%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP100-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.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 12:32:30 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.53s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 5
% Syntax : Number of formulae : 89 ( 83 unt; 0 def)
% Number of atoms : 105 ( 104 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 40 ( 24 ~; 16 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 183 ( 183 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y,Z] : double_divide(double_divide(X,double_divide(double_divide(Y,double_divide(X,Z)),double_divide(Z,identity))),double_divide(identity,identity)) = Y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] : multiply(X,Y) = double_divide(double_divide(Y,X),identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X] : inverse(X) = double_divide(X,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] : identity = double_divide(X,inverse(X)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2
| multiply(inverse(a1),a1) != identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,plain,
! [X0,X1,X2] : double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(X0,X2)),double_divide(X2,identity))),double_divide(identity,identity)) = X1,
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(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2
| multiply(inverse(a1),a1) != identity ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f11,plain,
! [X0,X1,X2] : double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(X0,X2)),double_divide(X2,identity))),inverse(identity)) = X1,
inference(backward_demodulation,[status(thm)],[f8,f6]) ).
fof(f12,plain,
! [X0,X1] : multiply(X0,X1) = inverse(double_divide(X1,X0)),
inference(backward_demodulation,[status(thm)],[f8,f7]) ).
fof(f13,plain,
! [X0,X1,X2] : double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(X0,X2)),inverse(X2))),inverse(identity)) = X1,
inference(forward_demodulation,[status(thm)],[f8,f11]) ).
fof(f14,plain,
! [X0] : multiply(inverse(X0),X0) = inverse(identity),
inference(paramodulation,[status(thm)],[f9,f12]) ).
fof(f15,plain,
! [X0] : multiply(identity,X0) = inverse(inverse(X0)),
inference(paramodulation,[status(thm)],[f8,f12]) ).
fof(f16,plain,
! [X0,X1] : identity = double_divide(double_divide(X0,X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f12,f9]) ).
fof(f17,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2
| inverse(identity) != identity ),
inference(backward_demodulation,[status(thm)],[f14,f10]) ).
fof(f19,plain,
! [X0,X1,X2,X3] : double_divide(double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(X0,X2)),inverse(X2))),double_divide(double_divide(X3,X1),inverse(inverse(identity)))),inverse(identity)) = X3,
inference(paramodulation,[status(thm)],[f13,f13]) ).
fof(f20,plain,
! [X0,X1] : double_divide(double_divide(X0,double_divide(double_divide(X1,identity),inverse(inverse(X0)))),inverse(identity)) = X1,
inference(paramodulation,[status(thm)],[f9,f13]) ).
fof(f24,plain,
! [X0,X1,X2,X3] : double_divide(double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(X0,X2)),inverse(X2))),double_divide(double_divide(X3,X1),multiply(identity,identity))),inverse(identity)) = X3,
inference(forward_demodulation,[status(thm)],[f15,f19]) ).
fof(f25,plain,
! [X0,X1] : double_divide(double_divide(X0,double_divide(inverse(X1),inverse(inverse(X0)))),inverse(identity)) = X1,
inference(forward_demodulation,[status(thm)],[f8,f20]) ).
fof(f26,plain,
! [X0,X1] : double_divide(double_divide(X0,double_divide(inverse(X1),multiply(identity,X0))),inverse(identity)) = X1,
inference(forward_demodulation,[status(thm)],[f15,f25]) ).
fof(f27,plain,
! [X0] : multiply(identity,inverse(X0)) = inverse(multiply(identity,X0)),
inference(paramodulation,[status(thm)],[f15,f15]) ).
fof(f29,plain,
! [X0,X1,X2] : double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(X0,inverse(X2))),multiply(identity,X2))),inverse(identity)) = X1,
inference(paramodulation,[status(thm)],[f15,f13]) ).
fof(f31,plain,
! [X0] : identity = double_divide(inverse(X0),multiply(identity,X0)),
inference(paramodulation,[status(thm)],[f15,f9]) ).
fof(f130,plain,
! [X0] : double_divide(double_divide(X0,identity),inverse(identity)) = X0,
inference(paramodulation,[status(thm)],[f31,f26]) ).
fof(f140,plain,
! [X0] : double_divide(inverse(X0),inverse(identity)) = X0,
inference(forward_demodulation,[status(thm)],[f8,f130]) ).
fof(f154,plain,
! [X0] : multiply(inverse(identity),inverse(X0)) = inverse(X0),
inference(paramodulation,[status(thm)],[f140,f12]) ).
fof(f182,plain,
! [X0,X1,X2,X3] : double_divide(double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(X0,multiply(identity,X2))),multiply(identity,inverse(X2)))),double_divide(double_divide(X3,X1),multiply(identity,identity))),inverse(identity)) = X3,
inference(paramodulation,[status(thm)],[f27,f24]) ).
fof(f185,plain,
! [X0,X1] : double_divide(double_divide(double_divide(X0,double_divide(double_divide(identity,double_divide(X0,X1)),inverse(X1))),identity),inverse(identity)) = identity,
inference(paramodulation,[status(thm)],[f16,f24]) ).
fof(f187,plain,
! [X0,X1,X2] : double_divide(double_divide(double_divide(X0,double_divide(double_divide(inverse(identity),double_divide(X0,X1)),inverse(X1))),double_divide(X2,multiply(identity,identity))),inverse(identity)) = inverse(X2),
inference(paramodulation,[status(thm)],[f140,f24]) ).
fof(f191,plain,
! [X0,X1,X2,X3,X4] : double_divide(double_divide(double_divide(X0,double_divide(double_divide(inverse(identity),double_divide(X0,X1)),inverse(X1))),double_divide(X2,multiply(identity,identity))),inverse(identity)) = double_divide(X3,double_divide(double_divide(X2,double_divide(X3,X4)),inverse(X4))),
inference(paramodulation,[status(thm)],[f13,f24]) ).
fof(f192,plain,
! [X0,X1,X2,X3] : double_divide(double_divide(double_divide(X0,double_divide(double_divide(multiply(X1,X2),double_divide(X0,X3)),inverse(X3))),double_divide(identity,multiply(identity,identity))),inverse(identity)) = double_divide(X2,X1),
inference(paramodulation,[status(thm)],[f16,f24]) ).
fof(f212,plain,
! [X0,X1] : double_divide(inverse(double_divide(X0,double_divide(double_divide(identity,double_divide(X0,X1)),inverse(X1)))),inverse(identity)) = identity,
inference(forward_demodulation,[status(thm)],[f8,f185]) ).
fof(f213,plain,
! [X0,X1] : double_divide(X0,double_divide(double_divide(identity,double_divide(X0,X1)),inverse(X1))) = identity,
inference(forward_demodulation,[status(thm)],[f140,f212]) ).
fof(f227,plain,
inverse(identity) = identity,
inference(backward_demodulation,[status(thm)],[f230,f213]) ).
fof(f230,plain,
! [X0,X1,X2] : inverse(X0) = double_divide(X1,double_divide(double_divide(X0,double_divide(X1,X2)),inverse(X2))),
inference(forward_demodulation,[status(thm)],[f187,f191]) ).
fof(f231,plain,
! [X0,X1] : double_divide(double_divide(inverse(multiply(X0,X1)),double_divide(identity,multiply(identity,identity))),inverse(identity)) = double_divide(X1,X0),
inference(forward_demodulation,[status(thm)],[f230,f192]) ).
fof(f246,plain,
! [X0] : multiply(identity,inverse(X0)) = inverse(X0),
inference(backward_demodulation,[status(thm)],[f227,f154]) ).
fof(f247,plain,
! [X0] : double_divide(inverse(X0),identity) = X0,
inference(backward_demodulation,[status(thm)],[f227,f140]) ).
fof(f252,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2
| identity != identity ),
inference(backward_demodulation,[status(thm)],[f227,f17]) ).
fof(f255,plain,
! [X0,X1] : double_divide(double_divide(inverse(multiply(X0,X1)),double_divide(identity,multiply(identity,identity))),identity) = double_divide(X1,X0),
inference(backward_demodulation,[status(thm)],[f227,f231]) ).
fof(f258,plain,
! [X0,X1,X2,X3] : double_divide(double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(X0,multiply(identity,X2))),multiply(identity,inverse(X2)))),double_divide(double_divide(X3,X1),multiply(identity,identity))),identity) = X3,
inference(backward_demodulation,[status(thm)],[f227,f182]) ).
fof(f270,plain,
! [X0,X1,X2] : double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(X0,inverse(X2))),multiply(identity,X2))),identity) = X1,
inference(backward_demodulation,[status(thm)],[f227,f29]) ).
fof(f277,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f8,f247]) ).
fof(f284,plain,
! [X0] : multiply(identity,X0) = X0,
inference(forward_demodulation,[status(thm)],[f15,f277]) ).
fof(f289,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| a2 != a2
| identity != identity ),
inference(forward_demodulation,[status(thm)],[f284,f252]) ).
fof(f290,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
inference(trivial_equality_resolution,[status(thm)],[f289]) ).
fof(f301,plain,
! [X0,X1] : inverse(double_divide(inverse(multiply(X0,X1)),double_divide(identity,multiply(identity,identity)))) = double_divide(X1,X0),
inference(forward_demodulation,[status(thm)],[f8,f255]) ).
fof(f302,plain,
! [X0,X1] : multiply(double_divide(identity,multiply(identity,identity)),inverse(multiply(X0,X1))) = double_divide(X1,X0),
inference(forward_demodulation,[status(thm)],[f12,f301]) ).
fof(f303,plain,
! [X0,X1] : multiply(double_divide(identity,identity),inverse(multiply(X0,X1))) = double_divide(X1,X0),
inference(forward_demodulation,[status(thm)],[f284,f302]) ).
fof(f304,plain,
! [X0,X1] : multiply(inverse(identity),inverse(multiply(X0,X1))) = double_divide(X1,X0),
inference(forward_demodulation,[status(thm)],[f8,f303]) ).
fof(f305,plain,
! [X0,X1] : inverse(multiply(X0,X1)) = double_divide(X1,X0),
inference(forward_demodulation,[status(thm)],[f154,f304]) ).
fof(f317,plain,
! [X0,X1,X2,X3] : inverse(double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(X0,multiply(identity,X2))),multiply(identity,inverse(X2)))),double_divide(double_divide(X3,X1),multiply(identity,identity)))) = X3,
inference(forward_demodulation,[status(thm)],[f8,f258]) ).
fof(f318,plain,
! [X0,X1,X2,X3] : multiply(double_divide(double_divide(X0,X1),multiply(identity,identity)),double_divide(X2,double_divide(double_divide(X1,double_divide(X2,multiply(identity,X3))),multiply(identity,inverse(X3))))) = X0,
inference(forward_demodulation,[status(thm)],[f12,f317]) ).
fof(f319,plain,
! [X0,X1,X2,X3] : multiply(double_divide(double_divide(X0,X1),identity),double_divide(X2,double_divide(double_divide(X1,double_divide(X2,multiply(identity,X3))),multiply(identity,inverse(X3))))) = X0,
inference(forward_demodulation,[status(thm)],[f284,f318]) ).
fof(f320,plain,
! [X0,X1,X2,X3] : multiply(inverse(double_divide(X0,X1)),double_divide(X2,double_divide(double_divide(X1,double_divide(X2,multiply(identity,X3))),multiply(identity,inverse(X3))))) = X0,
inference(forward_demodulation,[status(thm)],[f8,f319]) ).
fof(f321,plain,
! [X0,X1,X2,X3] : multiply(multiply(X0,X1),double_divide(X2,double_divide(double_divide(X0,double_divide(X2,multiply(identity,X3))),multiply(identity,inverse(X3))))) = X1,
inference(forward_demodulation,[status(thm)],[f12,f320]) ).
fof(f322,plain,
! [X0,X1,X2,X3] : multiply(multiply(X0,X1),double_divide(X2,double_divide(double_divide(X0,double_divide(X2,X3)),multiply(identity,inverse(X3))))) = X1,
inference(forward_demodulation,[status(thm)],[f284,f321]) ).
fof(f323,plain,
! [X0,X1,X2,X3] : multiply(multiply(X0,X1),double_divide(X2,double_divide(double_divide(X0,double_divide(X2,X3)),inverse(X3)))) = X1,
inference(forward_demodulation,[status(thm)],[f246,f322]) ).
fof(f324,plain,
! [X0,X1] : multiply(multiply(X0,X1),inverse(X0)) = X1,
inference(forward_demodulation,[status(thm)],[f230,f323]) ).
fof(f363,plain,
! [X0,X1,X2] : inverse(double_divide(X0,double_divide(double_divide(X1,double_divide(X0,inverse(X2))),multiply(identity,X2)))) = X1,
inference(forward_demodulation,[status(thm)],[f8,f270]) ).
fof(f364,plain,
! [X0,X1,X2] : multiply(double_divide(double_divide(X0,double_divide(X1,inverse(X2))),multiply(identity,X2)),X1) = X0,
inference(forward_demodulation,[status(thm)],[f12,f363]) ).
fof(f365,plain,
! [X0,X1,X2] : multiply(double_divide(double_divide(X0,double_divide(X1,inverse(X2))),X2),X1) = X0,
inference(forward_demodulation,[status(thm)],[f284,f364]) ).
fof(f419,plain,
! [X0,X1] : multiply(X0,inverse(multiply(X1,X0))) = inverse(X1),
inference(paramodulation,[status(thm)],[f324,f324]) ).
fof(f421,plain,
! [X0] : multiply(X0,inverse(identity)) = X0,
inference(paramodulation,[status(thm)],[f284,f324]) ).
fof(f428,plain,
! [X0,X1] : multiply(X0,double_divide(X0,X1)) = inverse(X1),
inference(forward_demodulation,[status(thm)],[f305,f419]) ).
fof(f432,plain,
! [X0] : multiply(X0,identity) = X0,
inference(forward_demodulation,[status(thm)],[f227,f421]) ).
fof(f438,plain,
! [X0] : inverse(X0) = double_divide(identity,X0),
inference(paramodulation,[status(thm)],[f432,f305]) ).
fof(f447,plain,
! [X0] : multiply(X0,identity) = inverse(inverse(X0)),
inference(paramodulation,[status(thm)],[f438,f12]) ).
fof(f451,plain,
! [X0] : X0 = inverse(inverse(X0)),
inference(forward_demodulation,[status(thm)],[f432,f447]) ).
fof(f502,plain,
! [X0,X1] : inverse(inverse(X0)) = double_divide(double_divide(X1,X0),X1),
inference(paramodulation,[status(thm)],[f428,f305]) ).
fof(f511,plain,
! [X0,X1] : X0 = double_divide(double_divide(X1,X0),X1),
inference(forward_demodulation,[status(thm)],[f451,f502]) ).
fof(f522,plain,
! [X0,X1] : multiply(double_divide(X0,X1),X1) = inverse(X0),
inference(paramodulation,[status(thm)],[f511,f428]) ).
fof(f754,plain,
! [X0,X1] : inverse(inverse(X0)) = double_divide(X1,double_divide(X1,X0)),
inference(paramodulation,[status(thm)],[f511,f230]) ).
fof(f758,plain,
! [X0,X1,X2] : inverse(double_divide(double_divide(X0,X1),X2)) = double_divide(X0,double_divide(X2,inverse(X1))),
inference(paramodulation,[status(thm)],[f511,f230]) ).
fof(f789,plain,
! [X0,X1] : X0 = double_divide(X1,double_divide(X1,X0)),
inference(forward_demodulation,[status(thm)],[f451,f754]) ).
fof(f797,plain,
! [X0,X1,X2] : multiply(double_divide(multiply(X0,double_divide(X1,X2)),X2),X0) = X1,
inference(backward_demodulation,[status(thm)],[f799,f365]) ).
fof(f799,plain,
! [X0,X1,X2] : multiply(X0,double_divide(X1,X2)) = double_divide(X1,double_divide(X0,inverse(X2))),
inference(forward_demodulation,[status(thm)],[f12,f758]) ).
fof(f875,plain,
! [X0,X1,X2] : multiply(double_divide(multiply(X0,X1),X2),X0) = double_divide(X2,X1),
inference(paramodulation,[status(thm)],[f511,f797]) ).
fof(f927,plain,
! [X0,X1] : multiply(X0,double_divide(X1,X0)) = inverse(X1),
inference(paramodulation,[status(thm)],[f789,f522]) ).
fof(f930,plain,
! [X0,X1] : multiply(X0,X1) = inverse(double_divide(X0,X1)),
inference(paramodulation,[status(thm)],[f789,f428]) ).
fof(f942,plain,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(backward_subsumption_resolution,[status(thm)],[f290,f943]) ).
fof(f943,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(forward_demodulation,[status(thm)],[f12,f930]) ).
fof(f1038,plain,
multiply(c3,multiply(a3,b3)) != multiply(a3,multiply(b3,c3)),
inference(paramodulation,[status(thm)],[f943,f942]) ).
fof(f2956,plain,
! [X0,X1,X2] : multiply(X0,X1) = double_divide(double_divide(multiply(X1,X2),X0),X2),
inference(paramodulation,[status(thm)],[f789,f875]) ).
fof(f3627,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = inverse(double_divide(multiply(X2,X0),X1)),
inference(paramodulation,[status(thm)],[f2956,f927]) ).
fof(f3696,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = multiply(X1,multiply(X2,X0)),
inference(forward_demodulation,[status(thm)],[f12,f3627]) ).
fof(f3697,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f1038,f3696]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP100-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n002.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 20:00:18 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.12/0.36 % Drodi V4.1.1
% 0.12/0.53 % Refutation found
% 0.12/0.53 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.53 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.29/0.54 % Elapsed time: 0.174535 seconds
% 0.29/0.54 % CPU time: 1.159185 seconds
% 0.29/0.54 % Total memory used: 88.122 MB
% 0.29/0.54 % Net memory used: 86.063 MB
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