%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP502-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 73.56s 19.89s
% Output : CNFRefutation 73.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 3
% Syntax : Number of formulae : 43 ( 43 unt; 0 def)
% Number of atoms : 43 ( 42 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 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 : 181 ( 181 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C,D] : double_divide(double_divide(A,inverse(double_divide(B,C))),double_divide(inverse(B),inverse(double_divide(D,double_divide(A,D))))) = C,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] : multiply(A,B) = inverse(double_divide(B,A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,plain,
! [X0,X1,X2,X3] : double_divide(double_divide(X0,inverse(double_divide(X1,X2))),double_divide(inverse(X1),inverse(double_divide(X3,double_divide(X0,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(inverse(a1),a1) != multiply(inverse(b1),b1),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f12,plain,
! [X0,X1,X2,X3] : double_divide(double_divide(X0,multiply(X1,X2)),double_divide(inverse(X2),inverse(double_divide(X3,double_divide(X0,X3))))) = X1,
inference(forward_demodulation,[status(thm)],[f5,f4]) ).
fof(f13,plain,
! [X0,X1,X2,X3] : double_divide(double_divide(X0,multiply(X1,X2)),double_divide(inverse(X2),multiply(double_divide(X0,X3),X3))) = X1,
inference(forward_demodulation,[status(thm)],[f5,f12]) ).
fof(f14,plain,
! [X0,X1,X2,X3,X4] : double_divide(double_divide(X0,multiply(X1,double_divide(X2,X3))),double_divide(multiply(X3,X2),multiply(double_divide(X0,X4),X4))) = X1,
inference(paramodulation,[status(thm)],[f5,f13]) ).
fof(f15,plain,
! [X0,X1,X2,X3,X4,X5] : double_divide(double_divide(double_divide(X0,multiply(X1,X2)),multiply(X3,X4)),double_divide(inverse(X4),multiply(X1,double_divide(inverse(X2),multiply(double_divide(X0,X5),X5))))) = X3,
inference(paramodulation,[status(thm)],[f13,f13]) ).
fof(f16,plain,
! [X0,X1,X2,X3] : multiply(double_divide(inverse(X0),multiply(double_divide(X1,X2),X2)),double_divide(X1,multiply(X3,X0))) = inverse(X3),
inference(paramodulation,[status(thm)],[f13,f5]) ).
fof(f17,plain,
! [X0,X1,X2,X3,X4] : multiply(double_divide(multiply(X0,X1),multiply(double_divide(X2,X3),X3)),double_divide(X2,multiply(X4,double_divide(X1,X0)))) = inverse(X4),
inference(paramodulation,[status(thm)],[f5,f16]) ).
fof(f20,plain,
! [X0,X1,X2,X3,X4,X5] : double_divide(double_divide(X0,inverse(X1)),double_divide(inverse(double_divide(X2,multiply(X1,X3))),multiply(double_divide(X0,X4),X4))) = double_divide(inverse(X3),multiply(double_divide(X2,X5),X5)),
inference(paramodulation,[status(thm)],[f16,f13]) ).
fof(f21,plain,
! [X0,X1,X2,X3,X4,X5] : double_divide(double_divide(X0,inverse(X1)),double_divide(multiply(multiply(X1,X2),X3),multiply(double_divide(X0,X4),X4))) = double_divide(inverse(X2),multiply(double_divide(X3,X5),X5)),
inference(forward_demodulation,[status(thm)],[f5,f20]) ).
fof(f121,plain,
! [X0,X1,X2,X3] : double_divide(inverse(X0),multiply(double_divide(X1,X2),X2)) = double_divide(inverse(X0),multiply(double_divide(X1,X3),X3)),
inference(paramodulation,[status(thm)],[f21,f21]) ).
fof(f247,plain,
! [X0,X1,X2,X3] : multiply(multiply(double_divide(X0,X1),X1),inverse(X2)) = inverse(double_divide(inverse(X2),multiply(double_divide(X0,X3),X3))),
inference(paramodulation,[status(thm)],[f121,f5]) ).
fof(f253,plain,
! [X0,X1,X2,X3] : multiply(multiply(double_divide(X0,X1),X1),inverse(X2)) = multiply(multiply(double_divide(X0,X3),X3),inverse(X2)),
inference(forward_demodulation,[status(thm)],[f5,f247]) ).
fof(f291,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] : double_divide(double_divide(double_divide(X0,multiply(X1,X2)),multiply(multiply(double_divide(X3,X4),X4),inverse(X5))),double_divide(inverse(inverse(X5)),multiply(X1,double_divide(inverse(X2),multiply(double_divide(X0,X6),X6))))) = multiply(double_divide(X3,X7),X7),
inference(paramodulation,[status(thm)],[f253,f15]) ).
fof(f298,plain,
! [X0,X1,X2] : multiply(double_divide(X0,X1),X1) = multiply(double_divide(X0,X2),X2),
inference(forward_demodulation,[status(thm)],[f15,f291]) ).
fof(f341,plain,
! [X0,X1,X2,X3,X4,X5] : double_divide(double_divide(X0,multiply(double_divide(X1,X2),X2)),double_divide(multiply(X3,X4),multiply(double_divide(X0,X5),X5))) = double_divide(X1,double_divide(X4,X3)),
inference(paramodulation,[status(thm)],[f298,f14]) ).
fof(f1961,plain,
! [X0,X1,X2,X3,X4,X5,X6] : double_divide(double_divide(X0,multiply(double_divide(X1,X2),X2)),double_divide(multiply(double_divide(X3,X4),X4),multiply(double_divide(X0,X5),X5))) = double_divide(X1,double_divide(X6,double_divide(X3,X6))),
inference(paramodulation,[status(thm)],[f298,f341]) ).
fof(f2027,plain,
! [X0,X1,X2,X3] : double_divide(X0,double_divide(X1,double_divide(X2,X1))) = double_divide(X0,double_divide(X3,double_divide(X2,X3))),
inference(forward_demodulation,[status(thm)],[f341,f1961]) ).
fof(f2358,plain,
! [X0,X1,X2,X3] : multiply(double_divide(X0,double_divide(X1,X0)),X2) = inverse(double_divide(X2,double_divide(X3,double_divide(X1,X3)))),
inference(paramodulation,[status(thm)],[f2027,f5]) ).
fof(f2359,plain,
! [X0,X1,X2,X3] : multiply(double_divide(X0,double_divide(X1,X0)),X2) = multiply(double_divide(X3,double_divide(X1,X3)),X2),
inference(forward_demodulation,[status(thm)],[f5,f2358]) ).
fof(f2511,plain,
! [X0,X1,X2,X3] : multiply(double_divide(X0,X1),X1) = multiply(double_divide(X2,double_divide(X3,X2)),double_divide(X3,X0)),
inference(paramodulation,[status(thm)],[f2359,f298]) ).
fof(f3965,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] : double_divide(double_divide(X0,inverse(double_divide(X1,double_divide(X2,X1)))),double_divide(multiply(multiply(double_divide(X3,X4),X4),X5),multiply(double_divide(X0,X6),X6))) = double_divide(inverse(double_divide(X2,X3)),multiply(double_divide(X5,X7),X7)),
inference(paramodulation,[status(thm)],[f2511,f21]) ).
fof(f3998,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] : double_divide(double_divide(X0,multiply(double_divide(X1,X2),X2)),double_divide(multiply(multiply(double_divide(X3,X4),X4),X5),multiply(double_divide(X0,X6),X6))) = double_divide(inverse(double_divide(X1,X3)),multiply(double_divide(X5,X7),X7)),
inference(forward_demodulation,[status(thm)],[f5,f3965]) ).
fof(f3999,plain,
! [X0,X1,X2,X3,X4] : double_divide(X0,double_divide(X1,multiply(double_divide(X2,X3),X3))) = double_divide(inverse(double_divide(X0,X2)),multiply(double_divide(X1,X4),X4)),
inference(forward_demodulation,[status(thm)],[f341,f3998]) ).
fof(f4000,plain,
! [X0,X1,X2,X3,X4] : double_divide(X0,double_divide(X1,multiply(double_divide(X2,X3),X3))) = double_divide(multiply(X2,X0),multiply(double_divide(X1,X4),X4)),
inference(forward_demodulation,[status(thm)],[f5,f3999]) ).
fof(f13146,plain,
! [X0,X1,X2,X3] : X0 = double_divide(multiply(X1,double_divide(X1,multiply(X0,X2))),multiply(double_divide(inverse(X2),X3),X3)),
inference(paramodulation,[status(thm)],[f13,f4000]) ).
fof(f13821,plain,
! [X0,X1,X2,X3] : multiply(X0,double_divide(inverse(X1),multiply(X2,double_divide(double_divide(X3,multiply(X0,X1)),X3)))) = inverse(X2),
inference(paramodulation,[status(thm)],[f13146,f17]) ).
fof(f14417,plain,
! [X0,X1,X2,X3] : X0 = double_divide(inverse(X0),multiply(double_divide(inverse(double_divide(double_divide(X1,multiply(inverse(X2),X2)),X1)),X3),X3)),
inference(paramodulation,[status(thm)],[f13821,f13146]) ).
fof(f14591,plain,
! [X0,X1,X2,X3] : X0 = double_divide(inverse(X0),multiply(double_divide(multiply(X1,double_divide(X1,multiply(inverse(X2),X2))),X3),X3)),
inference(forward_demodulation,[status(thm)],[f5,f14417]) ).
fof(f15074,plain,
! [X0,X1,X2,X3] : double_divide(double_divide(multiply(X0,double_divide(X0,multiply(inverse(X1),X1))),multiply(X2,X3)),X3) = X2,
inference(paramodulation,[status(thm)],[f14591,f13]) ).
fof(f17120,plain,
! [X0,X1,X2,X3,X4,X5] : double_divide(X0,double_divide(inverse(X1),multiply(X0,double_divide(inverse(multiply(X2,X1)),multiply(double_divide(multiply(X3,double_divide(X3,multiply(inverse(X4),X4))),X5),X5))))) = X2,
inference(paramodulation,[status(thm)],[f15074,f15]) ).
fof(f17312,plain,
! [X0,X1,X2] : double_divide(X0,double_divide(inverse(X1),multiply(X0,multiply(X2,X1)))) = X2,
inference(forward_demodulation,[status(thm)],[f14591,f17120]) ).
fof(f17825,plain,
! [X0,X1,X2,X3] : multiply(double_divide(X0,X1),X1) = multiply(X2,double_divide(inverse(X3),multiply(X0,multiply(X2,X3)))),
inference(paramodulation,[status(thm)],[f17312,f298]) ).
fof(f21904,plain,
! [X0,X1,X2,X3] : double_divide(double_divide(multiply(double_divide(inverse(multiply(inverse(X0),X0)),X1),X1),multiply(X2,X3)),X3) = X2,
inference(paramodulation,[status(thm)],[f17825,f15074]) ).
fof(f21908,plain,
! [X0,X1,X2,X3] : X0 = double_divide(multiply(double_divide(X0,X1),X1),multiply(double_divide(inverse(multiply(inverse(X2),X2)),X3),X3)),
inference(paramodulation,[status(thm)],[f17825,f13146]) ).
fof(f22455,plain,
! [X0,X1,X2] : double_divide(inverse(multiply(inverse(X0),X0)),X1) = double_divide(inverse(multiply(inverse(X2),X2)),X1),
inference(paramodulation,[status(thm)],[f21908,f21904]) ).
fof(f24104,plain,
! [X0,X1,X2,X3,X4] : multiply(inverse(X0),X0) = double_divide(inverse(multiply(inverse(X1),X1)),multiply(double_divide(multiply(X2,double_divide(X2,multiply(inverse(X3),X3))),X4),X4)),
inference(paramodulation,[status(thm)],[f14591,f22455]) ).
fof(f24774,plain,
! [X0,X1] : multiply(inverse(X0),X0) = multiply(inverse(X1),X1),
inference(forward_demodulation,[status(thm)],[f14591,f24104]) ).
fof(f24809,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f6,f24774]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP502-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/10.41 % Computer : n011.cluster.edu
% 0.13/10.41 % Model : x86_64 x86_64
% 0.13/10.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/10.41 % Memory : 8046.5625MB
% 0.13/10.41 % OS : Linux 6.8.0-71-generic
% 0.13/10.41 % CPULimit : 300
% 0.13/10.41 % WCLimit : 300
% 0.13/10.41 % DateTime : Sun Sep 20 20:15:21 UTC 2026
% 0.13/10.42 % CPUTime :
% 0.13/10.42 % Drodi V4.1.1
% 73.56/19.89 % Refutation found
% 73.56/19.89 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 73.56/19.89 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.64/20.12 % Elapsed time: 9.698379 seconds
% 2.64/20.12 % CPU time: 76.051341 seconds
% 2.64/20.12 % Total memory used: 690.043 MB
% 2.64/20.12 % Net memory used: 683.379 MB
%------------------------------------------------------------------------------