%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP012-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n006.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 0.61s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 47 ( 31 unt; 0 def)
% Number of atoms : 74 ( 18 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 56 ( 29 ~; 27 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 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 : 75 ( 75 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : product(identity,X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : product(X,identity,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X] : product(inverse(X),X,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] : product(X,inverse(X),identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y] : product(X,Y,multiply(X,Y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y,Z,W] :
( Z = W
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Y,U,Z,V,W] :
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,hypothesis,
product(a,b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,hypothesis,
product(inverse(b),inverse(a),d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
inverse(c) != d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,plain,
! [X0] : product(identity,X0,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f13,plain,
! [X0] : product(X0,identity,X0),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f14,plain,
! [X0] : product(inverse(X0),X0,identity),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f15,plain,
! [X0] : product(X0,inverse(X0),identity),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f16,plain,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f17,plain,
! [Z,W] :
( Z = W
| ! [X,Y] :
( ~ product(X,Y,W)
| ~ product(X,Y,Z) ) ),
inference(miniscoping,[status(thm)],[f6]) ).
fof(f18,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f19,plain,
! [X,V,W] :
( product(X,V,W)
| ! [U,Z] :
( ~ product(U,Z,W)
| ! [Y] :
( ~ product(Y,Z,V)
| ~ product(X,Y,U) ) ) ),
inference(miniscoping,[status(thm)],[f7]) ).
fof(f20,plain,
! [X0,X1,X2,X3,X4,X5] :
( product(X0,X4,X5)
| ~ product(X2,X3,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f23,plain,
product(a,b,c),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f24,plain,
product(inverse(b),inverse(a),d),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f25,plain,
inverse(c) != d,
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f30,plain,
! [X0,X1] :
( identity = X1
| ~ product(X0,inverse(X0),X1) ),
inference(resolution,[status(thm)],[f18,f15]) ).
fof(f31,plain,
! [X0,X1] :
( X0 = X1
| ~ product(X0,identity,X1) ),
inference(resolution,[status(thm)],[f18,f13]) ).
fof(f32,plain,
! [X0,X1,X2] :
( multiply(X0,X1) = X2
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f18,f16]) ).
fof(f41,plain,
! [X0,X1,X2,X3] :
( product(inverse(X0),X2,X3)
| ~ product(identity,X1,X3)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f20,f14]) ).
fof(f42,plain,
! [X0,X1,X2] :
( product(a,X1,X2)
| ~ product(c,X0,X2)
| ~ product(b,X0,X1) ),
inference(resolution,[status(thm)],[f20,f23]) ).
fof(f60,plain,
! [X0] : X0 = multiply(X0,identity),
inference(resolution,[status(thm)],[f31,f16]) ).
fof(f74,plain,
! [X0] : identity = multiply(X0,inverse(X0)),
inference(resolution,[status(thm)],[f30,f16]) ).
fof(f108,plain,
! [X0] :
( product(inverse(inverse(b)),d,X0)
| ~ product(identity,inverse(a),X0) ),
inference(resolution,[status(thm)],[f41,f24]) ).
fof(f109,plain,
! [X0,X1] :
( product(inverse(inverse(X0)),identity,X1)
| ~ product(identity,X0,X1) ),
inference(resolution,[status(thm)],[f41,f14]) ).
fof(f113,plain,
! [X0,X1,X2] :
( product(inverse(X2),multiply(X2,X0),X1)
| ~ product(identity,X0,X1) ),
inference(resolution,[status(thm)],[f41,f16]) ).
fof(f116,plain,
! [X0,X1] :
( product(a,multiply(b,X0),X1)
| ~ product(c,X0,X1) ),
inference(resolution,[status(thm)],[f42,f16]) ).
fof(f293,plain,
! [X0] : product(a,multiply(b,X0),multiply(c,X0)),
inference(resolution,[status(thm)],[f116,f16]) ).
fof(f313,plain,
! [X0] : multiply(a,multiply(b,X0)) = multiply(c,X0),
inference(resolution,[status(thm)],[f293,f32]) ).
fof(f373,plain,
! [X0] : product(inverse(inverse(X0)),identity,X0),
inference(resolution,[status(thm)],[f109,f12]) ).
fof(f385,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(resolution,[status(thm)],[f373,f31]) ).
fof(f439,plain,
! [X0] :
( product(b,d,X0)
| ~ product(identity,inverse(a),X0) ),
inference(forward_demodulation,[status(thm)],[f385,f108]) ).
fof(f440,plain,
product(b,d,inverse(a)),
inference(resolution,[status(thm)],[f439,f12]) ).
fof(f453,plain,
multiply(b,d) = inverse(a),
inference(resolution,[status(thm)],[f440,f32]) ).
fof(f456,plain,
multiply(a,inverse(a)) = multiply(c,d),
inference(paramodulation,[status(thm)],[f453,f313]) ).
fof(f461,plain,
identity = multiply(c,d),
inference(forward_demodulation,[status(thm)],[f74,f456]) ).
fof(f529,plain,
! [X0,X1] : product(inverse(X0),multiply(X0,X1),X1),
inference(resolution,[status(thm)],[f113,f12]) ).
fof(f550,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(resolution,[status(thm)],[f529,f32]) ).
fof(f577,plain,
multiply(inverse(c),identity) = d,
inference(paramodulation,[status(thm)],[f461,f550]) ).
fof(f594,plain,
inverse(c) = d,
inference(forward_demodulation,[status(thm)],[f60,f577]) ).
fof(f595,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f594,f25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP012-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.56 % Computer : n006.cluster.edu
% 0.09/0.56 % Model : x86_64 x86_64
% 0.09/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.56 % Memory : 8046.5625MB
% 0.09/0.56 % OS : Linux 6.8.0-71-generic
% 0.09/0.56 % CPULimit : 300
% 0.09/0.56 % WCLimit : 300
% 0.09/0.56 % DateTime : Sun Sep 20 19:53:32 UTC 2026
% 0.09/0.56 % CPUTime :
% 0.09/0.57 % Drodi V4.1.1
% 0.09/0.61 % Refutation found
% 0.09/0.61 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.64 % Elapsed time: 0.059646 seconds
% 0.13/0.64 % CPU time: 0.195417 seconds
% 0.13/0.64 % Total memory used: 45.156 MB
% 0.13/0.64 % Net memory used: 44.566 MB
%------------------------------------------------------------------------------