TSTP Solution File: RNG004-2 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : RNG004-2 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n014.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 20:37:39 EDT 2024
% Result : Unsatisfiable 1.59s 0.61s
% Output : CNFRefutation 1.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 16
% Syntax : Number of formulae : 69 ( 33 unt; 0 def)
% Number of atoms : 145 ( 21 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 154 ( 78 ~; 76 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 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 : 161 ( 161 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : sum(additive_identity,X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : sum(X,additive_identity,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(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/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(f18,axiom,
! [X,Y,Z,W] :
( ~ sum(X,Y,Z)
| ~ sum(X,W,Z)
| Y = W ),
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,hypothesis,
product(a,b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,hypothesis,
product(additive_inverse(a),additive_inverse(b),d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
c != d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,plain,
! [X0] : sum(additive_identity,X0,X0),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f24,plain,
! [X0] : sum(X0,additive_identity,X0),
inference(cnf_transformation,[status(esa)],[f2]) ).
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(f42,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(f43,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)],[f42]) ).
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(f50,plain,
! [Y,W] :
( ! [X,Z] :
( ~ sum(X,Y,Z)
| ~ sum(X,W,Z) )
| Y = W ),
inference(miniscoping,[status(esa)],[f18]) ).
fof(f51,plain,
! [X0,X1,X2,X3] :
( ~ sum(X0,X1,X2)
| ~ sum(X0,X3,X2)
| X1 = X3 ),
inference(cnf_transformation,[status(esa)],[f50]) ).
fof(f52,plain,
! [X,W] :
( ! [Y,Z] :
( ~ sum(X,Y,Z)
| ~ sum(W,Y,Z) )
| X = W ),
inference(miniscoping,[status(esa)],[f19]) ).
fof(f53,plain,
! [X0,X1,X2,X3] :
( ~ sum(X0,X1,X2)
| ~ sum(X3,X1,X2)
| X0 = X3 ),
inference(cnf_transformation,[status(esa)],[f52]) ).
fof(f54,plain,
product(a,b,c),
inference(cnf_transformation,[status(esa)],[f20]) ).
fof(f55,plain,
product(additive_inverse(a),additive_inverse(b),d),
inference(cnf_transformation,[status(esa)],[f21]) ).
fof(f56,plain,
c != d,
inference(cnf_transformation,[status(esa)],[f22]) ).
fof(f61,plain,
! [X0,X1] : sum(X0,X1,add(X1,X0)),
inference(resolution,[status(thm)],[f33,f26]) ).
fof(f68,plain,
! [X0,X1,X2] :
( ~ sum(X0,X1,X2)
| add(X0,X1) = X2 ),
inference(resolution,[status(thm)],[f47,f26]) ).
fof(f78,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(f144,plain,
! [X0,X1] :
( ~ sum(additive_inverse(X0),X1,additive_identity)
| X0 = X1 ),
inference(resolution,[status(thm)],[f51,f27]) ).
fof(f146,plain,
! [X0,X1] :
( ~ sum(X0,X1,additive_identity)
| additive_inverse(X0) = X1 ),
inference(resolution,[status(thm)],[f51,f28]) ).
fof(f147,plain,
! [X0,X1] :
( ~ sum(X0,X1,X0)
| additive_identity = X1 ),
inference(resolution,[status(thm)],[f51,f24]) ).
fof(f151,plain,
! [X0] : X0 = additive_inverse(additive_inverse(X0)),
inference(resolution,[status(thm)],[f144,f28]) ).
fof(f160,plain,
! [X0,X1,X2,X3] :
( ~ product(a,X0,X1)
| ~ sum(b,X0,X2)
| ~ product(a,X2,X3)
| sum(c,X1,X3) ),
inference(resolution,[status(thm)],[f39,f54]) ).
fof(f195,plain,
! [X0,X1,X2] :
( ~ sum(b,X0,X1)
| ~ product(a,X1,X2)
| sum(c,multiply(a,X0),X2) ),
inference(resolution,[status(thm)],[f160,f25]) ).
fof(f254,plain,
! [X0,X1,X2,X3] :
( ~ product(X0,additive_inverse(b),X1)
| ~ sum(additive_inverse(a),X0,X2)
| ~ product(X2,additive_inverse(b),X3)
| sum(d,X1,X3) ),
inference(resolution,[status(thm)],[f43,f55]) ).
fof(f311,plain,
! [X0] :
( ~ product(a,additive_identity,X0)
| sum(c,multiply(a,additive_inverse(b)),X0) ),
inference(resolution,[status(thm)],[f195,f28]) ).
fof(f312,plain,
! [X0] :
( ~ product(a,b,X0)
| sum(c,multiply(a,additive_identity),X0) ),
inference(resolution,[status(thm)],[f195,f24]) ).
fof(f315,plain,
sum(c,multiply(a,additive_identity),c),
inference(resolution,[status(thm)],[f312,f54]) ).
fof(f319,plain,
additive_identity = multiply(a,additive_identity),
inference(resolution,[status(thm)],[f315,f147]) ).
fof(f333,plain,
! [X0,X1,X2] :
( ~ sum(additive_inverse(a),X0,X1)
| ~ product(X1,additive_inverse(b),X2)
| sum(d,multiply(X0,additive_inverse(b)),X2) ),
inference(resolution,[status(thm)],[f254,f25]) ).
fof(f336,plain,
product(a,additive_identity,additive_identity),
inference(paramodulation,[status(thm)],[f319,f25]) ).
fof(f392,plain,
! [X0,X1,X2] :
( ~ sum(additive_identity,X0,X1)
| sum(additive_inverse(X2),add(X0,X2),X1) ),
inference(resolution,[status(thm)],[f78,f61]) ).
fof(f437,plain,
sum(c,multiply(a,additive_inverse(b)),additive_identity),
inference(resolution,[status(thm)],[f311,f336]) ).
fof(f441,plain,
additive_inverse(c) = multiply(a,additive_inverse(b)),
inference(resolution,[status(thm)],[f437,f146]) ).
fof(f999,plain,
! [X0,X1] : sum(additive_inverse(X0),add(X1,X0),X1),
inference(resolution,[status(thm)],[f392,f23]) ).
fof(f1195,plain,
! [X0,X1] : sum(X0,add(X1,additive_inverse(X0)),X1),
inference(paramodulation,[status(thm)],[f151,f999]) ).
fof(f1839,plain,
! [X0] :
( ~ product(additive_identity,additive_inverse(b),X0)
| sum(d,multiply(a,additive_inverse(b)),X0) ),
inference(resolution,[status(thm)],[f333,f27]) ).
fof(f1840,plain,
! [X0] :
( ~ product(additive_identity,additive_inverse(b),X0)
| sum(d,additive_inverse(c),X0) ),
inference(forward_demodulation,[status(thm)],[f441,f1839]) ).
fof(f1846,plain,
! [X0] :
( ~ product(additive_inverse(a),additive_inverse(b),X0)
| sum(d,multiply(additive_identity,additive_inverse(b)),X0) ),
inference(resolution,[status(thm)],[f333,f24]) ).
fof(f2199,plain,
sum(d,additive_inverse(c),multiply(additive_identity,additive_inverse(b))),
inference(resolution,[status(thm)],[f1840,f25]) ).
fof(f2212,plain,
add(d,additive_inverse(c)) = multiply(additive_identity,additive_inverse(b)),
inference(resolution,[status(thm)],[f2199,f68]) ).
fof(f2220,plain,
sum(c,multiply(additive_identity,additive_inverse(b)),d),
inference(paramodulation,[status(thm)],[f2212,f1195]) ).
fof(f2306,plain,
! [X0] :
( ~ sum(X0,multiply(additive_identity,additive_inverse(b)),d)
| c = X0 ),
inference(resolution,[status(thm)],[f2220,f53]) ).
fof(f5838,plain,
sum(d,multiply(additive_identity,additive_inverse(b)),d),
inference(resolution,[status(thm)],[f1846,f55]) ).
fof(f5867,plain,
c = d,
inference(resolution,[status(thm)],[f5838,f2306]) ).
fof(f5868,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f5867,f56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : RNG004-2 : TPTP v8.1.2. Released v1.0.0.
% 0.06/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.33 % Computer : n014.cluster.edu
% 0.10/0.33 % Model : x86_64 x86_64
% 0.10/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.33 % Memory : 8042.1875MB
% 0.10/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.33 % CPULimit : 300
% 0.10/0.33 % WCLimit : 300
% 0.10/0.33 % DateTime : Mon Apr 29 22:13:49 EDT 2024
% 0.10/0.33 % CPUTime :
% 0.10/0.34 % Drodi V3.6.0
% 1.59/0.61 % Refutation found
% 1.59/0.61 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 1.59/0.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.59/0.62 % Elapsed time: 0.287235 seconds
% 1.59/0.62 % CPU time: 2.133743 seconds
% 1.59/0.62 % Total memory used: 44.429 MB
% 1.59/0.62 % Net memory used: 40.977 MB
%------------------------------------------------------------------------------