%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP425-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.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 : Thu Sep 24 12:33:50 PM UTC 2026
% Result : Unsatisfiable 0.23s 0.98s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 5
% Syntax : Number of formulae : 59 ( 59 unt; 3 def)
% Number of atoms : 59 ( 58 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 15 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 122 ( 122 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : multiply(inverse(multiply(inverse(multiply(A,inverse(multiply(inverse(B),C)))),multiply(A,inverse(C)))),inverse(multiply(inverse(C),C))) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,plain,
! [X0,X1,X2] : multiply(inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),X2)))),multiply(X0,inverse(X2)))),inverse(multiply(inverse(X2),X2))) = X1,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f4,plain,
multiply(multiply(inverse(b2),b2),a2) != a2,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f5,definition,
sF2_fnc = inverse(b2),
introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition]) ).
fof(f6,definition,
sF1_fnc = multiply(sF2_fnc,b2),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f7,definition,
sF0_fnc = multiply(sF1_fnc,a2),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f8,plain,
sF0_fnc != a2,
inference(definition_folding,[],[f4,f7,f6,f5]) ).
fof(f10,plain,
! [X0,X1,X2,X3] : multiply(inverse(multiply(inverse(multiply(X0,inverse(X1))),multiply(X0,inverse(inverse(multiply(inverse(X2),X2)))))),inverse(multiply(inverse(inverse(multiply(inverse(X2),X2))),inverse(multiply(inverse(X2),X2))))) = multiply(inverse(multiply(X3,inverse(multiply(inverse(X1),X2)))),multiply(X3,inverse(X2))),
inference(paramodulation,[status(thm)],[f3,f3]) ).
fof(f11,plain,
! [X0,X1] : multiply(inverse(multiply(inverse(multiply(X0,inverse(multiply(sF2_fnc,X1)))),multiply(X0,inverse(X1)))),inverse(multiply(inverse(X1),X1))) = b2,
inference(paramodulation,[status(thm)],[f5,f3]) ).
fof(f13,plain,
! [X0,X1] : multiply(inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),b2)))),multiply(X0,sF2_fnc))),inverse(multiply(inverse(b2),b2))) = X1,
inference(paramodulation,[status(thm)],[f5,f3]) ).
fof(f15,plain,
! [X0,X1] : multiply(inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),b2)))),multiply(X0,sF2_fnc))),inverse(multiply(sF2_fnc,b2))) = X1,
inference(forward_demodulation,[status(thm)],[f5,f13]) ).
fof(f16,plain,
! [X0,X1] : multiply(inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),b2)))),multiply(X0,sF2_fnc))),inverse(sF1_fnc)) = X1,
inference(forward_demodulation,[status(thm)],[f6,f15]) ).
fof(f20,plain,
! [X0] : multiply(inverse(multiply(inverse(multiply(X0,inverse(multiply(sF2_fnc,b2)))),multiply(X0,sF2_fnc))),inverse(sF1_fnc)) = b2,
inference(paramodulation,[status(thm)],[f5,f16]) ).
fof(f24,plain,
! [X0] : multiply(inverse(multiply(inverse(multiply(X0,inverse(sF1_fnc))),multiply(X0,sF2_fnc))),inverse(sF1_fnc)) = b2,
inference(forward_demodulation,[status(thm)],[f6,f20]) ).
fof(f33,plain,
! [X0,X1] : multiply(inverse(multiply(inverse(b2),multiply(inverse(multiply(inverse(multiply(X0,inverse(multiply(sF2_fnc,X1)))),multiply(X0,inverse(X1)))),inverse(X1)))),inverse(multiply(inverse(X1),X1))) = X1,
inference(paramodulation,[status(thm)],[f11,f3]) ).
fof(f48,plain,
! [X0,X1] : multiply(inverse(multiply(sF2_fnc,multiply(inverse(multiply(inverse(multiply(X0,inverse(multiply(sF2_fnc,X1)))),multiply(X0,inverse(X1)))),inverse(X1)))),inverse(multiply(inverse(X1),X1))) = X1,
inference(forward_demodulation,[status(thm)],[f5,f33]) ).
fof(f208,plain,
! [X0,X1,X2] : X0 = multiply(inverse(multiply(X1,inverse(multiply(inverse(multiply(inverse(X0),inverse(multiply(inverse(X2),X2)))),X2)))),multiply(X1,inverse(X2))),
inference(paramodulation,[status(thm)],[f3,f10]) ).
fof(f209,plain,
! [X0,X1,X2,X3] : multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),X2)))),multiply(X0,inverse(X2))) = multiply(inverse(multiply(X3,inverse(multiply(inverse(X1),X2)))),multiply(X3,inverse(X2))),
inference(paramodulation,[status(thm)],[f10,f10]) ).
fof(f441,plain,
! [X0,X1] : X0 = multiply(inverse(multiply(X1,inverse(multiply(inverse(multiply(inverse(X0),inverse(multiply(sF2_fnc,b2)))),b2)))),multiply(X1,inverse(b2))),
inference(paramodulation,[status(thm)],[f5,f208]) ).
fof(f466,plain,
! [X0,X1] : X0 = multiply(inverse(multiply(X1,inverse(multiply(inverse(multiply(inverse(X0),inverse(sF1_fnc))),b2)))),multiply(X1,inverse(b2))),
inference(forward_demodulation,[status(thm)],[f6,f441]) ).
fof(f467,plain,
! [X0,X1] : X0 = multiply(inverse(multiply(X1,inverse(multiply(inverse(multiply(inverse(X0),inverse(sF1_fnc))),b2)))),multiply(X1,sF2_fnc)),
inference(forward_demodulation,[status(thm)],[f5,f466]) ).
fof(f616,plain,
! [X0,X1,X2,X3,X4] : multiply(inverse(multiply(X0,inverse(X1))),multiply(X0,inverse(multiply(X2,inverse(X3))))) = multiply(inverse(multiply(X4,inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(multiply(inverse(X1),inverse(multiply(inverse(X3),X3)))),X3)))),multiply(X2,inverse(X3)))))),multiply(X4,inverse(multiply(X2,inverse(X3))))),
inference(paramodulation,[status(thm)],[f208,f209]) ).
fof(f727,plain,
! [X0,X1,X2,X3,X4] : multiply(inverse(multiply(X0,inverse(X1))),multiply(X0,inverse(multiply(X2,inverse(X3))))) = multiply(inverse(multiply(X4,inverse(X1))),multiply(X4,inverse(multiply(X2,inverse(X3))))),
inference(forward_demodulation,[status(thm)],[f208,f616]) ).
fof(f2934,plain,
! [X0,X1,X2,X3,X4] : multiply(inverse(multiply(X0,inverse(X1))),multiply(X0,inverse(X2))) = multiply(inverse(multiply(X3,inverse(X1))),multiply(X3,inverse(multiply(inverse(multiply(sF2_fnc,multiply(inverse(multiply(inverse(multiply(X4,inverse(multiply(sF2_fnc,X2)))),multiply(X4,inverse(X2)))),inverse(X2)))),inverse(multiply(inverse(X2),X2)))))),
inference(paramodulation,[status(thm)],[f48,f727]) ).
fof(f3161,plain,
! [X0,X1,X2,X3] : multiply(inverse(multiply(X0,inverse(X1))),multiply(X0,inverse(X2))) = multiply(inverse(multiply(X3,inverse(X1))),multiply(X3,inverse(X2))),
inference(forward_demodulation,[status(thm)],[f48,f2934]) ).
fof(f3820,plain,
! [X0,X1,X2] : multiply(inverse(b2),multiply(inverse(multiply(inverse(multiply(X0,inverse(sF1_fnc))),multiply(X0,sF2_fnc))),inverse(X1))) = multiply(inverse(multiply(X2,inverse(sF1_fnc))),multiply(X2,inverse(X1))),
inference(paramodulation,[status(thm)],[f24,f3161]) ).
fof(f4045,plain,
! [X0,X1,X2] : multiply(sF2_fnc,multiply(inverse(multiply(inverse(multiply(X0,inverse(sF1_fnc))),multiply(X0,sF2_fnc))),inverse(X1))) = multiply(inverse(multiply(X2,inverse(sF1_fnc))),multiply(X2,inverse(X1))),
inference(forward_demodulation,[status(thm)],[f5,f3820]) ).
fof(f5060,plain,
! [X0,X1,X2] : multiply(sF2_fnc,multiply(inverse(multiply(inverse(multiply(X0,inverse(sF1_fnc))),multiply(X0,sF2_fnc))),inverse(sF1_fnc))) = multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,inverse(multiply(inverse(X2),b2)))),multiply(X1,sF2_fnc))),inverse(sF1_fnc))),X2),
inference(paramodulation,[status(thm)],[f16,f4045]) ).
fof(f5164,plain,
! [X0,X1] : multiply(sF2_fnc,b2) = multiply(inverse(multiply(inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),b2)))),multiply(X0,sF2_fnc))),inverse(sF1_fnc))),X1),
inference(forward_demodulation,[status(thm)],[f24,f5060]) ).
fof(f5165,plain,
! [X0,X1] : sF1_fnc = multiply(inverse(multiply(inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),b2)))),multiply(X0,sF2_fnc))),inverse(sF1_fnc))),X1),
inference(forward_demodulation,[status(thm)],[f6,f5164]) ).
fof(f5166,plain,
! [X0] : sF1_fnc = multiply(inverse(X0),X0),
inference(forward_demodulation,[status(thm)],[f16,f5165]) ).
fof(f5282,plain,
! [X0,X1,X2] : multiply(inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),X2)))),multiply(X0,inverse(X2)))),inverse(sF1_fnc)) = X1,
inference(backward_demodulation,[status(thm)],[f5166,f3]) ).
fof(f5290,plain,
! [X0] : inverse(sF1_fnc) = multiply(inverse(multiply(X0,inverse(multiply(inverse(sF1_fnc),b2)))),multiply(X0,sF2_fnc)),
inference(paramodulation,[status(thm)],[f5166,f467]) ).
fof(f5355,plain,
! [X0,X1,X2,X3] : multiply(inverse(multiply(inverse(multiply(X0,inverse(X1))),multiply(X0,inverse(inverse(sF1_fnc))))),inverse(sF1_fnc)) = multiply(inverse(multiply(X2,inverse(multiply(inverse(X1),X3)))),multiply(X2,inverse(X3))),
inference(paramodulation,[status(thm)],[f5282,f5282]) ).
fof(f5368,plain,
! [X0,X1] : multiply(inverse(multiply(inverse(multiply(X0,inverse(sF1_fnc))),multiply(X0,inverse(X1)))),inverse(sF1_fnc)) = X1,
inference(paramodulation,[status(thm)],[f5166,f5282]) ).
fof(f5598,plain,
multiply(inverse(sF1_fnc),inverse(sF1_fnc)) = sF1_fnc,
inference(paramodulation,[status(thm)],[f5166,f5368]) ).
fof(f5674,plain,
! [X0] : sF1_fnc = multiply(inverse(multiply(X0,inverse(multiply(inverse(sF1_fnc),b2)))),multiply(X0,sF2_fnc)),
inference(paramodulation,[status(thm)],[f5598,f467]) ).
fof(f5695,plain,
sF1_fnc = inverse(sF1_fnc),
inference(forward_demodulation,[status(thm)],[f5290,f5674]) ).
fof(f5701,plain,
! [X0,X1] : multiply(inverse(multiply(inverse(multiply(X0,inverse(sF1_fnc))),multiply(X0,inverse(X1)))),sF1_fnc) = X1,
inference(backward_demodulation,[status(thm)],[f5695,f5368]) ).
fof(f5706,plain,
! [X0,X1,X2] : multiply(inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),X2)))),multiply(X0,inverse(X2)))),sF1_fnc) = X1,
inference(backward_demodulation,[status(thm)],[f5695,f5282]) ).
fof(f5726,plain,
! [X0,X1] : multiply(inverse(multiply(inverse(multiply(X0,sF1_fnc)),multiply(X0,inverse(X1)))),sF1_fnc) = X1,
inference(forward_demodulation,[status(thm)],[f5695,f5701]) ).
fof(f5883,plain,
! [X0] : multiply(inverse(multiply(inverse(sF1_fnc),multiply(inverse(sF1_fnc),inverse(X0)))),sF1_fnc) = X0,
inference(paramodulation,[status(thm)],[f5166,f5726]) ).
fof(f5893,plain,
! [X0] : multiply(inverse(multiply(sF1_fnc,multiply(inverse(sF1_fnc),inverse(X0)))),sF1_fnc) = X0,
inference(forward_demodulation,[status(thm)],[f5695,f5883]) ).
fof(f5894,plain,
! [X0] : multiply(inverse(multiply(sF1_fnc,multiply(sF1_fnc,inverse(X0)))),sF1_fnc) = X0,
inference(forward_demodulation,[status(thm)],[f5695,f5893]) ).
fof(f6071,plain,
! [X0,X1,X2,X3] : multiply(inverse(multiply(inverse(multiply(X0,inverse(X1))),multiply(X0,inverse(sF1_fnc)))),inverse(sF1_fnc)) = multiply(inverse(multiply(X2,inverse(multiply(inverse(X1),X3)))),multiply(X2,inverse(X3))),
inference(forward_demodulation,[status(thm)],[f5695,f5355]) ).
fof(f6072,plain,
! [X0,X1,X2,X3] : multiply(inverse(multiply(inverse(multiply(X0,inverse(X1))),multiply(X0,sF1_fnc))),inverse(sF1_fnc)) = multiply(inverse(multiply(X2,inverse(multiply(inverse(X1),X3)))),multiply(X2,inverse(X3))),
inference(forward_demodulation,[status(thm)],[f5695,f6071]) ).
fof(f6073,plain,
! [X0,X1,X2,X3] : multiply(inverse(multiply(inverse(multiply(X0,inverse(X1))),multiply(X0,sF1_fnc))),sF1_fnc) = multiply(inverse(multiply(X2,inverse(multiply(inverse(X1),X3)))),multiply(X2,inverse(X3))),
inference(forward_demodulation,[status(thm)],[f5695,f6072]) ).
fof(f6076,plain,
! [X0,X1,X2] : multiply(inverse(multiply(inverse(multiply(X0,sF1_fnc)),multiply(X0,sF1_fnc))),sF1_fnc) = multiply(inverse(multiply(X1,inverse(multiply(inverse(sF1_fnc),X2)))),multiply(X1,inverse(X2))),
inference(paramodulation,[status(thm)],[f5695,f6073]) ).
fof(f6133,plain,
! [X0,X1] : multiply(inverse(sF1_fnc),sF1_fnc) = multiply(inverse(multiply(X0,inverse(multiply(inverse(sF1_fnc),X1)))),multiply(X0,inverse(X1))),
inference(forward_demodulation,[status(thm)],[f5166,f6076]) ).
fof(f6134,plain,
! [X0,X1] : sF1_fnc = multiply(inverse(multiply(X0,inverse(multiply(inverse(sF1_fnc),X1)))),multiply(X0,inverse(X1))),
inference(forward_demodulation,[status(thm)],[f5166,f6133]) ).
fof(f6135,plain,
! [X0,X1] : sF1_fnc = multiply(inverse(multiply(X0,inverse(multiply(sF1_fnc,X1)))),multiply(X0,inverse(X1))),
inference(forward_demodulation,[status(thm)],[f5695,f6134]) ).
fof(f6178,plain,
! [X0,X1,X2] : multiply(inverse(multiply(inverse(multiply(X0,inverse(sF1_fnc))),multiply(X0,inverse(multiply(X1,inverse(X2)))))),sF1_fnc) = multiply(X1,inverse(multiply(sF1_fnc,X2))),
inference(paramodulation,[status(thm)],[f6135,f5706]) ).
fof(f6187,plain,
! [X0,X1,X2] : multiply(inverse(multiply(inverse(multiply(X0,sF1_fnc)),multiply(X0,inverse(multiply(X1,inverse(X2)))))),sF1_fnc) = multiply(X1,inverse(multiply(sF1_fnc,X2))),
inference(forward_demodulation,[status(thm)],[f5695,f6178]) ).
fof(f6188,plain,
! [X0,X1] : multiply(X0,inverse(X1)) = multiply(X0,inverse(multiply(sF1_fnc,X1))),
inference(forward_demodulation,[status(thm)],[f5726,f6187]) ).
fof(f6202,plain,
! [X0] : multiply(inverse(multiply(sF1_fnc,multiply(sF1_fnc,inverse(X0)))),sF1_fnc) = multiply(sF1_fnc,X0),
inference(paramodulation,[status(thm)],[f6188,f5894]) ).
fof(f6221,plain,
! [X0] : X0 = multiply(sF1_fnc,X0),
inference(forward_demodulation,[status(thm)],[f5894,f6202]) ).
fof(f6236,plain,
sF0_fnc = a2,
inference(backward_demodulation,[status(thm)],[f6221,f7]) ).
fof(f6266,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f6236,f8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP425-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.66 % Computer : n002.cluster.edu
% 0.20/0.66 % Model : x86_64 x86_64
% 0.20/0.66 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.66 % Memory : 8046.5625MB
% 0.20/0.66 % OS : Linux 6.8.0-71-generic
% 0.20/0.66 % CPULimit : 300
% 0.20/0.66 % WCLimit : 300
% 0.20/0.66 % DateTime : Sun Sep 20 20:15:31 UTC 2026
% 0.20/0.66 % CPUTime :
% 0.20/0.67 % Drodi V4.1.1
% 0.23/0.98 % Refutation found
% 0.23/0.98 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.23/0.98 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 13.68/7.73 % Elapsed time: 7.047253 seconds
% 13.68/7.73 % CPU time: 39.307043 seconds
% 13.68/7.73 % Total memory used: 18.682 GB
% 13.68/7.73 % Net memory used: 18.681 GB
%------------------------------------------------------------------------------