TSTP Solution File: BOO005-1 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : BOO005-1 : 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 : Tue Apr 30 20:12:51 EDT 2024
% Result : Unsatisfiable 1.59s 0.57s
% Output : CNFRefutation 1.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 13
% Syntax : Number of formulae : 52 ( 24 unt; 0 def)
% Number of atoms : 118 ( 10 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 134 ( 68 ~; 66 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 157 ( 157 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] : sum(X,Y,add(X,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] : product(X,Y,multiply(X,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y,Z] :
( ~ product(X,Y,Z)
| product(Y,X,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X] : sum(additive_identity,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X] : product(multiplicative_identity,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,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(f10,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/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X,Y,V1,Z,V2,V3,V4] :
( ~ sum(X,Y,V1)
| ~ sum(X,Z,V2)
| ~ product(Y,Z,V3)
| ~ sum(X,V3,V4)
| product(V1,V2,V4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [X] : product(X,inverse(X),additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [X,Y,U,V] :
( ~ sum(X,Y,U)
| ~ sum(X,Y,V)
| U = V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [X,Y,U,V] :
( ~ product(X,Y,U)
| ~ product(X,Y,V)
| U = V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
~ sum(x,multiplicative_identity,multiplicative_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,plain,
! [X0,X1] : sum(X0,X1,add(X0,X1)),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f25,plain,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f26,plain,
! [X0,X1,X2] :
( ~ sum(X0,X1,X2)
| sum(X1,X0,X2) ),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f27,plain,
! [X0,X1,X2] :
( ~ product(X0,X1,X2)
| product(X1,X0,X2) ),
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f28,plain,
! [X0] : sum(additive_identity,X0,X0),
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f30,plain,
! [X0] : product(multiplicative_identity,X0,X0),
inference(cnf_transformation,[status(esa)],[f7]) ).
fof(f32,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)],[f9]) ).
fof(f33,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)],[f32]) ).
fof(f34,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)],[f10]) ).
fof(f35,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)],[f34]) ).
fof(f40,plain,
! [V1,V2,V4] :
( ! [X,V3] :
( ! [Y,Z] :
( ~ sum(X,Y,V1)
| ~ sum(X,Z,V2)
| ~ product(Y,Z,V3) )
| ~ sum(X,V3,V4) )
| product(V1,V2,V4) ),
inference(miniscoping,[status(esa)],[f13]) ).
fof(f41,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sum(X0,X1,X2)
| ~ sum(X0,X3,X4)
| ~ product(X1,X3,X5)
| ~ sum(X0,X5,X6)
| product(X2,X4,X6) ),
inference(cnf_transformation,[status(esa)],[f40]) ).
fof(f51,plain,
! [X0] : product(X0,inverse(X0),additive_identity),
inference(cnf_transformation,[status(esa)],[f20]) ).
fof(f52,plain,
! [U,V] :
( ! [X,Y] :
( ~ sum(X,Y,U)
| ~ sum(X,Y,V) )
| U = V ),
inference(miniscoping,[status(esa)],[f21]) ).
fof(f53,plain,
! [X0,X1,X2,X3] :
( ~ sum(X0,X1,X2)
| ~ sum(X0,X1,X3)
| X2 = X3 ),
inference(cnf_transformation,[status(esa)],[f52]) ).
fof(f54,plain,
! [U,V] :
( ! [X,Y] :
( ~ product(X,Y,U)
| ~ product(X,Y,V) )
| U = V ),
inference(miniscoping,[status(esa)],[f22]) ).
fof(f55,plain,
! [X0,X1,X2,X3] :
( ~ product(X0,X1,X2)
| ~ product(X0,X1,X3)
| X2 = X3 ),
inference(cnf_transformation,[status(esa)],[f54]) ).
fof(f56,plain,
~ sum(x,multiplicative_identity,multiplicative_identity),
inference(cnf_transformation,[status(esa)],[f23]) ).
fof(f58,plain,
! [X0,X1] : sum(X0,X1,add(X1,X0)),
inference(resolution,[status(thm)],[f24,f26]) ).
fof(f70,plain,
! [X0] : sum(X0,additive_identity,X0),
inference(resolution,[status(thm)],[f28,f26]) ).
fof(f85,plain,
! [X0,X1] :
( ~ sum(X0,additive_identity,X1)
| X1 = X0 ),
inference(resolution,[status(thm)],[f70,f53]) ).
fof(f116,plain,
! [X0,X1] : product(X0,X1,multiply(X1,X0)),
inference(resolution,[status(thm)],[f27,f25]) ).
fof(f121,plain,
! [X0,X1,X2] :
( ~ product(X0,X1,X2)
| ~ sum(X1,inverse(X0),inverse(X0))
| sum(X2,additive_identity,additive_identity) ),
inference(resolution,[status(thm)],[f33,f51]) ).
fof(f133,plain,
! [X0,X1,X2,X3,X4] :
( ~ product(multiplicative_identity,X0,X1)
| ~ sum(X0,X2,X3)
| ~ sum(X1,X2,X4)
| product(multiplicative_identity,X3,X4) ),
inference(resolution,[status(thm)],[f35,f30]) ).
fof(f309,plain,
! [X0,X1,X2] :
( ~ sum(X0,X1,X2)
| ~ product(X1,additive_identity,additive_identity)
| product(X2,X0,X0) ),
inference(resolution,[status(thm)],[f41,f70]) ).
fof(f443,plain,
! [X0,X1,X2,X3] :
( ~ sum(X0,X1,X2)
| ~ sum(X0,X1,X3)
| product(multiplicative_identity,X2,X3) ),
inference(resolution,[status(thm)],[f133,f30]) ).
fof(f648,plain,
! [X0,X1,X2] :
( ~ sum(X0,X1,X2)
| product(multiplicative_identity,X2,add(X1,X0)) ),
inference(resolution,[status(thm)],[f443,f58]) ).
fof(f729,plain,
! [X0,X1] : product(multiplicative_identity,add(X0,X1),add(X1,X0)),
inference(resolution,[status(thm)],[f648,f24]) ).
fof(f770,plain,
! [X0,X1] : product(add(X0,X1),multiplicative_identity,add(X1,X0)),
inference(resolution,[status(thm)],[f729,f27]) ).
fof(f826,plain,
! [X0,X1,X2] :
( ~ product(add(X0,X1),multiplicative_identity,X2)
| X2 = add(X1,X0) ),
inference(resolution,[status(thm)],[f770,f55]) ).
fof(f1024,plain,
! [X0,X1] :
( ~ product(X0,additive_identity,X1)
| sum(X1,additive_identity,additive_identity) ),
inference(resolution,[status(thm)],[f121,f28]) ).
fof(f1260,plain,
! [X0] : sum(multiply(additive_identity,X0),additive_identity,additive_identity),
inference(resolution,[status(thm)],[f1024,f116]) ).
fof(f1265,plain,
! [X0] : additive_identity = multiply(additive_identity,X0),
inference(resolution,[status(thm)],[f1260,f85]) ).
fof(f1311,plain,
! [X0] : product(X0,additive_identity,additive_identity),
inference(paramodulation,[status(thm)],[f1265,f116]) ).
fof(f2675,plain,
! [X0,X1,X2] :
( ~ sum(X0,X1,X2)
| product(X2,X0,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f309,f1311]) ).
fof(f2688,plain,
! [X0,X1] : product(add(X0,X1),X1,X1),
inference(resolution,[status(thm)],[f2675,f58]) ).
fof(f2739,plain,
! [X0] : multiplicative_identity = add(multiplicative_identity,X0),
inference(resolution,[status(thm)],[f2688,f826]) ).
fof(f2881,plain,
! [X0] : sum(X0,multiplicative_identity,multiplicative_identity),
inference(paramodulation,[status(thm)],[f2739,f58]) ).
fof(f3006,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f56,f2881]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : BOO005-1 : TPTP v8.1.2. Released v1.0.0.
% 0.04/0.14 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.35 % Computer : n027.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Apr 29 23:02:17 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.36 % Drodi V3.6.0
% 1.59/0.57 % Refutation found
% 1.59/0.57 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 1.59/0.57 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.59/0.59 % Elapsed time: 0.228962 seconds
% 1.59/0.59 % CPU time: 1.726744 seconds
% 1.59/0.59 % Total memory used: 40.050 MB
% 1.59/0.59 % Net memory used: 37.211 MB
%------------------------------------------------------------------------------