1.32 % SZS status Unsatisfiable for theBenchmark
% 2.52/1.32 % SZS output start Proof for theBenchmark
% See solution above
% 2.52/1.32 % (1755263)------------------------------
% 2.52/1.32 % (1755263)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.52/1.32 % (1755263)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.52/1.32 % (1755263)CaDiCaL version: 2.1.3
% 2.52/1.32 % (1755263)Termination reason: Refutation
% 2.52/1.32 % (1755263)Time elapsed: 0.001 s
% 2.52/1.32 % (1755263)Peak memory usage: 87 MB
% 2.52/1.32 % (1755263)Instructions burned: 1 (million)
% 2.52/1.32 % (1755263)------------------------------
% 2.52/1.32 % (1755263)------------------------------
% 2.52/1.32 % (1755194)Success in time 0.262 s
% 2.52/1.32 % Vampire exiting
%------------------------------------------------------------------------------