%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP500-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 12:34:32 PM UTC 2026
% Result : Unsatisfiable 5.88s 6.16s
% Output : CNFRefutation 5.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 3
% Syntax : Number of formulae : 54 ( 54 unt; 0 def)
% Number of atoms : 54 ( 53 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 209 ( 209 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C,D] : double_divide(inverse(A),inverse(double_divide(inverse(double_divide(A,double_divide(B,C))),double_divide(D,double_divide(B,D))))) = C,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] : multiply(A,B) = inverse(double_divide(B,A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,plain,
! [X0,X1,X2,X3] : double_divide(inverse(X0),inverse(double_divide(inverse(double_divide(X0,double_divide(X1,X2))),double_divide(X3,double_divide(X1,X3))))) = X2,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f5,plain,
! [X0,X1] : multiply(X0,X1) = inverse(double_divide(X1,X0)),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f6,plain,
multiply(multiply(inverse(b2),b2),a2) != a2,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f11,plain,
! [X0,X1,X2,X3] : double_divide(inverse(X0),multiply(double_divide(X1,double_divide(X2,X1)),inverse(double_divide(X0,double_divide(X2,X3))))) = X3,
inference(forward_demodulation,[status(thm)],[f5,f4]) ).
fof(f12,plain,
! [X0,X1,X2,X3] : double_divide(inverse(X0),multiply(double_divide(X1,double_divide(X2,X1)),multiply(double_divide(X2,X3),X0))) = X3,
inference(forward_demodulation,[status(thm)],[f5,f11]) ).
fof(f13,plain,
! [X0,X1,X2,X3,X4] : double_divide(multiply(X0,X1),multiply(double_divide(X2,double_divide(X3,X2)),multiply(double_divide(X3,X4),double_divide(X1,X0)))) = X4,
inference(paramodulation,[status(thm)],[f5,f12]) ).
fof(f15,plain,
! [X0,X1,X2,X3,X4,X5] : double_divide(inverse(X0),multiply(double_divide(X1,double_divide(inverse(X2),X1)),multiply(X3,X0))) = multiply(double_divide(X4,double_divide(X5,X4)),multiply(double_divide(X5,X3),X2)),
inference(paramodulation,[status(thm)],[f12,f12]) ).
fof(f16,plain,
! [X0,X1,X2,X3] : multiply(multiply(double_divide(X0,double_divide(X1,X0)),multiply(double_divide(X1,X2),X3)),inverse(X3)) = inverse(X2),
inference(paramodulation,[status(thm)],[f12,f5]) ).
fof(f19,plain,
! [X0,X1,X2,X3,X4] : multiply(multiply(double_divide(X0,double_divide(X1,X0)),multiply(double_divide(X1,X2),double_divide(X3,X4))),multiply(X4,X3)) = inverse(X2),
inference(paramodulation,[status(thm)],[f5,f16]) ).
fof(f206,plain,
! [X0,X1,X2,X3] : X0 = multiply(double_divide(X1,double_divide(X2,X1)),multiply(double_divide(X2,double_divide(inverse(X3),X0)),X3)),
inference(paramodulation,[status(thm)],[f12,f15]) ).
fof(f273,plain,
! [X0,X1,X2,X3,X4] : double_divide(multiply(X0,X1),double_divide(inverse(X2),multiply(double_divide(X3,double_divide(inverse(double_divide(X1,X0)),X3)),multiply(X4,X2)))) = X4,
inference(paramodulation,[status(thm)],[f15,f13]) ).
fof(f298,plain,
! [X0,X1,X2,X3,X4] : double_divide(multiply(X0,X1),double_divide(inverse(X2),multiply(double_divide(X3,double_divide(multiply(X0,X1),X3)),multiply(X4,X2)))) = X4,
inference(forward_demodulation,[status(thm)],[f5,f273]) ).
fof(f316,plain,
! [X0,X1,X2,X3,X4] : X0 = multiply(double_divide(X1,double_divide(X2,X1)),multiply(double_divide(X2,double_divide(multiply(X3,X4),X0)),double_divide(X4,X3))),
inference(paramodulation,[status(thm)],[f5,f206]) ).
fof(f337,plain,
! [X0,X1,X2,X3,X4] : multiply(multiply(double_divide(X0,double_divide(X1,X0)),X2),inverse(multiply(double_divide(X3,double_divide(inverse(X4),X2)),X4))) = inverse(double_divide(X3,X1)),
inference(paramodulation,[status(thm)],[f206,f16]) ).
fof(f338,plain,
! [X0,X1,X2,X3,X4] : double_divide(inverse(multiply(double_divide(X0,double_divide(inverse(X1),X2)),X1)),multiply(double_divide(X3,double_divide(X4,X3)),X2)) = double_divide(X0,X4),
inference(paramodulation,[status(thm)],[f206,f12]) ).
fof(f347,plain,
! [X0,X1,X2,X3,X4] : multiply(multiply(double_divide(X0,double_divide(X1,X0)),X2),inverse(multiply(double_divide(X3,double_divide(inverse(X4),X2)),X4))) = multiply(X1,X3),
inference(forward_demodulation,[status(thm)],[f5,f337]) ).
fof(f629,plain,
! [X0,X1,X2,X3,X4] : multiply(X0,inverse(multiply(double_divide(X1,double_divide(inverse(X2),multiply(double_divide(X3,double_divide(inverse(X4),X0)),X4))),X2))) = multiply(X3,X1),
inference(paramodulation,[status(thm)],[f206,f347]) ).
fof(f739,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] : double_divide(X0,double_divide(inverse(X1),multiply(double_divide(X2,double_divide(multiply(double_divide(X3,double_divide(X4,X3)),multiply(double_divide(X4,double_divide(multiply(X5,X6),X0)),double_divide(X6,X5))),X2)),multiply(X7,X1)))) = X7,
inference(paramodulation,[status(thm)],[f316,f298]) ).
fof(f816,plain,
! [X0,X1,X2,X3] : double_divide(X0,double_divide(inverse(X1),multiply(double_divide(X2,double_divide(X0,X2)),multiply(X3,X1)))) = X3,
inference(forward_demodulation,[status(thm)],[f316,f739]) ).
fof(f869,plain,
! [X0,X1,X2,X3,X4] : multiply(double_divide(X0,double_divide(X1,X0)),multiply(X2,X3)) = multiply(double_divide(X4,double_divide(X1,X4)),multiply(X2,X3)),
inference(paramodulation,[status(thm)],[f816,f206]) ).
fof(f903,plain,
! [X0,X1,X2,X3] : multiply(double_divide(inverse(X0),multiply(double_divide(X1,double_divide(X2,X1)),multiply(X3,X0))),X2) = inverse(X3),
inference(paramodulation,[status(thm)],[f816,f5]) ).
fof(f1819,plain,
! [X0,X1,X2,X3,X4,X5,X6] : multiply(double_divide(inverse(multiply(X0,X1)),multiply(double_divide(X2,double_divide(X3,X2)),multiply(double_divide(X4,double_divide(X5,X4)),multiply(X0,X1)))),X3) = inverse(double_divide(X6,double_divide(X5,X6))),
inference(paramodulation,[status(thm)],[f869,f903]) ).
fof(f1820,plain,
! [X0,X1,X2,X3,X4,X5,X6] : double_divide(X0,double_divide(inverse(multiply(X1,X2)),multiply(double_divide(X3,double_divide(X0,X3)),multiply(double_divide(X4,double_divide(X5,X4)),multiply(X1,X2))))) = double_divide(X6,double_divide(X5,X6)),
inference(paramodulation,[status(thm)],[f869,f816]) ).
fof(f1907,plain,
! [X0,X1,X2] : inverse(double_divide(X0,double_divide(X1,X0))) = inverse(double_divide(X2,double_divide(X1,X2))),
inference(forward_demodulation,[status(thm)],[f903,f1819]) ).
fof(f1908,plain,
! [X0,X1,X2] : multiply(double_divide(X0,X1),X1) = inverse(double_divide(X2,double_divide(X0,X2))),
inference(forward_demodulation,[status(thm)],[f5,f1907]) ).
fof(f1909,plain,
! [X0,X1,X2] : multiply(double_divide(X0,X1),X1) = multiply(double_divide(X0,X2),X2),
inference(forward_demodulation,[status(thm)],[f5,f1908]) ).
fof(f1910,plain,
! [X0,X1,X2] : double_divide(X0,double_divide(X1,X0)) = double_divide(X2,double_divide(X1,X2)),
inference(forward_demodulation,[status(thm)],[f816,f1820]) ).
fof(f2134,plain,
! [X0,X1,X2,X3] : double_divide(inverse(X0),multiply(double_divide(X1,double_divide(X2,X1)),multiply(double_divide(X2,X3),X3))) = X0,
inference(paramodulation,[status(thm)],[f1909,f12]) ).
fof(f2264,plain,
! [X0,X1,X2,X3] : X0 = multiply(double_divide(X1,double_divide(X0,X1)),multiply(double_divide(X2,double_divide(inverse(X3),X2)),X3)),
inference(paramodulation,[status(thm)],[f1910,f206]) ).
fof(f3331,plain,
! [X0,X1,X2,X3] : double_divide(X0,X1) = multiply(double_divide(X0,double_divide(inverse(X2),multiply(double_divide(X1,X3),X3))),X2),
inference(paramodulation,[status(thm)],[f338,f2134]) ).
fof(f3646,plain,
! [X0,X1,X2,X3] : X0 = multiply(double_divide(X1,double_divide(X0,X1)),double_divide(multiply(double_divide(X2,X3),X3),X2)),
inference(paramodulation,[status(thm)],[f3331,f2264]) ).
fof(f3730,plain,
! [X0,X1,X2,X3] : inverse(double_divide(multiply(double_divide(X0,X1),X1),X0)) = double_divide(multiply(double_divide(X2,X3),X3),X2),
inference(paramodulation,[status(thm)],[f3331,f3646]) ).
fof(f3840,plain,
! [X0,X1,X2,X3] : multiply(X0,multiply(double_divide(X0,X1),X1)) = double_divide(multiply(double_divide(X2,X3),X3),X2),
inference(forward_demodulation,[status(thm)],[f5,f3730]) ).
fof(f3947,plain,
! [X0,X1,X2,X3,X4,X5] : double_divide(inverse(multiply(double_divide(double_divide(X0,X1),X2),X2)),multiply(double_divide(X3,double_divide(X0,X3)),double_divide(multiply(double_divide(X4,X5),X5),X4))) = X1,
inference(paramodulation,[status(thm)],[f3840,f12]) ).
fof(f3958,plain,
! [X0,X1,X2,X3,X4,X5] : multiply(double_divide(inverse(multiply(double_divide(X0,X1),X1)),multiply(double_divide(X2,double_divide(X3,X2)),double_divide(multiply(double_divide(X4,X5),X5),X4))),X3) = inverse(X0),
inference(paramodulation,[status(thm)],[f3840,f903]) ).
fof(f4069,plain,
! [X0,X1,X2] : double_divide(inverse(multiply(double_divide(double_divide(X0,X1),X2),X2)),X0) = X1,
inference(forward_demodulation,[status(thm)],[f3646,f3947]) ).
fof(f4072,plain,
! [X0,X1,X2] : multiply(double_divide(inverse(multiply(double_divide(X0,X1),X1)),X2),X2) = inverse(X0),
inference(forward_demodulation,[status(thm)],[f3646,f3958]) ).
fof(f4879,plain,
! [X0,X1,X2,X3,X4] : double_divide(inverse(X0),multiply(double_divide(X1,X2),multiply(double_divide(inverse(multiply(double_divide(double_divide(X1,X2),X3),X3)),X4),X4))) = X0,
inference(paramodulation,[status(thm)],[f4069,f2134]) ).
fof(f4948,plain,
! [X0,X1,X2] : double_divide(inverse(X0),multiply(double_divide(X1,X2),inverse(double_divide(X1,X2)))) = X0,
inference(forward_demodulation,[status(thm)],[f4072,f4879]) ).
fof(f4949,plain,
! [X0,X1,X2] : double_divide(inverse(X0),multiply(double_divide(X1,X2),multiply(X2,X1))) = X0,
inference(forward_demodulation,[status(thm)],[f5,f4948]) ).
fof(f4991,plain,
! [X0,X1,X2,X3,X4,X5] : double_divide(inverse(X0),multiply(X1,multiply(multiply(double_divide(X2,double_divide(X3,X2)),multiply(double_divide(X3,X1),double_divide(X4,X5))),multiply(X5,X4)))) = X0,
inference(paramodulation,[status(thm)],[f13,f4949]) ).
fof(f5143,plain,
! [X0,X1] : double_divide(inverse(X0),multiply(X1,inverse(X1))) = X0,
inference(forward_demodulation,[status(thm)],[f19,f4991]) ).
fof(f5161,plain,
! [X0,X1,X2] : X0 = multiply(double_divide(double_divide(multiply(X1,inverse(X1)),X0),X2),X2),
inference(paramodulation,[status(thm)],[f4069,f5143]) ).
fof(f5181,plain,
! [X0,X1,X2,X3,X4] : multiply(multiply(X0,inverse(X0)),inverse(multiply(double_divide(X1,double_divide(inverse(X2),multiply(double_divide(X3,X4),X4))),X2))) = multiply(X3,X1),
inference(paramodulation,[status(thm)],[f5143,f629]) ).
fof(f5281,plain,
! [X0,X1,X2] : multiply(multiply(X0,inverse(X0)),inverse(double_divide(X1,X2))) = multiply(X2,X1),
inference(forward_demodulation,[status(thm)],[f3331,f5181]) ).
fof(f5282,plain,
! [X0,X1,X2] : multiply(multiply(X0,inverse(X0)),multiply(X1,X2)) = multiply(X1,X2),
inference(forward_demodulation,[status(thm)],[f5,f5281]) ).
fof(f6656,plain,
! [X0,X1,X2,X3] : multiply(multiply(X0,inverse(X0)),X1) = multiply(double_divide(double_divide(multiply(X2,inverse(X2)),X1),X3),X3),
inference(paramodulation,[status(thm)],[f5161,f5282]) ).
fof(f6716,plain,
! [X0,X1] : multiply(multiply(X0,inverse(X0)),X1) = X1,
inference(forward_demodulation,[status(thm)],[f5161,f6656]) ).
fof(f6752,plain,
! [X0,X1] : multiply(multiply(inverse(X0),X0),X1) = X1,
inference(paramodulation,[status(thm)],[f347,f6716]) ).
fof(f6804,plain,
a2 != a2,
inference(backward_demodulation,[status(thm)],[f6752,f6]) ).
fof(f6849,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f6804]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP500-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/5.36 % Computer : n001.cluster.edu
% 0.08/5.36 % Model : x86_64 x86_64
% 0.08/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.36 % Memory : 8046.5625MB
% 0.08/5.36 % OS : Linux 6.8.0-71-generic
% 0.08/5.36 % CPULimit : 300
% 0.08/5.36 % WCLimit : 300
% 0.08/5.36 % DateTime : Sun Sep 20 20:20:48 UTC 2026
% 0.08/5.36 % CPUTime :
% 0.08/5.37 % Drodi V4.1.1
% 5.88/6.16 % Refutation found
% 5.88/6.16 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 5.88/6.16 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 5.88/6.20 % Elapsed time: 0.817232 seconds
% 5.88/6.20 % CPU time: 6.364338 seconds
% 5.88/6.20 % Total memory used: 153.220 MB
% 5.88/6.20 % Net memory used: 149.764 MB
%------------------------------------------------------------------------------