%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP462-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 5.39s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 9
% Syntax : Number of formulae : 76 ( 76 unt; 4 def)
% Number of atoms : 76 ( 75 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 : 96 ( 96 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : divide(A,divide(divide(divide(identity,B),C),divide(divide(divide(A,A),A),C))) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] : multiply(A,B) = divide(A,divide(identity,B)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A] : inverse(A) = divide(identity,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A] : identity = divide(A,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,plain,
! [X0,X1,X2] : divide(X0,divide(divide(divide(identity,X1),X2),divide(divide(divide(X0,X0),X0),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,
inverse(identity) = identity,
inference(paramodulation,[status(thm)],[f9,f8]) ).
fof(f18,plain,
! [X0,X1] : multiply(X0,X1) = divide(X0,inverse(X1)),
inference(forward_demodulation,[status(thm)],[f8,f7]) ).
fof(f19,plain,
! [X0] : multiply(identity,X0) = inverse(inverse(X0)),
inference(paramodulation,[status(thm)],[f8,f18]) ).
fof(f21,plain,
! [X0] : multiply(X0,identity) = divide(X0,identity),
inference(paramodulation,[status(thm)],[f16,f18]) ).
fof(f25,plain,
! [X0,X1,X2] : divide(X0,divide(divide(inverse(X1),X2),divide(divide(divide(X0,X0),X0),X2))) = X1,
inference(forward_demodulation,[status(thm)],[f8,f6]) ).
fof(f26,plain,
! [X0,X1,X2] : divide(X0,divide(divide(inverse(X1),X2),divide(divide(identity,X0),X2))) = X1,
inference(forward_demodulation,[status(thm)],[f9,f25]) ).
fof(f27,plain,
! [X0,X1,X2] : divide(X0,divide(divide(inverse(X1),X2),divide(inverse(X0),X2))) = X1,
inference(forward_demodulation,[status(thm)],[f8,f26]) ).
fof(f28,plain,
! [X0,X1] : inverse(divide(divide(inverse(X0),X1),divide(inverse(identity),X1))) = X0,
inference(paramodulation,[status(thm)],[f8,f27]) ).
fof(f29,plain,
! [X0] : divide(X0,identity) = X0,
inference(paramodulation,[status(thm)],[f9,f27]) ).
fof(f30,plain,
! [X0,X1,X2,X3] : divide(X0,divide(X1,divide(inverse(X0),divide(divide(inverse(X1),X2),divide(inverse(inverse(X3)),X2))))) = X3,
inference(paramodulation,[status(thm)],[f27,f27]) ).
fof(f32,plain,
! [X0,X1] : divide(X0,divide(identity,divide(inverse(X0),inverse(X1)))) = X1,
inference(paramodulation,[status(thm)],[f9,f27]) ).
fof(f39,plain,
! [X0,X1] : inverse(divide(divide(inverse(X0),X1),divide(identity,X1))) = X0,
inference(forward_demodulation,[status(thm)],[f16,f28]) ).
fof(f40,plain,
! [X0,X1] : inverse(divide(divide(inverse(X0),X1),inverse(X1))) = X0,
inference(forward_demodulation,[status(thm)],[f8,f39]) ).
fof(f41,plain,
! [X0,X1] : inverse(multiply(divide(inverse(X0),X1),X1)) = X0,
inference(forward_demodulation,[status(thm)],[f18,f40]) ).
fof(f43,plain,
! [X0,X1] : divide(X0,inverse(divide(inverse(X0),inverse(X1)))) = X1,
inference(forward_demodulation,[status(thm)],[f8,f32]) ).
fof(f44,plain,
! [X0,X1] : multiply(X0,divide(inverse(X0),inverse(X1))) = X1,
inference(forward_demodulation,[status(thm)],[f18,f43]) ).
fof(f45,plain,
! [X0,X1] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(forward_demodulation,[status(thm)],[f18,f44]) ).
fof(f59,plain,
! [X0,X1] : divide(X0,divide(divide(inverse(X1),identity),inverse(X0))) = X1,
inference(paramodulation,[status(thm)],[f29,f27]) ).
fof(f63,plain,
! [X0,X1] : divide(X0,multiply(divide(inverse(X1),identity),X0)) = X1,
inference(forward_demodulation,[status(thm)],[f18,f59]) ).
fof(f64,plain,
! [X0,X1] : divide(X0,multiply(inverse(X1),X0)) = X1,
inference(forward_demodulation,[status(thm)],[f29,f63]) ).
fof(f67,plain,
! [X0] : multiply(X0,identity) = X0,
inference(forward_demodulation,[status(thm)],[f29,f21]) ).
fof(f77,plain,
! [X0] : multiply(X0,inverse(X0)) = identity,
inference(paramodulation,[status(thm)],[f67,f45]) ).
fof(f89,plain,
! [X0] : multiply(X0,identity) = inverse(inverse(X0)),
inference(paramodulation,[status(thm)],[f77,f45]) ).
fof(f96,plain,
! [X0] : X0 = inverse(inverse(X0)),
inference(forward_demodulation,[status(thm)],[f67,f89]) ).
fof(f97,plain,
! [X0] : multiply(identity,X0) = X0,
inference(backward_demodulation,[status(thm)],[f96,f19]) ).
fof(f101,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(paramodulation,[status(thm)],[f96,f45]) ).
fof(f105,plain,
! [X0,X1] : multiply(X0,inverse(X1)) = divide(X0,X1),
inference(paramodulation,[status(thm)],[f96,f18]) ).
fof(f117,plain,
! [X0,X1] : divide(multiply(inverse(inverse(X0)),X1),X1) = X0,
inference(paramodulation,[status(thm)],[f45,f64]) ).
fof(f119,plain,
! [X0,X1] : divide(X0,multiply(X1,X0)) = inverse(X1),
inference(paramodulation,[status(thm)],[f96,f64]) ).
fof(f126,plain,
! [X0,X1] : divide(multiply(X0,X1),X1) = X0,
inference(forward_demodulation,[status(thm)],[f96,f117]) ).
fof(f135,plain,
divide(sF0_fnc,c3) = sF1_fnc,
inference(paramodulation,[status(thm)],[f12,f126]) ).
fof(f136,plain,
divide(sF2_fnc,sF3_fnc) = a3,
inference(paramodulation,[status(thm)],[f14,f126]) ).
fof(f137,plain,
divide(sF1_fnc,b3) = a3,
inference(paramodulation,[status(thm)],[f11,f126]) ).
fof(f147,plain,
! [X0,X1,X2] : inverse(multiply(X0,divide(divide(inverse(X0),X1),divide(inverse(inverse(X2)),X1)))) = X2,
inference(paramodulation,[status(thm)],[f27,f41]) ).
fof(f164,plain,
! [X0,X1,X2] : inverse(multiply(X0,divide(divide(inverse(X0),X1),divide(X2,X1)))) = X2,
inference(forward_demodulation,[status(thm)],[f96,f147]) ).
fof(f168,plain,
! [X0,X1,X2,X3] : divide(X0,divide(X1,divide(inverse(X0),divide(divide(inverse(X1),X2),divide(X3,X2))))) = X3,
inference(forward_demodulation,[status(thm)],[f96,f30]) ).
fof(f185,plain,
! [X0,X1] : divide(X0,divide(X1,divide(inverse(X0),divide(divide(inverse(X1),sF3_fnc),a3)))) = sF2_fnc,
inference(paramodulation,[status(thm)],[f136,f168]) ).
fof(f285,plain,
! [X0] : inverse(divide(X0,divide(inverse(identity),divide(divide(inverse(X0),sF3_fnc),a3)))) = sF2_fnc,
inference(paramodulation,[status(thm)],[f8,f185]) ).
fof(f299,plain,
! [X0] : inverse(divide(X0,divide(identity,divide(divide(inverse(X0),sF3_fnc),a3)))) = sF2_fnc,
inference(forward_demodulation,[status(thm)],[f16,f285]) ).
fof(f300,plain,
! [X0] : inverse(divide(X0,inverse(divide(divide(inverse(X0),sF3_fnc),a3)))) = sF2_fnc,
inference(forward_demodulation,[status(thm)],[f8,f299]) ).
fof(f301,plain,
! [X0] : inverse(multiply(X0,divide(divide(inverse(X0),sF3_fnc),a3))) = sF2_fnc,
inference(forward_demodulation,[status(thm)],[f18,f300]) ).
fof(f318,plain,
inverse(divide(divide(inverse(identity),sF3_fnc),a3)) = sF2_fnc,
inference(paramodulation,[status(thm)],[f97,f301]) ).
fof(f338,plain,
inverse(divide(divide(identity,sF3_fnc),a3)) = sF2_fnc,
inference(forward_demodulation,[status(thm)],[f16,f318]) ).
fof(f339,plain,
inverse(divide(inverse(sF3_fnc),a3)) = sF2_fnc,
inference(forward_demodulation,[status(thm)],[f8,f338]) ).
fof(f358,plain,
divide(inverse(sF3_fnc),a3) = inverse(sF2_fnc),
inference(paramodulation,[status(thm)],[f339,f96]) ).
fof(f567,plain,
! [X0,X1] : multiply(inverse(X0),divide(X0,X1)) = inverse(X1),
inference(paramodulation,[status(thm)],[f105,f101]) ).
fof(f568,plain,
! [X0,X1] : divide(divide(X0,X1),inverse(X1)) = X0,
inference(paramodulation,[status(thm)],[f105,f126]) ).
fof(f576,plain,
! [X0,X1] : multiply(divide(X0,X1),X1) = X0,
inference(forward_demodulation,[status(thm)],[f18,f568]) ).
fof(f607,plain,
! [X0,X1] : divide(X0,X1) = inverse(divide(X1,X0)),
inference(paramodulation,[status(thm)],[f576,f119]) ).
fof(f612,plain,
divide(c3,sF3_fnc) = inverse(b3),
inference(paramodulation,[status(thm)],[f13,f119]) ).
fof(f1092,plain,
multiply(inverse(c3),inverse(b3)) = inverse(sF3_fnc),
inference(paramodulation,[status(thm)],[f612,f567]) ).
fof(f1126,plain,
divide(inverse(c3),b3) = inverse(sF3_fnc),
inference(forward_demodulation,[status(thm)],[f105,f1092]) ).
fof(f1181,plain,
! [X0] : inverse(multiply(X0,divide(divide(inverse(X0),b3),a3))) = sF1_fnc,
inference(paramodulation,[status(thm)],[f137,f164]) ).
fof(f1185,plain,
! [X0] : inverse(multiply(X0,divide(divide(inverse(X0),c3),sF1_fnc))) = sF0_fnc,
inference(paramodulation,[status(thm)],[f135,f164]) ).
fof(f1426,plain,
inverse(multiply(c3,divide(inverse(sF3_fnc),a3))) = sF1_fnc,
inference(paramodulation,[status(thm)],[f1126,f1181]) ).
fof(f1473,plain,
inverse(multiply(c3,inverse(sF2_fnc))) = sF1_fnc,
inference(forward_demodulation,[status(thm)],[f358,f1426]) ).
fof(f1474,plain,
inverse(divide(c3,sF2_fnc)) = sF1_fnc,
inference(forward_demodulation,[status(thm)],[f105,f1473]) ).
fof(f1475,plain,
divide(sF2_fnc,c3) = sF1_fnc,
inference(forward_demodulation,[status(thm)],[f607,f1474]) ).
fof(f1559,plain,
! [X0] : inverse(multiply(X0,divide(divide(inverse(X0),c3),sF1_fnc))) = sF2_fnc,
inference(paramodulation,[status(thm)],[f1475,f164]) ).
fof(f1565,plain,
sF0_fnc = sF2_fnc,
inference(forward_demodulation,[status(thm)],[f1185,f1559]) ).
fof(f1566,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1565,f15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP462-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.37 % Computer : n003.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Sun Sep 20 20:15:36 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.38 % Drodi V4.1.1
% 0.09/5.39 % Refutation found
% 0.09/5.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/5.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/5.41 % Elapsed time: 0.030920 seconds
% 0.13/5.41 % CPU time: 0.106149 seconds
% 0.13/5.41 % Total memory used: 4.914 MB
% 0.13/5.41 % Net memory used: 4.824 MB
%------------------------------------------------------------------------------