%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP576-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 10:14:54 AM UTC 2026
% Result : Unsatisfiable 3.38s 1.27s
% Output : Refutation 3.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 6
% Syntax : Number of formulae : 42 ( 42 unt; 1 def)
% Number of atoms : 42 ( 38 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 8 ( 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 : 52 ( 52 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(X2,X0)),double_divide(X2,identity))),double_divide(identity,identity)) = X1,
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(a,b) != multiply(b,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_4) ).
fof(f6,plain,
! [X0] : identity = double_divide(X0,double_divide(X0,identity)),
inference(definition_unfolding,[],[f4,f3]) ).
fof(f7,plain,
double_divide(double_divide(b,a),identity) != double_divide(double_divide(a,b),identity),
inference(definition_unfolding,[],[f5,f2,f2]) ).
fof(f8,definition,
~ sP0(double_divide(double_divide(b,a),identity)),
introduced(definition,[new_symbols(definition,[sP0])],[inequality_splitting_name_introduction]) ).
fof(f9,plain,
sP0(double_divide(double_divide(a,b),identity)),
inference(inequality_splitting,[],[f7,f8]) ).
fof(f10,plain,
! [X0,X1] : double_divide(double_divide(double_divide(X0,identity),double_divide(double_divide(X1,identity),double_divide(X0,identity))),double_divide(identity,identity)) = X1,
inference(superposition,[],[f1,f6]) ).
fof(f12,plain,
! [X0] : double_divide(double_divide(identity,double_divide(identity,double_divide(X0,identity))),double_divide(identity,identity)) = X0,
inference(superposition,[],[f1,f6]) ).
fof(f13,plain,
! [X2,X0,X1] : double_divide(X1,double_divide(double_divide(X0,double_divide(X2,X1)),double_divide(X2,identity))) = double_divide(double_divide(identity,double_divide(X0,double_divide(identity,identity))),double_divide(identity,identity)),
inference(superposition,[],[f1,f1]) ).
fof(f16,plain,
! [X0] : double_divide(identity,double_divide(identity,double_divide(X0,identity))) = double_divide(double_divide(identity,double_divide(X0,double_divide(identity,identity))),double_divide(identity,identity)),
inference(superposition,[],[f1,f12]) ).
fof(f18,plain,
! [X2,X0,X1] : double_divide(identity,double_divide(identity,double_divide(X0,identity))) = double_divide(X1,double_divide(double_divide(X0,double_divide(X2,X1)),double_divide(X2,identity))),
inference(backward_demodulation,[],[f13,f16]) ).
fof(f21,plain,
! [X0] : double_divide(double_divide(double_divide(double_divide(X0,identity),identity),identity),double_divide(identity,identity)) = X0,
inference(superposition,[],[f10,f6]) ).
fof(f24,plain,
! [X0,X1] : double_divide(double_divide(identity,identity),double_divide(double_divide(X1,X0),double_divide(double_divide(identity,double_divide(identity,double_divide(X0,identity))),identity))) = double_divide(identity,double_divide(identity,double_divide(X1,identity))),
inference(superposition,[],[f18,f12]) ).
fof(f32,plain,
! [X0] : double_divide(identity,double_divide(identity,double_divide(identity,identity))) = double_divide(double_divide(X0,identity),X0),
inference(superposition,[],[f18,f12]) ).
fof(f33,plain,
! [X0] : double_divide(identity,identity) = double_divide(double_divide(X0,identity),X0),
inference(forward_demodulation,[],[f32,f6]) ).
fof(f44,plain,
double_divide(identity,identity) = double_divide(double_divide(identity,double_divide(identity,double_divide(identity,identity))),double_divide(identity,identity)),
inference(superposition,[],[f12,f33]) ).
fof(f46,plain,
! [X0,X1] : double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(X0,X1),identity),identity))) = double_divide(X1,double_divide(double_divide(identity,identity),double_divide(X0,identity))),
inference(superposition,[],[f18,f33]) ).
fof(f48,plain,
identity = double_divide(identity,identity),
inference(forward_demodulation,[],[f44,f12]) ).
fof(f50,plain,
! [X0] : double_divide(double_divide(identity,double_divide(identity,double_divide(X0,identity))),identity) = X0,
inference(backward_demodulation,[],[f12,f48]) ).
fof(f53,plain,
! [X0] : double_divide(double_divide(double_divide(double_divide(X0,identity),identity),identity),identity) = X0,
inference(backward_demodulation,[],[f21,f48]) ).
fof(f54,plain,
! [X0,X1] : double_divide(identity,double_divide(identity,double_divide(X1,identity))) = double_divide(identity,double_divide(double_divide(X1,X0),double_divide(double_divide(identity,double_divide(identity,double_divide(X0,identity))),identity))),
inference(backward_demodulation,[],[f24,f48]) ).
fof(f58,plain,
! [X0,X1] : double_divide(identity,double_divide(identity,double_divide(double_divide(double_divide(X0,X1),identity),identity))) = double_divide(X1,double_divide(identity,double_divide(X0,identity))),
inference(backward_demodulation,[],[f46,f48]) ).
fof(f60,plain,
! [X0,X1] : double_divide(identity,double_divide(identity,double_divide(X1,identity))) = double_divide(identity,double_divide(double_divide(X1,X0),X0)),
inference(backward_demodulation,[],[f54,f50]) ).
fof(f62,plain,
! [X0,X1] : double_divide(X1,double_divide(identity,double_divide(X0,identity))) = double_divide(identity,double_divide(identity,double_divide(identity,double_divide(double_divide(X0,X1),identity)))),
inference(backward_demodulation,[],[f58,f60]) ).
fof(f63,plain,
! [X0] : double_divide(identity,double_divide(identity,double_divide(X0,identity))) = double_divide(double_divide(identity,double_divide(identity,X0)),identity),
inference(superposition,[],[f50,f50]) ).
fof(f66,plain,
! [X0] : identity = double_divide(double_divide(identity,double_divide(identity,double_divide(X0,identity))),X0),
inference(superposition,[],[f6,f50]) ).
fof(f68,plain,
! [X0] : double_divide(identity,double_divide(identity,double_divide(double_divide(X0,identity),identity))) = X0,
inference(backward_demodulation,[],[f50,f63]) ).
fof(f69,plain,
! [X0] : double_divide(identity,double_divide(identity,double_divide(identity,double_divide(X0,identity)))) = X0,
inference(forward_demodulation,[],[f68,f60]) ).
fof(f70,plain,
! [X0,X1] : double_divide(X0,X1) = double_divide(X1,double_divide(identity,double_divide(X0,identity))),
inference(backward_demodulation,[],[f62,f69]) ).
fof(f96,plain,
! [X0] : double_divide(double_divide(double_divide(X0,identity),identity),identity) = double_divide(identity,double_divide(identity,double_divide(identity,X0))),
inference(superposition,[],[f69,f53]) ).
fof(f102,plain,
! [X0] : double_divide(double_divide(identity,double_divide(identity,double_divide(identity,X0))),identity) = X0,
inference(backward_demodulation,[],[f53,f96]) ).
fof(f106,plain,
! [X0] : double_divide(identity,double_divide(identity,double_divide(double_divide(identity,X0),identity))) = X0,
inference(forward_demodulation,[],[f102,f63]) ).
fof(f131,plain,
! [X0,X1] : double_divide(X1,double_divide(identity,double_divide(X0,identity))) = double_divide(identity,double_divide(identity,double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(X0,X1),identity))),identity))),
inference(superposition,[],[f18,f66]) ).
fof(f134,plain,
! [X0,X1] : double_divide(X1,double_divide(identity,double_divide(X0,identity))) = double_divide(identity,double_divide(double_divide(X0,X1),identity)),
inference(forward_demodulation,[],[f131,f106]) ).
fof(f138,plain,
! [X0] : double_divide(identity,double_divide(X0,double_divide(identity,double_divide(identity,identity)))) = X0,
inference(backward_demodulation,[],[f106,f134]) ).
fof(f141,plain,
! [X0] : double_divide(identity,double_divide(X0,identity)) = X0,
inference(forward_demodulation,[],[f138,f6]) ).
fof(f154,plain,
! [X0,X1] : double_divide(X1,X0) = double_divide(X0,X1),
inference(backward_demodulation,[],[f70,f141]) ).
fof(f246,plain,
~ sP0(double_divide(double_divide(a,b),identity)),
inference(superposition,[],[f8,f154]) ).
fof(f247,plain,
$false,
inference(forward_subsumption_resolution,[],[f246,f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP576-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n018.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 10:09:23 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.42 Running first-order theorem proving
% 0.15/0.42 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
% 3.38/1.27 % (2102852)Detected a unit-equality problem, will run specialized UEQ schedule.
% 3.38/1.27 % (2102899)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=795154315:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 3.38/1.27 % (2102903)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=689783794:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 3.38/1.27 % (2102904)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=402388415:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 3.38/1.27 % (2102900)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=3590957789:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 3.38/1.27 % (2102907)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1420198071:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 3.38/1.27 % (2102906)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=3409653699:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 3.38/1.27 % (2102902)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=1429550159:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 3.38/1.27 % (2102903)First to succeed.
% 3.38/1.27 % (2102903)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2102852"
% 3.38/1.27 % (2102907)Also succeeded, but the first one will report.
% 3.38/1.27 % (2102904)Also succeeded, but the first one will report.
% 3.38/1.27 % (2102906)Also succeeded, but the first one will report.
% 3.38/1.27 % (2102903)Refutation found. Thanks to Tanya!
% 3.38/1.27 % SZS status Unsatisfiable for theBenchmark
% 3.38/1.27 % SZS output start Proof for theBenchmark
% See solution above
% 3.38/1.28 % (2102903)------------------------------
% 3.38/1.28 % (2102903)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.38/1.28 % (2102903)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.38/1.28 % (2102903)CaDiCaL version: 2.1.3
% 3.38/1.28 % (2102903)Termination reason: Refutation
% 3.38/1.28 % (2102903)Time elapsed: 0.012 s
% 3.38/1.28 % (2102903)Peak memory usage: 87 MB
% 3.38/1.28 % (2102903)Instructions burned: 18 (million)
% 3.38/1.28 % (2102903)------------------------------
% 3.38/1.28 % (2102903)------------------------------
% 3.38/1.28 % (2102852)Success in time 0.427 s
% 3.38/1.28 % Vampire exiting
%------------------------------------------------------------------------------