%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP109-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : 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 12:32:32 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.47s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 3
% Syntax : Number of formulae : 44 ( 33 unt; 0 def)
% Number of atoms : 77 ( 76 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 78 ( 45 ~; 33 |; 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 : 80 ( 80 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y,Z] : double_divide(inverse(double_divide(X,inverse(double_divide(inverse(Y),double_divide(X,Z))))),Z) = Y,
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(X0,inverse(double_divide(inverse(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(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(inverse(double_divide(X0,multiply(double_divide(X0,X1),inverse(X2)))),X1) = X2,
inference(backward_demodulation,[status(thm)],[f5,f4]) ).
fof(f8,plain,
! [X0,X1,X2] : double_divide(multiply(multiply(double_divide(X0,X1),inverse(X2)),X0),X1) = X2,
inference(forward_demodulation,[status(thm)],[f5,f7]) ).
fof(f9,plain,
! [X0,X1,X2,X3] : double_divide(multiply(multiply(X0,inverse(X1)),multiply(multiply(double_divide(X2,X3),inverse(X0)),X2)),X3) = X1,
inference(paramodulation,[status(thm)],[f8,f8]) ).
fof(f11,plain,
! [X0,X1,X2] : multiply(X0,multiply(multiply(double_divide(X1,X0),inverse(X2)),X1)) = inverse(X2),
inference(paramodulation,[status(thm)],[f8,f5]) ).
fof(f13,plain,
! [X0,X1,X2,X3] : multiply(X0,multiply(multiply(double_divide(X1,X0),multiply(X2,X3)),X1)) = inverse(double_divide(X3,X2)),
inference(paramodulation,[status(thm)],[f5,f11]) ).
fof(f14,plain,
! [X0,X1,X2,X3] : multiply(X0,multiply(multiply(double_divide(X1,X0),multiply(X2,X3)),X1)) = multiply(X2,X3),
inference(forward_demodulation,[status(thm)],[f5,f13]) ).
fof(f35,plain,
! [X0,X1] : double_divide(inverse(X0),multiply(X0,inverse(X1))) = X1,
inference(paramodulation,[status(thm)],[f11,f9]) ).
fof(f53,plain,
! [X0,X1] : multiply(multiply(X0,inverse(X1)),inverse(X0)) = inverse(X1),
inference(paramodulation,[status(thm)],[f35,f5]) ).
fof(f54,plain,
! [X0,X1] : multiply(inverse(X0),inverse(multiply(X1,inverse(X0)))) = inverse(X1),
inference(paramodulation,[status(thm)],[f53,f53]) ).
fof(f57,plain,
! [X0,X1] : double_divide(inverse(multiply(X0,inverse(X1))),inverse(X1)) = X0,
inference(paramodulation,[status(thm)],[f53,f35]) ).
fof(f81,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),inverse(multiply(X2,inverse(double_divide(X1,X0))))) = inverse(X2),
inference(paramodulation,[status(thm)],[f5,f54]) ).
fof(f91,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),inverse(multiply(X2,multiply(X0,X1)))) = inverse(X2),
inference(forward_demodulation,[status(thm)],[f5,f81]) ).
fof(f114,plain,
! [X0,X1,X2] : double_divide(inverse(multiply(X0,X1)),inverse(X2)) = multiply(X2,multiply(X0,X1)),
inference(paramodulation,[status(thm)],[f91,f35]) ).
fof(f133,plain,
! [X0,X1] : multiply(X0,multiply(X1,inverse(X0))) = X1,
inference(backward_demodulation,[status(thm)],[f114,f57]) ).
fof(f139,plain,
! [X0,X1] : inverse(X0) = multiply(double_divide(inverse(X1),X1),inverse(X0)),
inference(paramodulation,[status(thm)],[f11,f133]) ).
fof(f143,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = multiply(X1,inverse(double_divide(X2,X0))),
inference(paramodulation,[status(thm)],[f133,f14]) ).
fof(f150,plain,
! [X0,X1,X2] : multiply(multiply(X0,multiply(X1,inverse(X0))),inverse(multiply(X2,X1))) = inverse(X2),
inference(paramodulation,[status(thm)],[f133,f91]) ).
fof(f155,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = multiply(X1,multiply(X0,X2)),
inference(forward_demodulation,[status(thm)],[f5,f143]) ).
fof(f161,plain,
! [X0,X1] : multiply(X0,inverse(multiply(X1,X0))) = inverse(X1),
inference(forward_demodulation,[status(thm)],[f133,f150]) ).
fof(f176,plain,
! [X0,X1] : double_divide(inverse(X0),inverse(X1)) = multiply(X1,X0),
inference(paramodulation,[status(thm)],[f161,f35]) ).
fof(f247,plain,
! [X0,X1] : multiply(X0,inverse(X0)) = double_divide(inverse(X1),X1),
inference(paramodulation,[status(thm)],[f139,f133]) ).
fof(f248,plain,
! [X0,X1] : double_divide(inverse(double_divide(inverse(X0),X0)),inverse(X1)) = X1,
inference(paramodulation,[status(thm)],[f139,f35]) ).
fof(f255,plain,
! [X0,X1] : multiply(X0,double_divide(inverse(X1),X1)) = X0,
inference(forward_demodulation,[status(thm)],[f176,f248]) ).
fof(f269,plain,
! [X0,X1] : multiply(X0,inverse(X0)) = multiply(X1,inverse(X1)),
inference(paramodulation,[status(thm)],[f247,f247]) ).
fof(f278,plain,
! [X0,X1] : multiply(X0,multiply(X1,inverse(X1))) = X0,
inference(paramodulation,[status(thm)],[f247,f255]) ).
fof(f518,plain,
! [X0,X1,X2] : multiply(X0,X1) = multiply(X1,multiply(X0,double_divide(inverse(X2),X2))),
inference(paramodulation,[status(thm)],[f255,f155]) ).
fof(f558,plain,
( multiply(a4,b4) != multiply(a4,b4)
| 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(backward_demodulation,[status(thm)],[f588,f6]) ).
fof(f588,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(forward_demodulation,[status(thm)],[f255,f518]) ).
fof(f610,plain,
( multiply(a4,b4) != multiply(a4,b4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(a1,inverse(a1)) != multiply(inverse(b1),b1) ),
inference(forward_demodulation,[status(thm)],[f588,f558]) ).
fof(f611,plain,
( multiply(a4,b4) != multiply(a4,b4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(a1,inverse(a1)) != multiply(b1,inverse(b1)) ),
inference(forward_demodulation,[status(thm)],[f588,f610]) ).
fof(f612,plain,
( multiply(a4,b4) != multiply(a4,b4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(a2,multiply(inverse(b2),b2)) != a2
| multiply(a1,inverse(a1)) != multiply(b1,inverse(b1)) ),
inference(forward_demodulation,[status(thm)],[f588,f611]) ).
fof(f613,plain,
( multiply(a4,b4) != multiply(a4,b4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(a2,multiply(b2,inverse(b2))) != a2
| multiply(a1,inverse(a1)) != multiply(b1,inverse(b1)) ),
inference(forward_demodulation,[status(thm)],[f588,f612]) ).
fof(f614,plain,
( multiply(a4,b4) != multiply(a4,b4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| a2 != a2
| multiply(a1,inverse(a1)) != multiply(b1,inverse(b1)) ),
inference(forward_demodulation,[status(thm)],[f278,f613]) ).
fof(f615,plain,
( multiply(a4,b4) != multiply(a4,b4)
| multiply(c3,multiply(a3,b3)) != multiply(a3,multiply(b3,c3))
| a2 != a2
| multiply(a1,inverse(a1)) != multiply(b1,inverse(b1)) ),
inference(forward_demodulation,[status(thm)],[f588,f614]) ).
fof(f616,plain,
( multiply(a4,b4) != multiply(a4,b4)
| multiply(a3,multiply(c3,b3)) != multiply(a3,multiply(b3,c3))
| a2 != a2
| multiply(a1,inverse(a1)) != multiply(b1,inverse(b1)) ),
inference(forward_demodulation,[status(thm)],[f155,f615]) ).
fof(f617,plain,
( multiply(a4,b4) != multiply(a4,b4)
| multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3))
| a2 != a2
| multiply(a1,inverse(a1)) != multiply(b1,inverse(b1)) ),
inference(forward_demodulation,[status(thm)],[f588,f616]) ).
fof(f618,plain,
multiply(a1,inverse(a1)) != multiply(b1,inverse(b1)),
inference(trivial_equality_resolution,[status(thm)],[f617]) ).
fof(f619,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f618,f269]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP109-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n009.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 20 19:58:12 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.13/0.47 % Refutation found
% 0.13/0.47 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.90/0.50 % Elapsed time: 0.130432 seconds
% 0.90/0.50 % CPU time: 0.746476 seconds
% 0.90/0.50 % Total memory used: 86.326 MB
% 0.90/0.50 % Net memory used: 85.379 MB
%------------------------------------------------------------------------------