%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP568-1 : 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 : 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 10:14:53 AM UTC 2026
% Result : Unsatisfiable 2.25s 1.17s
% Output : Refutation 2.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 5
% Syntax : Number of formulae : 86 ( 86 unt; 0 def)
% Number of atoms : 86 ( 85 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 164 ( 164 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(X0,X2)),double_divide(identity,X2))),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,X1] : multiply(X0,X1) = inverse(double_divide(X1,X0)),
inference(forward_demodulation,[],[f2,f3]) ).
fof(f7,plain,
! [X0] : multiply(identity,X0) = inverse(inverse(X0)),
inference(superposition,[],[f6,f3]) ).
fof(f8,plain,
! [X0] : multiply(inverse(X0),X0) = inverse(identity),
inference(superposition,[],[f6,f4]) ).
fof(f10,plain,
! [X0,X1] : multiply(identity,double_divide(X1,X0)) = inverse(multiply(X0,X1)),
inference(superposition,[],[f7,f6]) ).
fof(f13,plain,
! [X0,X1] : inverse(identity) = multiply(multiply(X0,X1),double_divide(X1,X0)),
inference(superposition,[],[f8,f6]) ).
fof(f26,plain,
! [X2,X0,X1] : double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(X0,X2)),double_divide(identity,X2))),inverse(identity)) = X1,
inference(forward_demodulation,[],[f1,f3]) ).
fof(f81,plain,
! [X0,X1] : double_divide(double_divide(X0,double_divide(double_divide(X1,identity),double_divide(identity,inverse(X0)))),inverse(identity)) = X1,
inference(superposition,[],[f26,f4]) ).
fof(f83,plain,
! [X2,X3,X0,X1] : double_divide(double_divide(double_divide(X1,double_divide(double_divide(X0,double_divide(X1,X2)),double_divide(identity,X2))),double_divide(double_divide(X3,X0),double_divide(identity,inverse(identity)))),inverse(identity)) = X3,
inference(superposition,[],[f26,f26]) ).
fof(f86,plain,
! [X0,X1] : double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(X0,identity)),inverse(identity))),inverse(identity)) = X1,
inference(superposition,[],[f26,f3]) ).
fof(f91,plain,
! [X2,X0,X1] : inverse(X0) = multiply(inverse(identity),double_divide(X1,double_divide(double_divide(X0,double_divide(X1,X2)),double_divide(identity,X2)))),
inference(superposition,[],[f6,f26]) ).
fof(f93,plain,
! [X0,X1] : double_divide(double_divide(X0,double_divide(double_divide(X1,inverse(X0)),inverse(identity))),inverse(identity)) = X1,
inference(forward_demodulation,[],[f86,f3]) ).
fof(f96,plain,
! [X2,X3,X0,X1] : double_divide(double_divide(double_divide(X1,double_divide(double_divide(X0,double_divide(X1,X2)),double_divide(identity,X2))),double_divide(double_divide(X3,X0),identity)),inverse(identity)) = X3,
inference(forward_demodulation,[],[f83,f4]) ).
fof(f98,plain,
! [X0,X1] : double_divide(double_divide(X0,double_divide(inverse(X1),double_divide(identity,inverse(X0)))),inverse(identity)) = X1,
inference(forward_demodulation,[],[f81,f3]) ).
fof(f101,plain,
! [X2,X3,X0,X1] : double_divide(double_divide(double_divide(X1,double_divide(double_divide(X0,double_divide(X1,X2)),double_divide(identity,X2))),inverse(double_divide(X3,X0))),inverse(identity)) = X3,
inference(forward_demodulation,[],[f96,f3]) ).
fof(f102,plain,
! [X2,X3,X0,X1] : double_divide(double_divide(double_divide(X1,double_divide(double_divide(X0,double_divide(X1,X2)),double_divide(identity,X2))),multiply(X0,X3)),inverse(identity)) = X3,
inference(forward_demodulation,[],[f101,f6]) ).
fof(f161,plain,
! [X0] : double_divide(double_divide(X0,double_divide(identity,inverse(identity))),inverse(identity)) = X0,
inference(superposition,[],[f93,f4]) ).
fof(f173,plain,
! [X0] : double_divide(double_divide(X0,identity),inverse(identity)) = X0,
inference(forward_demodulation,[],[f161,f4]) ).
fof(f175,plain,
! [X0] : double_divide(inverse(X0),inverse(identity)) = X0,
inference(forward_demodulation,[],[f173,f3]) ).
fof(f177,plain,
! [X0,X1] : double_divide(X1,X0) = double_divide(multiply(X0,X1),inverse(identity)),
inference(superposition,[],[f175,f6]) ).
fof(f178,plain,
! [X0] : inverse(X0) = double_divide(multiply(identity,X0),inverse(identity)),
inference(superposition,[],[f175,f7]) ).
fof(f186,plain,
! [X0] : inverse(X0) = multiply(inverse(identity),inverse(X0)),
inference(superposition,[],[f6,f175]) ).
fof(f190,plain,
! [X0,X1] : multiply(X0,X1) = multiply(inverse(identity),multiply(X0,X1)),
inference(superposition,[],[f186,f6]) ).
fof(f199,plain,
! [X0] : multiply(identity,X0) = double_divide(double_divide(identity,double_divide(inverse(X0),inverse(identity))),inverse(identity)),
inference(superposition,[],[f93,f178]) ).
fof(f207,plain,
! [X0] : multiply(identity,X0) = double_divide(double_divide(identity,X0),inverse(identity)),
inference(forward_demodulation,[],[f199,f175]) ).
fof(f272,plain,
multiply(identity,identity) = double_divide(inverse(identity),inverse(identity)),
inference(superposition,[],[f207,f3]) ).
fof(f304,plain,
identity = multiply(identity,identity),
inference(forward_demodulation,[],[f272,f175]) ).
fof(f324,plain,
identity = multiply(inverse(identity),identity),
inference(superposition,[],[f190,f304]) ).
fof(f331,plain,
identity = inverse(identity),
inference(forward_demodulation,[],[f324,f8]) ).
fof(f351,plain,
! [X0] : double_divide(inverse(X0),identity) = X0,
inference(superposition,[],[f175,f331]) ).
fof(f366,plain,
! [X0] : double_divide(double_divide(identity,double_divide(inverse(X0),double_divide(identity,identity))),identity) = X0,
inference(superposition,[],[f98,f331]) ).
fof(f372,plain,
! [X0] : inverse(double_divide(identity,double_divide(inverse(X0),double_divide(identity,identity)))) = X0,
inference(forward_demodulation,[],[f366,f3]) ).
fof(f384,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[],[f351,f3]) ).
fof(f392,plain,
! [X0] : multiply(double_divide(inverse(X0),double_divide(identity,identity)),identity) = X0,
inference(forward_demodulation,[],[f372,f6]) ).
fof(f403,plain,
! [X0] : multiply(double_divide(inverse(X0),inverse(identity)),identity) = X0,
inference(forward_demodulation,[],[f392,f3]) ).
fof(f408,plain,
! [X0] : multiply(X0,identity) = X0,
inference(forward_demodulation,[],[f403,f175]) ).
fof(f415,plain,
! [X0] : multiply(identity,X0) = X0,
inference(superposition,[],[f384,f7]) ).
fof(f417,plain,
! [X0] : identity = double_divide(inverse(X0),X0),
inference(superposition,[],[f4,f384]) ).
fof(f449,plain,
! [X0] : double_divide(identity,X0) = double_divide(X0,inverse(identity)),
inference(superposition,[],[f177,f408]) ).
fof(f473,plain,
! [X0] : double_divide(X0,identity) = double_divide(identity,X0),
inference(forward_demodulation,[],[f449,f331]) ).
fof(f479,plain,
! [X0] : inverse(X0) = double_divide(identity,X0),
inference(forward_demodulation,[],[f473,f3]) ).
fof(f525,plain,
! [X2,X0,X1] : inverse(X0) = multiply(identity,double_divide(X1,double_divide(double_divide(X0,double_divide(X1,X2)),double_divide(identity,X2)))),
inference(forward_demodulation,[],[f91,f331]) ).
fof(f526,plain,
! [X2,X0,X1] : inverse(X0) = inverse(multiply(double_divide(double_divide(X0,double_divide(X1,X2)),double_divide(identity,X2)),X1)),
inference(forward_demodulation,[],[f525,f10]) ).
fof(f735,plain,
! [X2,X0,X1] : inverse(X0) = inverse(multiply(double_divide(double_divide(X0,double_divide(X1,X2)),inverse(X2)),X1)),
inference(forward_demodulation,[],[f526,f479]) ).
fof(f737,plain,
! [X0,X1] : inverse(X1) = inverse(multiply(double_divide(double_divide(X1,inverse(X0)),inverse(identity)),X0)),
inference(superposition,[],[f735,f3]) ).
fof(f738,plain,
! [X0,X1] : inverse(X0) = inverse(multiply(double_divide(double_divide(X0,identity),inverse(inverse(X1))),X1)),
inference(superposition,[],[f735,f4]) ).
fof(f815,plain,
! [X0,X1] : inverse(X0) = inverse(multiply(double_divide(double_divide(X0,identity),multiply(identity,X1)),X1)),
inference(forward_demodulation,[],[f738,f7]) ).
fof(f816,plain,
! [X0,X1] : inverse(X1) = inverse(multiply(double_divide(double_divide(X1,inverse(X0)),identity),X0)),
inference(forward_demodulation,[],[f737,f331]) ).
fof(f844,plain,
! [X0,X1] : inverse(X0) = inverse(multiply(double_divide(double_divide(X0,identity),X1),X1)),
inference(forward_demodulation,[],[f815,f415]) ).
fof(f845,plain,
! [X0,X1] : inverse(X1) = inverse(multiply(inverse(double_divide(X1,inverse(X0))),X0)),
inference(forward_demodulation,[],[f816,f3]) ).
fof(f866,plain,
! [X0,X1] : inverse(X0) = inverse(multiply(double_divide(inverse(X0),X1),X1)),
inference(forward_demodulation,[],[f844,f3]) ).
fof(f867,plain,
! [X0,X1] : inverse(X1) = inverse(multiply(multiply(inverse(X0),X1),X0)),
inference(forward_demodulation,[],[f845,f6]) ).
fof(f909,plain,
! [X2,X3,X0,X1] : double_divide(double_divide(double_divide(X1,double_divide(double_divide(X0,double_divide(X1,X2)),double_divide(identity,X2))),multiply(X0,X3)),identity) = X3,
inference(forward_demodulation,[],[f102,f331]) ).
fof(f910,plain,
! [X2,X3,X0,X1] : inverse(double_divide(double_divide(X1,double_divide(double_divide(X0,double_divide(X1,X2)),double_divide(identity,X2))),multiply(X0,X3))) = X3,
inference(forward_demodulation,[],[f909,f3]) ).
fof(f911,plain,
! [X2,X3,X0,X1] : multiply(multiply(X0,X3),double_divide(X1,double_divide(double_divide(X0,double_divide(X1,X2)),double_divide(identity,X2)))) = X3,
inference(forward_demodulation,[],[f910,f6]) ).
fof(f912,plain,
! [X2,X3,X0,X1] : multiply(multiply(X0,X3),double_divide(X1,double_divide(double_divide(X0,double_divide(X1,X2)),inverse(X2)))) = X3,
inference(forward_demodulation,[],[f911,f479]) ).
fof(f921,plain,
! [X2,X3,X0,X1] : double_divide(X1,X0) = multiply(inverse(identity),double_divide(X2,double_divide(double_divide(multiply(X0,X1),double_divide(X2,X3)),inverse(X3)))),
inference(superposition,[],[f912,f13]) ).
fof(f993,plain,
! [X2,X3,X0,X1] : double_divide(X1,X0) = multiply(identity,double_divide(X2,double_divide(double_divide(multiply(X0,X1),double_divide(X2,X3)),inverse(X3)))),
inference(forward_demodulation,[],[f921,f331]) ).
fof(f1027,plain,
! [X2,X3,X0,X1] : double_divide(X1,X0) = inverse(multiply(double_divide(double_divide(multiply(X0,X1),double_divide(X2,X3)),inverse(X3)),X2)),
inference(forward_demodulation,[],[f993,f10]) ).
fof(f1054,plain,
! [X0,X1] : double_divide(X1,X0) = inverse(multiply(X0,X1)),
inference(forward_demodulation,[],[f1027,f735]) ).
fof(f1102,plain,
! [X0,X1] : multiply(identity,X0) = inverse(multiply(double_divide(multiply(identity,X0),X1),X1)),
inference(superposition,[],[f866,f7]) ).
fof(f1120,plain,
! [X0,X1] : double_divide(inverse(X0),inverse(identity)) = multiply(double_divide(inverse(X0),X1),X1),
inference(superposition,[],[f175,f866]) ).
fof(f1129,plain,
! [X0,X1] : multiply(double_divide(inverse(X0),X1),X1) = X0,
inference(forward_demodulation,[],[f1120,f175]) ).
fof(f1145,plain,
! [X0,X1] : inverse(multiply(double_divide(X0,X1),X1)) = X0,
inference(forward_demodulation,[],[f1102,f415]) ).
fof(f1302,plain,
! [X0,X1] : double_divide(X1,double_divide(X0,X1)) = X0,
inference(forward_demodulation,[],[f1145,f1054]) ).
fof(f1324,plain,
! [X0,X1] : double_divide(double_divide(X0,double_divide(X0,double_divide(identity,X1))),inverse(identity)) = X1,
inference(superposition,[],[f26,f1302]) ).
fof(f1327,plain,
! [X2,X0,X1] : multiply(multiply(X0,X2),double_divide(X0,double_divide(inverse(X1),X1))) = X2,
inference(superposition,[],[f912,f1302]) ).
fof(f1351,plain,
! [X2,X0] : multiply(multiply(X0,X2),double_divide(X0,identity)) = X2,
inference(forward_demodulation,[],[f1327,f417]) ).
fof(f1354,plain,
! [X0,X1] : double_divide(double_divide(X0,double_divide(X0,double_divide(identity,X1))),identity) = X1,
inference(forward_demodulation,[],[f1324,f331]) ).
fof(f1377,plain,
! [X2,X0] : multiply(multiply(X0,X2),inverse(X0)) = X2,
inference(forward_demodulation,[],[f1351,f3]) ).
fof(f1380,plain,
! [X0,X1] : inverse(double_divide(X0,double_divide(X0,double_divide(identity,X1)))) = X1,
inference(forward_demodulation,[],[f1354,f3]) ).
fof(f1396,plain,
! [X0,X1] : multiply(double_divide(X0,double_divide(identity,X1)),X0) = X1,
inference(forward_demodulation,[],[f1380,f6]) ).
fof(f1408,plain,
! [X0,X1] : multiply(double_divide(X0,inverse(X1)),X0) = X1,
inference(forward_demodulation,[],[f1396,f479]) ).
fof(f1546,plain,
! [X0,X1] : inverse(X1) = double_divide(X0,multiply(inverse(X0),X1)),
inference(forward_demodulation,[],[f867,f1054]) ).
fof(f2141,plain,
! [X0,X1] : multiply(inverse(X0),multiply(inverse(inverse(X1)),X0)) = X1,
inference(superposition,[],[f1129,f1546]) ).
fof(f2144,plain,
! [X0,X1] : multiply(inverse(X0),multiply(multiply(identity,X1),X0)) = X1,
inference(forward_demodulation,[],[f2141,f7]) ).
fof(f2166,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X1,X0)) = X1,
inference(forward_demodulation,[],[f2144,f415]) ).
fof(f2463,plain,
! [X0,X1] : multiply(X0,inverse(double_divide(X1,inverse(X0)))) = X1,
inference(superposition,[],[f1377,f1408]) ).
fof(f2466,plain,
! [X0,X1] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(forward_demodulation,[],[f2463,f6]) ).
fof(f3053,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(superposition,[],[f2466,f2166]) ).
fof(f3266,plain,
multiply(a,b) != multiply(a,b),
inference(superposition,[],[f5,f3053]) ).
fof(f3267,plain,
$false,
inference(trivial_inequality_removal,[],[f3266]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP568-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n020.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 10:08:19 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 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
% 2.25/1.17 % (3156385)Detected a unit-equality problem, will run specialized UEQ schedule.
% 2.25/1.17 % (3156438)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=3558504361:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 2.25/1.17 % (3156438)First to succeed.
% 2.25/1.17 % (3156438)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3156385"
% 2.25/1.17 % (3156433)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=2109549101:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 2.25/1.17 % (3156436)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=3466621268:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 2.25/1.17 % (3156435)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=158268996:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 2.25/1.17 % (3156432)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=1270055800:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 2.25/1.17 % (3156434)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=3556424793:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 2.25/1.17 % (3156435)Also succeeded, but the first one will report.
% 2.25/1.17 % (3156437)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=274184147:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 2.25/1.17 % (3156436)Also succeeded, but the first one will report.
% 2.25/1.17 % (3156437)Also succeeded, but the first one will report.
% 2.25/1.17 % (3156438)Refutation found. Thanks to Tanya!
% 2.25/1.17 % SZS status Unsatisfiable for theBenchmark
% 2.25/1.17 % SZS output start Proof for theBenchmark
% See solution above
% 2.68/1.35 % (3156438)------------------------------
% 2.68/1.35 % (3156438)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.68/1.35 % (3156438)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/1.35 % (3156438)CaDiCaL version: 2.1.3
% 2.68/1.35 % (3156438)Termination reason: Refutation
% 2.68/1.35 % (3156438)Time elapsed: 0.026 s
% 2.68/1.35 % (3156438)Peak memory usage: 89 MB
% 2.68/1.35 % (3156438)Instructions burned: 83 (million)
% 2.68/1.35 % (3156438)------------------------------
% 2.68/1.35 % (3156438)------------------------------
% 2.68/1.35 % (3156385)Success in time 0.304 s
% 2.68/1.35 % Vampire exiting
%------------------------------------------------------------------------------