%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP492-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : 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 12:34:31 PM UTC 2026
% Result : Unsatisfiable 0.08s 6.01s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 9
% Syntax : Number of formulae : 95 ( 95 unt; 4 def)
% Number of atoms : 95 ( 94 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 7 ( 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 : 117 ( 117 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] : multiply(A,B) = double_divide(double_divide(B,A),identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A] : inverse(A) = double_divide(A,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A] : identity = double_divide(A,inverse(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] : double_divide(double_divide(identity,X0),double_divide(identity,double_divide(double_divide(double_divide(X0,X1),identity),double_divide(X2,X1)))) = X2,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f7,plain,
! [X0,X1] : multiply(X0,X1) = double_divide(double_divide(X1,X0),identity),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f8,plain,
! [X0] : inverse(X0) = double_divide(X0,identity),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f9,plain,
! [X0] : identity = double_divide(X0,inverse(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(f40,plain,
! [X0,X1] : multiply(X0,X1) = inverse(double_divide(X1,X0)),
inference(backward_demodulation,[status(thm)],[f8,f7]) ).
fof(f41,plain,
! [X0] : multiply(identity,X0) = inverse(inverse(X0)),
inference(paramodulation,[status(thm)],[f8,f40]) ).
fof(f51,plain,
! [X0,X1,X2] : double_divide(double_divide(identity,X0),double_divide(identity,double_divide(inverse(double_divide(X0,X1)),double_divide(X2,X1)))) = X2,
inference(forward_demodulation,[status(thm)],[f8,f6]) ).
fof(f52,plain,
! [X0,X1,X2] : double_divide(double_divide(identity,X0),double_divide(identity,double_divide(multiply(X1,X0),double_divide(X2,X1)))) = X2,
inference(forward_demodulation,[status(thm)],[f40,f51]) ).
fof(f53,plain,
! [X0,X1] : double_divide(inverse(identity),double_divide(identity,double_divide(multiply(X0,identity),double_divide(X1,X0)))) = X1,
inference(paramodulation,[status(thm)],[f8,f52]) ).
fof(f55,plain,
! [X0] : double_divide(double_divide(identity,c3),double_divide(identity,double_divide(sF3_fnc,double_divide(X0,b3)))) = X0,
inference(paramodulation,[status(thm)],[f13,f52]) ).
fof(f60,plain,
! [X0,X1] : double_divide(double_divide(identity,X0),double_divide(identity,double_divide(multiply(identity,X0),inverse(X1)))) = X1,
inference(paramodulation,[status(thm)],[f8,f52]) ).
fof(f61,plain,
! [X0,X1,X2] : multiply(double_divide(identity,double_divide(multiply(X0,X1),double_divide(X2,X0))),double_divide(identity,X1)) = inverse(X2),
inference(paramodulation,[status(thm)],[f52,f40]) ).
fof(f63,plain,
! [X0,X1] : double_divide(double_divide(identity,X0),double_divide(identity,double_divide(inverse(inverse(X0)),inverse(X1)))) = X1,
inference(forward_demodulation,[status(thm)],[f41,f60]) ).
fof(f73,plain,
! [X0,X1] : double_divide(identity,double_divide(identity,double_divide(multiply(X0,inverse(identity)),double_divide(X1,X0)))) = X1,
inference(paramodulation,[status(thm)],[f9,f52]) ).
fof(f74,plain,
! [X0] : double_divide(inverse(identity),double_divide(identity,double_divide(multiply(inverse(X0),identity),identity))) = X0,
inference(paramodulation,[status(thm)],[f9,f53]) ).
fof(f75,plain,
! [X0,X1] : double_divide(double_divide(identity,X0),double_divide(identity,double_divide(multiply(inverse(X1),X0),identity))) = X1,
inference(paramodulation,[status(thm)],[f9,f52]) ).
fof(f76,plain,
! [X0] : multiply(inverse(X0),X0) = inverse(identity),
inference(paramodulation,[status(thm)],[f9,f40]) ).
fof(f77,plain,
! [X0] : double_divide(inverse(identity),double_divide(identity,inverse(multiply(inverse(X0),identity)))) = X0,
inference(forward_demodulation,[status(thm)],[f8,f74]) ).
fof(f78,plain,
! [X0,X1] : double_divide(double_divide(identity,X0),double_divide(identity,inverse(multiply(inverse(X1),X0)))) = X1,
inference(forward_demodulation,[status(thm)],[f8,f75]) ).
fof(f202,plain,
double_divide(inverse(identity),double_divide(identity,inverse(inverse(identity)))) = identity,
inference(paramodulation,[status(thm)],[f76,f77]) ).
fof(f218,plain,
! [X0] : double_divide(double_divide(identity,X0),double_divide(identity,inverse(inverse(identity)))) = X0,
inference(paramodulation,[status(thm)],[f76,f78]) ).
fof(f225,plain,
double_divide(identity,double_divide(identity,inverse(inverse(identity)))) = inverse(identity),
inference(paramodulation,[status(thm)],[f9,f218]) ).
fof(f232,plain,
double_divide(inverse(identity),double_divide(identity,inverse(inverse(identity)))) = double_divide(identity,inverse(inverse(identity))),
inference(paramodulation,[status(thm)],[f225,f218]) ).
fof(f240,plain,
identity = double_divide(identity,inverse(inverse(identity))),
inference(forward_demodulation,[status(thm)],[f202,f232]) ).
fof(f242,plain,
! [X0] : double_divide(double_divide(identity,X0),identity) = X0,
inference(backward_demodulation,[status(thm)],[f240,f218]) ).
fof(f248,plain,
double_divide(inverse(identity),double_divide(identity,double_divide(multiply(inverse(inverse(identity)),identity),identity))) = identity,
inference(paramodulation,[status(thm)],[f240,f53]) ).
fof(f251,plain,
! [X0] : inverse(double_divide(identity,X0)) = X0,
inference(forward_demodulation,[status(thm)],[f8,f242]) ).
fof(f252,plain,
! [X0] : multiply(X0,identity) = X0,
inference(forward_demodulation,[status(thm)],[f40,f251]) ).
fof(f254,plain,
double_divide(inverse(identity),double_divide(identity,inverse(multiply(inverse(inverse(identity)),identity)))) = identity,
inference(forward_demodulation,[status(thm)],[f8,f248]) ).
fof(f255,plain,
inverse(identity) = identity,
inference(forward_demodulation,[status(thm)],[f77,f254]) ).
fof(f276,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(backward_demodulation,[status(thm)],[f255,f76]) ).
fof(f329,plain,
! [X0] : double_divide(double_divide(identity,X0),double_divide(identity,identity)) = inverse(inverse(X0)),
inference(paramodulation,[status(thm)],[f9,f63]) ).
fof(f344,plain,
! [X0] : double_divide(double_divide(identity,X0),inverse(identity)) = inverse(inverse(X0)),
inference(forward_demodulation,[status(thm)],[f8,f329]) ).
fof(f345,plain,
! [X0] : double_divide(double_divide(identity,X0),identity) = inverse(inverse(X0)),
inference(forward_demodulation,[status(thm)],[f255,f344]) ).
fof(f346,plain,
! [X0] : inverse(double_divide(identity,X0)) = inverse(inverse(X0)),
inference(forward_demodulation,[status(thm)],[f8,f345]) ).
fof(f347,plain,
! [X0] : multiply(X0,identity) = inverse(inverse(X0)),
inference(forward_demodulation,[status(thm)],[f40,f346]) ).
fof(f348,plain,
! [X0] : X0 = inverse(inverse(X0)),
inference(forward_demodulation,[status(thm)],[f252,f347]) ).
fof(f353,plain,
! [X0,X1] : double_divide(double_divide(identity,X0),double_divide(identity,double_divide(X0,inverse(X1)))) = X1,
inference(backward_demodulation,[status(thm)],[f348,f63]) ).
fof(f354,plain,
! [X0] : multiply(identity,X0) = X0,
inference(backward_demodulation,[status(thm)],[f348,f41]) ).
fof(f357,plain,
! [X0,X1] : double_divide(X0,X1) = inverse(multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f40,f348]) ).
fof(f359,plain,
! [X0] : identity = double_divide(inverse(X0),X0),
inference(paramodulation,[status(thm)],[f348,f9]) ).
fof(f369,plain,
! [X0] : multiply(X0,inverse(X0)) = identity,
inference(paramodulation,[status(thm)],[f348,f276]) ).
fof(f446,plain,
double_divide(c3,sF1_fnc) = inverse(sF0_fnc),
inference(paramodulation,[status(thm)],[f12,f357]) ).
fof(f448,plain,
double_divide(b3,a3) = inverse(sF1_fnc),
inference(paramodulation,[status(thm)],[f11,f357]) ).
fof(f450,plain,
! [X0] : double_divide(identity,X0) = inverse(X0),
inference(paramodulation,[status(thm)],[f252,f357]) ).
fof(f461,plain,
! [X0] : double_divide(inverse(c3),double_divide(identity,double_divide(sF3_fnc,double_divide(X0,b3)))) = X0,
inference(backward_demodulation,[status(thm)],[f450,f55]) ).
fof(f477,plain,
! [X0] : double_divide(inverse(c3),inverse(double_divide(sF3_fnc,double_divide(X0,b3)))) = X0,
inference(forward_demodulation,[status(thm)],[f450,f461]) ).
fof(f478,plain,
! [X0] : double_divide(inverse(c3),multiply(double_divide(X0,b3),sF3_fnc)) = X0,
inference(forward_demodulation,[status(thm)],[f40,f477]) ).
fof(f549,plain,
! [X0,X1,X2] : multiply(inverse(double_divide(multiply(X0,X1),double_divide(X2,X0))),double_divide(identity,X1)) = inverse(X2),
inference(forward_demodulation,[status(thm)],[f450,f61]) ).
fof(f550,plain,
! [X0,X1,X2] : multiply(multiply(double_divide(X0,X1),multiply(X1,X2)),double_divide(identity,X2)) = inverse(X0),
inference(forward_demodulation,[status(thm)],[f40,f549]) ).
fof(f551,plain,
! [X0,X1,X2] : multiply(multiply(double_divide(X0,X1),multiply(X1,X2)),inverse(X2)) = inverse(X0),
inference(forward_demodulation,[status(thm)],[f450,f550]) ).
fof(f558,plain,
! [X0,X1] : multiply(multiply(identity,multiply(X0,X1)),inverse(X1)) = inverse(inverse(X0)),
inference(paramodulation,[status(thm)],[f359,f551]) ).
fof(f569,plain,
! [X0,X1] : multiply(multiply(double_divide(X0,X1),identity),inverse(inverse(X1))) = inverse(X0),
inference(paramodulation,[status(thm)],[f369,f551]) ).
fof(f580,plain,
! [X0,X1] : multiply(multiply(X0,X1),inverse(X1)) = inverse(inverse(X0)),
inference(forward_demodulation,[status(thm)],[f354,f558]) ).
fof(f581,plain,
! [X0,X1] : multiply(multiply(X0,X1),inverse(X1)) = X0,
inference(forward_demodulation,[status(thm)],[f348,f580]) ).
fof(f589,plain,
! [X0,X1] : multiply(double_divide(X0,X1),inverse(inverse(X1))) = inverse(X0),
inference(forward_demodulation,[status(thm)],[f252,f569]) ).
fof(f590,plain,
! [X0,X1] : multiply(double_divide(X0,X1),X1) = inverse(X0),
inference(forward_demodulation,[status(thm)],[f348,f589]) ).
fof(f598,plain,
! [X0,X1] : inverse(double_divide(identity,double_divide(multiply(X0,inverse(identity)),double_divide(X1,X0)))) = X1,
inference(forward_demodulation,[status(thm)],[f450,f73]) ).
fof(f599,plain,
! [X0,X1] : multiply(double_divide(multiply(X0,inverse(identity)),double_divide(X1,X0)),identity) = X1,
inference(forward_demodulation,[status(thm)],[f40,f598]) ).
fof(f600,plain,
! [X0,X1] : double_divide(multiply(X0,inverse(identity)),double_divide(X1,X0)) = X1,
inference(forward_demodulation,[status(thm)],[f252,f599]) ).
fof(f601,plain,
! [X0,X1] : double_divide(multiply(X0,identity),double_divide(X1,X0)) = X1,
inference(forward_demodulation,[status(thm)],[f255,f600]) ).
fof(f602,plain,
! [X0,X1] : double_divide(X0,double_divide(X1,X0)) = X1,
inference(forward_demodulation,[status(thm)],[f252,f601]) ).
fof(f604,plain,
double_divide(a3,inverse(sF1_fnc)) = b3,
inference(paramodulation,[status(thm)],[f448,f602]) ).
fof(f612,plain,
! [X0,X1] : double_divide(double_divide(X0,X1),X0) = X1,
inference(paramodulation,[status(thm)],[f602,f602]) ).
fof(f625,plain,
double_divide(inverse(sF1_fnc),b3) = a3,
inference(paramodulation,[status(thm)],[f604,f602]) ).
fof(f696,plain,
! [X0,X1] : multiply(X0,double_divide(X0,X1)) = inverse(X1),
inference(paramodulation,[status(thm)],[f612,f40]) ).
fof(f748,plain,
! [X0,X1] : multiply(inverse(X0),inverse(X1)) = double_divide(X0,X1),
inference(paramodulation,[status(thm)],[f590,f581]) ).
fof(f784,plain,
! [X0,X1] : double_divide(inverse(X0),double_divide(identity,double_divide(X0,inverse(X1)))) = X1,
inference(forward_demodulation,[status(thm)],[f450,f353]) ).
fof(f785,plain,
! [X0,X1] : double_divide(inverse(X0),inverse(double_divide(X0,inverse(X1)))) = X1,
inference(forward_demodulation,[status(thm)],[f450,f784]) ).
fof(f786,plain,
! [X0,X1] : double_divide(inverse(X0),multiply(inverse(X1),X0)) = X1,
inference(forward_demodulation,[status(thm)],[f40,f785]) ).
fof(f798,plain,
! [X0,X1] : multiply(X0,multiply(inverse(X0),X1)) = inverse(inverse(X1)),
inference(paramodulation,[status(thm)],[f786,f590]) ).
fof(f814,plain,
! [X0,X1] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(forward_demodulation,[status(thm)],[f348,f798]) ).
fof(f842,plain,
! [X0,X1] : multiply(inverse(X0),inverse(double_divide(X1,X0))) = X1,
inference(paramodulation,[status(thm)],[f696,f581]) ).
fof(f858,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[status(thm)],[f40,f842]) ).
fof(f924,plain,
! [X0,X1] : multiply(X0,inverse(X1)) = double_divide(inverse(X0),X1),
inference(paramodulation,[status(thm)],[f696,f814]) ).
fof(f1130,plain,
double_divide(inverse(c3),multiply(a3,sF3_fnc)) = inverse(sF1_fnc),
inference(paramodulation,[status(thm)],[f625,f478]) ).
fof(f1144,plain,
double_divide(inverse(c3),sF2_fnc) = inverse(sF1_fnc),
inference(forward_demodulation,[status(thm)],[f14,f1130]) ).
fof(f2551,plain,
multiply(c3,inverse(sF2_fnc)) = inverse(sF1_fnc),
inference(forward_demodulation,[status(thm)],[f924,f1144]) ).
fof(f2559,plain,
multiply(inverse(c3),inverse(sF1_fnc)) = inverse(sF2_fnc),
inference(paramodulation,[status(thm)],[f2551,f858]) ).
fof(f2575,plain,
double_divide(c3,sF1_fnc) = inverse(sF2_fnc),
inference(forward_demodulation,[status(thm)],[f748,f2559]) ).
fof(f2576,plain,
inverse(sF0_fnc) = inverse(sF2_fnc),
inference(forward_demodulation,[status(thm)],[f446,f2575]) ).
fof(f2627,plain,
sF2_fnc = inverse(inverse(sF0_fnc)),
inference(paramodulation,[status(thm)],[f2576,f348]) ).
fof(f2632,plain,
sF2_fnc = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f348,f2627]) ).
fof(f2633,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f2632,f15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP492-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/5.98 % Computer : n002.cluster.edu
% 0.08/5.98 % Model : x86_64 x86_64
% 0.08/5.98 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.98 % Memory : 8046.5625MB
% 0.08/5.98 % OS : Linux 6.8.0-71-generic
% 0.08/5.98 % CPULimit : 300
% 0.08/5.98 % WCLimit : 300
% 0.08/5.98 % DateTime : Sun Sep 20 20:17:38 UTC 2026
% 0.08/5.98 % CPUTime :
% 0.08/5.99 % Drodi V4.1.1
% 0.08/6.01 % Refutation found
% 0.08/6.01 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.08/6.01 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.08/6.02 % Elapsed time: 0.031179 seconds
% 0.08/6.02 % CPU time: 0.113199 seconds
% 0.08/6.02 % Total memory used: 6.652 MB
% 0.08/6.02 % Net memory used: 6.441 MB
%------------------------------------------------------------------------------