%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP546-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : 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 12:34:38 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.37s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 30 ( 30 unt; 3 def)
% Number of atoms : 30 ( 29 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 : 4 ( 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 : 29 ( 29 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : divide(divide(identity,divide(A,B)),divide(divide(B,C),A)) = C,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] : multiply(A,B) = divide(A,divide(identity,B)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A] : inverse(A) = divide(identity,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A] : identity = divide(A,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,plain,
! [X0,X1,X2] : divide(divide(identity,divide(X0,X1)),divide(divide(X1,X2),X0)) = 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(inverse(b2),b2),a2) != a2,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f11,definition,
sF2_fnc = inverse(b2),
introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition]) ).
fof(f12,definition,
sF1_fnc = multiply(sF2_fnc,b2),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f13,definition,
sF0_fnc = multiply(sF1_fnc,a2),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f14,plain,
sF0_fnc != a2,
inference(definition_folding,[],[f10,f13,f12,f11]) ).
fof(f15,plain,
! [X0,X1] : multiply(X0,X1) = divide(X0,inverse(X1)),
inference(forward_demodulation,[status(thm)],[f8,f7]) ).
fof(f16,plain,
! [X0] : multiply(identity,X0) = inverse(inverse(X0)),
inference(paramodulation,[status(thm)],[f8,f15]) ).
fof(f17,plain,
! [X0] : multiply(X0,b2) = divide(X0,sF2_fnc),
inference(paramodulation,[status(thm)],[f11,f15]) ).
fof(f23,plain,
identity = inverse(identity),
inference(paramodulation,[status(thm)],[f8,f9]) ).
fof(f24,plain,
identity = multiply(sF2_fnc,b2),
inference(paramodulation,[status(thm)],[f17,f9]) ).
fof(f29,plain,
identity = sF1_fnc,
inference(forward_demodulation,[status(thm)],[f12,f24]) ).
fof(f31,plain,
sF0_fnc = multiply(identity,a2),
inference(backward_demodulation,[status(thm)],[f29,f13]) ).
fof(f33,plain,
sF0_fnc = inverse(inverse(a2)),
inference(forward_demodulation,[status(thm)],[f16,f31]) ).
fof(f62,plain,
! [X0,X1,X2] : divide(inverse(divide(X0,X1)),divide(divide(X1,X2),X0)) = X2,
inference(forward_demodulation,[status(thm)],[f8,f6]) ).
fof(f68,plain,
! [X0,X1] : divide(inverse(identity),divide(divide(X0,X1),X0)) = X1,
inference(paramodulation,[status(thm)],[f9,f62]) ).
fof(f82,plain,
! [X0,X1] : divide(identity,divide(divide(X0,X1),X0)) = X1,
inference(forward_demodulation,[status(thm)],[f23,f68]) ).
fof(f83,plain,
! [X0,X1] : inverse(divide(divide(X0,X1),X0)) = X1,
inference(forward_demodulation,[status(thm)],[f8,f82]) ).
fof(f98,plain,
! [X0] : inverse(divide(identity,X0)) = X0,
inference(paramodulation,[status(thm)],[f9,f83]) ).
fof(f105,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f8,f98]) ).
fof(f106,plain,
sF0_fnc = a2,
inference(backward_demodulation,[status(thm)],[f105,f33]) ).
fof(f114,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f106,f14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP546-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n002.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 20 20:19:01 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.12/0.36 % Drodi V4.1.1
% 0.12/0.37 % Refutation found
% 0.12/0.37 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.38 % Elapsed time: 0.023166 seconds
% 0.12/0.38 % CPU time: 0.029651 seconds
% 0.12/0.38 % Total memory used: 705.216 KB
% 0.12/0.38 % Net memory used: 703.072 KB
%------------------------------------------------------------------------------