TSTP Solution File: SYO664-1 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SYO664-1 : TPTP v8.1.2. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n020.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 12:49:28 EDT 2023
% Result : Unsatisfiable 0.11s 0.33s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 42 ( 8 unt; 0 def)
% Number of atoms : 187 ( 0 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 287 ( 142 ~; 145 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 7 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-1 aty)
% Number of variables : 109 (; 109 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [E,B_45,B_46,B_43,A_1,B_44] :
( ~ 'E'(s('0'),f(suc(B_45)))
| ~ 'E'(s('0'),f(B_45))
| ~ 'E'(s('0'),f(suc(B_46)))
| ~ 'E'(s('0'),f(suc(B_43)))
| ~ 'E'(s('0'),f(A_1))
| ~ 'E'(s('0'),f(suc(A_1)))
| ~ iLEQ(suc(A_1),suc(B_43))
| ~ 'E'(s('0'),f(B_43))
| ~ iLEQ(suc(B_44),suc(B_45))
| ~ 'E'(s('0'),f(B_46))
| ~ 'E'(s('0'),f(B_44))
| ~ iLEQ(suc(B_45),suc(B_46))
| ~ iLEQ(suc(B_43),suc(B_44))
| ~ 'E'(s('0'),f(suc(B_44))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [LE] : ~ 'LE'(f(z),'0'),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [LE,B_42,E] :
( ~ 'LE'(f(B_42),s(s('0')))
| 'E'(s('0'),f(B_42))
| 'LE'(f(B_42),s('0')) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [E,B_63,B_61,A_2,B_62,B_64] :
( ~ 'E'('0',f(B_63))
| ~ 'E'('0',f(suc(B_61)))
| ~ 'E'('0',f(suc(A_2)))
| ~ iLEQ(suc(A_2),suc(B_61))
| ~ iLEQ(suc(B_61),suc(B_62))
| ~ 'E'('0',f(suc(B_63)))
| ~ 'E'('0',f(A_2))
| ~ iLEQ(suc(B_62),suc(B_63))
| ~ 'E'('0',f(B_64))
| ~ iLEQ(suc(B_63),suc(B_64))
| ~ 'E'('0',f(suc(B_62)))
| ~ 'E'('0',f(B_61))
| ~ 'E'('0',f(suc(B_64)))
| ~ 'E'('0',f(B_62)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [LE,A] : 'LE'(f(A),s(s('0'))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [E,A_2] :
( ~ 'E'('0',f(A_2))
| ~ 'E'('0',f(suc(A_2)))
| iLEQ(suc(A_2),suc(A_2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [LE,B_60,E] :
( ~ 'LE'(f(suc(B_60)),s('0'))
| 'E'('0',f(suc(B_60)))
| 'LE'(f(B_60),'0') ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [LE,B_60,E] :
( ~ 'LE'(f(B_60),s('0'))
| 'E'('0',f(B_60))
| 'LE'(f(B_60),'0') ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [E,A_1] :
( ~ 'E'(s('0'),f(A_1))
| ~ 'E'(s('0'),f(suc(A_1)))
| iLEQ(suc(A_1),suc(A_1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [LE,B_42,E] :
( ~ 'LE'(f(suc(B_42)),s(s('0')))
| 'E'(s('0'),f(suc(B_42)))
| 'LE'(f(B_42),s('0')) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,plain,
! [B_44] :
( ! [B_43] :
( ! [B_45,B_46] :
( ! [A_1] :
( ~ 'E'(s('0'),f(suc(B_45)))
| ~ 'E'(s('0'),f(B_45))
| ~ 'E'(s('0'),f(suc(B_46)))
| ~ 'E'(s('0'),f(suc(B_43)))
| ~ 'E'(s('0'),f(A_1))
| ~ 'E'(s('0'),f(suc(A_1)))
| ~ iLEQ(suc(A_1),suc(B_43)) )
| ~ 'E'(s('0'),f(B_43))
| ~ iLEQ(suc(B_44),suc(B_45))
| ~ 'E'(s('0'),f(B_46))
| ~ 'E'(s('0'),f(B_44))
| ~ iLEQ(suc(B_45),suc(B_46)) )
| ~ iLEQ(suc(B_43),suc(B_44)) )
| ~ 'E'(s('0'),f(suc(B_44))) ),
inference(miniscoping,[status(esa)],[f1]) ).
fof(f12,plain,
! [E,X0,X1,X2,X3,X4] :
( ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(suc(X2)))
| ~ 'E'(s('0'),f(X3))
| ~ 'E'(s('0'),f(suc(X3)))
| ~ iLEQ(suc(X3),suc(X2))
| ~ 'E'(s('0'),f(X2))
| ~ iLEQ(suc(X4),suc(X0))
| ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(X4))
| ~ iLEQ(suc(X0),suc(X1))
| ~ iLEQ(suc(X2),suc(X4))
| ~ 'E'(s('0'),f(suc(X4))) ),
inference(cnf_transformation,[status(esa)],[f11]) ).
fof(f13,plain,
! [LE] : ~ 'LE'(f(z),'0'),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f14,plain,
! [B_42] :
( ~ 'LE'(f(B_42),s(s('0')))
| 'E'(s('0'),f(B_42))
| 'LE'(f(B_42),s('0')) ),
inference(miniscoping,[status(esa)],[f3]) ).
fof(f15,plain,
! [LE,X0,E] :
( ~ 'LE'(f(X0),s(s('0')))
| 'E'(s('0'),f(X0))
| 'LE'(f(X0),s('0')) ),
inference(cnf_transformation,[status(esa)],[f14]) ).
fof(f16,plain,
! [B_62] :
( ! [B_64] :
( ! [B_61] :
( ! [B_63] :
( ! [A_2] :
( ~ 'E'('0',f(B_63))
| ~ 'E'('0',f(suc(B_61)))
| ~ 'E'('0',f(suc(A_2)))
| ~ iLEQ(suc(A_2),suc(B_61))
| ~ iLEQ(suc(B_61),suc(B_62))
| ~ 'E'('0',f(suc(B_63)))
| ~ 'E'('0',f(A_2)) )
| ~ iLEQ(suc(B_62),suc(B_63))
| ~ 'E'('0',f(B_64))
| ~ iLEQ(suc(B_63),suc(B_64)) )
| ~ 'E'('0',f(suc(B_62)))
| ~ 'E'('0',f(B_61)) )
| ~ 'E'('0',f(suc(B_64))) )
| ~ 'E'('0',f(B_62)) ),
inference(miniscoping,[status(esa)],[f4]) ).
fof(f17,plain,
! [E,X0,X1,X2,X3,X4] :
( ~ 'E'('0',f(X0))
| ~ 'E'('0',f(suc(X1)))
| ~ 'E'('0',f(suc(X2)))
| ~ iLEQ(suc(X2),suc(X1))
| ~ iLEQ(suc(X1),suc(X3))
| ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(X2))
| ~ iLEQ(suc(X3),suc(X0))
| ~ 'E'('0',f(X4))
| ~ iLEQ(suc(X0),suc(X4))
| ~ 'E'('0',f(suc(X3)))
| ~ 'E'('0',f(X1))
| ~ 'E'('0',f(suc(X4)))
| ~ 'E'('0',f(X3)) ),
inference(cnf_transformation,[status(esa)],[f16]) ).
fof(f18,plain,
! [A] : 'LE'(f(A),s(s('0'))),
inference(miniscoping,[status(esa)],[f5]) ).
fof(f19,plain,
! [LE,X0] : 'LE'(f(X0),s(s('0'))),
inference(cnf_transformation,[status(esa)],[f18]) ).
fof(f20,plain,
! [A_2] :
( ~ 'E'('0',f(A_2))
| ~ 'E'('0',f(suc(A_2)))
| iLEQ(suc(A_2),suc(A_2)) ),
inference(miniscoping,[status(esa)],[f6]) ).
fof(f21,plain,
! [E,X0] :
( ~ 'E'('0',f(X0))
| ~ 'E'('0',f(suc(X0)))
| iLEQ(suc(X0),suc(X0)) ),
inference(cnf_transformation,[status(esa)],[f20]) ).
fof(f22,plain,
! [B_60] :
( ~ 'LE'(f(suc(B_60)),s('0'))
| 'E'('0',f(suc(B_60)))
| 'LE'(f(B_60),'0') ),
inference(miniscoping,[status(esa)],[f7]) ).
fof(f23,plain,
! [LE,X0,E] :
( ~ 'LE'(f(suc(X0)),s('0'))
| 'E'('0',f(suc(X0)))
| 'LE'(f(X0),'0') ),
inference(cnf_transformation,[status(esa)],[f22]) ).
fof(f24,plain,
! [B_60] :
( ~ 'LE'(f(B_60),s('0'))
| 'E'('0',f(B_60))
| 'LE'(f(B_60),'0') ),
inference(miniscoping,[status(esa)],[f8]) ).
fof(f25,plain,
! [LE,X0,E] :
( ~ 'LE'(f(X0),s('0'))
| 'E'('0',f(X0))
| 'LE'(f(X0),'0') ),
inference(cnf_transformation,[status(esa)],[f24]) ).
fof(f26,plain,
! [A_1] :
( ~ 'E'(s('0'),f(A_1))
| ~ 'E'(s('0'),f(suc(A_1)))
| iLEQ(suc(A_1),suc(A_1)) ),
inference(miniscoping,[status(esa)],[f9]) ).
fof(f27,plain,
! [E,X0] :
( ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(suc(X0)))
| iLEQ(suc(X0),suc(X0)) ),
inference(cnf_transformation,[status(esa)],[f26]) ).
fof(f28,plain,
! [B_42] :
( ~ 'LE'(f(suc(B_42)),s(s('0')))
| 'E'(s('0'),f(suc(B_42)))
| 'LE'(f(B_42),s('0')) ),
inference(miniscoping,[status(esa)],[f10]) ).
fof(f29,plain,
! [LE,X0,E] :
( ~ 'LE'(f(suc(X0)),s(s('0')))
| 'E'(s('0'),f(suc(X0)))
| 'LE'(f(X0),s('0')) ),
inference(cnf_transformation,[status(esa)],[f28]) ).
fof(f30,plain,
! [E,X0,LE] :
( 'E'(s('0'),f(suc(X0)))
| 'LE'(f(X0),s('0')) ),
inference(forward_subsumption_resolution,[status(thm)],[f29,f19]) ).
fof(f31,plain,
! [E,X0,LE] :
( 'E'(s('0'),f(X0))
| 'LE'(f(X0),s('0')) ),
inference(backward_subsumption_resolution,[status(thm)],[f15,f19]) ).
fof(f36,plain,
! [E,X0] :
( ~ 'E'('0',f(X0))
| ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(suc(X0)))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(X0))
| ~ 'E'('0',f(suc(X0))) ),
inference(resolution,[status(thm)],[f17,f21]) ).
fof(f37,plain,
! [E,X0] :
( ~ 'E'('0',f(X0))
| ~ 'E'('0',f(suc(X0))) ),
inference(duplicate_literals_removal,[status(esa)],[f36]) ).
fof(f60,plain,
! [E,X0] :
( ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(X0))
| ~ 'E'(s('0'),f(suc(X0))) ),
inference(resolution,[status(thm)],[f12,f27]) ).
fof(f61,plain,
! [E,X0] :
( ~ 'E'(s('0'),f(suc(X0)))
| ~ 'E'(s('0'),f(X0)) ),
inference(duplicate_literals_removal,[status(esa)],[f60]) ).
fof(f83,plain,
! [E,X0,LE] :
( ~ 'E'('0',f(X0))
| ~ 'LE'(f(suc(X0)),s('0'))
| 'LE'(f(X0),'0') ),
inference(resolution,[status(thm)],[f37,f23]) ).
fof(f84,plain,
! [E,X0,LE] :
( ~ 'E'(s('0'),f(X0))
| 'LE'(f(X0),s('0')) ),
inference(resolution,[status(thm)],[f61,f30]) ).
fof(f85,plain,
! [LE,X0] : 'LE'(f(X0),s('0')),
inference(forward_subsumption_resolution,[status(thm)],[f84,f31]) ).
fof(f87,plain,
! [E,X0,LE] :
( 'E'('0',f(X0))
| 'LE'(f(X0),'0') ),
inference(backward_subsumption_resolution,[status(thm)],[f25,f85]) ).
fof(f90,plain,
! [E,X0,LE] :
( ~ 'E'('0',f(X0))
| 'LE'(f(X0),'0') ),
inference(backward_subsumption_resolution,[status(thm)],[f83,f85]) ).
fof(f91,plain,
! [LE,X0] : 'LE'(f(X0),'0'),
inference(forward_subsumption_resolution,[status(thm)],[f90,f87]) ).
fof(f92,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f13,f91]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SYO664-1 : TPTP v8.1.2. Released v7.3.0.
% 0.07/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.32 % Computer : n020.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Tue May 30 10:05:28 EDT 2023
% 0.11/0.32 % CPUTime :
% 0.11/0.33 % Drodi V3.5.1
% 0.11/0.33 % Refutation found
% 0.11/0.33 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.11/0.33 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.20/0.55 % Elapsed time: 0.008748 seconds
% 0.20/0.55 % CPU time: 0.031195 seconds
% 0.20/0.55 % Memory used: 518.440 KB
%------------------------------------------------------------------------------