%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP012-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.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 0.14s 5.43s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 35 ( 23 unt; 0 def)
% Number of atoms : 58 ( 17 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 49 ( 26 ~; 23 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 78 ( 78 !; 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(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,negated_conjecture,
inverse(multiply(a,b)) != multiply(inverse(b),inverse(a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,plain,
! [X0] : product(identity,X0,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f11,plain,
! [X0] : product(X0,identity,X0),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f12,plain,
! [X0] : product(inverse(X0),X0,identity),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f14,plain,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f15,plain,
! [Z,W] :
( Z = W
| ! [X,Y] :
( ~ product(X,Y,W)
| ~ product(X,Y,Z) ) ),
inference(miniscoping,[status(thm)],[f6]) ).
fof(f16,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f17,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(f18,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)],[f17]) ).
fof(f21,plain,
inverse(multiply(a,b)) != multiply(inverse(b),inverse(a)),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f25,plain,
! [X0,X1] :
( X0 = X1
| ~ product(X0,identity,X1) ),
inference(resolution,[status(thm)],[f16,f11]) ).
fof(f26,plain,
! [X0,X1,X2] :
( multiply(X0,X1) = X2
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f16,f14]) ).
fof(f27,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(resolution,[status(thm)],[f26,f12]) ).
fof(f30,plain,
! [X0] : multiply(X0,identity) = X0,
inference(resolution,[status(thm)],[f26,f11]) ).
fof(f46,plain,
! [X0,X1,X2,X3] :
( product(inverse(X0),X2,X3)
| ~ product(identity,X1,X3)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f18,f12]) ).
fof(f50,plain,
! [X0,X1,X2,X3,X4] :
( product(X3,X2,X4)
| ~ product(multiply(X3,X0),X1,X4)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f18,f14]) ).
fof(f107,plain,
! [X0,X1,X2] :
( product(inverse(X2),multiply(X2,X0),X1)
| ~ product(identity,X0,X1) ),
inference(resolution,[status(thm)],[f46,f14]) ).
fof(f122,plain,
! [X0,X1,X2] :
( product(X0,identity,X2)
| ~ product(multiply(X0,inverse(X1)),X1,X2) ),
inference(resolution,[status(thm)],[f50,f12]) ).
fof(f138,plain,
! [X0,X1] : product(inverse(X0),multiply(X0,X1),X1),
inference(resolution,[status(thm)],[f107,f10]) ).
fof(f153,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(resolution,[status(thm)],[f138,f26]) ).
fof(f170,plain,
! [X0] : multiply(inverse(inverse(X0)),identity) = X0,
inference(paramodulation,[status(thm)],[f27,f153]) ).
fof(f178,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f30,f170]) ).
fof(f266,plain,
! [X0,X1] : product(X0,identity,multiply(multiply(X0,inverse(X1)),X1)),
inference(resolution,[status(thm)],[f122,f14]) ).
fof(f364,plain,
! [X0,X1] : X0 = multiply(multiply(X0,inverse(X1)),X1),
inference(resolution,[status(thm)],[f266,f25]) ).
fof(f421,plain,
! [X0,X1] : X0 = multiply(multiply(X0,X1),inverse(X1)),
inference(paramodulation,[status(thm)],[f178,f364]) ).
fof(f438,plain,
! [X0,X1] : inverse(X0) = multiply(X1,inverse(multiply(X0,X1))),
inference(paramodulation,[status(thm)],[f153,f421]) ).
fof(f607,plain,
! [X0,X1] : inverse(multiply(X0,X1)) = multiply(inverse(X1),inverse(X0)),
inference(paramodulation,[status(thm)],[f421,f438]) ).
fof(f1348,plain,
inverse(multiply(a,b)) != inverse(multiply(a,b)),
inference(backward_demodulation,[status(thm)],[f607,f21]) ).
fof(f1390,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f1348]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP012-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.36 % Computer : n001.cluster.edu
% 0.09/5.36 % Model : x86_64 x86_64
% 0.09/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.36 % Memory : 8046.5625MB
% 0.09/5.36 % OS : Linux 6.8.0-71-generic
% 0.09/5.36 % CPULimit : 300
% 0.09/5.36 % WCLimit : 300
% 0.09/5.36 % DateTime : Sun Sep 20 19:59:19 UTC 2026
% 0.09/5.36 % CPUTime :
% 0.09/5.37 % Drodi V4.1.1
% 0.14/5.43 % Refutation found
% 0.14/5.43 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/5.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/5.45 % Elapsed time: 0.084903 seconds
% 0.14/5.45 % CPU time: 0.391037 seconds
% 0.14/5.45 % Total memory used: 47.505 MB
% 0.14/5.45 % Net memory used: 46.496 MB
%------------------------------------------------------------------------------