%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : BOO006-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : 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 12:06:18 PM UTC 2026
% Result : Unsatisfiable 0.15s 0.45s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 27 ( 14 unt; 0 def)
% Number of atoms : 55 ( 6 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 58 ( 30 ~; 28 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 66 ( 66 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X,Y] : product(X,Y,multiply(X,Y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y,Z] :
( product(Y,X,Z)
| ~ product(X,Y,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X] : sum(additive_identity,X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X] : sum(X,additive_identity,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X,Y,V1,Z,V2,V3,V4] :
( product(X,V3,V4)
| ~ sum(V1,V2,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [X] : product(X,inverse(X),additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [X,Y,U,V] :
( U = V
| ~ product(X,Y,V)
| ~ product(X,Y,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
~ product(x,additive_identity,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,plain,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f27,plain,
! [X0,X1,X2] :
( product(X1,X0,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f28,plain,
! [X0] : sum(additive_identity,X0,X0),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f29,plain,
! [X0] : sum(X0,additive_identity,X0),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f34,plain,
! [X,V3,V4] :
( product(X,V3,V4)
| ! [V1,V2] :
( ~ sum(V1,V2,V4)
| ! [Y,Z] :
( ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ) ) ),
inference(miniscoping,[status(thm)],[f10]) ).
fof(f35,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( product(X0,X5,X6)
| ~ sum(X2,X4,X6)
| ~ sum(X1,X3,X5)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f51,plain,
! [X0] : product(X0,inverse(X0),additive_identity),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f54,plain,
! [U,V] :
( U = V
| ! [X,Y] :
( ~ product(X,Y,V)
| ~ product(X,Y,U) ) ),
inference(miniscoping,[status(thm)],[f22]) ).
fof(f55,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f56,plain,
~ product(x,additive_identity,additive_identity),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f68,plain,
! [X0,X1] : product(X0,X1,multiply(X1,X0)),
inference(resolution,[status(thm)],[f25,f27]) ).
fof(f114,plain,
! [X0,X1] :
( X1 = additive_identity
| ~ product(X0,inverse(X0),X1) ),
inference(resolution,[status(thm)],[f51,f55]) ).
fof(f173,plain,
! [X0,X1,X2,X3,X4] :
( product(X0,X2,X4)
| ~ sum(X1,X3,X4)
| ~ product(X0,X2,X3)
| ~ product(X0,additive_identity,X1) ),
inference(resolution,[status(thm)],[f35,f28]) ).
fof(f289,plain,
! [X0,X1,X2] :
( product(X0,X2,X1)
| ~ product(X0,X2,additive_identity)
| ~ product(X0,additive_identity,X1) ),
inference(resolution,[status(thm)],[f173,f29]) ).
fof(f879,plain,
! [X0,X1] :
( product(X0,X1,multiply(additive_identity,X0))
| ~ product(X0,X1,additive_identity) ),
inference(resolution,[status(thm)],[f289,f68]) ).
fof(f903,plain,
! [X0] :
( multiply(additive_identity,X0) = additive_identity
| ~ product(X0,inverse(X0),additive_identity) ),
inference(resolution,[status(thm)],[f879,f114]) ).
fof(f941,plain,
! [X0] : multiply(additive_identity,X0) = additive_identity,
inference(forward_subsumption_resolution,[status(thm)],[f903,f51]) ).
fof(f970,plain,
! [X0] : product(X0,additive_identity,additive_identity),
inference(paramodulation,[status(thm)],[f941,f68]) ).
fof(f993,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f56,f970]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO006-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n006.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 13:47:12 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.15/0.45 % Refutation found
% 0.15/0.45 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.15/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.48 % Elapsed time: 0.109728 seconds
% 0.15/0.48 % CPU time: 0.604756 seconds
% 0.15/0.48 % Total memory used: 49.341 MB
% 0.15/0.48 % Net memory used: 48.284 MB
%------------------------------------------------------------------------------