%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP587-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n006.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 12:34:44 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.47s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 3
% Syntax : Number of formulae : 35 ( 35 unt; 0 def)
% Number of atoms : 35 ( 34 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 4 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 87 ( 87 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : double_divide(A,inverse(double_divide(inverse(double_divide(double_divide(A,B),inverse(C))),B))) = C,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] : multiply(A,B) = inverse(double_divide(B,A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,plain,
! [X0,X1,X2] : double_divide(X0,inverse(double_divide(inverse(double_divide(double_divide(X0,X1),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(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f12,plain,
! [X0,X1,X2] : double_divide(X0,inverse(double_divide(multiply(inverse(X1),double_divide(X0,X2)),X2))) = X1,
inference(backward_demodulation,[status(thm)],[f5,f4]) ).
fof(f13,plain,
! [X0,X1,X2] : double_divide(X0,multiply(X1,multiply(inverse(X2),double_divide(X0,X1)))) = X2,
inference(forward_demodulation,[status(thm)],[f5,f12]) ).
fof(f14,plain,
! [X0,X1,X2,X3] : double_divide(X0,multiply(X1,multiply(multiply(X2,X3),double_divide(X0,X1)))) = double_divide(X3,X2),
inference(paramodulation,[status(thm)],[f5,f13]) ).
fof(f15,plain,
! [X0,X1,X2,X3] : double_divide(X0,multiply(multiply(X1,multiply(inverse(X2),double_divide(X0,X1))),multiply(inverse(X3),X2))) = X3,
inference(paramodulation,[status(thm)],[f13,f13]) ).
fof(f16,plain,
! [X0,X1,X2] : multiply(multiply(X0,multiply(inverse(X1),double_divide(X2,X0))),X2) = inverse(X1),
inference(paramodulation,[status(thm)],[f13,f5]) ).
fof(f29,plain,
! [X0,X1] : double_divide(multiply(inverse(X0),X1),inverse(X1)) = X0,
inference(paramodulation,[status(thm)],[f16,f15]) ).
fof(f45,plain,
! [X0,X1] : multiply(inverse(X0),multiply(inverse(X1),X0)) = inverse(X1),
inference(paramodulation,[status(thm)],[f29,f5]) ).
fof(f48,plain,
! [X0,X1,X2] : multiply(inverse(X0),multiply(multiply(X1,X2),X0)) = inverse(double_divide(X2,X1)),
inference(paramodulation,[status(thm)],[f5,f45]) ).
fof(f52,plain,
! [X0,X1,X2] : multiply(inverse(X0),multiply(multiply(X1,X2),X0)) = multiply(X1,X2),
inference(forward_demodulation,[status(thm)],[f5,f48]) ).
fof(f73,plain,
! [X0,X1,X2] : multiply(inverse(multiply(multiply(X0,X1),X2)),multiply(X0,X1)) = inverse(X2),
inference(paramodulation,[status(thm)],[f52,f45]) ).
fof(f74,plain,
! [X0,X1,X2] : double_divide(multiply(X0,X1),inverse(multiply(multiply(X0,X1),X2))) = X2,
inference(paramodulation,[status(thm)],[f52,f29]) ).
fof(f145,plain,
! [X0,X1,X2] : double_divide(inverse(X0),inverse(multiply(X1,X2))) = multiply(multiply(X1,X2),X0),
inference(paramodulation,[status(thm)],[f73,f29]) ).
fof(f148,plain,
! [X0,X1,X2,X3] : double_divide(inverse(X0),inverse(multiply(multiply(inverse(multiply(multiply(X1,X2),X0)),multiply(X1,X2)),X3))) = X3,
inference(paramodulation,[status(thm)],[f73,f74]) ).
fof(f164,plain,
! [X0,X1,X2,X3] : multiply(multiply(multiply(inverse(multiply(multiply(X0,X1),X2)),multiply(X0,X1)),X3),X2) = X3,
inference(forward_demodulation,[status(thm)],[f145,f148]) ).
fof(f166,plain,
! [X0,X1] : multiply(multiply(inverse(X0),X1),X0) = X1,
inference(forward_demodulation,[status(thm)],[f73,f164]) ).
fof(f175,plain,
! [X0,X1,X2] : double_divide(X0,multiply(X1,X2)) = double_divide(X2,inverse(double_divide(X0,X1))),
inference(paramodulation,[status(thm)],[f166,f14]) ).
fof(f190,plain,
! [X0,X1,X2] : double_divide(X0,multiply(X1,X2)) = double_divide(X2,multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f5,f175]) ).
fof(f223,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = inverse(double_divide(X1,multiply(X0,X2))),
inference(paramodulation,[status(thm)],[f190,f5]) ).
fof(f235,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(multiply(X0,X2),X1),
inference(forward_demodulation,[status(thm)],[f5,f223]) ).
fof(f326,plain,
! [X0,X1] : X0 = multiply(multiply(inverse(X1),X1),X0),
inference(paramodulation,[status(thm)],[f166,f235]) ).
fof(f393,plain,
! [X0,X1,X2] : multiply(multiply(multiply(inverse(X0),X0),X1),X2) = multiply(X2,X1),
inference(paramodulation,[status(thm)],[f326,f235]) ).
fof(f403,plain,
multiply(c3,multiply(a3,b3)) != multiply(a3,multiply(b3,c3)),
inference(backward_demodulation,[status(thm)],[f414,f6]) ).
fof(f414,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(forward_demodulation,[status(thm)],[f326,f393]) ).
fof(f447,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X1,multiply(X0,X2)),
inference(paramodulation,[status(thm)],[f235,f414]) ).
fof(f460,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(multiply(X2,X0),X1),
inference(paramodulation,[status(thm)],[f414,f235]) ).
fof(f518,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = multiply(multiply(X2,X1),X0),
inference(forward_demodulation,[status(thm)],[f447,f460]) ).
fof(f521,plain,
multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3)),
inference(backward_demodulation,[status(thm)],[f523,f403]) ).
fof(f523,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = multiply(X1,multiply(X2,X0)),
inference(forward_demodulation,[status(thm)],[f447,f518]) ).
fof(f607,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f521]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP587-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n006.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 20:17:12 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.12/0.36 % Drodi V4.1.1
% 0.12/0.47 % Refutation found
% 0.12/0.47 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.49 % Elapsed time: 0.126893 seconds
% 0.12/0.49 % CPU time: 0.875620 seconds
% 0.12/0.49 % Total memory used: 41.048 MB
% 0.12/0.49 % Net memory used: 40.199 MB
%------------------------------------------------------------------------------