%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP603-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 12:34:46 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.50s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 3
% Syntax : Number of formulae : 58 ( 58 unt; 0 def)
% Number of atoms : 58 ( 57 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 8 ( 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 : 195 ( 195 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : inverse(double_divide(inverse(double_divide(A,inverse(double_divide(B,double_divide(A,C))))),C)) = B,
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(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,plain,
! [X0,X1,X2] : inverse(double_divide(inverse(double_divide(X0,inverse(double_divide(X1,double_divide(X0,X2))))),X2)) = X1,
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(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f12,plain,
! [X0,X1,X2] : multiply(X0,inverse(double_divide(X1,inverse(double_divide(X2,double_divide(X1,X0)))))) = X2,
inference(backward_demodulation,[status(thm)],[f5,f4]) ).
fof(f13,plain,
! [X0,X1,X2] : multiply(X0,multiply(inverse(double_divide(X1,double_divide(X2,X0))),X2)) = X1,
inference(forward_demodulation,[status(thm)],[f5,f12]) ).
fof(f14,plain,
! [X0,X1,X2] : multiply(X0,multiply(multiply(double_divide(X1,X0),X2),X1)) = X2,
inference(forward_demodulation,[status(thm)],[f5,f13]) ).
fof(f15,plain,
! [X0,X1,X2,X3] : multiply(X0,multiply(X1,X2)) = multiply(multiply(double_divide(X3,double_divide(X2,X0)),X1),X3),
inference(paramodulation,[status(thm)],[f14,f14]) ).
fof(f17,plain,
! [X0,X1,X2] : multiply(double_divide(X0,X1),multiply(X1,multiply(X2,X0))) = X2,
inference(paramodulation,[status(thm)],[f15,f14]) ).
fof(f19,plain,
! [X0,X1,X2] : multiply(double_divide(multiply(X0,X1),double_divide(X1,X2)),X0) = X2,
inference(paramodulation,[status(thm)],[f17,f17]) ).
fof(f20,plain,
! [X0,X1,X2,X3,X4] : multiply(double_divide(X0,multiply(double_divide(multiply(X1,X0),double_divide(X2,X3)),X4)),multiply(X3,multiply(X4,X2))) = X1,
inference(paramodulation,[status(thm)],[f15,f17]) ).
fof(f22,plain,
! [X0,X1,X2,X3] : multiply(double_divide(multiply(X0,multiply(X1,X2)),X3),multiply(X3,X1)) = double_divide(X2,X0),
inference(paramodulation,[status(thm)],[f17,f17]) ).
fof(f27,plain,
! [X0,X1,X2,X3] : multiply(double_divide(X0,double_divide(X1,X2)),double_divide(multiply(X1,X3),double_divide(X3,X0))) = X2,
inference(paramodulation,[status(thm)],[f19,f19]) ).
fof(f28,plain,
! [X0,X1,X2,X3] : multiply(double_divide(X0,double_divide(multiply(X1,multiply(X0,X2)),X3)),double_divide(X2,X1)) = X3,
inference(paramodulation,[status(thm)],[f17,f19]) ).
fof(f30,plain,
! [X0,X1,X2,X3] : multiply(double_divide(X0,double_divide(multiply(multiply(double_divide(X1,X2),X0),X1),X3)),X2) = X3,
inference(paramodulation,[status(thm)],[f14,f19]) ).
fof(f33,plain,
! [X0,X1,X2,X3] : multiply(double_divide(X0,double_divide(multiply(multiply(X1,X0),X2),double_divide(X2,X3))),X3) = X1,
inference(paramodulation,[status(thm)],[f19,f17]) ).
fof(f47,plain,
! [X0,X1,X2,X3,X4] : multiply(double_divide(double_divide(multiply(X0,X1),double_divide(X1,X2)),double_divide(multiply(X3,X2),X4)),double_divide(X0,X3)) = X4,
inference(paramodulation,[status(thm)],[f27,f30]) ).
fof(f76,plain,
! [X0,X1,X2] : double_divide(multiply(X0,X1),double_divide(X1,multiply(X2,X0))) = X2,
inference(paramodulation,[status(thm)],[f28,f33]) ).
fof(f116,plain,
! [X0,X1,X2,X3] : multiply(double_divide(X0,X1),X2) = double_divide(X3,multiply(X1,multiply(double_divide(X3,X2),X0))),
inference(paramodulation,[status(thm)],[f76,f30]) ).
fof(f118,plain,
! [X0,X1,X2,X3] : multiply(double_divide(X0,X1),double_divide(X2,X3)) = double_divide(multiply(X0,X2),multiply(X1,X3)),
inference(paramodulation,[status(thm)],[f76,f28]) ).
fof(f128,plain,
! [X0,X1,X2,X3] : multiply(double_divide(multiply(X0,multiply(X1,X2)),X3),X0) = double_divide(X2,multiply(X3,X1)),
inference(paramodulation,[status(thm)],[f76,f19]) ).
fof(f136,plain,
! [X0,X1,X2,X3,X4] : double_divide(multiply(double_divide(multiply(X0,X1),double_divide(X1,X2)),X0),multiply(double_divide(multiply(X3,X2),X4),X3)) = X4,
inference(backward_demodulation,[status(thm)],[f118,f47]) ).
fof(f164,plain,
! [X0,X1,X2] : double_divide(X0,multiply(double_divide(multiply(X1,X0),X2),X1)) = X2,
inference(forward_demodulation,[status(thm)],[f19,f136]) ).
fof(f209,plain,
! [X0,X1,X2,X3,X4] : multiply(multiply(double_divide(multiply(X0,X1),X2),X0),multiply(X3,X1)) = multiply(multiply(double_divide(X4,X2),X3),X4),
inference(paramodulation,[status(thm)],[f164,f15]) ).
fof(f211,plain,
! [X0,X1,X2] : multiply(multiply(double_divide(multiply(X0,X1),X2),X0),X1) = inverse(X2),
inference(paramodulation,[status(thm)],[f164,f5]) ).
fof(f233,plain,
! [X0,X1,X2,X3] : multiply(double_divide(X0,multiply(double_divide(multiply(X1,multiply(X2,X0)),X3),X1)),inverse(X3)) = X2,
inference(paramodulation,[status(thm)],[f211,f17]) ).
fof(f247,plain,
! [X0,X1,X2] : multiply(double_divide(X0,double_divide(X0,multiply(X1,X2))),inverse(X1)) = X2,
inference(forward_demodulation,[status(thm)],[f128,f233]) ).
fof(f253,plain,
! [X0,X1,X2,X3] : multiply(double_divide(X0,double_divide(X0,X1)),inverse(double_divide(X2,X3))) = multiply(X3,multiply(X1,X2)),
inference(paramodulation,[status(thm)],[f17,f247]) ).
fof(f256,plain,
! [X0,X1,X2,X3] : multiply(double_divide(X0,double_divide(X0,X1)),inverse(X2)) = multiply(multiply(double_divide(X3,X2),X1),X3),
inference(paramodulation,[status(thm)],[f14,f247]) ).
fof(f258,plain,
! [X0,X1,X2] : multiply(X0,X1) = inverse(double_divide(multiply(inverse(X2),X1),multiply(X2,X0))),
inference(paramodulation,[status(thm)],[f247,f211]) ).
fof(f259,plain,
! [X0,X1,X2] : double_divide(X0,X1) = double_divide(multiply(inverse(X2),X0),multiply(X2,X1)),
inference(paramodulation,[status(thm)],[f247,f164]) ).
fof(f279,plain,
! [X0,X1,X2,X3] : multiply(double_divide(X0,double_divide(X0,X1)),multiply(X2,X3)) = multiply(X2,multiply(X1,X3)),
inference(forward_demodulation,[status(thm)],[f5,f253]) ).
fof(f281,plain,
! [X0,X1,X2] : multiply(X0,X1) = multiply(multiply(X2,X0),multiply(inverse(X2),X1)),
inference(forward_demodulation,[status(thm)],[f5,f258]) ).
fof(f296,plain,
! [X0,X1,X2,X3] : multiply(X0,multiply(multiply(double_divide(X1,inverse(X2)),X3),X1)) = multiply(multiply(X2,X0),X3),
inference(paramodulation,[status(thm)],[f14,f281]) ).
fof(f303,plain,
! [X0,X1,X2,X3] : double_divide(multiply(multiply(inverse(X0),X1),X2),double_divide(X2,multiply(X3,X1))) = multiply(X0,X3),
inference(paramodulation,[status(thm)],[f281,f76]) ).
fof(f330,plain,
! [X0,X1,X2,X3] : double_divide(X0,multiply(X1,multiply(X2,X3))) = double_divide(multiply(inverse(double_divide(X3,X1)),X0),X2),
inference(paramodulation,[status(thm)],[f17,f259]) ).
fof(f353,plain,
! [X0,X1,X2,X3] : double_divide(X0,multiply(inverse(X1),multiply(double_divide(X0,multiply(X2,X3)),X3))) = multiply(X1,X2),
inference(backward_demodulation,[status(thm)],[f383,f303]) ).
fof(f383,plain,
! [X0,X1,X2,X3] : double_divide(X0,multiply(X1,multiply(X2,X3))) = double_divide(multiply(multiply(X1,X3),X0),X2),
inference(forward_demodulation,[status(thm)],[f5,f330]) ).
fof(f392,plain,
! [X0,X1,X2] : multiply(double_divide(X0,inverse(X1)),multiply(X2,X0)) = multiply(X1,X2),
inference(forward_demodulation,[status(thm)],[f116,f353]) ).
fof(f447,plain,
! [X0,X1,X2,X3,X4,X5] : double_divide(multiply(multiply(X0,multiply(X1,X2)),X3),double_divide(X3,X4)) = double_divide(X5,multiply(double_divide(multiply(X4,X5),double_divide(X2,X0)),X1)),
inference(paramodulation,[status(thm)],[f20,f76]) ).
fof(f450,plain,
! [X0,X1,X2,X3,X4,X5] : multiply(double_divide(multiply(X0,multiply(X1,X2)),X3),multiply(X3,X4)) = double_divide(X5,multiply(double_divide(multiply(X4,X5),double_divide(X2,X0)),X1)),
inference(paramodulation,[status(thm)],[f20,f17]) ).
fof(f492,plain,
! [X0,X1,X2,X3,X4,X5] : double_divide(X0,multiply(X1,multiply(double_divide(X0,X2),multiply(X3,X4)))) = double_divide(X5,multiply(double_divide(multiply(X2,X5),double_divide(X4,X1)),X3)),
inference(forward_demodulation,[status(thm)],[f383,f447]) ).
fof(f507,plain,
! [X0,X1,X2,X3,X4] : multiply(double_divide(multiply(X0,X1),X2),X3) = double_divide(X4,multiply(double_divide(multiply(X3,X4),double_divide(X1,X2)),X0)),
inference(forward_demodulation,[status(thm)],[f116,f492]) ).
fof(f512,plain,
! [X0,X1,X2] : multiply(double_divide(multiply(X0,X1),X2),X0) = double_divide(X1,X2),
inference(backward_demodulation,[status(thm)],[f513,f22]) ).
fof(f513,plain,
! [X0,X1,X2,X3,X4] : multiply(double_divide(multiply(X0,multiply(X1,X2)),X3),multiply(X3,X4)) = multiply(double_divide(multiply(X1,X2),X0),X4),
inference(forward_demodulation,[status(thm)],[f507,f450]) ).
fof(f525,plain,
! [X0,X1] : double_divide(X0,double_divide(X0,X1)) = X1,
inference(backward_demodulation,[status(thm)],[f512,f19]) ).
fof(f543,plain,
! [X0,X1,X2,X3] : multiply(double_divide(X0,X1),multiply(X2,X0)) = multiply(multiply(double_divide(X3,X1),X2),X3),
inference(backward_demodulation,[status(thm)],[f512,f209]) ).
fof(f554,plain,
! [X0,X1,X2] : multiply(X0,inverse(X1)) = multiply(multiply(double_divide(X2,X1),X0),X2),
inference(backward_demodulation,[status(thm)],[f525,f256]) ).
fof(f555,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = multiply(X1,multiply(X0,X2)),
inference(backward_demodulation,[status(thm)],[f525,f279]) ).
fof(f655,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,inverse(inverse(X2)))) = multiply(multiply(X2,X0),X1),
inference(backward_demodulation,[status(thm)],[f554,f296]) ).
fof(f657,plain,
! [X0,X1,X2] : multiply(double_divide(X0,X1),multiply(X2,X0)) = multiply(X2,inverse(X1)),
inference(backward_demodulation,[status(thm)],[f554,f543]) ).
fof(f784,plain,
! [X0,X1] : multiply(X0,inverse(inverse(X1))) = multiply(X1,X0),
inference(backward_demodulation,[status(thm)],[f657,f392]) ).
fof(f809,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = multiply(multiply(X1,X0),X2),
inference(backward_demodulation,[status(thm)],[f784,f655]) ).
fof(f815,plain,
multiply(b3,multiply(a3,c3)) != multiply(a3,multiply(b3,c3)),
inference(backward_demodulation,[status(thm)],[f809,f6]) ).
fof(f865,plain,
multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3)),
inference(forward_demodulation,[status(thm)],[f555,f815]) ).
fof(f866,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f865]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP603-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n009.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 20:17:42 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.13/0.50 % Refutation found
% 0.13/0.50 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.53 % Elapsed time: 0.149102 seconds
% 0.13/0.53 % CPU time: 1.038626 seconds
% 0.13/0.53 % Total memory used: 44.277 MB
% 0.13/0.53 % Net memory used: 43.806 MB
%------------------------------------------------------------------------------