%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP013-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.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 12:32:16 PM UTC 2026
% Result : Unsatisfiable 0.11s 0.60s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 31 ( 23 unt; 0 def)
% Number of atoms : 42 ( 12 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 25 ( 14 ~; 11 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 36 ( 36 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X] : product(X,identity,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X] : product(inverse(X),X,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y] : product(X,Y,multiply(X,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y,Z,W] :
( Z = W
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,hypothesis,
! [A] : product(A,A,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,hypothesis,
product(a,b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,hypothesis,
product(inverse(a),inverse(b),d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,hypothesis,
! [A,B,C] :
( product(A,C,B)
| ~ product(inverse(A),inverse(B),C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ product(c,d,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,plain,
! [X0] : product(X0,identity,X0),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f16,plain,
! [X0] : product(inverse(X0),X0,identity),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f18,plain,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f19,plain,
! [Z,W] :
( Z = W
| ! [X,Y] :
( ~ product(X,Y,W)
| ~ product(X,Y,Z) ) ),
inference(miniscoping,[status(thm)],[f6]) ).
fof(f20,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f25,plain,
! [X0] : product(X0,X0,identity),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f26,plain,
product(a,b,c),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f27,plain,
product(inverse(a),inverse(b),d),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f28,plain,
! [X0,X1,X2] :
( product(X0,X2,X1)
| ~ product(inverse(X0),inverse(X1),X2) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f29,plain,
~ product(c,d,identity),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f30,plain,
! [X0] :
( c = X0
| ~ product(a,b,X0) ),
inference(resolution,[status(thm)],[f20,f26]) ).
fof(f34,plain,
! [X0,X1] :
( X0 = X1
| ~ product(X0,identity,X1) ),
inference(resolution,[status(thm)],[f20,f15]) ).
fof(f62,plain,
c = multiply(a,b),
inference(resolution,[status(thm)],[f18,f30]) ).
fof(f68,plain,
! [X0,X1,X2] :
( multiply(X0,X1) = X2
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f18,f20]) ).
fof(f102,plain,
multiply(inverse(a),inverse(b)) = d,
inference(resolution,[status(thm)],[f27,f68]) ).
fof(f108,plain,
! [X0] : product(inverse(X0),identity,X0),
inference(resolution,[status(thm)],[f28,f16]) ).
fof(f132,plain,
! [X0] : inverse(X0) = X0,
inference(resolution,[status(thm)],[f108,f34]) ).
fof(f140,plain,
multiply(inverse(a),b) = d,
inference(backward_demodulation,[status(thm)],[f132,f102]) ).
fof(f152,plain,
multiply(a,b) = d,
inference(forward_demodulation,[status(thm)],[f132,f140]) ).
fof(f153,plain,
c = d,
inference(forward_demodulation,[status(thm)],[f62,f152]) ).
fof(f164,plain,
~ product(c,c,identity),
inference(backward_demodulation,[status(thm)],[f153,f29]) ).
fof(f165,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f164,f25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP013-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.56 % Computer : n011.cluster.edu
% 0.11/0.56 % Model : x86_64 x86_64
% 0.11/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.56 % Memory : 8046.5625MB
% 0.11/0.56 % OS : Linux 6.8.0-71-generic
% 0.11/0.57 % CPULimit : 300
% 0.11/0.57 % WCLimit : 300
% 0.11/0.57 % DateTime : Sun Sep 20 19:53:40 UTC 2026
% 0.11/0.57 % CPUTime :
% 0.11/0.58 % Drodi V4.1.1
% 0.11/0.60 % Refutation found
% 0.11/0.60 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.11/0.60 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.62 % Elapsed time: 0.045642 seconds
% 0.11/0.62 % CPU time: 0.142891 seconds
% 0.11/0.62 % Total memory used: 38.924 MB
% 0.11/0.62 % Net memory used: 38.528 MB
%------------------------------------------------------------------------------