%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : BOO004-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 12:06:17 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.54s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of formulae : 41 ( 20 unt; 0 def)
% Number of atoms : 88 ( 10 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 96 ( 49 ~; 47 |; 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 104 ( 104 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] : sum(X,Y,add(X,Y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] :
( sum(Y,X,Z)
| ~ sum(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(f8,axiom,
! [X] : product(X,multiplicative_identity,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X,Y,V1,Z,V2,V3,V4] :
( sum(V1,V2,V4)
| ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X,Y,V1,Z,V2,V3,V4] :
( product(V1,V2,V4)
| ~ sum(X,V3,V4)
| ~ product(Y,Z,V3)
| ~ sum(X,Z,V2)
| ~ sum(X,Y,V1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [X] : sum(inverse(X),X,multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [X] : product(inverse(X),X,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [X,Y,U,V] :
( U = V
| ~ sum(X,Y,V)
| ~ sum(X,Y,U) ),
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,
~ sum(x,x,x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,plain,
! [X0,X1] : sum(X0,X1,add(X0,X1)),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f26,plain,
! [X0,X1,X2] :
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f28,plain,
! [X0] : sum(additive_identity,X0,X0),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f31,plain,
! [X0] : product(X0,multiplicative_identity,X0),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f32,plain,
! [V1,V2,V4] :
( sum(V1,V2,V4)
| ! [X,V3] :
( ~ product(X,V3,V4)
| ! [Y,Z] :
( ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ) ) ),
inference(miniscoping,[status(thm)],[f9]) ).
fof(f33,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( sum(X2,X4,X6)
| ~ product(X0,X5,X6)
| ~ sum(X1,X3,X5)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f40,plain,
! [V1,V2,V4] :
( product(V1,V2,V4)
| ! [X,V3] :
( ~ sum(X,V3,V4)
| ! [Y,Z] :
( ~ product(Y,Z,V3)
| ~ sum(X,Z,V2)
| ~ sum(X,Y,V1) ) ) ),
inference(miniscoping,[status(thm)],[f13]) ).
fof(f41,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( product(X2,X4,X6)
| ~ sum(X0,X5,X6)
| ~ product(X1,X3,X5)
| ~ sum(X0,X3,X4)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f48,plain,
! [X0] : sum(inverse(X0),X0,multiplicative_identity),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f50,plain,
! [X0] : product(inverse(X0),X0,additive_identity),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f52,plain,
! [U,V] :
( U = V
| ! [X,Y] :
( ~ sum(X,Y,V)
| ~ sum(X,Y,U) ) ),
inference(miniscoping,[status(thm)],[f21]) ).
fof(f53,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
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,
~ sum(x,x,x),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f58,plain,
! [X0] : sum(X0,additive_identity,X0),
inference(resolution,[status(thm)],[f28,f26]) ).
fof(f59,plain,
! [X0,X1] :
( X1 = X0
| ~ sum(X0,additive_identity,X1) ),
inference(resolution,[status(thm)],[f58,f53]) ).
fof(f68,plain,
! [X0,X1] : sum(X0,X1,add(X1,X0)),
inference(resolution,[status(thm)],[f24,f26]) ).
fof(f103,plain,
multiplicative_identity = inverse(additive_identity),
inference(resolution,[status(thm)],[f48,f59]) ).
fof(f146,plain,
! [X0,X1,X2] :
( sum(X2,X0,X0)
| ~ sum(X1,multiplicative_identity,multiplicative_identity)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f33,f31]) ).
fof(f200,plain,
! [X0,X1] :
( X1 = X0
| ~ product(X0,multiplicative_identity,X1) ),
inference(resolution,[status(thm)],[f55,f31]) ).
fof(f293,plain,
! [X0,X1,X2] :
( product(X2,X0,X0)
| ~ product(X1,additive_identity,additive_identity)
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[f41,f58]) ).
fof(f312,plain,
! [X0,X1] :
( product(X1,X0,X0)
| ~ sum(X0,inverse(additive_identity),X1) ),
inference(resolution,[status(thm)],[f293,f50]) ).
fof(f314,plain,
! [X0,X1] :
( product(X1,X0,X0)
| ~ sum(X0,multiplicative_identity,X1) ),
inference(forward_demodulation,[status(thm)],[f103,f312]) ).
fof(f323,plain,
! [X0] : product(add(multiplicative_identity,X0),X0,X0),
inference(resolution,[status(thm)],[f314,f68]) ).
fof(f328,plain,
multiplicative_identity = add(multiplicative_identity,multiplicative_identity),
inference(resolution,[status(thm)],[f323,f200]) ).
fof(f352,plain,
sum(multiplicative_identity,multiplicative_identity,multiplicative_identity),
inference(paramodulation,[status(thm)],[f328,f68]) ).
fof(f1061,plain,
! [X0] :
( sum(X0,X0,X0)
| ~ sum(multiplicative_identity,multiplicative_identity,multiplicative_identity) ),
inference(resolution,[status(thm)],[f146,f31]) ).
fof(f1065,plain,
! [X0] : sum(X0,X0,X0),
inference(forward_subsumption_resolution,[status(thm)],[f1061,f352]) ).
fof(f1067,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f56,f1065]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO004-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n005.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 13:45:49 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.14/0.38 % Drodi V4.1.1
% 0.14/0.54 % Refutation found
% 0.14/0.54 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.54 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.54 % Elapsed time: 0.172010 seconds
% 0.14/0.54 % CPU time: 1.116277 seconds
% 0.14/0.54 % Total memory used: 53.804 MB
% 0.14/0.54 % Net memory used: 51.632 MB
%------------------------------------------------------------------------------