%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP551-1 : 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 12:34:39 PM UTC 2026
% Result : Unsatisfiable 0.09s 0.38s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 9
% Syntax : Number of formulae : 87 ( 87 unt; 4 def)
% Number of atoms : 87 ( 86 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 : 104 ( 104 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : divide(divide(identity,A),divide(divide(divide(B,A),C),B)) = C,
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(divide(identity,X0),divide(divide(divide(X1,X0),X2),X1)) = X2,
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] : divide(identity,divide(divide(divide(X0,identity),X1),X0)) = X1,
inference(paramodulation,[status(thm)],[f9,f6]) ).
fof(f17,plain,
! [X0,X1,X2] : divide(divide(identity,X0),divide(X1,identity)) = divide(divide(divide(X2,X0),X1),X2),
inference(paramodulation,[status(thm)],[f6,f6]) ).
fof(f19,plain,
! [X0,X1,X2,X3] : divide(divide(identity,divide(divide(divide(X0,X1),X2),X0)),divide(divide(X2,X3),divide(identity,X1))) = X3,
inference(paramodulation,[status(thm)],[f6,f6]) ).
fof(f21,plain,
! [X0,X1,X2] : divide(inverse(X0),divide(divide(divide(X1,X0),X2),X1)) = X2,
inference(backward_demodulation,[status(thm)],[f8,f6]) ).
fof(f22,plain,
inverse(identity) = identity,
inference(paramodulation,[status(thm)],[f9,f8]) ).
fof(f24,plain,
! [X0,X1] : multiply(X0,X1) = divide(X0,inverse(X1)),
inference(forward_demodulation,[status(thm)],[f8,f7]) ).
fof(f25,plain,
! [X0] : multiply(identity,X0) = inverse(inverse(X0)),
inference(paramodulation,[status(thm)],[f8,f24]) ).
fof(f27,plain,
! [X0] : multiply(X0,identity) = divide(X0,identity),
inference(paramodulation,[status(thm)],[f22,f24]) ).
fof(f45,plain,
! [X0,X1] : inverse(divide(divide(divide(X0,identity),X1),X0)) = X1,
inference(forward_demodulation,[status(thm)],[f8,f16]) ).
fof(f46,plain,
! [X0,X1] : inverse(divide(divide(multiply(X0,identity),X1),X0)) = X1,
inference(forward_demodulation,[status(thm)],[f27,f45]) ).
fof(f51,plain,
! [X0] : inverse(divide(identity,X0)) = multiply(X0,identity),
inference(paramodulation,[status(thm)],[f9,f46]) ).
fof(f52,plain,
! [X0] : inverse(divide(divide(inverse(inverse(identity)),X0),identity)) = X0,
inference(paramodulation,[status(thm)],[f25,f46]) ).
fof(f60,plain,
! [X0] : inverse(inverse(X0)) = multiply(X0,identity),
inference(forward_demodulation,[status(thm)],[f8,f51]) ).
fof(f61,plain,
! [X0] : inverse(multiply(divide(inverse(inverse(identity)),X0),identity)) = X0,
inference(forward_demodulation,[status(thm)],[f27,f52]) ).
fof(f62,plain,
! [X0] : inverse(multiply(divide(inverse(identity),X0),identity)) = X0,
inference(forward_demodulation,[status(thm)],[f22,f61]) ).
fof(f63,plain,
! [X0] : inverse(multiply(divide(identity,X0),identity)) = X0,
inference(forward_demodulation,[status(thm)],[f22,f62]) ).
fof(f64,plain,
! [X0] : inverse(multiply(inverse(X0),identity)) = X0,
inference(forward_demodulation,[status(thm)],[f8,f63]) ).
fof(f83,plain,
! [X0,X1] : divide(inverse(X0),divide(identity,X1)) = divide(X1,X0),
inference(paramodulation,[status(thm)],[f9,f21]) ).
fof(f92,plain,
! [X0,X1] : divide(inverse(X0),inverse(X1)) = divide(X1,X0),
inference(forward_demodulation,[status(thm)],[f8,f83]) ).
fof(f93,plain,
! [X0,X1] : multiply(inverse(X0),X1) = divide(X1,X0),
inference(forward_demodulation,[status(thm)],[f24,f92]) ).
fof(f99,plain,
! [X0,X1,X2] : divide(inverse(X0),divide(X1,identity)) = divide(divide(divide(X2,X0),X1),X2),
inference(forward_demodulation,[status(thm)],[f8,f17]) ).
fof(f100,plain,
! [X0,X1] : divide(inverse(X0),divide(inverse(X0),multiply(X1,identity))) = X1,
inference(backward_demodulation,[status(thm)],[f101,f21]) ).
fof(f101,plain,
! [X0,X1,X2] : divide(inverse(X0),multiply(X1,identity)) = divide(divide(divide(X2,X0),X1),X2),
inference(forward_demodulation,[status(thm)],[f27,f99]) ).
fof(f128,plain,
! [X0] : inverse(inverse(X0)) = divide(X0,identity),
inference(backward_demodulation,[status(thm)],[f60,f27]) ).
fof(f138,plain,
! [X0] : inverse(inverse(inverse(inverse(X0)))) = X0,
inference(forward_demodulation,[status(thm)],[f60,f64]) ).
fof(f149,plain,
! [X0] : inverse(inverse(inverse(X0))) = divide(identity,X0),
inference(paramodulation,[status(thm)],[f60,f93]) ).
fof(f153,plain,
! [X0] : inverse(inverse(inverse(X0))) = inverse(X0),
inference(forward_demodulation,[status(thm)],[f8,f149]) ).
fof(f165,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(backward_demodulation,[status(thm)],[f153,f138]) ).
fof(f175,plain,
! [X0] : X0 = divide(X0,identity),
inference(backward_demodulation,[status(thm)],[f165,f128]) ).
fof(f176,plain,
! [X0] : X0 = multiply(X0,identity),
inference(backward_demodulation,[status(thm)],[f165,f60]) ).
fof(f180,plain,
! [X0,X1] : multiply(X0,X1) = divide(X1,inverse(X0)),
inference(paramodulation,[status(thm)],[f165,f93]) ).
fof(f182,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(forward_demodulation,[status(thm)],[f24,f180]) ).
fof(f193,plain,
sF0_fnc = multiply(c3,sF1_fnc),
inference(paramodulation,[status(thm)],[f12,f182]) ).
fof(f212,plain,
! [X0,X1] : divide(inverse(X0),divide(inverse(X0),X1)) = X1,
inference(forward_demodulation,[status(thm)],[f176,f100]) ).
fof(f213,plain,
! [X0,X1] : divide(X0,divide(inverse(inverse(X0)),X1)) = X1,
inference(paramodulation,[status(thm)],[f165,f212]) ).
fof(f221,plain,
! [X0,X1] : divide(X0,divide(X0,X1)) = X1,
inference(forward_demodulation,[status(thm)],[f165,f213]) ).
fof(f235,plain,
! [X0,X1,X2,X3] : divide(inverse(divide(divide(divide(X0,X1),X2),X0)),divide(divide(X2,X3),divide(identity,X1))) = X3,
inference(forward_demodulation,[status(thm)],[f8,f19]) ).
fof(f236,plain,
! [X0,X1,X2,X3] : divide(inverse(divide(divide(divide(X0,X1),X2),X0)),divide(divide(X2,X3),inverse(X1))) = X3,
inference(forward_demodulation,[status(thm)],[f8,f235]) ).
fof(f237,plain,
! [X0,X1,X2,X3] : divide(inverse(divide(divide(divide(X0,X1),X2),X0)),multiply(divide(X2,X3),X1)) = X3,
inference(forward_demodulation,[status(thm)],[f24,f236]) ).
fof(f281,plain,
! [X0,X1] : divide(X0,multiply(X0,X1)) = inverse(X1),
inference(paramodulation,[status(thm)],[f24,f221]) ).
fof(f335,plain,
divide(c3,sF0_fnc) = inverse(sF1_fnc),
inference(paramodulation,[status(thm)],[f193,f281]) ).
fof(f338,plain,
divide(b3,sF3_fnc) = inverse(c3),
inference(paramodulation,[status(thm)],[f13,f281]) ).
fof(f339,plain,
divide(sF1_fnc,sF0_fnc) = inverse(c3),
inference(paramodulation,[status(thm)],[f12,f281]) ).
fof(f344,plain,
! [X0,X1] : divide(X0,multiply(X1,X0)) = inverse(X1),
inference(paramodulation,[status(thm)],[f182,f281]) ).
fof(f359,plain,
! [X0,X1] : divide(inverse(divide(divide(divide(X0,X1),c3),X0)),multiply(inverse(sF1_fnc),X1)) = sF0_fnc,
inference(paramodulation,[status(thm)],[f335,f237]) ).
fof(f362,plain,
! [X0,X1] : divide(inverse(divide(divide(divide(X0,X1),c3),X0)),divide(X1,sF1_fnc)) = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f93,f359]) ).
fof(f364,plain,
! [X0,X1] : divide(inverse(divide(divide(divide(X0,X1),b3),X0)),multiply(inverse(c3),X1)) = sF3_fnc,
inference(paramodulation,[status(thm)],[f338,f237]) ).
fof(f367,plain,
! [X0,X1] : divide(inverse(divide(divide(divide(X0,X1),b3),X0)),divide(X1,c3)) = sF3_fnc,
inference(forward_demodulation,[status(thm)],[f93,f364]) ).
fof(f396,plain,
! [X0] : divide(inverse(divide(divide(X0,c3),X0)),divide(identity,sF1_fnc)) = sF0_fnc,
inference(paramodulation,[status(thm)],[f175,f362]) ).
fof(f413,plain,
! [X0] : divide(inverse(divide(divide(X0,c3),X0)),inverse(sF1_fnc)) = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f8,f396]) ).
fof(f414,plain,
! [X0] : multiply(inverse(divide(divide(X0,c3),X0)),sF1_fnc) = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f24,f413]) ).
fof(f415,plain,
! [X0] : divide(sF1_fnc,divide(divide(X0,c3),X0)) = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f93,f414]) ).
fof(f430,plain,
! [X0] : divide(sF1_fnc,sF0_fnc) = divide(divide(X0,c3),X0),
inference(paramodulation,[status(thm)],[f415,f221]) ).
fof(f439,plain,
! [X0] : inverse(c3) = divide(divide(X0,c3),X0),
inference(forward_demodulation,[status(thm)],[f339,f430]) ).
fof(f452,plain,
! [X0] : divide(divide(X0,c3),inverse(c3)) = X0,
inference(paramodulation,[status(thm)],[f439,f221]) ).
fof(f459,plain,
! [X0] : multiply(divide(X0,c3),c3) = X0,
inference(forward_demodulation,[status(thm)],[f24,f452]) ).
fof(f529,plain,
divide(inverse(divide(inverse(c3),b3)),divide(c3,c3)) = sF3_fnc,
inference(paramodulation,[status(thm)],[f439,f367]) ).
fof(f557,plain,
divide(inverse(divide(inverse(c3),b3)),identity) = sF3_fnc,
inference(forward_demodulation,[status(thm)],[f9,f529]) ).
fof(f558,plain,
inverse(divide(inverse(c3),b3)) = sF3_fnc,
inference(forward_demodulation,[status(thm)],[f175,f557]) ).
fof(f590,plain,
divide(sF3_fnc,sF2_fnc) = inverse(a3),
inference(paramodulation,[status(thm)],[f14,f344]) ).
fof(f591,plain,
divide(b3,sF1_fnc) = inverse(a3),
inference(paramodulation,[status(thm)],[f11,f344]) ).
fof(f640,plain,
divide(sF3_fnc,inverse(a3)) = sF2_fnc,
inference(paramodulation,[status(thm)],[f590,f221]) ).
fof(f644,plain,
multiply(sF3_fnc,a3) = sF2_fnc,
inference(forward_demodulation,[status(thm)],[f24,f640]) ).
fof(f928,plain,
inverse(sF3_fnc) = divide(inverse(c3),b3),
inference(paramodulation,[status(thm)],[f558,f165]) ).
fof(f954,plain,
divide(inverse(divide(divide(inverse(sF3_fnc),c3),inverse(c3))),divide(b3,sF1_fnc)) = sF0_fnc,
inference(paramodulation,[status(thm)],[f928,f362]) ).
fof(f964,plain,
divide(inverse(multiply(divide(inverse(sF3_fnc),c3),c3)),divide(b3,sF1_fnc)) = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f24,f954]) ).
fof(f965,plain,
divide(inverse(inverse(sF3_fnc)),divide(b3,sF1_fnc)) = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f459,f964]) ).
fof(f966,plain,
divide(sF3_fnc,divide(b3,sF1_fnc)) = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f165,f965]) ).
fof(f967,plain,
divide(sF3_fnc,inverse(a3)) = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f591,f966]) ).
fof(f968,plain,
multiply(sF3_fnc,a3) = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f24,f967]) ).
fof(f969,plain,
sF2_fnc = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f644,f968]) ).
fof(f970,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f969,f15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP551-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n003.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 20:18:01 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.38 % Refutation found
% 0.09/0.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.42/1.61 % Elapsed time: 1.029892 seconds
% 1.42/1.61 % CPU time: 0.084873 seconds
% 1.42/1.61 % Total memory used: 3.547 MB
% 1.42/1.61 % Net memory used: 3.439 MB
%------------------------------------------------------------------------------