%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : RNG001-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 02:04:36 PM UTC 2026
% Result : Unsatisfiable 13.73s 2.27s
% Output : CNFRefutation 13.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 13
% Syntax : Number of formulae : 59 ( 26 unt; 0 def)
% Number of atoms : 139 ( 14 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 162 ( 82 ~; 80 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 181 ( 181 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : sum(additive_identity,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : sum(X,additive_identity,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y] : product(X,Y,multiply(X,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y] : sum(X,Y,add(X,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X] : sum(additive_inverse(X),X,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X] : sum(X,additive_inverse(X),additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Y,U,Z,V,W] :
( sum(X,V,W)
| ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X,Y,Z] :
( sum(Y,X,Z)
| ~ sum(X,Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X,Y,U,Z,V,W] :
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,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(f14,axiom,
! [Y,X,V1,Z,V2,V3,V4] :
( sum(V1,V2,V4)
| ~ product(V3,X,V4)
| ~ sum(Y,Z,V3)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [X,Y,U,V] :
( U = V
| ~ sum(X,Y,V)
| ~ sum(X,Y,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
~ product(a,additive_identity,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,plain,
! [X0] : sum(additive_identity,X0,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f20,plain,
! [X0] : sum(X0,additive_identity,X0),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f21,plain,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f22,plain,
! [X0,X1] : sum(X0,X1,add(X0,X1)),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f23,plain,
! [X0] : sum(additive_inverse(X0),X0,additive_identity),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f24,plain,
! [X0] : sum(X0,additive_inverse(X0),additive_identity),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f25,plain,
! [X,V,W] :
( sum(X,V,W)
| ! [U,Z] :
( ~ sum(U,Z,W)
| ! [Y] :
( ~ sum(Y,Z,V)
| ~ sum(X,Y,U) ) ) ),
inference(miniscoping,[status(thm)],[f7]) ).
fof(f26,plain,
! [X0,X1,X2,X3,X4,X5] :
( sum(X0,X4,X5)
| ~ sum(X2,X3,X5)
| ~ sum(X1,X3,X4)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f29,plain,
! [X0,X1,X2] :
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f30,plain,
! [X,V,W] :
( product(X,V,W)
| ! [U,Z] :
( ~ product(U,Z,W)
| ! [Y] :
( ~ product(Y,Z,V)
| ~ product(X,Y,U) ) ) ),
inference(miniscoping,[status(thm)],[f10]) ).
fof(f31,plain,
! [X0,X1,X2,X3,X4,X5] :
( product(X0,X4,X5)
| ~ product(X2,X3,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f34,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)],[f12]) ).
fof(f35,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)],[f34]) ).
fof(f38,plain,
! [V1,V2,V4] :
( sum(V1,V2,V4)
| ! [X,V3] :
( ~ product(V3,X,V4)
| ! [Y,Z] :
( ~ sum(Y,Z,V3)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ) ) ),
inference(miniscoping,[status(thm)],[f14]) ).
fof(f39,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( sum(X2,X4,X6)
| ~ product(X5,X1,X6)
| ~ sum(X0,X3,X5)
| ~ product(X3,X1,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f42,plain,
! [U,V] :
( U = V
| ! [X,Y] :
( ~ sum(X,Y,V)
| ~ sum(X,Y,U) ) ),
inference(miniscoping,[status(thm)],[f16]) ).
fof(f43,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f46,plain,
~ product(a,additive_identity,additive_identity),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f47,plain,
! [X0,X1] :
( X1 = X0
| ~ sum(additive_identity,X0,X1) ),
inference(resolution,[status(thm)],[f43,f19]) ).
fof(f48,plain,
! [X0,X1] :
( X1 = X0
| ~ sum(X0,additive_identity,X1) ),
inference(resolution,[status(thm)],[f43,f20]) ).
fof(f95,plain,
! [X0] : add(additive_identity,X0) = X0,
inference(resolution,[status(thm)],[f22,f47]) ).
fof(f107,plain,
additive_identity = additive_inverse(additive_identity),
inference(resolution,[status(thm)],[f23,f48]) ).
fof(f140,plain,
! [X0,X1] :
( sum(X0,additive_identity,additive_identity)
| ~ sum(X0,X1,X1) ),
inference(resolution,[status(thm)],[f26,f24]) ).
fof(f182,plain,
! [X0,X1] : sum(X0,X1,add(X1,X0)),
inference(resolution,[status(thm)],[f29,f22]) ).
fof(f230,plain,
! [X0,X1,X2] :
( X2 = add(X1,X0)
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[f182,f43]) ).
fof(f241,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ product(X6,X4,X0)
| ~ sum(X3,X5,X6)
| ~ product(X5,X4,X1)
| ~ product(X3,X4,X2)
| X0 = add(X1,X2) ),
inference(resolution,[status(thm)],[f230,f39]) ).
fof(f285,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ product(X5,X2,X4)
| ~ sum(X1,X3,X5)
| ~ product(X3,X2,X4)
| ~ product(X1,X2,X0)
| sum(X0,additive_identity,additive_identity) ),
inference(resolution,[status(thm)],[f140,f39]) ).
fof(f286,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ product(X1,X5,X4)
| ~ sum(X2,X3,X5)
| ~ product(X1,X3,X4)
| ~ product(X1,X2,X0)
| sum(X0,additive_identity,additive_identity) ),
inference(resolution,[status(thm)],[f140,f35]) ).
fof(f288,plain,
! [X0,X1,X2,X3] :
( ~ sum(X1,X3,X3)
| ~ product(X1,X2,X0)
| sum(X0,additive_identity,additive_identity) ),
inference(resolution,[status(thm)],[f285,f21]) ).
fof(f291,plain,
! [X0,X1,X2] :
( ~ sum(X0,X2,X2)
| sum(multiply(X0,X1),additive_identity,additive_identity) ),
inference(resolution,[status(thm)],[f288,f21]) ).
fof(f297,plain,
! [X0,X1,X2,X3] :
( ~ sum(X2,X3,X3)
| ~ product(X1,X2,X0)
| sum(X0,additive_identity,additive_identity) ),
inference(resolution,[status(thm)],[f286,f21]) ).
fof(f326,plain,
! [X0] : sum(multiply(additive_inverse(additive_identity),X0),additive_identity,additive_identity),
inference(resolution,[status(thm)],[f291,f23]) ).
fof(f331,plain,
! [X0] : sum(multiply(additive_identity,X0),additive_identity,additive_identity),
inference(forward_demodulation,[status(thm)],[f107,f326]) ).
fof(f333,plain,
! [X0] : additive_identity = multiply(additive_identity,X0),
inference(resolution,[status(thm)],[f331,f48]) ).
fof(f374,plain,
! [X0] : product(additive_identity,X0,additive_identity),
inference(paramodulation,[status(thm)],[f333,f21]) ).
fof(f454,plain,
! [X0,X1,X2] :
( ~ sum(X1,additive_identity,additive_identity)
| ~ product(X1,X2,X0)
| additive_identity = add(additive_identity,X0) ),
inference(resolution,[status(thm)],[f374,f241]) ).
fof(f514,plain,
! [X0,X1,X2,X3] :
( product(X0,additive_identity,X3)
| ~ product(X1,X2,X3)
| ~ product(X0,additive_identity,X1) ),
inference(resolution,[status(thm)],[f374,f31]) ).
fof(f546,plain,
! [X0,X1,X2] :
( ~ sum(X1,additive_identity,additive_identity)
| ~ product(X1,X2,X0)
| additive_identity = X0 ),
inference(forward_demodulation,[status(thm)],[f95,f454]) ).
fof(f571,plain,
! [X0,X1] :
( ~ sum(X0,additive_identity,additive_identity)
| additive_identity = multiply(X0,X1) ),
inference(resolution,[status(thm)],[f546,f21]) ).
fof(f595,plain,
! [X0,X1,X2] :
( product(X0,additive_identity,X2)
| ~ product(multiply(X0,additive_identity),X1,X2) ),
inference(resolution,[status(thm)],[f514,f21]) ).
fof(f599,plain,
! [X0,X1] : product(X0,additive_identity,multiply(multiply(X0,additive_identity),X1)),
inference(resolution,[status(thm)],[f595,f21]) ).
fof(f639,plain,
! [X0,X1] :
( ~ product(X1,additive_identity,X0)
| sum(X0,additive_identity,additive_identity) ),
inference(resolution,[status(thm)],[f19,f297]) ).
fof(f780,plain,
! [X0] : sum(multiply(X0,additive_identity),additive_identity,additive_identity),
inference(resolution,[status(thm)],[f639,f21]) ).
fof(f1333,plain,
! [X0,X1] : additive_identity = multiply(multiply(X0,additive_identity),X1),
inference(resolution,[status(thm)],[f780,f571]) ).
fof(f1376,plain,
! [X0] : product(X0,additive_identity,additive_identity),
inference(backward_demodulation,[status(thm)],[f1333,f599]) ).
fof(f1451,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f46,f1376]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : RNG001-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.45 % Computer : n013.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Mon Sep 21 04:08:55 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.46 % Drodi V4.1.1
% 13.73/2.27 % Refutation found
% 13.73/2.27 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 13.73/2.27 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 9.58/2.33 % Elapsed time: 1.860418 seconds
% 9.58/2.33 % CPU time: 14.288690 seconds
% 9.58/2.33 % Total memory used: 85.980 MB
% 9.58/2.33 % Net memory used: 75.853 MB
%------------------------------------------------------------------------------