TSTP Solution File: RNG006-3 by Drodi---3.5.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : RNG006-3 : 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 12:32:34 EDT 2023
% Result : Unsatisfiable 7.44s 1.27s
% Output : CNFRefutation 7.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 16
% Syntax : Number of formulae : 87 ( 51 unt; 0 def)
% Number of atoms : 163 ( 33 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 154 ( 78 ~; 76 |; 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 : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 181 (; 181 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : sum(additive_identity,X,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(f6,axiom,
! [X] : sum(X,additive_inverse(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(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/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,hypothesis,
sum(b,additive_inverse(c),bS_Ic),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,hypothesis,
product(a,b,aPb),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,hypothesis,
product(a,c,aPc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,hypothesis,
sum(aPb,additive_inverse(aPc),aPb_S_IaPc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
~ product(a,bS_Ic,aPb_S_IaPc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,plain,
! [X0] : sum(additive_identity,X0,X0),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f25,plain,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f26,plain,
! [X0,X1] : sum(X0,X1,add(X0,X1)),
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f27,plain,
! [X0] : sum(additive_inverse(X0),X0,additive_identity),
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f28,plain,
! [X0] : sum(X0,additive_inverse(X0),additive_identity),
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f29,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(f30,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)],[f29]) ).
fof(f33,plain,
! [X0,X1,X2] :
( ~ sum(X0,X1,X2)
| sum(X1,X0,X2) ),
inference(cnf_transformation,[status(esa)],[f9]) ).
fof(f38,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(f39,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)],[f38]) ).
fof(f40,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(f41,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)],[f40]) ).
fof(f46,plain,
! [U,V] :
( ! [X,Y] :
( ~ sum(X,Y,U)
| ~ sum(X,Y,V) )
| U = V ),
inference(miniscoping,[status(esa)],[f16]) ).
fof(f47,plain,
! [X0,X1,X2,X3] :
( ~ sum(X0,X1,X2)
| ~ sum(X0,X1,X3)
| X2 = X3 ),
inference(cnf_transformation,[status(esa)],[f46]) ).
fof(f48,plain,
! [U,V] :
( ! [X,Y] :
( ~ product(X,Y,U)
| ~ product(X,Y,V) )
| U = V ),
inference(miniscoping,[status(esa)],[f17]) ).
fof(f49,plain,
! [X0,X1,X2,X3] :
( ~ product(X0,X1,X2)
| ~ product(X0,X1,X3)
| X2 = X3 ),
inference(cnf_transformation,[status(esa)],[f48]) ).
fof(f50,plain,
sum(b,additive_inverse(c),bS_Ic),
inference(cnf_transformation,[status(esa)],[f18]) ).
fof(f51,plain,
product(a,b,aPb),
inference(cnf_transformation,[status(esa)],[f19]) ).
fof(f52,plain,
product(a,c,aPc),
inference(cnf_transformation,[status(esa)],[f20]) ).
fof(f53,plain,
sum(aPb,additive_inverse(aPc),aPb_S_IaPc),
inference(cnf_transformation,[status(esa)],[f21]) ).
fof(f54,plain,
~ product(a,bS_Ic,aPb_S_IaPc),
inference(cnf_transformation,[status(esa)],[f22]) ).
fof(f57,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)],[f25,f41]) ).
fof(f58,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)],[f25,f39]) ).
fof(f61,plain,
! [X0,X1,X2] :
( ~ product(X0,X1,X2)
| multiply(X0,X1) = X2 ),
inference(resolution,[status(thm)],[f25,f49]) ).
fof(f72,plain,
! [X0,X1,X2,X3] :
( ~ product(a,X0,X1)
| ~ sum(b,X0,X2)
| ~ sum(aPb,X1,X3)
| product(a,X2,X3) ),
inference(resolution,[status(thm)],[f51,f41]) ).
fof(f80,plain,
multiply(a,c) = aPc,
inference(resolution,[status(thm)],[f52,f61]) ).
fof(f87,plain,
! [X0] :
( ~ product(a,c,X0)
| aPc = X0 ),
inference(resolution,[status(thm)],[f52,f49]) ).
fof(f98,plain,
! [X0,X1] : sum(X0,X1,add(X1,X0)),
inference(resolution,[status(thm)],[f33,f26]) ).
fof(f106,plain,
! [X0,X1] :
( ~ sum(additive_inverse(X0),X0,X1)
| additive_identity = X1 ),
inference(resolution,[status(thm)],[f47,f27]) ).
fof(f107,plain,
! [X0,X1] :
( ~ sum(additive_identity,X0,X1)
| X0 = X1 ),
inference(resolution,[status(thm)],[f47,f23]) ).
fof(f112,plain,
! [X0,X1,X2] :
( ~ sum(X0,X1,X2)
| add(X1,X0) = X2 ),
inference(resolution,[status(thm)],[f47,f98]) ).
fof(f113,plain,
! [X0,X1,X2] :
( ~ sum(X0,X1,X2)
| add(X0,X1) = X2 ),
inference(resolution,[status(thm)],[f47,f26]) ).
fof(f114,plain,
additive_inverse(additive_identity) = additive_identity,
inference(resolution,[status(thm)],[f107,f28]) ).
fof(f116,plain,
! [X0] : X0 = add(additive_identity,X0),
inference(resolution,[status(thm)],[f107,f26]) ).
fof(f119,plain,
! [X0,X1,X2,X3] :
( ~ sum(X0,X1,X2)
| ~ sum(additive_identity,X1,X3)
| sum(additive_inverse(X0),X2,X3) ),
inference(resolution,[status(thm)],[f30,f27]) ).
fof(f139,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)],[f57,f25]) ).
fof(f150,plain,
! [X0,X1,X2] :
( ~ sum(X0,c,X1)
| ~ product(a,X1,X2)
| sum(multiply(a,X0),aPc,X2) ),
inference(resolution,[status(thm)],[f58,f52]) ).
fof(f373,plain,
! [X0,X1,X2] :
( ~ sum(b,X0,X1)
| ~ sum(aPb,multiply(a,X0),X2)
| product(a,X1,X2) ),
inference(resolution,[status(thm)],[f72,f25]) ).
fof(f449,plain,
! [X0] : additive_identity = add(additive_inverse(X0),X0),
inference(resolution,[status(thm)],[f106,f26]) ).
fof(f473,plain,
! [X0,X1] : add(X0,X1) = add(X1,X0),
inference(resolution,[status(thm)],[f112,f26]) ).
fof(f543,plain,
! [X0,X1,X2] :
( ~ sum(additive_identity,X0,X1)
| sum(additive_inverse(X2),add(X0,X2),X1) ),
inference(resolution,[status(thm)],[f119,f98]) ).
fof(f544,plain,
! [X0,X1,X2] :
( ~ sum(additive_identity,X0,X1)
| sum(additive_inverse(X2),add(X2,X0),X1) ),
inference(resolution,[status(thm)],[f119,f26]) ).
fof(f1478,plain,
! [X0,X1,X2] :
( ~ sum(multiply(X0,additive_identity),multiply(X0,X1),X2)
| product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f139,f23]) ).
fof(f1707,plain,
! [X0] :
( ~ product(a,additive_identity,X0)
| sum(multiply(a,additive_inverse(c)),aPc,X0) ),
inference(resolution,[status(thm)],[f150,f27]) ).
fof(f2718,plain,
! [X0] :
( ~ sum(aPb,multiply(a,additive_inverse(c)),X0)
| product(a,bS_Ic,X0) ),
inference(resolution,[status(thm)],[f373,f50]) ).
fof(f5224,plain,
! [X0,X1] : sum(additive_inverse(X0),add(X1,X0),X1),
inference(resolution,[status(thm)],[f543,f23]) ).
fof(f5235,plain,
! [X0,X1] : sum(additive_inverse(X0),add(X0,X1),X1),
inference(resolution,[status(thm)],[f544,f23]) ).
fof(f5829,plain,
! [X0,X1] : add(additive_inverse(X0),add(X1,X0)) = X1,
inference(resolution,[status(thm)],[f5224,f113]) ).
fof(f5897,plain,
! [X0,X1] : add(additive_inverse(X0),add(X0,X1)) = X1,
inference(resolution,[status(thm)],[f5235,f113]) ).
fof(f6971,plain,
! [X0,X1] : add(additive_inverse(add(X0,X1)),X1) = additive_inverse(X0),
inference(paramodulation,[status(thm)],[f5897,f5829]) ).
fof(f6972,plain,
! [X0,X1] : add(X0,additive_inverse(add(X1,X0))) = additive_inverse(X1),
inference(forward_demodulation,[status(thm)],[f473,f6971]) ).
fof(f15724,plain,
! [X0,X1] : product(X0,X1,add(multiply(X0,X1),multiply(X0,additive_identity))),
inference(resolution,[status(thm)],[f1478,f98]) ).
fof(f15858,plain,
aPc = add(multiply(a,c),multiply(a,additive_identity)),
inference(resolution,[status(thm)],[f15724,f87]) ).
fof(f15859,plain,
aPc = add(multiply(a,additive_identity),multiply(a,c)),
inference(forward_demodulation,[status(thm)],[f473,f15858]) ).
fof(f15860,plain,
aPc = add(multiply(a,additive_identity),aPc),
inference(forward_demodulation,[status(thm)],[f80,f15859]) ).
fof(f15861,plain,
aPc = add(aPc,multiply(a,additive_identity)),
inference(forward_demodulation,[status(thm)],[f473,f15860]) ).
fof(f15989,plain,
add(additive_inverse(aPc),aPc) = multiply(a,additive_identity),
inference(paramodulation,[status(thm)],[f15861,f5897]) ).
fof(f15990,plain,
additive_identity = multiply(a,additive_identity),
inference(forward_demodulation,[status(thm)],[f449,f15989]) ).
fof(f16044,plain,
product(a,additive_identity,add(additive_identity,multiply(a,additive_identity))),
inference(paramodulation,[status(thm)],[f15990,f15724]) ).
fof(f16045,plain,
product(a,additive_identity,multiply(a,additive_identity)),
inference(forward_demodulation,[status(thm)],[f116,f16044]) ).
fof(f16046,plain,
product(a,additive_identity,additive_identity),
inference(forward_demodulation,[status(thm)],[f15990,f16045]) ).
fof(f16736,plain,
sum(multiply(a,additive_inverse(c)),aPc,additive_identity),
inference(resolution,[status(thm)],[f1707,f16046]) ).
fof(f16832,plain,
add(multiply(a,additive_inverse(c)),aPc) = additive_identity,
inference(resolution,[status(thm)],[f16736,f113]) ).
fof(f16833,plain,
add(aPc,multiply(a,additive_inverse(c))) = additive_identity,
inference(forward_demodulation,[status(thm)],[f473,f16832]) ).
fof(f16866,plain,
add(multiply(a,additive_inverse(c)),additive_inverse(additive_identity)) = additive_inverse(aPc),
inference(paramodulation,[status(thm)],[f16833,f6972]) ).
fof(f16867,plain,
add(additive_inverse(additive_identity),multiply(a,additive_inverse(c))) = additive_inverse(aPc),
inference(forward_demodulation,[status(thm)],[f473,f16866]) ).
fof(f16868,plain,
add(additive_identity,multiply(a,additive_inverse(c))) = additive_inverse(aPc),
inference(forward_demodulation,[status(thm)],[f114,f16867]) ).
fof(f16869,plain,
multiply(a,additive_inverse(c)) = additive_inverse(aPc),
inference(forward_demodulation,[status(thm)],[f116,f16868]) ).
fof(f21856,plain,
! [X0] :
( ~ sum(aPb,additive_inverse(aPc),X0)
| product(a,bS_Ic,X0) ),
inference(forward_demodulation,[status(thm)],[f16869,f2718]) ).
fof(f21857,plain,
product(a,bS_Ic,aPb_S_IaPc),
inference(resolution,[status(thm)],[f21856,f53]) ).
fof(f21858,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f21857,f54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : RNG006-3 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.07 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.06/0.25 % Computer : n009.cluster.edu
% 0.06/0.25 % Model : x86_64 x86_64
% 0.06/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.25 % Memory : 8042.1875MB
% 0.06/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.25 % CPULimit : 300
% 0.06/0.25 % WCLimit : 300
% 0.06/0.25 % DateTime : Tue May 30 10:32:46 EDT 2023
% 0.06/0.25 % CPUTime :
% 0.06/0.26 % Drodi V3.5.1
% 7.44/1.27 % Refutation found
% 7.44/1.27 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 7.44/1.27 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 7.44/1.29 % Elapsed time: 1.035472 seconds
% 7.44/1.29 % CPU time: 8.118135 seconds
% 7.44/1.29 % Memory used: 92.747 MB
%------------------------------------------------------------------------------