%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : BOO013-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 143.59s 23.74s
% Output : CNFRefutation 45.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 17
% Syntax : Number of formulae : 77 ( 41 unt; 0 def)
% Number of atoms : 149 ( 23 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 146 ( 74 ~; 72 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 149 ( 149 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X,Y] : product(X,Y,multiply(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(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(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(f14,axiom,
! [X,Y,V1,Z,V2,V3,V4] :
( sum(X,V3,V4)
| ~ product(V1,V2,V4)
| ~ product(Y,Z,V3)
| ~ sum(X,Z,V2)
| ~ sum(X,Y,V1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [X] : sum(X,inverse(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,axiom,
! [X] : inverse(inverse(X)) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
sum(x,y,multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
sum(x,z,multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
product(x,y,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
product(x,z,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
y != z,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,plain,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f31,plain,
! [X0,X1,X2] :
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f32,plain,
! [X0,X1,X2] :
( product(X1,X0,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f33,plain,
! [X0] : sum(additive_identity,X0,X0),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f36,plain,
! [X0] : product(X0,multiplicative_identity,X0),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f37,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(f38,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)],[f37]) ).
fof(f47,plain,
! [X,V3,V4] :
( sum(X,V3,V4)
| ! [V1,V2] :
( ~ product(V1,V2,V4)
| ! [Y,Z] :
( ~ product(Y,Z,V3)
| ~ sum(X,Z,V2)
| ~ sum(X,Y,V1) ) ) ),
inference(miniscoping,[status(thm)],[f14]) ).
fof(f48,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( sum(X0,X5,X6)
| ~ product(X2,X4,X6)
| ~ product(X1,X3,X5)
| ~ sum(X0,X3,X4)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f54,plain,
! [X0] : sum(X0,inverse(X0),multiplicative_identity),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f55,plain,
! [X0] : product(inverse(X0),X0,additive_identity),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f57,plain,
! [U,V] :
( U = V
| ! [X,Y] :
( ~ sum(X,Y,V)
| ~ sum(X,Y,U) ) ),
inference(miniscoping,[status(thm)],[f21]) ).
fof(f58,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f59,plain,
! [U,V] :
( U = V
| ! [X,Y] :
( ~ product(X,Y,V)
| ~ product(X,Y,U) ) ),
inference(miniscoping,[status(thm)],[f22]) ).
fof(f60,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f61,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f62,plain,
sum(x,y,multiplicative_identity),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f63,plain,
sum(x,z,multiplicative_identity),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f64,plain,
product(x,y,additive_identity),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f65,plain,
product(x,z,additive_identity),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f66,plain,
y != z,
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f77,plain,
sum(y,x,multiplicative_identity),
inference(resolution,[status(thm)],[f62,f31]) ).
fof(f78,plain,
sum(z,x,multiplicative_identity),
inference(resolution,[status(thm)],[f63,f31]) ).
fof(f83,plain,
! [X0,X1] : product(X0,X1,multiply(X1,X0)),
inference(resolution,[status(thm)],[f32,f30]) ).
fof(f86,plain,
! [X0,X1,X2,X3] :
( sum(additive_identity,X1,X3)
| ~ product(x,X2,X3)
| ~ sum(z,X0,X2)
| ~ product(x,X0,X1) ),
inference(resolution,[status(thm)],[f38,f65]) ).
fof(f87,plain,
! [X0,X1,X2,X3] :
( sum(additive_identity,X1,X3)
| ~ product(x,X2,X3)
| ~ sum(y,X0,X2)
| ~ product(x,X0,X1) ),
inference(resolution,[status(thm)],[f38,f64]) ).
fof(f88,plain,
! [X0,X1,X2,X3,X4] :
( sum(additive_identity,X2,X4)
| ~ product(inverse(X0),X3,X4)
| ~ sum(X0,X1,X3)
| ~ product(inverse(X0),X1,X2) ),
inference(resolution,[status(thm)],[f38,f55]) ).
fof(f127,plain,
! [X0,X1] :
( X0 = X1
| ~ sum(additive_identity,X0,X1) ),
inference(resolution,[status(thm)],[f58,f33]) ).
fof(f186,plain,
! [X0,X1,X2,X3,X4] :
( sum(additive_identity,X3,X4)
| ~ product(X2,X1,X4)
| ~ product(X2,X0,X3)
| ~ sum(additive_identity,X0,X1) ),
inference(resolution,[status(thm)],[f48,f33]) ).
fof(f250,plain,
! [X0,X1,X2] :
( multiply(X1,X0) = X2
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f60,f83]) ).
fof(f268,plain,
! [X0,X1,X2] :
( sum(additive_identity,multiply(X0,x),X2)
| ~ product(x,X1,X2)
| ~ sum(z,X0,X1) ),
inference(resolution,[status(thm)],[f86,f83]) ).
fof(f285,plain,
! [X0,X1,X2] :
( sum(additive_identity,multiply(X0,x),X2)
| ~ product(x,X1,X2)
| ~ sum(y,X0,X1) ),
inference(resolution,[status(thm)],[f87,f83]) ).
fof(f326,plain,
! [X0,X1,X2,X3] :
( sum(additive_identity,multiply(X1,inverse(X0)),X3)
| ~ product(inverse(X0),X2,X3)
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[f88,f83]) ).
fof(f452,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(resolution,[status(thm)],[f250,f30]) ).
fof(f1708,plain,
! [X0,X1,X2,X3] :
( sum(additive_identity,X2,X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f186,f33]) ).
fof(f2021,plain,
! [X0,X1,X2] :
( sum(additive_identity,multiply(X1,X0),X2)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f1708,f83]) ).
fof(f2121,plain,
! [X0,X1] : sum(additive_identity,multiply(X0,X1),multiply(X1,X0)),
inference(resolution,[status(thm)],[f2021,f30]) ).
fof(f2185,plain,
! [X0,X1,X2] :
( multiply(X1,X0) = X2
| ~ sum(additive_identity,multiply(X0,X1),X2) ),
inference(resolution,[status(thm)],[f2121,f58]) ).
fof(f4992,plain,
! [X0] :
( sum(additive_identity,multiply(inverse(z),x),X0)
| ~ product(x,multiplicative_identity,X0) ),
inference(resolution,[status(thm)],[f268,f54]) ).
fof(f4999,plain,
! [X0] :
( sum(additive_identity,multiply(x,inverse(z)),X0)
| ~ product(x,multiplicative_identity,X0) ),
inference(forward_demodulation,[status(thm)],[f452,f4992]) ).
fof(f5077,plain,
! [X0] :
( sum(additive_identity,multiply(inverse(y),x),X0)
| ~ product(x,multiplicative_identity,X0) ),
inference(resolution,[status(thm)],[f285,f54]) ).
fof(f5084,plain,
! [X0] :
( sum(additive_identity,multiply(x,inverse(y)),X0)
| ~ product(x,multiplicative_identity,X0) ),
inference(forward_demodulation,[status(thm)],[f452,f5077]) ).
fof(f5153,plain,
! [X0] :
( sum(additive_identity,multiply(x,inverse(z)),X0)
| ~ product(inverse(z),multiplicative_identity,X0) ),
inference(resolution,[status(thm)],[f326,f78]) ).
fof(f5154,plain,
! [X0] :
( sum(additive_identity,multiply(x,inverse(y)),X0)
| ~ product(inverse(y),multiplicative_identity,X0) ),
inference(resolution,[status(thm)],[f326,f77]) ).
fof(f42414,plain,
sum(additive_identity,multiply(x,inverse(z)),x),
inference(resolution,[status(thm)],[f4999,f36]) ).
fof(f42419,plain,
multiply(inverse(z),x) = x,
inference(resolution,[status(thm)],[f42414,f2185]) ).
fof(f42500,plain,
multiply(x,inverse(z)) = x,
inference(forward_demodulation,[status(thm)],[f452,f42419]) ).
fof(f44098,plain,
sum(additive_identity,multiply(x,inverse(y)),x),
inference(resolution,[status(thm)],[f5084,f36]) ).
fof(f44103,plain,
multiply(inverse(y),x) = x,
inference(resolution,[status(thm)],[f44098,f2185]) ).
fof(f44184,plain,
multiply(x,inverse(y)) = x,
inference(forward_demodulation,[status(thm)],[f452,f44103]) ).
fof(f45822,plain,
! [X0] :
( sum(additive_identity,x,X0)
| ~ product(inverse(z),multiplicative_identity,X0) ),
inference(forward_demodulation,[status(thm)],[f42500,f5153]) ).
fof(f45823,plain,
sum(additive_identity,x,inverse(z)),
inference(resolution,[status(thm)],[f45822,f36]) ).
fof(f45837,plain,
x = inverse(z),
inference(resolution,[status(thm)],[f45823,f127]) ).
fof(f46138,plain,
inverse(x) = z,
inference(paramodulation,[status(thm)],[f45837,f61]) ).
fof(f46178,plain,
! [X0] :
( sum(additive_identity,x,X0)
| ~ product(inverse(y),multiplicative_identity,X0) ),
inference(forward_demodulation,[status(thm)],[f44184,f5154]) ).
fof(f46179,plain,
sum(additive_identity,x,inverse(y)),
inference(resolution,[status(thm)],[f46178,f36]) ).
fof(f46444,plain,
x = inverse(y),
inference(resolution,[status(thm)],[f46179,f127]) ).
fof(f46754,plain,
inverse(x) = y,
inference(paramodulation,[status(thm)],[f46444,f61]) ).
fof(f46855,plain,
y = z,
inference(backward_demodulation,[status(thm)],[f46754,f46138]) ).
fof(f46955,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f46855,f66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO013-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.37 % Computer : n004.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Mon Sep 21 13:47:55 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.38 % Drodi V4.1.1
% 143.59/23.74 % Refutation found
% 143.59/23.74 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 143.59/23.74 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 45.47/23.77 % Elapsed time: 18.381842 seconds
% 45.47/23.77 % CPU time: 145.574972 seconds
% 45.47/23.77 % Total memory used: 208.818 MB
% 45.47/23.77 % Net memory used: 167.382 MB
%------------------------------------------------------------------------------