%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP012-4 : 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 : n011.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 10:12:07 AM UTC 2026
% Result : Unsatisfiable 3.36s 1.35s
% Output : Refutation 3.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 23 ( 20 unt; 1 def)
% Number of atoms : 26 ( 16 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 7 ( 4 ~; 2 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 2 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 21 ( 0 sgn 21 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
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(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity) ).
fof(f5,axiom,
! [X0] : multiply(X0,identity) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_identity) ).
fof(f6,axiom,
! [X0] : multiply(X0,inverse(X0)) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_inverse) ).
fof(f7,plain,
! [X0] : identity = multiply(X0,inverse(X0)),
inference(reorient_equations,[],[f6]) ).
fof(f8,negated_conjecture,
inverse(multiply(a,b)) != multiply(inverse(b),inverse(a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_inverse_of_product_is_product_of_inverses) ).
fof(f10,definition,
( spl0_1
<=> inverse(multiply(a,b)) = multiply(inverse(b),inverse(a)) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f12,plain,
( inverse(multiply(a,b)) != multiply(inverse(b),inverse(a))
| spl0_1 ),
inference(avatar_component_clause,[],[f10]) ).
fof(f13,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f8,f10]) ).
fof(f27,plain,
! [X0,X1] : multiply(identity,X1) = multiply(inverse(X0),multiply(X0,X1)),
inference(superposition,[],[f4,f3]) ).
fof(f31,plain,
! [X0,X1] : identity = multiply(X0,multiply(X1,inverse(multiply(X0,X1)))),
inference(superposition,[],[f7,f4]) ).
fof(f32,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f27,f1]) ).
fof(f85,plain,
! [X0,X1] : multiply(X1,inverse(multiply(X0,X1))) = multiply(inverse(X0),identity),
inference(superposition,[],[f32,f31]) ).
fof(f96,plain,
! [X0,X1] : inverse(X0) = multiply(X1,inverse(multiply(X0,X1))),
inference(forward_demodulation,[],[f85,f5]) ).
fof(f127,plain,
! [X0,X1] : inverse(multiply(X0,X1)) = multiply(inverse(X1),inverse(X0)),
inference(superposition,[],[f32,f96]) ).
fof(f134,plain,
( $false
| spl0_1 ),
inference(backward_subsumption_resolution,[],[f12,f127]) ).
fof(f135,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f134]) ).
cnf(s1,plain,
~ spl0_1,
inference(sat_conversion,[],[f13]) ).
cnf(s4,plain,
spl0_1,
inference(sat_conversion,[],[f135]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s1,s4]) ).
fof(f147,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP012-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n011.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 09:13:45 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 3.36/1.35 % (2135761)Detected a unit-equality problem, will run specialized UEQ schedule.
% 3.36/1.35 % (2135779)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=3444985983:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 3.36/1.35 % (2135782)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=3816988966:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 3.36/1.35 % (2135782)First to succeed.
% 3.36/1.35 % (2135782)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2135761"
% 3.36/1.35 % (2135778)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=2765904769:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 3.36/1.35 % (2135783)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=233630473:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 3.36/1.35 % (2135777)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=545133945:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 3.36/1.35 % (2135780)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=902699703:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 3.36/1.35 % (2135781)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=2699779911:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 3.36/1.35 % (2135781)Also succeeded, but the first one will report.
% 3.36/1.35 % (2135783)Also succeeded, but the first one will report.
% 3.36/1.35 % (2135780)Also succeeded, but the first one will report.
% 3.36/1.35 % (2135782)Refutation found. Thanks to Tanya!
% 3.36/1.35 % SZS status Unsatisfiable for theBenchmark
% 3.36/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 3.36/1.35 % (2135782)------------------------------
% 3.36/1.35 % (2135782)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.36/1.35 % (2135782)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.36/1.35 % (2135782)CaDiCaL version: 2.1.3
% 3.36/1.35 % (2135782)Termination reason: Refutation
% 3.36/1.35 % (2135782)Time elapsed: 0.005 s
% 3.36/1.35 % (2135782)Peak memory usage: 89 MB
% 3.36/1.35 % (2135782)Instructions burned: 5 (million)
% 3.36/1.35 % (2135782)------------------------------
% 3.36/1.35 % (2135782)------------------------------
% 3.36/1.35 % (2135761)Success in time 0.413 s
% 3.36/1.35 % Vampire exiting
%------------------------------------------------------------------------------