%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP010-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/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 12:32:15 PM UTC 2026
% Result : Unsatisfiable 0.09s 0.37s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 23 ( 23 unt; 1 def)
% Number of atoms : 23 ( 22 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 : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 17 ( 17 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y,Z] : multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : multiply(identity,X) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X] : multiply(inverse(X),X) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,hypothesis,
multiply(c,b) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
multiply(b,c) != identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f7,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f8,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f9,plain,
multiply(c,b) = identity,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f10,plain,
multiply(b,c) != identity,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f11,definition,
sF0_fnc = multiply(b,c),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f12,plain,
sF0_fnc != identity,
inference(definition_folding,[],[f10,f11]) ).
fof(f14,plain,
! [X0] : multiply(identity,X0) = multiply(c,multiply(b,X0)),
inference(paramodulation,[status(thm)],[f9,f6]) ).
fof(f16,plain,
! [X0] : multiply(sF0_fnc,X0) = multiply(b,multiply(c,X0)),
inference(paramodulation,[status(thm)],[f11,f6]) ).
fof(f19,plain,
! [X0] : X0 = multiply(c,multiply(b,X0)),
inference(forward_demodulation,[status(thm)],[f7,f14]) ).
fof(f28,plain,
c = multiply(c,sF0_fnc),
inference(paramodulation,[status(thm)],[f11,f19]) ).
fof(f32,plain,
multiply(sF0_fnc,sF0_fnc) = multiply(b,c),
inference(paramodulation,[status(thm)],[f28,f16]) ).
fof(f34,plain,
multiply(sF0_fnc,sF0_fnc) = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f11,f32]) ).
fof(f61,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f8,f6]) ).
fof(f62,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f7,f61]) ).
fof(f67,plain,
sF0_fnc = multiply(inverse(sF0_fnc),sF0_fnc),
inference(paramodulation,[status(thm)],[f34,f62]) ).
fof(f79,plain,
sF0_fnc = identity,
inference(forward_demodulation,[status(thm)],[f8,f67]) ).
fof(f80,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f79,f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP010-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n018.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 19:55:30 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.37 % Refutation found
% 0.09/0.37 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.39 % Elapsed time: 0.026286 seconds
% 0.13/0.39 % CPU time: 0.022753 seconds
% 0.13/0.39 % Total memory used: 853.744 KB
% 0.13/0.39 % Net memory used: 810.320 KB
%------------------------------------------------------------------------------