TSTP Solution File: GRP774+1 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : GRP774+1 : TPTP v8.1.2. Released v4.1.0.
% 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 : Wed May 31 12:12:40 EDT 2023
% Result : Theorem 8.99s 1.62s
% Output : CNFRefutation 8.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 6
% Syntax : Number of formulae : 83 ( 59 unt; 0 def)
% Number of atoms : 121 ( 79 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 64 ( 26 ~; 22 |; 11 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 118 (; 114 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [C,B,A] : product(product(A,B),C) = product(A,product(B,C)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A] : product(A,A) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X0,X1] :
( d(X0,X1)
<=> ( product(X0,product(X1,X0)) = X0
& product(X1,product(X0,X1)) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,conjecture,
! [X2,X3,X4,X5] :
( ( d(X2,X3)
& d(X4,X5) )
=> d(product(X2,X4),product(X3,X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
~ ! [X2,X3,X4,X5] :
( ( d(X2,X3)
& d(X4,X5) )
=> d(product(X2,X4),product(X3,X5)) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
fof(f6,plain,
! [X0,X1,X2] : product(product(X0,X1),X2) = product(X0,product(X1,X2)),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f7,plain,
! [X0] : product(X0,X0) = X0,
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f8,plain,
! [X0,X1] :
( ( ~ d(X0,X1)
| ( product(X0,product(X1,X0)) = X0
& product(X1,product(X0,X1)) = X1 ) )
& ( d(X0,X1)
| product(X0,product(X1,X0)) != X0
| product(X1,product(X0,X1)) != X1 ) ),
inference(NNF_transformation,[status(esa)],[f3]) ).
fof(f9,plain,
( ! [X0,X1] :
( ~ d(X0,X1)
| ( product(X0,product(X1,X0)) = X0
& product(X1,product(X0,X1)) = X1 ) )
& ! [X0,X1] :
( d(X0,X1)
| product(X0,product(X1,X0)) != X0
| product(X1,product(X0,X1)) != X1 ) ),
inference(miniscoping,[status(esa)],[f8]) ).
fof(f10,plain,
! [X0,X1] :
( ~ d(X0,X1)
| product(X0,product(X1,X0)) = X0 ),
inference(cnf_transformation,[status(esa)],[f9]) ).
fof(f11,plain,
! [X0,X1] :
( ~ d(X0,X1)
| product(X1,product(X0,X1)) = X1 ),
inference(cnf_transformation,[status(esa)],[f9]) ).
fof(f12,plain,
! [X0,X1] :
( d(X0,X1)
| product(X0,product(X1,X0)) != X0
| product(X1,product(X0,X1)) != X1 ),
inference(cnf_transformation,[status(esa)],[f9]) ).
fof(f13,plain,
? [X2,X3,X4,X5] :
( d(X2,X3)
& d(X4,X5)
& ~ d(product(X2,X4),product(X3,X5)) ),
inference(pre_NNF_transformation,[status(esa)],[f5]) ).
fof(f14,plain,
( d(sk0_0,sk0_1)
& d(sk0_2,sk0_3)
& ~ d(product(sk0_0,sk0_2),product(sk0_1,sk0_3)) ),
inference(skolemization,[status(esa)],[f13]) ).
fof(f15,plain,
d(sk0_0,sk0_1),
inference(cnf_transformation,[status(esa)],[f14]) ).
fof(f16,plain,
d(sk0_2,sk0_3),
inference(cnf_transformation,[status(esa)],[f14]) ).
fof(f17,plain,
~ d(product(sk0_0,sk0_2),product(sk0_1,sk0_3)),
inference(cnf_transformation,[status(esa)],[f14]) ).
fof(f18,plain,
product(sk0_2,product(sk0_3,sk0_2)) = sk0_2,
inference(resolution,[status(thm)],[f10,f16]) ).
fof(f19,plain,
product(sk0_0,product(sk0_1,sk0_0)) = sk0_0,
inference(resolution,[status(thm)],[f10,f15]) ).
fof(f20,plain,
product(sk0_3,product(sk0_2,sk0_3)) = sk0_3,
inference(resolution,[status(thm)],[f11,f16]) ).
fof(f21,plain,
product(sk0_1,product(sk0_0,sk0_1)) = sk0_1,
inference(resolution,[status(thm)],[f11,f15]) ).
fof(f22,plain,
! [X0,X1] : product(X0,X1) = product(X0,product(X1,product(X0,X1))),
inference(paramodulation,[status(thm)],[f7,f6]) ).
fof(f26,plain,
! [X0] : product(sk0_2,X0) = product(sk0_2,product(product(sk0_3,sk0_2),X0)),
inference(paramodulation,[status(thm)],[f18,f6]) ).
fof(f27,plain,
! [X0] : product(sk0_2,X0) = product(sk0_2,product(sk0_3,product(sk0_2,X0))),
inference(forward_demodulation,[status(thm)],[f6,f26]) ).
fof(f28,plain,
! [X0,X1] : product(X0,X1) = product(X0,product(X0,X1)),
inference(paramodulation,[status(thm)],[f7,f6]) ).
fof(f30,plain,
! [X0,X1,X2] : product(product(X0,X1),X2) = product(X0,product(X1,product(product(X0,X1),X2))),
inference(paramodulation,[status(thm)],[f6,f28]) ).
fof(f31,plain,
! [X0,X1,X2] : product(X0,product(X1,X2)) = product(X0,product(X1,product(product(X0,X1),X2))),
inference(forward_demodulation,[status(thm)],[f6,f30]) ).
fof(f32,plain,
! [X0,X1,X2] : product(X0,product(X1,X2)) = product(X0,product(X1,product(X0,product(X1,X2)))),
inference(forward_demodulation,[status(thm)],[f6,f31]) ).
fof(f44,plain,
! [X0,X1,X2] : product(product(X0,X1),X2) = product(X0,product(X1,product(X2,product(product(X0,X1),X2)))),
inference(paramodulation,[status(thm)],[f6,f22]) ).
fof(f45,plain,
! [X0,X1,X2] : product(X0,product(X1,X2)) = product(X0,product(X1,product(X2,product(product(X0,X1),X2)))),
inference(forward_demodulation,[status(thm)],[f6,f44]) ).
fof(f46,plain,
! [X0,X1,X2] : product(X0,product(X1,X2)) = product(X0,product(X1,product(X2,product(X0,product(X1,X2))))),
inference(forward_demodulation,[status(thm)],[f6,f45]) ).
fof(f100,plain,
( spl0_0
<=> product(product(sk0_0,sk0_2),product(product(sk0_1,sk0_3),product(sk0_0,sk0_2))) = product(sk0_0,sk0_2) ),
introduced(split_symbol_definition) ).
fof(f102,plain,
( product(product(sk0_0,sk0_2),product(product(sk0_1,sk0_3),product(sk0_0,sk0_2))) != product(sk0_0,sk0_2)
| spl0_0 ),
inference(component_clause,[status(thm)],[f100]) ).
fof(f103,plain,
( spl0_1
<=> product(product(sk0_1,sk0_3),product(product(sk0_0,sk0_2),product(sk0_1,sk0_3))) = product(sk0_1,sk0_3) ),
introduced(split_symbol_definition) ).
fof(f105,plain,
( product(product(sk0_1,sk0_3),product(product(sk0_0,sk0_2),product(sk0_1,sk0_3))) != product(sk0_1,sk0_3)
| spl0_1 ),
inference(component_clause,[status(thm)],[f103]) ).
fof(f106,plain,
( product(product(sk0_0,sk0_2),product(product(sk0_1,sk0_3),product(sk0_0,sk0_2))) != product(sk0_0,sk0_2)
| product(product(sk0_1,sk0_3),product(product(sk0_0,sk0_2),product(sk0_1,sk0_3))) != product(sk0_1,sk0_3) ),
inference(resolution,[status(thm)],[f12,f17]) ).
fof(f107,plain,
( ~ spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f106,f100,f103]) ).
fof(f108,plain,
( product(sk0_0,product(sk0_2,product(product(sk0_1,sk0_3),product(sk0_0,sk0_2)))) != product(sk0_0,sk0_2)
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f6,f102]) ).
fof(f109,plain,
( product(sk0_0,product(sk0_2,product(sk0_1,product(sk0_3,product(sk0_0,sk0_2))))) != product(sk0_0,sk0_2)
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f6,f108]) ).
fof(f116,plain,
! [X0] : product(sk0_0,X0) = product(sk0_0,product(product(sk0_1,sk0_0),X0)),
inference(paramodulation,[status(thm)],[f19,f6]) ).
fof(f117,plain,
! [X0] : product(sk0_0,X0) = product(sk0_0,product(sk0_1,product(sk0_0,X0))),
inference(forward_demodulation,[status(thm)],[f6,f116]) ).
fof(f141,plain,
! [X0] : product(sk0_3,X0) = product(sk0_3,product(product(sk0_2,sk0_3),X0)),
inference(paramodulation,[status(thm)],[f20,f6]) ).
fof(f142,plain,
! [X0] : product(sk0_3,X0) = product(sk0_3,product(sk0_2,product(sk0_3,X0))),
inference(forward_demodulation,[status(thm)],[f6,f141]) ).
fof(f166,plain,
! [X0] : product(sk0_1,X0) = product(sk0_1,product(product(sk0_0,sk0_1),X0)),
inference(paramodulation,[status(thm)],[f21,f6]) ).
fof(f167,plain,
! [X0] : product(sk0_1,X0) = product(sk0_1,product(sk0_0,product(sk0_1,X0))),
inference(forward_demodulation,[status(thm)],[f6,f166]) ).
fof(f168,plain,
! [X0,X1,X2,X3] : product(product(X0,X1),product(X2,X3)) = product(X0,product(X1,product(X2,product(product(X0,X1),product(X2,X3))))),
inference(paramodulation,[status(thm)],[f6,f32]) ).
fof(f169,plain,
! [X0,X1,X2,X3] : product(X0,product(X1,product(X2,X3))) = product(X0,product(X1,product(X2,product(product(X0,X1),product(X2,X3))))),
inference(forward_demodulation,[status(thm)],[f6,f168]) ).
fof(f170,plain,
! [X0,X1,X2,X3] : product(X0,product(X1,product(X2,X3))) = product(X0,product(X1,product(X2,product(X0,product(X1,product(X2,X3)))))),
inference(forward_demodulation,[status(thm)],[f6,f169]) ).
fof(f269,plain,
! [X0,X1,X2,X3] : product(product(X0,X1),product(X2,X3)) = product(X0,product(X1,product(X2,product(X3,product(product(X0,X1),product(X2,X3)))))),
inference(paramodulation,[status(thm)],[f6,f46]) ).
fof(f270,plain,
! [X0,X1,X2,X3] : product(X0,product(X1,product(X2,X3))) = product(X0,product(X1,product(X2,product(X3,product(product(X0,X1),product(X2,X3)))))),
inference(forward_demodulation,[status(thm)],[f6,f269]) ).
fof(f271,plain,
! [X0,X1,X2,X3] : product(X0,product(X1,product(X2,X3))) = product(X0,product(X1,product(X2,product(X3,product(X0,product(X1,product(X2,X3))))))),
inference(forward_demodulation,[status(thm)],[f6,f270]) ).
fof(f465,plain,
! [X0] : product(sk0_1,product(X0,product(sk0_0,product(sk0_1,X0)))) = product(sk0_1,product(sk0_0,product(sk0_1,X0))),
inference(paramodulation,[status(thm)],[f46,f167]) ).
fof(f466,plain,
! [X0] : product(sk0_1,product(X0,product(sk0_0,product(sk0_1,X0)))) = product(sk0_1,X0),
inference(forward_demodulation,[status(thm)],[f167,f465]) ).
fof(f1433,plain,
! [X0,X1] : product(X0,product(sk0_1,product(sk0_0,product(sk0_1,X1)))) = product(X0,product(sk0_1,product(sk0_0,product(X0,product(sk0_1,X1))))),
inference(paramodulation,[status(thm)],[f167,f170]) ).
fof(f1434,plain,
! [X0,X1] : product(X0,product(sk0_1,X1)) = product(X0,product(sk0_1,product(sk0_0,product(X0,product(sk0_1,X1))))),
inference(forward_demodulation,[status(thm)],[f167,f1433]) ).
fof(f1441,plain,
! [X0,X1] : product(X0,product(sk0_3,product(sk0_2,product(sk0_3,X1)))) = product(X0,product(sk0_3,product(sk0_2,product(X0,product(sk0_3,X1))))),
inference(paramodulation,[status(thm)],[f142,f170]) ).
fof(f1442,plain,
! [X0,X1] : product(X0,product(sk0_3,X1)) = product(X0,product(sk0_3,product(sk0_2,product(X0,product(sk0_3,X1))))),
inference(forward_demodulation,[status(thm)],[f142,f1441]) ).
fof(f1443,plain,
! [X0] : product(X0,product(sk0_3,product(sk0_2,sk0_3))) = product(X0,product(sk0_3,product(sk0_2,product(X0,sk0_3)))),
inference(paramodulation,[status(thm)],[f20,f170]) ).
fof(f1444,plain,
! [X0] : product(X0,sk0_3) = product(X0,product(sk0_3,product(sk0_2,product(X0,sk0_3)))),
inference(forward_demodulation,[status(thm)],[f20,f1443]) ).
fof(f1449,plain,
! [X0,X1] : product(X0,product(sk0_0,product(sk0_1,product(sk0_0,X1)))) = product(X0,product(sk0_0,product(sk0_1,product(X0,product(sk0_0,X1))))),
inference(paramodulation,[status(thm)],[f117,f170]) ).
fof(f1450,plain,
! [X0,X1] : product(X0,product(sk0_0,X1)) = product(X0,product(sk0_0,product(sk0_1,product(X0,product(sk0_0,X1))))),
inference(forward_demodulation,[status(thm)],[f117,f1449]) ).
fof(f1460,plain,
! [X0,X1] : product(X0,product(sk0_2,product(sk0_3,product(sk0_2,X1)))) = product(X0,product(sk0_2,product(sk0_3,product(X0,product(sk0_2,X1))))),
inference(paramodulation,[status(thm)],[f27,f170]) ).
fof(f1461,plain,
! [X0,X1] : product(X0,product(sk0_2,X1)) = product(X0,product(sk0_2,product(sk0_3,product(X0,product(sk0_2,X1))))),
inference(forward_demodulation,[status(thm)],[f27,f1460]) ).
fof(f1462,plain,
! [X0] : product(X0,product(sk0_2,product(sk0_3,sk0_2))) = product(X0,product(sk0_2,product(sk0_3,product(X0,sk0_2)))),
inference(paramodulation,[status(thm)],[f18,f170]) ).
fof(f1463,plain,
! [X0] : product(X0,sk0_2) = product(X0,product(sk0_2,product(sk0_3,product(X0,sk0_2)))),
inference(forward_demodulation,[status(thm)],[f18,f1462]) ).
fof(f3601,plain,
! [X0,X1] : product(X0,product(sk0_1,product(X1,product(sk0_0,product(X0,product(sk0_1,X1)))))) = product(X0,product(sk0_1,product(sk0_0,product(X0,product(sk0_1,X1))))),
inference(paramodulation,[status(thm)],[f271,f1434]) ).
fof(f3602,plain,
! [X0,X1] : product(X0,product(sk0_1,product(X1,product(sk0_0,product(X0,product(sk0_1,X1)))))) = product(X0,product(sk0_1,X1)),
inference(forward_demodulation,[status(thm)],[f1434,f3601]) ).
fof(f4134,plain,
! [X0,X1] : product(X0,product(sk0_0,product(X1,product(sk0_1,product(X0,product(sk0_0,X1)))))) = product(X0,product(sk0_0,product(sk0_1,product(X0,product(sk0_0,X1))))),
inference(paramodulation,[status(thm)],[f271,f1450]) ).
fof(f4135,plain,
! [X0,X1] : product(X0,product(sk0_0,product(X1,product(sk0_1,product(X0,product(sk0_0,X1)))))) = product(X0,product(sk0_0,X1)),
inference(forward_demodulation,[status(thm)],[f1450,f4134]) ).
fof(f9303,plain,
product(sk0_1,product(sk0_3,product(sk0_0,product(sk0_2,product(sk0_1,sk0_3))))) = product(sk0_1,product(sk0_3,product(sk0_2,product(sk0_1,sk0_3)))),
inference(paramodulation,[status(thm)],[f3602,f1442]) ).
fof(f9304,plain,
product(sk0_1,product(sk0_3,product(sk0_0,product(sk0_2,product(sk0_1,sk0_3))))) = product(sk0_1,sk0_3),
inference(forward_demodulation,[status(thm)],[f1444,f9303]) ).
fof(f10928,plain,
product(sk0_3,product(sk0_0,product(sk0_2,product(sk0_1,sk0_3)))) = product(sk0_3,product(sk0_0,product(sk0_1,sk0_3))),
inference(paramodulation,[status(thm)],[f9304,f1450]) ).
fof(f18601,plain,
product(sk0_0,product(sk0_2,product(sk0_1,product(sk0_3,product(sk0_0,sk0_2))))) = product(sk0_0,product(sk0_2,product(sk0_3,product(sk0_0,sk0_2)))),
inference(paramodulation,[status(thm)],[f4135,f1461]) ).
fof(f18602,plain,
product(sk0_0,product(sk0_2,product(sk0_1,product(sk0_3,product(sk0_0,sk0_2))))) = product(sk0_0,sk0_2),
inference(forward_demodulation,[status(thm)],[f1463,f18601]) ).
fof(f18603,plain,
( $false
| spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f18602,f109]) ).
fof(f18604,plain,
spl0_0,
inference(contradiction_clause,[status(thm)],[f18603]) ).
fof(f18952,plain,
( product(sk0_1,product(sk0_3,product(product(sk0_0,sk0_2),product(sk0_1,sk0_3)))) != product(sk0_1,sk0_3)
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f6,f105]) ).
fof(f18953,plain,
( product(sk0_1,product(sk0_3,product(sk0_0,product(sk0_2,product(sk0_1,sk0_3))))) != product(sk0_1,sk0_3)
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f6,f18952]) ).
fof(f18954,plain,
( product(sk0_1,product(sk0_3,product(sk0_0,product(sk0_1,sk0_3)))) != product(sk0_1,sk0_3)
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f10928,f18953]) ).
fof(f18955,plain,
( product(sk0_1,sk0_3) != product(sk0_1,sk0_3)
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f466,f18954]) ).
fof(f18956,plain,
( $false
| spl0_1 ),
inference(trivial_equality_resolution,[status(esa)],[f18955]) ).
fof(f18957,plain,
spl0_1,
inference(contradiction_clause,[status(thm)],[f18956]) ).
fof(f18958,plain,
$false,
inference(sat_refutation,[status(thm)],[f107,f18604,f18957]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : GRP774+1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.11 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.31 % Computer : n003.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Tue May 30 11:28:23 EDT 2023
% 0.10/0.31 % CPUTime :
% 0.15/0.32 % Drodi V3.5.1
% 8.99/1.62 % Refutation found
% 8.99/1.62 % SZS status Theorem for theBenchmark: Theorem is valid
% 8.99/1.62 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 9.66/1.68 % Elapsed time: 1.355093 seconds
% 9.66/1.68 % CPU time: 9.703402 seconds
% 9.66/1.68 % Memory used: 193.868 MB
%------------------------------------------------------------------------------