%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP487-1 : 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 : n013.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 10:14:07 AM UTC 2026
% Result : Unsatisfiable 2.68s 1.32s
% Output : Refutation 2.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 23 ( 23 unt; 1 def)
% Number of atoms : 23 ( 18 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 : 15 ( 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : double_divide(X0,double_divide(double_divide(double_divide(identity,double_divide(double_divide(X0,identity),double_divide(X1,X2))),X1),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,plain,
! [X0] : double_divide(X0,identity) = inverse(X0),
inference(reorient_equations,[],[f3]) ).
fof(f5,axiom,
! [X0] : identity = double_divide(X0,inverse(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity) ).
fof(f6,negated_conjecture,
multiply(inverse(a1),a1) != identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_1) ).
fof(f7,plain,
identity != multiply(inverse(a1),a1),
inference(reorient_equations,[],[f6]) ).
fof(f8,plain,
! [X0] : identity = double_divide(X0,double_divide(X0,identity)),
inference(definition_unfolding,[],[f5,f4]) ).
fof(f9,plain,
identity != double_divide(double_divide(a1,double_divide(a1,identity)),identity),
inference(definition_unfolding,[],[f7,f2,f4]) ).
fof(f10,definition,
~ sP0(double_divide(double_divide(a1,double_divide(a1,identity)),identity)),
introduced(definition,[new_symbols(definition,[sP0])],[inequality_splitting_name_introduction]) ).
fof(f11,plain,
sP0(identity),
inference(inequality_splitting,[],[f9,f10]) ).
fof(f12,plain,
~ sP0(double_divide(identity,identity)),
inference(backward_demodulation,[],[f10,f8]) ).
fof(f13,plain,
! [X0,X1] : double_divide(X1,identity) = double_divide(X0,double_divide(double_divide(double_divide(identity,double_divide(double_divide(X0,identity),identity)),X1),identity)),
inference(superposition,[],[f1,f8]) ).
fof(f15,plain,
! [X0] : identity = double_divide(X0,double_divide(double_divide(double_divide(identity,identity),double_divide(X0,identity)),identity)),
inference(superposition,[],[f1,f8]) ).
fof(f17,plain,
identity = double_divide(double_divide(identity,identity),double_divide(identity,identity)),
inference(superposition,[],[f15,f8]) ).
fof(f34,plain,
! [X0] : double_divide(identity,identity) = double_divide(X0,double_divide(double_divide(double_divide(identity,double_divide(double_divide(X0,identity),identity)),double_divide(identity,identity)),identity)),
inference(superposition,[],[f1,f17]) ).
fof(f35,plain,
double_divide(identity,identity) = double_divide(double_divide(identity,identity),identity),
inference(forward_demodulation,[],[f34,f13]) ).
fof(f67,plain,
! [X0] : double_divide(X0,identity) = double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(identity,identity)),X0),identity)),
inference(superposition,[],[f13,f35]) ).
fof(f73,plain,
! [X0] : double_divide(X0,identity) = double_divide(identity,double_divide(double_divide(identity,X0),identity)),
inference(forward_demodulation,[],[f67,f8]) ).
fof(f141,plain,
double_divide(identity,identity) = double_divide(identity,double_divide(identity,identity)),
inference(superposition,[],[f73,f35]) ).
fof(f147,plain,
identity = double_divide(identity,identity),
inference(forward_demodulation,[],[f141,f8]) ).
fof(f153,plain,
~ sP0(identity),
inference(backward_demodulation,[],[f12,f147]) ).
fof(f204,plain,
$false,
inference(forward_subsumption_resolution,[],[f153,f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP487-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n013.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 10:05:22 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.41 Running first-order theorem proving
% 0.13/0.42 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
% 2.68/1.32 % (4174810)Detected a unit-equality problem, will run specialized UEQ schedule.
% 2.68/1.32 % (4174822)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=1814447006:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 2.68/1.32 % (4174822)First to succeed.
% 2.68/1.32 % (4174822)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4174810"
% 2.68/1.32 % (4174819)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=2646441291:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 2.68/1.32 % (4174820)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=302324633:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 2.68/1.32 % (4174821)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=849657730:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 2.68/1.32 % (4174824)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=266194715:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 2.68/1.32 % (4174823)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=3218398406:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 2.68/1.32 % (4174825)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=2802659411:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 2.68/1.32 % (4174825)Also succeeded, but the first one will report.
% 2.68/1.32 % (4174823)Also succeeded, but the first one will report.
% 2.68/1.32 % (4174824)Also succeeded, but the first one will report.
% 2.68/1.32 % (4174822)Refutation found. Thanks to Tanya!
% 2.68/1.32 % SZS status Unsatisfiable for theBenchmark
% 2.68/1.32 % SZS output start Proof for theBenchmark
% See solution above
% 2.68/1.32 % (4174822)------------------------------
% 2.68/1.32 % (4174822)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.68/1.32 % (4174822)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/1.32 % (4174822)CaDiCaL version: 2.1.3
% 2.68/1.32 % (4174822)Termination reason: Refutation
% 2.68/1.32 % (4174822)Time elapsed: 0.009 s
% 2.68/1.32 % (4174822)Peak memory usage: 88 MB
% 2.68/1.32 % (4174822)Instructions burned: 26 (million)
% 2.68/1.32 % (4174822)------------------------------
% 2.68/1.32 % (4174822)------------------------------
% 2.68/1.32 % (4174810)Success in time 0.29 s
% 2.68/1.32 % Vampire exiting
%------------------------------------------------------------------------------