%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP576-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.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 12:34:42 PM UTC 2026
% Result : Unsatisfiable 0.07s 0.36s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 7
% Syntax : Number of formulae : 80 ( 80 unt; 2 def)
% Number of atoms : 80 ( 79 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 121 ( 121 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : double_divide(double_divide(A,double_divide(double_divide(B,double_divide(C,A)),double_divide(C,identity))),double_divide(identity,identity)) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] : multiply(A,B) = double_divide(double_divide(B,A),identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A] : inverse(A) = double_divide(A,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A] : identity = double_divide(A,inverse(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
multiply(a,b) != multiply(b,a),
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(X2,X0)),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(a,b) != multiply(b,a),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f11,definition,
sF0_fnc = multiply(a,b),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f12,definition,
sF1_fnc = multiply(b,a),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f13,plain,
sF0_fnc != sF1_fnc,
inference(definition_folding,[],[f10,f12,f11]) ).
fof(f28,plain,
! [X0,X1] : multiply(X0,X1) = inverse(double_divide(X1,X0)),
inference(backward_demodulation,[status(thm)],[f8,f7]) ).
fof(f29,plain,
! [X0] : multiply(identity,X0) = inverse(inverse(X0)),
inference(paramodulation,[status(thm)],[f8,f28]) ).
fof(f35,plain,
! [X0,X1] : identity = double_divide(double_divide(X0,X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f28,f9]) ).
fof(f36,plain,
! [X0] : multiply(inverse(X0),X0) = inverse(identity),
inference(paramodulation,[status(thm)],[f9,f28]) ).
fof(f44,plain,
identity = double_divide(double_divide(b,a),sF0_fnc),
inference(paramodulation,[status(thm)],[f11,f35]) ).
fof(f53,plain,
multiply(sF0_fnc,double_divide(b,a)) = inverse(identity),
inference(paramodulation,[status(thm)],[f44,f28]) ).
fof(f85,plain,
! [X0,X1,X2] : double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(X2,X0)),inverse(X2))),double_divide(identity,identity)) = X1,
inference(forward_demodulation,[status(thm)],[f8,f6]) ).
fof(f86,plain,
! [X0,X1,X2] : double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(X2,X0)),inverse(X2))),inverse(identity)) = X1,
inference(forward_demodulation,[status(thm)],[f8,f85]) ).
fof(f89,plain,
! [X0,X1,X2,X3] : double_divide(double_divide(inverse(identity),double_divide(double_divide(X0,X1),inverse(double_divide(X2,double_divide(double_divide(X1,double_divide(X3,X2)),inverse(X3)))))),inverse(identity)) = X0,
inference(paramodulation,[status(thm)],[f86,f86]) ).
fof(f91,plain,
! [X0,X1] : double_divide(double_divide(inverse(X0),double_divide(double_divide(X1,identity),inverse(X0))),inverse(identity)) = X1,
inference(paramodulation,[status(thm)],[f9,f86]) ).
fof(f93,plain,
! [X0,X1,X2,X3] : double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(double_divide(X2,X3),X0)),multiply(X3,X2))),inverse(identity)) = X1,
inference(paramodulation,[status(thm)],[f28,f86]) ).
fof(f103,plain,
! [X0,X1,X2,X3] : double_divide(double_divide(inverse(identity),double_divide(double_divide(X0,X1),multiply(double_divide(double_divide(X1,double_divide(X2,X3)),inverse(X2)),X3))),inverse(identity)) = X0,
inference(forward_demodulation,[status(thm)],[f28,f89]) ).
fof(f106,plain,
! [X0,X1] : double_divide(double_divide(inverse(X0),double_divide(inverse(X1),inverse(X0))),inverse(identity)) = X1,
inference(forward_demodulation,[status(thm)],[f8,f91]) ).
fof(f120,plain,
! [X0] : double_divide(double_divide(inverse(inverse(X0)),identity),inverse(identity)) = X0,
inference(paramodulation,[status(thm)],[f9,f106]) ).
fof(f128,plain,
! [X0] : double_divide(inverse(inverse(inverse(X0))),inverse(identity)) = X0,
inference(forward_demodulation,[status(thm)],[f8,f120]) ).
fof(f132,plain,
! [X0] : double_divide(double_divide(inverse(identity),X0),inverse(identity)) = inverse(inverse(X0)),
inference(paramodulation,[status(thm)],[f128,f106]) ).
fof(f136,plain,
! [X0] : multiply(inverse(identity),inverse(inverse(inverse(X0)))) = inverse(X0),
inference(paramodulation,[status(thm)],[f128,f28]) ).
fof(f162,plain,
! [X0] : X0 = inverse(inverse(double_divide(inverse(X0),inverse(identity)))),
inference(paramodulation,[status(thm)],[f106,f132]) ).
fof(f164,plain,
double_divide(identity,inverse(identity)) = inverse(inverse(inverse(inverse(identity)))),
inference(paramodulation,[status(thm)],[f9,f132]) ).
fof(f173,plain,
! [X0] : X0 = inverse(multiply(inverse(identity),inverse(X0))),
inference(forward_demodulation,[status(thm)],[f28,f162]) ).
fof(f175,plain,
identity = inverse(inverse(inverse(inverse(identity)))),
inference(forward_demodulation,[status(thm)],[f9,f164]) ).
fof(f199,plain,
multiply(inverse(identity),identity) = inverse(inverse(identity)),
inference(paramodulation,[status(thm)],[f175,f136]) ).
fof(f214,plain,
inverse(identity) = inverse(inverse(identity)),
inference(forward_demodulation,[status(thm)],[f36,f199]) ).
fof(f226,plain,
! [X0,X1,X2,X3] : inverse(inverse(double_divide(double_divide(X0,X1),multiply(double_divide(double_divide(X1,double_divide(X2,X3)),inverse(X2)),X3)))) = X0,
inference(forward_demodulation,[status(thm)],[f132,f103]) ).
fof(f227,plain,
! [X0,X1,X2,X3] : inverse(multiply(multiply(double_divide(double_divide(X0,double_divide(X1,X2)),inverse(X1)),X2),double_divide(X3,X0))) = X3,
inference(forward_demodulation,[status(thm)],[f28,f226]) ).
fof(f513,plain,
identity = inverse(inverse(inverse(identity))),
inference(backward_demodulation,[status(thm)],[f214,f175]) ).
fof(f530,plain,
identity = inverse(inverse(identity)),
inference(forward_demodulation,[status(thm)],[f214,f513]) ).
fof(f531,plain,
identity = inverse(identity),
inference(forward_demodulation,[status(thm)],[f214,f530]) ).
fof(f555,plain,
! [X0,X1,X2,X3] : double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(double_divide(X2,X3),X0)),multiply(X3,X2))),identity) = X1,
inference(backward_demodulation,[status(thm)],[f531,f93]) ).
fof(f557,plain,
! [X0] : X0 = inverse(multiply(identity,inverse(X0))),
inference(backward_demodulation,[status(thm)],[f531,f173]) ).
fof(f558,plain,
! [X0] : double_divide(double_divide(inverse(identity),X0),identity) = inverse(inverse(X0)),
inference(backward_demodulation,[status(thm)],[f531,f132]) ).
fof(f565,plain,
! [X0,X1,X2] : double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(X2,X0)),inverse(X2))),identity) = X1,
inference(backward_demodulation,[status(thm)],[f531,f86]) ).
fof(f566,plain,
multiply(sF0_fnc,double_divide(b,a)) = identity,
inference(backward_demodulation,[status(thm)],[f531,f53]) ).
fof(f569,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(backward_demodulation,[status(thm)],[f531,f36]) ).
fof(f580,plain,
! [X0,X1,X2,X3] : inverse(double_divide(X0,double_divide(double_divide(X1,double_divide(double_divide(X2,X3),X0)),multiply(X3,X2)))) = X1,
inference(forward_demodulation,[status(thm)],[f8,f555]) ).
fof(f581,plain,
! [X0,X1,X2,X3] : multiply(double_divide(double_divide(X0,double_divide(double_divide(X1,X2),X3)),multiply(X2,X1)),X3) = X0,
inference(forward_demodulation,[status(thm)],[f28,f580]) ).
fof(f584,plain,
! [X0] : X0 = inverse(inverse(inverse(inverse(X0)))),
inference(forward_demodulation,[status(thm)],[f29,f557]) ).
fof(f585,plain,
! [X0] : inverse(double_divide(inverse(identity),X0)) = inverse(inverse(X0)),
inference(forward_demodulation,[status(thm)],[f8,f558]) ).
fof(f586,plain,
! [X0] : multiply(X0,inverse(identity)) = inverse(inverse(X0)),
inference(forward_demodulation,[status(thm)],[f28,f585]) ).
fof(f587,plain,
! [X0] : multiply(X0,identity) = inverse(inverse(X0)),
inference(forward_demodulation,[status(thm)],[f531,f586]) ).
fof(f597,plain,
! [X0,X1,X2] : inverse(double_divide(X0,double_divide(double_divide(X1,double_divide(X2,X0)),inverse(X2)))) = X1,
inference(forward_demodulation,[status(thm)],[f8,f565]) ).
fof(f598,plain,
! [X0,X1,X2] : multiply(double_divide(double_divide(X0,double_divide(X1,X2)),inverse(X1)),X2) = X0,
inference(forward_demodulation,[status(thm)],[f28,f597]) ).
fof(f616,plain,
! [X0] : multiply(X0,inverse(inverse(inverse(X0)))) = identity,
inference(paramodulation,[status(thm)],[f584,f569]) ).
fof(f618,plain,
! [X0] : identity = double_divide(inverse(inverse(inverse(X0))),X0),
inference(paramodulation,[status(thm)],[f584,f9]) ).
fof(f635,plain,
! [X0,X1] : inverse(multiply(X0,double_divide(X1,X0))) = X1,
inference(backward_demodulation,[status(thm)],[f598,f227]) ).
fof(f794,plain,
! [X0,X1] : multiply(double_divide(double_divide(X0,identity),inverse(inverse(inverse(inverse(X1))))),X1) = X0,
inference(paramodulation,[status(thm)],[f618,f598]) ).
fof(f804,plain,
! [X0,X1] : multiply(double_divide(inverse(X0),inverse(inverse(inverse(inverse(X1))))),X1) = X0,
inference(forward_demodulation,[status(thm)],[f8,f794]) ).
fof(f805,plain,
! [X0,X1] : multiply(double_divide(inverse(X0),X1),X1) = X0,
inference(forward_demodulation,[status(thm)],[f584,f804]) ).
fof(f838,plain,
! [X0,X1] : multiply(double_divide(double_divide(X0,double_divide(identity,X1)),multiply(sF0_fnc,double_divide(b,a))),X1) = X0,
inference(paramodulation,[status(thm)],[f44,f581]) ).
fof(f875,plain,
! [X0,X1] : multiply(double_divide(double_divide(X0,double_divide(identity,X1)),identity),X1) = X0,
inference(forward_demodulation,[status(thm)],[f566,f838]) ).
fof(f876,plain,
! [X0,X1] : multiply(inverse(double_divide(X0,double_divide(identity,X1))),X1) = X0,
inference(forward_demodulation,[status(thm)],[f8,f875]) ).
fof(f877,plain,
! [X0,X1] : multiply(multiply(double_divide(identity,X0),X1),X0) = X1,
inference(forward_demodulation,[status(thm)],[f28,f876]) ).
fof(f932,plain,
! [X0] : multiply(identity,X0) = inverse(inverse(inverse(double_divide(identity,X0)))),
inference(paramodulation,[status(thm)],[f616,f877]) ).
fof(f945,plain,
! [X0] : inverse(inverse(X0)) = inverse(inverse(inverse(double_divide(identity,X0)))),
inference(forward_demodulation,[status(thm)],[f29,f932]) ).
fof(f946,plain,
! [X0] : inverse(inverse(X0)) = inverse(inverse(multiply(X0,identity))),
inference(forward_demodulation,[status(thm)],[f28,f945]) ).
fof(f947,plain,
! [X0] : inverse(inverse(X0)) = inverse(inverse(inverse(inverse(X0)))),
inference(forward_demodulation,[status(thm)],[f587,f946]) ).
fof(f948,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f584,f947]) ).
fof(f966,plain,
! [X0,X1] : inverse(X0) = multiply(X1,double_divide(X0,X1)),
inference(paramodulation,[status(thm)],[f635,f948]) ).
fof(f969,plain,
! [X0,X1] : inverse(multiply(X0,X1)) = double_divide(X1,X0),
inference(paramodulation,[status(thm)],[f28,f948]) ).
fof(f970,plain,
! [X0,X1] : multiply(double_divide(X0,X1),X1) = inverse(X0),
inference(paramodulation,[status(thm)],[f948,f805]) ).
fof(f1104,plain,
! [X0,X1] : inverse(inverse(X0)) = double_divide(double_divide(X0,X1),X1),
inference(paramodulation,[status(thm)],[f966,f969]) ).
fof(f1119,plain,
! [X0,X1] : X0 = double_divide(double_divide(X0,X1),X1),
inference(forward_demodulation,[status(thm)],[f948,f1104]) ).
fof(f1181,plain,
! [X0,X1] : multiply(X0,X1) = inverse(double_divide(X0,X1)),
inference(paramodulation,[status(thm)],[f1119,f970]) ).
fof(f1202,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(forward_demodulation,[status(thm)],[f28,f1181]) ).
fof(f1213,plain,
sF1_fnc = multiply(a,b),
inference(paramodulation,[status(thm)],[f12,f1202]) ).
fof(f1248,plain,
sF1_fnc = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f11,f1213]) ).
fof(f1249,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1248,f13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP576-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n010.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Sun Sep 20 20:17:25 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 % Drodi V4.1.1
% 0.07/0.36 % Refutation found
% 0.07/0.36 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.07/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.43/1.60 % Elapsed time: 1.034814 seconds
% 1.43/1.60 % CPU time: 0.098243 seconds
% 1.43/1.60 % Total memory used: 4.930 MB
% 1.43/1.60 % Net memory used: 4.686 MB
%------------------------------------------------------------------------------