%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP090-1 : 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 12:32:29 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.40s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 4
% Syntax : Number of formulae : 50 ( 44 unt; 0 def)
% Number of atoms : 65 ( 64 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 39 ( 24 ~; 15 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 6 ( 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 : 97 ( 97 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y,Z] : divide(divide(X,divide(Y,Z)),divide(X,Y)) = Z,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y,Z] : multiply(X,Y) = divide(X,divide(divide(Z,Z),Y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Z] : inverse(X) = divide(divide(Z,Z),X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,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(f5,plain,
! [X0,X1,X2] : divide(divide(X0,divide(X1,X2)),divide(X0,X1)) = X2,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f6,plain,
! [X0,X1,X2] : multiply(X0,X1) = divide(X0,divide(divide(X2,X2),X1)),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f7,plain,
! [X0,X1] : inverse(X0) = divide(divide(X1,X1),X0),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f8,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)],[f4]) ).
fof(f9,plain,
! [X0,X1] : multiply(X0,X1) = divide(X0,inverse(X1)),
inference(backward_demodulation,[status(thm)],[f7,f6]) ).
fof(f11,plain,
! [X0,X1] : multiply(divide(X0,X0),X1) = inverse(inverse(X1)),
inference(paramodulation,[status(thm)],[f7,f9]) ).
fof(f13,plain,
! [X0,X1] : inverse(X0) = divide(multiply(inverse(X1),X1),X0),
inference(paramodulation,[status(thm)],[f9,f7]) ).
fof(f22,plain,
! [X0,X1] : multiply(multiply(inverse(X0),X0),X1) = inverse(inverse(X1)),
inference(paramodulation,[status(thm)],[f9,f11]) ).
fof(f23,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| inverse(inverse(a2)) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(backward_demodulation,[status(thm)],[f22,f8]) ).
fof(f194,plain,
! [X0,X1] : inverse(divide(divide(X0,X1),X0)) = X1,
inference(paramodulation,[status(thm)],[f7,f5]) ).
fof(f195,plain,
! [X0,X1,X2] : divide(inverse(divide(X0,X1)),divide(multiply(inverse(X2),X2),X0)) = X1,
inference(paramodulation,[status(thm)],[f13,f5]) ).
fof(f204,plain,
! [X0,X1,X2] : divide(X0,divide(divide(X1,divide(X2,X0)),X1)) = X2,
inference(paramodulation,[status(thm)],[f5,f5]) ).
fof(f216,plain,
! [X0,X1,X2] : divide(divide(X0,inverse(X1)),divide(X0,divide(X2,X2))) = X1,
inference(paramodulation,[status(thm)],[f7,f5]) ).
fof(f227,plain,
! [X0,X1,X2,X3] : divide(divide(divide(X0,divide(X1,X2)),divide(divide(X0,X1),X3)),X2) = X3,
inference(paramodulation,[status(thm)],[f5,f5]) ).
fof(f231,plain,
! [X0,X1] : divide(inverse(divide(X0,X1)),inverse(X0)) = X1,
inference(forward_demodulation,[status(thm)],[f13,f195]) ).
fof(f232,plain,
! [X0,X1] : multiply(inverse(divide(X0,X1)),X0) = X1,
inference(forward_demodulation,[status(thm)],[f9,f231]) ).
fof(f268,plain,
! [X0,X1,X2] : divide(multiply(X0,X1),divide(X0,divide(X2,X2))) = X1,
inference(forward_demodulation,[status(thm)],[f9,f216]) ).
fof(f289,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(paramodulation,[status(thm)],[f7,f194]) ).
fof(f321,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)],[f289,f23]) ).
fof(f383,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(trivial_equality_resolution,[status(thm)],[f321]) ).
fof(f409,plain,
! [X0,X1] : inverse(X0) = divide(divide(X1,X0),X1),
inference(paramodulation,[status(thm)],[f194,f289]) ).
fof(f412,plain,
! [X0,X1] : multiply(X0,inverse(X1)) = divide(X0,X1),
inference(paramodulation,[status(thm)],[f289,f9]) ).
fof(f414,plain,
! [X0,X1] : divide(X0,inverse(divide(X1,X0))) = X1,
inference(backward_demodulation,[status(thm)],[f409,f204]) ).
fof(f422,plain,
! [X0,X1] : multiply(X0,divide(X1,X0)) = X1,
inference(forward_demodulation,[status(thm)],[f9,f414]) ).
fof(f426,plain,
! [X0,X1,X2] : multiply(divide(X0,X1),X2) = divide(X0,divide(X1,X2)),
inference(paramodulation,[status(thm)],[f5,f422]) ).
fof(f433,plain,
! [X0,X1,X2] : multiply(divide(multiply(X0,X1),X0),divide(X2,X2)) = X1,
inference(backward_demodulation,[status(thm)],[f426,f268]) ).
fof(f436,plain,
! [X0,X1,X2,X3] : divide(multiply(divide(divide(X0,divide(X1,X2)),divide(X0,X1)),X3),X2) = X3,
inference(backward_demodulation,[status(thm)],[f426,f227]) ).
fof(f445,plain,
! [X0,X1] : multiply(X0,divide(X1,X1)) = X0,
inference(backward_demodulation,[status(thm)],[f447,f433]) ).
fof(f447,plain,
! [X0,X1] : divide(multiply(X0,X1),X0) = X1,
inference(forward_demodulation,[status(thm)],[f5,f436]) ).
fof(f503,plain,
! [X0,X1] : multiply(X0,inverse(divide(X1,X1))) = X0,
inference(paramodulation,[status(thm)],[f7,f445]) ).
fof(f517,plain,
! [X0,X1] : divide(X0,divide(X1,X1)) = X0,
inference(forward_demodulation,[status(thm)],[f412,f503]) ).
fof(f519,plain,
! [X0,X1] : multiply(divide(X0,X1),X1) = X0,
inference(forward_demodulation,[status(thm)],[f426,f517]) ).
fof(f522,plain,
! [X0,X1] : multiply(inverse(X0),X0) = multiply(inverse(X1),X1),
inference(paramodulation,[status(thm)],[f13,f519]) ).
fof(f523,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(paramodulation,[status(thm)],[f447,f519]) ).
fof(f527,plain,
! [X0,X1] : multiply(multiply(X0,X1),inverse(X1)) = X0,
inference(paramodulation,[status(thm)],[f9,f519]) ).
fof(f533,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
inference(backward_subsumption_resolution,[status(thm)],[f383,f522]) ).
fof(f534,plain,
! [X0,X1] : divide(multiply(X0,X1),X1) = X0,
inference(forward_demodulation,[status(thm)],[f412,f527]) ).
fof(f537,plain,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(forward_subsumption_resolution,[status(thm)],[f533,f523]) ).
fof(f614,plain,
! [X0,X1] : divide(X0,X1) = inverse(divide(X1,X0)),
inference(paramodulation,[status(thm)],[f232,f534]) ).
fof(f702,plain,
! [X0,X1,X2] : multiply(X0,divide(X1,X2)) = divide(X0,divide(X2,X1)),
inference(paramodulation,[status(thm)],[f614,f412]) ).
fof(f716,plain,
! [X0,X1,X2] : multiply(X0,divide(X1,X2)) = multiply(divide(X0,X2),X1),
inference(forward_demodulation,[status(thm)],[f426,f702]) ).
fof(f920,plain,
! [X0,X1,X2] : multiply(X0,divide(X1,inverse(X2))) = multiply(multiply(X0,X2),X1),
inference(paramodulation,[status(thm)],[f9,f716]) ).
fof(f951,plain,
multiply(a3,multiply(c3,b3)) != multiply(a3,multiply(b3,c3)),
inference(backward_demodulation,[status(thm)],[f954,f537]) ).
fof(f954,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = multiply(multiply(X0,X2),X1),
inference(forward_demodulation,[status(thm)],[f9,f920]) ).
fof(f978,plain,
multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3)),
inference(paramodulation,[status(thm)],[f523,f951]) ).
fof(f980,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f978]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP090-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n005.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 19:57:03 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.13/0.40 % Refutation found
% 0.13/0.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.43 % Elapsed time: 0.066332 seconds
% 0.13/0.43 % CPU time: 0.195067 seconds
% 0.13/0.43 % Total memory used: 67.882 MB
% 0.13/0.43 % Net memory used: 67.249 MB
%------------------------------------------------------------------------------