%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP459-1 : 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 12:34:16 PM UTC 2026
% Result : Unsatisfiable 0.09s 0.53s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 9
% Syntax : Number of formulae : 64 ( 64 unt; 4 def)
% Number of atoms : 64 ( 63 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 : 8 ( 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 : 80 ( 80 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : divide(divide(divide(A,A),divide(A,divide(B,divide(divide(identity,A),C)))),C) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] : multiply(A,B) = divide(A,divide(identity,B)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A] : inverse(A) = divide(identity,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(divide(X0,X0),divide(X0,divide(X1,divide(divide(identity,X0),X2)))),X2) = X1,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f7,plain,
! [X0,X1] : multiply(X0,X1) = divide(X0,divide(identity,X1)),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f8,plain,
! [X0] : inverse(X0) = divide(identity,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] : divide(divide(identity,divide(X0,divide(X1,divide(divide(identity,X0),X2)))),X2) = X1,
inference(forward_demodulation,[status(thm)],[f9,f6]) ).
fof(f19,plain,
! [X0,X1,X2,X3] : divide(divide(identity,divide(divide(X0,divide(X1,divide(divide(identity,X0),X2))),divide(X3,X1))),X2) = X3,
inference(paramodulation,[status(thm)],[f16,f16]) ).
fof(f22,plain,
! [X0,X1,X2] : divide(inverse(divide(X0,divide(X1,divide(divide(identity,X0),X2)))),X2) = X1,
inference(backward_demodulation,[status(thm)],[f8,f16]) ).
fof(f23,plain,
inverse(identity) = identity,
inference(paramodulation,[status(thm)],[f9,f8]) ).
fof(f25,plain,
! [X0,X1,X2] : divide(inverse(divide(X0,divide(X1,divide(inverse(X0),X2)))),X2) = X1,
inference(forward_demodulation,[status(thm)],[f8,f22]) ).
fof(f26,plain,
! [X0,X1] : multiply(X0,X1) = divide(X0,inverse(X1)),
inference(forward_demodulation,[status(thm)],[f8,f7]) ).
fof(f27,plain,
! [X0] : multiply(identity,X0) = inverse(inverse(X0)),
inference(paramodulation,[status(thm)],[f8,f26]) ).
fof(f29,plain,
! [X0] : multiply(X0,identity) = divide(X0,identity),
inference(paramodulation,[status(thm)],[f23,f26]) ).
fof(f49,plain,
! [X0,X1] : divide(inverse(inverse(divide(X0,divide(inverse(identity),X1)))),X1) = X0,
inference(paramodulation,[status(thm)],[f8,f25]) ).
fof(f56,plain,
! [X0,X1] : divide(inverse(divide(X0,divide(X1,identity))),inverse(X0)) = X1,
inference(paramodulation,[status(thm)],[f9,f25]) ).
fof(f62,plain,
! [X0,X1] : divide(inverse(inverse(divide(X0,divide(identity,X1)))),X1) = X0,
inference(forward_demodulation,[status(thm)],[f23,f49]) ).
fof(f63,plain,
! [X0,X1] : divide(inverse(inverse(divide(X0,inverse(X1)))),X1) = X0,
inference(forward_demodulation,[status(thm)],[f8,f62]) ).
fof(f64,plain,
! [X0,X1] : divide(inverse(inverse(multiply(X0,X1))),X1) = X0,
inference(forward_demodulation,[status(thm)],[f26,f63]) ).
fof(f69,plain,
! [X0,X1] : multiply(inverse(divide(X0,divide(X1,identity))),X0) = X1,
inference(forward_demodulation,[status(thm)],[f26,f56]) ).
fof(f70,plain,
! [X0,X1] : multiply(inverse(divide(X0,multiply(X1,identity))),X0) = X1,
inference(forward_demodulation,[status(thm)],[f29,f69]) ).
fof(f80,plain,
divide(inverse(inverse(sF3_fnc)),c3) = b3,
inference(paramodulation,[status(thm)],[f13,f64]) ).
fof(f83,plain,
divide(inverse(inverse(sF1_fnc)),b3) = a3,
inference(paramodulation,[status(thm)],[f11,f64]) ).
fof(f90,plain,
! [X0] : divide(inverse(divide(inverse(sF3_fnc),divide(X0,b3))),c3) = X0,
inference(paramodulation,[status(thm)],[f80,f25]) ).
fof(f97,plain,
! [X0] : multiply(inverse(identity),multiply(X0,identity)) = X0,
inference(paramodulation,[status(thm)],[f9,f70]) ).
fof(f102,plain,
! [X0] : multiply(identity,multiply(X0,identity)) = X0,
inference(forward_demodulation,[status(thm)],[f23,f97]) ).
fof(f103,plain,
! [X0] : inverse(inverse(multiply(X0,identity))) = X0,
inference(forward_demodulation,[status(thm)],[f27,f102]) ).
fof(f110,plain,
! [X0] : inverse(inverse(X0)) = inverse(divide(identity,multiply(X0,identity))),
inference(paramodulation,[status(thm)],[f70,f103]) ).
fof(f112,plain,
! [X0] : divide(X0,identity) = X0,
inference(paramodulation,[status(thm)],[f103,f64]) ).
fof(f119,plain,
! [X0] : inverse(inverse(X0)) = inverse(inverse(multiply(X0,identity))),
inference(forward_demodulation,[status(thm)],[f8,f110]) ).
fof(f120,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f103,f119]) ).
fof(f121,plain,
! [X0] : multiply(X0,identity) = X0,
inference(forward_demodulation,[status(thm)],[f29,f112]) ).
fof(f122,plain,
divide(sF1_fnc,b3) = a3,
inference(backward_demodulation,[status(thm)],[f120,f83]) ).
fof(f127,plain,
! [X0,X1] : divide(multiply(X0,X1),X1) = X0,
inference(backward_demodulation,[status(thm)],[f120,f64]) ).
fof(f128,plain,
! [X0] : multiply(identity,X0) = X0,
inference(backward_demodulation,[status(thm)],[f120,f27]) ).
fof(f133,plain,
! [X0,X1] : multiply(X0,inverse(X1)) = divide(X0,X1),
inference(paramodulation,[status(thm)],[f120,f26]) ).
fof(f134,plain,
! [X0,X1] : multiply(inverse(divide(X0,X1)),X0) = X1,
inference(backward_demodulation,[status(thm)],[f121,f70]) ).
fof(f135,plain,
! [X0] : X0 = divide(X0,identity),
inference(backward_demodulation,[status(thm)],[f121,f29]) ).
fof(f178,plain,
! [X0,X1] : divide(divide(X0,X1),inverse(X1)) = X0,
inference(paramodulation,[status(thm)],[f133,f127]) ).
fof(f182,plain,
! [X0,X1] : multiply(divide(X0,X1),X1) = X0,
inference(forward_demodulation,[status(thm)],[f26,f178]) ).
fof(f251,plain,
! [X0,X1,X2,X3] : divide(inverse(divide(divide(X0,divide(X1,divide(divide(identity,X0),X2))),divide(X3,X1))),X2) = X3,
inference(forward_demodulation,[status(thm)],[f8,f19]) ).
fof(f252,plain,
! [X0,X1,X2,X3] : divide(inverse(divide(divide(X0,divide(X1,divide(inverse(X0),X2))),divide(X3,X1))),X2) = X3,
inference(forward_demodulation,[status(thm)],[f8,f251]) ).
fof(f316,plain,
divide(inverse(divide(inverse(sF3_fnc),a3)),c3) = sF1_fnc,
inference(paramodulation,[status(thm)],[f122,f90]) ).
fof(f333,plain,
multiply(sF1_fnc,c3) = inverse(divide(inverse(sF3_fnc),a3)),
inference(paramodulation,[status(thm)],[f316,f182]) ).
fof(f334,plain,
sF0_fnc = inverse(divide(inverse(sF3_fnc),a3)),
inference(forward_demodulation,[status(thm)],[f12,f333]) ).
fof(f340,plain,
inverse(sF0_fnc) = divide(inverse(sF3_fnc),a3),
inference(paramodulation,[status(thm)],[f334,f120]) ).
fof(f347,plain,
! [X0] : divide(inverse(divide(sF3_fnc,divide(X0,inverse(sF0_fnc)))),a3) = X0,
inference(paramodulation,[status(thm)],[f340,f25]) ).
fof(f352,plain,
! [X0] : divide(inverse(divide(sF3_fnc,multiply(X0,sF0_fnc))),a3) = X0,
inference(forward_demodulation,[status(thm)],[f26,f347]) ).
fof(f411,plain,
divide(inverse(divide(sF3_fnc,sF0_fnc)),a3) = identity,
inference(paramodulation,[status(thm)],[f128,f352]) ).
fof(f422,plain,
! [X0,X1] : divide(inverse(divide(divide(X0,divide(a3,divide(inverse(X0),X1))),identity)),X1) = inverse(divide(sF3_fnc,sF0_fnc)),
inference(paramodulation,[status(thm)],[f411,f252]) ).
fof(f428,plain,
! [X0,X1] : divide(inverse(divide(X0,divide(a3,divide(inverse(X0),X1)))),X1) = inverse(divide(sF3_fnc,sF0_fnc)),
inference(forward_demodulation,[status(thm)],[f135,f422]) ).
fof(f429,plain,
a3 = inverse(divide(sF3_fnc,sF0_fnc)),
inference(forward_demodulation,[status(thm)],[f25,f428]) ).
fof(f475,plain,
multiply(a3,sF3_fnc) = sF0_fnc,
inference(paramodulation,[status(thm)],[f429,f134]) ).
fof(f500,plain,
sF2_fnc = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f14,f475]) ).
fof(f501,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f500,f15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP459-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.52 % Computer : n001.cluster.edu
% 0.09/0.52 % Model : x86_64 x86_64
% 0.09/0.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.52 % Memory : 8046.5625MB
% 0.09/0.52 % OS : Linux 6.8.0-71-generic
% 0.09/0.52 % CPULimit : 300
% 0.09/0.52 % WCLimit : 300
% 0.09/0.52 % DateTime : Sun Sep 20 20:19:28 UTC 2026
% 0.09/0.52 % CPUTime :
% 0.09/0.53 % Drodi V4.1.1
% 0.09/0.53 % Refutation found
% 0.09/0.53 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.53 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.35/1.77 % Elapsed time: 1.033501 seconds
% 1.35/1.77 % CPU time: 0.057866 seconds
% 1.35/1.77 % Total memory used: 2.782 MB
% 1.35/1.77 % Net memory used: 2.723 MB
%------------------------------------------------------------------------------