%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP011-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.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 0.93s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 23 ( 23 unt; 0 def)
% Number of atoms : 23 ( 22 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 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 : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 21 ( 21 !; 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(b,c) = multiply(d,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
b != d,
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(b,c) = multiply(d,c),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f10,plain,
b != d,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f12,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f8,f6]) ).
fof(f14,plain,
! [X0] : multiply(multiply(b,c),X0) = multiply(d,multiply(c,X0)),
inference(paramodulation,[status(thm)],[f9,f6]) ).
fof(f17,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f7,f12]) ).
fof(f18,plain,
! [X0] : multiply(b,multiply(c,X0)) = multiply(d,multiply(c,X0)),
inference(forward_demodulation,[status(thm)],[f6,f14]) ).
fof(f24,plain,
! [X0,X1] : multiply(X0,X1) = multiply(inverse(inverse(X0)),X1),
inference(paramodulation,[status(thm)],[f17,f17]) ).
fof(f25,plain,
! [X0] : X0 = multiply(inverse(inverse(X0)),identity),
inference(paramodulation,[status(thm)],[f8,f17]) ).
fof(f101,plain,
! [X0] : X0 = multiply(X0,identity),
inference(backward_demodulation,[status(thm)],[f24,f25]) ).
fof(f103,plain,
! [X0] : multiply(X0,inverse(X0)) = identity,
inference(paramodulation,[status(thm)],[f8,f24]) ).
fof(f144,plain,
multiply(b,multiply(c,inverse(c))) = multiply(d,identity),
inference(paramodulation,[status(thm)],[f103,f18]) ).
fof(f151,plain,
multiply(b,identity) = multiply(d,identity),
inference(forward_demodulation,[status(thm)],[f103,f144]) ).
fof(f152,plain,
b = multiply(d,identity),
inference(forward_demodulation,[status(thm)],[f101,f151]) ).
fof(f153,plain,
b = d,
inference(forward_demodulation,[status(thm)],[f101,f152]) ).
fof(f154,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f153,f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP011-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.91 % Computer : n007.cluster.edu
% 0.09/0.91 % Model : x86_64 x86_64
% 0.09/0.91 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.91 % Memory : 8046.5625MB
% 0.09/0.91 % OS : Linux 6.8.0-71-generic
% 0.09/0.91 % CPULimit : 300
% 0.09/0.91 % WCLimit : 300
% 0.09/0.91 % DateTime : Sun Sep 20 19:51:22 UTC 2026
% 0.09/0.91 % CPUTime :
% 0.09/0.92 % Drodi V4.1.1
% 0.09/0.93 % Refutation found
% 0.09/0.93 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.93 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.95 % Elapsed time: 0.026029 seconds
% 0.09/0.95 % CPU time: 0.038699 seconds
% 0.09/0.95 % Total memory used: 1.221 MB
% 0.09/0.95 % Net memory used: 1.145 MB
%------------------------------------------------------------------------------