%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP012-1 : 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 12:32:15 PM UTC 2026
% Result : Unsatisfiable 0.02s 0.40s
% Output : CNFRefutation 0.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of formulae : 48 ( 30 unt; 0 def)
% Number of atoms : 83 ( 16 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 72 ( 37 ~; 35 |; 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 : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 91 ( 91 !; 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(f8,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(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,
~ product(c,d,identity),
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(f21,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)],[f8]) ).
fof(f22,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)],[f21]) ).
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,
~ product(c,d,identity),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f27,plain,
! [X0,X1] :
( X0 = X1
| ~ product(identity,X0,X1) ),
inference(resolution,[status(thm)],[f18,f12]) ).
fof(f34,plain,
! [X0] :
( d = X0
| ~ product(inverse(b),inverse(a),X0) ),
inference(resolution,[status(thm)],[f24,f18]) ).
fof(f37,plain,
! [X0,X1,X2] :
( product(a,X1,X2)
| ~ product(c,X0,X2)
| ~ product(b,X0,X1) ),
inference(resolution,[status(thm)],[f20,f23]) ).
fof(f54,plain,
! [X0,X1,X2,X3] :
( product(identity,X1,X3)
| ~ product(inverse(X0),X2,X3)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f14,f22]) ).
fof(f64,plain,
! [X0,X1] :
( identity = X1
| ~ product(X0,inverse(X0),X1) ),
inference(resolution,[status(thm)],[f15,f18]) ).
fof(f67,plain,
d = multiply(inverse(b),inverse(a)),
inference(resolution,[status(thm)],[f16,f34]) ).
fof(f75,plain,
! [X0,X1,X2] :
( multiply(X0,X1) = X2
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f16,f18]) ).
fof(f92,plain,
! [X0] : identity = multiply(X0,inverse(X0)),
inference(resolution,[status(thm)],[f64,f16]) ).
fof(f100,plain,
! [X0,X1] :
( product(a,multiply(b,X0),X1)
| ~ product(c,X0,X1) ),
inference(resolution,[status(thm)],[f37,f16]) ).
fof(f173,plain,
! [X0,X1] :
( product(identity,X0,X1)
| ~ product(inverse(inverse(X0)),identity,X1) ),
inference(resolution,[status(thm)],[f54,f14]) ).
fof(f178,plain,
! [X0,X1,X2] :
( product(identity,X1,X2)
| ~ product(inverse(X0),multiply(X0,X1),X2) ),
inference(resolution,[status(thm)],[f54,f16]) ).
fof(f310,plain,
! [X0] : product(a,multiply(b,X0),multiply(c,X0)),
inference(resolution,[status(thm)],[f100,f16]) ).
fof(f330,plain,
! [X0] : multiply(a,multiply(b,X0)) = multiply(c,X0),
inference(resolution,[status(thm)],[f310,f75]) ).
fof(f391,plain,
! [X0] : product(identity,X0,inverse(inverse(X0))),
inference(resolution,[status(thm)],[f173,f13]) ).
fof(f402,plain,
! [X0] : X0 = inverse(inverse(X0)),
inference(resolution,[status(thm)],[f391,f27]) ).
fof(f533,plain,
! [X0,X1] : product(identity,X0,multiply(inverse(X1),multiply(X1,X0))),
inference(resolution,[status(thm)],[f178,f16]) ).
fof(f556,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(resolution,[status(thm)],[f533,f27]) ).
fof(f622,plain,
inverse(a) = multiply(inverse(inverse(b)),d),
inference(paramodulation,[status(thm)],[f67,f556]) ).
fof(f637,plain,
inverse(a) = multiply(b,d),
inference(forward_demodulation,[status(thm)],[f402,f622]) ).
fof(f668,plain,
multiply(a,inverse(a)) = multiply(c,d),
inference(paramodulation,[status(thm)],[f637,f330]) ).
fof(f675,plain,
identity = multiply(c,d),
inference(forward_demodulation,[status(thm)],[f92,f668]) ).
fof(f681,plain,
product(c,d,identity),
inference(paramodulation,[status(thm)],[f675,f16]) ).
fof(f684,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f681,f25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP012-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.02/0.35 % Computer : n010.cluster.edu
% 0.02/0.35 % Model : x86_64 x86_64
% 0.02/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.35 % Memory : 8046.5625MB
% 0.02/0.35 % OS : Linux 6.8.0-71-generic
% 0.02/0.36 % CPULimit : 300
% 0.02/0.36 % WCLimit : 300
% 0.02/0.36 % DateTime : Sun Sep 20 19:53:56 UTC 2026
% 0.02/0.36 % CPUTime :
% 0.02/0.37 % Drodi V4.1.1
% 0.02/0.40 % Refutation found
% 0.02/0.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.02/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.02/0.42 % Elapsed time: 0.050169 seconds
% 0.02/0.42 % CPU time: 0.273812 seconds
% 0.02/0.42 % Total memory used: 37.441 MB
% 0.02/0.42 % Net memory used: 36.885 MB
%------------------------------------------------------------------------------