%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP105-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 12:32:31 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.63s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 3
% Syntax : Number of formulae : 62 ( 54 unt; 0 def)
% Number of atoms : 77 ( 76 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 42 ( 27 ~; 15 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 124 ( 124 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y,Z] : double_divide(inverse(double_divide(double_divide(X,Y),inverse(double_divide(X,inverse(Z))))),Y) = Z,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] : multiply(X,Y) = inverse(double_divide(Y,X)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,plain,
! [X0,X1,X2] : double_divide(inverse(double_divide(double_divide(X0,X1),inverse(double_divide(X0,inverse(X2))))),X1) = 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(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f7,plain,
! [X0,X1,X2] : double_divide(multiply(inverse(double_divide(X0,inverse(X1))),double_divide(X0,X2)),X2) = X1,
inference(backward_demodulation,[status(thm)],[f5,f4]) ).
fof(f8,plain,
! [X0,X1,X2] : double_divide(multiply(multiply(inverse(X0),X1),double_divide(X1,X2)),X2) = X0,
inference(forward_demodulation,[status(thm)],[f5,f7]) ).
fof(f10,plain,
! [X0,X1,X2,X3] : double_divide(multiply(multiply(inverse(X0),multiply(multiply(inverse(X1),X2),double_divide(X2,X3))),X1),X3) = X0,
inference(paramodulation,[status(thm)],[f8,f8]) ).
fof(f11,plain,
! [X0,X1,X2] : multiply(X0,multiply(multiply(inverse(X1),X2),double_divide(X2,X0))) = inverse(X1),
inference(paramodulation,[status(thm)],[f8,f5]) ).
fof(f14,plain,
! [X0,X1,X2,X3] : multiply(X0,multiply(multiply(inverse(X1),multiply(multiply(inverse(X2),X3),double_divide(X3,X0))),X2)) = inverse(X1),
inference(paramodulation,[status(thm)],[f8,f11]) ).
fof(f39,plain,
! [X0,X1] : double_divide(multiply(inverse(X0),X0),inverse(X1)) = X1,
inference(paramodulation,[status(thm)],[f11,f10]) ).
fof(f57,plain,
! [X0,X1,X2] : multiply(inverse(X0),multiply(multiply(inverse(X1),multiply(inverse(X2),X2)),X0)) = inverse(X1),
inference(paramodulation,[status(thm)],[f39,f11]) ).
fof(f58,plain,
! [X0,X1,X2] : double_divide(multiply(multiply(inverse(X0),multiply(inverse(X1),X1)),X2),inverse(X2)) = X0,
inference(paramodulation,[status(thm)],[f39,f8]) ).
fof(f59,plain,
! [X0,X1] : multiply(inverse(X0),multiply(inverse(X1),X1)) = inverse(X0),
inference(paramodulation,[status(thm)],[f39,f5]) ).
fof(f60,plain,
! [X0,X1] : double_divide(multiply(inverse(X0),X1),inverse(X1)) = X0,
inference(backward_demodulation,[status(thm)],[f59,f58]) ).
fof(f61,plain,
! [X0,X1] : multiply(inverse(X0),multiply(inverse(X1),X0)) = inverse(X1),
inference(backward_demodulation,[status(thm)],[f59,f57]) ).
fof(f79,plain,
! [X0,X1] : double_divide(inverse(X0),inverse(multiply(inverse(X1),X1))) = X0,
inference(paramodulation,[status(thm)],[f59,f60]) ).
fof(f80,plain,
! [X0,X1] : double_divide(inverse(multiply(inverse(X0),X0)),inverse(X1)) = X1,
inference(paramodulation,[status(thm)],[f59,f39]) ).
fof(f107,plain,
! [X0,X1,X2] : double_divide(multiply(X0,X1),inverse(multiply(inverse(X2),X2))) = double_divide(X1,X0),
inference(paramodulation,[status(thm)],[f5,f79]) ).
fof(f114,plain,
! [X0,X1,X2] : double_divide(multiply(multiply(inverse(X0),inverse(X1)),X1),inverse(multiply(inverse(X2),X2))) = X0,
inference(paramodulation,[status(thm)],[f79,f8]) ).
fof(f118,plain,
! [X0,X1] : double_divide(X0,multiply(inverse(X1),inverse(X0))) = X1,
inference(forward_demodulation,[status(thm)],[f107,f114]) ).
fof(f163,plain,
! [X0,X1] : multiply(inverse(X0),X0) = multiply(inverse(X1),X1),
inference(paramodulation,[status(thm)],[f79,f80]) ).
fof(f175,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2 ),
inference(backward_subsumption_resolution,[status(thm)],[f6,f163]) ).
fof(f190,plain,
! [X0,X1] : double_divide(X0,multiply(inverse(X1),X1)) = inverse(X0),
inference(paramodulation,[status(thm)],[f163,f118]) ).
fof(f192,plain,
! [X0,X1,X2,X3] : double_divide(multiply(multiply(inverse(X0),X0),X1),X2) = multiply(multiply(inverse(X1),X3),double_divide(X3,X2)),
inference(paramodulation,[status(thm)],[f163,f10]) ).
fof(f202,plain,
! [X0,X1,X2] : double_divide(multiply(multiply(inverse(X0),X0),double_divide(X1,X2)),X2) = X1,
inference(paramodulation,[status(thm)],[f163,f8]) ).
fof(f228,plain,
! [X0,X1] : double_divide(X0,inverse(multiply(inverse(X1),X1))) = inverse(X0),
inference(paramodulation,[status(thm)],[f59,f190]) ).
fof(f242,plain,
! [X0,X1] : multiply(multiply(inverse(X0),X0),X1) = inverse(inverse(X1)),
inference(paramodulation,[status(thm)],[f190,f5]) ).
fof(f246,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(backward_demodulation,[status(thm)],[f228,f79]) ).
fof(f247,plain,
! [X0,X1] : inverse(multiply(X0,X1)) = double_divide(X1,X0),
inference(backward_demodulation,[status(thm)],[f228,f107]) ).
fof(f254,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| inverse(inverse(a2)) != a2 ),
inference(backward_demodulation,[status(thm)],[f242,f175]) ).
fof(f259,plain,
! [X0,X1] : double_divide(inverse(inverse(double_divide(X0,X1))),X1) = X0,
inference(backward_demodulation,[status(thm)],[f242,f202]) ).
fof(f262,plain,
! [X0,X1,X2] : double_divide(inverse(inverse(X0)),X1) = multiply(multiply(inverse(X0),X2),double_divide(X2,X1)),
inference(backward_demodulation,[status(thm)],[f242,f192]) ).
fof(f289,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| a2 != a2 ),
inference(forward_demodulation,[status(thm)],[f246,f254]) ).
fof(f290,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
inference(trivial_equality_resolution,[status(thm)],[f289]) ).
fof(f296,plain,
! [X0,X1] : double_divide(double_divide(X0,X1),X1) = X0,
inference(forward_demodulation,[status(thm)],[f246,f259]) ).
fof(f322,plain,
! [X0,X1,X2] : multiply(X0,multiply(multiply(inverse(X1),double_divide(X2,X0)),X2)) = inverse(X1),
inference(backward_demodulation,[status(thm)],[f323,f14]) ).
fof(f323,plain,
! [X0,X1,X2] : double_divide(X0,X1) = multiply(multiply(inverse(X0),X2),double_divide(X2,X1)),
inference(forward_demodulation,[status(thm)],[f246,f262]) ).
fof(f336,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X1,X0)) = inverse(inverse(X1)),
inference(paramodulation,[status(thm)],[f246,f61]) ).
fof(f348,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X1,X0)) = X1,
inference(forward_demodulation,[status(thm)],[f246,f336]) ).
fof(f397,plain,
! [X0,X1,X2] : multiply(double_divide(X0,X1),multiply(X2,multiply(X1,X0))) = X2,
inference(paramodulation,[status(thm)],[f247,f348]) ).
fof(f400,plain,
! [X0,X1] : multiply(inverse(multiply(X0,X1)),X0) = inverse(X1),
inference(paramodulation,[status(thm)],[f348,f348]) ).
fof(f408,plain,
! [X0,X1] : multiply(double_divide(X0,X1),X1) = inverse(X0),
inference(forward_demodulation,[status(thm)],[f247,f400]) ).
fof(f473,plain,
! [X0,X1] : multiply(X0,X1) = inverse(double_divide(X0,X1)),
inference(paramodulation,[status(thm)],[f296,f408]) ).
fof(f480,plain,
( multiply(a4,b4) != multiply(a4,b4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
inference(backward_demodulation,[status(thm)],[f524,f290]) ).
fof(f498,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,multiply(inverse(X2),double_divide(X1,X0)))) = inverse(X2),
inference(backward_demodulation,[status(thm)],[f524,f322]) ).
fof(f524,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(forward_demodulation,[status(thm)],[f5,f473]) ).
fof(f539,plain,
( multiply(a4,b4) != multiply(a4,b4)
| multiply(c3,multiply(a3,b3)) != multiply(a3,multiply(b3,c3)) ),
inference(forward_demodulation,[status(thm)],[f524,f480]) ).
fof(f540,plain,
multiply(c3,multiply(a3,b3)) != multiply(a3,multiply(b3,c3)),
inference(trivial_equality_resolution,[status(thm)],[f539]) ).
fof(f574,plain,
! [X0,X1] : inverse(multiply(X0,X1)) = double_divide(X0,X1),
inference(paramodulation,[status(thm)],[f524,f247]) ).
fof(f606,plain,
! [X0,X1] : double_divide(X0,X1) = double_divide(X1,X0),
inference(forward_demodulation,[status(thm)],[f247,f574]) ).
fof(f684,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,multiply(X2,double_divide(X1,X0)))) = inverse(inverse(X2)),
inference(paramodulation,[status(thm)],[f246,f498]) ).
fof(f708,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,multiply(X2,double_divide(X1,X0)))) = X2,
inference(forward_demodulation,[status(thm)],[f246,f684]) ).
fof(f1420,plain,
! [X0,X1,X2] : multiply(double_divide(X0,X1),multiply(X2,multiply(X0,X1))) = X2,
inference(paramodulation,[status(thm)],[f606,f397]) ).
fof(f2124,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,multiply(double_divide(X1,X0),X2))) = X2,
inference(paramodulation,[status(thm)],[f524,f708]) ).
fof(f4005,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = multiply(X2,multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f1420,f2124]) ).
fof(f4006,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = multiply(X2,multiply(X0,X1)),
inference(paramodulation,[status(thm)],[f397,f2124]) ).
fof(f4126,plain,
multiply(b3,multiply(a3,c3)) != multiply(a3,multiply(b3,c3)),
inference(backward_demodulation,[status(thm)],[f4005,f540]) ).
fof(f4282,plain,
multiply(a3,multiply(c3,b3)) != multiply(a3,multiply(b3,c3)),
inference(forward_demodulation,[status(thm)],[f4006,f4126]) ).
fof(f4283,plain,
multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3)),
inference(forward_demodulation,[status(thm)],[f524,f4282]) ).
fof(f4284,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f4283]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP105-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.37 % Computer : n005.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Sun Sep 20 19:57:18 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.38 % Drodi V4.1.1
% 0.14/0.63 % Refutation found
% 0.14/0.63 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.63 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.68 % Elapsed time: 0.293003 seconds
% 0.14/0.68 % CPU time: 1.912078 seconds
% 0.14/0.68 % Total memory used: 101.313 MB
% 0.14/0.68 % Net memory used: 100.174 MB
%------------------------------------------------------------------------------