%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP554-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 12:34:39 PM UTC 2026
% Result : Unsatisfiable 0.09s 0.38s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 3
% Syntax : Number of formulae : 31 ( 31 unt; 0 def)
% Number of atoms : 31 ( 30 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 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 : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 62 ( 62 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : divide(divide(A,inverse(divide(B,divide(A,C)))),C) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] : multiply(A,B) = divide(A,inverse(B)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,plain,
! [X0,X1,X2] : divide(divide(X0,inverse(divide(X1,divide(X0,X2)))),X2) = X1,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f5,plain,
! [X0,X1] : multiply(X0,X1) = divide(X0,inverse(X1)),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f6,plain,
multiply(multiply(inverse(b2),b2),a2) != a2,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f11,plain,
! [X0,X1,X2] : divide(multiply(X0,divide(X1,divide(X0,X2))),X2) = X1,
inference(forward_demodulation,[status(thm)],[f5,f4]) ).
fof(f12,plain,
! [X0,X1,X2] : multiply(multiply(X0,divide(X1,divide(X0,inverse(X2)))),X2) = X1,
inference(paramodulation,[status(thm)],[f5,f11]) ).
fof(f13,plain,
! [X0,X1,X2,X3] : divide(multiply(X0,X1),X2) = multiply(X3,divide(X1,divide(X3,divide(X0,X2)))),
inference(paramodulation,[status(thm)],[f11,f11]) ).
fof(f17,plain,
! [X0,X1,X2] : multiply(multiply(X0,divide(X1,multiply(X0,X2))),X2) = X1,
inference(forward_demodulation,[status(thm)],[f5,f12]) ).
fof(f21,plain,
! [X0,X1,X2,X3] : multiply(multiply(multiply(X0,divide(X1,multiply(X0,X2))),divide(X3,X1)),X2) = X3,
inference(paramodulation,[status(thm)],[f17,f17]) ).
fof(f26,plain,
! [X0,X1,X2] : divide(divide(multiply(X0,X1),X2),divide(X0,X2)) = X1,
inference(paramodulation,[status(thm)],[f13,f11]) ).
fof(f32,plain,
! [X0,X1,X2] : divide(multiply(multiply(X0,X1),X2),divide(X0,inverse(X2))) = X1,
inference(paramodulation,[status(thm)],[f5,f26]) ).
fof(f43,plain,
! [X0,X1,X2] : divide(multiply(multiply(X0,X1),X2),multiply(X0,X2)) = X1,
inference(forward_demodulation,[status(thm)],[f5,f32]) ).
fof(f51,plain,
! [X0,X1,X2] : divide(X0,divide(multiply(X1,X0),multiply(X1,X2))) = X2,
inference(paramodulation,[status(thm)],[f43,f26]) ).
fof(f56,plain,
! [X0,X1,X2] : divide(divide(X0,divide(X1,multiply(X1,X2))),X0) = X2,
inference(paramodulation,[status(thm)],[f11,f51]) ).
fof(f143,plain,
! [X0,X1] : multiply(X0,divide(X1,X0)) = X1,
inference(paramodulation,[status(thm)],[f17,f21]) ).
fof(f176,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X1,X0)) = X1,
inference(paramodulation,[status(thm)],[f5,f143]) ).
fof(f196,plain,
! [X0,X1] : multiply(inverse(divide(X0,X1)),X0) = X1,
inference(paramodulation,[status(thm)],[f143,f176]) ).
fof(f391,plain,
! [X0,X1] : multiply(inverse(X0),X1) = inverse(divide(X0,X1)),
inference(paramodulation,[status(thm)],[f196,f176]) ).
fof(f434,plain,
! [X0,X1] : inverse(divide(divide(X0,X1),X0)) = X1,
inference(backward_demodulation,[status(thm)],[f391,f196]) ).
fof(f435,plain,
multiply(inverse(divide(b2,b2)),a2) != a2,
inference(backward_demodulation,[status(thm)],[f391,f6]) ).
fof(f461,plain,
inverse(divide(divide(b2,b2),a2)) != a2,
inference(forward_demodulation,[status(thm)],[f391,f435]) ).
fof(f521,plain,
! [X0,X1] : inverse(X0) = divide(X1,multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f56,f434]) ).
fof(f535,plain,
! [X0,X1] : divide(divide(X0,inverse(X1)),X0) = X1,
inference(backward_demodulation,[status(thm)],[f521,f56]) ).
fof(f543,plain,
! [X0,X1] : inverse(divide(X0,X1)) = divide(X1,X0),
inference(paramodulation,[status(thm)],[f143,f521]) ).
fof(f564,plain,
! [X0,X1] : divide(multiply(X0,X1),X0) = X1,
inference(forward_demodulation,[status(thm)],[f5,f535]) ).
fof(f662,plain,
! [X0,X1] : X0 = divide(X0,divide(X1,X1)),
inference(paramodulation,[status(thm)],[f11,f564]) ).
fof(f763,plain,
divide(a2,divide(b2,b2)) != a2,
inference(forward_demodulation,[status(thm)],[f543,f461]) ).
fof(f764,plain,
a2 != a2,
inference(forward_demodulation,[status(thm)],[f662,f763]) ).
fof(f765,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f764]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP554-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n016.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 20:21:25 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.38 % Refutation found
% 0.09/0.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.40 % Elapsed time: 0.029240 seconds
% 0.09/0.40 % CPU time: 0.073412 seconds
% 0.09/0.40 % Total memory used: 3.576 MB
% 0.09/0.40 % Net memory used: 3.482 MB
%------------------------------------------------------------------------------