%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : BOO013-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 12:06:21 PM UTC 2026
% Result : Unsatisfiable 8.44s 1.65s
% Output : CNFRefutation 8.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 12
% Syntax : Number of formulae : 51 ( 26 unt; 0 def)
% Number of atoms : 101 ( 27 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 102 ( 52 ~; 50 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 88 ( 88 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X,Y] : product(X,Y,multiply(X,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y,Z] :
( product(Y,X,Z)
| ~ product(X,Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X] : sum(additive_identity,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X] : product(X,multiplicative_identity,X),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [X,Y,U,V] :
( U = V
| ~ sum(X,Y,V)
| ~ sum(X,Y,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [X,Y,U,V] :
( U = V
| ~ product(X,Y,V)
| ~ product(X,Y,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
sum(x,y,multiplicative_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
sum(x,z,multiplicative_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
product(x,y,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
product(x,z,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
y != z,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,plain,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f31,plain,
! [X0,X1,X2] :
( product(X1,X0,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f32,plain,
! [X0] : sum(additive_identity,X0,X0),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f35,plain,
! [X0] : product(X0,multiplicative_identity,X0),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f36,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(f37,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)],[f36]) ).
fof(f56,plain,
! [U,V] :
( U = V
| ! [X,Y] :
( ~ sum(X,Y,V)
| ~ sum(X,Y,U) ) ),
inference(miniscoping,[status(thm)],[f21]) ).
fof(f57,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f58,plain,
! [U,V] :
( U = V
| ! [X,Y] :
( ~ product(X,Y,V)
| ~ product(X,Y,U) ) ),
inference(miniscoping,[status(thm)],[f22]) ).
fof(f59,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f60,plain,
sum(x,y,multiplicative_identity),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f61,plain,
sum(x,z,multiplicative_identity),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f62,plain,
product(x,y,additive_identity),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f63,plain,
product(x,z,additive_identity),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f64,plain,
y != z,
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f68,plain,
! [X0,X1] :
( X1 = X0
| ~ sum(additive_identity,X0,X1) ),
inference(resolution,[status(thm)],[f57,f32]) ).
fof(f78,plain,
! [X0,X1,X2,X3,X4,X5] :
( X5 = X3
| ~ product(X0,X4,X5)
| ~ sum(X1,X2,X4)
| ~ product(X0,X2,X3)
| ~ product(X0,X1,additive_identity) ),
inference(resolution,[status(thm)],[f37,f68]) ).
fof(f219,plain,
! [X0] :
( X0 = additive_identity
| ~ product(x,z,X0) ),
inference(resolution,[status(thm)],[f59,f63]) ).
fof(f220,plain,
! [X0] :
( X0 = additive_identity
| ~ product(x,y,X0) ),
inference(resolution,[status(thm)],[f59,f62]) ).
fof(f229,plain,
! [X0,X1,X2,X3] :
( ~ product(X1,X0,X3)
| X2 = X3
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f59,f31]) ).
fof(f291,plain,
! [X0] :
( ~ product(z,x,X0)
| X0 = additive_identity ),
inference(resolution,[status(thm)],[f219,f31]) ).
fof(f299,plain,
! [X0] :
( ~ product(y,x,X0)
| X0 = additive_identity ),
inference(resolution,[status(thm)],[f220,f31]) ).
fof(f338,plain,
multiply(z,x) = additive_identity,
inference(resolution,[status(thm)],[f291,f29]) ).
fof(f344,plain,
product(z,x,additive_identity),
inference(paramodulation,[status(thm)],[f338,f29]) ).
fof(f351,plain,
multiply(y,x) = additive_identity,
inference(resolution,[status(thm)],[f299,f29]) ).
fof(f397,plain,
product(y,x,additive_identity),
inference(paramodulation,[status(thm)],[f351,f29]) ).
fof(f747,plain,
! [X0,X1,X2] :
( X2 = X1
| ~ product(X0,multiplicative_identity,X2)
| ~ product(X0,z,X1)
| ~ product(X0,x,additive_identity) ),
inference(resolution,[status(thm)],[f78,f61]) ).
fof(f748,plain,
! [X0,X1,X2] :
( X2 = X1
| ~ product(X0,multiplicative_identity,X2)
| ~ product(X0,y,X1)
| ~ product(X0,x,additive_identity) ),
inference(resolution,[status(thm)],[f78,f60]) ).
fof(f867,plain,
! [X0,X1] :
( X1 = X0
| ~ product(y,multiplicative_identity,X1)
| ~ product(y,z,X0) ),
inference(resolution,[status(thm)],[f747,f397]) ).
fof(f890,plain,
! [X0] :
( X0 = multiply(y,z)
| ~ product(y,multiplicative_identity,X0) ),
inference(resolution,[status(thm)],[f867,f29]) ).
fof(f896,plain,
y = multiply(y,z),
inference(resolution,[status(thm)],[f890,f35]) ).
fof(f905,plain,
product(y,z,y),
inference(paramodulation,[status(thm)],[f896,f29]) ).
fof(f916,plain,
! [X0] :
( X0 = y
| ~ product(z,y,X0) ),
inference(resolution,[status(thm)],[f905,f229]) ).
fof(f928,plain,
multiply(z,y) = y,
inference(resolution,[status(thm)],[f916,f29]) ).
fof(f934,plain,
product(z,y,y),
inference(paramodulation,[status(thm)],[f928,f29]) ).
fof(f1063,plain,
! [X0,X1] :
( X1 = X0
| ~ product(z,multiplicative_identity,X1)
| ~ product(z,y,X0) ),
inference(resolution,[status(thm)],[f748,f344]) ).
fof(f1150,plain,
! [X0] :
( X0 = y
| ~ product(z,multiplicative_identity,X0) ),
inference(resolution,[status(thm)],[f1063,f934]) ).
fof(f1158,plain,
z = y,
inference(resolution,[status(thm)],[f1150,f35]) ).
fof(f1165,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1158,f64]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : BOO013-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.51 % Computer : n018.cluster.edu
% 0.08/0.51 % Model : x86_64 x86_64
% 0.08/0.51 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.51 % Memory : 8046.5625MB
% 0.08/0.51 % OS : Linux 6.8.0-71-generic
% 0.08/0.51 % CPULimit : 300
% 0.08/0.51 % WCLimit : 300
% 0.08/0.51 % DateTime : Mon Sep 21 13:50:00 UTC 2026
% 0.08/0.51 % CPUTime :
% 0.08/0.52 % Drodi V4.1.1
% 8.44/1.65 % Refutation found
% 8.44/1.65 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 8.44/1.65 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 8.44/1.67 % Elapsed time: 1.146772 seconds
% 8.44/1.67 % CPU time: 8.895795 seconds
% 8.44/1.67 % Total memory used: 86.358 MB
% 8.44/1.67 % Net memory used: 76.375 MB
%------------------------------------------------------------------------------