TSTP Solution File: RNG004-1 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : RNG004-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n008.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 3.57s 0.83s
% Output : CNFRefutation 3.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 14
% Syntax : Number of formulae : 79 ( 47 unt; 0 def)
% Number of atoms : 147 ( 20 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 138 ( 70 ~; 68 |; 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 : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 153 ( 153 !; 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,hypothesis,
product(a,b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,hypothesis,
product(additive_inverse(a),additive_inverse(b),d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
c != d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,plain,
! [X0] : sum(additive_identity,X0,X0),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f22,plain,
! [X0] : sum(X0,additive_identity,X0),
inference(cnf_transformation,[status(esa)],[f2]) ).
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(f25,plain,
! [X0] : sum(additive_inverse(X0),X0,additive_identity),
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f26,plain,
! [X0] : sum(X0,additive_inverse(X0),additive_identity),
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f27,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(f28,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)],[f27]) ).
fof(f31,plain,
! [X0,X1,X2] :
( ~ sum(X0,X1,X2)
| sum(X1,X0,X2) ),
inference(cnf_transformation,[status(esa)],[f9]) ).
fof(f36,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(f37,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)],[f36]) ).
fof(f40,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(f41,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)],[f40]) ).
fof(f44,plain,
! [U,V] :
( ! [X,Y] :
( ~ sum(X,Y,U)
| ~ sum(X,Y,V) )
| U = V ),
inference(miniscoping,[status(esa)],[f16]) ).
fof(f45,plain,
! [X0,X1,X2,X3] :
( ~ sum(X0,X1,X2)
| ~ sum(X0,X1,X3)
| X2 = X3 ),
inference(cnf_transformation,[status(esa)],[f44]) ).
fof(f48,plain,
product(a,b,c),
inference(cnf_transformation,[status(esa)],[f18]) ).
fof(f49,plain,
product(additive_inverse(a),additive_inverse(b),d),
inference(cnf_transformation,[status(esa)],[f19]) ).
fof(f50,plain,
c != d,
inference(cnf_transformation,[status(esa)],[f20]) ).
fof(f55,plain,
! [X0,X1] : sum(X0,X1,add(X1,X0)),
inference(resolution,[status(thm)],[f31,f24]) ).
fof(f58,plain,
! [X0,X1] :
( ~ sum(additive_identity,X0,X1)
| X1 = X0 ),
inference(resolution,[status(thm)],[f45,f21]) ).
fof(f60,plain,
! [X0,X1] :
( ~ sum(X0,additive_identity,X1)
| X1 = X0 ),
inference(resolution,[status(thm)],[f45,f22]) ).
fof(f61,plain,
! [X0,X1,X2] :
( ~ sum(X0,X1,X2)
| X2 = add(X1,X0) ),
inference(resolution,[status(thm)],[f45,f55]) ).
fof(f62,plain,
! [X0,X1,X2] :
( ~ sum(X0,X1,X2)
| X2 = add(X0,X1) ),
inference(resolution,[status(thm)],[f45,f24]) ).
fof(f64,plain,
! [X0] : add(X0,additive_identity) = X0,
inference(resolution,[status(thm)],[f58,f55]) ).
fof(f76,plain,
! [X0,X1] :
( ~ sum(X0,X1,X1)
| sum(X0,additive_identity,additive_identity) ),
inference(resolution,[status(thm)],[f28,f26]) ).
fof(f84,plain,
! [X0,X1,X2,X3] :
( ~ sum(X0,X1,additive_identity)
| ~ sum(X1,X2,X3)
| sum(X0,X3,X2) ),
inference(resolution,[status(thm)],[f28,f21]) ).
fof(f133,plain,
! [X0,X1] : add(X0,X1) = add(X1,X0),
inference(resolution,[status(thm)],[f61,f24]) ).
fof(f195,plain,
! [X0,X1] :
( ~ product(a,X0,X1)
| ~ sum(X0,b,b)
| sum(X1,c,c) ),
inference(resolution,[status(thm)],[f37,f48]) ).
fof(f196,plain,
! [X0,X1,X2,X3] :
( ~ product(a,X0,X1)
| ~ sum(X0,b,X2)
| ~ product(a,X2,X3)
| sum(X1,c,X3) ),
inference(resolution,[status(thm)],[f37,f48]) ).
fof(f257,plain,
! [X0] :
( ~ sum(X0,b,b)
| sum(multiply(a,X0),c,c) ),
inference(resolution,[status(thm)],[f195,f23]) ).
fof(f258,plain,
sum(multiply(a,additive_identity),c,c),
inference(resolution,[status(thm)],[f257,f21]) ).
fof(f259,plain,
sum(multiply(a,additive_identity),additive_identity,additive_identity),
inference(resolution,[status(thm)],[f258,f76]) ).
fof(f274,plain,
additive_identity = multiply(a,additive_identity),
inference(resolution,[status(thm)],[f259,f60]) ).
fof(f292,plain,
product(a,additive_identity,additive_identity),
inference(paramodulation,[status(thm)],[f274,f23]) ).
fof(f331,plain,
! [X0,X1] :
( ~ product(a,X0,X1)
| ~ sum(X0,b,additive_identity)
| sum(X1,c,additive_identity) ),
inference(resolution,[status(thm)],[f196,f292]) ).
fof(f438,plain,
! [X0,X1] :
( ~ product(X0,additive_inverse(b),X1)
| ~ sum(X0,additive_inverse(a),additive_inverse(a))
| sum(X1,d,d) ),
inference(resolution,[status(thm)],[f41,f49]) ).
fof(f439,plain,
! [X0,X1,X2,X3] :
( ~ product(X0,additive_inverse(b),X1)
| ~ sum(X0,additive_inverse(a),X2)
| ~ product(X2,additive_inverse(b),X3)
| sum(X1,d,X3) ),
inference(resolution,[status(thm)],[f41,f49]) ).
fof(f573,plain,
! [X0] :
( ~ product(additive_identity,additive_inverse(b),X0)
| sum(X0,d,d) ),
inference(resolution,[status(thm)],[f438,f21]) ).
fof(f612,plain,
sum(multiply(additive_identity,additive_inverse(b)),d,d),
inference(resolution,[status(thm)],[f573,f23]) ).
fof(f615,plain,
sum(multiply(additive_identity,additive_inverse(b)),additive_identity,additive_identity),
inference(resolution,[status(thm)],[f612,f76]) ).
fof(f630,plain,
additive_identity = multiply(additive_identity,additive_inverse(b)),
inference(resolution,[status(thm)],[f615,f60]) ).
fof(f676,plain,
! [X0,X1,X2] :
( ~ product(X0,additive_inverse(b),X1)
| ~ sum(X0,additive_inverse(a),X2)
| sum(X1,d,multiply(X2,additive_inverse(b))) ),
inference(resolution,[status(thm)],[f439,f23]) ).
fof(f757,plain,
! [X0,X1,X2] :
( ~ sum(X0,X1,X2)
| sum(additive_inverse(X0),X2,X1) ),
inference(resolution,[status(thm)],[f84,f25]) ).
fof(f759,plain,
! [X0,X1,X2] :
( ~ sum(additive_inverse(X0),X1,X2)
| sum(X0,X2,X1) ),
inference(resolution,[status(thm)],[f84,f26]) ).
fof(f761,plain,
! [X0] : sum(additive_inverse(additive_inverse(X0)),additive_identity,X0),
inference(resolution,[status(thm)],[f757,f25]) ).
fof(f767,plain,
! [X0,X1] : sum(additive_inverse(X0),add(X0,X1),X1),
inference(resolution,[status(thm)],[f757,f24]) ).
fof(f773,plain,
! [X0] : X0 = additive_inverse(additive_inverse(X0)),
inference(resolution,[status(thm)],[f761,f60]) ).
fof(f861,plain,
! [X0,X1] : X0 = add(additive_inverse(X1),add(X1,X0)),
inference(resolution,[status(thm)],[f767,f62]) ).
fof(f871,plain,
! [X0,X1] : sum(add(X0,X1),additive_inverse(X0),X1),
inference(resolution,[status(thm)],[f767,f31]) ).
fof(f1378,plain,
! [X0,X1] : sum(add(additive_inverse(X0),X1),X0,X1),
inference(paramodulation,[status(thm)],[f773,f871]) ).
fof(f1826,plain,
! [X0,X1] :
( ~ sum(X0,additive_inverse(a),X1)
| sum(multiply(X0,additive_inverse(b)),d,multiply(X1,additive_inverse(b))) ),
inference(resolution,[status(thm)],[f676,f23]) ).
fof(f2318,plain,
! [X0] :
( ~ sum(X0,b,additive_identity)
| sum(multiply(a,X0),c,additive_identity) ),
inference(resolution,[status(thm)],[f331,f23]) ).
fof(f2319,plain,
sum(multiply(a,add(additive_inverse(b),additive_identity)),c,additive_identity),
inference(resolution,[status(thm)],[f2318,f1378]) ).
fof(f2320,plain,
sum(multiply(a,additive_inverse(b)),c,additive_identity),
inference(forward_demodulation,[status(thm)],[f64,f2319]) ).
fof(f2329,plain,
additive_identity = add(multiply(a,additive_inverse(b)),c),
inference(resolution,[status(thm)],[f2320,f62]) ).
fof(f2330,plain,
additive_identity = add(c,multiply(a,additive_inverse(b))),
inference(forward_demodulation,[status(thm)],[f133,f2329]) ).
fof(f2341,plain,
multiply(a,additive_inverse(b)) = add(additive_inverse(c),additive_identity),
inference(paramodulation,[status(thm)],[f2330,f861]) ).
fof(f2342,plain,
multiply(a,additive_inverse(b)) = additive_inverse(c),
inference(forward_demodulation,[status(thm)],[f64,f2341]) ).
fof(f3588,plain,
sum(multiply(additive_inverse(additive_inverse(a)),additive_inverse(b)),d,multiply(additive_identity,additive_inverse(b))),
inference(resolution,[status(thm)],[f1826,f25]) ).
fof(f3589,plain,
sum(multiply(a,additive_inverse(b)),d,multiply(additive_identity,additive_inverse(b))),
inference(forward_demodulation,[status(thm)],[f773,f3588]) ).
fof(f3590,plain,
sum(additive_inverse(c),d,multiply(additive_identity,additive_inverse(b))),
inference(forward_demodulation,[status(thm)],[f2342,f3589]) ).
fof(f3591,plain,
sum(additive_inverse(c),d,additive_identity),
inference(forward_demodulation,[status(thm)],[f630,f3590]) ).
fof(f3601,plain,
sum(c,additive_identity,d),
inference(resolution,[status(thm)],[f3591,f759]) ).
fof(f3624,plain,
d = c,
inference(resolution,[status(thm)],[f3601,f60]) ).
fof(f3625,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f3624,f50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : RNG004-1 : TPTP v8.1.2. Released v1.0.0.
% 0.08/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.34 % Computer : n008.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Apr 29 22:21:13 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.36 % Drodi V3.6.0
% 3.57/0.83 % Refutation found
% 3.57/0.83 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 3.57/0.83 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.57/0.86 % Elapsed time: 0.503152 seconds
% 3.57/0.86 % CPU time: 3.845637 seconds
% 3.57/0.86 % Total memory used: 57.059 MB
% 3.57/0.86 % Net memory used: 52.586 MB
%------------------------------------------------------------------------------