%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : RNG041-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.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 02:04:46 PM UTC 2026
% Result : Unsatisfiable 0.13s 10.40s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 32 ( 17 unt; 0 def)
% Number of atoms : 57 ( 20 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 49 ( 24 ~; 25 |; 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 : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 54 ( 54 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X,Y] : product(X,Y,multiply(X,Y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,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(f17,axiom,
! [X,Y,U,V] :
( U = V
| ~ product(X,Y,V)
| ~ product(X,Y,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,hypothesis,
! [A] : product(additive_identity,A,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,hypothesis,
! [A] : product(A,multiplicative_identity,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,hypothesis,
! [A] :
( A = additive_identity
| product(A,h(A),multiplicative_identity) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
product(a,b,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
a != additive_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
b != additive_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,plain,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f38,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)],[f10]) ).
fof(f39,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)],[f38]) ).
fof(f52,plain,
! [U,V] :
( U = V
| ! [X,Y] :
( ~ product(X,Y,V)
| ~ product(X,Y,U) ) ),
inference(miniscoping,[status(thm)],[f17]) ).
fof(f53,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f54,plain,
! [X0] : product(additive_identity,X0,additive_identity),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f56,plain,
! [X0] : product(X0,multiplicative_identity,X0),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f58,plain,
! [X0] :
( X0 = additive_identity
| product(X0,h(X0),multiplicative_identity) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f60,plain,
product(a,b,additive_identity),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f61,plain,
a != additive_identity,
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f62,plain,
b != additive_identity,
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f64,plain,
! [X0,X1,X2] :
( product(a,X1,X2)
| ~ product(additive_identity,X0,X2)
| ~ product(b,X0,X1) ),
inference(resolution,[status(thm)],[f39,f60]) ).
fof(f97,plain,
! [X0,X1] :
( X0 = X1
| ~ product(X0,multiplicative_identity,X1) ),
inference(resolution,[status(thm)],[f56,f53]) ).
fof(f105,plain,
! [X0,X1] :
( product(a,multiply(b,X0),X1)
| ~ product(additive_identity,X0,X1) ),
inference(resolution,[status(thm)],[f29,f64]) ).
fof(f114,plain,
! [X0,X1,X2] :
( multiply(X0,X1) = X2
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f29,f53]) ).
fof(f123,plain,
! [X0] : X0 = multiply(X0,multiplicative_identity),
inference(resolution,[status(thm)],[f97,f29]) ).
fof(f155,plain,
! [X0] :
( multiply(X0,h(X0)) = multiplicative_identity
| X0 = additive_identity ),
inference(resolution,[status(thm)],[f58,f114]) ).
fof(f189,plain,
! [X0] : product(a,multiply(b,X0),additive_identity),
inference(resolution,[status(thm)],[f105,f54]) ).
fof(f198,plain,
! [X0] : multiply(a,multiply(b,X0)) = additive_identity,
inference(resolution,[status(thm)],[f189,f114]) ).
fof(f219,plain,
( b = additive_identity
| multiply(a,multiplicative_identity) = additive_identity ),
inference(paramodulation,[status(thm)],[f155,f198]) ).
fof(f224,plain,
( b = additive_identity
| a = additive_identity ),
inference(forward_demodulation,[status(thm)],[f123,f219]) ).
fof(f225,plain,
b = additive_identity,
inference(forward_subsumption_resolution,[status(thm)],[f224,f61]) ).
fof(f227,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f225,f62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG041-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/10.37 % Computer : n002.cluster.edu
% 0.09/10.37 % Model : x86_64 x86_64
% 0.09/10.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/10.37 % Memory : 8046.5625MB
% 0.09/10.37 % OS : Linux 6.8.0-71-generic
% 0.09/10.37 % CPULimit : 300
% 0.09/10.37 % WCLimit : 300
% 0.09/10.37 % DateTime : Mon Sep 21 04:17:28 UTC 2026
% 0.09/10.37 % CPUTime :
% 0.09/10.38 % Drodi V4.1.1
% 0.13/10.40 % Refutation found
% 0.13/10.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/10.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/10.43 % Elapsed time: 0.049622 seconds
% 0.13/10.43 % CPU time: 0.173365 seconds
% 0.13/10.43 % Total memory used: 78.711 MB
% 0.13/10.43 % Net memory used: 78.351 MB
%------------------------------------------------------------------------------