%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP582-1 : 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 : 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 10:14:55 AM UTC 2026
% Result : Unsatisfiable 3.22s 1.35s
% Output : Refutation 4.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 6
% Syntax : Number of formulae : 63 ( 63 unt; 1 def)
% Number of atoms : 63 ( 57 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 7 ( 7 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 72 ( 72 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : double_divide(double_divide(X0,double_divide(double_divide(identity,X1),double_divide(X2,double_divide(X1,X0)))),double_divide(identity,identity)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,axiom,
! [X0,X1] : multiply(X0,X1) = double_divide(double_divide(X1,X0),identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
fof(f3,axiom,
! [X0] : inverse(X0) = double_divide(X0,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse) ).
fof(f4,axiom,
! [X0] : identity = double_divide(X0,inverse(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity) ).
fof(f5,negated_conjecture,
multiply(identity,a2) != a2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_2) ).
fof(f6,plain,
a2 != multiply(identity,a2),
inference(reorient_equations,[],[f5]) ).
fof(f7,plain,
! [X0] : identity = double_divide(X0,double_divide(X0,identity)),
inference(definition_unfolding,[],[f4,f3]) ).
fof(f8,plain,
a2 != double_divide(double_divide(a2,identity),identity),
inference(definition_unfolding,[],[f6,f2]) ).
fof(f9,definition,
~ sP0(double_divide(double_divide(a2,identity),identity)),
introduced(definition,[new_symbols(definition,[sP0])],[inequality_splitting_name_introduction]) ).
fof(f10,plain,
sP0(a2),
inference(inequality_splitting,[],[f8,f9]) ).
fof(f11,plain,
! [X0,X1] : double_divide(double_divide(X0,double_divide(identity,double_divide(X1,double_divide(double_divide(identity,identity),X0)))),double_divide(identity,identity)) = X1,
inference(superposition,[],[f1,f7]) ).
fof(f12,plain,
! [X0,X1] : double_divide(double_divide(double_divide(X0,identity),double_divide(double_divide(identity,X0),double_divide(X1,identity))),double_divide(identity,identity)) = X1,
inference(superposition,[],[f1,f7]) ).
fof(f14,plain,
! [X0] : double_divide(double_divide(identity,double_divide(double_divide(identity,X0),identity)),double_divide(identity,identity)) = X0,
inference(superposition,[],[f1,f7]) ).
fof(f15,plain,
! [X2,X0,X1] : double_divide(X1,double_divide(double_divide(identity,X2),double_divide(X0,double_divide(X2,X1)))) = double_divide(double_divide(identity,double_divide(double_divide(identity,identity),X0)),double_divide(identity,identity)),
inference(superposition,[],[f1,f1]) ).
fof(f16,plain,
double_divide(identity,identity) = double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(identity,identity)),
inference(superposition,[],[f14,f7]) ).
fof(f17,plain,
! [X0] : double_divide(identity,double_divide(double_divide(identity,X0),identity)) = double_divide(double_divide(identity,double_divide(double_divide(identity,identity),X0)),double_divide(identity,identity)),
inference(superposition,[],[f1,f14]) ).
fof(f18,plain,
! [X0,X1] : double_divide(double_divide(double_divide(identity,identity),double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(identity,X0),identity))),double_divide(X1,X0))),double_divide(identity,identity)) = X1,
inference(superposition,[],[f1,f14]) ).
fof(f19,plain,
double_divide(identity,identity) = double_divide(identity,double_divide(identity,identity)),
inference(forward_demodulation,[],[f16,f7]) ).
fof(f20,plain,
identity = double_divide(identity,identity),
inference(forward_demodulation,[],[f19,f7]) ).
fof(f21,plain,
! [X2,X0,X1] : double_divide(double_divide(X0,double_divide(double_divide(identity,X1),double_divide(X2,double_divide(X1,X0)))),identity) = X2,
inference(backward_demodulation,[],[f1,f20]) ).
fof(f22,plain,
! [X0,X1] : double_divide(double_divide(X0,double_divide(identity,double_divide(X1,double_divide(identity,X0)))),identity) = X1,
inference(backward_demodulation,[],[f11,f20]) ).
fof(f23,plain,
! [X0,X1] : double_divide(double_divide(double_divide(X0,identity),double_divide(double_divide(identity,X0),double_divide(X1,identity))),identity) = X1,
inference(backward_demodulation,[],[f12,f20]) ).
fof(f25,plain,
! [X0] : double_divide(double_divide(identity,double_divide(double_divide(identity,X0),identity)),identity) = X0,
inference(backward_demodulation,[],[f14,f20]) ).
fof(f26,plain,
! [X2,X0,X1] : double_divide(X1,double_divide(double_divide(identity,X2),double_divide(X0,double_divide(X2,X1)))) = double_divide(double_divide(identity,double_divide(identity,X0)),identity),
inference(backward_demodulation,[],[f15,f20]) ).
fof(f27,plain,
! [X0] : double_divide(identity,double_divide(double_divide(identity,X0),identity)) = double_divide(double_divide(identity,double_divide(identity,X0)),identity),
inference(backward_demodulation,[],[f17,f20]) ).
fof(f28,plain,
! [X0,X1] : double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(identity,X0),identity))),double_divide(X1,X0))),identity) = X1,
inference(backward_demodulation,[],[f18,f20]) ).
fof(f37,plain,
! [X0] : double_divide(double_divide(identity,double_divide(identity,double_divide(X0,identity))),identity) = X0,
inference(superposition,[],[f21,f20]) ).
fof(f38,plain,
! [X0] : double_divide(identity,double_divide(double_divide(identity,double_divide(X0,identity)),identity)) = X0,
inference(forward_demodulation,[],[f37,f27]) ).
fof(f42,plain,
! [X0] : identity = double_divide(double_divide(identity,double_divide(double_divide(identity,X0),identity)),X0),
inference(superposition,[],[f7,f25]) ).
fof(f63,plain,
! [X0] : double_divide(identity,double_divide(double_divide(identity,double_divide(identity,X0)),identity)) = double_divide(double_divide(X0,double_divide(identity,identity)),identity),
inference(superposition,[],[f22,f42]) ).
fof(f65,plain,
! [X0] : double_divide(double_divide(identity,X0),identity) = double_divide(identity,double_divide(X0,double_divide(identity,identity))),
inference(superposition,[],[f25,f22]) ).
fof(f68,plain,
! [X0] : double_divide(double_divide(identity,X0),identity) = double_divide(identity,double_divide(X0,identity)),
inference(forward_demodulation,[],[f65,f20]) ).
fof(f70,plain,
! [X0] : double_divide(identity,double_divide(double_divide(identity,double_divide(identity,X0)),identity)) = double_divide(double_divide(X0,identity),identity),
inference(forward_demodulation,[],[f63,f20]) ).
fof(f74,plain,
! [X0,X1] : double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(identity,X0),identity))),double_divide(X1,X0)),identity)) = X1,
inference(backward_demodulation,[],[f28,f68]) ).
fof(f78,plain,
! [X2,X0,X1] : double_divide(X1,double_divide(double_divide(identity,X2),double_divide(X0,double_divide(X2,X1)))) = double_divide(identity,double_divide(double_divide(identity,X0),identity)),
inference(backward_demodulation,[],[f26,f68]) ).
fof(f79,plain,
! [X0] : double_divide(identity,double_divide(identity,double_divide(double_divide(X0,identity),identity))) = X0,
inference(backward_demodulation,[],[f38,f68]) ).
fof(f82,plain,
! [X0] : identity = double_divide(double_divide(identity,double_divide(identity,double_divide(X0,identity))),X0),
inference(backward_demodulation,[],[f42,f68]) ).
fof(f84,plain,
! [X0] : double_divide(identity,double_divide(identity,double_divide(double_divide(identity,X0),identity))) = double_divide(double_divide(X0,identity),identity),
inference(forward_demodulation,[],[f70,f68]) ).
fof(f91,plain,
! [X2,X0,X1] : double_divide(X1,double_divide(double_divide(identity,X2),double_divide(X0,double_divide(X2,X1)))) = double_divide(identity,double_divide(identity,double_divide(X0,identity))),
inference(forward_demodulation,[],[f78,f68]) ).
fof(f93,plain,
! [X0,X1] : double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(X0,identity)))),double_divide(X1,X0)),identity)) = X1,
inference(forward_demodulation,[],[f74,f68]) ).
fof(f94,plain,
! [X0] : double_divide(double_divide(X0,identity),identity) = double_divide(identity,double_divide(identity,double_divide(identity,double_divide(X0,identity)))),
inference(forward_demodulation,[],[f84,f68]) ).
fof(f102,plain,
! [X0] : double_divide(identity,double_divide(identity,double_divide(identity,double_divide(identity,double_divide(identity,double_divide(X0,identity)))))) = X0,
inference(backward_demodulation,[],[f79,f94]) ).
fof(f103,plain,
~ sP0(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(a2,identity))))),
inference(backward_demodulation,[],[f9,f94]) ).
fof(f116,plain,
! [X0] : identity = double_divide(double_divide(double_divide(X0,identity),double_divide(double_divide(identity,X0),identity)),identity),
inference(superposition,[],[f23,f20]) ).
fof(f120,plain,
! [X0] : identity = double_divide(double_divide(double_divide(X0,identity),double_divide(identity,double_divide(X0,identity))),identity),
inference(forward_demodulation,[],[f116,f68]) ).
fof(f265,plain,
! [X0] : identity = double_divide(double_divide(X0,double_divide(identity,X0)),identity),
inference(superposition,[],[f120,f22]) ).
fof(f331,plain,
! [X0] : identity = double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(X0,double_divide(identity,X0))),
inference(superposition,[],[f82,f265]) ).
fof(f334,plain,
! [X0] : identity = double_divide(identity,double_divide(X0,double_divide(identity,X0))),
inference(forward_demodulation,[],[f331,f7]) ).
fof(f353,plain,
! [X0] : double_divide(X0,double_divide(identity,X0)) = double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(identity,identity)))),identity),identity)),
inference(superposition,[],[f93,f265]) ).
fof(f381,plain,
! [X0] : double_divide(X0,double_divide(identity,X0)) = double_divide(identity,double_divide(identity,double_divide(identity,double_divide(identity,double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(identity,identity)))),identity))))),
inference(forward_demodulation,[],[f353,f94]) ).
fof(f398,plain,
! [X0] : double_divide(X0,double_divide(identity,X0)) = double_divide(identity,double_divide(identity,double_divide(identity,double_divide(identity,double_divide(identity,double_divide(double_divide(identity,double_divide(identity,double_divide(identity,identity))),identity)))))),
inference(forward_demodulation,[],[f381,f68]) ).
fof(f411,plain,
! [X0] : double_divide(identity,double_divide(identity,double_divide(identity,identity))) = double_divide(X0,double_divide(identity,X0)),
inference(forward_demodulation,[],[f398,f102]) ).
fof(f419,plain,
! [X0] : identity = double_divide(X0,double_divide(identity,X0)),
inference(forward_demodulation,[],[f411,f334]) ).
fof(f432,plain,
! [X0] : double_divide(double_divide(X0,double_divide(identity,identity)),identity) = X0,
inference(superposition,[],[f22,f419]) ).
fof(f433,plain,
! [X0] : double_divide(identity,double_divide(identity,double_divide(X0,identity))) = double_divide(X0,double_divide(double_divide(identity,identity),identity)),
inference(superposition,[],[f91,f419]) ).
fof(f455,plain,
! [X0] : double_divide(identity,double_divide(identity,double_divide(X0,identity))) = double_divide(X0,double_divide(identity,double_divide(identity,identity))),
inference(forward_demodulation,[],[f433,f68]) ).
fof(f456,plain,
! [X0] : double_divide(double_divide(X0,identity),identity) = X0,
inference(forward_demodulation,[],[f432,f20]) ).
fof(f465,plain,
! [X0] : double_divide(X0,identity) = double_divide(identity,double_divide(identity,double_divide(X0,identity))),
inference(forward_demodulation,[],[f455,f7]) ).
fof(f466,plain,
! [X0] : double_divide(identity,double_divide(identity,double_divide(identity,double_divide(X0,identity)))) = X0,
inference(backward_demodulation,[],[f94,f456]) ).
fof(f501,plain,
~ sP0(double_divide(identity,double_divide(a2,identity))),
inference(backward_demodulation,[],[f103,f465]) ).
fof(f502,plain,
! [X0] : double_divide(identity,double_divide(X0,identity)) = X0,
inference(forward_demodulation,[],[f466,f465]) ).
fof(f545,plain,
~ sP0(a2),
inference(backward_demodulation,[],[f501,f502]) ).
fof(f569,plain,
$false,
inference(forward_subsumption_resolution,[],[f545,f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP582-1 : 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 : n005.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 10:07:32 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 3.22/1.35 % (3769814)Detected a unit-equality problem, will run specialized UEQ schedule.
% 3.22/1.35 % (3769925)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=3923465459:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 3.22/1.35 % (3769921)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=3370695063:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 3.22/1.35 % (3769920)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=2439959356:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 3.22/1.35 % (3769922)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=854970698:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 3.22/1.35 % (3769926)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=3398186195:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 3.22/1.35 % (3769924)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=2459118686:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 3.22/1.35 % (3769923)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=555437013:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 3.22/1.35 % (3769925)Instruction limit reached!
% 3.22/1.35 % (3769925)------------------------------
% 3.22/1.35 % (3769925)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.22/1.35 % (3769925)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.22/1.35 % (3769925)CaDiCaL version: 2.1.3
% 3.22/1.35 % (3769925)Termination reason: Instruction limit
% 3.22/1.35 % (3769925)Termination phase: Saturation
% 3.22/1.35 % (3769925)Time elapsed: 0.070 s
% 3.22/1.35 % (3769925)Peak memory usage: 89 MB
% 3.22/1.35 % (3769925)Instructions burned: 259 (million)
% 3.22/1.35 % (3769923)First to succeed.
% 3.22/1.35 % (3769923)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3769814"
% 3.22/1.35 % (3769926)Also succeeded, but the first one will report.
% 3.22/1.35 % (3769924)Also succeeded, but the first one will report.
% 3.22/1.35 % (3769936)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=2212780731:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 3.22/1.35 % (3769923)Refutation found. Thanks to Tanya!
% 3.22/1.35 % SZS status Unsatisfiable for theBenchmark
% 3.22/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 4.02/1.56 % (3769923)------------------------------
% 4.02/1.56 % (3769923)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.02/1.56 % (3769923)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.02/1.56 % (3769923)CaDiCaL version: 2.1.3
% 4.02/1.56 % (3769923)Termination reason: Refutation
% 4.02/1.56 % (3769923)Time elapsed: 0.021 s
% 4.02/1.56 % (3769923)Peak memory usage: 88 MB
% 4.02/1.56 % (3769923)Instructions burned: 35 (million)
% 4.02/1.56 % (3769923)------------------------------
% 4.02/1.56 % (3769923)------------------------------
% 4.02/1.56 % (3769814)Success in time 0.487 s
% 4.02/1.56 % Vampire exiting
%------------------------------------------------------------------------------