%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP656-10 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 10:15:27 AM UTC 2026
% Result : Unsatisfiable 2.77s 1.35s
% Output : Refutation 2.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 14 ( 14 unt; 0 def)
% Number of atoms : 14 ( 13 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 0 con; 1-2 aty)
% Number of variables : 25 ( 25 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : mult(X0,ld(X0,X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f01) ).
fof(f2,axiom,
! [X0,X1] : ld(X0,mult(X0,X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f02) ).
fof(f4,axiom,
! [X0,X1] : rd(mult(X0,X1),X1) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f04) ).
fof(f5,axiom,
! [X2,X0,X1] : mult(mult(X0,X1),mult(X2,X0)) = mult(mult(X0,mult(X1,X2)),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f05) ).
fof(f6,negated_conjecture,
! [X0] : tuple(mult(X0,x1(X0)),mult(x1_2(X0),X0)) != tuple(x1(X0),x1_2(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
fof(f13,plain,
! [X2,X0,X1] : mult(mult(X1,X2),mult(ld(X2,X0),X1)) = mult(mult(X1,X0),X1),
inference(superposition,[],[f5,f1]) ).
fof(f31,plain,
! [X2,X0,X1] : mult(ld(X2,X1),X0) = ld(mult(X0,X2),mult(mult(X0,X1),X0)),
inference(superposition,[],[f2,f13]) ).
fof(f151,plain,
! [X0,X1] : mult(ld(X1,X1),X0) = X0,
inference(superposition,[],[f31,f2]) ).
fof(f165,plain,
! [X0,X1] : ld(X1,X1) = rd(X0,X0),
inference(superposition,[],[f4,f151]) ).
fof(f182,plain,
! [X0] : tuple(x1(ld(X0,X0)),x1_2(ld(X0,X0))) != tuple(x1(ld(X0,X0)),mult(x1_2(ld(X0,X0)),ld(X0,X0))),
inference(superposition,[],[f6,f151]) ).
fof(f255,plain,
! [X0,X1] : mult(X1,rd(X0,X0)) = X1,
inference(superposition,[],[f1,f165]) ).
fof(f257,plain,
! [X0] : tuple(x1(rd(X0,X0)),x1_2(rd(X0,X0))) != tuple(x1(rd(X0,X0)),mult(x1_2(rd(X0,X0)),rd(X0,X0))),
inference(superposition,[],[f182,f165]) ).
fof(f444,plain,
! [X0] : tuple(x1(rd(X0,X0)),x1_2(rd(X0,X0))) != tuple(x1(rd(X0,X0)),x1_2(rd(X0,X0))),
inference(superposition,[],[f257,f255]) ).
fof(f446,plain,
$false,
inference(trivial_inequality_removal,[],[f444]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP656-10 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n014.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 10:32:16 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 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
% 2.77/1.35 % (597364)Detected a unit-equality problem, will run specialized UEQ schedule.
% 2.77/1.35 % (597476)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=2748119013:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 2.77/1.35 % (597476)First to succeed.
% 2.77/1.35 % (597476)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-597364"
% 2.77/1.35 % (597472)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=387445091:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 2.77/1.35 % (597471)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=205962349:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 2.77/1.35 % (597475)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=3263868234:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 2.77/1.35 % (597474)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=3650300254:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 2.77/1.35 % (597470)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=662485113:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 2.77/1.35 % (597473)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=3944216199:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 2.77/1.35 % (597474)Also succeeded, but the first one will report.
% 2.77/1.35 % (597473)Also succeeded, but the first one will report.
% 2.77/1.35 % (597475)Also succeeded, but the first one will report.
% 2.77/1.35 % (597476)Refutation found. Thanks to Tanya!
% 2.77/1.35 % SZS status Unsatisfiable for theBenchmark
% 2.77/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 2.77/1.35 % (597476)------------------------------
% 2.77/1.35 % (597476)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.77/1.35 % (597476)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.77/1.35 % (597476)CaDiCaL version: 2.1.3
% 2.77/1.35 % (597476)Termination reason: Refutation
% 2.77/1.35 % (597476)Time elapsed: 0.008 s
% 2.77/1.35 % (597476)Peak memory usage: 88 MB
% 2.77/1.35 % (597476)Instructions burned: 21 (million)
% 2.77/1.35 % (597476)------------------------------
% 2.77/1.35 % (597476)------------------------------
% 2.77/1.35 % (597364)Success in time 0.313 s
% 2.77/1.35 % Vampire exiting
%------------------------------------------------------------------------------