%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP513-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 10:14:45 AM UTC 2026
% Result : Unsatisfiable 3.42s 1.37s
% Output : Refutation 3.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 2
% Syntax : Number of formulae : 19 ( 19 unt; 0 def)
% Number of atoms : 19 ( 18 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 41 ( 41 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : multiply(X0,multiply(multiply(X1,X2),inverse(multiply(X0,X2)))) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_1) ).
fof(f3,plain,
! [X2,X3,X0,X1] : multiply(X1,multiply(X0,inverse(multiply(X1,multiply(multiply(X0,X3),inverse(multiply(X2,X3))))))) = X2,
inference(superposition,[],[f1,f1]) ).
fof(f4,plain,
! [X2,X3,X0,X1] : multiply(X1,multiply(multiply(X2,multiply(multiply(X0,X3),inverse(multiply(X1,X3)))),inverse(X0))) = X2,
inference(superposition,[],[f1,f1]) ).
fof(f9,plain,
! [X0,X1] : multiply(X1,multiply(X0,inverse(X0))) = X1,
inference(superposition,[],[f3,f1]) ).
fof(f12,plain,
! [X0,X1] : multiply(X0,multiply(X1,inverse(X0))) = X1,
inference(superposition,[],[f3,f9]) ).
fof(f21,plain,
! [X2,X0,X1] : multiply(multiply(X2,X1),multiply(X0,inverse(multiply(X0,X1)))) = X2,
inference(superposition,[],[f3,f12]) ).
fof(f36,plain,
! [X2,X0,X1] : multiply(X2,X1) = multiply(multiply(X0,X1),multiply(X2,inverse(X0))),
inference(superposition,[],[f3,f21]) ).
fof(f72,plain,
! [X2,X0,X1] : multiply(X2,X1) = multiply(X2,multiply(multiply(X0,X1),inverse(X0))),
inference(superposition,[],[f4,f12]) ).
fof(f97,plain,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(multiply(X0,X2),X1),
inference(superposition,[],[f72,f36]) ).
fof(f148,plain,
! [X2,X0,X1] : multiply(X2,X1) = multiply(X2,multiply(multiply(X0,inverse(X0)),X1)),
inference(superposition,[],[f72,f97]) ).
fof(f208,plain,
! [X0,X1] : multiply(X0,inverse(X0)) = multiply(X1,inverse(X1)),
inference(superposition,[],[f148,f12]) ).
fof(f209,plain,
! [X0,X1] : multiply(X0,inverse(multiply(X1,inverse(X1)))) = X0,
inference(superposition,[],[f148,f9]) ).
fof(f334,plain,
! [X0,X1] : multiply(multiply(X1,inverse(X1)),X0) = X0,
inference(superposition,[],[f12,f209]) ).
fof(f404,plain,
! [X2,X0,X1] : multiply(X0,X2) = multiply(multiply(multiply(X1,inverse(X1)),X2),X0),
inference(superposition,[],[f97,f334]) ).
fof(f433,plain,
! [X2,X0] : multiply(X0,X2) = multiply(X2,X0),
inference(forward_demodulation,[],[f404,f334]) ).
fof(f619,plain,
multiply(inverse(a1),a1) != multiply(b1,inverse(b1)),
inference(superposition,[],[f2,f433]) ).
fof(f663,plain,
multiply(b1,inverse(b1)) != multiply(a1,inverse(a1)),
inference(forward_demodulation,[],[f619,f433]) ).
fof(f676,plain,
$false,
inference(forward_subsumption_resolution,[],[f663,f208]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP513-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n006.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 10:05:58 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 3.42/1.37 % (2753741)Detected a unit-equality problem, will run specialized UEQ schedule.
% 3.42/1.37 % (2753748)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=1978301587:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 3.42/1.37 % (2753751)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=1337266151:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 3.42/1.37 % (2753752)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1138160250:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 3.42/1.37 % (2753750)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=2610965061:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 3.42/1.37 % (2753749)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=1095168185:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 3.42/1.37 % (2753747)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=1019416513:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 3.42/1.37 % (2753746)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=3238153603:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 3.42/1.37 % (2753752)First to succeed.
% 3.42/1.37 % (2753752)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2753741"
% 3.42/1.37 % (2753751)Also succeeded, but the first one will report.
% 3.42/1.37 % (2753750)Also succeeded, but the first one will report.
% 3.42/1.37 % (2753749)Instruction limit reached!
% 3.42/1.37 % (2753749)------------------------------
% 3.42/1.37 % (2753749)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.42/1.37 % (2753749)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.42/1.37 % (2753749)CaDiCaL version: 2.1.3
% 3.42/1.37 % (2753749)Termination reason: Instruction limit
% 3.42/1.37 % (2753749)Termination phase: Saturation
% 3.42/1.37 % (2753749)Time elapsed: 0.082 s
% 3.42/1.37 % (2753749)Peak memory usage: 89 MB
% 3.42/1.37 % (2753749)Instructions burned: 136 (million)
% 3.42/1.37 % (2753760)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=1627232484:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 3.42/1.37 % (2753752)Refutation found. Thanks to Tanya!
% 3.42/1.37 % SZS status Unsatisfiable for theBenchmark
% 3.42/1.37 % SZS output start Proof for theBenchmark
% See solution above
% 3.42/1.37 % (2753752)------------------------------
% 3.42/1.37 % (2753752)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.42/1.37 % (2753752)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.42/1.37 % (2753752)CaDiCaL version: 2.1.3
% 3.42/1.37 % (2753752)Termination reason: Refutation
% 3.42/1.37 % (2753752)Time elapsed: 0.019 s
% 3.42/1.37 % (2753752)Peak memory usage: 88 MB
% 3.42/1.37 % (2753752)Instructions burned: 31 (million)
% 3.42/1.37 % (2753752)------------------------------
% 3.42/1.37 % (2753752)------------------------------
% 3.42/1.37 % (2753741)Success in time 0.417 s
% 3.42/1.37 % Vampire exiting
%------------------------------------------------------------------------------