%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : BOO005-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 2.76s 0.79s
% Output : CNFRefutation 2.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 14
% Syntax : Number of formulae : 67 ( 32 unt; 0 def)
% Number of atoms : 133 ( 16 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 134 ( 68 ~; 66 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 166 ( 166 !; 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(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(f15,axiom,
! [Y,X,V1,Z,V2,V3,V4] :
( product(V1,V2,V4)
| ~ sum(V3,X,V4)
| ~ product(Y,Z,V3)
| ~ sum(Z,X,V2)
| ~ sum(Y,X,V1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [X] : sum(inverse(X),X,multiplicative_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [X] : product(inverse(X),X,additive_identity),
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,negated_conjecture,
~ sum(x,multiplicative_identity,multiplicative_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,plain,
! [X0,X1] : sum(X0,X1,add(X0,X1)),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f25,plain,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f26,plain,
! [X0,X1,X2] :
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
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(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(f44,plain,
! [V1,V2,V4] :
( product(V1,V2,V4)
| ! [X,V3] :
( ~ sum(V3,X,V4)
| ! [Y,Z] :
( ~ product(Y,Z,V3)
| ~ sum(Z,X,V2)
| ~ sum(Y,X,V1) ) ) ),
inference(miniscoping,[status(thm)],[f15]) ).
fof(f45,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( product(X2,X4,X6)
| ~ sum(X5,X1,X6)
| ~ product(X0,X3,X5)
| ~ sum(X3,X1,X4)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f44]) ).
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(f51,plain,
! [X0] : product(X0,inverse(X0),additive_identity),
inference(cnf_transformation,[status(thm)],[f20]) ).
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,multiplicative_identity,multiplicative_identity),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f57,plain,
! [X0,X1] :
( X1 = X0
| ~ sum(additive_identity,X0,X1) ),
inference(resolution,[status(thm)],[f28,f53]) ).
fof(f58,plain,
! [X0] : sum(X0,additive_identity,X0),
inference(resolution,[status(thm)],[f28,f26]) ).
fof(f61,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(f145,plain,
! [X0,X1,X2] :
( sum(X2,additive_identity,additive_identity)
| ~ sum(X1,X0,X0)
| ~ product(inverse(X0),X1,X2) ),
inference(resolution,[status(thm)],[f33,f50]) ).
fof(f149,plain,
! [X0,X1,X2] :
( sum(X2,additive_identity,additive_identity)
| ~ sum(X1,inverse(X0),inverse(X0))
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f33,f51]) ).
fof(f151,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(f160,plain,
! [X0,X1,X2,X3,X4] :
( sum(X2,X4,X0)
| ~ sum(X1,X3,multiplicative_identity)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f33,f31]) ).
fof(f222,plain,
! [X0,X1] :
( sum(X1,X0,X0)
| ~ product(X0,additive_identity,X1) ),
inference(resolution,[status(thm)],[f151,f28]) ).
fof(f231,plain,
! [X0,X1] :
( ~ product(additive_identity,X1,X0)
| sum(X0,X1,X1) ),
inference(resolution,[status(thm)],[f222,f27]) ).
fof(f284,plain,
! [X0] : sum(multiply(additive_identity,X0),X0,X0),
inference(resolution,[status(thm)],[f231,f25]) ).
fof(f494,plain,
! [X0,X1,X2,X3] :
( sum(X2,X3,X0)
| ~ product(X0,X1,X3)
| ~ product(X0,inverse(X1),X2) ),
inference(resolution,[status(thm)],[f160,f48]) ).
fof(f521,plain,
! [X0,X1] :
( X1 = X0
| ~ product(X0,multiplicative_identity,X1) ),
inference(resolution,[status(thm)],[f55,f31]) ).
fof(f522,plain,
! [X0,X1,X2] :
( X2 = multiply(X0,X1)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f55,f25]) ).
fof(f653,plain,
! [X0,X1,X2] :
( ~ product(X2,X1,X0)
| X0 = multiply(X1,X2) ),
inference(resolution,[status(thm)],[f522,f27]) ).
fof(f739,plain,
! [X0,X1] :
( sum(X1,additive_identity,additive_identity)
| ~ product(inverse(X0),additive_identity,X1) ),
inference(resolution,[status(thm)],[f145,f28]) ).
fof(f878,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(resolution,[status(thm)],[f653,f25]) ).
fof(f915,plain,
! [X0,X1] : product(X0,X1,multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f878,f25]) ).
fof(f999,plain,
! [X0] : sum(multiply(additive_identity,inverse(X0)),additive_identity,additive_identity),
inference(resolution,[status(thm)],[f739,f915]) ).
fof(f1009,plain,
! [X0] : additive_identity = multiply(additive_identity,inverse(X0)),
inference(resolution,[status(thm)],[f999,f61]) ).
fof(f1124,plain,
! [X0,X1] :
( sum(X1,additive_identity,additive_identity)
| ~ product(X0,multiply(additive_identity,inverse(X0)),X1) ),
inference(resolution,[status(thm)],[f149,f284]) ).
fof(f1131,plain,
! [X0,X1] :
( sum(X1,additive_identity,additive_identity)
| ~ product(X0,additive_identity,X1) ),
inference(forward_demodulation,[status(thm)],[f1009,f1124]) ).
fof(f1155,plain,
! [X0] : sum(multiply(additive_identity,X0),additive_identity,additive_identity),
inference(resolution,[status(thm)],[f1131,f915]) ).
fof(f1164,plain,
! [X0] : additive_identity = multiply(additive_identity,X0),
inference(resolution,[status(thm)],[f1155,f61]) ).
fof(f1214,plain,
! [X0] : product(X0,additive_identity,additive_identity),
inference(paramodulation,[status(thm)],[f1164,f915]) ).
fof(f1374,plain,
! [X0,X1] :
( sum(additive_identity,X1,X0)
| ~ product(X0,X0,X1) ),
inference(resolution,[status(thm)],[f494,f51]) ).
fof(f1406,plain,
! [X0] : sum(additive_identity,multiply(X0,X0),X0),
inference(resolution,[status(thm)],[f1374,f915]) ).
fof(f1412,plain,
! [X0] : X0 = multiply(X0,X0),
inference(resolution,[status(thm)],[f1406,f57]) ).
fof(f1419,plain,
! [X0,X1,X2] :
( product(X2,X1,X1)
| ~ product(X0,additive_identity,additive_identity)
| ~ sum(X0,multiply(X1,X1),X2) ),
inference(resolution,[status(thm)],[f1406,f45]) ).
fof(f1436,plain,
! [X0,X1,X2] :
( product(X2,X1,X1)
| ~ sum(X0,multiply(X1,X1),X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f1419,f1214]) ).
fof(f1517,plain,
! [X0,X1,X2] :
( product(X2,X1,X1)
| ~ sum(X0,X1,X2) ),
inference(forward_demodulation,[status(thm)],[f1412,f1436]) ).
fof(f1522,plain,
! [X0,X1] : product(add(X0,X1),X0,X0),
inference(resolution,[status(thm)],[f1517,f68]) ).
fof(f1528,plain,
! [X0] : multiplicative_identity = add(multiplicative_identity,X0),
inference(resolution,[status(thm)],[f1522,f521]) ).
fof(f1566,plain,
! [X0] : sum(X0,multiplicative_identity,multiplicative_identity),
inference(paramodulation,[status(thm)],[f1528,f68]) ).
fof(f1590,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f56,f1566]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO005-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n010.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 13:46:11 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.13/0.37 % Drodi V4.1.1
% 2.76/0.79 % Refutation found
% 2.76/0.79 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 2.76/0.79 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.21/0.80 % Elapsed time: 0.438997 seconds
% 0.21/0.80 % CPU time: 3.173130 seconds
% 0.21/0.80 % Total memory used: 63.485 MB
% 0.21/0.80 % Net memory used: 59.028 MB
%------------------------------------------------------------------------------