%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP557-1 : 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 12:34:40 PM UTC 2026
% Result : Unsatisfiable 0.15s 0.38s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 32 ( 32 unt; 4 def)
% Number of atoms : 32 ( 31 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 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 : 48 ( 48 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : divide(A,inverse(divide(divide(B,C),divide(A,C)))) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] : multiply(A,B) = divide(A,inverse(B)),
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] : divide(X0,inverse(divide(divide(X1,X2),divide(X0,X2)))) = X1,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f5,plain,
! [X0,X1] : multiply(X0,X1) = divide(X0,inverse(X1)),
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,X3] : divide(X0,inverse(divide(X1,divide(X0,inverse(divide(divide(X1,X2),divide(X3,X2))))))) = X3,
inference(paramodulation,[status(thm)],[f4,f4]) ).
fof(f13,plain,
! [X0,X1,X2,X3] : divide(X0,inverse(divide(divide(X1,inverse(divide(divide(X2,X3),divide(X0,X3)))),X2))) = X1,
inference(paramodulation,[status(thm)],[f4,f4]) ).
fof(f14,plain,
! [X0,X1,X2] : multiply(X0,divide(divide(X1,X2),divide(X0,X2))) = X1,
inference(backward_demodulation,[status(thm)],[f5,f4]) ).
fof(f15,plain,
! [X0] : multiply(X0,b1) = divide(X0,sF3_fnc),
inference(paramodulation,[status(thm)],[f9,f5]) ).
fof(f16,plain,
! [X0] : multiply(X0,a1) = divide(X0,sF1_fnc),
inference(paramodulation,[status(thm)],[f7,f5]) ).
fof(f17,plain,
sF2_fnc = divide(sF3_fnc,sF3_fnc),
inference(backward_demodulation,[status(thm)],[f15,f10]) ).
fof(f18,plain,
sF0_fnc = divide(sF1_fnc,sF1_fnc),
inference(backward_demodulation,[status(thm)],[f16,f8]) ).
fof(f29,plain,
! [X0,X1,X2,X3] : multiply(X0,divide(X1,divide(X0,inverse(divide(divide(X1,X2),divide(X3,X2)))))) = X3,
inference(forward_demodulation,[status(thm)],[f5,f12]) ).
fof(f30,plain,
! [X0,X1,X2,X3] : multiply(X0,divide(X1,multiply(X0,divide(divide(X1,X2),divide(X3,X2))))) = X3,
inference(forward_demodulation,[status(thm)],[f5,f29]) ).
fof(f31,plain,
! [X0,X1] : multiply(X0,divide(X1,X1)) = X0,
inference(paramodulation,[status(thm)],[f14,f30]) ).
fof(f40,plain,
! [X0,X1,X2,X3] : multiply(X0,divide(divide(X1,inverse(divide(divide(X2,X3),divide(X0,X3)))),X2)) = X1,
inference(forward_demodulation,[status(thm)],[f5,f13]) ).
fof(f41,plain,
! [X0,X1,X2,X3] : multiply(X0,divide(multiply(X1,divide(divide(X2,X3),divide(X0,X3))),X2)) = X1,
inference(forward_demodulation,[status(thm)],[f5,f40]) ).
fof(f55,plain,
! [X0] : multiply(X0,sF0_fnc) = X0,
inference(paramodulation,[status(thm)],[f18,f31]) ).
fof(f56,plain,
! [X0] : multiply(X0,sF2_fnc) = X0,
inference(paramodulation,[status(thm)],[f17,f31]) ).
fof(f58,plain,
! [X0,X1] : multiply(X0,divide(X1,X0)) = X1,
inference(paramodulation,[status(thm)],[f31,f41]) ).
fof(f65,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X1,X0)) = X1,
inference(paramodulation,[status(thm)],[f5,f58]) ).
fof(f91,plain,
! [X0] : multiply(inverse(sF2_fnc),X0) = X0,
inference(paramodulation,[status(thm)],[f56,f65]) ).
fof(f111,plain,
inverse(sF2_fnc) = sF2_fnc,
inference(paramodulation,[status(thm)],[f56,f91]) ).
fof(f112,plain,
inverse(sF2_fnc) = sF0_fnc,
inference(paramodulation,[status(thm)],[f55,f91]) ).
fof(f154,plain,
sF2_fnc = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f111,f112]) ).
fof(f155,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f154,f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP557-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n009.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 20 20:16:42 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.15/0.37 % Drodi V4.1.1
% 0.15/0.38 % Refutation found
% 0.15/0.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.15/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.40 % Elapsed time: 0.028645 seconds
% 0.15/0.40 % CPU time: 0.075144 seconds
% 0.15/0.40 % Total memory used: 3.840 MB
% 0.15/0.40 % Net memory used: 3.775 MB
%------------------------------------------------------------------------------