TSTP Solution File: RNG001-4 by Drodi---3.6.0
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%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : RNG001-4 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n006.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 20:37:38 EDT 2024
% Result : Unsatisfiable 1.93s 0.65s
% Output : CNFRefutation 2.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 31 ( 15 unt; 0 def)
% Number of atoms : 65 ( 10 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 70 ( 36 ~; 34 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 90 ( 90 !; 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(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(f17,axiom,
! [X,Y,U,V] :
( ~ product(X,Y,U)
| ~ product(X,Y,V)
| U = V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [X,Y,Z,W] :
( ~ sum(X,Y,Z)
| ~ sum(W,Y,Z)
| X = W ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
~ product(a,additive_identity,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,plain,
! [X0] : sum(additive_identity,X0,X0),
inference(cnf_transformation,[status(esa)],[f1]) ).
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(f31,plain,
! [X0,X1,X2] :
( ~ sum(X0,X1,X2)
| sum(X1,X0,X2) ),
inference(cnf_transformation,[status(esa)],[f9]) ).
fof(f38,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(f39,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)],[f38]) ).
fof(f46,plain,
! [U,V] :
( ! [X,Y] :
( ~ product(X,Y,U)
| ~ product(X,Y,V) )
| U = V ),
inference(miniscoping,[status(esa)],[f17]) ).
fof(f47,plain,
! [X0,X1,X2,X3] :
( ~ product(X0,X1,X2)
| ~ product(X0,X1,X3)
| X2 = X3 ),
inference(cnf_transformation,[status(esa)],[f46]) ).
fof(f50,plain,
! [X,W] :
( ! [Y,Z] :
( ~ sum(X,Y,Z)
| ~ sum(W,Y,Z) )
| X = W ),
inference(miniscoping,[status(esa)],[f19]) ).
fof(f51,plain,
! [X0,X1,X2,X3] :
( ~ sum(X0,X1,X2)
| ~ sum(X3,X1,X2)
| X0 = X3 ),
inference(cnf_transformation,[status(esa)],[f50]) ).
fof(f52,plain,
~ product(a,additive_identity,additive_identity),
inference(cnf_transformation,[status(esa)],[f20]) ).
fof(f55,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)],[f23,f39]) ).
fof(f59,plain,
! [X0,X1,X2] :
( ~ product(X0,X1,X2)
| multiply(X0,X1) = X2 ),
inference(resolution,[status(thm)],[f23,f47]) ).
fof(f90,plain,
! [X0,X1] : sum(X0,X1,add(X1,X0)),
inference(resolution,[status(thm)],[f31,f24]) ).
fof(f171,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)],[f55,f23]) ).
fof(f763,plain,
! [X0,X1,X2] :
( ~ sum(multiply(X0,additive_identity),multiply(X0,X1),X2)
| product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f171,f21]) ).
fof(f997,plain,
! [X0,X1] :
( ~ sum(X0,X1,X1)
| additive_identity = X0 ),
inference(resolution,[status(thm)],[f51,f21]) ).
fof(f2916,plain,
! [X0,X1] : product(X0,X1,add(multiply(X0,X1),multiply(X0,additive_identity))),
inference(resolution,[status(thm)],[f763,f90]) ).
fof(f3000,plain,
! [X0,X1] : multiply(X0,X1) = add(multiply(X0,X1),multiply(X0,additive_identity)),
inference(resolution,[status(thm)],[f2916,f59]) ).
fof(f3185,plain,
! [X0,X1] : sum(multiply(X0,additive_identity),multiply(X0,X1),multiply(X0,X1)),
inference(paramodulation,[status(thm)],[f3000,f90]) ).
fof(f3358,plain,
! [X0] : additive_identity = multiply(X0,additive_identity),
inference(resolution,[status(thm)],[f3185,f997]) ).
fof(f3473,plain,
! [X0] : product(X0,additive_identity,additive_identity),
inference(paramodulation,[status(thm)],[f3358,f23]) ).
fof(f3498,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f52,f3473]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : RNG001-4 : 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 : n006.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 22:15:05 EDT 2024
% 0.11/0.34 % CPUTime :
% 0.11/0.35 % Drodi V3.6.0
% 1.93/0.65 % Refutation found
% 1.93/0.65 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 1.93/0.65 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.32/0.66 % Elapsed time: 0.310950 seconds
% 2.32/0.66 % CPU time: 2.346171 seconds
% 2.32/0.66 % Total memory used: 42.200 MB
% 2.32/0.66 % Net memory used: 38.798 MB
%------------------------------------------------------------------------------