TSTP Solution File: SWW379+1 by E-SAT---3.1
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%------------------------------------------------------------------------------
% File : E-SAT---3.1
% Problem : SWW379+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n019.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 : 2400s
% WCLimit : 300s
% DateTime : Tue Oct 10 20:11:11 EDT 2023
% Result : ContradictoryAxioms 7.14s 3.19s
% Output : CNFRefutation 7.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 23
% Syntax : Number of formulae : 118 ( 80 unt; 0 def)
% Number of atoms : 162 ( 108 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 93 ( 49 ~; 38 |; 2 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 25 ( 25 usr; 9 con; 0-3 aty)
% Number of variables : 182 ( 39 sgn; 85 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_Collect__neg__eq,axiom,
! [X18,X5] : hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5),c_fNot),X18)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_OCollect(X5),X18)),
file('/export/starexec/sandbox2/tmp/tmp.tUAvdwtkEl/E---3.1_11519.p',fact_Collect__neg__eq) ).
fof(fact_Collect__def,axiom,
! [X18,X5] : hAPP(c_Set_OCollect(X5),X18) = X18,
file('/export/starexec/sandbox2/tmp/tmp.tUAvdwtkEl/E---3.1_11519.p',fact_Collect__def) ).
fof(fact_Collect__empty__eq,axiom,
! [X18,X5] :
( hAPP(c_Set_OCollect(X5),X18) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
<=> ! [X3] : ~ hBOOL(hAPP(X18,X3)) ),
file('/export/starexec/sandbox2/tmp/tmp.tUAvdwtkEl/E---3.1_11519.p',fact_Collect__empty__eq) ).
fof(fact_Compl__empty__eq,axiom,
! [X5] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),
file('/export/starexec/sandbox2/tmp/tmp.tUAvdwtkEl/E---3.1_11519.p',fact_Compl__empty__eq) ).
fof(help_c__COMBB__1,axiom,
! [X36,X16,X18,X47,X5,X29] : hAPP(hAPP(hAPP(c_COMBB(X29,X5,X47),X18),X16),X36) = hAPP(X18,hAPP(X16,X36)),
file('/export/starexec/sandbox2/tmp/tmp.tUAvdwtkEl/E---3.1_11519.p',help_c__COMBB__1) ).
fof(fact_top1I,axiom,
! [X31,X5] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),X31)),
file('/export/starexec/sandbox2/tmp/tmp.tUAvdwtkEl/E---3.1_11519.p',fact_top1I) ).
fof(help_c__fNot__1,axiom,
! [X18] :
( ~ hBOOL(hAPP(c_fNot,X18))
| ~ hBOOL(X18) ),
file('/export/starexec/sandbox2/tmp/tmp.tUAvdwtkEl/E---3.1_11519.p',help_c__fNot__1) ).
fof(help_c__COMBK__1,axiom,
! [X323,X22,X29,X5] : hAPP(hAPP(c_COMBK(X5,X29),X22),X323) = X22,
file('/export/starexec/sandbox2/tmp/tmp.tUAvdwtkEl/E---3.1_11519.p',help_c__COMBK__1) ).
fof(fact_mult__Pls,axiom,
! [X160] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),X160) = c_Int_OPls,
file('/export/starexec/sandbox2/tmp/tmp.tUAvdwtkEl/E---3.1_11519.p',fact_mult__Pls) ).
fof(fact_double__complement,axiom,
! [X30,X5] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X30)) = X30,
file('/export/starexec/sandbox2/tmp/tmp.tUAvdwtkEl/E---3.1_11519.p',fact_double__complement) ).
fof(fact_rel__simps_I39_J,axiom,
! [X133] : c_Int_OPls != c_Int_OBit1(X133),
file('/export/starexec/sandbox2/tmp/tmp.tUAvdwtkEl/E---3.1_11519.p',fact_rel__simps_I39_J) ).
fof(fact_Un__empty__right,axiom,
! [X30,X5] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X30),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))) = X30,
file('/export/starexec/sandbox2/tmp/tmp.tUAvdwtkEl/E---3.1_11519.p',fact_Un__empty__right) ).
fof(fact_rel__simps_I51_J,axiom,
! [X157,X106] :
( c_Int_OBit1(X106) = c_Int_OBit1(X157)
<=> X106 = X157 ),
file('/export/starexec/sandbox2/tmp/tmp.tUAvdwtkEl/E---3.1_11519.p',fact_rel__simps_I51_J) ).
fof(fact_add__eq__self__zero,axiom,
! [X108,X110] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X110),X108) = X110
=> X108 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox2/tmp/tmp.tUAvdwtkEl/E---3.1_11519.p',fact_add__eq__self__zero) ).
fof(fact_transfer__nat__int__numerals_I1_J,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
file('/export/starexec/sandbox2/tmp/tmp.tUAvdwtkEl/E---3.1_11519.p',fact_transfer__nat__int__numerals_I1_J) ).
fof(fact_Pls__def,axiom,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.tUAvdwtkEl/E---3.1_11519.p',fact_Pls__def) ).
fof(fact_Zero__not__Suc,axiom,
! [X110] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X110),
file('/export/starexec/sandbox2/tmp/tmp.tUAvdwtkEl/E---3.1_11519.p',fact_Zero__not__Suc) ).
fof(fact_WT_Oequations_I1_J,axiom,
hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)),
file('/export/starexec/sandbox2/tmp/tmp.tUAvdwtkEl/E---3.1_11519.p',fact_WT_Oequations_I1_J) ).
fof(fact_option_Osimps_I2_J,axiom,
! [X182,X5] : c_Option_Ooption_ONone(X5) != hAPP(c_Option_Ooption_OSome(X5),X182),
file('/export/starexec/sandbox2/tmp/tmp.tUAvdwtkEl/E---3.1_11519.p',fact_option_Osimps_I2_J) ).
fof(fact_add__Suc__right,axiom,
! [X108,X110] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X110),hAPP(c_Nat_OSuc,X108)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X110),X108)),
file('/export/starexec/sandbox2/tmp/tmp.tUAvdwtkEl/E---3.1_11519.p',fact_add__Suc__right) ).
fof(fact_n__not__Suc__n,axiom,
! [X108] : X108 != hAPP(c_Nat_OSuc,X108),
file('/export/starexec/sandbox2/tmp/tmp.tUAvdwtkEl/E---3.1_11519.p',fact_n__not__Suc__n) ).
fof(help_c__fNot__2,axiom,
! [X18] :
( ~ ~ hBOOL(X18)
| hBOOL(hAPP(c_fNot,X18)) ),
file('/export/starexec/sandbox2/tmp/tmp.tUAvdwtkEl/E---3.1_11519.p',help_c__fNot__2) ).
fof(fact_Nat_Oadd__0__right,axiom,
! [X110] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X110),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X110,
file('/export/starexec/sandbox2/tmp/tmp.tUAvdwtkEl/E---3.1_11519.p',fact_Nat_Oadd__0__right) ).
fof(c_0_23,plain,
! [X1560,X1561] : hAPP(c_Set_OCollect(X1561),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1561),c_fNot),X1560)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1561,tc_HOL_Obool)),hAPP(c_Set_OCollect(X1561),X1560)),
inference(variable_rename,[status(thm)],[fact_Collect__neg__eq]) ).
fof(c_0_24,plain,
! [X3763,X3764] : hAPP(c_Set_OCollect(X3764),X3763) = X3763,
inference(variable_rename,[status(thm)],[fact_Collect__def]) ).
fof(c_0_25,plain,
! [X18,X5] :
( hAPP(c_Set_OCollect(X5),X18) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
<=> ! [X3] : ~ hBOOL(hAPP(X18,X3)) ),
inference(fof_simplification,[status(thm)],[fact_Collect__empty__eq]) ).
fof(c_0_26,plain,
! [X1830] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1830,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1830,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X1830,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_Compl__empty__eq]) ).
cnf(c_0_27,plain,
hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),X2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_OCollect(X1),X2)),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_28,plain,
hAPP(c_Set_OCollect(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_29,plain,
! [X3757,X3758,X3759,X3760,X3762] :
( ( hAPP(c_Set_OCollect(X3758),X3757) != c_Orderings_Obot__class_Obot(tc_fun(X3758,tc_HOL_Obool))
| ~ hBOOL(hAPP(X3757,X3759)) )
& ( hBOOL(hAPP(X3760,esk95_1(X3760)))
| hAPP(c_Set_OCollect(X3762),X3760) = c_Orderings_Obot__class_Obot(tc_fun(X3762,tc_HOL_Obool)) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_25])])])])]) ).
fof(c_0_30,plain,
! [X619,X620,X621,X622,X623,X624] : hAPP(hAPP(hAPP(c_COMBB(X624,X623,X622),X621),X620),X619) = hAPP(X621,hAPP(X620,X619)),
inference(variable_rename,[status(thm)],[help_c__COMBB__1]) ).
cnf(c_0_31,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_32,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2) = hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28]),c_0_28]) ).
cnf(c_0_33,plain,
( hAPP(c_Set_OCollect(X1),X2) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ~ hBOOL(hAPP(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_34,plain,
( hBOOL(hAPP(X1,esk95_1(X1)))
| hAPP(c_Set_OCollect(X2),X1) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
fof(c_0_35,plain,
! [X1825,X1826] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1826,tc_HOL_Obool)),X1825)),
inference(variable_rename,[status(thm)],[fact_top1I]) ).
cnf(c_0_36,plain,
hAPP(hAPP(hAPP(c_COMBB(X1,X2,X3),X4),X5),X6) = hAPP(X4,hAPP(X5,X6)),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_37,plain,
hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),
inference(rw,[status(thm)],[c_0_31,c_0_32]) ).
fof(c_0_38,plain,
! [X18] :
( ~ hBOOL(hAPP(c_fNot,X18))
| ~ hBOOL(X18) ),
inference(fof_simplification,[status(thm)],[help_c__fNot__1]) ).
cnf(c_0_39,plain,
~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2)),
inference(er,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_28])]) ).
cnf(c_0_40,plain,
( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| hBOOL(hAPP(X1,esk95_1(X1))) ),
inference(rw,[status(thm)],[c_0_34,c_0_28]) ).
cnf(c_0_41,plain,
hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2)),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_42,plain,
hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2) = hAPP(c_fNot,hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2)),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
fof(c_0_43,plain,
! [X1379,X1380,X1381,X1382] : hAPP(hAPP(c_COMBK(X1382,X1381),X1380),X1379) = X1380,
inference(variable_rename,[status(thm)],[help_c__COMBK__1]) ).
fof(c_0_44,plain,
! [X5936] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),X5936) = c_Int_OPls,
inference(variable_rename,[status(thm)],[fact_mult__Pls]) ).
fof(c_0_45,plain,
! [X1573] :
( ~ hBOOL(hAPP(c_fNot,X1573))
| ~ hBOOL(X1573) ),
inference(variable_rename,[status(thm)],[c_0_38]) ).
cnf(c_0_46,plain,
( hBOOL(hAPP(X1,esk95_1(X1)))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_47,plain,
hBOOL(hAPP(c_fNot,hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2))),
inference(rw,[status(thm)],[c_0_41,c_0_42]) ).
fof(c_0_48,plain,
! [X2526,X2527] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2527,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2527,tc_HOL_Obool)),X2526)) = X2526,
inference(variable_rename,[status(thm)],[fact_double__complement]) ).
cnf(c_0_49,plain,
hAPP(hAPP(c_COMBK(X1,X2),X3),X4) = X3,
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_50,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),X1) = c_Int_OPls,
inference(split_conjunct,[status(thm)],[c_0_44]) ).
fof(c_0_51,plain,
! [X5891] : c_Int_OPls != c_Int_OBit1(X5891),
inference(variable_rename,[status(thm)],[fact_rel__simps_I39_J]) ).
cnf(c_0_52,plain,
( ~ hBOOL(hAPP(c_fNot,X1))
| ~ hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_53,plain,
hBOOL(hAPP(c_fNot,esk95_1(c_fNot))),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_54,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_48]) ).
fof(c_0_55,plain,
! [X896,X897] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X897,tc_HOL_Obool)),X896),c_Orderings_Obot__class_Obot(tc_fun(X897,tc_HOL_Obool))) = X896,
inference(variable_rename,[status(thm)],[fact_Un__empty__right]) ).
cnf(c_0_56,plain,
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2) = X3
| hBOOL(X3) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_40]),c_0_49]) ).
cnf(c_0_57,plain,
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls)
| hBOOL(c_Int_OPls) ),
inference(spm,[status(thm)],[c_0_40,c_0_50]) ).
cnf(c_0_58,plain,
c_Int_OPls != c_Int_OBit1(X1),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_59,plain,
~ hBOOL(esk95_1(c_fNot)),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_60,plain,
hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),X2)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_32]),c_0_32]) ).
cnf(c_0_61,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = X2,
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_62,plain,
( c_Int_OPls = X1
| hBOOL(c_Int_OPls)
| hBOOL(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_50]) ).
cnf(c_0_63,plain,
( hBOOL(c_Int_OBit1(X1))
| hAPP(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)),X3) != c_Int_OPls ),
inference(spm,[status(thm)],[c_0_58,c_0_56]) ).
cnf(c_0_64,plain,
hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2) = esk95_1(c_fNot),
inference(spm,[status(thm)],[c_0_59,c_0_56]) ).
cnf(c_0_65,plain,
hAPP(c_fNot,hAPP(c_fNot,hAPP(X1,X2))) = hAPP(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_60]),c_0_36]) ).
cnf(c_0_66,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))) = X2,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_40]),c_0_39]) ).
cnf(c_0_67,plain,
( hAPP(c_fNot,X1) = c_Int_OPls
| hBOOL(c_Int_OPls)
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_52,c_0_62]) ).
cnf(c_0_68,plain,
( hBOOL(c_Int_OBit1(X1))
| hBOOL(c_Int_OPls) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_57]),c_0_50])]) ).
cnf(c_0_69,plain,
( esk95_1(c_fNot) = X1
| hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_56,c_0_64]) ).
fof(c_0_70,plain,
! [X5883,X5884] :
( ( c_Int_OBit1(X5884) != c_Int_OBit1(X5883)
| X5884 = X5883 )
& ( X5884 != X5883
| c_Int_OBit1(X5884) = c_Int_OBit1(X5883) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I51_J])]) ).
cnf(c_0_71,plain,
hAPP(c_fNot,hAPP(c_fNot,X1)) = X1,
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_72,plain,
( hAPP(c_fNot,c_Int_OBit1(X1)) = c_Int_OPls
| hBOOL(c_Int_OPls) ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
fof(c_0_73,plain,
! [X3449,X3450] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3450),X3449) != X3450
| X3449 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__eq__self__zero])]) ).
cnf(c_0_74,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(split_conjunct,[status(thm)],[fact_transfer__nat__int__numerals_I1_J]) ).
cnf(c_0_75,plain,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[fact_Pls__def]) ).
fof(c_0_76,plain,
! [X2756] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X2756),
inference(variable_rename,[status(thm)],[fact_Zero__not__Suc]) ).
cnf(c_0_77,plain,
( esk95_1(c_fNot) = hAPP(c_fNot,X1)
| ~ hBOOL(X1) ),
inference(spm,[status(thm)],[c_0_52,c_0_69]) ).
cnf(c_0_78,plain,
hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)),
inference(split_conjunct,[status(thm)],[fact_WT_Oequations_I1_J]) ).
fof(c_0_79,plain,
! [X2864,X2865] : c_Option_Ooption_ONone(X2865) != hAPP(c_Option_Ooption_OSome(X2865),X2864),
inference(variable_rename,[status(thm)],[fact_option_Osimps_I2_J]) ).
cnf(c_0_80,plain,
( X1 = X2
| c_Int_OBit1(X1) != c_Int_OBit1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_81,plain,
( c_Int_OBit1(X1) = hAPP(c_fNot,c_Int_OPls)
| hBOOL(c_Int_OPls) ),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_82,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2) != X1 ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_83,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Int_OPls),
inference(rw,[status(thm)],[c_0_74,c_0_75]) ).
fof(c_0_84,plain,
! [X2766,X2767] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2767),hAPP(c_Nat_OSuc,X2766)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2767),X2766)),
inference(variable_rename,[status(thm)],[fact_add__Suc__right]) ).
cnf(c_0_85,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_86,plain,
esk95_1(c_fNot) = hAPP(c_fNot,hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_87,plain,
c_Option_Ooption_ONone(X1) != hAPP(c_Option_Ooption_OSome(X1),X2),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_88,plain,
( X1 = X2
| hBOOL(c_Int_OPls) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_81]) ).
cnf(c_0_89,plain,
( X1 = hAPP(c_Int_Onat,c_Int_OPls)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1) != X2 ),
inference(rw,[status(thm)],[c_0_82,c_0_83]) ).
cnf(c_0_90,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
cnf(c_0_91,plain,
hAPP(c_Int_Onat,c_Int_OPls) != hAPP(c_Nat_OSuc,X1),
inference(rw,[status(thm)],[c_0_85,c_0_83]) ).
cnf(c_0_92,plain,
( hAPP(c_fNot,hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)) = hAPP(c_fNot,X1)
| ~ hBOOL(X1) ),
inference(rw,[status(thm)],[c_0_77,c_0_86]) ).
cnf(c_0_93,plain,
hBOOL(c_Int_OPls),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88])]) ).
fof(c_0_94,plain,
! [X2736] : X2736 != hAPP(c_Nat_OSuc,X2736),
inference(variable_rename,[status(thm)],[fact_n__not__Suc__n]) ).
fof(c_0_95,plain,
! [X18] :
( hBOOL(X18)
| hBOOL(hAPP(c_fNot,X18)) ),
inference(fof_simplification,[status(thm)],[help_c__fNot__2]) ).
cnf(c_0_96,plain,
hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)) != X1,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_91]) ).
fof(c_0_97,plain,
! [X3446] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3446),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X3446,
inference(variable_rename,[status(thm)],[fact_Nat_Oadd__0__right]) ).
cnf(c_0_98,plain,
hAPP(c_fNot,hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)) = hAPP(c_fNot,c_Int_OPls),
inference(spm,[status(thm)],[c_0_92,c_0_93]) ).
cnf(c_0_99,plain,
X1 != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
fof(c_0_100,plain,
! [X1574] :
( hBOOL(X1574)
| hBOOL(hAPP(c_fNot,X1574)) ),
inference(variable_rename,[status(thm)],[c_0_95]) ).
cnf(c_0_101,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))) != X1,
inference(spm,[status(thm)],[c_0_96,c_0_90]) ).
cnf(c_0_102,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
inference(split_conjunct,[status(thm)],[c_0_97]) ).
cnf(c_0_103,plain,
( hAPP(c_fNot,c_Int_OPls) = hAPP(c_fNot,X1)
| ~ hBOOL(X1) ),
inference(rw,[status(thm)],[c_0_92,c_0_98]) ).
cnf(c_0_104,plain,
hBOOL(hAPP(c_Nat_OSuc,esk95_1(c_fNot))),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_69])]) ).
cnf(c_0_105,plain,
hAPP(c_Com_OWT,c_Com_Ocom_OSKIP) = c_Int_OPls,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_98]),c_0_71]) ).
cnf(c_0_106,plain,
( hBOOL(X1)
| hBOOL(hAPP(c_fNot,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_107,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)))) != X1,
inference(spm,[status(thm)],[c_0_101,c_0_90]) ).
cnf(c_0_108,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Int_Onat,c_Int_OPls)) = X1,
inference(rw,[status(thm)],[c_0_102,c_0_83]) ).
cnf(c_0_109,plain,
hAPP(c_fNot,hAPP(c_Nat_OSuc,hAPP(c_fNot,c_Int_OPls))) = hAPP(c_fNot,c_Int_OPls),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_86]),c_0_105]) ).
cnf(c_0_110,plain,
( hAPP(c_fNot,c_Int_OPls) = X1
| hBOOL(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_106]),c_0_71]) ).
cnf(c_0_111,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1))) != X1,
inference(spm,[status(thm)],[c_0_107,c_0_108]) ).
cnf(c_0_112,plain,
hAPP(c_Nat_OSuc,hAPP(c_fNot,c_Int_OPls)) = c_Int_OPls,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_109]),c_0_71]) ).
cnf(c_0_113,plain,
( hAPP(c_fNot,c_Int_OPls) = hAPP(c_fNot,X1)
| hAPP(c_fNot,c_Int_OPls) = X1 ),
inference(spm,[status(thm)],[c_0_103,c_0_110]) ).
cnf(c_0_114,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Int_OPls)) != hAPP(c_fNot,c_Int_OPls),
inference(spm,[status(thm)],[c_0_111,c_0_112]) ).
cnf(c_0_115,plain,
( hAPP(c_fNot,c_Int_OPls) = X1
| c_Int_OPls = X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_113]),c_0_71]) ).
cnf(c_0_116,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)) != X1,
inference(spm,[status(thm)],[c_0_101,c_0_108]) ).
cnf(c_0_117,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_115]),c_0_116]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.09 % Problem : SWW379+1 : TPTP v8.1.2. Released v5.2.0.
% 0.04/0.10 % Command : run_E %s %d THM
% 0.10/0.30 % Computer : n019.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 2400
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Mon Oct 2 22:43:51 EDT 2023
% 0.10/0.30 % CPUTime :
% 1.30/1.49 Running first-order model finding
% 1.30/1.49 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.tUAvdwtkEl/E---3.1_11519.p
% 7.14/3.19 # Version: 3.1pre001
% 7.14/3.19 # Preprocessing class: FMLMSLSMSSSNFFN.
% 7.14/3.19 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 7.14/3.19 # Starting SAT001_MinMin_p005000_rr_RG with 1500s (5) cores
% 7.14/3.19 # Starting new_bool_3 with 300s (1) cores
% 7.14/3.19 # Starting new_bool_1 with 300s (1) cores
% 7.14/3.19 # Starting sh5l with 300s (1) cores
% 7.14/3.19 # new_bool_3 with pid 11597 completed with status 0
% 7.14/3.19 # Result found by new_bool_3
% 7.14/3.19 # Preprocessing class: FMLMSLSMSSSNFFN.
% 7.14/3.19 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 7.14/3.19 # Starting SAT001_MinMin_p005000_rr_RG with 1500s (5) cores
% 7.14/3.19 # Starting new_bool_3 with 300s (1) cores
% 7.14/3.19 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 7.14/3.19 # Search class: FGHSM-SMLM33-DFFFFFNN
% 7.14/3.19 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 7.14/3.19 # Starting SAT001_MinMin_p005000_rr with 163s (1) cores
% 7.14/3.19 # SAT001_MinMin_p005000_rr with pid 11601 completed with status 0
% 7.14/3.19 # Result found by SAT001_MinMin_p005000_rr
% 7.14/3.19 # Preprocessing class: FMLMSLSMSSSNFFN.
% 7.14/3.19 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 7.14/3.19 # Starting SAT001_MinMin_p005000_rr_RG with 1500s (5) cores
% 7.14/3.19 # Starting new_bool_3 with 300s (1) cores
% 7.14/3.19 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 7.14/3.19 # Search class: FGHSM-SMLM33-DFFFFFNN
% 7.14/3.19 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 7.14/3.19 # Starting SAT001_MinMin_p005000_rr with 163s (1) cores
% 7.14/3.19 # Preprocessing time : 0.058 s
% 7.14/3.19 # Presaturation interreduction done
% 7.14/3.19
% 7.14/3.19 # Proof found!
% 7.14/3.19 # SZS status ContradictoryAxioms
% 7.14/3.19 # SZS output start CNFRefutation
% See solution above
% 7.14/3.19 # Parsed axioms : 5240
% 7.14/3.19 # Removed by relevancy pruning/SinE : 3274
% 7.14/3.19 # Initial clauses : 3054
% 7.14/3.19 # Removed in clause preprocessing : 87
% 7.14/3.19 # Initial clauses in saturation : 2967
% 7.14/3.19 # Processed clauses : 5661
% 7.14/3.19 # ...of these trivial : 160
% 7.14/3.19 # ...subsumed : 1665
% 7.14/3.19 # ...remaining for further processing : 3836
% 7.14/3.19 # Other redundant clauses eliminated : 1632
% 7.14/3.19 # Clauses deleted for lack of memory : 0
% 7.14/3.19 # Backward-subsumed : 54
% 7.14/3.19 # Backward-rewritten : 364
% 7.14/3.19 # Generated clauses : 39266
% 7.14/3.19 # ...of the previous two non-redundant : 35213
% 7.14/3.19 # ...aggressively subsumed : 0
% 7.14/3.19 # Contextual simplify-reflections : 18
% 7.14/3.19 # Paramodulations : 37620
% 7.14/3.19 # Factorizations : 6
% 7.14/3.19 # NegExts : 0
% 7.14/3.19 # Equation resolutions : 1676
% 7.14/3.19 # Total rewrite steps : 7574
% 7.14/3.19 # Propositional unsat checks : 0
% 7.14/3.19 # Propositional check models : 0
% 7.14/3.19 # Propositional check unsatisfiable : 0
% 7.14/3.19 # Propositional clauses : 0
% 7.14/3.19 # Propositional clauses after purity: 0
% 7.14/3.19 # Propositional unsat core size : 0
% 7.14/3.19 # Propositional preprocessing time : 0.000
% 7.14/3.19 # Propositional encoding time : 0.000
% 7.14/3.19 # Propositional solver time : 0.000
% 7.14/3.19 # Success case prop preproc time : 0.000
% 7.14/3.19 # Success case prop encoding time : 0.000
% 7.14/3.19 # Success case prop solver time : 0.000
% 7.14/3.19 # Current number of processed clauses : 948
% 7.14/3.19 # Positive orientable unit clauses : 411
% 7.14/3.19 # Positive unorientable unit clauses: 2
% 7.14/3.19 # Negative unit clauses : 160
% 7.14/3.19 # Non-unit-clauses : 375
% 7.14/3.19 # Current number of unprocessed clauses: 22126
% 7.14/3.19 # ...number of literals in the above : 48581
% 7.14/3.19 # Current number of archived formulas : 0
% 7.14/3.19 # Current number of archived clauses : 2638
% 7.14/3.19 # Clause-clause subsumption calls (NU) : 494793
% 7.14/3.19 # Rec. Clause-clause subsumption calls : 252694
% 7.14/3.19 # Non-unit clause-clause subsumptions : 937
% 7.14/3.19 # Unit Clause-clause subsumption calls : 9495
% 7.14/3.19 # Rewrite failures with RHS unbound : 251
% 7.14/3.19 # BW rewrite match attempts : 9113
% 7.14/3.19 # BW rewrite match successes : 476
% 7.14/3.19 # Condensation attempts : 0
% 7.14/3.19 # Condensation successes : 0
% 7.14/3.19 # Termbank termtop insertions : 898458
% 7.14/3.19
% 7.14/3.19 # -------------------------------------------------
% 7.14/3.19 # User time : 1.378 s
% 7.14/3.19 # System time : 0.061 s
% 7.14/3.19 # Total time : 1.439 s
% 7.14/3.19 # Maximum resident set size: 18088 pages
% 7.14/3.19
% 7.14/3.19 # -------------------------------------------------
% 7.14/3.19 # User time : 1.609 s
% 7.14/3.19 # System time : 0.071 s
% 7.14/3.19 # Total time : 1.680 s
% 7.14/3.19 # Maximum resident set size: 9552 pages
% 7.14/3.19 % E---3.1 exiting
%------------------------------------------------------------------------------