TSTP Solution File: BOO017-1 by Drodi---3.6.0
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%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : BOO017-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n003.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 20:12:57 EDT 2024
% Result : Unsatisfiable 1.88s 0.60s
% Output : CNFRefutation 1.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 15
% Syntax : Number of formulae : 57 ( 27 unt; 0 def)
% Number of atoms : 129 ( 10 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 146 ( 74 ~; 72 |; 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 : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 163 ( 163 !; 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(f6,axiom,
! [X] : sum(X,additive_identity,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(f8,axiom,
! [X] : product(X,multiplicative_identity,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,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(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(f15,axiom,
! [Y,X,V1,Z,V2,V3,V4] :
( ~ sum(Y,X,V1)
| ~ sum(Z,X,V2)
| ~ product(Y,Z,V3)
| ~ sum(V3,X,V4)
| product(V1,V2,V4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [X] : sum(inverse(X),X,multiplicative_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,hypothesis,
sum(x,y,z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
~ product(x,z,x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,plain,
! [X0,X1] : sum(X0,X1,add(X0,X1)),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f26,plain,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f27,plain,
! [X0,X1,X2] :
( ~ sum(X0,X1,X2)
| sum(X1,X0,X2) ),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f28,plain,
! [X0,X1,X2] :
( ~ product(X0,X1,X2)
| product(X1,X0,X2) ),
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f30,plain,
! [X0] : sum(X0,additive_identity,X0),
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f31,plain,
! [X0] : product(multiplicative_identity,X0,X0),
inference(cnf_transformation,[status(esa)],[f7]) ).
fof(f32,plain,
! [X0] : product(X0,multiplicative_identity,X0),
inference(cnf_transformation,[status(esa)],[f8]) ).
fof(f37,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)],[f11]) ).
fof(f38,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)],[f37]) ).
fof(f41,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(f42,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)],[f41]) ).
fof(f45,plain,
! [V1,V2,V4] :
( ! [X,V3] :
( ! [Y,Z] :
( ~ sum(Y,X,V1)
| ~ sum(Z,X,V2)
| ~ product(Y,Z,V3) )
| ~ sum(V3,X,V4) )
| product(V1,V2,V4) ),
inference(miniscoping,[status(esa)],[f15]) ).
fof(f46,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sum(X0,X1,X2)
| ~ sum(X3,X1,X4)
| ~ product(X0,X3,X5)
| ~ sum(X5,X1,X6)
| product(X2,X4,X6) ),
inference(cnf_transformation,[status(esa)],[f45]) ).
fof(f49,plain,
! [X0] : sum(inverse(X0),X0,multiplicative_identity),
inference(cnf_transformation,[status(esa)],[f17]) ).
fof(f53,plain,
! [U,V] :
( ! [X,Y] :
( ~ sum(X,Y,U)
| ~ sum(X,Y,V) )
| U = V ),
inference(miniscoping,[status(esa)],[f21]) ).
fof(f54,plain,
! [X0,X1,X2,X3] :
( ~ sum(X0,X1,X2)
| ~ sum(X0,X1,X3)
| X2 = X3 ),
inference(cnf_transformation,[status(esa)],[f53]) ).
fof(f55,plain,
! [U,V] :
( ! [X,Y] :
( ~ product(X,Y,U)
| ~ product(X,Y,V) )
| U = V ),
inference(miniscoping,[status(esa)],[f22]) ).
fof(f56,plain,
! [X0,X1,X2,X3] :
( ~ product(X0,X1,X2)
| ~ product(X0,X1,X3)
| X2 = X3 ),
inference(cnf_transformation,[status(esa)],[f55]) ).
fof(f57,plain,
sum(x,y,z),
inference(cnf_transformation,[status(esa)],[f23]) ).
fof(f58,plain,
~ product(x,z,x),
inference(cnf_transformation,[status(esa)],[f24]) ).
fof(f60,plain,
! [X0,X1,X2,X3,X4] :
( ~ product(X0,X1,X2)
| ~ product(X3,X1,X4)
| ~ sum(X0,X3,X3)
| sum(X2,X4,X4) ),
inference(factoring,[status(esa)],[f38]) ).
fof(f61,plain,
! [X0,X1,X2,X3,X4] :
( ~ sum(X0,X1,X2)
| ~ sum(X0,X3,X4)
| ~ product(X1,X3,X3)
| product(X2,X4,X4) ),
inference(factoring,[status(esa)],[f42]) ).
fof(f63,plain,
! [X0,X1,X2,X3,X4] :
( ~ sum(X0,X1,X2)
| ~ sum(X3,X1,X4)
| ~ product(X0,X3,X3)
| product(X2,X4,X4) ),
inference(factoring,[status(esa)],[f46]) ).
fof(f100,plain,
! [X0,X1,X2] :
( ~ sum(X0,X1,X2)
| ~ product(X1,additive_identity,additive_identity)
| product(X2,X0,X0) ),
inference(resolution,[status(thm)],[f30,f61]) ).
fof(f107,plain,
! [X0,X1,X2,X3] :
( ~ sum(multiplicative_identity,X0,X1)
| ~ sum(X2,X0,X3)
| product(X1,X3,X3) ),
inference(resolution,[status(thm)],[f31,f63]) ).
fof(f114,plain,
! [X0,X1,X2] :
( ~ product(X0,X1,X2)
| ~ sum(X0,multiplicative_identity,multiplicative_identity)
| sum(X2,X1,X1) ),
inference(resolution,[status(thm)],[f31,f60]) ).
fof(f147,plain,
! [X0,X1] :
( ~ product(X0,multiplicative_identity,X1)
| X1 = X0 ),
inference(resolution,[status(thm)],[f32,f56]) ).
fof(f174,plain,
! [X0,X1] : product(X0,X1,multiply(X1,X0)),
inference(resolution,[status(thm)],[f26,f28]) ).
fof(f286,plain,
! [X0,X1] :
( ~ sum(X0,additive_identity,X1)
| X1 = X0 ),
inference(resolution,[status(thm)],[f54,f30]) ).
fof(f492,plain,
! [X0,X1,X2] :
( ~ sum(X0,X1,X2)
| product(add(multiplicative_identity,X1),X2,X2) ),
inference(resolution,[status(thm)],[f107,f25]) ).
fof(f506,plain,
! [X0] : product(add(multiplicative_identity,X0),multiplicative_identity,multiplicative_identity),
inference(resolution,[status(thm)],[f492,f49]) ).
fof(f612,plain,
! [X0] : multiplicative_identity = add(multiplicative_identity,X0),
inference(resolution,[status(thm)],[f506,f147]) ).
fof(f671,plain,
! [X0] : sum(multiplicative_identity,X0,multiplicative_identity),
inference(paramodulation,[status(thm)],[f612,f25]) ).
fof(f681,plain,
! [X0] : sum(X0,multiplicative_identity,multiplicative_identity),
inference(resolution,[status(thm)],[f671,f27]) ).
fof(f1280,plain,
! [X0,X1,X2] :
( ~ product(X0,X1,X2)
| sum(X2,X1,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f114,f681]) ).
fof(f1285,plain,
! [X0,X1] : sum(multiply(X0,X1),X0,X0),
inference(resolution,[status(thm)],[f1280,f174]) ).
fof(f1363,plain,
! [X0] : additive_identity = multiply(additive_identity,X0),
inference(resolution,[status(thm)],[f1285,f286]) ).
fof(f1401,plain,
! [X0] : product(X0,additive_identity,additive_identity),
inference(paramodulation,[status(thm)],[f1363,f174]) ).
fof(f1410,plain,
! [X0,X1,X2] :
( ~ sum(X0,X1,X2)
| product(X2,X0,X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f100,f1401]) ).
fof(f1829,plain,
product(z,x,x),
inference(resolution,[status(thm)],[f1410,f57]) ).
fof(f2035,plain,
product(x,z,x),
inference(resolution,[status(thm)],[f1829,f28]) ).
fof(f2036,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f2035,f58]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : BOO017-1 : TPTP v8.1.2. Released v1.0.0.
% 0.03/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.34 % Computer : n003.cluster.edu
% 0.11/0.34 % Model : x86_64 x86_64
% 0.11/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.34 % Memory : 8042.1875MB
% 0.11/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.34 % CPULimit : 300
% 0.11/0.34 % WCLimit : 300
% 0.11/0.34 % DateTime : Mon Apr 29 22:40:48 EDT 2024
% 0.11/0.35 % CPUTime :
% 0.11/0.35 % Drodi V3.6.0
% 1.88/0.60 % Refutation found
% 1.88/0.60 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 1.88/0.60 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.88/0.62 % Elapsed time: 0.265205 seconds
% 1.88/0.62 % CPU time: 1.970349 seconds
% 1.88/0.62 % Total memory used: 37.177 MB
% 1.88/0.62 % Net memory used: 34.180 MB
%------------------------------------------------------------------------------