TSTP Solution File: RNG007-1 by Drodi---3.5.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : RNG007-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed May 31 12:32:34 EDT 2023
% Result : Unsatisfiable 0.19s 0.57s
% Output : CNFRefutation 1.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 16
% Syntax : Number of formulae : 101 ( 57 unt; 0 def)
% Number of atoms : 196 ( 33 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 192 ( 97 ~; 95 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 4 ( 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 : 274 (; 274 !; 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(f8,axiom,
! [X,Y,U,Z,V,W] :
( ~ sum(X,Y,U)
| ~ sum(Y,Z,V)
| ~ sum(X,V,W)
| sum(U,Z,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X,Y,Z] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X,Y,U,Z,V,W] :
( ~ product(X,Y,U)
| ~ product(Y,Z,V)
| ~ product(U,Z,W)
| product(X,V,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X,Y,U,Z,V,W] :
( ~ product(X,Y,U)
| ~ product(Y,Z,V)
| ~ product(X,V,W)
| product(U,Z,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X,Y,V1,Z,V2,V3,V4] :
( ~ product(X,Y,V1)
| ~ product(X,Z,V2)
| ~ sum(Y,Z,V3)
| ~ product(X,V3,V4)
| sum(V1,V2,V4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [Y,X,V1,Z,V2,V3,V4] :
( ~ product(Y,X,V1)
| ~ product(Z,X,V2)
| ~ sum(Y,Z,V3)
| ~ product(V3,X,V4)
| sum(V1,V2,V4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [X,Y,U,V] :
( ~ sum(X,Y,U)
| ~ sum(X,Y,V)
| U = V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [X,Y,U,V] :
( ~ product(X,Y,U)
| ~ product(X,Y,V)
| U = V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,hypothesis,
! [X] : product(X,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
~ sum(a,a,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,plain,
! [X0] : sum(additive_identity,X0,X0),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f21,plain,
! [X0] : sum(X0,additive_identity,X0),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f22,plain,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f23,plain,
! [X0,X1] : sum(X0,X1,add(X0,X1)),
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f24,plain,
! [X0] : sum(additive_inverse(X0),X0,additive_identity),
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f25,plain,
! [X0] : sum(X0,additive_inverse(X0),additive_identity),
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f28,plain,
! [U,Z,W] :
( ! [X,V] :
( ! [Y] :
( ~ sum(X,Y,U)
| ~ sum(Y,Z,V) )
| ~ sum(X,V,W) )
| sum(U,Z,W) ),
inference(miniscoping,[status(esa)],[f8]) ).
fof(f29,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sum(X0,X1,X2)
| ~ sum(X1,X3,X4)
| ~ sum(X0,X4,X5)
| sum(X2,X3,X5) ),
inference(cnf_transformation,[status(esa)],[f28]) ).
fof(f30,plain,
! [X0,X1,X2] :
( ~ sum(X0,X1,X2)
| sum(X1,X0,X2) ),
inference(cnf_transformation,[status(esa)],[f9]) ).
fof(f31,plain,
! [X,V,W] :
( ! [U,Z] :
( ! [Y] :
( ~ product(X,Y,U)
| ~ product(Y,Z,V) )
| ~ product(U,Z,W) )
| product(X,V,W) ),
inference(miniscoping,[status(esa)],[f10]) ).
fof(f32,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ product(X0,X1,X2)
| ~ product(X1,X3,X4)
| ~ product(X2,X3,X5)
| product(X0,X4,X5) ),
inference(cnf_transformation,[status(esa)],[f31]) ).
fof(f33,plain,
! [U,Z,W] :
( ! [X,V] :
( ! [Y] :
( ~ product(X,Y,U)
| ~ product(Y,Z,V) )
| ~ product(X,V,W) )
| product(U,Z,W) ),
inference(miniscoping,[status(esa)],[f11]) ).
fof(f34,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ product(X0,X1,X2)
| ~ product(X1,X3,X4)
| ~ product(X0,X4,X5)
| product(X2,X3,X5) ),
inference(cnf_transformation,[status(esa)],[f33]) ).
fof(f35,plain,
! [V1,V2,V4] :
( ! [X,V3] :
( ! [Y,Z] :
( ~ product(X,Y,V1)
| ~ product(X,Z,V2)
| ~ sum(Y,Z,V3) )
| ~ product(X,V3,V4) )
| sum(V1,V2,V4) ),
inference(miniscoping,[status(esa)],[f12]) ).
fof(f36,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ product(X0,X1,X2)
| ~ product(X0,X3,X4)
| ~ sum(X1,X3,X5)
| ~ product(X0,X5,X6)
| sum(X2,X4,X6) ),
inference(cnf_transformation,[status(esa)],[f35]) ).
fof(f39,plain,
! [V1,V2,V4] :
( ! [X,V3] :
( ! [Y,Z] :
( ~ product(Y,X,V1)
| ~ product(Z,X,V2)
| ~ sum(Y,Z,V3) )
| ~ product(V3,X,V4) )
| sum(V1,V2,V4) ),
inference(miniscoping,[status(esa)],[f14]) ).
fof(f40,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ product(X0,X1,X2)
| ~ product(X3,X1,X4)
| ~ sum(X0,X3,X5)
| ~ product(X5,X1,X6)
| sum(X2,X4,X6) ),
inference(cnf_transformation,[status(esa)],[f39]) ).
fof(f43,plain,
! [U,V] :
( ! [X,Y] :
( ~ sum(X,Y,U)
| ~ sum(X,Y,V) )
| U = V ),
inference(miniscoping,[status(esa)],[f16]) ).
fof(f44,plain,
! [X0,X1,X2,X3] :
( ~ sum(X0,X1,X2)
| ~ sum(X0,X1,X3)
| X2 = X3 ),
inference(cnf_transformation,[status(esa)],[f43]) ).
fof(f45,plain,
! [U,V] :
( ! [X,Y] :
( ~ product(X,Y,U)
| ~ product(X,Y,V) )
| U = V ),
inference(miniscoping,[status(esa)],[f17]) ).
fof(f46,plain,
! [X0,X1,X2,X3] :
( ~ product(X0,X1,X2)
| ~ product(X0,X1,X3)
| X2 = X3 ),
inference(cnf_transformation,[status(esa)],[f45]) ).
fof(f47,plain,
! [X0] : product(X0,X0,X0),
inference(cnf_transformation,[status(esa)],[f18]) ).
fof(f48,plain,
~ sum(a,a,additive_identity),
inference(cnf_transformation,[status(esa)],[f19]) ).
fof(f51,plain,
! [X0,X1] :
( ~ sum(additive_identity,X0,X1)
| X0 = X1 ),
inference(resolution,[status(thm)],[f44,f20]) ).
fof(f52,plain,
! [X0,X1] :
( ~ sum(X0,additive_identity,X1)
| X0 = X1 ),
inference(resolution,[status(thm)],[f44,f21]) ).
fof(f61,plain,
! [X0] : X0 = add(additive_identity,X0),
inference(resolution,[status(thm)],[f23,f51]) ).
fof(f62,plain,
! [X0] : X0 = add(X0,additive_identity),
inference(resolution,[status(thm)],[f23,f52]) ).
fof(f64,plain,
! [X0,X1,X2,X3,X4] :
( ~ sum(X0,X1,X2)
| ~ sum(X3,X2,X4)
| sum(add(X3,X0),X1,X4) ),
inference(resolution,[status(thm)],[f23,f29]) ).
fof(f67,plain,
! [X0,X1,X2] :
( ~ sum(X0,X1,X2)
| add(X0,X1) = X2 ),
inference(resolution,[status(thm)],[f23,f44]) ).
fof(f68,plain,
! [X0,X1] : sum(X0,X1,add(X1,X0)),
inference(resolution,[status(thm)],[f23,f30]) ).
fof(f71,plain,
! [X0,X1,X2,X3] :
( ~ sum(X0,add(X1,X2),X3)
| sum(add(X0,X1),X2,X3) ),
inference(resolution,[status(thm)],[f64,f23]) ).
fof(f109,plain,
! [X0,X1,X2] :
( ~ sum(X0,X1,X2)
| add(X1,X0) = X2 ),
inference(resolution,[status(thm)],[f68,f44]) ).
fof(f113,plain,
! [X0] : add(additive_inverse(X0),X0) = additive_identity,
inference(resolution,[status(thm)],[f67,f24]) ).
fof(f115,plain,
! [X0] : add(X0,additive_inverse(X0)) = additive_identity,
inference(resolution,[status(thm)],[f67,f25]) ).
fof(f117,plain,
! [X0,X1] : add(X0,X1) = add(X1,X0),
inference(resolution,[status(thm)],[f67,f68]) ).
fof(f158,plain,
! [X0,X1] :
( ~ product(X0,X0,X1)
| X0 = X1 ),
inference(resolution,[status(thm)],[f46,f47]) ).
fof(f159,plain,
! [X0,X1,X2,X3,X4] :
( ~ product(X0,X1,X2)
| ~ product(multiply(X3,X0),X1,X4)
| product(X3,X2,X4) ),
inference(resolution,[status(thm)],[f32,f22]) ).
fof(f161,plain,
! [X0,X1,X2,X3,X4] :
( ~ product(X0,X1,X2)
| ~ product(X3,X2,X4)
| product(multiply(X3,X0),X1,X4) ),
inference(resolution,[status(thm)],[f34,f22]) ).
fof(f163,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ product(X0,X1,X2)
| ~ sum(X3,X1,X4)
| ~ product(X0,X4,X5)
| sum(multiply(X0,X3),X2,X5) ),
inference(resolution,[status(thm)],[f36,f22]) ).
fof(f346,plain,
! [X0] : X0 = multiply(X0,X0),
inference(resolution,[status(thm)],[f158,f22]) ).
fof(f406,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ product(X0,X1,X2)
| ~ sum(X3,X0,X4)
| ~ product(X4,X1,X5)
| sum(multiply(X3,X1),X2,X5) ),
inference(resolution,[status(thm)],[f40,f22]) ).
fof(f416,plain,
! [X0,X1,X2] : sum(add(X0,X1),X2,add(add(X1,X2),X0)),
inference(resolution,[status(thm)],[f71,f68]) ).
fof(f510,plain,
! [X0,X1] : sum(add(X0,additive_inverse(X1)),X1,add(additive_identity,X0)),
inference(paramodulation,[status(thm)],[f113,f416]) ).
fof(f511,plain,
! [X0,X1] : sum(add(X0,additive_inverse(X1)),X1,X0),
inference(forward_demodulation,[status(thm)],[f61,f510]) ).
fof(f514,plain,
! [X0,X1] : sum(add(X0,X1),additive_inverse(X1),add(additive_identity,X0)),
inference(paramodulation,[status(thm)],[f115,f416]) ).
fof(f515,plain,
! [X0,X1] : sum(add(X0,X1),additive_inverse(X1),X0),
inference(forward_demodulation,[status(thm)],[f61,f514]) ).
fof(f536,plain,
! [X0,X1] : add(X0,add(X1,additive_inverse(X0))) = X1,
inference(resolution,[status(thm)],[f511,f109]) ).
fof(f561,plain,
! [X0,X1] : add(additive_inverse(X0),add(X1,X0)) = X1,
inference(resolution,[status(thm)],[f515,f109]) ).
fof(f589,plain,
! [X0] : add(X0,additive_identity) = additive_inverse(additive_inverse(X0)),
inference(paramodulation,[status(thm)],[f113,f536]) ).
fof(f590,plain,
! [X0] : X0 = additive_inverse(additive_inverse(X0)),
inference(forward_demodulation,[status(thm)],[f62,f589]) ).
fof(f593,plain,
! [X0,X1] : add(X0,add(additive_inverse(X0),X1)) = X1,
inference(paramodulation,[status(thm)],[f117,f536]) ).
fof(f744,plain,
! [X0,X1] : add(additive_inverse(X0),add(X0,X1)) = X1,
inference(paramodulation,[status(thm)],[f117,f561]) ).
fof(f1010,plain,
! [X0,X1,X2,X3] :
( ~ product(multiply(X0,X1),X2,X3)
| product(X0,multiply(X1,X2),X3) ),
inference(resolution,[status(thm)],[f159,f22]) ).
fof(f1013,plain,
! [X0,X1,X2,X3] :
( ~ product(X0,multiply(X1,X2),X3)
| product(multiply(X0,X1),X2,X3) ),
inference(resolution,[status(thm)],[f161,f22]) ).
fof(f1978,plain,
! [X0,X1,X2,X3] :
( ~ sum(X0,X1,X2)
| ~ product(X1,X2,X3)
| sum(multiply(X1,X0),X1,X3) ),
inference(resolution,[status(thm)],[f163,f47]) ).
fof(f2166,plain,
! [X0,X1,X2,X3] :
( ~ sum(X0,X1,X2)
| ~ product(X2,X1,X3)
| sum(multiply(X0,X1),X1,X3) ),
inference(resolution,[status(thm)],[f406,f47]) ).
fof(f4661,plain,
! [X0,X1,X2] : product(X0,multiply(X1,X2),multiply(multiply(X0,X1),X2)),
inference(resolution,[status(thm)],[f1010,f22]) ).
fof(f4669,plain,
! [X0,X1,X2] : product(multiply(X0,X1),X2,multiply(X0,multiply(X1,X2))),
inference(resolution,[status(thm)],[f1013,f22]) ).
fof(f5123,plain,
! [X0,X1] :
( ~ product(X0,additive_identity,X1)
| sum(multiply(X0,additive_inverse(X0)),X0,X1) ),
inference(resolution,[status(thm)],[f1978,f24]) ).
fof(f5125,plain,
! [X0,X1] :
( ~ product(X0,X0,X1)
| sum(multiply(X0,additive_identity),X0,X1) ),
inference(resolution,[status(thm)],[f1978,f20]) ).
fof(f7869,plain,
! [X0,X1] :
( ~ product(X0,X0,X1)
| sum(multiply(additive_identity,X0),X0,X1) ),
inference(resolution,[status(thm)],[f2166,f20]) ).
fof(f7881,plain,
! [X0,X1,X2] :
( ~ product(add(X0,X1),X0,X2)
| sum(multiply(X1,X0),X0,X2) ),
inference(resolution,[status(thm)],[f2166,f68]) ).
fof(f8920,plain,
! [X0] : sum(multiply(X0,additive_identity),X0,multiply(X0,X0)),
inference(resolution,[status(thm)],[f5125,f22]) ).
fof(f8921,plain,
! [X0] : sum(multiply(X0,additive_identity),X0,X0),
inference(forward_demodulation,[status(thm)],[f346,f8920]) ).
fof(f8966,plain,
! [X0] : add(X0,multiply(X0,additive_identity)) = X0,
inference(resolution,[status(thm)],[f8921,f109]) ).
fof(f9087,plain,
! [X0] : add(additive_inverse(X0),X0) = multiply(X0,additive_identity),
inference(paramodulation,[status(thm)],[f8966,f744]) ).
fof(f9088,plain,
! [X0] : additive_identity = multiply(X0,additive_identity),
inference(forward_demodulation,[status(thm)],[f113,f9087]) ).
fof(f9127,plain,
! [X0,X1] : product(X0,multiply(X1,additive_identity),additive_identity),
inference(paramodulation,[status(thm)],[f9088,f4661]) ).
fof(f9128,plain,
! [X0] : product(X0,additive_identity,additive_identity),
inference(forward_demodulation,[status(thm)],[f9088,f9127]) ).
fof(f9852,plain,
! [X0] : sum(multiply(additive_identity,X0),X0,multiply(X0,X0)),
inference(resolution,[status(thm)],[f7869,f22]) ).
fof(f9853,plain,
! [X0] : sum(multiply(additive_identity,X0),X0,X0),
inference(forward_demodulation,[status(thm)],[f346,f9852]) ).
fof(f9909,plain,
! [X0] : add(X0,multiply(additive_identity,X0)) = X0,
inference(resolution,[status(thm)],[f9853,f109]) ).
fof(f10040,plain,
! [X0] : add(additive_inverse(X0),X0) = multiply(additive_identity,X0),
inference(paramodulation,[status(thm)],[f9909,f744]) ).
fof(f10041,plain,
! [X0] : additive_identity = multiply(additive_identity,X0),
inference(forward_demodulation,[status(thm)],[f113,f10040]) ).
fof(f10083,plain,
! [X0,X1] : product(multiply(additive_identity,X0),X1,additive_identity),
inference(paramodulation,[status(thm)],[f10041,f4669]) ).
fof(f10084,plain,
! [X0] : product(additive_identity,X0,additive_identity),
inference(forward_demodulation,[status(thm)],[f10041,f10083]) ).
fof(f10244,plain,
! [X0] : sum(multiply(X0,additive_inverse(X0)),X0,additive_identity),
inference(resolution,[status(thm)],[f5123,f9128]) ).
fof(f10391,plain,
! [X0] : add(X0,multiply(X0,additive_inverse(X0))) = additive_identity,
inference(resolution,[status(thm)],[f10244,f109]) ).
fof(f10444,plain,
! [X0] : add(X0,additive_identity) = multiply(additive_inverse(X0),additive_inverse(additive_inverse(X0))),
inference(paramodulation,[status(thm)],[f10391,f593]) ).
fof(f10445,plain,
! [X0] : X0 = multiply(additive_inverse(X0),additive_inverse(additive_inverse(X0))),
inference(forward_demodulation,[status(thm)],[f62,f10444]) ).
fof(f10446,plain,
! [X0] : X0 = multiply(additive_inverse(X0),X0),
inference(forward_demodulation,[status(thm)],[f590,f10445]) ).
fof(f12067,plain,
! [X0,X1] :
( ~ product(additive_identity,X0,X1)
| sum(multiply(additive_inverse(X0),X0),X0,X1) ),
inference(paramodulation,[status(thm)],[f115,f7881]) ).
fof(f12068,plain,
! [X0,X1] :
( ~ product(additive_identity,X0,X1)
| sum(X0,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f10446,f12067]) ).
fof(f12074,plain,
! [X0] : sum(X0,X0,additive_identity),
inference(resolution,[status(thm)],[f12068,f10084]) ).
fof(f12106,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f48,f12074]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : RNG007-1 : TPTP v8.1.2. Released v1.0.0.
% 0.11/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.34 % Computer : n027.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue May 30 10:54:48 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.12/0.35 % Drodi V3.5.1
% 0.19/0.57 % Refutation found
% 0.19/0.57 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.19/0.57 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.73/0.58 % Elapsed time: 0.232094 seconds
% 1.73/0.58 % CPU time: 1.745639 seconds
% 1.73/0.58 % Memory used: 31.658 MB
%------------------------------------------------------------------------------