%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP613-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 12:34:48 PM UTC 2026
% Result : Unsatisfiable 0.02s 0.51s
% Output : CNFRefutation 0.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 3
% Syntax : Number of formulae : 39 ( 39 unt; 0 def)
% Number of atoms : 39 ( 38 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 4 avg)
% Maximal term depth : 8 ( 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 : 94 ( 94 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : double_divide(inverse(double_divide(inverse(double_divide(A,inverse(B))),C)),double_divide(A,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(inverse(a1),a1) != multiply(inverse(b1),b1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,plain,
! [X0,X1,X2] : double_divide(inverse(double_divide(inverse(double_divide(X0,inverse(X1))),X2)),double_divide(X0,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(inverse(a1),a1) != multiply(inverse(b1),b1),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f12,plain,
! [X0,X1,X2] : double_divide(multiply(X0,inverse(double_divide(X1,inverse(X2)))),double_divide(X1,X0)) = X2,
inference(backward_demodulation,[status(thm)],[f5,f4]) ).
fof(f13,plain,
! [X0,X1,X2] : double_divide(multiply(X0,multiply(inverse(X1),X2)),double_divide(X2,X0)) = X1,
inference(forward_demodulation,[status(thm)],[f5,f12]) ).
fof(f14,plain,
! [X0,X1,X2,X3] : double_divide(multiply(X0,multiply(multiply(X1,X2),X3)),double_divide(X3,X0)) = double_divide(X2,X1),
inference(paramodulation,[status(thm)],[f5,f13]) ).
fof(f16,plain,
! [X0,X1,X2] : multiply(double_divide(X0,X1),multiply(X1,multiply(inverse(X2),X0))) = inverse(X2),
inference(paramodulation,[status(thm)],[f13,f5]) ).
fof(f17,plain,
! [X0,X1,X2,X3] : multiply(X0,multiply(double_divide(X1,X2),multiply(inverse(X3),multiply(X2,multiply(inverse(X0),X1))))) = inverse(X3),
inference(paramodulation,[status(thm)],[f13,f16]) ).
fof(f18,plain,
! [X0,X1,X2] : multiply(double_divide(multiply(inverse(X0),X1),double_divide(X1,inverse(X2))),inverse(X0)) = inverse(X2),
inference(paramodulation,[status(thm)],[f16,f16]) ).
fof(f19,plain,
! [X0,X1,X2,X3] : multiply(double_divide(X0,X1),multiply(X1,multiply(multiply(X2,X3),X0))) = inverse(double_divide(X3,X2)),
inference(paramodulation,[status(thm)],[f5,f16]) ).
fof(f20,plain,
! [X0,X1,X2] : double_divide(inverse(X0),double_divide(multiply(inverse(X0),X1),double_divide(X1,inverse(X2)))) = X2,
inference(paramodulation,[status(thm)],[f16,f13]) ).
fof(f21,plain,
! [X0,X1,X2,X3] : multiply(double_divide(X0,X1),multiply(X1,multiply(multiply(X2,X3),X0))) = multiply(X2,X3),
inference(forward_demodulation,[status(thm)],[f5,f19]) ).
fof(f22,plain,
! [X0,X1,X2,X3] : double_divide(inverse(X0),double_divide(multiply(inverse(X0),X1),double_divide(X1,multiply(X2,X3)))) = double_divide(X3,X2),
inference(paramodulation,[status(thm)],[f16,f14]) ).
fof(f31,plain,
! [X0,X1,X2,X3] : double_divide(multiply(X0,X1),double_divide(multiply(inverse(double_divide(X1,X0)),X2),double_divide(X2,inverse(X3)))) = X3,
inference(paramodulation,[status(thm)],[f5,f20]) ).
fof(f38,plain,
! [X0,X1,X2,X3] : double_divide(multiply(X0,X1),double_divide(multiply(multiply(X0,X1),X2),double_divide(X2,inverse(X3)))) = X3,
inference(forward_demodulation,[status(thm)],[f5,f31]) ).
fof(f44,plain,
! [X0,X1,X2,X3] : multiply(double_divide(multiply(inverse(X0),X1),double_divide(X1,multiply(X2,X3))),inverse(X0)) = multiply(X2,X3),
inference(paramodulation,[status(thm)],[f16,f21]) ).
fof(f187,plain,
! [X0,X1,X2,X3] : multiply(X0,multiply(double_divide(multiply(X1,multiply(inverse(inverse(X2)),X3)),double_divide(X3,X1)),inverse(X0))) = inverse(X2),
inference(paramodulation,[status(thm)],[f17,f17]) ).
fof(f212,plain,
! [X0,X1] : multiply(X0,multiply(inverse(X1),inverse(X0))) = inverse(X1),
inference(forward_demodulation,[status(thm)],[f13,f187]) ).
fof(f318,plain,
! [X0,X1] : double_divide(inverse(X0),double_divide(inverse(X1),X1)) = X0,
inference(paramodulation,[status(thm)],[f212,f13]) ).
fof(f338,plain,
! [X0,X1,X2] : double_divide(multiply(X0,X1),double_divide(inverse(X2),X2)) = double_divide(X1,X0),
inference(paramodulation,[status(thm)],[f5,f318]) ).
fof(f399,plain,
! [X0,X1,X2] : double_divide(multiply(X0,X1),double_divide(inverse(inverse(X2)),multiply(X0,X1))) = X2,
inference(paramodulation,[status(thm)],[f338,f38]) ).
fof(f404,plain,
! [X0,X1] : multiply(double_divide(inverse(inverse(X0)),inverse(X1)),inverse(X1)) = inverse(X0),
inference(paramodulation,[status(thm)],[f338,f18]) ).
fof(f405,plain,
! [X0,X1] : double_divide(inverse(X0),double_divide(inverse(inverse(X1)),inverse(X0))) = X1,
inference(paramodulation,[status(thm)],[f338,f20]) ).
fof(f507,plain,
! [X0,X1] : double_divide(inverse(X0),X1) = double_divide(inverse(inverse(X1)),inverse(X0)),
inference(paramodulation,[status(thm)],[f399,f22]) ).
fof(f508,plain,
! [X0,X1] : multiply(X0,inverse(X1)) = multiply(inverse(X1),inverse(inverse(X0))),
inference(paramodulation,[status(thm)],[f399,f44]) ).
fof(f537,plain,
! [X0,X1] : multiply(double_divide(inverse(X0),X1),inverse(X0)) = inverse(X1),
inference(backward_demodulation,[status(thm)],[f507,f404]) ).
fof(f538,plain,
! [X0,X1] : double_divide(inverse(X0),double_divide(inverse(X0),X1)) = X1,
inference(backward_demodulation,[status(thm)],[f507,f405]) ).
fof(f605,plain,
! [X0,X1] : multiply(X0,inverse(X0)) = inverse(double_divide(inverse(X1),X1)),
inference(paramodulation,[status(thm)],[f318,f537]) ).
fof(f618,plain,
! [X0,X1] : multiply(X0,inverse(X0)) = multiply(X1,inverse(X1)),
inference(forward_demodulation,[status(thm)],[f5,f605]) ).
fof(f673,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,inverse(X1))) = inverse(X1),
inference(paramodulation,[status(thm)],[f508,f212]) ).
fof(f941,plain,
! [X0,X1] : double_divide(inverse(X0),double_divide(inverse(X0),inverse(inverse(X1)))) = X1,
inference(paramodulation,[status(thm)],[f673,f13]) ).
fof(f974,plain,
! [X0,X1] : multiply(X0,inverse(X1)) = multiply(inverse(X1),X0),
inference(backward_demodulation,[status(thm)],[f1004,f508]) ).
fof(f1004,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f538,f941]) ).
fof(f1023,plain,
multiply(inverse(a1),a1) != multiply(b1,inverse(b1)),
inference(backward_demodulation,[status(thm)],[f974,f6]) ).
fof(f1138,plain,
multiply(a1,inverse(a1)) != multiply(b1,inverse(b1)),
inference(forward_demodulation,[status(thm)],[f974,f1023]) ).
fof(f1139,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1138,f618]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP613-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n014.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 20:17:49 UTC 2026
% 0.02/0.36 % CPUTime :
% 0.02/0.37 % Drodi V4.1.1
% 0.02/0.51 % Refutation found
% 0.02/0.51 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.02/0.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.02/0.53 % Elapsed time: 0.162543 seconds
% 0.02/0.53 % CPU time: 1.155009 seconds
% 0.02/0.53 % Total memory used: 60.024 MB
% 0.02/0.53 % Net memory used: 59.485 MB
%------------------------------------------------------------------------------