%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP498-1 : 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 12:34:32 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.66s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 5
% Syntax : Number of formulae : 82 ( 82 unt; 0 def)
% Number of atoms : 82 ( 81 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 206 ( 206 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)) = C,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] : multiply(A,B) = double_divide(double_divide(B,A),identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A] : inverse(A) = double_divide(A,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A] : identity = double_divide(A,inverse(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,plain,
! [X0,X1,X2] : double_divide(double_divide(identity,double_divide(X0,double_divide(X1,identity))),double_divide(double_divide(X1,double_divide(X2,X0)),identity)) = X2,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f7,plain,
! [X0,X1] : multiply(X0,X1) = double_divide(double_divide(X1,X0),identity),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f8,plain,
! [X0] : inverse(X0) = double_divide(X0,identity),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f9,plain,
! [X0] : identity = double_divide(X0,inverse(X0)),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f10,plain,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f16,plain,
! [X0,X1,X2] : double_divide(double_divide(identity,double_divide(X0,double_divide(X1,identity))),multiply(double_divide(X2,X0),X1)) = X2,
inference(backward_demodulation,[status(thm)],[f7,f6]) ).
fof(f17,plain,
! [X0,X1] : multiply(X0,X1) = inverse(double_divide(X1,X0)),
inference(backward_demodulation,[status(thm)],[f8,f7]) ).
fof(f18,plain,
! [X0,X1,X2] : double_divide(double_divide(identity,double_divide(X0,inverse(X1))),multiply(double_divide(X2,X0),X1)) = X2,
inference(forward_demodulation,[status(thm)],[f8,f16]) ).
fof(f19,plain,
! [X0,X1,X2,X3] : double_divide(double_divide(identity,double_divide(multiply(double_divide(X0,X1),X2),inverse(X3))),multiply(X0,X3)) = double_divide(identity,double_divide(X1,inverse(X2))),
inference(paramodulation,[status(thm)],[f18,f18]) ).
fof(f20,plain,
! [X0,X1,X2] : multiply(multiply(double_divide(X0,X1),X2),double_divide(identity,double_divide(X1,inverse(X2)))) = inverse(X0),
inference(paramodulation,[status(thm)],[f18,f17]) ).
fof(f21,plain,
! [X0,X1,X2,X3] : double_divide(double_divide(identity,double_divide(X0,multiply(X1,X2))),multiply(double_divide(X3,X0),double_divide(X2,X1))) = X3,
inference(paramodulation,[status(thm)],[f17,f18]) ).
fof(f22,plain,
! [X0,X1,X2,X3] : multiply(multiply(X0,X1),double_divide(identity,double_divide(multiply(double_divide(X0,X2),X3),inverse(X1)))) = inverse(double_divide(identity,double_divide(X2,inverse(X3)))),
inference(paramodulation,[status(thm)],[f18,f20]) ).
fof(f24,plain,
! [X0,X1,X2,X3] : multiply(multiply(X0,X1),double_divide(identity,double_divide(multiply(double_divide(X0,X2),X3),inverse(X1)))) = multiply(double_divide(X2,inverse(X3)),identity),
inference(forward_demodulation,[status(thm)],[f17,f22]) ).
fof(f154,plain,
! [X0] : multiply(identity,X0) = inverse(inverse(X0)),
inference(paramodulation,[status(thm)],[f8,f17]) ).
fof(f155,plain,
! [X0,X1] : double_divide(double_divide(identity,double_divide(identity,inverse(X0))),multiply(inverse(X1),X0)) = X1,
inference(paramodulation,[status(thm)],[f8,f18]) ).
fof(f159,plain,
! [X0,X1] : identity = double_divide(double_divide(X0,X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f17,f9]) ).
fof(f164,plain,
! [X0,X1] : double_divide(double_divide(identity,identity),multiply(double_divide(X0,X1),X1)) = X0,
inference(paramodulation,[status(thm)],[f9,f18]) ).
fof(f169,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),double_divide(identity,double_divide(multiply(identity,X2),inverse(X1)))) = multiply(double_divide(inverse(X0),inverse(X2)),identity),
inference(paramodulation,[status(thm)],[f9,f24]) ).
fof(f174,plain,
! [X0] : multiply(inverse(X0),X0) = inverse(identity),
inference(paramodulation,[status(thm)],[f9,f17]) ).
fof(f179,plain,
! [X0,X1] : double_divide(inverse(identity),multiply(double_divide(X0,X1),X1)) = X0,
inference(forward_demodulation,[status(thm)],[f8,f164]) ).
fof(f184,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),double_divide(identity,double_divide(inverse(inverse(X2)),inverse(X1)))) = multiply(double_divide(inverse(X0),inverse(X2)),identity),
inference(forward_demodulation,[status(thm)],[f154,f169]) ).
fof(f195,plain,
! [X0,X1,X2] : multiply(inverse(inverse(X0)),double_divide(identity,double_divide(multiply(double_divide(identity,X1),X2),inverse(X0)))) = multiply(double_divide(X1,inverse(X2)),identity),
inference(paramodulation,[status(thm)],[f154,f24]) ).
fof(f196,plain,
! [X0,X1,X2] : double_divide(double_divide(identity,double_divide(multiply(double_divide(identity,X0),X1),inverse(X2))),inverse(inverse(X2))) = double_divide(identity,double_divide(X0,inverse(X1))),
inference(paramodulation,[status(thm)],[f154,f19]) ).
fof(f226,plain,
identity = inverse(identity),
inference(paramodulation,[status(thm)],[f18,f159]) ).
fof(f251,plain,
! [X0,X1,X2] : multiply(multiply(identity,X0),double_divide(identity,double_divide(multiply(X1,X2),inverse(X0)))) = inverse(double_divide(X2,X1)),
inference(paramodulation,[status(thm)],[f159,f20]) ).
fof(f253,plain,
! [X0,X1,X2] : double_divide(double_divide(identity,double_divide(multiply(X0,X1),inverse(X2))),multiply(identity,X2)) = double_divide(X1,X0),
inference(paramodulation,[status(thm)],[f159,f18]) ).
fof(f255,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(backward_demodulation,[status(thm)],[f226,f174]) ).
fof(f256,plain,
! [X0,X1] : double_divide(identity,multiply(double_divide(X0,X1),X1)) = X0,
inference(backward_demodulation,[status(thm)],[f226,f179]) ).
fof(f289,plain,
! [X0,X1,X2] : multiply(inverse(inverse(X0)),double_divide(identity,double_divide(multiply(X1,X2),inverse(X0)))) = inverse(double_divide(X2,X1)),
inference(forward_demodulation,[status(thm)],[f154,f251]) ).
fof(f290,plain,
! [X0,X1] : multiply(double_divide(identity,X0),X1) = multiply(double_divide(X0,inverse(X1)),identity),
inference(backward_demodulation,[status(thm)],[f291,f195]) ).
fof(f291,plain,
! [X0,X1,X2] : multiply(inverse(inverse(X0)),double_divide(identity,double_divide(multiply(X1,X2),inverse(X0)))) = multiply(X1,X2),
inference(forward_demodulation,[status(thm)],[f17,f289]) ).
fof(f297,plain,
! [X0,X1] : double_divide(X0,double_divide(identity,X1)) = double_divide(identity,double_divide(X1,inverse(X0))),
inference(backward_demodulation,[status(thm)],[f298,f196]) ).
fof(f298,plain,
! [X0,X1,X2] : double_divide(double_divide(identity,double_divide(multiply(X0,X1),inverse(X2))),inverse(inverse(X2))) = double_divide(X1,X0),
inference(forward_demodulation,[status(thm)],[f154,f253]) ).
fof(f300,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),double_divide(identity,double_divide(inverse(inverse(X2)),inverse(X1)))) = multiply(double_divide(identity,inverse(X0)),X2),
inference(backward_demodulation,[status(thm)],[f290,f184]) ).
fof(f318,plain,
! [X0,X1] : double_divide(double_divide(X0,double_divide(identity,identity)),multiply(inverse(X1),X0)) = X1,
inference(backward_demodulation,[status(thm)],[f297,f155]) ).
fof(f319,plain,
! [X0,X1,X2,X3] : double_divide(double_divide(X0,double_divide(identity,multiply(double_divide(X1,X2),X3))),multiply(X1,X0)) = double_divide(identity,double_divide(X2,inverse(X3))),
inference(backward_demodulation,[status(thm)],[f297,f19]) ).
fof(f320,plain,
! [X0,X1,X2] : multiply(multiply(double_divide(X0,X1),X2),double_divide(X2,double_divide(identity,X1))) = inverse(X0),
inference(backward_demodulation,[status(thm)],[f297,f20]) ).
fof(f321,plain,
! [X0,X1,X2] : double_divide(double_divide(X0,double_divide(identity,X1)),multiply(double_divide(X2,X1),X0)) = X2,
inference(backward_demodulation,[status(thm)],[f297,f18]) ).
fof(f351,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),double_divide(X1,double_divide(identity,inverse(inverse(X2))))) = multiply(double_divide(identity,inverse(X0)),X2),
inference(forward_demodulation,[status(thm)],[f297,f300]) ).
fof(f370,plain,
! [X0,X1] : double_divide(double_divide(X0,inverse(identity)),multiply(inverse(X1),X0)) = X1,
inference(forward_demodulation,[status(thm)],[f8,f318]) ).
fof(f371,plain,
! [X0,X1] : double_divide(double_divide(X0,identity),multiply(inverse(X1),X0)) = X1,
inference(forward_demodulation,[status(thm)],[f226,f370]) ).
fof(f372,plain,
! [X0,X1] : double_divide(inverse(X0),multiply(inverse(X1),X0)) = X1,
inference(forward_demodulation,[status(thm)],[f8,f371]) ).
fof(f373,plain,
! [X0,X1,X2,X3] : double_divide(double_divide(X0,double_divide(identity,multiply(double_divide(X1,X2),X3))),multiply(X1,X0)) = double_divide(X3,double_divide(identity,X2)),
inference(forward_demodulation,[status(thm)],[f297,f319]) ).
fof(f411,plain,
! [X0,X1,X2,X3,X4] : double_divide(double_divide(X0,double_divide(identity,multiply(double_divide(X1,X2),double_divide(X3,X4)))),multiply(X1,X0)) = double_divide(identity,double_divide(X2,multiply(X4,X3))),
inference(paramodulation,[status(thm)],[f21,f321]) ).
fof(f436,plain,
! [X0,X1,X2] : double_divide(double_divide(X0,X1),double_divide(identity,X2)) = double_divide(identity,double_divide(X2,multiply(X1,X0))),
inference(forward_demodulation,[status(thm)],[f373,f411]) ).
fof(f469,plain,
! [X0,X1] : double_divide(identity,multiply(identity,multiply(X0,X1))) = double_divide(X1,X0),
inference(paramodulation,[status(thm)],[f159,f256]) ).
fof(f470,plain,
! [X0] : double_divide(identity,multiply(identity,inverse(X0))) = X0,
inference(paramodulation,[status(thm)],[f9,f256]) ).
fof(f490,plain,
! [X0,X1] : double_divide(identity,inverse(inverse(multiply(X0,X1)))) = double_divide(X1,X0),
inference(forward_demodulation,[status(thm)],[f154,f469]) ).
fof(f491,plain,
! [X0] : double_divide(identity,inverse(inverse(inverse(X0)))) = X0,
inference(forward_demodulation,[status(thm)],[f154,f470]) ).
fof(f510,plain,
! [X0] : double_divide(inverse(X0),identity) = X0,
inference(paramodulation,[status(thm)],[f255,f372]) ).
fof(f526,plain,
! [X0] : double_divide(identity,inverse(X0)) = X0,
inference(backward_demodulation,[status(thm)],[f536,f491]) ).
fof(f527,plain,
! [X0,X1] : double_divide(identity,multiply(X0,X1)) = double_divide(X1,X0),
inference(backward_demodulation,[status(thm)],[f536,f490]) ).
fof(f535,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),double_divide(X1,double_divide(identity,X2))) = multiply(double_divide(identity,inverse(X0)),X2),
inference(backward_demodulation,[status(thm)],[f536,f351]) ).
fof(f536,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f8,f510]) ).
fof(f549,plain,
! [X0,X1] : double_divide(X0,double_divide(X1,X0)) = X1,
inference(backward_demodulation,[status(thm)],[f527,f256]) ).
fof(f563,plain,
! [X0,X1,X2,X3] : double_divide(double_divide(X0,double_divide(X1,double_divide(X2,X3))),multiply(X2,X0)) = double_divide(X1,double_divide(identity,X3)),
inference(backward_demodulation,[status(thm)],[f527,f373]) ).
fof(f581,plain,
! [X0,X1] : multiply(double_divide(X0,X1),X1) = inverse(X0),
inference(backward_demodulation,[status(thm)],[f582,f320]) ).
fof(f582,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),double_divide(X1,double_divide(identity,X2))) = multiply(X0,X2),
inference(forward_demodulation,[status(thm)],[f526,f535]) ).
fof(f634,plain,
! [X0,X1,X2,X3] : double_divide(double_divide(identity,double_divide(double_divide(X0,X1),multiply(X2,X3))),multiply(X0,double_divide(X3,X2))) = X1,
inference(paramodulation,[status(thm)],[f549,f21]) ).
fof(f687,plain,
! [X0,X1,X2] : double_divide(X0,multiply(X1,double_divide(X1,X2))) = double_divide(X0,double_divide(identity,X2)),
inference(paramodulation,[status(thm)],[f549,f563]) ).
fof(f693,plain,
! [X0,X1,X2,X3] : double_divide(double_divide(X0,double_divide(X1,X2)),multiply(X3,X0)) = double_divide(X1,double_divide(identity,double_divide(X2,X3))),
inference(paramodulation,[status(thm)],[f549,f563]) ).
fof(f748,plain,
! [X0,X1] : multiply(X0,double_divide(X0,X1)) = inverse(X1),
inference(paramodulation,[status(thm)],[f549,f581]) ).
fof(f762,plain,
! [X0,X1] : double_divide(X0,inverse(X1)) = double_divide(X0,double_divide(identity,X1)),
inference(backward_demodulation,[status(thm)],[f748,f687]) ).
fof(f788,plain,
! [X0,X1,X2] : double_divide(double_divide(X0,X1),inverse(X2)) = double_divide(identity,double_divide(X2,multiply(X1,X0))),
inference(backward_demodulation,[status(thm)],[f762,f436]) ).
fof(f802,plain,
! [X0,X1,X2,X3] : double_divide(double_divide(X0,double_divide(X1,X2)),multiply(X3,X0)) = double_divide(X1,inverse(double_divide(X2,X3))),
inference(backward_demodulation,[status(thm)],[f762,f693]) ).
fof(f843,plain,
! [X0,X1,X2,X3] : double_divide(double_divide(double_divide(X0,X1),inverse(double_divide(X2,X3))),multiply(X2,double_divide(X0,X1))) = X3,
inference(backward_demodulation,[status(thm)],[f788,f634]) ).
fof(f877,plain,
! [X0,X1,X2,X3] : double_divide(double_divide(X0,double_divide(X1,X2)),multiply(X3,X0)) = double_divide(X1,multiply(X3,X2)),
inference(forward_demodulation,[status(thm)],[f17,f802]) ).
fof(f906,plain,
! [X0,X1,X2,X3] : double_divide(double_divide(double_divide(X0,X1),multiply(X2,X3)),multiply(X3,double_divide(X0,X1))) = X2,
inference(forward_demodulation,[status(thm)],[f17,f843]) ).
fof(f1359,plain,
! [X0,X1,X2,X3] : multiply(multiply(X0,X1),double_divide(X1,double_divide(X2,X3))) = inverse(double_divide(X2,multiply(X0,X3))),
inference(paramodulation,[status(thm)],[f877,f17]) ).
fof(f1435,plain,
! [X0,X1,X2,X3] : multiply(multiply(X0,X1),double_divide(X1,double_divide(X2,X3))) = multiply(multiply(X0,X3),X2),
inference(forward_demodulation,[status(thm)],[f17,f1359]) ).
fof(f1571,plain,
! [X0,X1,X2,X3] : multiply(X0,multiply(X1,double_divide(X2,X3))) = inverse(double_divide(double_divide(X2,X3),multiply(X0,X1))),
inference(paramodulation,[status(thm)],[f906,f581]) ).
fof(f1643,plain,
! [X0,X1,X2,X3] : multiply(X0,multiply(X1,double_divide(X1,double_divide(X2,X3)))) = multiply(multiply(X0,X3),X2),
inference(backward_demodulation,[status(thm)],[f1645,f1435]) ).
fof(f1645,plain,
! [X0,X1,X2,X3] : multiply(X0,multiply(X1,double_divide(X2,X3))) = multiply(multiply(X0,X1),double_divide(X2,X3)),
inference(forward_demodulation,[status(thm)],[f17,f1571]) ).
fof(f1670,plain,
! [X0,X1,X2] : multiply(X0,inverse(double_divide(X1,X2))) = multiply(multiply(X0,X2),X1),
inference(forward_demodulation,[status(thm)],[f748,f1643]) ).
fof(f1671,plain,
multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3)),
inference(backward_demodulation,[status(thm)],[f1687,f10]) ).
fof(f1687,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = multiply(multiply(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f17,f1670]) ).
fof(f1694,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f1671]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP498-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.57 % Computer : n006.cluster.edu
% 0.09/0.57 % Model : x86_64 x86_64
% 0.09/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.57 % Memory : 8046.5625MB
% 0.09/0.57 % OS : Linux 6.8.0-71-generic
% 0.09/0.57 % CPULimit : 300
% 0.09/0.57 % WCLimit : 300
% 0.09/0.57 % DateTime : Sun Sep 20 20:14:29 UTC 2026
% 0.09/0.57 % CPUTime :
% 0.09/0.58 % Drodi V4.1.1
% 0.13/0.66 % Refutation found
% 0.13/0.66 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.66 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.68 % Elapsed time: 0.103471 seconds
% 0.13/0.68 % CPU time: 0.688177 seconds
% 0.13/0.68 % Total memory used: 28.376 MB
% 0.13/0.68 % Net memory used: 27.506 MB
%------------------------------------------------------------------------------