%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP206-1 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 12:33:06 PM UTC 2026
% Result : Unsatisfiable 0.07s 0.71s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 25 ( 25 unt; 6 def)
% Number of atoms : 25 ( 24 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 : 11 ( 11 usr; 10 con; 0-2 aty)
% Number of variables : 12 ( 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : multiply(identity,X) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : multiply(X,identity) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X,Y,Z] : multiply(X,multiply(multiply(Y,Z),X)) = multiply(multiply(X,Y),multiply(Z,X)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
multiply(multiply(a,multiply(b,c)),a) != multiply(multiply(a,b),multiply(c,a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f12,plain,
! [X0] : multiply(X0,identity) = X0,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f19,plain,
! [X0,X1,X2] : multiply(X0,multiply(multiply(X1,X2),X0)) = multiply(multiply(X0,X1),multiply(X2,X0)),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f20,plain,
multiply(multiply(a,multiply(b,c)),a) != multiply(multiply(a,b),multiply(c,a)),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f21,definition,
sF2_fnc = multiply(b,c),
introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition]) ).
fof(f22,definition,
sF1_fnc = multiply(a,sF2_fnc),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f23,definition,
sF0_fnc = multiply(sF1_fnc,a),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f24,definition,
sF4_fnc = multiply(a,b),
introduced(definition,[new_symbols(definition,[sF4_fnc])],[function_definition]) ).
fof(f25,definition,
sF5_fnc = multiply(c,a),
introduced(definition,[new_symbols(definition,[sF5_fnc])],[function_definition]) ).
fof(f26,definition,
sF3_fnc = multiply(sF4_fnc,sF5_fnc),
introduced(definition,[new_symbols(definition,[sF3_fnc])],[function_definition]) ).
fof(f27,plain,
sF0_fnc != sF3_fnc,
inference(definition_folding,[],[f20,f26,f25,f24,f23,f22,f21]) ).
fof(f32,plain,
! [X0] : multiply(a,multiply(multiply(b,X0),a)) = multiply(sF4_fnc,multiply(X0,a)),
inference(paramodulation,[status(thm)],[f24,f19]) ).
fof(f33,plain,
! [X0] : multiply(a,multiply(multiply(sF2_fnc,X0),a)) = multiply(sF1_fnc,multiply(X0,a)),
inference(paramodulation,[status(thm)],[f22,f19]) ).
fof(f62,plain,
multiply(a,multiply(sF2_fnc,a)) = multiply(sF4_fnc,multiply(c,a)),
inference(paramodulation,[status(thm)],[f21,f32]) ).
fof(f67,plain,
multiply(a,multiply(sF2_fnc,a)) = multiply(sF4_fnc,sF5_fnc),
inference(forward_demodulation,[status(thm)],[f25,f62]) ).
fof(f68,plain,
multiply(a,multiply(sF2_fnc,a)) = sF3_fnc,
inference(forward_demodulation,[status(thm)],[f26,f67]) ).
fof(f353,plain,
multiply(a,multiply(sF2_fnc,a)) = multiply(sF1_fnc,multiply(identity,a)),
inference(paramodulation,[status(thm)],[f12,f33]) ).
fof(f368,plain,
sF3_fnc = multiply(sF1_fnc,multiply(identity,a)),
inference(forward_demodulation,[status(thm)],[f68,f353]) ).
fof(f369,plain,
sF3_fnc = multiply(sF1_fnc,a),
inference(forward_demodulation,[status(thm)],[f11,f368]) ).
fof(f370,plain,
sF3_fnc = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f23,f369]) ).
fof(f371,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f370,f27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP206-1 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.04/0.69 % Computer : n012.cluster.edu
% 0.04/0.69 % Model : x86_64 x86_64
% 0.04/0.69 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.69 % Memory : 8046.5625MB
% 0.04/0.69 % OS : Linux 6.8.0-71-generic
% 0.04/0.69 % CPULimit : 300
% 0.04/0.69 % WCLimit : 300
% 0.04/0.70 % DateTime : Sun Sep 20 20:06:10 UTC 2026
% 0.07/0.70 % CPUTime :
% 0.07/0.70 % Drodi V4.1.1
% 0.07/0.71 % Refutation found
% 0.07/0.71 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.07/0.71 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.07/0.72 % Elapsed time: 0.017454 seconds
% 0.07/0.72 % CPU time: 0.037318 seconds
% 0.07/0.72 % Total memory used: 3.157 MB
% 0.07/0.72 % Net memory used: 3.101 MB
%------------------------------------------------------------------------------