TSTP Solution File: RNG005-1 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : RNG005-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n025.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 12:32:33 EDT 2023
% Result : Unsatisfiable 3.65s 0.84s
% Output : CNFRefutation 3.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 13
% Syntax : Number of formulae : 72 ( 44 unt; 0 def)
% Number of atoms : 125 ( 20 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 108 ( 55 ~; 53 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 148 (; 148 !; 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,Y,U)
| ~ sum(Y,Z,V)
| ~ sum(U,Z,W)
| sum(X,V,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(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(f18,hypothesis,
product(a,b,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,hypothesis,
product(additive_inverse(a),b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
~ sum(c,d,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,plain,
! [X0] : sum(additive_identity,X0,X0),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f22,plain,
! [X0] : sum(X0,additive_identity,X0),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f23,plain,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f24,plain,
! [X0,X1] : sum(X0,X1,add(X0,X1)),
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f25,plain,
! [X0] : sum(additive_inverse(X0),X0,additive_identity),
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f26,plain,
! [X0] : sum(X0,additive_inverse(X0),additive_identity),
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f27,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(f28,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)],[f27]) ).
fof(f31,plain,
! [X0,X1,X2] :
( ~ sum(X0,X1,X2)
| sum(X1,X0,X2) ),
inference(cnf_transformation,[status(esa)],[f9]) ).
fof(f40,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(f41,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)],[f40]) ).
fof(f44,plain,
! [U,V] :
( ! [X,Y] :
( ~ sum(X,Y,U)
| ~ sum(X,Y,V) )
| U = V ),
inference(miniscoping,[status(esa)],[f16]) ).
fof(f45,plain,
! [X0,X1,X2,X3] :
( ~ sum(X0,X1,X2)
| ~ sum(X0,X1,X3)
| X2 = X3 ),
inference(cnf_transformation,[status(esa)],[f44]) ).
fof(f48,plain,
product(a,b,d),
inference(cnf_transformation,[status(esa)],[f18]) ).
fof(f49,plain,
product(additive_inverse(a),b,c),
inference(cnf_transformation,[status(esa)],[f19]) ).
fof(f50,plain,
~ sum(c,d,additive_identity),
inference(cnf_transformation,[status(esa)],[f20]) ).
fof(f56,plain,
! [X0,X1,X2,X3] :
( ~ sum(X0,X1,additive_identity)
| ~ sum(X1,X2,X3)
| sum(X0,X3,X2) ),
inference(resolution,[status(thm)],[f28,f21]) ).
fof(f58,plain,
! [X0,X1,X2,X3] :
( ~ sum(X0,X1,X1)
| ~ sum(X1,X2,X3)
| sum(X0,X3,X3) ),
inference(factoring,[status(esa)],[f28]) ).
fof(f62,plain,
! [X0,X1] :
( ~ sum(X0,additive_identity,X1)
| X1 = X0 ),
inference(resolution,[status(thm)],[f45,f22]) ).
fof(f85,plain,
! [X0,X1,X2] :
( ~ sum(X0,X1,X2)
| X2 = add(X0,X1) ),
inference(resolution,[status(thm)],[f24,f45]) ).
fof(f90,plain,
! [X0,X1] : sum(X0,X1,add(X1,X0)),
inference(resolution,[status(thm)],[f24,f31]) ).
fof(f98,plain,
! [X0,X1,X2] :
( ~ sum(X0,X1,X2)
| sum(additive_inverse(X0),X2,X1) ),
inference(resolution,[status(thm)],[f25,f56]) ).
fof(f119,plain,
! [X0,X1] :
( ~ sum(X0,additive_inverse(X0),X1)
| X1 = additive_identity ),
inference(resolution,[status(thm)],[f26,f45]) ).
fof(f127,plain,
! [X0] : add(X0,additive_inverse(X0)) = additive_identity,
inference(resolution,[status(thm)],[f119,f24]) ).
fof(f142,plain,
! [X0,X1,X2] :
( ~ sum(X0,X1,X2)
| X2 = add(X1,X0) ),
inference(resolution,[status(thm)],[f90,f45]) ).
fof(f199,plain,
! [X0,X1] : add(X0,X1) = add(X1,X0),
inference(resolution,[status(thm)],[f85,f90]) ).
fof(f221,plain,
! [X0] : sum(additive_inverse(additive_inverse(X0)),additive_identity,X0),
inference(resolution,[status(thm)],[f98,f25]) ).
fof(f226,plain,
! [X0,X1] : sum(additive_inverse(X0),add(X1,X0),X1),
inference(resolution,[status(thm)],[f98,f90]) ).
fof(f227,plain,
! [X0,X1] : sum(additive_inverse(X0),add(X0,X1),X1),
inference(resolution,[status(thm)],[f98,f24]) ).
fof(f234,plain,
! [X0] : X0 = additive_inverse(additive_inverse(X0)),
inference(resolution,[status(thm)],[f221,f62]) ).
fof(f310,plain,
! [X0,X1] : X0 = add(add(X0,X1),additive_inverse(X1)),
inference(resolution,[status(thm)],[f226,f142]) ).
fof(f311,plain,
! [X0,X1] : X0 = add(additive_inverse(X1),add(X0,X1)),
inference(forward_demodulation,[status(thm)],[f199,f310]) ).
fof(f322,plain,
! [X0,X1] : sum(X0,add(X1,additive_inverse(X0)),X1),
inference(paramodulation,[status(thm)],[f234,f226]) ).
fof(f338,plain,
! [X0,X1] : X0 = add(add(X1,X0),additive_inverse(X1)),
inference(resolution,[status(thm)],[f227,f142]) ).
fof(f339,plain,
! [X0,X1] : X0 = add(additive_inverse(X1),add(X1,X0)),
inference(forward_demodulation,[status(thm)],[f199,f338]) ).
fof(f349,plain,
! [X0,X1] : sum(add(X0,X1),additive_inverse(X0),X1),
inference(resolution,[status(thm)],[f227,f31]) ).
fof(f365,plain,
! [X0,X1] : additive_inverse(X0) = add(additive_inverse(add(X1,X0)),X1),
inference(paramodulation,[status(thm)],[f311,f311]) ).
fof(f366,plain,
! [X0,X1] : additive_inverse(X0) = add(X1,additive_inverse(add(X1,X0))),
inference(forward_demodulation,[status(thm)],[f199,f365]) ).
fof(f429,plain,
! [X0,X1,X2] :
( ~ sum(X0,X1,X1)
| sum(X0,X2,X2) ),
inference(resolution,[status(thm)],[f322,f58]) ).
fof(f447,plain,
! [X0,X1] : X0 = add(X1,add(additive_inverse(X1),X0)),
inference(paramodulation,[status(thm)],[f234,f339]) ).
fof(f472,plain,
! [X0,X1] :
( ~ product(X0,b,X1)
| ~ sum(X0,additive_inverse(a),additive_inverse(a))
| sum(X1,c,c) ),
inference(resolution,[status(thm)],[f41,f49]) ).
fof(f473,plain,
! [X0,X1,X2,X3] :
( ~ product(X0,b,X1)
| ~ sum(X0,additive_inverse(a),X2)
| ~ product(X2,b,X3)
| sum(X1,c,X3) ),
inference(resolution,[status(thm)],[f41,f49]) ).
fof(f519,plain,
! [X0,X1] : sum(add(additive_inverse(X0),X1),X0,X1),
inference(paramodulation,[status(thm)],[f234,f349]) ).
fof(f861,plain,
! [X0,X1] : additive_inverse(add(X0,X1)) = add(additive_inverse(X0),additive_inverse(X1)),
inference(paramodulation,[status(thm)],[f339,f366]) ).
fof(f866,plain,
! [X0,X1] : additive_inverse(add(additive_inverse(X0),X1)) = add(X0,additive_inverse(X1)),
inference(paramodulation,[status(thm)],[f447,f366]) ).
fof(f3752,plain,
! [X0] :
( ~ product(add(additive_inverse(additive_inverse(a)),additive_inverse(a)),b,X0)
| sum(X0,c,c) ),
inference(resolution,[status(thm)],[f472,f519]) ).
fof(f3753,plain,
! [X0] :
( ~ product(additive_inverse(add(additive_inverse(a),a)),b,X0)
| sum(X0,c,c) ),
inference(forward_demodulation,[status(thm)],[f861,f3752]) ).
fof(f3754,plain,
! [X0] :
( ~ product(add(a,additive_inverse(a)),b,X0)
| sum(X0,c,c) ),
inference(forward_demodulation,[status(thm)],[f866,f3753]) ).
fof(f3755,plain,
! [X0] :
( ~ product(additive_identity,b,X0)
| sum(X0,c,c) ),
inference(forward_demodulation,[status(thm)],[f127,f3754]) ).
fof(f4250,plain,
! [X0,X1] :
( ~ product(additive_inverse(additive_inverse(a)),b,X0)
| ~ product(additive_identity,b,X1)
| sum(X0,c,X1) ),
inference(resolution,[status(thm)],[f473,f25]) ).
fof(f4251,plain,
! [X0,X1] :
( ~ product(a,b,X0)
| ~ product(additive_identity,b,X1)
| sum(X0,c,X1) ),
inference(forward_demodulation,[status(thm)],[f234,f4250]) ).
fof(f4675,plain,
sum(multiply(additive_identity,b),c,c),
inference(resolution,[status(thm)],[f3755,f23]) ).
fof(f4689,plain,
! [X0] : sum(multiply(additive_identity,b),X0,X0),
inference(resolution,[status(thm)],[f4675,f429]) ).
fof(f4768,plain,
additive_identity = multiply(additive_identity,b),
inference(resolution,[status(thm)],[f4689,f62]) ).
fof(f4810,plain,
product(additive_identity,b,additive_identity),
inference(paramodulation,[status(thm)],[f4768,f23]) ).
fof(f12753,plain,
! [X0] :
( ~ product(additive_identity,b,X0)
| sum(d,c,X0) ),
inference(resolution,[status(thm)],[f4251,f48]) ).
fof(f12756,plain,
sum(d,c,additive_identity),
inference(resolution,[status(thm)],[f12753,f4810]) ).
fof(f12818,plain,
sum(c,d,additive_identity),
inference(resolution,[status(thm)],[f12756,f31]) ).
fof(f12819,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f12818,f50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.09 % Problem : RNG005-1 : TPTP v8.1.2. Released v1.0.0.
% 0.04/0.10 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.30 % Computer : n025.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Tue May 30 10:46:12 EDT 2023
% 0.09/0.30 % CPUTime :
% 0.09/0.31 % Drodi V3.5.1
% 3.65/0.84 % Refutation found
% 3.65/0.84 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 3.65/0.84 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.86/0.87 % Elapsed time: 0.557677 seconds
% 3.86/0.87 % CPU time: 3.934201 seconds
% 3.86/0.87 % Memory used: 45.276 MB
%------------------------------------------------------------------------------