TSTP Solution File: SYO068^4.020 by E---3.1.00
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- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SYO068^4.020 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n025.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 May 21 08:44:31 EDT 2024
% Result : Theorem 0.37s 0.53s
% Output : CNFRefutation 0.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 67
% Number of leaves : 100
% Syntax : Number of formulae : 238 ( 46 unt; 70 typ; 0 def)
% Number of atoms : 999 ( 16 equ; 0 cnn)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 2774 ( 429 ~; 506 |; 60 &;1693 @)
% ( 0 <=>; 86 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 133 ( 133 >; 0 *; 0 +; 0 <<)
% Number of symbols : 72 ( 70 usr; 2 con; 0-3 aty)
% Number of variables : 389 ( 34 ^ 355 !; 0 ?; 389 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_22,type,
irel: $i > $i > $o ).
thf(decl_23,type,
mnot: ( $i > $o ) > $i > $o ).
thf(decl_24,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_26,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_27,type,
mbox_s4: ( $i > $o ) > $i > $o ).
thf(decl_28,type,
iatom: ( $i > $o ) > $i > $o ).
thf(decl_34,type,
iimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_38,type,
ivalid: ( $i > $o ) > $o ).
thf(decl_42,type,
p0: $i > $o ).
thf(decl_43,type,
p1: $i > $o ).
thf(decl_44,type,
p10: $i > $o ).
thf(decl_45,type,
p11: $i > $o ).
thf(decl_46,type,
p12: $i > $o ).
thf(decl_47,type,
p13: $i > $o ).
thf(decl_48,type,
p14: $i > $o ).
thf(decl_49,type,
p15: $i > $o ).
thf(decl_50,type,
p16: $i > $o ).
thf(decl_51,type,
p17: $i > $o ).
thf(decl_52,type,
p18: $i > $o ).
thf(decl_53,type,
p19: $i > $o ).
thf(decl_54,type,
p2: $i > $o ).
thf(decl_55,type,
p20: $i > $o ).
thf(decl_56,type,
p3: $i > $o ).
thf(decl_57,type,
p4: $i > $o ).
thf(decl_58,type,
p5: $i > $o ).
thf(decl_59,type,
p6: $i > $o ).
thf(decl_60,type,
p7: $i > $o ).
thf(decl_61,type,
p8: $i > $o ).
thf(decl_62,type,
p9: $i > $o ).
thf(decl_63,type,
esk1_1: $i > $i ).
thf(decl_64,type,
esk2_2: $i > $i > $i ).
thf(decl_65,type,
esk3_1: $i > $i ).
thf(decl_66,type,
esk4_2: $i > $i > $i ).
thf(decl_67,type,
esk5_1: $i > $i ).
thf(decl_68,type,
esk6_2: $i > $i > $i ).
thf(decl_69,type,
esk7_1: $i > $i ).
thf(decl_70,type,
esk8_2: $i > $i > $i ).
thf(decl_71,type,
esk9_1: $i > $i ).
thf(decl_72,type,
esk10_2: $i > $i > $i ).
thf(decl_73,type,
esk11_1: $i > $i ).
thf(decl_74,type,
esk12_2: $i > $i > $i ).
thf(decl_75,type,
esk13_1: $i > $i ).
thf(decl_76,type,
esk14_2: $i > $i > $i ).
thf(decl_77,type,
esk15_1: $i > $i ).
thf(decl_78,type,
esk16_2: $i > $i > $i ).
thf(decl_79,type,
esk17_1: $i > $i ).
thf(decl_80,type,
esk18_2: $i > $i > $i ).
thf(decl_81,type,
esk19_1: $i > $i ).
thf(decl_82,type,
esk20_2: $i > $i > $i ).
thf(decl_83,type,
esk21_1: $i > $i ).
thf(decl_84,type,
esk22_2: $i > $i > $i ).
thf(decl_85,type,
esk23_1: $i > $i ).
thf(decl_86,type,
esk24_2: $i > $i > $i ).
thf(decl_87,type,
esk25_1: $i > $i ).
thf(decl_88,type,
esk26_2: $i > $i > $i ).
thf(decl_89,type,
esk27_1: $i > $i ).
thf(decl_90,type,
esk28_2: $i > $i > $i ).
thf(decl_91,type,
esk29_1: $i > $i ).
thf(decl_92,type,
esk30_2: $i > $i > $i ).
thf(decl_93,type,
esk31_1: $i > $i ).
thf(decl_94,type,
esk32_2: $i > $i > $i ).
thf(decl_95,type,
esk33_1: $i > $i ).
thf(decl_96,type,
esk34_2: $i > $i > $i ).
thf(decl_97,type,
esk35_1: $i > $i ).
thf(decl_98,type,
esk36_2: $i > $i > $i ).
thf(decl_99,type,
esk37_1: $i > $i ).
thf(decl_100,type,
esk38_2: $i > $i > $i ).
thf(decl_101,type,
esk39_1: $i > $i ).
thf(decl_102,type,
esk40_2: $i > $i > $i ).
thf(decl_103,type,
esk41_0: $i ).
thf(mimplies,axiom,
( mimplies
= ( ^ [X10: $i > $o,X11: $i > $o] : ( mor @ ( mnot @ X10 ) @ X11 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',mimplies) ).
thf(mnot,axiom,
( mnot
= ( ^ [X4: $i > $o,X5: $i] :
~ ( X4 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',mnot) ).
thf(mor,axiom,
( mor
= ( ^ [X6: $i > $o,X7: $i > $o,X5: $i] :
( ( X6 @ X5 )
| ( X7 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',mor) ).
thf(iimplies,axiom,
( iimplies
= ( ^ [X12: $i > $o,X14: $i > $o] : ( mimplies @ ( mbox_s4 @ X12 ) @ ( mbox_s4 @ X14 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',iimplies) ).
thf(mbox_s4,axiom,
( mbox_s4
= ( ^ [X12: $i > $o,X1: $i] :
! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( X12 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',mbox_s4) ).
thf(iatom,axiom,
( iatom
= ( ^ [X12: $i > $o] : X12 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',iatom) ).
thf(ivalid,axiom,
( ivalid
= ( ^ [X15: $i > $o] :
! [X13: $i] : ( X15 @ X13 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',ivalid) ).
thf(axiom21,axiom,
ivalid @ ( iimplies @ ( iatom @ p20 ) @ ( iimplies @ ( iatom @ p20 ) @ ( iatom @ p19 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom21) ).
thf(axiom1,axiom,
ivalid @ ( iatom @ p20 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom1) ).
thf(refl_axiom,axiom,
! [X1: $i] : ( irel @ X1 @ X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',refl_axiom) ).
thf(axiom20,axiom,
ivalid @ ( iimplies @ ( iatom @ p19 ) @ ( iimplies @ ( iatom @ p19 ) @ ( iatom @ p18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom20) ).
thf(axiom19,axiom,
ivalid @ ( iimplies @ ( iatom @ p18 ) @ ( iimplies @ ( iatom @ p18 ) @ ( iatom @ p17 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom19) ).
thf(axiom18,axiom,
ivalid @ ( iimplies @ ( iatom @ p17 ) @ ( iimplies @ ( iatom @ p17 ) @ ( iatom @ p16 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom18) ).
thf(axiom17,axiom,
ivalid @ ( iimplies @ ( iatom @ p16 ) @ ( iimplies @ ( iatom @ p16 ) @ ( iatom @ p15 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom17) ).
thf(axiom16,axiom,
ivalid @ ( iimplies @ ( iatom @ p15 ) @ ( iimplies @ ( iatom @ p15 ) @ ( iatom @ p14 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom16) ).
thf(axiom15,axiom,
ivalid @ ( iimplies @ ( iatom @ p14 ) @ ( iimplies @ ( iatom @ p14 ) @ ( iatom @ p13 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom15) ).
thf(axiom14,axiom,
ivalid @ ( iimplies @ ( iatom @ p13 ) @ ( iimplies @ ( iatom @ p13 ) @ ( iatom @ p12 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom14) ).
thf(axiom13,axiom,
ivalid @ ( iimplies @ ( iatom @ p12 ) @ ( iimplies @ ( iatom @ p12 ) @ ( iatom @ p11 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom13) ).
thf(axiom12,axiom,
ivalid @ ( iimplies @ ( iatom @ p11 ) @ ( iimplies @ ( iatom @ p11 ) @ ( iatom @ p10 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom12) ).
thf(axiom11,axiom,
ivalid @ ( iimplies @ ( iatom @ p10 ) @ ( iimplies @ ( iatom @ p10 ) @ ( iatom @ p9 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom11) ).
thf(axiom10,axiom,
ivalid @ ( iimplies @ ( iatom @ p9 ) @ ( iimplies @ ( iatom @ p9 ) @ ( iatom @ p8 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom10) ).
thf(axiom9,axiom,
ivalid @ ( iimplies @ ( iatom @ p8 ) @ ( iimplies @ ( iatom @ p8 ) @ ( iatom @ p7 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom9) ).
thf(axiom8,axiom,
ivalid @ ( iimplies @ ( iatom @ p7 ) @ ( iimplies @ ( iatom @ p7 ) @ ( iatom @ p6 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom8) ).
thf(axiom7,axiom,
ivalid @ ( iimplies @ ( iatom @ p6 ) @ ( iimplies @ ( iatom @ p6 ) @ ( iatom @ p5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom7) ).
thf(axiom6,axiom,
ivalid @ ( iimplies @ ( iatom @ p5 ) @ ( iimplies @ ( iatom @ p5 ) @ ( iatom @ p4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom6) ).
thf(axiom5,axiom,
ivalid @ ( iimplies @ ( iatom @ p4 ) @ ( iimplies @ ( iatom @ p4 ) @ ( iatom @ p3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom5) ).
thf(axiom4,axiom,
ivalid @ ( iimplies @ ( iatom @ p3 ) @ ( iimplies @ ( iatom @ p3 ) @ ( iatom @ p2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom4) ).
thf(axiom3,axiom,
ivalid @ ( iimplies @ ( iatom @ p2 ) @ ( iimplies @ ( iatom @ p2 ) @ ( iatom @ p1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom3) ).
thf(axiom2,axiom,
ivalid @ ( iimplies @ ( iatom @ p1 ) @ ( iimplies @ ( iatom @ p1 ) @ ( iatom @ p0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom2) ).
thf(con,conjecture,
ivalid @ ( iatom @ p0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
thf(c_0_30,plain,
( mimplies
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mimplies]) ).
thf(c_0_31,plain,
( mnot
= ( ^ [Z0: $i > $o,Z1: $i] :
~ ( Z0 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mnot]) ).
thf(c_0_32,plain,
( mor
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mor]) ).
thf(c_0_33,plain,
( iimplies
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ~ ! [X24: $i] :
( ( irel @ Z2 @ X24 )
=> ( Z0 @ X24 ) )
| ! [X25: $i] :
( ( irel @ Z2 @ X25 )
=> ( Z1 @ X25 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[iimplies]) ).
thf(c_0_34,plain,
( mimplies
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_30,c_0_31]),c_0_32]) ).
thf(c_0_35,plain,
( mbox_s4
= ( ^ [Z0: $i > $o,Z1: $i] :
! [X2: $i] :
( ( irel @ Z1 @ X2 )
=> ( Z0 @ X2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mbox_s4]) ).
thf(c_0_36,plain,
( iatom
= ( ^ [Z0: $i > $o] : Z0 ) ),
inference(fof_simplification,[status(thm)],[iatom]) ).
thf(c_0_37,plain,
( iimplies
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ~ ! [X24: $i] :
( ( irel @ Z2 @ X24 )
=> ( Z0 @ X24 ) )
| ! [X25: $i] :
( ( irel @ Z2 @ X25 )
=> ( Z1 @ X25 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_33,c_0_34]),c_0_35]) ).
thf(c_0_38,plain,
( ivalid
= ( ^ [Z0: $i > $o] :
! [X13: $i] : ( Z0 @ X13 ) ) ),
inference(fof_simplification,[status(thm)],[ivalid]) ).
thf(c_0_39,plain,
! [X137: $i] :
( ~ ! [X135: $i] :
( ( irel @ X137 @ X135 )
=> ( p20 @ X135 ) )
| ! [X136: $i] :
( ( irel @ X137 @ X136 )
=> ( ~ ! [X133: $i] :
( ( irel @ X136 @ X133 )
=> ( p20 @ X133 ) )
| ! [X134: $i] :
( ( irel @ X136 @ X134 )
=> ( p19 @ X134 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[axiom21,c_0_36]),c_0_37]),c_0_38]) ).
thf(c_0_40,plain,
! [X37: $i] : ( p20 @ X37 ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[axiom1,c_0_36]),c_0_38]) ).
thf(c_0_41,plain,
! [X239: $i,X241: $i,X243: $i] :
( ( ( irel @ X241 @ ( esk40_2 @ X239 @ X241 ) )
| ~ ( irel @ X241 @ X243 )
| ( p19 @ X243 )
| ~ ( irel @ X239 @ X241 )
| ( irel @ X239 @ ( esk39_1 @ X239 ) ) )
& ( ~ ( p20 @ ( esk40_2 @ X239 @ X241 ) )
| ~ ( irel @ X241 @ X243 )
| ( p19 @ X243 )
| ~ ( irel @ X239 @ X241 )
| ( irel @ X239 @ ( esk39_1 @ X239 ) ) )
& ( ( irel @ X241 @ ( esk40_2 @ X239 @ X241 ) )
| ~ ( irel @ X241 @ X243 )
| ( p19 @ X243 )
| ~ ( irel @ X239 @ X241 )
| ~ ( p20 @ ( esk39_1 @ X239 ) ) )
& ( ~ ( p20 @ ( esk40_2 @ X239 @ X241 ) )
| ~ ( irel @ X241 @ X243 )
| ( p19 @ X243 )
| ~ ( irel @ X239 @ X241 )
| ~ ( p20 @ ( esk39_1 @ X239 ) ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_39])])])])])]) ).
thf(c_0_42,plain,
! [X143: $i] : ( p20 @ X143 ),
inference(variable_rename,[status(thm)],[c_0_40]) ).
thf(c_0_43,plain,
! [X3: $i,X2: $i,X1: $i] :
( ( p19 @ X3 )
| ~ ( p20 @ ( esk40_2 @ X1 @ X2 ) )
| ~ ( irel @ X2 @ X3 )
| ~ ( irel @ X1 @ X2 )
| ~ ( p20 @ ( esk39_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
thf(c_0_44,plain,
! [X1: $i] : ( p20 @ X1 ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
thf(c_0_45,plain,
! [X139: $i] : ( irel @ X139 @ X139 ),
inference(variable_rename,[status(thm)],[refl_axiom]) ).
thf(c_0_46,plain,
! [X132: $i] :
( ~ ! [X130: $i] :
( ( irel @ X132 @ X130 )
=> ( p19 @ X130 ) )
| ! [X131: $i] :
( ( irel @ X132 @ X131 )
=> ( ~ ! [X128: $i] :
( ( irel @ X131 @ X128 )
=> ( p19 @ X128 ) )
| ! [X129: $i] :
( ( irel @ X131 @ X129 )
=> ( p18 @ X129 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[axiom20,c_0_36]),c_0_37]),c_0_38]) ).
thf(c_0_47,plain,
! [X1: $i,X3: $i,X2: $i] :
( ( p19 @ X1 )
| ~ ( irel @ X2 @ X1 )
| ~ ( irel @ X3 @ X2 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_44]),c_0_44])]) ).
thf(c_0_48,plain,
! [X1: $i] : ( irel @ X1 @ X1 ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
thf(c_0_49,plain,
! [X234: $i,X236: $i,X238: $i] :
( ( ( irel @ X236 @ ( esk38_2 @ X234 @ X236 ) )
| ~ ( irel @ X236 @ X238 )
| ( p18 @ X238 )
| ~ ( irel @ X234 @ X236 )
| ( irel @ X234 @ ( esk37_1 @ X234 ) ) )
& ( ~ ( p19 @ ( esk38_2 @ X234 @ X236 ) )
| ~ ( irel @ X236 @ X238 )
| ( p18 @ X238 )
| ~ ( irel @ X234 @ X236 )
| ( irel @ X234 @ ( esk37_1 @ X234 ) ) )
& ( ( irel @ X236 @ ( esk38_2 @ X234 @ X236 ) )
| ~ ( irel @ X236 @ X238 )
| ( p18 @ X238 )
| ~ ( irel @ X234 @ X236 )
| ~ ( p19 @ ( esk37_1 @ X234 ) ) )
& ( ~ ( p19 @ ( esk38_2 @ X234 @ X236 ) )
| ~ ( irel @ X236 @ X238 )
| ( p18 @ X238 )
| ~ ( irel @ X234 @ X236 )
| ~ ( p19 @ ( esk37_1 @ X234 ) ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_46])])])])])]) ).
thf(c_0_50,plain,
! [X2: $i,X1: $i] :
( ( p19 @ X1 )
| ~ ( irel @ X2 @ X1 ) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
thf(c_0_51,plain,
! [X3: $i,X2: $i,X1: $i] :
( ( p18 @ X3 )
| ~ ( p19 @ ( esk38_2 @ X1 @ X2 ) )
| ~ ( irel @ X2 @ X3 )
| ~ ( irel @ X1 @ X2 )
| ~ ( p19 @ ( esk37_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
thf(c_0_52,plain,
! [X1: $i] : ( p19 @ X1 ),
inference(spm,[status(thm)],[c_0_50,c_0_48]) ).
thf(c_0_53,plain,
! [X127: $i] :
( ~ ! [X125: $i] :
( ( irel @ X127 @ X125 )
=> ( p18 @ X125 ) )
| ! [X126: $i] :
( ( irel @ X127 @ X126 )
=> ( ~ ! [X123: $i] :
( ( irel @ X126 @ X123 )
=> ( p18 @ X123 ) )
| ! [X124: $i] :
( ( irel @ X126 @ X124 )
=> ( p17 @ X124 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[axiom19,c_0_36]),c_0_37]),c_0_38]) ).
thf(c_0_54,plain,
! [X1: $i,X3: $i,X2: $i] :
( ( p18 @ X1 )
| ~ ( irel @ X2 @ X1 )
| ~ ( irel @ X3 @ X2 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_52]),c_0_52])]) ).
thf(c_0_55,plain,
! [X229: $i,X231: $i,X233: $i] :
( ( ( irel @ X231 @ ( esk36_2 @ X229 @ X231 ) )
| ~ ( irel @ X231 @ X233 )
| ( p17 @ X233 )
| ~ ( irel @ X229 @ X231 )
| ( irel @ X229 @ ( esk35_1 @ X229 ) ) )
& ( ~ ( p18 @ ( esk36_2 @ X229 @ X231 ) )
| ~ ( irel @ X231 @ X233 )
| ( p17 @ X233 )
| ~ ( irel @ X229 @ X231 )
| ( irel @ X229 @ ( esk35_1 @ X229 ) ) )
& ( ( irel @ X231 @ ( esk36_2 @ X229 @ X231 ) )
| ~ ( irel @ X231 @ X233 )
| ( p17 @ X233 )
| ~ ( irel @ X229 @ X231 )
| ~ ( p18 @ ( esk35_1 @ X229 ) ) )
& ( ~ ( p18 @ ( esk36_2 @ X229 @ X231 ) )
| ~ ( irel @ X231 @ X233 )
| ( p17 @ X233 )
| ~ ( irel @ X229 @ X231 )
| ~ ( p18 @ ( esk35_1 @ X229 ) ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_53])])])])])]) ).
thf(c_0_56,plain,
! [X2: $i,X1: $i] :
( ( p18 @ X1 )
| ~ ( irel @ X2 @ X1 ) ),
inference(spm,[status(thm)],[c_0_54,c_0_48]) ).
thf(c_0_57,plain,
! [X3: $i,X2: $i,X1: $i] :
( ( p17 @ X3 )
| ~ ( p18 @ ( esk36_2 @ X1 @ X2 ) )
| ~ ( irel @ X2 @ X3 )
| ~ ( irel @ X1 @ X2 )
| ~ ( p18 @ ( esk35_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
thf(c_0_58,plain,
! [X1: $i] : ( p18 @ X1 ),
inference(spm,[status(thm)],[c_0_56,c_0_48]) ).
thf(c_0_59,plain,
! [X122: $i] :
( ~ ! [X120: $i] :
( ( irel @ X122 @ X120 )
=> ( p17 @ X120 ) )
| ! [X121: $i] :
( ( irel @ X122 @ X121 )
=> ( ~ ! [X118: $i] :
( ( irel @ X121 @ X118 )
=> ( p17 @ X118 ) )
| ! [X119: $i] :
( ( irel @ X121 @ X119 )
=> ( p16 @ X119 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[axiom18,c_0_36]),c_0_37]),c_0_38]) ).
thf(c_0_60,plain,
! [X1: $i,X3: $i,X2: $i] :
( ( p17 @ X1 )
| ~ ( irel @ X2 @ X1 )
| ~ ( irel @ X3 @ X2 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_58]),c_0_58])]) ).
thf(c_0_61,plain,
! [X224: $i,X226: $i,X228: $i] :
( ( ( irel @ X226 @ ( esk34_2 @ X224 @ X226 ) )
| ~ ( irel @ X226 @ X228 )
| ( p16 @ X228 )
| ~ ( irel @ X224 @ X226 )
| ( irel @ X224 @ ( esk33_1 @ X224 ) ) )
& ( ~ ( p17 @ ( esk34_2 @ X224 @ X226 ) )
| ~ ( irel @ X226 @ X228 )
| ( p16 @ X228 )
| ~ ( irel @ X224 @ X226 )
| ( irel @ X224 @ ( esk33_1 @ X224 ) ) )
& ( ( irel @ X226 @ ( esk34_2 @ X224 @ X226 ) )
| ~ ( irel @ X226 @ X228 )
| ( p16 @ X228 )
| ~ ( irel @ X224 @ X226 )
| ~ ( p17 @ ( esk33_1 @ X224 ) ) )
& ( ~ ( p17 @ ( esk34_2 @ X224 @ X226 ) )
| ~ ( irel @ X226 @ X228 )
| ( p16 @ X228 )
| ~ ( irel @ X224 @ X226 )
| ~ ( p17 @ ( esk33_1 @ X224 ) ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_59])])])])])]) ).
thf(c_0_62,plain,
! [X2: $i,X1: $i] :
( ( p17 @ X1 )
| ~ ( irel @ X2 @ X1 ) ),
inference(spm,[status(thm)],[c_0_60,c_0_48]) ).
thf(c_0_63,plain,
! [X3: $i,X2: $i,X1: $i] :
( ( p16 @ X3 )
| ~ ( p17 @ ( esk34_2 @ X1 @ X2 ) )
| ~ ( irel @ X2 @ X3 )
| ~ ( irel @ X1 @ X2 )
| ~ ( p17 @ ( esk33_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
thf(c_0_64,plain,
! [X1: $i] : ( p17 @ X1 ),
inference(spm,[status(thm)],[c_0_62,c_0_48]) ).
thf(c_0_65,plain,
! [X117: $i] :
( ~ ! [X115: $i] :
( ( irel @ X117 @ X115 )
=> ( p16 @ X115 ) )
| ! [X116: $i] :
( ( irel @ X117 @ X116 )
=> ( ~ ! [X113: $i] :
( ( irel @ X116 @ X113 )
=> ( p16 @ X113 ) )
| ! [X114: $i] :
( ( irel @ X116 @ X114 )
=> ( p15 @ X114 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[axiom17,c_0_36]),c_0_37]),c_0_38]) ).
thf(c_0_66,plain,
! [X1: $i,X3: $i,X2: $i] :
( ( p16 @ X1 )
| ~ ( irel @ X2 @ X1 )
| ~ ( irel @ X3 @ X2 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_63,c_0_64]),c_0_64])]) ).
thf(c_0_67,plain,
! [X219: $i,X221: $i,X223: $i] :
( ( ( irel @ X221 @ ( esk32_2 @ X219 @ X221 ) )
| ~ ( irel @ X221 @ X223 )
| ( p15 @ X223 )
| ~ ( irel @ X219 @ X221 )
| ( irel @ X219 @ ( esk31_1 @ X219 ) ) )
& ( ~ ( p16 @ ( esk32_2 @ X219 @ X221 ) )
| ~ ( irel @ X221 @ X223 )
| ( p15 @ X223 )
| ~ ( irel @ X219 @ X221 )
| ( irel @ X219 @ ( esk31_1 @ X219 ) ) )
& ( ( irel @ X221 @ ( esk32_2 @ X219 @ X221 ) )
| ~ ( irel @ X221 @ X223 )
| ( p15 @ X223 )
| ~ ( irel @ X219 @ X221 )
| ~ ( p16 @ ( esk31_1 @ X219 ) ) )
& ( ~ ( p16 @ ( esk32_2 @ X219 @ X221 ) )
| ~ ( irel @ X221 @ X223 )
| ( p15 @ X223 )
| ~ ( irel @ X219 @ X221 )
| ~ ( p16 @ ( esk31_1 @ X219 ) ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_65])])])])])]) ).
thf(c_0_68,plain,
! [X2: $i,X1: $i] :
( ( p16 @ X1 )
| ~ ( irel @ X2 @ X1 ) ),
inference(spm,[status(thm)],[c_0_66,c_0_48]) ).
thf(c_0_69,plain,
! [X3: $i,X2: $i,X1: $i] :
( ( p15 @ X3 )
| ~ ( p16 @ ( esk32_2 @ X1 @ X2 ) )
| ~ ( irel @ X2 @ X3 )
| ~ ( irel @ X1 @ X2 )
| ~ ( p16 @ ( esk31_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
thf(c_0_70,plain,
! [X1: $i] : ( p16 @ X1 ),
inference(spm,[status(thm)],[c_0_68,c_0_48]) ).
thf(c_0_71,plain,
! [X112: $i] :
( ~ ! [X110: $i] :
( ( irel @ X112 @ X110 )
=> ( p15 @ X110 ) )
| ! [X111: $i] :
( ( irel @ X112 @ X111 )
=> ( ~ ! [X108: $i] :
( ( irel @ X111 @ X108 )
=> ( p15 @ X108 ) )
| ! [X109: $i] :
( ( irel @ X111 @ X109 )
=> ( p14 @ X109 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[axiom16,c_0_36]),c_0_37]),c_0_38]) ).
thf(c_0_72,plain,
! [X1: $i,X3: $i,X2: $i] :
( ( p15 @ X1 )
| ~ ( irel @ X2 @ X1 )
| ~ ( irel @ X3 @ X2 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_69,c_0_70]),c_0_70])]) ).
thf(c_0_73,plain,
! [X214: $i,X216: $i,X218: $i] :
( ( ( irel @ X216 @ ( esk30_2 @ X214 @ X216 ) )
| ~ ( irel @ X216 @ X218 )
| ( p14 @ X218 )
| ~ ( irel @ X214 @ X216 )
| ( irel @ X214 @ ( esk29_1 @ X214 ) ) )
& ( ~ ( p15 @ ( esk30_2 @ X214 @ X216 ) )
| ~ ( irel @ X216 @ X218 )
| ( p14 @ X218 )
| ~ ( irel @ X214 @ X216 )
| ( irel @ X214 @ ( esk29_1 @ X214 ) ) )
& ( ( irel @ X216 @ ( esk30_2 @ X214 @ X216 ) )
| ~ ( irel @ X216 @ X218 )
| ( p14 @ X218 )
| ~ ( irel @ X214 @ X216 )
| ~ ( p15 @ ( esk29_1 @ X214 ) ) )
& ( ~ ( p15 @ ( esk30_2 @ X214 @ X216 ) )
| ~ ( irel @ X216 @ X218 )
| ( p14 @ X218 )
| ~ ( irel @ X214 @ X216 )
| ~ ( p15 @ ( esk29_1 @ X214 ) ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_71])])])])])]) ).
thf(c_0_74,plain,
! [X2: $i,X1: $i] :
( ( p15 @ X1 )
| ~ ( irel @ X2 @ X1 ) ),
inference(spm,[status(thm)],[c_0_72,c_0_48]) ).
thf(c_0_75,plain,
! [X3: $i,X2: $i,X1: $i] :
( ( p14 @ X3 )
| ~ ( p15 @ ( esk30_2 @ X1 @ X2 ) )
| ~ ( irel @ X2 @ X3 )
| ~ ( irel @ X1 @ X2 )
| ~ ( p15 @ ( esk29_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
thf(c_0_76,plain,
! [X1: $i] : ( p15 @ X1 ),
inference(spm,[status(thm)],[c_0_74,c_0_48]) ).
thf(c_0_77,plain,
! [X107: $i] :
( ~ ! [X105: $i] :
( ( irel @ X107 @ X105 )
=> ( p14 @ X105 ) )
| ! [X106: $i] :
( ( irel @ X107 @ X106 )
=> ( ~ ! [X103: $i] :
( ( irel @ X106 @ X103 )
=> ( p14 @ X103 ) )
| ! [X104: $i] :
( ( irel @ X106 @ X104 )
=> ( p13 @ X104 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[axiom15,c_0_36]),c_0_37]),c_0_38]) ).
thf(c_0_78,plain,
! [X1: $i,X3: $i,X2: $i] :
( ( p14 @ X1 )
| ~ ( irel @ X2 @ X1 )
| ~ ( irel @ X3 @ X2 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_75,c_0_76]),c_0_76])]) ).
thf(c_0_79,plain,
! [X209: $i,X211: $i,X213: $i] :
( ( ( irel @ X211 @ ( esk28_2 @ X209 @ X211 ) )
| ~ ( irel @ X211 @ X213 )
| ( p13 @ X213 )
| ~ ( irel @ X209 @ X211 )
| ( irel @ X209 @ ( esk27_1 @ X209 ) ) )
& ( ~ ( p14 @ ( esk28_2 @ X209 @ X211 ) )
| ~ ( irel @ X211 @ X213 )
| ( p13 @ X213 )
| ~ ( irel @ X209 @ X211 )
| ( irel @ X209 @ ( esk27_1 @ X209 ) ) )
& ( ( irel @ X211 @ ( esk28_2 @ X209 @ X211 ) )
| ~ ( irel @ X211 @ X213 )
| ( p13 @ X213 )
| ~ ( irel @ X209 @ X211 )
| ~ ( p14 @ ( esk27_1 @ X209 ) ) )
& ( ~ ( p14 @ ( esk28_2 @ X209 @ X211 ) )
| ~ ( irel @ X211 @ X213 )
| ( p13 @ X213 )
| ~ ( irel @ X209 @ X211 )
| ~ ( p14 @ ( esk27_1 @ X209 ) ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_77])])])])])]) ).
thf(c_0_80,plain,
! [X2: $i,X1: $i] :
( ( p14 @ X1 )
| ~ ( irel @ X2 @ X1 ) ),
inference(spm,[status(thm)],[c_0_78,c_0_48]) ).
thf(c_0_81,plain,
! [X3: $i,X2: $i,X1: $i] :
( ( p13 @ X3 )
| ~ ( p14 @ ( esk28_2 @ X1 @ X2 ) )
| ~ ( irel @ X2 @ X3 )
| ~ ( irel @ X1 @ X2 )
| ~ ( p14 @ ( esk27_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
thf(c_0_82,plain,
! [X1: $i] : ( p14 @ X1 ),
inference(spm,[status(thm)],[c_0_80,c_0_48]) ).
thf(c_0_83,plain,
! [X102: $i] :
( ~ ! [X100: $i] :
( ( irel @ X102 @ X100 )
=> ( p13 @ X100 ) )
| ! [X101: $i] :
( ( irel @ X102 @ X101 )
=> ( ~ ! [X98: $i] :
( ( irel @ X101 @ X98 )
=> ( p13 @ X98 ) )
| ! [X99: $i] :
( ( irel @ X101 @ X99 )
=> ( p12 @ X99 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[axiom14,c_0_36]),c_0_37]),c_0_38]) ).
thf(c_0_84,plain,
! [X1: $i,X3: $i,X2: $i] :
( ( p13 @ X1 )
| ~ ( irel @ X2 @ X1 )
| ~ ( irel @ X3 @ X2 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_81,c_0_82]),c_0_82])]) ).
thf(c_0_85,plain,
! [X204: $i,X206: $i,X208: $i] :
( ( ( irel @ X206 @ ( esk26_2 @ X204 @ X206 ) )
| ~ ( irel @ X206 @ X208 )
| ( p12 @ X208 )
| ~ ( irel @ X204 @ X206 )
| ( irel @ X204 @ ( esk25_1 @ X204 ) ) )
& ( ~ ( p13 @ ( esk26_2 @ X204 @ X206 ) )
| ~ ( irel @ X206 @ X208 )
| ( p12 @ X208 )
| ~ ( irel @ X204 @ X206 )
| ( irel @ X204 @ ( esk25_1 @ X204 ) ) )
& ( ( irel @ X206 @ ( esk26_2 @ X204 @ X206 ) )
| ~ ( irel @ X206 @ X208 )
| ( p12 @ X208 )
| ~ ( irel @ X204 @ X206 )
| ~ ( p13 @ ( esk25_1 @ X204 ) ) )
& ( ~ ( p13 @ ( esk26_2 @ X204 @ X206 ) )
| ~ ( irel @ X206 @ X208 )
| ( p12 @ X208 )
| ~ ( irel @ X204 @ X206 )
| ~ ( p13 @ ( esk25_1 @ X204 ) ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_83])])])])])]) ).
thf(c_0_86,plain,
! [X2: $i,X1: $i] :
( ( p13 @ X1 )
| ~ ( irel @ X2 @ X1 ) ),
inference(spm,[status(thm)],[c_0_84,c_0_48]) ).
thf(c_0_87,plain,
! [X3: $i,X2: $i,X1: $i] :
( ( p12 @ X3 )
| ~ ( p13 @ ( esk26_2 @ X1 @ X2 ) )
| ~ ( irel @ X2 @ X3 )
| ~ ( irel @ X1 @ X2 )
| ~ ( p13 @ ( esk25_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_85]) ).
thf(c_0_88,plain,
! [X1: $i] : ( p13 @ X1 ),
inference(spm,[status(thm)],[c_0_86,c_0_48]) ).
thf(c_0_89,plain,
! [X97: $i] :
( ~ ! [X95: $i] :
( ( irel @ X97 @ X95 )
=> ( p12 @ X95 ) )
| ! [X96: $i] :
( ( irel @ X97 @ X96 )
=> ( ~ ! [X93: $i] :
( ( irel @ X96 @ X93 )
=> ( p12 @ X93 ) )
| ! [X94: $i] :
( ( irel @ X96 @ X94 )
=> ( p11 @ X94 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[axiom13,c_0_36]),c_0_37]),c_0_38]) ).
thf(c_0_90,plain,
! [X1: $i,X3: $i,X2: $i] :
( ( p12 @ X1 )
| ~ ( irel @ X2 @ X1 )
| ~ ( irel @ X3 @ X2 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_87,c_0_88]),c_0_88])]) ).
thf(c_0_91,plain,
! [X199: $i,X201: $i,X203: $i] :
( ( ( irel @ X201 @ ( esk24_2 @ X199 @ X201 ) )
| ~ ( irel @ X201 @ X203 )
| ( p11 @ X203 )
| ~ ( irel @ X199 @ X201 )
| ( irel @ X199 @ ( esk23_1 @ X199 ) ) )
& ( ~ ( p12 @ ( esk24_2 @ X199 @ X201 ) )
| ~ ( irel @ X201 @ X203 )
| ( p11 @ X203 )
| ~ ( irel @ X199 @ X201 )
| ( irel @ X199 @ ( esk23_1 @ X199 ) ) )
& ( ( irel @ X201 @ ( esk24_2 @ X199 @ X201 ) )
| ~ ( irel @ X201 @ X203 )
| ( p11 @ X203 )
| ~ ( irel @ X199 @ X201 )
| ~ ( p12 @ ( esk23_1 @ X199 ) ) )
& ( ~ ( p12 @ ( esk24_2 @ X199 @ X201 ) )
| ~ ( irel @ X201 @ X203 )
| ( p11 @ X203 )
| ~ ( irel @ X199 @ X201 )
| ~ ( p12 @ ( esk23_1 @ X199 ) ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_89])])])])])]) ).
thf(c_0_92,plain,
! [X2: $i,X1: $i] :
( ( p12 @ X1 )
| ~ ( irel @ X2 @ X1 ) ),
inference(spm,[status(thm)],[c_0_90,c_0_48]) ).
thf(c_0_93,plain,
! [X3: $i,X2: $i,X1: $i] :
( ( p11 @ X3 )
| ~ ( p12 @ ( esk24_2 @ X1 @ X2 ) )
| ~ ( irel @ X2 @ X3 )
| ~ ( irel @ X1 @ X2 )
| ~ ( p12 @ ( esk23_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_91]) ).
thf(c_0_94,plain,
! [X1: $i] : ( p12 @ X1 ),
inference(spm,[status(thm)],[c_0_92,c_0_48]) ).
thf(c_0_95,plain,
! [X92: $i] :
( ~ ! [X90: $i] :
( ( irel @ X92 @ X90 )
=> ( p11 @ X90 ) )
| ! [X91: $i] :
( ( irel @ X92 @ X91 )
=> ( ~ ! [X88: $i] :
( ( irel @ X91 @ X88 )
=> ( p11 @ X88 ) )
| ! [X89: $i] :
( ( irel @ X91 @ X89 )
=> ( p10 @ X89 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[axiom12,c_0_36]),c_0_37]),c_0_38]) ).
thf(c_0_96,plain,
! [X1: $i,X3: $i,X2: $i] :
( ( p11 @ X1 )
| ~ ( irel @ X2 @ X1 )
| ~ ( irel @ X3 @ X2 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_93,c_0_94]),c_0_94])]) ).
thf(c_0_97,plain,
! [X194: $i,X196: $i,X198: $i] :
( ( ( irel @ X196 @ ( esk22_2 @ X194 @ X196 ) )
| ~ ( irel @ X196 @ X198 )
| ( p10 @ X198 )
| ~ ( irel @ X194 @ X196 )
| ( irel @ X194 @ ( esk21_1 @ X194 ) ) )
& ( ~ ( p11 @ ( esk22_2 @ X194 @ X196 ) )
| ~ ( irel @ X196 @ X198 )
| ( p10 @ X198 )
| ~ ( irel @ X194 @ X196 )
| ( irel @ X194 @ ( esk21_1 @ X194 ) ) )
& ( ( irel @ X196 @ ( esk22_2 @ X194 @ X196 ) )
| ~ ( irel @ X196 @ X198 )
| ( p10 @ X198 )
| ~ ( irel @ X194 @ X196 )
| ~ ( p11 @ ( esk21_1 @ X194 ) ) )
& ( ~ ( p11 @ ( esk22_2 @ X194 @ X196 ) )
| ~ ( irel @ X196 @ X198 )
| ( p10 @ X198 )
| ~ ( irel @ X194 @ X196 )
| ~ ( p11 @ ( esk21_1 @ X194 ) ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_95])])])])])]) ).
thf(c_0_98,plain,
! [X2: $i,X1: $i] :
( ( p11 @ X1 )
| ~ ( irel @ X2 @ X1 ) ),
inference(spm,[status(thm)],[c_0_96,c_0_48]) ).
thf(c_0_99,plain,
! [X3: $i,X2: $i,X1: $i] :
( ( p10 @ X3 )
| ~ ( p11 @ ( esk22_2 @ X1 @ X2 ) )
| ~ ( irel @ X2 @ X3 )
| ~ ( irel @ X1 @ X2 )
| ~ ( p11 @ ( esk21_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_97]) ).
thf(c_0_100,plain,
! [X1: $i] : ( p11 @ X1 ),
inference(spm,[status(thm)],[c_0_98,c_0_48]) ).
thf(c_0_101,plain,
! [X87: $i] :
( ~ ! [X85: $i] :
( ( irel @ X87 @ X85 )
=> ( p10 @ X85 ) )
| ! [X86: $i] :
( ( irel @ X87 @ X86 )
=> ( ~ ! [X83: $i] :
( ( irel @ X86 @ X83 )
=> ( p10 @ X83 ) )
| ! [X84: $i] :
( ( irel @ X86 @ X84 )
=> ( p9 @ X84 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[axiom11,c_0_36]),c_0_37]),c_0_38]) ).
thf(c_0_102,plain,
! [X1: $i,X3: $i,X2: $i] :
( ( p10 @ X1 )
| ~ ( irel @ X2 @ X1 )
| ~ ( irel @ X3 @ X2 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_99,c_0_100]),c_0_100])]) ).
thf(c_0_103,plain,
! [X189: $i,X191: $i,X193: $i] :
( ( ( irel @ X191 @ ( esk20_2 @ X189 @ X191 ) )
| ~ ( irel @ X191 @ X193 )
| ( p9 @ X193 )
| ~ ( irel @ X189 @ X191 )
| ( irel @ X189 @ ( esk19_1 @ X189 ) ) )
& ( ~ ( p10 @ ( esk20_2 @ X189 @ X191 ) )
| ~ ( irel @ X191 @ X193 )
| ( p9 @ X193 )
| ~ ( irel @ X189 @ X191 )
| ( irel @ X189 @ ( esk19_1 @ X189 ) ) )
& ( ( irel @ X191 @ ( esk20_2 @ X189 @ X191 ) )
| ~ ( irel @ X191 @ X193 )
| ( p9 @ X193 )
| ~ ( irel @ X189 @ X191 )
| ~ ( p10 @ ( esk19_1 @ X189 ) ) )
& ( ~ ( p10 @ ( esk20_2 @ X189 @ X191 ) )
| ~ ( irel @ X191 @ X193 )
| ( p9 @ X193 )
| ~ ( irel @ X189 @ X191 )
| ~ ( p10 @ ( esk19_1 @ X189 ) ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_101])])])])])]) ).
thf(c_0_104,plain,
! [X2: $i,X1: $i] :
( ( p10 @ X1 )
| ~ ( irel @ X2 @ X1 ) ),
inference(spm,[status(thm)],[c_0_102,c_0_48]) ).
thf(c_0_105,plain,
! [X3: $i,X2: $i,X1: $i] :
( ( p9 @ X3 )
| ~ ( p10 @ ( esk20_2 @ X1 @ X2 ) )
| ~ ( irel @ X2 @ X3 )
| ~ ( irel @ X1 @ X2 )
| ~ ( p10 @ ( esk19_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
thf(c_0_106,plain,
! [X1: $i] : ( p10 @ X1 ),
inference(spm,[status(thm)],[c_0_104,c_0_48]) ).
thf(c_0_107,plain,
! [X82: $i] :
( ~ ! [X80: $i] :
( ( irel @ X82 @ X80 )
=> ( p9 @ X80 ) )
| ! [X81: $i] :
( ( irel @ X82 @ X81 )
=> ( ~ ! [X78: $i] :
( ( irel @ X81 @ X78 )
=> ( p9 @ X78 ) )
| ! [X79: $i] :
( ( irel @ X81 @ X79 )
=> ( p8 @ X79 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[axiom10,c_0_36]),c_0_37]),c_0_38]) ).
thf(c_0_108,plain,
! [X1: $i,X3: $i,X2: $i] :
( ( p9 @ X1 )
| ~ ( irel @ X2 @ X1 )
| ~ ( irel @ X3 @ X2 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_105,c_0_106]),c_0_106])]) ).
thf(c_0_109,plain,
! [X184: $i,X186: $i,X188: $i] :
( ( ( irel @ X186 @ ( esk18_2 @ X184 @ X186 ) )
| ~ ( irel @ X186 @ X188 )
| ( p8 @ X188 )
| ~ ( irel @ X184 @ X186 )
| ( irel @ X184 @ ( esk17_1 @ X184 ) ) )
& ( ~ ( p9 @ ( esk18_2 @ X184 @ X186 ) )
| ~ ( irel @ X186 @ X188 )
| ( p8 @ X188 )
| ~ ( irel @ X184 @ X186 )
| ( irel @ X184 @ ( esk17_1 @ X184 ) ) )
& ( ( irel @ X186 @ ( esk18_2 @ X184 @ X186 ) )
| ~ ( irel @ X186 @ X188 )
| ( p8 @ X188 )
| ~ ( irel @ X184 @ X186 )
| ~ ( p9 @ ( esk17_1 @ X184 ) ) )
& ( ~ ( p9 @ ( esk18_2 @ X184 @ X186 ) )
| ~ ( irel @ X186 @ X188 )
| ( p8 @ X188 )
| ~ ( irel @ X184 @ X186 )
| ~ ( p9 @ ( esk17_1 @ X184 ) ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_107])])])])])]) ).
thf(c_0_110,plain,
! [X2: $i,X1: $i] :
( ( p9 @ X1 )
| ~ ( irel @ X2 @ X1 ) ),
inference(spm,[status(thm)],[c_0_108,c_0_48]) ).
thf(c_0_111,plain,
! [X3: $i,X2: $i,X1: $i] :
( ( p8 @ X3 )
| ~ ( p9 @ ( esk18_2 @ X1 @ X2 ) )
| ~ ( irel @ X2 @ X3 )
| ~ ( irel @ X1 @ X2 )
| ~ ( p9 @ ( esk17_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_109]) ).
thf(c_0_112,plain,
! [X1: $i] : ( p9 @ X1 ),
inference(spm,[status(thm)],[c_0_110,c_0_48]) ).
thf(c_0_113,plain,
! [X77: $i] :
( ~ ! [X75: $i] :
( ( irel @ X77 @ X75 )
=> ( p8 @ X75 ) )
| ! [X76: $i] :
( ( irel @ X77 @ X76 )
=> ( ~ ! [X73: $i] :
( ( irel @ X76 @ X73 )
=> ( p8 @ X73 ) )
| ! [X74: $i] :
( ( irel @ X76 @ X74 )
=> ( p7 @ X74 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[axiom9,c_0_36]),c_0_37]),c_0_38]) ).
thf(c_0_114,plain,
! [X1: $i,X3: $i,X2: $i] :
( ( p8 @ X1 )
| ~ ( irel @ X2 @ X1 )
| ~ ( irel @ X3 @ X2 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_111,c_0_112]),c_0_112])]) ).
thf(c_0_115,plain,
! [X179: $i,X181: $i,X183: $i] :
( ( ( irel @ X181 @ ( esk16_2 @ X179 @ X181 ) )
| ~ ( irel @ X181 @ X183 )
| ( p7 @ X183 )
| ~ ( irel @ X179 @ X181 )
| ( irel @ X179 @ ( esk15_1 @ X179 ) ) )
& ( ~ ( p8 @ ( esk16_2 @ X179 @ X181 ) )
| ~ ( irel @ X181 @ X183 )
| ( p7 @ X183 )
| ~ ( irel @ X179 @ X181 )
| ( irel @ X179 @ ( esk15_1 @ X179 ) ) )
& ( ( irel @ X181 @ ( esk16_2 @ X179 @ X181 ) )
| ~ ( irel @ X181 @ X183 )
| ( p7 @ X183 )
| ~ ( irel @ X179 @ X181 )
| ~ ( p8 @ ( esk15_1 @ X179 ) ) )
& ( ~ ( p8 @ ( esk16_2 @ X179 @ X181 ) )
| ~ ( irel @ X181 @ X183 )
| ( p7 @ X183 )
| ~ ( irel @ X179 @ X181 )
| ~ ( p8 @ ( esk15_1 @ X179 ) ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_113])])])])])]) ).
thf(c_0_116,plain,
! [X2: $i,X1: $i] :
( ( p8 @ X1 )
| ~ ( irel @ X2 @ X1 ) ),
inference(spm,[status(thm)],[c_0_114,c_0_48]) ).
thf(c_0_117,plain,
! [X3: $i,X2: $i,X1: $i] :
( ( p7 @ X3 )
| ~ ( p8 @ ( esk16_2 @ X1 @ X2 ) )
| ~ ( irel @ X2 @ X3 )
| ~ ( irel @ X1 @ X2 )
| ~ ( p8 @ ( esk15_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_115]) ).
thf(c_0_118,plain,
! [X1: $i] : ( p8 @ X1 ),
inference(spm,[status(thm)],[c_0_116,c_0_48]) ).
thf(c_0_119,plain,
! [X72: $i] :
( ~ ! [X70: $i] :
( ( irel @ X72 @ X70 )
=> ( p7 @ X70 ) )
| ! [X71: $i] :
( ( irel @ X72 @ X71 )
=> ( ~ ! [X68: $i] :
( ( irel @ X71 @ X68 )
=> ( p7 @ X68 ) )
| ! [X69: $i] :
( ( irel @ X71 @ X69 )
=> ( p6 @ X69 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[axiom8,c_0_36]),c_0_37]),c_0_38]) ).
thf(c_0_120,plain,
! [X1: $i,X3: $i,X2: $i] :
( ( p7 @ X1 )
| ~ ( irel @ X2 @ X1 )
| ~ ( irel @ X3 @ X2 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_117,c_0_118]),c_0_118])]) ).
thf(c_0_121,plain,
! [X174: $i,X176: $i,X178: $i] :
( ( ( irel @ X176 @ ( esk14_2 @ X174 @ X176 ) )
| ~ ( irel @ X176 @ X178 )
| ( p6 @ X178 )
| ~ ( irel @ X174 @ X176 )
| ( irel @ X174 @ ( esk13_1 @ X174 ) ) )
& ( ~ ( p7 @ ( esk14_2 @ X174 @ X176 ) )
| ~ ( irel @ X176 @ X178 )
| ( p6 @ X178 )
| ~ ( irel @ X174 @ X176 )
| ( irel @ X174 @ ( esk13_1 @ X174 ) ) )
& ( ( irel @ X176 @ ( esk14_2 @ X174 @ X176 ) )
| ~ ( irel @ X176 @ X178 )
| ( p6 @ X178 )
| ~ ( irel @ X174 @ X176 )
| ~ ( p7 @ ( esk13_1 @ X174 ) ) )
& ( ~ ( p7 @ ( esk14_2 @ X174 @ X176 ) )
| ~ ( irel @ X176 @ X178 )
| ( p6 @ X178 )
| ~ ( irel @ X174 @ X176 )
| ~ ( p7 @ ( esk13_1 @ X174 ) ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_119])])])])])]) ).
thf(c_0_122,plain,
! [X2: $i,X1: $i] :
( ( p7 @ X1 )
| ~ ( irel @ X2 @ X1 ) ),
inference(spm,[status(thm)],[c_0_120,c_0_48]) ).
thf(c_0_123,plain,
! [X3: $i,X2: $i,X1: $i] :
( ( p6 @ X3 )
| ~ ( p7 @ ( esk14_2 @ X1 @ X2 ) )
| ~ ( irel @ X2 @ X3 )
| ~ ( irel @ X1 @ X2 )
| ~ ( p7 @ ( esk13_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_121]) ).
thf(c_0_124,plain,
! [X1: $i] : ( p7 @ X1 ),
inference(spm,[status(thm)],[c_0_122,c_0_48]) ).
thf(c_0_125,plain,
! [X67: $i] :
( ~ ! [X65: $i] :
( ( irel @ X67 @ X65 )
=> ( p6 @ X65 ) )
| ! [X66: $i] :
( ( irel @ X67 @ X66 )
=> ( ~ ! [X63: $i] :
( ( irel @ X66 @ X63 )
=> ( p6 @ X63 ) )
| ! [X64: $i] :
( ( irel @ X66 @ X64 )
=> ( p5 @ X64 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[axiom7,c_0_36]),c_0_37]),c_0_38]) ).
thf(c_0_126,plain,
! [X1: $i,X3: $i,X2: $i] :
( ( p6 @ X1 )
| ~ ( irel @ X2 @ X1 )
| ~ ( irel @ X3 @ X2 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_123,c_0_124]),c_0_124])]) ).
thf(c_0_127,plain,
! [X169: $i,X171: $i,X173: $i] :
( ( ( irel @ X171 @ ( esk12_2 @ X169 @ X171 ) )
| ~ ( irel @ X171 @ X173 )
| ( p5 @ X173 )
| ~ ( irel @ X169 @ X171 )
| ( irel @ X169 @ ( esk11_1 @ X169 ) ) )
& ( ~ ( p6 @ ( esk12_2 @ X169 @ X171 ) )
| ~ ( irel @ X171 @ X173 )
| ( p5 @ X173 )
| ~ ( irel @ X169 @ X171 )
| ( irel @ X169 @ ( esk11_1 @ X169 ) ) )
& ( ( irel @ X171 @ ( esk12_2 @ X169 @ X171 ) )
| ~ ( irel @ X171 @ X173 )
| ( p5 @ X173 )
| ~ ( irel @ X169 @ X171 )
| ~ ( p6 @ ( esk11_1 @ X169 ) ) )
& ( ~ ( p6 @ ( esk12_2 @ X169 @ X171 ) )
| ~ ( irel @ X171 @ X173 )
| ( p5 @ X173 )
| ~ ( irel @ X169 @ X171 )
| ~ ( p6 @ ( esk11_1 @ X169 ) ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_125])])])])])]) ).
thf(c_0_128,plain,
! [X2: $i,X1: $i] :
( ( p6 @ X1 )
| ~ ( irel @ X2 @ X1 ) ),
inference(spm,[status(thm)],[c_0_126,c_0_48]) ).
thf(c_0_129,plain,
! [X3: $i,X2: $i,X1: $i] :
( ( p5 @ X3 )
| ~ ( p6 @ ( esk12_2 @ X1 @ X2 ) )
| ~ ( irel @ X2 @ X3 )
| ~ ( irel @ X1 @ X2 )
| ~ ( p6 @ ( esk11_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_127]) ).
thf(c_0_130,plain,
! [X1: $i] : ( p6 @ X1 ),
inference(spm,[status(thm)],[c_0_128,c_0_48]) ).
thf(c_0_131,plain,
! [X62: $i] :
( ~ ! [X60: $i] :
( ( irel @ X62 @ X60 )
=> ( p5 @ X60 ) )
| ! [X61: $i] :
( ( irel @ X62 @ X61 )
=> ( ~ ! [X58: $i] :
( ( irel @ X61 @ X58 )
=> ( p5 @ X58 ) )
| ! [X59: $i] :
( ( irel @ X61 @ X59 )
=> ( p4 @ X59 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[axiom6,c_0_36]),c_0_37]),c_0_38]) ).
thf(c_0_132,plain,
! [X1: $i,X3: $i,X2: $i] :
( ( p5 @ X1 )
| ~ ( irel @ X2 @ X1 )
| ~ ( irel @ X3 @ X2 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_129,c_0_130]),c_0_130])]) ).
thf(c_0_133,plain,
! [X164: $i,X166: $i,X168: $i] :
( ( ( irel @ X166 @ ( esk10_2 @ X164 @ X166 ) )
| ~ ( irel @ X166 @ X168 )
| ( p4 @ X168 )
| ~ ( irel @ X164 @ X166 )
| ( irel @ X164 @ ( esk9_1 @ X164 ) ) )
& ( ~ ( p5 @ ( esk10_2 @ X164 @ X166 ) )
| ~ ( irel @ X166 @ X168 )
| ( p4 @ X168 )
| ~ ( irel @ X164 @ X166 )
| ( irel @ X164 @ ( esk9_1 @ X164 ) ) )
& ( ( irel @ X166 @ ( esk10_2 @ X164 @ X166 ) )
| ~ ( irel @ X166 @ X168 )
| ( p4 @ X168 )
| ~ ( irel @ X164 @ X166 )
| ~ ( p5 @ ( esk9_1 @ X164 ) ) )
& ( ~ ( p5 @ ( esk10_2 @ X164 @ X166 ) )
| ~ ( irel @ X166 @ X168 )
| ( p4 @ X168 )
| ~ ( irel @ X164 @ X166 )
| ~ ( p5 @ ( esk9_1 @ X164 ) ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_131])])])])])]) ).
thf(c_0_134,plain,
! [X2: $i,X1: $i] :
( ( p5 @ X1 )
| ~ ( irel @ X2 @ X1 ) ),
inference(spm,[status(thm)],[c_0_132,c_0_48]) ).
thf(c_0_135,plain,
! [X3: $i,X2: $i,X1: $i] :
( ( p4 @ X3 )
| ~ ( p5 @ ( esk10_2 @ X1 @ X2 ) )
| ~ ( irel @ X2 @ X3 )
| ~ ( irel @ X1 @ X2 )
| ~ ( p5 @ ( esk9_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_133]) ).
thf(c_0_136,plain,
! [X1: $i] : ( p5 @ X1 ),
inference(spm,[status(thm)],[c_0_134,c_0_48]) ).
thf(c_0_137,plain,
! [X57: $i] :
( ~ ! [X55: $i] :
( ( irel @ X57 @ X55 )
=> ( p4 @ X55 ) )
| ! [X56: $i] :
( ( irel @ X57 @ X56 )
=> ( ~ ! [X53: $i] :
( ( irel @ X56 @ X53 )
=> ( p4 @ X53 ) )
| ! [X54: $i] :
( ( irel @ X56 @ X54 )
=> ( p3 @ X54 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[axiom5,c_0_36]),c_0_37]),c_0_38]) ).
thf(c_0_138,plain,
! [X1: $i,X3: $i,X2: $i] :
( ( p4 @ X1 )
| ~ ( irel @ X2 @ X1 )
| ~ ( irel @ X3 @ X2 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_135,c_0_136]),c_0_136])]) ).
thf(c_0_139,plain,
! [X159: $i,X161: $i,X163: $i] :
( ( ( irel @ X161 @ ( esk8_2 @ X159 @ X161 ) )
| ~ ( irel @ X161 @ X163 )
| ( p3 @ X163 )
| ~ ( irel @ X159 @ X161 )
| ( irel @ X159 @ ( esk7_1 @ X159 ) ) )
& ( ~ ( p4 @ ( esk8_2 @ X159 @ X161 ) )
| ~ ( irel @ X161 @ X163 )
| ( p3 @ X163 )
| ~ ( irel @ X159 @ X161 )
| ( irel @ X159 @ ( esk7_1 @ X159 ) ) )
& ( ( irel @ X161 @ ( esk8_2 @ X159 @ X161 ) )
| ~ ( irel @ X161 @ X163 )
| ( p3 @ X163 )
| ~ ( irel @ X159 @ X161 )
| ~ ( p4 @ ( esk7_1 @ X159 ) ) )
& ( ~ ( p4 @ ( esk8_2 @ X159 @ X161 ) )
| ~ ( irel @ X161 @ X163 )
| ( p3 @ X163 )
| ~ ( irel @ X159 @ X161 )
| ~ ( p4 @ ( esk7_1 @ X159 ) ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_137])])])])])]) ).
thf(c_0_140,plain,
! [X2: $i,X1: $i] :
( ( p4 @ X1 )
| ~ ( irel @ X2 @ X1 ) ),
inference(spm,[status(thm)],[c_0_138,c_0_48]) ).
thf(c_0_141,plain,
! [X3: $i,X2: $i,X1: $i] :
( ( p3 @ X3 )
| ~ ( p4 @ ( esk8_2 @ X1 @ X2 ) )
| ~ ( irel @ X2 @ X3 )
| ~ ( irel @ X1 @ X2 )
| ~ ( p4 @ ( esk7_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_139]) ).
thf(c_0_142,plain,
! [X1: $i] : ( p4 @ X1 ),
inference(spm,[status(thm)],[c_0_140,c_0_48]) ).
thf(c_0_143,plain,
! [X52: $i] :
( ~ ! [X50: $i] :
( ( irel @ X52 @ X50 )
=> ( p3 @ X50 ) )
| ! [X51: $i] :
( ( irel @ X52 @ X51 )
=> ( ~ ! [X48: $i] :
( ( irel @ X51 @ X48 )
=> ( p3 @ X48 ) )
| ! [X49: $i] :
( ( irel @ X51 @ X49 )
=> ( p2 @ X49 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[axiom4,c_0_36]),c_0_37]),c_0_38]) ).
thf(c_0_144,plain,
! [X1: $i,X3: $i,X2: $i] :
( ( p3 @ X1 )
| ~ ( irel @ X2 @ X1 )
| ~ ( irel @ X3 @ X2 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_141,c_0_142]),c_0_142])]) ).
thf(c_0_145,plain,
! [X154: $i,X156: $i,X158: $i] :
( ( ( irel @ X156 @ ( esk6_2 @ X154 @ X156 ) )
| ~ ( irel @ X156 @ X158 )
| ( p2 @ X158 )
| ~ ( irel @ X154 @ X156 )
| ( irel @ X154 @ ( esk5_1 @ X154 ) ) )
& ( ~ ( p3 @ ( esk6_2 @ X154 @ X156 ) )
| ~ ( irel @ X156 @ X158 )
| ( p2 @ X158 )
| ~ ( irel @ X154 @ X156 )
| ( irel @ X154 @ ( esk5_1 @ X154 ) ) )
& ( ( irel @ X156 @ ( esk6_2 @ X154 @ X156 ) )
| ~ ( irel @ X156 @ X158 )
| ( p2 @ X158 )
| ~ ( irel @ X154 @ X156 )
| ~ ( p3 @ ( esk5_1 @ X154 ) ) )
& ( ~ ( p3 @ ( esk6_2 @ X154 @ X156 ) )
| ~ ( irel @ X156 @ X158 )
| ( p2 @ X158 )
| ~ ( irel @ X154 @ X156 )
| ~ ( p3 @ ( esk5_1 @ X154 ) ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_143])])])])])]) ).
thf(c_0_146,plain,
! [X2: $i,X1: $i] :
( ( p3 @ X1 )
| ~ ( irel @ X2 @ X1 ) ),
inference(spm,[status(thm)],[c_0_144,c_0_48]) ).
thf(c_0_147,plain,
! [X3: $i,X2: $i,X1: $i] :
( ( p2 @ X3 )
| ~ ( p3 @ ( esk6_2 @ X1 @ X2 ) )
| ~ ( irel @ X2 @ X3 )
| ~ ( irel @ X1 @ X2 )
| ~ ( p3 @ ( esk5_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_145]) ).
thf(c_0_148,plain,
! [X1: $i] : ( p3 @ X1 ),
inference(spm,[status(thm)],[c_0_146,c_0_48]) ).
thf(c_0_149,plain,
! [X47: $i] :
( ~ ! [X45: $i] :
( ( irel @ X47 @ X45 )
=> ( p2 @ X45 ) )
| ! [X46: $i] :
( ( irel @ X47 @ X46 )
=> ( ~ ! [X43: $i] :
( ( irel @ X46 @ X43 )
=> ( p2 @ X43 ) )
| ! [X44: $i] :
( ( irel @ X46 @ X44 )
=> ( p1 @ X44 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[axiom3,c_0_36]),c_0_37]),c_0_38]) ).
thf(c_0_150,plain,
! [X1: $i,X3: $i,X2: $i] :
( ( p2 @ X1 )
| ~ ( irel @ X2 @ X1 )
| ~ ( irel @ X3 @ X2 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_147,c_0_148]),c_0_148])]) ).
thf(c_0_151,plain,
! [X149: $i,X151: $i,X153: $i] :
( ( ( irel @ X151 @ ( esk4_2 @ X149 @ X151 ) )
| ~ ( irel @ X151 @ X153 )
| ( p1 @ X153 )
| ~ ( irel @ X149 @ X151 )
| ( irel @ X149 @ ( esk3_1 @ X149 ) ) )
& ( ~ ( p2 @ ( esk4_2 @ X149 @ X151 ) )
| ~ ( irel @ X151 @ X153 )
| ( p1 @ X153 )
| ~ ( irel @ X149 @ X151 )
| ( irel @ X149 @ ( esk3_1 @ X149 ) ) )
& ( ( irel @ X151 @ ( esk4_2 @ X149 @ X151 ) )
| ~ ( irel @ X151 @ X153 )
| ( p1 @ X153 )
| ~ ( irel @ X149 @ X151 )
| ~ ( p2 @ ( esk3_1 @ X149 ) ) )
& ( ~ ( p2 @ ( esk4_2 @ X149 @ X151 ) )
| ~ ( irel @ X151 @ X153 )
| ( p1 @ X153 )
| ~ ( irel @ X149 @ X151 )
| ~ ( p2 @ ( esk3_1 @ X149 ) ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_149])])])])])]) ).
thf(c_0_152,plain,
! [X2: $i,X1: $i] :
( ( p2 @ X1 )
| ~ ( irel @ X2 @ X1 ) ),
inference(spm,[status(thm)],[c_0_150,c_0_48]) ).
thf(c_0_153,plain,
! [X3: $i,X2: $i,X1: $i] :
( ( p1 @ X3 )
| ~ ( p2 @ ( esk4_2 @ X1 @ X2 ) )
| ~ ( irel @ X2 @ X3 )
| ~ ( irel @ X1 @ X2 )
| ~ ( p2 @ ( esk3_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_151]) ).
thf(c_0_154,plain,
! [X1: $i] : ( p2 @ X1 ),
inference(spm,[status(thm)],[c_0_152,c_0_48]) ).
thf(c_0_155,plain,
! [X42: $i] :
( ~ ! [X40: $i] :
( ( irel @ X42 @ X40 )
=> ( p1 @ X40 ) )
| ! [X41: $i] :
( ( irel @ X42 @ X41 )
=> ( ~ ! [X38: $i] :
( ( irel @ X41 @ X38 )
=> ( p1 @ X38 ) )
| ! [X39: $i] :
( ( irel @ X41 @ X39 )
=> ( p0 @ X39 ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[axiom2,c_0_36]),c_0_37]),c_0_38]) ).
thf(c_0_156,plain,
! [X1: $i,X3: $i,X2: $i] :
( ( p1 @ X1 )
| ~ ( irel @ X2 @ X1 )
| ~ ( irel @ X3 @ X2 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_153,c_0_154]),c_0_154])]) ).
thf(c_0_157,plain,
! [X144: $i,X146: $i,X148: $i] :
( ( ( irel @ X146 @ ( esk2_2 @ X144 @ X146 ) )
| ~ ( irel @ X146 @ X148 )
| ( p0 @ X148 )
| ~ ( irel @ X144 @ X146 )
| ( irel @ X144 @ ( esk1_1 @ X144 ) ) )
& ( ~ ( p1 @ ( esk2_2 @ X144 @ X146 ) )
| ~ ( irel @ X146 @ X148 )
| ( p0 @ X148 )
| ~ ( irel @ X144 @ X146 )
| ( irel @ X144 @ ( esk1_1 @ X144 ) ) )
& ( ( irel @ X146 @ ( esk2_2 @ X144 @ X146 ) )
| ~ ( irel @ X146 @ X148 )
| ( p0 @ X148 )
| ~ ( irel @ X144 @ X146 )
| ~ ( p1 @ ( esk1_1 @ X144 ) ) )
& ( ~ ( p1 @ ( esk2_2 @ X144 @ X146 ) )
| ~ ( irel @ X146 @ X148 )
| ( p0 @ X148 )
| ~ ( irel @ X144 @ X146 )
| ~ ( p1 @ ( esk1_1 @ X144 ) ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_155])])])])])]) ).
thf(c_0_158,plain,
! [X2: $i,X1: $i] :
( ( p1 @ X1 )
| ~ ( irel @ X2 @ X1 ) ),
inference(spm,[status(thm)],[c_0_156,c_0_48]) ).
thf(c_0_159,plain,
! [X3: $i,X2: $i,X1: $i] :
( ( p0 @ X3 )
| ~ ( p1 @ ( esk2_2 @ X1 @ X2 ) )
| ~ ( irel @ X2 @ X3 )
| ~ ( irel @ X1 @ X2 )
| ~ ( p1 @ ( esk1_1 @ X1 ) ) ),
inference(split_conjunct,[status(thm)],[c_0_157]) ).
thf(c_0_160,plain,
! [X1: $i] : ( p1 @ X1 ),
inference(spm,[status(thm)],[c_0_158,c_0_48]) ).
thf(c_0_161,negated_conjecture,
~ ! [X138: $i] : ( p0 @ X138 ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[con]),c_0_36]),c_0_38]) ).
thf(c_0_162,plain,
! [X1: $i,X3: $i,X2: $i] :
( ( p0 @ X1 )
| ~ ( irel @ X2 @ X1 )
| ~ ( irel @ X3 @ X2 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_159,c_0_160]),c_0_160])]) ).
thf(c_0_163,negated_conjecture,
~ ( p0 @ esk41_0 ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_161])])])]) ).
thf(c_0_164,plain,
! [X2: $i,X1: $i] :
( ( p0 @ X1 )
| ~ ( irel @ X2 @ X1 ) ),
inference(spm,[status(thm)],[c_0_162,c_0_48]) ).
thf(c_0_165,negated_conjecture,
~ ( p0 @ esk41_0 ),
inference(split_conjunct,[status(thm)],[c_0_163]) ).
thf(c_0_166,plain,
! [X1: $i] : ( p0 @ X1 ),
inference(spm,[status(thm)],[c_0_164,c_0_48]) ).
thf(c_0_167,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_165,c_0_166])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SYO068^4.020 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.14 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n025.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon May 20 08:50:53 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.21/0.48 Running higher-order theorem proving
% 0.21/0.48 Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.37/0.53 # Version: 3.1.0-ho
% 0.37/0.53 # Preprocessing class: HSMSSMSSMLSNHSN.
% 0.37/0.53 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.37/0.53 # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.37/0.53 # Starting post_as_ho3 with 300s (1) cores
% 0.37/0.53 # Starting post_as_ho11 with 300s (1) cores
% 0.37/0.53 # Starting full_lambda_8 with 300s (1) cores
% 0.37/0.53 # post_as_ho3 with pid 24167 completed with status 0
% 0.37/0.53 # Result found by post_as_ho3
% 0.37/0.53 # Preprocessing class: HSMSSMSSMLSNHSN.
% 0.37/0.53 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.37/0.53 # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.37/0.53 # Starting post_as_ho3 with 300s (1) cores
% 0.37/0.53 # No SInE strategy applied
% 0.37/0.53 # Search class: HGUNS-FSMF21-SHSSMFNN
% 0.37/0.53 # partial match(1): HGUNS-FFMF21-SHSSMFNN
% 0.37/0.53 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.37/0.53 # Starting new_ho_10 with 163s (1) cores
% 0.37/0.53 # new_ho_10 with pid 24171 completed with status 0
% 0.37/0.53 # Result found by new_ho_10
% 0.37/0.53 # Preprocessing class: HSMSSMSSMLSNHSN.
% 0.37/0.53 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.37/0.53 # Starting new_ho_10_cnf2 with 1500s (5) cores
% 0.37/0.53 # Starting post_as_ho3 with 300s (1) cores
% 0.37/0.53 # No SInE strategy applied
% 0.37/0.53 # Search class: HGUNS-FSMF21-SHSSMFNN
% 0.37/0.53 # partial match(1): HGUNS-FFMF21-SHSSMFNN
% 0.37/0.53 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.37/0.53 # Starting new_ho_10 with 163s (1) cores
% 0.37/0.53 # Preprocessing time : 0.004 s
% 0.37/0.53 # Presaturation interreduction done
% 0.37/0.53
% 0.37/0.53 # Proof found!
% 0.37/0.53 # SZS status Theorem
% 0.37/0.53 # SZS output start CNFRefutation
% See solution above
% 0.37/0.53 # Parsed axioms : 84
% 0.37/0.53 # Removed by relevancy pruning/SinE : 0
% 0.37/0.53 # Initial clauses : 125
% 0.37/0.53 # Removed in clause preprocessing : 41
% 0.37/0.53 # Initial clauses in saturation : 84
% 0.37/0.53 # Processed clauses : 215
% 0.37/0.53 # ...of these trivial : 26
% 0.37/0.53 # ...subsumed : 13
% 0.37/0.53 # ...remaining for further processing : 176
% 0.37/0.53 # Other redundant clauses eliminated : 0
% 0.37/0.53 # Clauses deleted for lack of memory : 0
% 0.37/0.53 # Backward-subsumed : 21
% 0.37/0.53 # Backward-rewritten : 51
% 0.37/0.53 # Generated clauses : 52
% 0.37/0.53 # ...of the previous two non-redundant : 81
% 0.37/0.53 # ...aggressively subsumed : 0
% 0.37/0.53 # Contextual simplify-reflections : 0
% 0.37/0.53 # Paramodulations : 52
% 0.37/0.53 # Factorizations : 0
% 0.37/0.53 # NegExts : 0
% 0.37/0.53 # Equation resolutions : 0
% 0.37/0.53 # Disequality decompositions : 0
% 0.37/0.53 # Total rewrite steps : 125
% 0.37/0.53 # ...of those cached : 20
% 0.37/0.53 # Propositional unsat checks : 0
% 0.37/0.53 # Propositional check models : 0
% 0.37/0.53 # Propositional check unsatisfiable : 0
% 0.37/0.53 # Propositional clauses : 0
% 0.37/0.53 # Propositional clauses after purity: 0
% 0.37/0.53 # Propositional unsat core size : 0
% 0.37/0.53 # Propositional preprocessing time : 0.000
% 0.37/0.53 # Propositional encoding time : 0.000
% 0.37/0.53 # Propositional solver time : 0.000
% 0.37/0.53 # Success case prop preproc time : 0.000
% 0.37/0.53 # Success case prop encoding time : 0.000
% 0.37/0.53 # Success case prop solver time : 0.000
% 0.37/0.53 # Current number of processed clauses : 23
% 0.37/0.53 # Positive orientable unit clauses : 22
% 0.37/0.53 # Positive unorientable unit clauses: 0
% 0.37/0.53 # Negative unit clauses : 0
% 0.37/0.53 # Non-unit-clauses : 1
% 0.37/0.53 # Current number of unprocessed clauses: 31
% 0.37/0.53 # ...number of literals in the above : 144
% 0.37/0.53 # Current number of archived formulas : 0
% 0.37/0.53 # Current number of archived clauses : 153
% 0.37/0.53 # Clause-clause subsumption calls (NU) : 1964
% 0.37/0.53 # Rec. Clause-clause subsumption calls : 400
% 0.37/0.53 # Non-unit clause-clause subsumptions : 34
% 0.37/0.53 # Unit Clause-clause subsumption calls : 196
% 0.37/0.53 # Rewrite failures with RHS unbound : 0
% 0.37/0.53 # BW rewrite match attempts : 59
% 0.37/0.53 # BW rewrite match successes : 59
% 0.37/0.53 # Condensation attempts : 228
% 0.37/0.53 # Condensation successes : 0
% 0.37/0.53 # Termbank termtop insertions : 15088
% 0.37/0.53 # Search garbage collected termcells : 4163
% 0.37/0.53
% 0.37/0.53 # -------------------------------------------------
% 0.37/0.53 # User time : 0.028 s
% 0.37/0.53 # System time : 0.006 s
% 0.37/0.53 # Total time : 0.034 s
% 0.37/0.53 # Maximum resident set size: 2496 pages
% 0.37/0.53
% 0.37/0.53 # -------------------------------------------------
% 0.37/0.53 # User time : 0.029 s
% 0.37/0.53 # System time : 0.009 s
% 0.37/0.53 # Total time : 0.039 s
% 0.37/0.53 # Maximum resident set size: 1784 pages
% 0.37/0.53 % E---3.1 exiting
% 0.37/0.53 % E exiting
%------------------------------------------------------------------------------