%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP538-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 10:14:49 AM UTC 2026
% Result : Unsatisfiable 2.69s 1.34s
% Output : Refutation 2.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 18 ( 18 unt; 1 def)
% Number of atoms : 18 ( 10 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 8 ( 8 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 15 ( 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : divide(divide(X0,X1),divide(divide(X0,X2),X1)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,axiom,
! [X2,X0,X1] : multiply(X0,X1) = divide(X0,divide(divide(X2,X2),X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply) ).
fof(f3,axiom,
! [X0,X1] : inverse(X0) = divide(divide(X1,X1),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse) ).
fof(f4,axiom,
! [X0] : identity = divide(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity) ).
fof(f5,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_2) ).
fof(f6,plain,
a2 != multiply(multiply(inverse(b2),b2),a2),
inference(reorient_equations,[],[f5]) ).
fof(f7,definition,
~ sP0(multiply(multiply(inverse(b2),b2),a2)),
introduced(definition,[new_symbols(definition,[sP0])],[inequality_splitting_name_introduction]) ).
fof(f8,plain,
sP0(a2),
inference(inequality_splitting,[],[f6,f7]) ).
fof(f9,plain,
! [X0] : inverse(X0) = divide(identity,X0),
inference(forward_demodulation,[],[f3,f4]) ).
fof(f10,plain,
! [X0,X1] : multiply(X0,X1) = divide(X0,divide(identity,X1)),
inference(forward_demodulation,[],[f2,f4]) ).
fof(f11,plain,
~ sP0(multiply(multiply(divide(identity,b2),b2),a2)),
inference(backward_demodulation,[],[f7,f9]) ).
fof(f12,plain,
~ sP0(divide(multiply(divide(identity,b2),b2),divide(identity,a2))),
inference(forward_demodulation,[],[f11,f10]) ).
fof(f13,plain,
~ sP0(divide(divide(divide(identity,b2),divide(identity,b2)),divide(identity,a2))),
inference(forward_demodulation,[],[f12,f10]) ).
fof(f14,plain,
~ sP0(divide(identity,divide(identity,a2))),
inference(forward_demodulation,[],[f13,f4]) ).
fof(f15,plain,
! [X0,X1] : divide(identity,divide(divide(X0,X1),X0)) = X1,
inference(superposition,[],[f1,f4]) ).
fof(f21,plain,
! [X0] : divide(identity,divide(identity,X0)) = X0,
inference(superposition,[],[f15,f4]) ).
fof(f36,plain,
~ sP0(a2),
inference(backward_demodulation,[],[f14,f21]) ).
fof(f45,plain,
$false,
inference(forward_subsumption_resolution,[],[f36,f8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP538-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 % Computer : n006.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sun Sep 27 10:06:10 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.43 Running first-order theorem proving
% 0.13/0.43 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
% 2.69/1.34 % (2754539)Detected a unit-equality problem, will run specialized UEQ schedule.
% 2.69/1.34 % (2754597)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=924685736:i=136:bd=preordered:ins=2:av=off_3000 on theBenchmark for (3000ds/136Mi)
% 2.69/1.34 % (2754597)First to succeed.
% 2.69/1.34 % (2754597)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2754539"
% 2.69/1.34 % (2754596)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2933010230:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_3000 on theBenchmark for (3000ds/130716Mi)
% 2.69/1.34 % (2754595)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=1343815184:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_3000 on theBenchmark for (3000ds/130792Mi)
% 2.69/1.34 % (2754598)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=2381255794:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_3000 on theBenchmark for (3000ds/181Mi)
% 2.69/1.34 % (2754600)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=12584701:i=1187:sd=4:av=off:ss=axioms:sgt=32_3000 on theBenchmark for (3000ds/1187Mi)
% 2.69/1.34 % (2754594)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=1683338157:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_3000 on theBenchmark for (3000ds/138329Mi)
% 2.69/1.34 % (2754599)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2658607176:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_3000 on theBenchmark for (3000ds/257Mi)
% 2.69/1.34 % (2754599)Also succeeded, but the first one will report.
% 2.69/1.34 % (2754600)Also succeeded, but the first one will report.
% 2.69/1.34 % (2754598)Also succeeded, but the first one will report.
% 2.69/1.34 % (2754597)Refutation found. Thanks to Tanya!
% 2.69/1.34 % SZS status Unsatisfiable for theBenchmark
% 2.69/1.34 % SZS output start Proof for theBenchmark
% See solution above
% 2.69/1.34 % (2754597)------------------------------
% 2.69/1.34 % (2754597)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.69/1.34 % (2754597)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/1.34 % (2754597)CaDiCaL version: 2.1.3
% 2.69/1.34 % (2754597)Termination reason: Refutation
% 2.69/1.34 % (2754597)Time elapsed: 0.002 s
% 2.69/1.34 % (2754597)Peak memory usage: 87 MB
% 2.69/1.34 % (2754597)Instructions burned: 2 (million)
% 2.69/1.34 % (2754597)------------------------------
% 2.69/1.34 % (2754597)------------------------------
% 2.69/1.34 % (2754539)Success in time 0.282 s
% 2.69/1.34 % Vampire exiting
%------------------------------------------------------------------------------