%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP565-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 12:34:41 PM UTC 2026
% Result : Unsatisfiable 0.11s 0.38s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 35 ( 35 unt; 2 def)
% Number of atoms : 35 ( 34 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 : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 46 ( 46 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity)) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] : multiply(A,B) = double_divide(double_divide(B,A),identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A] : inverse(A) = double_divide(A,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A] : identity = double_divide(A,inverse(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
multiply(inverse(a1),a1) != identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,plain,
! [X0,X1,X2] : double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(X0,X2)),double_divide(identity,X2))),double_divide(identity,identity)) = X1,
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(inverse(a1),a1) != identity,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f11,definition,
sF1_fnc = inverse(a1),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f12,definition,
sF0_fnc = multiply(sF1_fnc,a1),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f13,plain,
sF0_fnc != identity,
inference(definition_folding,[],[f10,f12,f11]) ).
fof(f14,plain,
identity = double_divide(a1,sF1_fnc),
inference(paramodulation,[status(thm)],[f11,f9]) ).
fof(f15,plain,
! [X0,X1,X2] : double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(X0,X2)),double_divide(identity,X2))),inverse(identity)) = X1,
inference(forward_demodulation,[status(thm)],[f8,f6]) ).
fof(f16,plain,
! [X0,X1,X2,X3] : double_divide(double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(X0,X2)),double_divide(identity,X2))),double_divide(double_divide(X3,X1),double_divide(identity,inverse(identity)))),inverse(identity)) = X3,
inference(paramodulation,[status(thm)],[f15,f15]) ).
fof(f22,plain,
! [X0,X1,X2,X3] : double_divide(double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(X0,X2)),double_divide(identity,X2))),double_divide(double_divide(X3,X1),identity)),inverse(identity)) = X3,
inference(forward_demodulation,[status(thm)],[f9,f16]) ).
fof(f23,plain,
! [X0,X1,X2,X3] : double_divide(double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(X0,X2)),double_divide(identity,X2))),inverse(double_divide(X3,X1))),inverse(identity)) = X3,
inference(forward_demodulation,[status(thm)],[f8,f22]) ).
fof(f29,plain,
! [X0,X1] : multiply(X0,X1) = inverse(double_divide(X1,X0)),
inference(forward_demodulation,[status(thm)],[f8,f7]) ).
fof(f31,plain,
multiply(sF1_fnc,a1) = inverse(identity),
inference(paramodulation,[status(thm)],[f14,f29]) ).
fof(f35,plain,
sF0_fnc = inverse(identity),
inference(forward_demodulation,[status(thm)],[f12,f31]) ).
fof(f36,plain,
! [X0,X1,X2] : double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(X0,X2)),double_divide(identity,X2))),sF0_fnc) = X1,
inference(backward_demodulation,[status(thm)],[f35,f15]) ).
fof(f37,plain,
identity = double_divide(identity,sF0_fnc),
inference(paramodulation,[status(thm)],[f35,f9]) ).
fof(f38,plain,
multiply(sF0_fnc,identity) = inverse(identity),
inference(paramodulation,[status(thm)],[f37,f29]) ).
fof(f39,plain,
multiply(sF0_fnc,identity) = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f35,f38]) ).
fof(f158,plain,
! [X0,X1,X2,X3] : double_divide(double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(X0,X2)),double_divide(identity,X2))),multiply(X1,X3)),inverse(identity)) = X3,
inference(forward_demodulation,[status(thm)],[f29,f23]) ).
fof(f159,plain,
! [X0,X1,X2,X3] : double_divide(double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(X0,X2)),double_divide(identity,X2))),multiply(X1,X3)),sF0_fnc) = X3,
inference(forward_demodulation,[status(thm)],[f35,f158]) ).
fof(f176,plain,
! [X0,X1] : double_divide(double_divide(double_divide(X0,double_divide(double_divide(sF0_fnc,double_divide(X0,X1)),double_divide(identity,X1))),sF0_fnc),sF0_fnc) = identity,
inference(paramodulation,[status(thm)],[f39,f159]) ).
fof(f208,plain,
double_divide(sF0_fnc,sF0_fnc) = identity,
inference(forward_demodulation,[status(thm)],[f36,f176]) ).
fof(f232,plain,
multiply(sF0_fnc,sF0_fnc) = inverse(identity),
inference(paramodulation,[status(thm)],[f208,f29]) ).
fof(f241,plain,
multiply(sF0_fnc,sF0_fnc) = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f35,f232]) ).
fof(f254,plain,
! [X0,X1] : double_divide(double_divide(double_divide(X0,double_divide(double_divide(sF0_fnc,double_divide(X0,X1)),double_divide(identity,X1))),sF0_fnc),sF0_fnc) = sF0_fnc,
inference(paramodulation,[status(thm)],[f241,f159]) ).
fof(f257,plain,
double_divide(sF0_fnc,sF0_fnc) = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f36,f254]) ).
fof(f258,plain,
identity = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f208,f257]) ).
fof(f259,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f258,f13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP565-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n018.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 20 20:18:57 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Drodi V4.1.1
% 0.11/0.38 % Refutation found
% 0.11/0.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.11/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.40 % Elapsed time: 0.024712 seconds
% 0.15/0.40 % CPU time: 0.028905 seconds
% 0.15/0.40 % Total memory used: 798.640 KB
% 0.15/0.40 % Net memory used: 782.880 KB
%------------------------------------------------------------------------------