%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP610-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 12:34:47 PM UTC 2026
% Result : Unsatisfiable 0.08s 0.43s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 3
% Syntax : Number of formulae : 50 ( 50 unt; 0 def)
% Number of atoms : 50 ( 49 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 8 ( 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 : 136 ( 136 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : inverse(double_divide(inverse(double_divide(inverse(double_divide(A,B)),C)),double_divide(A,C))) = B,
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(inverse(b2),b2),a2) != a2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,plain,
! [X0,X1,X2] : inverse(double_divide(inverse(double_divide(inverse(double_divide(X0,X1)),X2)),double_divide(X0,X2))) = X1,
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(inverse(b2),b2),a2) != a2,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f11,plain,
! [X0,X1,X2] : multiply(double_divide(X0,X1),inverse(double_divide(inverse(double_divide(X0,X2)),X1))) = X2,
inference(backward_demodulation,[status(thm)],[f5,f4]) ).
fof(f12,plain,
! [X0,X1,X2] : multiply(double_divide(X0,X1),multiply(X1,inverse(double_divide(X0,X2)))) = X2,
inference(forward_demodulation,[status(thm)],[f5,f11]) ).
fof(f13,plain,
! [X0,X1,X2] : multiply(double_divide(X0,X1),multiply(X1,multiply(X2,X0))) = X2,
inference(forward_demodulation,[status(thm)],[f5,f12]) ).
fof(f14,plain,
! [X0,X1,X2] : multiply(double_divide(multiply(X0,X1),double_divide(X1,X2)),X0) = X2,
inference(paramodulation,[status(thm)],[f13,f13]) ).
fof(f15,plain,
! [X0,X1,X2,X3] : multiply(double_divide(multiply(X0,multiply(X1,X2)),X3),multiply(X3,X1)) = double_divide(X2,X0),
inference(paramodulation,[status(thm)],[f13,f13]) ).
fof(f34,plain,
! [X0,X1,X2] : X0 = double_divide(X1,multiply(double_divide(multiply(X2,X1),X0),X2)),
inference(paramodulation,[status(thm)],[f14,f15]) ).
fof(f59,plain,
! [X0,X1,X2] : X0 = double_divide(multiply(X1,X2),double_divide(X2,multiply(X0,X1))),
inference(paramodulation,[status(thm)],[f15,f34]) ).
fof(f62,plain,
! [X0,X1,X2,X3] : multiply(double_divide(multiply(X0,multiply(X1,X2)),X3),X0) = double_divide(X2,multiply(X3,X1)),
inference(paramodulation,[status(thm)],[f34,f34]) ).
fof(f68,plain,
! [X0,X1,X2,X3,X4] : multiply(X0,multiply(multiply(double_divide(multiply(X1,multiply(X2,multiply(X3,X4))),X0),X1),X3)) = double_divide(X4,X2),
inference(paramodulation,[status(thm)],[f34,f15]) ).
fof(f75,plain,
! [X0,X1,X2] : multiply(multiply(double_divide(multiply(X0,X1),X2),X0),X1) = inverse(X2),
inference(paramodulation,[status(thm)],[f34,f5]) ).
fof(f76,plain,
! [X0,X1,X2,X3] : multiply(X0,multiply(double_divide(multiply(X1,X2),multiply(X0,X3)),X1)) = double_divide(X2,X3),
inference(forward_demodulation,[status(thm)],[f62,f68]) ).
fof(f137,plain,
! [X0,X1,X2,X3] : multiply(double_divide(X0,multiply(double_divide(multiply(X1,multiply(X2,X0)),X3),X1)),inverse(X3)) = X2,
inference(paramodulation,[status(thm)],[f75,f13]) ).
fof(f139,plain,
! [X0,X1,X2,X3] : X0 = double_divide(inverse(X1),double_divide(X2,multiply(X0,multiply(double_divide(multiply(X3,X2),X1),X3)))),
inference(paramodulation,[status(thm)],[f75,f59]) ).
fof(f143,plain,
! [X0,X1,X2,X3] : multiply(double_divide(inverse(X0),double_divide(X1,X2)),multiply(double_divide(multiply(X3,X1),X0),X3)) = X2,
inference(paramodulation,[status(thm)],[f75,f14]) ).
fof(f151,plain,
! [X0,X1,X2] : multiply(double_divide(X0,double_divide(X0,multiply(X1,X2))),inverse(X1)) = X2,
inference(forward_demodulation,[status(thm)],[f62,f137]) ).
fof(f160,plain,
! [X0,X1,X2] : double_divide(multiply(inverse(X0),X1),multiply(X0,X2)) = double_divide(X1,X2),
inference(paramodulation,[status(thm)],[f151,f34]) ).
fof(f213,plain,
! [X0,X1,X2] : multiply(X0,X1) = double_divide(X2,multiply(double_divide(X2,X1),inverse(X0))),
inference(paramodulation,[status(thm)],[f160,f34]) ).
fof(f245,plain,
! [X0,X1,X2] : multiply(X0,double_divide(X1,X2)) = double_divide(multiply(inverse(X0),X1),X2),
inference(paramodulation,[status(thm)],[f14,f213]) ).
fof(f247,plain,
! [X0,X1,X2,X3] : multiply(X0,multiply(X1,X2)) = double_divide(multiply(inverse(X1),X3),multiply(double_divide(X3,X2),inverse(X0))),
inference(paramodulation,[status(thm)],[f160,f213]) ).
fof(f249,plain,
! [X0,X1,X2,X3] : multiply(X0,multiply(double_divide(multiply(X1,X2),X3),X1)) = double_divide(X2,multiply(X3,inverse(X0))),
inference(paramodulation,[status(thm)],[f34,f213]) ).
fof(f250,plain,
! [X0,X1,X2,X3] : multiply(X0,multiply(double_divide(X1,X2),inverse(X3))) = double_divide(X1,multiply(multiply(X3,X2),inverse(X0))),
inference(paramodulation,[status(thm)],[f213,f213]) ).
fof(f266,plain,
! [X0,X1,X2,X3] : multiply(X0,multiply(X1,X2)) = multiply(X1,double_divide(X3,multiply(double_divide(X3,X2),inverse(X0)))),
inference(forward_demodulation,[status(thm)],[f245,f247]) ).
fof(f268,plain,
! [X0,X1,X2] : multiply(X0,multiply(double_divide(X1,X0),multiply(X2,X1))) = X2,
inference(backward_demodulation,[status(thm)],[f283,f13]) ).
fof(f283,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = multiply(X1,multiply(X0,X2)),
inference(forward_demodulation,[status(thm)],[f213,f266]) ).
fof(f284,plain,
! [X0,X1,X2] : double_divide(X0,multiply(X1,inverse(double_divide(inverse(X1),double_divide(X0,X2))))) = X2,
inference(backward_demodulation,[status(thm)],[f249,f143]) ).
fof(f287,plain,
! [X0,X1,X2] : double_divide(X0,multiply(multiply(X1,X2),inverse(X1))) = double_divide(X0,X2),
inference(backward_demodulation,[status(thm)],[f249,f76]) ).
fof(f288,plain,
! [X0,X1,X2] : X0 = double_divide(inverse(X1),double_divide(X2,double_divide(X2,multiply(X1,inverse(X0))))),
inference(backward_demodulation,[status(thm)],[f249,f139]) ).
fof(f323,plain,
! [X0,X1,X2] : double_divide(X0,multiply(X1,multiply(double_divide(X0,X2),inverse(X1)))) = X2,
inference(forward_demodulation,[status(thm)],[f5,f284]) ).
fof(f324,plain,
! [X0,X1,X2] : double_divide(X0,double_divide(X0,multiply(multiply(X1,X2),inverse(X1)))) = X2,
inference(forward_demodulation,[status(thm)],[f250,f323]) ).
fof(f327,plain,
! [X0,X1] : double_divide(X0,double_divide(X0,X1)) = X1,
inference(backward_demodulation,[status(thm)],[f287,f324]) ).
fof(f346,plain,
! [X0,X1] : X0 = double_divide(inverse(X1),multiply(X1,inverse(X0))),
inference(backward_demodulation,[status(thm)],[f327,f288]) ).
fof(f368,plain,
! [X0,X1,X2] : double_divide(multiply(X0,X1),X2) = double_divide(X1,multiply(X2,X0)),
inference(paramodulation,[status(thm)],[f59,f327]) ).
fof(f371,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = inverse(double_divide(multiply(X1,X2),X0)),
inference(paramodulation,[status(thm)],[f327,f75]) ).
fof(f375,plain,
! [X0,X1] : multiply(double_divide(X0,X1),X0) = inverse(X1),
inference(paramodulation,[status(thm)],[f327,f5]) ).
fof(f380,plain,
! [X0,X1,X2] : multiply(X0,double_divide(X1,X2)) = double_divide(X1,multiply(X2,inverse(X0))),
inference(backward_demodulation,[status(thm)],[f368,f245]) ).
fof(f407,plain,
multiply(inverse(b2),multiply(b2,a2)) != a2,
inference(backward_demodulation,[status(thm)],[f428,f6]) ).
fof(f428,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(forward_demodulation,[status(thm)],[f5,f371]) ).
fof(f436,plain,
! [X0,X1] : X0 = multiply(X0,double_divide(inverse(X1),X1)),
inference(backward_demodulation,[status(thm)],[f380,f346]) ).
fof(f464,plain,
multiply(b2,multiply(inverse(b2),a2)) != a2,
inference(forward_demodulation,[status(thm)],[f283,f407]) ).
fof(f483,plain,
! [X0,X1] : double_divide(double_divide(inverse(X0),X0),X1) = inverse(X1),
inference(paramodulation,[status(thm)],[f436,f375]) ).
fof(f507,plain,
! [X0,X1,X2] : multiply(X0,multiply(double_divide(double_divide(inverse(X1),X1),X0),X2)) = X2,
inference(paramodulation,[status(thm)],[f436,f268]) ).
fof(f517,plain,
a2 != a2,
inference(backward_demodulation,[status(thm)],[f519,f464]) ).
fof(f519,plain,
! [X0,X1] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(forward_demodulation,[status(thm)],[f483,f507]) ).
fof(f520,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f517]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP610-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n017.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 20 20:13:11 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.08/0.43 % Refutation found
% 0.08/0.43 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.08/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.08/0.44 % Elapsed time: 0.076912 seconds
% 0.08/0.44 % CPU time: 0.461043 seconds
% 0.08/0.44 % Total memory used: 22.624 MB
% 0.08/0.44 % Net memory used: 22.094 MB
%------------------------------------------------------------------------------