%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP490-1 : 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 : n020.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 10:14:08 AM UTC 2026
% Result : Unsatisfiable 3.53s 1.47s
% Output : Refutation 3.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 27 ( 27 unt; 1 def)
% Number of atoms : 27 ( 22 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 7 ( 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 : 17 ( 17 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : double_divide(double_divide(identity,X0),double_divide(identity,double_divide(double_divide(double_divide(X0,X1),identity),double_divide(X2,X1)))) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,axiom,
! [X0,X1] : multiply(X0,X1) = double_divide(double_divide(X1,X0),identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply) ).
fof(f3,axiom,
! [X0] : inverse(X0) = double_divide(X0,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse) ).
fof(f4,axiom,
! [X0] : identity = double_divide(X0,inverse(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity) ).
fof(f5,negated_conjecture,
multiply(inverse(a1),a1) != identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_1) ).
fof(f6,plain,
identity != multiply(inverse(a1),a1),
inference(reorient_equations,[],[f5]) ).
fof(f7,plain,
! [X0] : identity = double_divide(X0,double_divide(X0,identity)),
inference(definition_unfolding,[],[f4,f3]) ).
fof(f8,plain,
identity != double_divide(double_divide(a1,double_divide(a1,identity)),identity),
inference(definition_unfolding,[],[f6,f2,f3]) ).
fof(f9,definition,
~ sP0(double_divide(double_divide(a1,double_divide(a1,identity)),identity)),
introduced(definition,[new_symbols(definition,[sP0])],[inequality_splitting_name_introduction]) ).
fof(f10,plain,
sP0(identity),
inference(inequality_splitting,[],[f8,f9]) ).
fof(f11,plain,
~ sP0(double_divide(identity,identity)),
inference(backward_demodulation,[],[f9,f7]) ).
fof(f12,plain,
! [X0,X1] : double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),X0),identity),double_divide(X1,X0)))) = X1,
inference(superposition,[],[f1,f7]) ).
fof(f17,plain,
! [X0] : double_divide(double_divide(X0,identity),identity) = double_divide(double_divide(identity,X0),double_divide(identity,identity)),
inference(superposition,[],[f1,f7]) ).
fof(f27,plain,
! [X0] : double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),identity),identity),double_divide(X0,double_divide(identity,identity))))) = X0,
inference(superposition,[],[f12,f17]) ).
fof(f34,plain,
! [X0] : double_divide(X0,identity) = double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,identity),identity),identity),double_divide(double_divide(identity,X0),double_divide(identity,identity))))),
inference(superposition,[],[f12,f17]) ).
fof(f35,plain,
double_divide(identity,double_divide(identity,identity)) = double_divide(double_divide(double_divide(identity,identity),identity),identity),
inference(superposition,[],[f12,f7]) ).
fof(f40,plain,
identity = double_divide(double_divide(double_divide(identity,identity),identity),identity),
inference(forward_demodulation,[],[f35,f7]) ).
fof(f44,plain,
! [X0] : double_divide(identity,X0) = double_divide(X0,identity),
inference(backward_demodulation,[],[f34,f27]) ).
fof(f56,plain,
! [X0] : double_divide(double_divide(identity,X0),double_divide(identity,identity)) = double_divide(double_divide(identity,X0),identity),
inference(superposition,[],[f17,f44]) ).
fof(f59,plain,
! [X0] : double_divide(double_divide(identity,X0),double_divide(identity,identity)) = double_divide(identity,double_divide(X0,identity)),
inference(superposition,[],[f17,f44]) ).
fof(f72,plain,
! [X0] : double_divide(identity,double_divide(X0,identity)) = double_divide(double_divide(identity,X0),identity),
inference(forward_demodulation,[],[f56,f59]) ).
fof(f74,plain,
identity = double_divide(double_divide(identity,double_divide(identity,identity)),identity),
inference(backward_demodulation,[],[f40,f72]) ).
fof(f79,plain,
identity = double_divide(identity,double_divide(double_divide(identity,identity),identity)),
inference(forward_demodulation,[],[f74,f72]) ).
fof(f80,plain,
identity = double_divide(identity,double_divide(identity,double_divide(identity,identity))),
inference(forward_demodulation,[],[f79,f72]) ).
fof(f81,plain,
identity = double_divide(identity,identity),
inference(forward_demodulation,[],[f80,f7]) ).
fof(f82,plain,
~ sP0(identity),
inference(backward_demodulation,[],[f11,f81]) ).
fof(f104,plain,
$false,
inference(forward_subsumption_resolution,[],[f82,f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP490-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n020.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 27 10:06:51 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 3.53/1.47 % (3152522)Detected a unit-equality problem, will run specialized UEQ schedule.
% 3.53/1.47 % (3152625)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2061628406:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_3000 on theBenchmark for (3000ds/257Mi)
% 3.53/1.47 % (3152616)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=2916171772:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_3000 on theBenchmark for (3000ds/138329Mi)
% 3.53/1.47 % (3152620)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2268479112:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_3000 on theBenchmark for (3000ds/130716Mi)
% 3.53/1.47 % (3152618)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=650591134:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_3000 on theBenchmark for (3000ds/130792Mi)
% 3.53/1.47 % (3152621)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2061628328:i=136:bd=preordered:ins=2:av=off_3000 on theBenchmark for (3000ds/136Mi)
% 3.53/1.47 % (3152621)First to succeed.
% 3.53/1.47 % (3152621)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3152522"
% 3.53/1.47 % (3152626)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=753901501:i=1187:sd=4:av=off:ss=axioms:sgt=32_3000 on theBenchmark for (3000ds/1187Mi)
% 3.53/1.47 % (3152623)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=3693463719:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_3000 on theBenchmark for (3000ds/181Mi)
% 3.53/1.47 % (3152625)Also succeeded, but the first one will report.
% 3.53/1.47 % (3152623)Also succeeded, but the first one will report.
% 3.53/1.47 % (3152626)Also succeeded, but the first one will report.
% 3.53/1.47 % (3152621)Refutation found. Thanks to Tanya!
% 3.53/1.47 % SZS status Unsatisfiable for theBenchmark
% 3.53/1.47 % SZS output start Proof for theBenchmark
% See solution above
% 3.53/1.47 % (3152621)------------------------------
% 3.53/1.47 % (3152621)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.53/1.47 % (3152621)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.53/1.47 % (3152621)CaDiCaL version: 2.1.3
% 3.53/1.47 % (3152621)Termination reason: Refutation
% 3.53/1.47 % (3152621)Time elapsed: 0.008 s
% 3.53/1.47 % (3152621)Peak memory usage: 88 MB
% 3.53/1.47 % (3152621)Instructions burned: 10 (million)
% 3.53/1.47 % (3152621)------------------------------
% 3.53/1.47 % (3152621)------------------------------
% 3.53/1.47 % (3152522)Success in time 0.408 s
% 3.53/1.47 % Vampire exiting
%------------------------------------------------------------------------------