%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP524-1 : 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 12:34:35 PM UTC 2026
% Result : Unsatisfiable 0.08s 5.39s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 32 ( 32 unt; 2 def)
% Number of atoms : 32 ( 31 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 7 ( 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 : 50 ( 50 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : divide(A,divide(B,divide(C,divide(A,B)))) = C,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B,C] : multiply(A,B) = divide(A,divide(divide(C,C),B)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A,B] : inverse(A) = divide(divide(B,B),A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
multiply(a,b) != multiply(b,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,plain,
! [X0,X1,X2] : divide(X0,divide(X1,divide(X2,divide(X0,X1)))) = X2,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f6,plain,
! [X0,X1,X2] : multiply(X0,X1) = divide(X0,divide(divide(X2,X2),X1)),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f7,plain,
! [X0,X1] : inverse(X0) = divide(divide(X1,X1),X0),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f8,plain,
multiply(a,b) != multiply(b,a),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f9,definition,
sF0_fnc = multiply(a,b),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f10,definition,
sF1_fnc = multiply(b,a),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f11,plain,
sF0_fnc != sF1_fnc,
inference(definition_folding,[],[f8,f10,f9]) ).
fof(f343,plain,
! [X0,X1] : multiply(X0,X1) = divide(X0,inverse(X1)),
inference(backward_demodulation,[status(thm)],[f7,f6]) ).
fof(f361,plain,
! [X0,X1] : inverse(X0) = divide(multiply(inverse(X1),X1),X0),
inference(paramodulation,[status(thm)],[f343,f7]) ).
fof(f396,plain,
! [X0,X1,X2] : inverse(divide(X0,divide(X1,divide(multiply(inverse(X2),X2),X0)))) = X1,
inference(paramodulation,[status(thm)],[f361,f5]) ).
fof(f401,plain,
! [X0,X1,X2] : divide(X0,inverse(divide(X1,divide(X0,divide(X2,X2))))) = X1,
inference(paramodulation,[status(thm)],[f7,f5]) ).
fof(f404,plain,
! [X0,X1,X2] : divide(X0,divide(X1,inverse(divide(X0,X1)))) = divide(X2,X2),
inference(paramodulation,[status(thm)],[f7,f5]) ).
fof(f414,plain,
! [X0,X1] : inverse(divide(X0,divide(X1,inverse(X0)))) = X1,
inference(forward_demodulation,[status(thm)],[f361,f396]) ).
fof(f415,plain,
! [X0,X1] : inverse(divide(X0,multiply(X1,X0))) = X1,
inference(forward_demodulation,[status(thm)],[f343,f414]) ).
fof(f423,plain,
! [X0,X1,X2] : multiply(X0,divide(X1,divide(X0,divide(X2,X2)))) = X1,
inference(forward_demodulation,[status(thm)],[f343,f401]) ).
fof(f426,plain,
! [X0,X1,X2] : divide(X0,multiply(X1,divide(X0,X1))) = divide(X2,X2),
inference(forward_demodulation,[status(thm)],[f343,f404]) ).
fof(f443,plain,
inverse(divide(a,sF1_fnc)) = b,
inference(paramodulation,[status(thm)],[f10,f415]) ).
fof(f454,plain,
! [X0,X1] : multiply(X0,divide(X1,X0)) = X1,
inference(paramodulation,[status(thm)],[f5,f423]) ).
fof(f476,plain,
! [X0] : multiply(X0,divide(a,sF1_fnc)) = divide(X0,b),
inference(paramodulation,[status(thm)],[f443,f343]) ).
fof(f496,plain,
divide(sF1_fnc,b) = a,
inference(paramodulation,[status(thm)],[f476,f454]) ).
fof(f510,plain,
! [X0,X1] : divide(X0,X0) = divide(X1,X1),
inference(forward_demodulation,[status(thm)],[f454,f426]) ).
fof(f530,plain,
! [X0,X1] : multiply(X0,divide(X1,X1)) = X0,
inference(paramodulation,[status(thm)],[f510,f454]) ).
fof(f592,plain,
! [X0,X1] : divide(X0,divide(X1,X1)) = X0,
inference(paramodulation,[status(thm)],[f423,f530]) ).
fof(f635,plain,
! [X0,X1] : divide(X0,divide(X0,X1)) = X1,
inference(paramodulation,[status(thm)],[f592,f5]) ).
fof(f677,plain,
divide(sF1_fnc,a) = b,
inference(paramodulation,[status(thm)],[f496,f635]) ).
fof(f710,plain,
multiply(a,b) = sF1_fnc,
inference(paramodulation,[status(thm)],[f677,f454]) ).
fof(f712,plain,
sF0_fnc = sF1_fnc,
inference(forward_demodulation,[status(thm)],[f9,f710]) ).
fof(f713,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f712,f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP524-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/5.37 % Computer : n002.cluster.edu
% 0.08/5.37 % Model : x86_64 x86_64
% 0.08/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.37 % Memory : 8046.5625MB
% 0.08/5.37 % OS : Linux 6.8.0-71-generic
% 0.08/5.37 % CPULimit : 300
% 0.08/5.37 % WCLimit : 300
% 0.08/5.37 % DateTime : Sun Sep 20 20:18:25 UTC 2026
% 0.08/5.37 % CPUTime :
% 0.08/5.38 % Drodi V4.1.1
% 0.08/5.39 % Refutation found
% 0.08/5.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.08/5.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/5.41 % Elapsed time: 0.033181 seconds
% 0.14/5.41 % CPU time: 0.126718 seconds
% 0.14/5.41 % Total memory used: 5.238 MB
% 0.14/5.41 % Net memory used: 5.158 MB
%------------------------------------------------------------------------------