%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP116-1 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 10:12:37 AM UTC 2026
% Result : Unsatisfiable 4.61s 1.64s
% Output : Refutation 4.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 2
% Syntax : Number of formulae : 21 ( 21 unt; 0 def)
% Number of atoms : 21 ( 20 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 39 ( 39 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : multiply(X0,multiply(multiply(X0,multiply(multiply(X0,X1),X2)),multiply(identity,multiply(X2,X2)))) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,negated_conjecture,
multiply(identity,a) != a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_order3) ).
fof(f3,plain,
a != multiply(identity,a),
inference(reorient_equations,[],[f2]) ).
fof(f7,plain,
! [X2,X0,X1] : multiply(X1,multiply(multiply(X1,multiply(multiply(X1,X2),multiply(identity,multiply(multiply(identity,X0),multiply(identity,X0))))),X0)) = X2,
inference(superposition,[],[f1,f1]) ).
fof(f13,plain,
! [X2,X0,X1] : multiply(multiply(X1,X0),multiply(identity,X2)) = multiply(X1,multiply(X0,X2)),
inference(superposition,[],[f7,f1]) ).
fof(f23,plain,
! [X2,X0,X1] : multiply(X0,multiply(X0,multiply(multiply(multiply(X0,X1),X2),multiply(X2,X2)))) = X1,
inference(superposition,[],[f1,f13]) ).
fof(f25,plain,
! [X2,X0,X1] : multiply(X0,multiply(multiply(X0,multiply(X0,multiply(X1,X2))),multiply(identity,multiply(multiply(identity,X2),multiply(identity,X2))))) = X1,
inference(superposition,[],[f1,f13]) ).
fof(f36,plain,
! [X2,X0,X1] : multiply(X0,multiply(X0,multiply(multiply(X0,multiply(X1,X2)),multiply(multiply(identity,X2),multiply(identity,X2))))) = X1,
inference(forward_demodulation,[],[f25,f13]) ).
fof(f46,plain,
! [X2,X0,X1] : multiply(X0,multiply(X0,multiply(multiply(X0,multiply(X1,X2)),multiply(identity,multiply(X2,X2))))) = X1,
inference(forward_demodulation,[],[f36,f13]) ).
fof(f51,plain,
! [X2,X0,X1] : multiply(X0,multiply(X0,multiply(X0,multiply(multiply(X1,X2),multiply(X2,X2))))) = X1,
inference(forward_demodulation,[],[f46,f13]) ).
fof(f61,plain,
! [X0,X1] : multiply(X0,multiply(X0,multiply(multiply(X0,X1),multiply(identity,identity)))) = X1,
inference(superposition,[],[f23,f13]) ).
fof(f72,plain,
! [X0,X1] : multiply(X0,multiply(X0,multiply(X0,multiply(X1,identity)))) = X1,
inference(forward_demodulation,[],[f61,f13]) ).
fof(f109,plain,
! [X0,X1] : multiply(multiply(X1,multiply(X0,X0)),X0) = X1,
inference(superposition,[],[f51,f51]) ).
fof(f148,plain,
! [X0,X1] : multiply(X0,multiply(multiply(multiply(identity,X1),multiply(identity,X1)),X1)) = X0,
inference(superposition,[],[f13,f109]) ).
fof(f160,plain,
! [X0,X1] : multiply(X0,multiply(multiply(identity,multiply(X1,X1)),X1)) = X0,
inference(forward_demodulation,[],[f148,f13]) ).
fof(f166,plain,
! [X0] : multiply(X0,identity) = X0,
inference(forward_demodulation,[],[f160,f109]) ).
fof(f177,plain,
! [X0,X1] : multiply(X1,multiply(X1,multiply(X1,X0))) = X0,
inference(superposition,[],[f72,f166]) ).
fof(f220,plain,
! [X0] : identity = multiply(X0,multiply(X0,X0)),
inference(superposition,[],[f177,f166]) ).
fof(f262,plain,
! [X0] : multiply(identity,X0) = X0,
inference(superposition,[],[f109,f220]) ).
fof(f296,plain,
a != a,
inference(superposition,[],[f3,f262]) ).
fof(f330,plain,
$false,
inference(trivial_inequality_removal,[],[f296]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP116-1 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n005.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 09:19:17 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 4.61/1.63 % (3727858)Detected a unit-equality problem, will run specialized UEQ schedule.
% 4.61/1.63 % (3727932)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2492418062:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 4.61/1.63 % (3727935)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=3074742105:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 4.61/1.63 % (3727931)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=4124735361:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 4.61/1.63 % (3727933)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=10132671:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 4.61/1.63 % (3727930)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=198807793:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 4.61/1.64 % (3727939)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2517498781:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 4.61/1.64 % (3727944)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=2200024777:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 4.61/1.64 % (3727944)First to succeed.
% 4.61/1.64 % (3727944)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3727858"
% 4.61/1.64 % (3727939)Also succeeded, but the first one will report.
% 4.61/1.64 % (3727933)Also succeeded, but the first one will report.
% 4.61/1.64 % (3727935)Also succeeded, but the first one will report.
% 4.61/1.64 % (3727944)Refutation found. Thanks to Tanya!
% 4.61/1.64 % SZS status Unsatisfiable for theBenchmark
% 4.61/1.64 % SZS output start Proof for theBenchmark
% See solution above
% 4.61/1.64 % (3727944)------------------------------
% 4.61/1.64 % (3727944)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.61/1.64 % (3727944)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.61/1.64 % (3727944)CaDiCaL version: 2.1.3
% 4.61/1.64 % (3727944)Termination reason: Refutation
% 4.61/1.64 % (3727944)Time elapsed: 0.016 s
% 4.61/1.64 % (3727944)Peak memory usage: 88 MB
% 4.61/1.64 % (3727944)Instructions burned: 14 (million)
% 4.61/1.64 % (3727944)------------------------------
% 4.61/1.64 % (3727944)------------------------------
% 4.61/1.64 % (3727858)Success in time 0.567 s
% 4.61/1.64 % Vampire exiting
%------------------------------------------------------------------------------