%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : RNG001-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n006.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 02:04:37 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.44s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 32 ( 13 unt; 0 def)
% Number of atoms : 83 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 104 ( 53 ~; 51 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 115 ( 115 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : sum(additive_identity,X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : sum(additive_inverse(X),X,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y,U,Z,V,W] :
( sum(U,Z,W)
| ~ sum(X,V,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y] : product(X,Y,multiply(X,Y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,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(f7,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
~ product(a,additive_identity,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,plain,
! [X0] : sum(additive_identity,X0,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f10,plain,
! [X0] : sum(additive_inverse(X0),X0,additive_identity),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f13,plain,
! [U,Z,W] :
( sum(U,Z,W)
| ! [X,V] :
( ~ sum(X,V,W)
| ! [Y] :
( ~ sum(Y,Z,V)
| ~ sum(X,Y,U) ) ) ),
inference(miniscoping,[status(thm)],[f4]) ).
fof(f14,plain,
! [X0,X1,X2,X3,X4,X5] :
( sum(X2,X3,X5)
| ~ sum(X0,X4,X5)
| ~ sum(X1,X3,X4)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f15,plain,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f16,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)],[f6]) ).
fof(f17,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)],[f16]) ).
fof(f18,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)],[f7]) ).
fof(f19,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)],[f18]) ).
fof(f20,plain,
~ product(a,additive_identity,additive_identity),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f26,plain,
! [X0,X1,X2,X3] :
( sum(additive_identity,X1,X3)
| ~ sum(additive_inverse(X0),X2,X3)
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[f14,f10]) ).
fof(f27,plain,
! [X0,X1,X2,X3] :
( sum(X0,X1,X3)
| ~ sum(additive_identity,X2,X3)
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[f14,f9]) ).
fof(f33,plain,
! [X0,X1,X2,X3,X4,X5] :
( sum(multiply(X0,X3),X2,X5)
| ~ product(X0,X4,X5)
| ~ sum(X3,X1,X4)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f17,f15]) ).
fof(f43,plain,
! [X0,X1,X2,X3,X4,X5] :
( product(X0,X4,X5)
| ~ sum(multiply(X0,X3),X2,X5)
| ~ sum(X3,X1,X4)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f19,f15]) ).
fof(f80,plain,
! [X0,X1,X2,X3,X4] :
( sum(multiply(X3,X0),multiply(X3,X1),X4)
| ~ product(X3,X2,X4)
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[f33,f15]) ).
fof(f87,plain,
! [X0,X1,X2,X3,X4] :
( product(X3,X2,X4)
| ~ sum(multiply(X3,X0),multiply(X3,X1),X4)
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[f43,f15]) ).
fof(f129,plain,
! [X0,X1,X2] :
( sum(multiply(X0,additive_identity),multiply(X0,X1),X2)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f80,f9]) ).
fof(f146,plain,
! [X0,X1,X2] :
( product(X0,X1,X2)
| ~ sum(multiply(X0,additive_identity),multiply(X0,X1),X2) ),
inference(resolution,[status(thm)],[f87,f9]) ).
fof(f152,plain,
! [X0,X1] : sum(multiply(X0,additive_identity),multiply(X0,X1),multiply(X0,X1)),
inference(resolution,[status(thm)],[f129,f15]) ).
fof(f155,plain,
! [X0,X1,X2] :
( sum(additive_identity,multiply(X0,X1),X2)
| ~ sum(additive_inverse(multiply(X0,additive_identity)),multiply(X0,X1),X2) ),
inference(resolution,[status(thm)],[f152,f26]) ).
fof(f157,plain,
! [X0,X1,X2] :
( sum(multiply(X0,additive_identity),multiply(X0,X1),X2)
| ~ sum(additive_identity,multiply(X0,X1),X2) ),
inference(resolution,[status(thm)],[f152,f27]) ).
fof(f620,plain,
! [X0] : sum(additive_identity,multiply(X0,additive_identity),additive_identity),
inference(resolution,[status(thm)],[f155,f10]) ).
fof(f697,plain,
! [X0] : sum(multiply(X0,additive_identity),multiply(X0,additive_identity),additive_identity),
inference(resolution,[status(thm)],[f157,f620]) ).
fof(f917,plain,
! [X0] : product(X0,additive_identity,additive_identity),
inference(resolution,[status(thm)],[f697,f146]) ).
fof(f933,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f20,f917]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG001-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.38 % Computer : n006.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Mon Sep 21 04:09:27 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.39 % Drodi V4.1.1
% 0.10/0.44 % Refutation found
% 0.10/0.44 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.48 % Elapsed time: 0.083699 seconds
% 0.10/0.48 % CPU time: 0.461328 seconds
% 0.10/0.48 % Total memory used: 53.275 MB
% 0.10/0.48 % Net memory used: 52.539 MB
%------------------------------------------------------------------------------