%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP535-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 12:34:37 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.42s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of formulae : 45 ( 45 unt; 4 def)
% Number of atoms : 45 ( 44 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 6 ( 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 : 58 ( 58 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : divide(divide(A,divide(divide(A,B),C)),B) = C,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B,C] : multiply(A,B) = divide(A,divide(divide(C,C),B)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A,B] : inverse(A) = divide(divide(B,B),A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A] : identity = divide(A,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,plain,
! [X0,X1,X2] : divide(divide(X0,divide(divide(X0,X1),X2)),X1) = X2,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f7,plain,
! [X0,X1,X2] : multiply(X0,X1) = divide(X0,divide(divide(X2,X2),X1)),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f8,plain,
! [X0,X1] : inverse(X0) = divide(divide(X1,X1),X0),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f9,plain,
! [X0] : identity = divide(X0,X0),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f10,plain,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f11,definition,
sF1_fnc = multiply(a3,b3),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f12,definition,
sF0_fnc = multiply(sF1_fnc,c3),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f13,definition,
sF3_fnc = multiply(b3,c3),
introduced(definition,[new_symbols(definition,[sF3_fnc])],[function_definition]) ).
fof(f14,definition,
sF2_fnc = multiply(a3,sF3_fnc),
introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition]) ).
fof(f15,plain,
sF0_fnc != sF2_fnc,
inference(definition_folding,[],[f10,f14,f13,f12,f11]) ).
fof(f16,plain,
! [X0,X1,X2,X3] : multiply(X0,divide(divide(X1,X1),X2)) = divide(X0,multiply(divide(X3,X3),X2)),
inference(paramodulation,[status(thm)],[f7,f7]) ).
fof(f348,plain,
! [X0,X1,X2] : multiply(X0,divide(divide(X1,X1),X2)) = divide(X0,multiply(identity,X2)),
inference(backward_demodulation,[status(thm)],[f9,f16]) ).
fof(f349,plain,
! [X0,X1] : multiply(X0,X1) = divide(X0,divide(identity,X1)),
inference(backward_demodulation,[status(thm)],[f9,f7]) ).
fof(f355,plain,
! [X0,X1] : multiply(X0,divide(identity,X1)) = divide(X0,multiply(identity,X1)),
inference(forward_demodulation,[status(thm)],[f9,f348]) ).
fof(f356,plain,
! [X0] : inverse(X0) = divide(identity,X0),
inference(forward_demodulation,[status(thm)],[f9,f8]) ).
fof(f359,plain,
! [X0,X1] : multiply(X0,X1) = divide(X0,inverse(X1)),
inference(forward_demodulation,[status(thm)],[f356,f349]) ).
fof(f360,plain,
! [X0] : multiply(identity,X0) = inverse(inverse(X0)),
inference(paramodulation,[status(thm)],[f356,f359]) ).
fof(f361,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(paramodulation,[status(thm)],[f9,f359]) ).
fof(f381,plain,
! [X0,X1,X2] : multiply(divide(X0,divide(divide(X0,inverse(X1)),X2)),X1) = X2,
inference(paramodulation,[status(thm)],[f359,f6]) ).
fof(f391,plain,
! [X0,X1] : divide(divide(X0,divide(identity,X1)),X0) = X1,
inference(paramodulation,[status(thm)],[f9,f6]) ).
fof(f395,plain,
! [X0,X1,X2] : multiply(divide(X0,divide(multiply(X0,X1),X2)),X1) = X2,
inference(forward_demodulation,[status(thm)],[f359,f381]) ).
fof(f401,plain,
! [X0,X1] : divide(divide(X0,inverse(X1)),X0) = X1,
inference(forward_demodulation,[status(thm)],[f356,f391]) ).
fof(f402,plain,
! [X0,X1] : divide(multiply(X0,X1),X0) = X1,
inference(forward_demodulation,[status(thm)],[f359,f401]) ).
fof(f408,plain,
! [X0] : divide(identity,inverse(X0)) = X0,
inference(paramodulation,[status(thm)],[f361,f402]) ).
fof(f411,plain,
divide(sF2_fnc,a3) = sF3_fnc,
inference(paramodulation,[status(thm)],[f14,f402]) ).
fof(f412,plain,
divide(sF1_fnc,a3) = b3,
inference(paramodulation,[status(thm)],[f11,f402]) ).
fof(f418,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f356,f408]) ).
fof(f420,plain,
! [X0] : multiply(identity,X0) = X0,
inference(backward_demodulation,[status(thm)],[f418,f360]) ).
fof(f450,plain,
! [X0,X1] : multiply(X0,inverse(X1)) = divide(X0,multiply(identity,X1)),
inference(forward_demodulation,[status(thm)],[f356,f355]) ).
fof(f451,plain,
! [X0,X1] : multiply(X0,inverse(X1)) = divide(X0,X1),
inference(forward_demodulation,[status(thm)],[f420,f450]) ).
fof(f458,plain,
! [X0,X1] : divide(divide(X0,X1),X0) = inverse(X1),
inference(paramodulation,[status(thm)],[f451,f402]) ).
fof(f465,plain,
! [X0,X1] : multiply(divide(X0,X1),X1) = X0,
inference(paramodulation,[status(thm)],[f402,f395]) ).
fof(f472,plain,
! [X0] : multiply(divide(b3,divide(sF3_fnc,X0)),c3) = X0,
inference(paramodulation,[status(thm)],[f13,f395]) ).
fof(f542,plain,
multiply(b3,a3) = sF1_fnc,
inference(paramodulation,[status(thm)],[f412,f465]) ).
fof(f1022,plain,
divide(sF3_fnc,sF2_fnc) = inverse(a3),
inference(paramodulation,[status(thm)],[f411,f458]) ).
fof(f1256,plain,
multiply(divide(b3,inverse(a3)),c3) = sF2_fnc,
inference(paramodulation,[status(thm)],[f1022,f472]) ).
fof(f1267,plain,
multiply(multiply(b3,a3),c3) = sF2_fnc,
inference(forward_demodulation,[status(thm)],[f359,f1256]) ).
fof(f1268,plain,
multiply(sF1_fnc,c3) = sF2_fnc,
inference(forward_demodulation,[status(thm)],[f542,f1267]) ).
fof(f1269,plain,
sF0_fnc = sF2_fnc,
inference(forward_demodulation,[status(thm)],[f12,f1268]) ).
fof(f1270,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1269,f15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP535-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.40 % Computer : n001.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Sun Sep 20 20:21:42 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.41 % Drodi V4.1.1
% 0.14/0.42 % Refutation found
% 0.14/0.42 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.44/1.65 % Elapsed time: 1.027623 seconds
% 1.44/1.65 % CPU time: 0.133484 seconds
% 1.44/1.65 % Total memory used: 5.646 MB
% 1.44/1.65 % Net memory used: 5.519 MB
%------------------------------------------------------------------------------