%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP106-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 0.15s 5.61s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 3
% Syntax : Number of formulae : 63 ( 58 unt; 0 def)
% Number of atoms : 76 ( 75 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 32 ( 19 ~; 13 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 4 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 : 167 ( 167 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y,Z] : inverse(double_divide(double_divide(X,Y),inverse(double_divide(X,inverse(double_divide(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] : inverse(double_divide(double_divide(X0,X1),inverse(double_divide(X0,inverse(double_divide(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] : multiply(inverse(double_divide(X0,inverse(double_divide(X1,X2)))),double_divide(X0,X2)) = X1,
inference(backward_demodulation,[status(thm)],[f5,f4]) ).
fof(f8,plain,
! [X0,X1,X2] : multiply(multiply(inverse(double_divide(X0,X1)),X2),double_divide(X2,X1)) = X0,
inference(forward_demodulation,[status(thm)],[f5,f7]) ).
fof(f9,plain,
! [X0,X1,X2] : multiply(multiply(multiply(X0,X1),X2),double_divide(X2,X0)) = X1,
inference(forward_demodulation,[status(thm)],[f5,f8]) ).
fof(f10,plain,
! [X0,X1,X2] : multiply(X0,double_divide(double_divide(X1,X2),multiply(X2,X0))) = X1,
inference(paramodulation,[status(thm)],[f9,f9]) ).
fof(f11,plain,
! [X0,X1,X2,X3] : multiply(multiply(X0,X1),double_divide(X1,multiply(multiply(X2,X0),X3))) = double_divide(X3,X2),
inference(paramodulation,[status(thm)],[f9,f9]) ).
fof(f12,plain,
! [X0,X1,X2,X3] : multiply(double_divide(X0,X1),double_divide(double_divide(X2,multiply(multiply(X1,X3),X0)),X3)) = X2,
inference(paramodulation,[status(thm)],[f9,f10]) ).
fof(f16,plain,
! [X0,X1,X2] : X0 = double_divide(multiply(X1,double_divide(X0,multiply(X2,X1))),X2),
inference(paramodulation,[status(thm)],[f10,f11]) ).
fof(f32,plain,
! [X0,X1,X2] : X0 = double_divide(double_divide(multiply(X1,X0),X2),multiply(X2,X1)),
inference(paramodulation,[status(thm)],[f11,f16]) ).
fof(f34,plain,
! [X0,X1,X2,X3] : multiply(X0,double_divide(X1,multiply(multiply(X2,X3),X0))) = double_divide(multiply(X3,X1),X2),
inference(paramodulation,[status(thm)],[f16,f16]) ).
fof(f41,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,double_divide(X2,multiply(X0,X1)))) = inverse(X2),
inference(paramodulation,[status(thm)],[f16,f5]) ).
fof(f79,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),double_divide(multiply(X1,X2),X0)) = inverse(X2),
inference(paramodulation,[status(thm)],[f32,f5]) ).
fof(f95,plain,
! [X0,X1,X2,X3] : multiply(inverse(X0),double_divide(multiply(X1,double_divide(X0,multiply(multiply(X2,X3),X1))),X2)) = X3,
inference(paramodulation,[status(thm)],[f41,f9]) ).
fof(f108,plain,
! [X0,X1,X2] : multiply(inverse(X0),double_divide(double_divide(multiply(X1,X0),X2),X2)) = X1,
inference(forward_demodulation,[status(thm)],[f34,f95]) ).
fof(f118,plain,
! [X0,X1,X2,X3] : multiply(multiply(X0,multiply(multiply(X1,X2),X3)),double_divide(X2,X0)) = inverse(double_divide(X3,X1)),
inference(paramodulation,[status(thm)],[f9,f79]) ).
fof(f139,plain,
! [X0,X1,X2,X3] : multiply(multiply(X0,multiply(multiply(X1,X2),X3)),double_divide(X2,X0)) = multiply(X1,X3),
inference(forward_demodulation,[status(thm)],[f5,f118]) ).
fof(f146,plain,
! [X0,X1,X2,X3] : multiply(multiply(X0,X1),double_divide(double_divide(multiply(X2,double_divide(X1,X0)),X3),X3)) = X2,
inference(paramodulation,[status(thm)],[f5,f108]) ).
fof(f150,plain,
! [X0,X1,X2,X3] : multiply(inverse(double_divide(X0,X1)),double_divide(double_divide(X2,X3),X3)) = multiply(multiply(X1,X2),X0),
inference(paramodulation,[status(thm)],[f9,f108]) ).
fof(f151,plain,
! [X0,X1,X2,X3] : multiply(inverse(double_divide(multiply(X0,X1),X2)),double_divide(double_divide(inverse(X1),X3),X3)) = multiply(X2,X0),
inference(paramodulation,[status(thm)],[f79,f108]) ).
fof(f173,plain,
! [X0,X1,X2] : multiply(multiply(X0,multiply(X1,double_divide(X2,X0))),X2) = X1,
inference(backward_demodulation,[status(thm)],[f174,f146]) ).
fof(f174,plain,
! [X0,X1,X2,X3] : multiply(multiply(X0,X1),double_divide(double_divide(X2,X3),X3)) = multiply(multiply(X0,X2),X1),
inference(forward_demodulation,[status(thm)],[f5,f150]) ).
fof(f175,plain,
! [X0,X1,X2,X3] : multiply(multiply(X0,multiply(X1,X2)),double_divide(double_divide(inverse(X2),X3),X3)) = multiply(X0,X1),
inference(forward_demodulation,[status(thm)],[f5,f151]) ).
fof(f177,plain,
! [X0,X1,X2] : multiply(multiply(X0,inverse(X1)),multiply(X2,X1)) = multiply(X0,X2),
inference(forward_demodulation,[status(thm)],[f174,f175]) ).
fof(f192,plain,
! [X0,X1,X2,X3] : multiply(multiply(X0,X1),X2) = multiply(X3,multiply(X1,double_divide(double_divide(X2,X0),X3))),
inference(paramodulation,[status(thm)],[f173,f173]) ).
fof(f220,plain,
! [X0,X1,X2,X3] : multiply(multiply(X0,inverse(double_divide(X1,X2))),X3) = multiply(X0,multiply(multiply(X2,X3),X1)),
inference(paramodulation,[status(thm)],[f9,f177]) ).
fof(f244,plain,
! [X0,X1,X2] : multiply(X0,multiply(multiply(X1,X2),double_divide(X2,X0))) = X1,
inference(backward_demodulation,[status(thm)],[f261,f173]) ).
fof(f247,plain,
! [X0,X1,X2,X3] : multiply(X0,multiply(multiply(multiply(X1,X2),double_divide(X2,X0)),X3)) = multiply(X1,X3),
inference(backward_demodulation,[status(thm)],[f261,f139]) ).
fof(f261,plain,
! [X0,X1,X2,X3] : multiply(multiply(X0,multiply(X1,X2)),X3) = multiply(X0,multiply(multiply(X1,X3),X2)),
inference(forward_demodulation,[status(thm)],[f5,f220]) ).
fof(f287,plain,
! [X0,X1,X2,X3] : multiply(X0,multiply(X1,double_divide(multiply(multiply(X1,X2),double_divide(X2,X3)),X0))) = X3,
inference(paramodulation,[status(thm)],[f244,f244]) ).
fof(f299,plain,
! [X0,X1,X2,X3] : multiply(X0,multiply(multiply(multiply(X1,X2),double_divide(X2,X0)),double_divide(X3,X1))) = inverse(X3),
inference(paramodulation,[status(thm)],[f244,f41]) ).
fof(f316,plain,
! [X0,X1] : multiply(X0,double_divide(X1,X0)) = inverse(X1),
inference(forward_demodulation,[status(thm)],[f247,f299]) ).
fof(f319,plain,
! [X0,X1] : X0 = inverse(double_divide(multiply(X0,X1),inverse(X1))),
inference(paramodulation,[status(thm)],[f108,f316]) ).
fof(f320,plain,
! [X0,X1,X2] : X0 = inverse(double_divide(X0,multiply(multiply(X1,double_divide(X2,X1)),X2))),
inference(paramodulation,[status(thm)],[f12,f316]) ).
fof(f321,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = inverse(double_divide(multiply(X1,X2),X0)),
inference(paramodulation,[status(thm)],[f32,f316]) ).
fof(f325,plain,
! [X0,X1] : multiply(multiply(X0,X1),inverse(X1)) = X0,
inference(paramodulation,[status(thm)],[f316,f244]) ).
fof(f329,plain,
! [X0,X1,X2] : multiply(X0,multiply(inverse(X1),double_divide(double_divide(X1,X2),X0))) = X2,
inference(paramodulation,[status(thm)],[f316,f244]) ).
fof(f343,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X0,X1)),
inference(forward_demodulation,[status(thm)],[f5,f319]) ).
fof(f344,plain,
! [X0,X1,X2] : X0 = multiply(multiply(multiply(X1,double_divide(X2,X1)),X2),X0),
inference(forward_demodulation,[status(thm)],[f5,f320]) ).
fof(f345,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| a2 != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(backward_demodulation,[status(thm)],[f346,f6]) ).
fof(f346,plain,
! [X0,X1] : X0 = multiply(multiply(inverse(X1),X1),X0),
inference(forward_demodulation,[status(thm)],[f316,f344]) ).
fof(f349,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,double_divide(multiply(X1,X2),X0))) = inverse(X2),
inference(backward_demodulation,[status(thm)],[f437,f79]) ).
fof(f355,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(backward_demodulation,[status(thm)],[f437,f346]) ).
fof(f416,plain,
! [X0,X1,X2,X3] : multiply(X0,multiply(X1,double_divide(multiply(X1,multiply(X2,double_divide(X2,X3))),X0))) = X3,
inference(backward_demodulation,[status(thm)],[f437,f287]) ).
fof(f437,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(forward_demodulation,[status(thm)],[f5,f321]) ).
fof(f443,plain,
! [X0,X1] : multiply(X0,multiply(X1,inverse(X1))) = X0,
inference(forward_demodulation,[status(thm)],[f437,f325]) ).
fof(f445,plain,
! [X0,X1] : multiply(multiply(X0,inverse(X1)),X1) = X0,
inference(forward_demodulation,[status(thm)],[f192,f329]) ).
fof(f446,plain,
! [X0,X1] : multiply(X0,multiply(inverse(X1),X1)) = X0,
inference(forward_demodulation,[status(thm)],[f437,f445]) ).
fof(f461,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3))
| a2 != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(forward_demodulation,[status(thm)],[f437,f345]) ).
fof(f462,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(trivial_equality_resolution,[status(thm)],[f461]) ).
fof(f581,plain,
! [X0,X1] : inverse(multiply(X0,double_divide(X0,X1))) = X1,
inference(forward_demodulation,[status(thm)],[f349,f416]) ).
fof(f716,plain,
! [X0] : X0 = inverse(inverse(X0)),
inference(paramodulation,[status(thm)],[f343,f443]) ).
fof(f736,plain,
! [X0,X1] : double_divide(X0,X1) = inverse(multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f5,f716]) ).
fof(f742,plain,
! [X0,X1] : double_divide(double_divide(X0,X1),X0) = X1,
inference(backward_demodulation,[status(thm)],[f736,f581]) ).
fof(f761,plain,
! [X0,X1] : multiply(X0,X1) = inverse(double_divide(X0,X1)),
inference(paramodulation,[status(thm)],[f742,f316]) ).
fof(f767,plain,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
inference(backward_subsumption_resolution,[status(thm)],[f462,f768]) ).
fof(f768,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(forward_demodulation,[status(thm)],[f5,f761]) ).
fof(f918,plain,
! [X0,X1] : multiply(inverse(X0),X0) = multiply(inverse(X1),X1),
inference(paramodulation,[status(thm)],[f446,f355]) ).
fof(f930,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f767,f918]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP106-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.38 % Computer : n026.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Sun Sep 20 20:00:28 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.40 % Drodi V4.1.1
% 0.15/5.61 % Refutation found
% 0.15/5.61 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.15/5.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/5.65 % Elapsed time: 0.259581 seconds
% 0.15/5.65 % CPU time: 1.314340 seconds
% 0.15/5.65 % Total memory used: 89.912 MB
% 0.15/5.65 % Net memory used: 88.827 MB
%------------------------------------------------------------------------------