TSTP Solution File: RNG001-1 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : RNG001-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n009.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 12:32:32 EDT 2023
% Result : Unsatisfiable 0.19s 0.47s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of formulae : 50 ( 24 unt; 0 def)
% Number of atoms : 103 ( 14 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 108 ( 55 ~; 53 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 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 : 148 (; 148 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : sum(additive_identity,X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : sum(X,additive_identity,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y] : product(X,Y,multiply(X,Y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y] : sum(X,Y,add(X,Y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X] : sum(additive_inverse(X),X,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Y,U,Z,V,W] :
( ~ sum(X,Y,U)
| ~ sum(Y,Z,V)
| ~ sum(U,Z,W)
| sum(X,V,W) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X,Y,Z] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X,Y,V1,Z,V2,V3,V4] :
( ~ product(X,Y,V1)
| ~ product(X,Z,V2)
| ~ sum(Y,Z,V3)
| ~ sum(V1,V2,V4)
| product(X,V3,V4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [X,Y,U,V] :
( ~ sum(X,Y,U)
| ~ sum(X,Y,V)
| U = V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [X,Y,U,V] :
( ~ product(X,Y,U)
| ~ product(X,Y,V)
| U = V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
~ product(a,additive_identity,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,plain,
! [X0] : sum(additive_identity,X0,X0),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f20,plain,
! [X0] : sum(X0,additive_identity,X0),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f21,plain,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f22,plain,
! [X0,X1] : sum(X0,X1,add(X0,X1)),
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f23,plain,
! [X0] : sum(additive_inverse(X0),X0,additive_identity),
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f25,plain,
! [X,V,W] :
( ! [U,Z] :
( ! [Y] :
( ~ sum(X,Y,U)
| ~ sum(Y,Z,V) )
| ~ sum(U,Z,W) )
| sum(X,V,W) ),
inference(miniscoping,[status(esa)],[f7]) ).
fof(f26,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sum(X0,X1,X2)
| ~ sum(X1,X3,X4)
| ~ sum(X2,X3,X5)
| sum(X0,X4,X5) ),
inference(cnf_transformation,[status(esa)],[f25]) ).
fof(f29,plain,
! [X0,X1,X2] :
( ~ sum(X0,X1,X2)
| sum(X1,X0,X2) ),
inference(cnf_transformation,[status(esa)],[f9]) ).
fof(f36,plain,
! [X,V3,V4] :
( ! [V1,V2] :
( ! [Y,Z] :
( ~ product(X,Y,V1)
| ~ product(X,Z,V2)
| ~ sum(Y,Z,V3) )
| ~ sum(V1,V2,V4) )
| product(X,V3,V4) ),
inference(miniscoping,[status(esa)],[f13]) ).
fof(f37,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ product(X0,X1,X2)
| ~ product(X0,X3,X4)
| ~ sum(X1,X3,X5)
| ~ sum(X2,X4,X6)
| product(X0,X5,X6) ),
inference(cnf_transformation,[status(esa)],[f36]) ).
fof(f42,plain,
! [U,V] :
( ! [X,Y] :
( ~ sum(X,Y,U)
| ~ sum(X,Y,V) )
| U = V ),
inference(miniscoping,[status(esa)],[f16]) ).
fof(f43,plain,
! [X0,X1,X2,X3] :
( ~ sum(X0,X1,X2)
| ~ sum(X0,X1,X3)
| X2 = X3 ),
inference(cnf_transformation,[status(esa)],[f42]) ).
fof(f44,plain,
! [U,V] :
( ! [X,Y] :
( ~ product(X,Y,U)
| ~ product(X,Y,V) )
| U = V ),
inference(miniscoping,[status(esa)],[f17]) ).
fof(f45,plain,
! [X0,X1,X2,X3] :
( ~ product(X0,X1,X2)
| ~ product(X0,X1,X3)
| X2 = X3 ),
inference(cnf_transformation,[status(esa)],[f44]) ).
fof(f46,plain,
~ product(a,additive_identity,additive_identity),
inference(cnf_transformation,[status(esa)],[f18]) ).
fof(f49,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ product(X0,X1,X2)
| ~ sum(X3,X1,X4)
| ~ sum(multiply(X0,X3),X2,X5)
| product(X0,X4,X5) ),
inference(resolution,[status(thm)],[f21,f37]) ).
fof(f53,plain,
! [X0,X1,X2] :
( ~ product(X0,X1,X2)
| multiply(X0,X1) = X2 ),
inference(resolution,[status(thm)],[f21,f45]) ).
fof(f84,plain,
! [X0,X1] : sum(X0,X1,add(X1,X0)),
inference(resolution,[status(thm)],[f29,f22]) ).
fof(f86,plain,
! [X0,X1] :
( ~ sum(additive_inverse(X0),X0,X1)
| additive_identity = X1 ),
inference(resolution,[status(thm)],[f43,f23]) ).
fof(f106,plain,
! [X0] : additive_identity = add(additive_inverse(X0),X0),
inference(resolution,[status(thm)],[f86,f22]) ).
fof(f122,plain,
! [X0,X1,X2,X3] :
( ~ sum(X0,X1,X2)
| ~ sum(additive_identity,X1,X3)
| sum(additive_inverse(X0),X2,X3) ),
inference(resolution,[status(thm)],[f26,f23]) ).
fof(f123,plain,
! [X0,X1,X2,X3] :
( ~ sum(X0,X1,X2)
| ~ sum(X0,X1,X3)
| sum(additive_identity,X2,X3) ),
inference(resolution,[status(thm)],[f26,f19]) ).
fof(f125,plain,
! [X0,X1,X2,X3] :
( ~ sum(additive_identity,X0,X1)
| ~ sum(X2,X0,X3)
| sum(X2,X1,X3) ),
inference(resolution,[status(thm)],[f26,f20]) ).
fof(f136,plain,
! [X0,X1,X2,X3,X4] :
( ~ sum(X0,X1,X2)
| ~ sum(multiply(X3,X0),multiply(X3,X1),X4)
| product(X3,X2,X4) ),
inference(resolution,[status(thm)],[f49,f21]) ).
fof(f143,plain,
! [X0,X1,X2] :
( ~ sum(X0,X1,X2)
| sum(additive_identity,add(X1,X0),X2) ),
inference(resolution,[status(thm)],[f123,f84]) ).
fof(f168,plain,
! [X0,X1] : sum(additive_identity,add(X0,X1),add(X1,X0)),
inference(resolution,[status(thm)],[f143,f22]) ).
fof(f288,plain,
! [X0,X1,X2,X3] :
( ~ sum(X0,add(X1,X2),X3)
| sum(X0,add(X2,X1),X3) ),
inference(resolution,[status(thm)],[f125,f168]) ).
fof(f343,plain,
! [X0,X1,X2] : sum(X0,add(X1,X2),add(X0,add(X2,X1))),
inference(resolution,[status(thm)],[f288,f22]) ).
fof(f455,plain,
! [X0,X1,X2,X3] :
( ~ sum(X0,add(X1,X2),X3)
| add(X0,add(X2,X1)) = X3 ),
inference(resolution,[status(thm)],[f343,f43]) ).
fof(f753,plain,
! [X0,X1,X2] :
( ~ sum(multiply(X0,additive_identity),multiply(X0,X1),X2)
| product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f136,f19]) ).
fof(f1306,plain,
! [X0,X1,X2] :
( ~ sum(additive_identity,X0,X1)
| sum(additive_inverse(X2),add(X0,X2),X1) ),
inference(resolution,[status(thm)],[f122,f84]) ).
fof(f1754,plain,
! [X0,X1] : product(X0,X1,add(multiply(X0,X1),multiply(X0,additive_identity))),
inference(resolution,[status(thm)],[f753,f84]) ).
fof(f1776,plain,
! [X0,X1] : multiply(X0,X1) = add(multiply(X0,X1),multiply(X0,additive_identity)),
inference(resolution,[status(thm)],[f1754,f53]) ).
fof(f2305,plain,
! [X0,X1] : sum(additive_inverse(X0),add(X1,X0),X1),
inference(resolution,[status(thm)],[f1306,f19]) ).
fof(f2321,plain,
! [X0,X1] : add(additive_inverse(X0),add(X0,X1)) = X1,
inference(resolution,[status(thm)],[f2305,f455]) ).
fof(f2431,plain,
! [X0,X1] : add(additive_inverse(multiply(X0,X1)),multiply(X0,X1)) = multiply(X0,additive_identity),
inference(paramodulation,[status(thm)],[f1776,f2321]) ).
fof(f2432,plain,
! [X0] : additive_identity = multiply(X0,additive_identity),
inference(forward_demodulation,[status(thm)],[f106,f2431]) ).
fof(f2662,plain,
! [X0] : product(X0,additive_identity,additive_identity),
inference(paramodulation,[status(thm)],[f2432,f21]) ).
fof(f2710,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f46,f2662]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : RNG001-1 : TPTP v8.1.2. Released v1.0.0.
% 0.10/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue May 30 10:33:01 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.12/0.34 % Drodi V3.5.1
% 0.19/0.47 % Refutation found
% 0.19/0.47 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.19/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/0.49 % Elapsed time: 0.152400 seconds
% 0.19/0.49 % CPU time: 0.762937 seconds
% 0.19/0.49 % Memory used: 21.416 MB
%------------------------------------------------------------------------------