%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP607-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.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 0.13s 0.39s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 3
% Syntax : Number of formulae : 71 ( 71 unt; 0 def)
% Number of atoms : 71 ( 70 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 7 ( 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 : 166 ( 166 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : double_divide(inverse(double_divide(A,inverse(double_divide(inverse(B),double_divide(A,C))))),C) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] : multiply(A,B) = inverse(double_divide(B,A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,plain,
! [X0,X1,X2] : double_divide(inverse(double_divide(X0,inverse(double_divide(inverse(X1),double_divide(X0,X2))))),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(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f12,plain,
! [X0,X1,X2] : double_divide(inverse(double_divide(X0,multiply(double_divide(X0,X1),inverse(X2)))),X1) = X2,
inference(backward_demodulation,[status(thm)],[f5,f4]) ).
fof(f13,plain,
! [X0,X1,X2] : double_divide(multiply(multiply(double_divide(X0,X1),inverse(X2)),X0),X1) = X2,
inference(forward_demodulation,[status(thm)],[f5,f12]) ).
fof(f14,plain,
! [X0,X1,X2,X3] : double_divide(multiply(multiply(X0,inverse(X1)),multiply(multiply(double_divide(X2,X3),inverse(X0)),X2)),X3) = X1,
inference(paramodulation,[status(thm)],[f13,f13]) ).
fof(f15,plain,
! [X0,X1,X2,X3] : double_divide(multiply(multiply(double_divide(X0,X1),multiply(X2,X3)),X0),X1) = double_divide(X3,X2),
inference(paramodulation,[status(thm)],[f5,f13]) ).
fof(f16,plain,
! [X0,X1,X2] : multiply(X0,multiply(multiply(double_divide(X1,X0),inverse(X2)),X1)) = inverse(X2),
inference(paramodulation,[status(thm)],[f13,f5]) ).
fof(f18,plain,
! [X0,X1,X2,X3] : multiply(X0,multiply(multiply(double_divide(X1,X0),multiply(X2,X3)),X1)) = inverse(double_divide(X3,X2)),
inference(paramodulation,[status(thm)],[f5,f16]) ).
fof(f19,plain,
! [X0,X1,X2,X3] : multiply(X0,multiply(multiply(double_divide(X1,X0),multiply(X2,X3)),X1)) = multiply(X2,X3),
inference(forward_demodulation,[status(thm)],[f5,f18]) ).
fof(f27,plain,
! [X0,X1] : double_divide(inverse(X0),multiply(X0,inverse(X1))) = X1,
inference(paramodulation,[status(thm)],[f16,f14]) ).
fof(f42,plain,
! [X0,X1] : multiply(multiply(X0,inverse(X1)),inverse(X0)) = inverse(X1),
inference(paramodulation,[status(thm)],[f27,f5]) ).
fof(f46,plain,
! [X0,X1] : double_divide(inverse(multiply(X0,inverse(X1))),inverse(X1)) = X0,
inference(paramodulation,[status(thm)],[f42,f27]) ).
fof(f51,plain,
! [X0,X1] : double_divide(inverse(inverse(X0)),inverse(X1)) = multiply(X1,inverse(X0)),
inference(paramodulation,[status(thm)],[f42,f46]) ).
fof(f61,plain,
! [X0,X1,X2] : double_divide(inverse(multiply(X0,X1)),inverse(X2)) = multiply(X2,inverse(double_divide(X1,X0))),
inference(paramodulation,[status(thm)],[f5,f51]) ).
fof(f68,plain,
! [X0,X1] : multiply(X0,multiply(X1,inverse(X0))) = X1,
inference(backward_demodulation,[status(thm)],[f69,f46]) ).
fof(f69,plain,
! [X0,X1,X2] : double_divide(inverse(multiply(X0,X1)),inverse(X2)) = multiply(X2,multiply(X0,X1)),
inference(forward_demodulation,[status(thm)],[f5,f61]) ).
fof(f71,plain,
! [X0,X1] : inverse(X0) = multiply(double_divide(inverse(X1),X1),inverse(X0)),
inference(paramodulation,[status(thm)],[f16,f68]) ).
fof(f73,plain,
! [X0,X1,X2] : multiply(double_divide(X0,X1),multiply(X2,multiply(X1,X0))) = X2,
inference(paramodulation,[status(thm)],[f5,f68]) ).
fof(f74,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = multiply(X1,inverse(double_divide(X2,X0))),
inference(paramodulation,[status(thm)],[f68,f19]) ).
fof(f80,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = multiply(X1,multiply(X0,X2)),
inference(forward_demodulation,[status(thm)],[f5,f74]) ).
fof(f89,plain,
! [X0,X1] : multiply(double_divide(inverse(X0),X1),X1) = X0,
inference(paramodulation,[status(thm)],[f68,f73]) ).
fof(f101,plain,
! [X0,X1,X2] : double_divide(multiply(multiply(X0,inverse(X1)),multiply(X2,inverse(X2))),inverse(X0)) = X1,
inference(paramodulation,[status(thm)],[f89,f14]) ).
fof(f102,plain,
! [X0,X1] : double_divide(multiply(X0,inverse(X0)),inverse(X1)) = X1,
inference(paramodulation,[status(thm)],[f89,f13]) ).
fof(f103,plain,
! [X0,X1] : multiply(X0,X1) = double_divide(inverse(X1),inverse(X0)),
inference(paramodulation,[status(thm)],[f89,f68]) ).
fof(f105,plain,
! [X0,X1] : double_divide(inverse(double_divide(inverse(X0),inverse(X1))),X0) = X1,
inference(paramodulation,[status(thm)],[f89,f27]) ).
fof(f107,plain,
! [X0,X1,X2] : multiply(double_divide(X0,X1),X2) = double_divide(inverse(X2),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f89,f73]) ).
fof(f112,plain,
! [X0,X1] : double_divide(multiply(inverse(X0),inverse(X1)),X1) = X0,
inference(forward_demodulation,[status(thm)],[f5,f105]) ).
fof(f119,plain,
! [X0,X1,X2] : double_divide(multiply(X0,inverse(X0)),multiply(X1,X2)) = double_divide(X2,X1),
inference(paramodulation,[status(thm)],[f5,f102]) ).
fof(f126,plain,
! [X0,X1,X2] : multiply(X0,double_divide(X1,X2)) = double_divide(multiply(X2,X1),inverse(X0)),
inference(paramodulation,[status(thm)],[f5,f103]) ).
fof(f128,plain,
! [X0,X1] : multiply(multiply(X0,X1),inverse(X0)) = X1,
inference(paramodulation,[status(thm)],[f103,f89]) ).
fof(f132,plain,
! [X0,X1] : multiply(inverse(X0),inverse(X1)) = inverse(multiply(X0,X1)),
inference(paramodulation,[status(thm)],[f103,f5]) ).
fof(f139,plain,
! [X0,X1,X2] : multiply(X0,double_divide(multiply(X1,inverse(X1)),multiply(X0,inverse(X2)))) = X2,
inference(backward_demodulation,[status(thm)],[f126,f101]) ).
fof(f151,plain,
! [X0,X1] : double_divide(inverse(multiply(X0,X1)),X1) = X0,
inference(backward_demodulation,[status(thm)],[f132,f112]) ).
fof(f156,plain,
! [X0,X1] : multiply(X0,double_divide(inverse(X1),X0)) = X1,
inference(forward_demodulation,[status(thm)],[f119,f139]) ).
fof(f160,plain,
! [X0,X1,X2] : multiply(double_divide(double_divide(inverse(X0),X1),X1),multiply(X2,X0)) = X2,
inference(paramodulation,[status(thm)],[f156,f73]) ).
fof(f163,plain,
! [X0,X1,X2] : double_divide(multiply(X0,X1),X2) = double_divide(multiply(X2,X1),X0),
inference(paramodulation,[status(thm)],[f73,f15]) ).
fof(f171,plain,
! [X0,X1,X2,X3] : double_divide(multiply(multiply(double_divide(X0,X1),X2),X0),X1) = double_divide(double_divide(inverse(X2),X3),X3),
inference(paramodulation,[status(thm)],[f156,f15]) ).
fof(f177,plain,
! [X0,X1,X2,X3] : double_divide(multiply(X0,X1),multiply(double_divide(X1,X0),multiply(X2,X3))) = double_divide(X3,X2),
inference(backward_demodulation,[status(thm)],[f163,f15]) ).
fof(f186,plain,
! [X0,X1,X2,X3] : double_divide(multiply(X0,X1),multiply(double_divide(X1,X0),X2)) = double_divide(double_divide(inverse(X2),X3),X3),
inference(forward_demodulation,[status(thm)],[f163,f171]) ).
fof(f220,plain,
! [X0,X1] : multiply(X0,inverse(X1)) = double_divide(inverse(X0),X1),
inference(paramodulation,[status(thm)],[f156,f128]) ).
fof(f225,plain,
! [X0,X1,X2,X3] : double_divide(multiply(X0,X1),multiply(double_divide(X1,X0),X2)) = double_divide(inverse(X3),multiply(X3,X2)),
inference(paramodulation,[status(thm)],[f128,f177]) ).
fof(f230,plain,
! [X0,X1] : double_divide(inverse(multiply(X0,X1)),X0) = X1,
inference(backward_demodulation,[status(thm)],[f220,f128]) ).
fof(f234,plain,
! [X0,X1] : inverse(X0) = double_divide(inverse(double_divide(inverse(X1),X1)),X0),
inference(backward_demodulation,[status(thm)],[f220,f71]) ).
fof(f266,plain,
! [X0,X1,X2] : double_divide(double_divide(inverse(X0),X0),multiply(X1,X2)) = double_divide(X2,X1),
inference(backward_demodulation,[status(thm)],[f220,f119]) ).
fof(f269,plain,
! [X0,X1,X2,X3] : double_divide(multiply(X0,X1),multiply(double_divide(X1,X0),X2)) = multiply(double_divide(X2,X3),X3),
inference(forward_demodulation,[status(thm)],[f107,f225]) ).
fof(f276,plain,
! [X0,X1] : inverse(X0) = double_divide(multiply(X1,inverse(X1)),X0),
inference(forward_demodulation,[status(thm)],[f5,f234]) ).
fof(f277,plain,
! [X0,X1] : inverse(X0) = double_divide(double_divide(inverse(X1),X1),X0),
inference(forward_demodulation,[status(thm)],[f220,f276]) ).
fof(f354,plain,
! [X0,X1] : double_divide(double_divide(X0,X1),X1) = X0,
inference(backward_demodulation,[status(thm)],[f356,f230]) ).
fof(f355,plain,
! [X0,X1] : double_divide(double_divide(X0,X1),X0) = X1,
inference(backward_demodulation,[status(thm)],[f356,f151]) ).
fof(f356,plain,
! [X0,X1] : inverse(multiply(X0,X1)) = double_divide(X1,X0),
inference(forward_demodulation,[status(thm)],[f277,f266]) ).
fof(f360,plain,
! [X0,X1,X2] : double_divide(multiply(X0,X1),multiply(double_divide(X1,X0),X2)) = inverse(X2),
inference(backward_demodulation,[status(thm)],[f354,f186]) ).
fof(f361,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X1,X0)) = X1,
inference(backward_demodulation,[status(thm)],[f354,f160]) ).
fof(f363,plain,
! [X0,X1] : inverse(X0) = multiply(double_divide(X0,X1),X1),
inference(backward_demodulation,[status(thm)],[f360,f269]) ).
fof(f366,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(backward_demodulation,[status(thm)],[f363,f89]) ).
fof(f377,plain,
! [X0,X1] : multiply(inverse(X0),X1) = double_divide(inverse(X1),X0),
inference(paramodulation,[status(thm)],[f366,f103]) ).
fof(f378,plain,
! [X0,X1] : multiply(X0,inverse(X1)) = double_divide(X1,inverse(X0)),
inference(paramodulation,[status(thm)],[f366,f103]) ).
fof(f383,plain,
! [X0,X1] : double_divide(inverse(multiply(X0,X1)),X1) = X0,
inference(backward_demodulation,[status(thm)],[f377,f361]) ).
fof(f390,plain,
! [X0,X1] : double_divide(inverse(X0),X1) = double_divide(X1,inverse(X0)),
inference(forward_demodulation,[status(thm)],[f220,f378]) ).
fof(f396,plain,
! [X0,X1] : double_divide(X0,inverse(multiply(X1,X0))) = X1,
inference(forward_demodulation,[status(thm)],[f390,f383]) ).
fof(f398,plain,
! [X0,X1] : double_divide(X0,double_divide(X0,X1)) = X1,
inference(forward_demodulation,[status(thm)],[f356,f396]) ).
fof(f424,plain,
! [X0,X1] : double_divide(X0,X1) = double_divide(X1,X0),
inference(paramodulation,[status(thm)],[f398,f355]) ).
fof(f465,plain,
! [X0,X1] : multiply(X0,X1) = double_divide(inverse(X0),inverse(X1)),
inference(paramodulation,[status(thm)],[f103,f424]) ).
fof(f481,plain,
multiply(c3,multiply(a3,b3)) != multiply(a3,multiply(b3,c3)),
inference(backward_demodulation,[status(thm)],[f500,f6]) ).
fof(f500,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(forward_demodulation,[status(thm)],[f103,f465]) ).
fof(f506,plain,
multiply(a3,multiply(c3,b3)) != multiply(a3,multiply(b3,c3)),
inference(forward_demodulation,[status(thm)],[f80,f481]) ).
fof(f507,plain,
multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3)),
inference(forward_demodulation,[status(thm)],[f500,f506]) ).
fof(f508,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f507]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP607-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n008.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 20:18:39 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.13/0.39 % Refutation found
% 0.13/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.41 % Elapsed time: 0.040370 seconds
% 0.13/0.41 % CPU time: 0.147370 seconds
% 0.13/0.41 % Total memory used: 7.793 MB
% 0.13/0.41 % Net memory used: 7.485 MB
%------------------------------------------------------------------------------