%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : BOO016-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 12:06:23 PM UTC 2026
% Result : Unsatisfiable 0.17s 0.76s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 16
% Syntax : Number of formulae : 62 ( 31 unt; 0 def)
% Number of atoms : 134 ( 10 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 146 ( 74 ~; 72 |; 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 : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 173 ( 173 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] : sum(X,Y,add(X,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] : product(X,Y,multiply(X,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] :
( sum(Y,X,Z)
| ~ sum(X,Y,Z) ),
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(f6,axiom,
! [X] : sum(X,additive_identity,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X] : product(multiplicative_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(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/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [X] : product(X,inverse(X),additive_identity),
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,hypothesis,
product(x,y,z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
~ sum(x,z,x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,plain,
! [X0,X1] : sum(X0,X1,add(X0,X1)),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f26,plain,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f27,plain,
! [X0,X1,X2] :
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f28,plain,
! [X0,X1,X2] :
( product(X1,X0,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f29,plain,
! [X0] : sum(additive_identity,X0,X0),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f30,plain,
! [X0] : sum(X0,additive_identity,X0),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f31,plain,
! [X0] : product(multiplicative_identity,X0,X0),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f32,plain,
! [X0] : product(X0,multiplicative_identity,X0),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f33,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(f34,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)],[f33]) ).
fof(f35,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(f36,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)],[f35]) ).
fof(f41,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(f42,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)],[f41]) ).
fof(f52,plain,
! [X0] : product(X0,inverse(X0),additive_identity),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f53,plain,
! [U,V] :
( U = V
| ! [X,Y] :
( ~ sum(X,Y,V)
| ~ sum(X,Y,U) ) ),
inference(miniscoping,[status(thm)],[f21]) ).
fof(f54,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f55,plain,
! [U,V] :
( U = V
| ! [X,Y] :
( ~ product(X,Y,V)
| ~ product(X,Y,U) ) ),
inference(miniscoping,[status(thm)],[f22]) ).
fof(f56,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f57,plain,
product(x,y,z),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f58,plain,
~ sum(x,z,x),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f59,plain,
! [X0,X1,X2,X3,X4] :
( sum(X2,X4,X4)
| ~ sum(X1,X3,X3)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ),
inference(factoring,[status(thm)],[f34]) ).
fof(f72,plain,
! [X0,X1,X2,X3] :
( sum(X1,X3,X3)
| ~ product(X0,X2,X3)
| ~ product(X0,additive_identity,X1) ),
inference(resolution,[status(thm)],[f29,f59]) ).
fof(f86,plain,
! [X0,X1] :
( X1 = X0
| ~ sum(X0,additive_identity,X1) ),
inference(resolution,[status(thm)],[f30,f54]) ).
fof(f95,plain,
! [X0,X1,X2,X3,X4] :
( product(multiplicative_identity,X3,X4)
| ~ sum(X1,X2,X4)
| ~ sum(X0,X2,X3)
| ~ product(multiplicative_identity,X0,X1) ),
inference(resolution,[status(thm)],[f31,f36]) ).
fof(f107,plain,
! [X0,X1,X2] :
( sum(X2,X0,X0)
| ~ sum(X1,multiplicative_identity,multiplicative_identity)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f32,f34]) ).
fof(f122,plain,
! [X0,X1] : sum(X0,X1,add(X1,X0)),
inference(resolution,[status(thm)],[f25,f27]) ).
fof(f135,plain,
! [X0,X1] : product(X0,X1,multiply(X1,X0)),
inference(resolution,[status(thm)],[f28,f26]) ).
fof(f138,plain,
! [X0,X1,X2] :
( product(X2,X0,X0)
| ~ product(X1,additive_identity,additive_identity)
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[f42,f30]) ).
fof(f416,plain,
! [X0,X1,X2] :
( sum(multiply(additive_identity,X0),X2,X2)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f72,f135]) ).
fof(f473,plain,
! [X0] : sum(multiply(additive_identity,X0),additive_identity,additive_identity),
inference(resolution,[status(thm)],[f416,f52]) ).
fof(f623,plain,
! [X0,X1,X2,X3] :
( product(multiplicative_identity,X2,X3)
| ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[f95,f31]) ).
fof(f634,plain,
! [X0] : additive_identity = multiply(additive_identity,X0),
inference(resolution,[status(thm)],[f473,f86]) ).
fof(f677,plain,
! [X0] : product(X0,additive_identity,additive_identity),
inference(paramodulation,[status(thm)],[f634,f135]) ).
fof(f968,plain,
! [X0,X1,X2] :
( product(multiplicative_identity,X2,add(X1,X0))
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[f623,f122]) ).
fof(f1020,plain,
! [X0,X1] : product(multiplicative_identity,add(X0,X1),add(X1,X0)),
inference(resolution,[status(thm)],[f968,f25]) ).
fof(f1053,plain,
! [X0,X1] : product(add(X0,X1),multiplicative_identity,add(X1,X0)),
inference(resolution,[status(thm)],[f1020,f28]) ).
fof(f1096,plain,
! [X0,X1,X2] :
( X2 = add(X1,X0)
| ~ product(add(X0,X1),multiplicative_identity,X2) ),
inference(resolution,[status(thm)],[f1053,f56]) ).
fof(f1855,plain,
! [X0,X1,X2] :
( product(X2,X0,X0)
| ~ sum(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f138,f677]) ).
fof(f1864,plain,
! [X0,X1] : product(add(X0,X1),X1,X1),
inference(resolution,[status(thm)],[f1855,f122]) ).
fof(f1965,plain,
! [X0] : multiplicative_identity = add(multiplicative_identity,X0),
inference(resolution,[status(thm)],[f1864,f1096]) ).
fof(f2053,plain,
! [X0] : sum(X0,multiplicative_identity,multiplicative_identity),
inference(paramodulation,[status(thm)],[f1965,f122]) ).
fof(f2124,plain,
! [X0,X1,X2] :
( sum(X2,X0,X0)
| ~ product(X0,X1,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f107,f2053]) ).
fof(f2804,plain,
sum(z,x,x),
inference(resolution,[status(thm)],[f2124,f57]) ).
fof(f3047,plain,
sum(x,z,x),
inference(resolution,[status(thm)],[f2804,f27]) ).
fof(f3048,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f3047,f58]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO016-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.40 % Computer : n026.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Mon Sep 21 13:51:07 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.17/0.43 % Drodi V4.1.1
% 0.17/0.76 % Refutation found
% 0.17/0.76 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.17/0.76 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/0.81 % Elapsed time: 0.385472 seconds
% 0.17/0.81 % CPU time: 2.591275 seconds
% 0.17/0.81 % Total memory used: 60.018 MB
% 0.17/0.81 % Net memory used: 56.468 MB
%------------------------------------------------------------------------------