%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP048-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.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 12:32:23 PM UTC 2026
% Result : Unsatisfiable 8.75s 1.58s
% Output : CNFRefutation 8.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 9
% Syntax : Number of formulae : 64 ( 25 unt; 0 def)
% Number of atoms : 129 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 132 ( 67 ~; 65 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 144 ( 144 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : product(identity,X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : product(inverse(X),X,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y] : product(X,Y,multiply(X,Y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y,Z,W] :
( equalish(Z,W)
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,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(f6,axiom,
! [X,Y,U,Z,V,W] :
( product(U,Z,W)
| ~ product(X,V,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Y,W,Z] :
( product(W,Z,Y)
| ~ product(W,Z,X)
| ~ equalish(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,hypothesis,
equalish(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
~ equalish(inverse(a),inverse(b)),
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(inverse(X0),X0,identity),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f12,plain,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f13,plain,
! [Z,W] :
( equalish(Z,W)
| ! [X,Y] :
( ~ product(X,Y,W)
| ~ product(X,Y,Z) ) ),
inference(miniscoping,[status(thm)],[f4]) ).
fof(f14,plain,
! [X0,X1,X2,X3] :
( equalish(X2,X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f15,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)],[f5]) ).
fof(f16,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)],[f15]) ).
fof(f17,plain,
! [U,Z,W] :
( product(U,Z,W)
| ! [X,V] :
( ~ product(X,V,W)
| ! [Y] :
( ~ product(Y,Z,V)
| ~ product(X,Y,U) ) ) ),
inference(miniscoping,[status(thm)],[f6]) ).
fof(f18,plain,
! [X0,X1,X2,X3,X4,X5] :
( product(X2,X3,X5)
| ~ product(X0,X4,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f19,plain,
! [Y,W,Z] :
( product(W,Z,Y)
| ! [X] :
( ~ product(W,Z,X)
| ~ equalish(X,Y) ) ),
inference(miniscoping,[status(thm)],[f7]) ).
fof(f20,plain,
! [X0,X1,X2,X3] :
( product(X2,X3,X1)
| ~ product(X2,X3,X0)
| ~ equalish(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f21,plain,
equalish(a,b),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f22,plain,
~ equalish(inverse(a),inverse(b)),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f23,plain,
! [X0,X1] :
( product(identity,X0,X1)
| ~ equalish(X0,X1) ),
inference(resolution,[status(thm)],[f10,f20]) ).
fof(f24,plain,
! [X0,X1] :
( equalish(X1,X0)
| ~ product(identity,X0,X1) ),
inference(resolution,[status(thm)],[f10,f14]) ).
fof(f25,plain,
! [X0,X1,X2] :
( product(identity,X0,X2)
| ~ equalish(X1,X2)
| ~ equalish(X0,X1) ),
inference(resolution,[status(thm)],[f23,f20]) ).
fof(f26,plain,
! [X0,X1,X2] :
( equalish(X2,X1)
| ~ product(identity,X0,X2)
| ~ equalish(X0,X1) ),
inference(resolution,[status(thm)],[f23,f14]) ).
fof(f27,plain,
! [X0,X1] :
( ~ equalish(X1,X0)
| equalish(X0,X1) ),
inference(resolution,[status(thm)],[f24,f23]) ).
fof(f28,plain,
! [X0] : equalish(X0,X0),
inference(resolution,[status(thm)],[f24,f10]) ).
fof(f32,plain,
! [X0,X1,X2] :
( equalish(X2,X0)
| ~ equalish(X1,X2)
| ~ equalish(X0,X1) ),
inference(resolution,[status(thm)],[f25,f24]) ).
fof(f36,plain,
! [X0] :
( equalish(b,X0)
| ~ equalish(X0,a) ),
inference(resolution,[status(thm)],[f32,f21]) ).
fof(f43,plain,
! [X0,X1,X2] :
( ~ equalish(X0,X2)
| equalish(X2,X1)
| ~ equalish(X0,X1) ),
inference(resolution,[status(thm)],[f26,f23]) ).
fof(f57,plain,
! [X0,X1] :
( equalish(X1,identity)
| ~ product(inverse(X0),X0,X1) ),
inference(resolution,[status(thm)],[f11,f14]) ).
fof(f60,plain,
! [X0] : equalish(multiply(identity,X0),X0),
inference(resolution,[status(thm)],[f12,f24]) ).
fof(f61,plain,
! [X0,X1,X2] :
( product(X0,X1,X2)
| ~ equalish(multiply(X0,X1),X2) ),
inference(resolution,[status(thm)],[f12,f20]) ).
fof(f62,plain,
! [X0,X1,X2] :
( equalish(X2,multiply(X0,X1))
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f12,f14]) ).
fof(f63,plain,
equalish(b,multiply(identity,a)),
inference(resolution,[status(thm)],[f60,f36]) ).
fof(f80,plain,
equalish(multiply(identity,a),b),
inference(resolution,[status(thm)],[f63,f27]) ).
fof(f111,plain,
! [X0,X1,X2,X3] :
( product(X0,identity,X3)
| ~ product(X2,X1,X3)
| ~ product(X0,inverse(X1),X2) ),
inference(resolution,[status(thm)],[f16,f11]) ).
fof(f126,plain,
! [X0,X1,X2,X3] :
( product(X0,X3,X2)
| ~ product(X1,X2,X3)
| ~ product(X0,X1,identity) ),
inference(resolution,[status(thm)],[f16,f10]) ).
fof(f138,plain,
! [X0,X1,X2,X3] :
( product(X1,X2,X3)
| ~ product(X0,X2,X3)
| ~ product(X0,identity,X1) ),
inference(resolution,[status(thm)],[f18,f10]) ).
fof(f162,plain,
! [X0] : equalish(multiply(inverse(X0),X0),identity),
inference(resolution,[status(thm)],[f57,f12]) ).
fof(f164,plain,
! [X0,X1] :
( equalish(identity,X1)
| ~ equalish(multiply(inverse(X0),X0),X1) ),
inference(resolution,[status(thm)],[f162,f43]) ).
fof(f166,plain,
! [X0] : equalish(identity,multiply(inverse(X0),X0)),
inference(resolution,[status(thm)],[f162,f27]) ).
fof(f169,plain,
! [X0,X1] :
( equalish(multiply(inverse(X1),X1),X0)
| ~ equalish(X0,identity) ),
inference(resolution,[status(thm)],[f166,f32]) ).
fof(f181,plain,
product(identity,a,b),
inference(resolution,[status(thm)],[f61,f80]) ).
fof(f192,plain,
! [X0,X1,X2] :
( equalish(multiply(X0,X1),X2)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f62,f27]) ).
fof(f997,plain,
! [X0,X1] :
( ~ product(inverse(X1),X1,X0)
| equalish(identity,X0) ),
inference(resolution,[status(thm)],[f164,f192]) ).
fof(f1065,plain,
! [X0,X1] :
( product(inverse(X1),X1,X0)
| ~ equalish(X0,identity) ),
inference(resolution,[status(thm)],[f169,f61]) ).
fof(f1143,plain,
! [X0,X1,X2] :
( ~ equalish(identity,identity)
| product(inverse(X0),X2,X1)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f126,f1065]) ).
fof(f1158,plain,
! [X0,X1,X2] :
( product(inverse(X0),X2,X1)
| ~ product(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f1143,f28]) ).
fof(f1239,plain,
! [X0,X1] :
( equalish(identity,X1)
| ~ product(X0,X1,X0) ),
inference(resolution,[status(thm)],[f1158,f997]) ).
fof(f1266,plain,
! [X0,X1] :
( ~ product(X1,inverse(X1),X0)
| equalish(identity,X0) ),
inference(resolution,[status(thm)],[f1239,f1158]) ).
fof(f1364,plain,
! [X0] : equalish(identity,multiply(X0,inverse(X0))),
inference(resolution,[status(thm)],[f1266,f12]) ).
fof(f1378,plain,
! [X0] : equalish(multiply(X0,inverse(X0)),identity),
inference(resolution,[status(thm)],[f1364,f27]) ).
fof(f1386,plain,
! [X0] : product(X0,inverse(X0),identity),
inference(resolution,[status(thm)],[f1378,f61]) ).
fof(f1400,plain,
! [X0,X1] :
( product(X0,identity,X1)
| ~ product(identity,X0,X1) ),
inference(resolution,[status(thm)],[f1386,f111]) ).
fof(f1664,plain,
product(a,identity,b),
inference(resolution,[status(thm)],[f1400,f181]) ).
fof(f1675,plain,
! [X0] : product(X0,identity,X0),
inference(resolution,[status(thm)],[f1400,f10]) ).
fof(f1720,plain,
! [X0,X1] :
( equalish(X1,X0)
| ~ product(X0,identity,X1) ),
inference(resolution,[status(thm)],[f1675,f14]) ).
fof(f1721,plain,
! [X0,X1] :
( product(b,X0,X1)
| ~ product(a,X0,X1) ),
inference(resolution,[status(thm)],[f1664,f138]) ).
fof(f1868,plain,
! [X0,X1] :
( ~ product(X1,X0,identity)
| equalish(X0,inverse(X1)) ),
inference(resolution,[status(thm)],[f1720,f1158]) ).
fof(f3230,plain,
product(b,inverse(a),identity),
inference(resolution,[status(thm)],[f1721,f1386]) ).
fof(f3466,plain,
equalish(inverse(a),inverse(b)),
inference(resolution,[status(thm)],[f1868,f3230]) ).
fof(f3510,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f3466,f22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP048-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n010.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 20 19:56:09 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 8.75/1.58 % Refutation found
% 8.75/1.58 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 8.75/1.58 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.11/1.60 % Elapsed time: 1.231539 seconds
% 1.11/1.60 % CPU time: 9.446459 seconds
% 1.11/1.60 % Total memory used: 104.264 MB
% 1.11/1.60 % Net memory used: 92.420 MB
%------------------------------------------------------------------------------