%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP601-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 12:34:46 PM UTC 2026
% Result : Unsatisfiable 0.08s 0.38s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 7
% Syntax : Number of formulae : 43 ( 43 unt; 4 def)
% Number of atoms : 43 ( 42 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 74 ( 74 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : inverse(double_divide(inverse(double_divide(A,inverse(double_divide(B,double_divide(A,C))))),C)) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] : multiply(A,B) = inverse(double_divide(B,A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,plain,
! [X0,X1,X2] : inverse(double_divide(inverse(double_divide(X0,inverse(double_divide(X1,double_divide(X0,X2))))),X2)) = X1,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f5,plain,
! [X0,X1] : multiply(X0,X1) = inverse(double_divide(X1,X0)),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f6,plain,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f7,definition,
sF1_fnc = inverse(a1),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f8,definition,
sF0_fnc = multiply(sF1_fnc,a1),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f9,definition,
sF3_fnc = inverse(b1),
introduced(definition,[new_symbols(definition,[sF3_fnc])],[function_definition]) ).
fof(f10,definition,
sF2_fnc = multiply(sF3_fnc,b1),
introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition]) ).
fof(f11,plain,
sF0_fnc != sF2_fnc,
inference(definition_folding,[],[f6,f10,f9,f8,f7]) ).
fof(f12,plain,
! [X0,X1,X2] : multiply(X0,inverse(double_divide(X1,inverse(double_divide(X2,double_divide(X1,X0)))))) = X2,
inference(forward_demodulation,[status(thm)],[f5,f4]) ).
fof(f13,plain,
! [X0,X1,X2] : multiply(X0,multiply(inverse(double_divide(X1,double_divide(X2,X0))),X2)) = X1,
inference(forward_demodulation,[status(thm)],[f5,f12]) ).
fof(f14,plain,
! [X0,X1,X2] : multiply(X0,multiply(multiply(double_divide(X1,X0),X2),X1)) = X2,
inference(forward_demodulation,[status(thm)],[f5,f13]) ).
fof(f15,plain,
! [X0,X1,X2,X3] : multiply(X0,multiply(X1,X2)) = multiply(multiply(double_divide(X3,double_divide(X2,X0)),X1),X3),
inference(paramodulation,[status(thm)],[f14,f14]) ).
fof(f17,plain,
! [X0,X1,X2] : multiply(double_divide(X0,X1),multiply(X1,multiply(X2,X0))) = X2,
inference(paramodulation,[status(thm)],[f15,f14]) ).
fof(f19,plain,
! [X0,X1,X2] : multiply(double_divide(multiply(X0,X1),double_divide(X1,X2)),X0) = X2,
inference(paramodulation,[status(thm)],[f17,f17]) ).
fof(f20,plain,
! [X0,X1,X2,X3,X4] : multiply(double_divide(X0,multiply(double_divide(multiply(X1,X0),double_divide(X2,X3)),X4)),multiply(X3,multiply(X4,X2))) = X1,
inference(paramodulation,[status(thm)],[f15,f17]) ).
fof(f22,plain,
! [X0,X1,X2,X3] : multiply(double_divide(multiply(X0,multiply(X1,X2)),X3),multiply(X3,X1)) = double_divide(X2,X0),
inference(paramodulation,[status(thm)],[f17,f17]) ).
fof(f63,plain,
! [X0,X1,X2] : X0 = double_divide(X1,multiply(double_divide(multiply(X2,X1),X0),X2)),
inference(paramodulation,[status(thm)],[f19,f22]) ).
fof(f100,plain,
! [X0,X1,X2] : X0 = double_divide(multiply(X1,X2),double_divide(X2,multiply(X0,X1))),
inference(paramodulation,[status(thm)],[f22,f63]) ).
fof(f268,plain,
! [X0,X1,X2] : multiply(double_divide(X0,multiply(X1,X2)),multiply(X2,X0)) = inverse(X1),
inference(paramodulation,[status(thm)],[f100,f5]) ).
fof(f392,plain,
! [X0,X1,X2] : X0 = inverse(double_divide(multiply(X0,multiply(X1,X2)),double_divide(X2,X1))),
inference(paramodulation,[status(thm)],[f20,f268]) ).
fof(f444,plain,
! [X0,X1,X2] : X0 = multiply(double_divide(X1,X2),multiply(X0,multiply(X2,X1))),
inference(forward_demodulation,[status(thm)],[f5,f392]) ).
fof(f467,plain,
! [X0,X1,X2,X3] : X0 = multiply(X1,multiply(X0,multiply(double_divide(X2,multiply(X1,X3)),multiply(X3,X2)))),
inference(paramodulation,[status(thm)],[f100,f444]) ).
fof(f521,plain,
! [X0,X1] : X0 = multiply(X1,multiply(X0,inverse(X1))),
inference(forward_demodulation,[status(thm)],[f268,f467]) ).
fof(f526,plain,
! [X0,X1] : multiply(double_divide(inverse(X0),X0),X1) = X1,
inference(paramodulation,[status(thm)],[f14,f521]) ).
fof(f531,plain,
! [X0] : X0 = multiply(b1,multiply(X0,sF3_fnc)),
inference(paramodulation,[status(thm)],[f9,f521]) ).
fof(f539,plain,
! [X0,X1] : X0 = multiply(double_divide(inverse(X0),X1),X1),
inference(paramodulation,[status(thm)],[f521,f444]) ).
fof(f565,plain,
! [X0,X1] : X0 = multiply(X0,multiply(X1,inverse(X1))),
inference(paramodulation,[status(thm)],[f444,f526]) ).
fof(f571,plain,
! [X0] : multiply(double_divide(sF1_fnc,a1),X0) = X0,
inference(paramodulation,[status(thm)],[f7,f526]) ).
fof(f619,plain,
! [X0] : b1 = multiply(double_divide(sF3_fnc,X0),X0),
inference(paramodulation,[status(thm)],[f531,f444]) ).
fof(f1006,plain,
b1 = inverse(sF3_fnc),
inference(paramodulation,[status(thm)],[f268,f619]) ).
fof(f1101,plain,
! [X0] : X0 = inverse(inverse(X0)),
inference(paramodulation,[status(thm)],[f268,f539]) ).
fof(f1148,plain,
a1 = inverse(sF1_fnc),
inference(paramodulation,[status(thm)],[f7,f1101]) ).
fof(f1172,plain,
! [X0] : X0 = multiply(X0,multiply(sF1_fnc,a1)),
inference(paramodulation,[status(thm)],[f1148,f565]) ).
fof(f1174,plain,
! [X0] : X0 = multiply(X0,multiply(sF3_fnc,b1)),
inference(paramodulation,[status(thm)],[f1006,f565]) ).
fof(f1229,plain,
! [X0] : X0 = multiply(X0,sF0_fnc),
inference(forward_demodulation,[status(thm)],[f8,f1172]) ).
fof(f1230,plain,
! [X0] : X0 = multiply(X0,sF2_fnc),
inference(forward_demodulation,[status(thm)],[f10,f1174]) ).
fof(f1236,plain,
double_divide(sF1_fnc,a1) = sF0_fnc,
inference(paramodulation,[status(thm)],[f571,f1229]) ).
fof(f1339,plain,
! [X0] : multiply(sF0_fnc,X0) = X0,
inference(backward_demodulation,[status(thm)],[f1236,f571]) ).
fof(f1359,plain,
sF0_fnc = sF2_fnc,
inference(paramodulation,[status(thm)],[f1230,f1339]) ).
fof(f1399,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1359,f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP601-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n009.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 20 20:17:42 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.08/0.38 % Refutation found
% 0.08/0.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.08/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.43 % Elapsed time: 0.057486 seconds
% 0.13/0.43 % CPU time: 0.049520 seconds
% 0.13/0.43 % Total memory used: 1.952 MB
% 0.13/0.43 % Net memory used: 1.910 MB
%------------------------------------------------------------------------------