TSTP Solution File: SYO069^4.001 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SYO069^4.001 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n021.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 08:44:32 EDT 2024
% Result : Theorem 55.51s 7.47s
% Output : CNFRefutation 55.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 44
% Syntax : Number of formulae : 175 ( 29 unt; 30 typ; 0 def)
% Number of atoms : 713 ( 21 equ; 0 cnn)
% Maximal formula atoms : 54 ( 4 avg)
% Number of connectives : 1920 ( 316 ~; 403 |; 40 &;1106 @)
% ( 2 <=>; 53 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 89 ( 89 >; 0 *; 0 +; 0 <<)
% Number of symbols : 32 ( 30 usr; 4 con; 0-3 aty)
% Number of variables : 306 ( 48 ^ 258 !; 0 ?; 306 :)
% 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_25,type,
mand: ( $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_32,type,
iand: ( $i > $o ) > ( $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,
a0: $i > $o ).
thf(decl_43,type,
a1: $i > $o ).
thf(decl_44,type,
b0: $i > $o ).
thf(decl_45,type,
b1: $i > $o ).
thf(decl_46,type,
f: $i > $o ).
thf(decl_47,type,
epred1_1: $i > $o ).
thf(decl_48,type,
epred2_1: $i > $o ).
thf(decl_49,type,
esk1_0: $i ).
thf(decl_50,type,
esk2_0: $i ).
thf(decl_51,type,
esk3_0: $i ).
thf(decl_52,type,
esk4_1: $i > $i ).
thf(decl_53,type,
esk5_1: $i > $i ).
thf(decl_54,type,
esk6_1: $i > $i ).
thf(decl_55,type,
esk7_1: $i > $i ).
thf(decl_56,type,
esk8_1: $i > $i ).
thf(decl_57,type,
esk9_1: $i > $i ).
thf(decl_58,type,
esk10_1: $i > $i ).
thf(decl_59,type,
esk11_1: $i > $i ).
thf(decl_60,type,
esk12_1: $i > $i ).
thf(decl_61,type,
esk13_1: $i > $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(refl_axiom,axiom,
! [X1: $i] : ( irel @ X1 @ X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',refl_axiom) ).
thf(trans_axiom,axiom,
! [X1: $i,X2: $i,X3: $i] :
( ( ( irel @ X1 @ X2 )
& ( irel @ X2 @ X3 ) )
=> ( irel @ X1 @ X3 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',trans_axiom) ).
thf(iand,axiom,
( iand
= ( ^ [X12: $i > $o,X14: $i > $o] : ( mand @ X12 @ X14 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',iand) ).
thf(mand,axiom,
( mand
= ( ^ [X8: $i > $o,X9: $i > $o,X5: $i] :
( ( X8 @ X5 )
& ( X9 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',mand) ).
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(con,conjecture,
ivalid @ ( iand @ ( iimplies @ ( iand @ ( iimplies @ ( iatom @ a0 ) @ ( iatom @ f ) ) @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b1 ) @ ( iatom @ b0 ) ) @ ( iatom @ a1 ) ) @ ( iimplies @ ( iimplies @ ( iatom @ b0 ) @ ( iatom @ a1 ) ) @ ( iatom @ a0 ) ) ) ) @ ( iatom @ f ) ) @ ( iimplies @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b0 ) @ ( iatom @ a1 ) ) @ ( iatom @ a0 ) ) @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b1 ) @ ( iatom @ b0 ) ) @ ( iatom @ a1 ) ) @ ( iimplies @ ( iatom @ a0 ) @ ( iatom @ f ) ) ) ) @ ( iatom @ f ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
thf(c_0_12,plain,
! [X59: $i] :
( ( epred2_1 @ X59 )
<=> ( ( ~ ! [X51: $i] :
( ( irel @ X59 @ X51 )
=> ( ~ ! [X49: $i] :
( ( irel @ X51 @ X49 )
=> ( b0 @ X49 ) )
| ! [X50: $i] :
( ( irel @ X51 @ X50 )
=> ( a1 @ X50 ) ) ) )
| ! [X52: $i] :
( ( irel @ X59 @ X52 )
=> ( a0 @ X52 ) ) )
& ( ~ ! [X55: $i] :
( ( irel @ X59 @ X55 )
=> ( ~ ! [X53: $i] :
( ( irel @ X55 @ X53 )
=> ( b1 @ X53 ) )
| ! [X54: $i] :
( ( irel @ X55 @ X54 )
=> ( b0 @ X54 ) ) ) )
| ! [X56: $i] :
( ( irel @ X59 @ X56 )
=> ( a1 @ X56 ) ) )
& ( ~ ! [X57: $i] :
( ( irel @ X59 @ X57 )
=> ( a0 @ X57 ) )
| ! [X58: $i] :
( ( irel @ X59 @ X58 )
=> ( f @ X58 ) ) ) ) ),
introduced(definition) ).
thf(c_0_13,plain,
! [X47: $i] :
( ( epred1_1 @ X47 )
<=> ( ( ~ ! [X37: $i] :
( ( irel @ X47 @ X37 )
=> ( a0 @ X37 ) )
| ! [X38: $i] :
( ( irel @ X47 @ X38 )
=> ( f @ X38 ) ) )
& ( ~ ! [X41: $i] :
( ( irel @ X47 @ X41 )
=> ( ~ ! [X39: $i] :
( ( irel @ X41 @ X39 )
=> ( b1 @ X39 ) )
| ! [X40: $i] :
( ( irel @ X41 @ X40 )
=> ( b0 @ X40 ) ) ) )
| ! [X42: $i] :
( ( irel @ X47 @ X42 )
=> ( a1 @ X42 ) ) )
& ( ~ ! [X45: $i] :
( ( irel @ X47 @ X45 )
=> ( ~ ! [X43: $i] :
( ( irel @ X45 @ X43 )
=> ( b0 @ X43 ) )
| ! [X44: $i] :
( ( irel @ X45 @ X44 )
=> ( a1 @ X44 ) ) ) )
| ! [X46: $i] :
( ( irel @ X47 @ X46 )
=> ( a0 @ X46 ) ) ) ) ),
introduced(definition) ).
thf(c_0_14,plain,
! [X59: $i] :
( ( epred2_1 @ X59 )
=> ( ( ~ ! [X51: $i] :
( ( irel @ X59 @ X51 )
=> ( ~ ! [X49: $i] :
( ( irel @ X51 @ X49 )
=> ( b0 @ X49 ) )
| ! [X50: $i] :
( ( irel @ X51 @ X50 )
=> ( a1 @ X50 ) ) ) )
| ! [X52: $i] :
( ( irel @ X59 @ X52 )
=> ( a0 @ X52 ) ) )
& ( ~ ! [X55: $i] :
( ( irel @ X59 @ X55 )
=> ( ~ ! [X53: $i] :
( ( irel @ X55 @ X53 )
=> ( b1 @ X53 ) )
| ! [X54: $i] :
( ( irel @ X55 @ X54 )
=> ( b0 @ X54 ) ) ) )
| ! [X56: $i] :
( ( irel @ X59 @ X56 )
=> ( a1 @ X56 ) ) )
& ( ~ ! [X57: $i] :
( ( irel @ X59 @ X57 )
=> ( a0 @ X57 ) )
| ! [X58: $i] :
( ( irel @ X59 @ X58 )
=> ( f @ X58 ) ) ) ) ),
inference(split_equiv,[status(thm)],[c_0_12]) ).
thf(c_0_15,plain,
! [X47: $i] :
( ( epred1_1 @ X47 )
=> ( ( ~ ! [X37: $i] :
( ( irel @ X47 @ X37 )
=> ( a0 @ X37 ) )
| ! [X38: $i] :
( ( irel @ X47 @ X38 )
=> ( f @ X38 ) ) )
& ( ~ ! [X41: $i] :
( ( irel @ X47 @ X41 )
=> ( ~ ! [X39: $i] :
( ( irel @ X41 @ X39 )
=> ( b1 @ X39 ) )
| ! [X40: $i] :
( ( irel @ X41 @ X40 )
=> ( b0 @ X40 ) ) ) )
| ! [X42: $i] :
( ( irel @ X47 @ X42 )
=> ( a1 @ X42 ) ) )
& ( ~ ! [X45: $i] :
( ( irel @ X47 @ X45 )
=> ( ~ ! [X43: $i] :
( ( irel @ X45 @ X43 )
=> ( b0 @ X43 ) )
| ! [X44: $i] :
( ( irel @ X45 @ X44 )
=> ( a1 @ X44 ) ) ) )
| ! [X46: $i] :
( ( irel @ X47 @ X46 )
=> ( a0 @ X46 ) ) ) ) ),
inference(split_equiv,[status(thm)],[c_0_13]) ).
thf(c_0_16,plain,
( mimplies
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ~ ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mimplies]) ).
thf(c_0_17,plain,
( mnot
= ( ^ [Z0: $i > $o,Z1: $i] :
~ ( Z0 @ Z1 ) ) ),
inference(fof_simplification,[status(thm)],[mnot]) ).
thf(c_0_18,plain,
( mor
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
| ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mor]) ).
thf(c_0_19,plain,
! [X82: $i,X84: $i,X86: $i,X88: $i,X90: $i,X92: $i] :
( ( ( irel @ X82 @ ( esk9_1 @ X82 ) )
| ~ ( irel @ X82 @ X86 )
| ( a0 @ X86 )
| ~ ( epred2_1 @ X82 ) )
& ( ~ ( irel @ ( esk9_1 @ X82 ) @ X84 )
| ( b0 @ X84 )
| ~ ( irel @ X82 @ X86 )
| ( a0 @ X86 )
| ~ ( epred2_1 @ X82 ) )
& ( ( irel @ ( esk9_1 @ X82 ) @ ( esk10_1 @ X82 ) )
| ~ ( irel @ X82 @ X86 )
| ( a0 @ X86 )
| ~ ( epred2_1 @ X82 ) )
& ( ~ ( a1 @ ( esk10_1 @ X82 ) )
| ~ ( irel @ X82 @ X86 )
| ( a0 @ X86 )
| ~ ( epred2_1 @ X82 ) )
& ( ( irel @ X82 @ ( esk11_1 @ X82 ) )
| ~ ( irel @ X82 @ X90 )
| ( a1 @ X90 )
| ~ ( epred2_1 @ X82 ) )
& ( ~ ( irel @ ( esk11_1 @ X82 ) @ X88 )
| ( b1 @ X88 )
| ~ ( irel @ X82 @ X90 )
| ( a1 @ X90 )
| ~ ( epred2_1 @ X82 ) )
& ( ( irel @ ( esk11_1 @ X82 ) @ ( esk12_1 @ X82 ) )
| ~ ( irel @ X82 @ X90 )
| ( a1 @ X90 )
| ~ ( epred2_1 @ X82 ) )
& ( ~ ( b0 @ ( esk12_1 @ X82 ) )
| ~ ( irel @ X82 @ X90 )
| ( a1 @ X90 )
| ~ ( epred2_1 @ X82 ) )
& ( ( irel @ X82 @ ( esk13_1 @ X82 ) )
| ~ ( irel @ X82 @ X92 )
| ( f @ X92 )
| ~ ( epred2_1 @ X82 ) )
& ( ~ ( a0 @ ( esk13_1 @ X82 ) )
| ~ ( irel @ X82 @ X92 )
| ( f @ X92 )
| ~ ( epred2_1 @ X82 ) ) ),
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_14])])])])])]) ).
thf(c_0_20,plain,
! [X62: $i] : ( irel @ X62 @ X62 ),
inference(variable_rename,[status(thm)],[refl_axiom]) ).
thf(c_0_21,plain,
! [X63: $i,X64: $i,X65: $i] :
( ~ ( irel @ X63 @ X64 )
| ~ ( irel @ X64 @ X65 )
| ( irel @ X63 @ X65 ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[trans_axiom])])]) ).
thf(c_0_22,plain,
! [X71: $i,X73: $i,X75: $i,X77: $i,X79: $i,X81: $i] :
( ( ( irel @ X71 @ ( esk4_1 @ X71 ) )
| ~ ( irel @ X71 @ X73 )
| ( f @ X73 )
| ~ ( epred1_1 @ X71 ) )
& ( ~ ( a0 @ ( esk4_1 @ X71 ) )
| ~ ( irel @ X71 @ X73 )
| ( f @ X73 )
| ~ ( epred1_1 @ X71 ) )
& ( ( irel @ X71 @ ( esk5_1 @ X71 ) )
| ~ ( irel @ X71 @ X77 )
| ( a1 @ X77 )
| ~ ( epred1_1 @ X71 ) )
& ( ~ ( irel @ ( esk5_1 @ X71 ) @ X75 )
| ( b1 @ X75 )
| ~ ( irel @ X71 @ X77 )
| ( a1 @ X77 )
| ~ ( epred1_1 @ X71 ) )
& ( ( irel @ ( esk5_1 @ X71 ) @ ( esk6_1 @ X71 ) )
| ~ ( irel @ X71 @ X77 )
| ( a1 @ X77 )
| ~ ( epred1_1 @ X71 ) )
& ( ~ ( b0 @ ( esk6_1 @ X71 ) )
| ~ ( irel @ X71 @ X77 )
| ( a1 @ X77 )
| ~ ( epred1_1 @ X71 ) )
& ( ( irel @ X71 @ ( esk7_1 @ X71 ) )
| ~ ( irel @ X71 @ X81 )
| ( a0 @ X81 )
| ~ ( epred1_1 @ X71 ) )
& ( ~ ( irel @ ( esk7_1 @ X71 ) @ X79 )
| ( b0 @ X79 )
| ~ ( irel @ X71 @ X81 )
| ( a0 @ X81 )
| ~ ( epred1_1 @ X71 ) )
& ( ( irel @ ( esk7_1 @ X71 ) @ ( esk8_1 @ X71 ) )
| ~ ( irel @ X71 @ X81 )
| ( a0 @ X81 )
| ~ ( epred1_1 @ X71 ) )
& ( ~ ( a1 @ ( esk8_1 @ X71 ) )
| ~ ( irel @ X71 @ X81 )
| ( a0 @ X81 )
| ~ ( epred1_1 @ X71 ) ) ),
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_15])])])])])]) ).
thf(c_0_23,plain,
( iand
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
& ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[iand]) ).
thf(c_0_24,plain,
( mand
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
& ( Z1 @ Z2 ) ) ) ),
inference(fof_simplification,[status(thm)],[mand]) ).
thf(c_0_25,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_26,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_16,c_0_17]),c_0_18]) ).
thf(c_0_27,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_28,plain,
! [X3: $i,X2: $i,X1: $i] :
( ( b0 @ X2 )
| ( a0 @ X3 )
| ~ ( irel @ ( esk9_1 @ X1 ) @ X2 )
| ~ ( irel @ X1 @ X3 )
| ~ ( epred2_1 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_29,plain,
! [X1: $i] : ( irel @ X1 @ X1 ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_30,plain,
! [X1: $i,X2: $i,X3: $i] :
( ( irel @ X1 @ X3 )
| ~ ( irel @ X1 @ X2 )
| ~ ( irel @ X2 @ X3 ) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_31,plain,
! [X2: $i,X1: $i] :
( ( irel @ ( esk9_1 @ X1 ) @ ( esk10_1 @ X1 ) )
| ( a0 @ X2 )
| ~ ( irel @ X1 @ X2 )
| ~ ( epred2_1 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_32,plain,
! [X2: $i,X1: $i] :
( ( irel @ ( esk11_1 @ X1 ) @ ( esk12_1 @ X1 ) )
| ( a1 @ X2 )
| ~ ( irel @ X1 @ X2 )
| ~ ( epred2_1 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_33,plain,
! [X3: $i,X2: $i,X1: $i] :
( ( b0 @ X2 )
| ( a0 @ X3 )
| ~ ( irel @ ( esk7_1 @ X1 ) @ X2 )
| ~ ( irel @ X1 @ X3 )
| ~ ( epred1_1 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_34,plain,
! [X2: $i,X1: $i] :
( ( irel @ ( esk7_1 @ X1 ) @ ( esk8_1 @ X1 ) )
| ( a0 @ X2 )
| ~ ( irel @ X1 @ X2 )
| ~ ( epred1_1 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_35,plain,
! [X2: $i,X1: $i] :
( ( irel @ ( esk5_1 @ X1 ) @ ( esk6_1 @ X1 ) )
| ( a1 @ X2 )
| ~ ( irel @ X1 @ X2 )
| ~ ( epred1_1 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_36,plain,
( iatom
= ( ^ [Z0: $i > $o] : Z0 ) ),
inference(fof_simplification,[status(thm)],[iatom]) ).
thf(c_0_37,plain,
( iand
= ( ^ [Z0: $i > $o,Z1: $i > $o,Z2: $i] :
( ( Z0 @ Z2 )
& ( Z1 @ Z2 ) ) ) ),
inference(apply_def,[status(thm)],[c_0_23,c_0_24]) ).
thf(c_0_38,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_25,c_0_26]),c_0_27]) ).
thf(c_0_39,plain,
( ivalid
= ( ^ [Z0: $i > $o] :
! [X13: $i] : ( Z0 @ X13 ) ) ),
inference(fof_simplification,[status(thm)],[ivalid]) ).
thf(c_0_40,plain,
! [X2: $i,X1: $i] :
( ( a1 @ X2 )
| ~ ( b0 @ ( esk12_1 @ X1 ) )
| ~ ( irel @ X1 @ X2 )
| ~ ( epred2_1 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_41,plain,
! [X2: $i,X1: $i] :
( ( a0 @ X1 )
| ( b0 @ X2 )
| ~ ( irel @ ( esk9_1 @ X1 ) @ X2 )
| ~ ( epred2_1 @ X1 ) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
thf(c_0_42,plain,
! [X3: $i,X2: $i,X1: $i] :
( ( irel @ ( esk9_1 @ X1 ) @ X2 )
| ( a0 @ X3 )
| ~ ( irel @ ( esk10_1 @ X1 ) @ X2 )
| ~ ( irel @ X1 @ X3 )
| ~ ( epred2_1 @ X1 ) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
thf(c_0_43,plain,
! [X2: $i,X1: $i] :
( ( irel @ X1 @ ( esk11_1 @ X1 ) )
| ( a1 @ X2 )
| ~ ( irel @ X1 @ X2 )
| ~ ( epred2_1 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_44,plain,
! [X3: $i,X2: $i,X1: $i] :
( ( irel @ ( esk11_1 @ X1 ) @ X2 )
| ( a1 @ X3 )
| ~ ( irel @ ( esk12_1 @ X1 ) @ X2 )
| ~ ( irel @ X1 @ X3 )
| ~ ( epred2_1 @ X1 ) ),
inference(spm,[status(thm)],[c_0_30,c_0_32]) ).
thf(c_0_45,plain,
! [X2: $i,X1: $i] :
( ( a1 @ X2 )
| ~ ( b0 @ ( esk6_1 @ X1 ) )
| ~ ( irel @ X1 @ X2 )
| ~ ( epred1_1 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_46,plain,
! [X2: $i,X1: $i] :
( ( a0 @ X1 )
| ( b0 @ X2 )
| ~ ( irel @ ( esk7_1 @ X1 ) @ X2 )
| ~ ( epred1_1 @ X1 ) ),
inference(spm,[status(thm)],[c_0_33,c_0_29]) ).
thf(c_0_47,plain,
! [X3: $i,X2: $i,X1: $i] :
( ( irel @ ( esk7_1 @ X1 ) @ X2 )
| ( a0 @ X3 )
| ~ ( irel @ ( esk8_1 @ X1 ) @ X2 )
| ~ ( irel @ X1 @ X3 )
| ~ ( epred1_1 @ X1 ) ),
inference(spm,[status(thm)],[c_0_30,c_0_34]) ).
thf(c_0_48,plain,
! [X2: $i,X1: $i] :
( ( irel @ X1 @ ( esk5_1 @ X1 ) )
| ( a1 @ X2 )
| ~ ( irel @ X1 @ X2 )
| ~ ( epred1_1 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_49,plain,
! [X3: $i,X2: $i,X1: $i] :
( ( irel @ ( esk5_1 @ X1 ) @ X2 )
| ( a1 @ X3 )
| ~ ( irel @ ( esk6_1 @ X1 ) @ X2 )
| ~ ( irel @ X1 @ X3 )
| ~ ( epred1_1 @ X1 ) ),
inference(spm,[status(thm)],[c_0_30,c_0_35]) ).
thf(c_0_50,negated_conjecture,
~ ! [X61: $i] :
( ( ~ ! [X47: $i] :
( ( irel @ X61 @ X47 )
=> ( epred1_1 @ X47 ) )
| ! [X48: $i] :
( ( irel @ X61 @ X48 )
=> ( f @ X48 ) ) )
& ( ~ ! [X59: $i] :
( ( irel @ X61 @ X59 )
=> ( epred2_1 @ X59 ) )
| ! [X60: $i] :
( ( irel @ X61 @ X60 )
=> ( f @ X60 ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[con]),c_0_36]),c_0_37]),c_0_38]),c_0_39]),c_0_13]),c_0_12]) ).
thf(c_0_51,plain,
! [X1: $i] :
( ( a1 @ X1 )
| ~ ( b0 @ ( esk12_1 @ X1 ) )
| ~ ( epred2_1 @ X1 ) ),
inference(spm,[status(thm)],[c_0_40,c_0_29]) ).
thf(c_0_52,plain,
! [X1: $i,X3: $i,X2: $i] :
( ( b0 @ X1 )
| ( a0 @ X2 )
| ~ ( irel @ ( esk9_1 @ X2 ) @ X3 )
| ~ ( irel @ X3 @ X1 )
| ~ ( epred2_1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_41,c_0_30]) ).
thf(c_0_53,plain,
! [X2: $i,X1: $i] :
( ( irel @ ( esk9_1 @ X1 ) @ X2 )
| ( a0 @ X1 )
| ~ ( irel @ ( esk10_1 @ X1 ) @ X2 )
| ~ ( epred2_1 @ X1 ) ),
inference(spm,[status(thm)],[c_0_42,c_0_29]) ).
thf(c_0_54,plain,
! [X3: $i,X2: $i,X1: $i] :
( ( irel @ X1 @ X2 )
| ( a1 @ X3 )
| ~ ( irel @ ( esk11_1 @ X1 ) @ X2 )
| ~ ( irel @ X1 @ X3 )
| ~ ( epred2_1 @ X1 ) ),
inference(spm,[status(thm)],[c_0_30,c_0_43]) ).
thf(c_0_55,plain,
! [X2: $i,X1: $i] :
( ( irel @ ( esk11_1 @ X1 ) @ X2 )
| ( a1 @ X1 )
| ~ ( irel @ ( esk12_1 @ X1 ) @ X2 )
| ~ ( epred2_1 @ X1 ) ),
inference(spm,[status(thm)],[c_0_44,c_0_29]) ).
thf(c_0_56,plain,
! [X2: $i,X1: $i] :
( ( irel @ X1 @ ( esk9_1 @ X1 ) )
| ( a0 @ X2 )
| ~ ( irel @ X1 @ X2 )
| ~ ( epred2_1 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_57,plain,
! [X1: $i] :
( ( a1 @ X1 )
| ~ ( b0 @ ( esk6_1 @ X1 ) )
| ~ ( epred1_1 @ X1 ) ),
inference(spm,[status(thm)],[c_0_45,c_0_29]) ).
thf(c_0_58,plain,
! [X1: $i,X3: $i,X2: $i] :
( ( b0 @ X1 )
| ( a0 @ X2 )
| ~ ( irel @ ( esk7_1 @ X2 ) @ X3 )
| ~ ( irel @ X3 @ X1 )
| ~ ( epred1_1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_46,c_0_30]) ).
thf(c_0_59,plain,
! [X2: $i,X1: $i] :
( ( irel @ ( esk7_1 @ X1 ) @ X2 )
| ( a0 @ X1 )
| ~ ( irel @ ( esk8_1 @ X1 ) @ X2 )
| ~ ( epred1_1 @ X1 ) ),
inference(spm,[status(thm)],[c_0_47,c_0_29]) ).
thf(c_0_60,plain,
! [X3: $i,X2: $i,X1: $i] :
( ( irel @ X1 @ X2 )
| ( a1 @ X3 )
| ~ ( irel @ ( esk5_1 @ X1 ) @ X2 )
| ~ ( irel @ X1 @ X3 )
| ~ ( epred1_1 @ X1 ) ),
inference(spm,[status(thm)],[c_0_30,c_0_48]) ).
thf(c_0_61,plain,
! [X2: $i,X1: $i] :
( ( irel @ ( esk5_1 @ X1 ) @ X2 )
| ( a1 @ X1 )
| ~ ( irel @ ( esk6_1 @ X1 ) @ X2 )
| ~ ( epred1_1 @ X1 ) ),
inference(spm,[status(thm)],[c_0_49,c_0_29]) ).
thf(c_0_62,plain,
! [X2: $i,X1: $i] :
( ( irel @ X1 @ ( esk7_1 @ X1 ) )
| ( a0 @ X2 )
| ~ ( irel @ X1 @ X2 )
| ~ ( epred1_1 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_63,negated_conjecture,
! [X67: $i,X69: $i] :
( ( ~ ( irel @ esk1_0 @ X69 )
| ( epred2_1 @ X69 )
| ~ ( irel @ esk1_0 @ X67 )
| ( epred1_1 @ X67 ) )
& ( ( irel @ esk1_0 @ esk3_0 )
| ~ ( irel @ esk1_0 @ X67 )
| ( epred1_1 @ X67 ) )
& ( ~ ( f @ esk3_0 )
| ~ ( irel @ esk1_0 @ X67 )
| ( epred1_1 @ X67 ) )
& ( ~ ( irel @ esk1_0 @ X69 )
| ( epred2_1 @ X69 )
| ( irel @ esk1_0 @ esk2_0 ) )
& ( ( irel @ esk1_0 @ esk3_0 )
| ( irel @ esk1_0 @ esk2_0 ) )
& ( ~ ( f @ esk3_0 )
| ( irel @ esk1_0 @ esk2_0 ) )
& ( ~ ( irel @ esk1_0 @ X69 )
| ( epred2_1 @ X69 )
| ~ ( f @ esk2_0 ) )
& ( ( irel @ esk1_0 @ esk3_0 )
| ~ ( f @ esk2_0 ) )
& ( ~ ( f @ esk3_0 )
| ~ ( f @ esk2_0 ) ) ),
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_50])])])])])]) ).
thf(c_0_64,plain,
! [X3: $i,X2: $i,X1: $i] :
( ( a0 @ X1 )
| ( a1 @ X2 )
| ~ ( irel @ ( esk9_1 @ X1 ) @ X3 )
| ~ ( irel @ X3 @ ( esk12_1 @ X2 ) )
| ~ ( epred2_1 @ X2 )
| ~ ( epred2_1 @ X1 ) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
thf(c_0_65,plain,
! [X1: $i] :
( ( irel @ ( esk9_1 @ X1 ) @ ( esk10_1 @ X1 ) )
| ( a0 @ X1 )
| ~ ( epred2_1 @ X1 ) ),
inference(spm,[status(thm)],[c_0_53,c_0_29]) ).
thf(c_0_66,plain,
! [X2: $i,X1: $i] :
( ( irel @ X1 @ X2 )
| ( a1 @ X1 )
| ~ ( irel @ ( esk11_1 @ X1 ) @ X2 )
| ~ ( epred2_1 @ X1 ) ),
inference(spm,[status(thm)],[c_0_54,c_0_29]) ).
thf(c_0_67,plain,
! [X1: $i] :
( ( irel @ ( esk11_1 @ X1 ) @ ( esk12_1 @ X1 ) )
| ( a1 @ X1 )
| ~ ( epred2_1 @ X1 ) ),
inference(spm,[status(thm)],[c_0_55,c_0_29]) ).
thf(c_0_68,plain,
! [X2: $i,X1: $i] :
( ( a0 @ X2 )
| ~ ( a1 @ ( esk10_1 @ X1 ) )
| ~ ( irel @ X1 @ X2 )
| ~ ( epred2_1 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_69,plain,
! [X3: $i,X2: $i,X1: $i] :
( ( irel @ X1 @ X2 )
| ( a0 @ X3 )
| ~ ( irel @ ( esk9_1 @ X1 ) @ X2 )
| ~ ( irel @ X1 @ X3 )
| ~ ( epred2_1 @ X1 ) ),
inference(spm,[status(thm)],[c_0_30,c_0_56]) ).
thf(c_0_70,plain,
! [X3: $i,X2: $i,X1: $i] :
( ( a0 @ X1 )
| ( a1 @ X2 )
| ~ ( irel @ ( esk7_1 @ X1 ) @ X3 )
| ~ ( irel @ X3 @ ( esk6_1 @ X2 ) )
| ~ ( epred1_1 @ X2 )
| ~ ( epred1_1 @ X1 ) ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
thf(c_0_71,plain,
! [X1: $i] :
( ( irel @ ( esk7_1 @ X1 ) @ ( esk8_1 @ X1 ) )
| ( a0 @ X1 )
| ~ ( epred1_1 @ X1 ) ),
inference(spm,[status(thm)],[c_0_59,c_0_29]) ).
thf(c_0_72,plain,
! [X2: $i,X1: $i] :
( ( irel @ X1 @ X2 )
| ( a1 @ X1 )
| ~ ( irel @ ( esk5_1 @ X1 ) @ X2 )
| ~ ( epred1_1 @ X1 ) ),
inference(spm,[status(thm)],[c_0_60,c_0_29]) ).
thf(c_0_73,plain,
! [X1: $i] :
( ( irel @ ( esk5_1 @ X1 ) @ ( esk6_1 @ X1 ) )
| ( a1 @ X1 )
| ~ ( epred1_1 @ X1 ) ),
inference(spm,[status(thm)],[c_0_61,c_0_29]) ).
thf(c_0_74,plain,
! [X2: $i,X1: $i] :
( ( a0 @ X2 )
| ~ ( a1 @ ( esk8_1 @ X1 ) )
| ~ ( irel @ X1 @ X2 )
| ~ ( epred1_1 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_75,plain,
! [X3: $i,X2: $i,X1: $i] :
( ( irel @ X1 @ X2 )
| ( a0 @ X3 )
| ~ ( irel @ ( esk7_1 @ X1 ) @ X2 )
| ~ ( irel @ X1 @ X3 )
| ~ ( epred1_1 @ X1 ) ),
inference(spm,[status(thm)],[c_0_30,c_0_62]) ).
thf(c_0_76,plain,
! [X2: $i,X1: $i] :
( ( f @ X2 )
| ~ ( a0 @ ( esk13_1 @ X1 ) )
| ~ ( irel @ X1 @ X2 )
| ~ ( epred2_1 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_77,negated_conjecture,
( ( irel @ esk1_0 @ esk3_0 )
| ( irel @ esk1_0 @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
thf(c_0_78,plain,
! [X1: $i,X2: $i] :
( ( a1 @ X1 )
| ( a0 @ X2 )
| ~ ( irel @ ( esk10_1 @ X2 ) @ ( esk12_1 @ X1 ) )
| ~ ( epred2_1 @ X1 )
| ~ ( epred2_1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
thf(c_0_79,plain,
! [X1: $i] :
( ( irel @ X1 @ ( esk12_1 @ X1 ) )
| ( a1 @ X1 )
| ~ ( epred2_1 @ X1 ) ),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
thf(c_0_80,plain,
! [X1: $i] :
( ( a0 @ X1 )
| ~ ( a1 @ ( esk10_1 @ X1 ) )
| ~ ( epred2_1 @ X1 ) ),
inference(spm,[status(thm)],[c_0_68,c_0_29]) ).
thf(c_0_81,plain,
! [X2: $i,X1: $i] :
( ( irel @ X1 @ X2 )
| ( a0 @ X1 )
| ~ ( irel @ ( esk9_1 @ X1 ) @ X2 )
| ~ ( epred2_1 @ X1 ) ),
inference(spm,[status(thm)],[c_0_69,c_0_29]) ).
thf(c_0_82,plain,
! [X1: $i,X2: $i] :
( ( a1 @ X1 )
| ( a0 @ X2 )
| ~ ( irel @ ( esk8_1 @ X2 ) @ ( esk6_1 @ X1 ) )
| ~ ( epred1_1 @ X1 )
| ~ ( epred1_1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
thf(c_0_83,plain,
! [X1: $i] :
( ( irel @ X1 @ ( esk6_1 @ X1 ) )
| ( a1 @ X1 )
| ~ ( epred1_1 @ X1 ) ),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
thf(c_0_84,plain,
! [X1: $i] :
( ( a0 @ X1 )
| ~ ( a1 @ ( esk8_1 @ X1 ) )
| ~ ( epred1_1 @ X1 ) ),
inference(spm,[status(thm)],[c_0_74,c_0_29]) ).
thf(c_0_85,plain,
! [X2: $i,X1: $i] :
( ( irel @ X1 @ X2 )
| ( a0 @ X1 )
| ~ ( irel @ ( esk7_1 @ X1 ) @ X2 )
| ~ ( epred1_1 @ X1 ) ),
inference(spm,[status(thm)],[c_0_75,c_0_29]) ).
thf(c_0_86,plain,
! [X2: $i,X1: $i] :
( ( irel @ X1 @ ( esk4_1 @ X1 ) )
| ( f @ X2 )
| ~ ( irel @ X1 @ X2 )
| ~ ( epred1_1 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_87,plain,
! [X1: $i,X3: $i,X2: $i] :
( ( f @ X1 )
| ~ ( a0 @ ( esk13_1 @ X2 ) )
| ~ ( irel @ X3 @ X1 )
| ~ ( irel @ X2 @ X3 )
| ~ ( epred2_1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_76,c_0_30]) ).
thf(c_0_88,negated_conjecture,
! [X1: $i] :
( ( irel @ esk1_0 @ esk2_0 )
| ( irel @ X1 @ esk3_0 )
| ~ ( irel @ X1 @ esk1_0 ) ),
inference(spm,[status(thm)],[c_0_30,c_0_77]) ).
thf(c_0_89,negated_conjecture,
( ( irel @ esk1_0 @ esk2_0 )
| ~ ( f @ esk3_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
thf(c_0_90,plain,
! [X1: $i] :
( ( a0 @ X1 )
| ~ ( epred2_1 @ ( esk10_1 @ X1 ) )
| ~ ( epred2_1 @ X1 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_80]) ).
thf(c_0_91,negated_conjecture,
! [X1: $i] :
( ( epred2_1 @ X1 )
| ( irel @ esk1_0 @ esk2_0 )
| ~ ( irel @ esk1_0 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
thf(c_0_92,plain,
! [X1: $i] :
( ( irel @ X1 @ ( esk10_1 @ X1 ) )
| ( a0 @ X1 )
| ~ ( epred2_1 @ X1 ) ),
inference(spm,[status(thm)],[c_0_81,c_0_65]) ).
thf(c_0_93,plain,
! [X1: $i] :
( ( a0 @ X1 )
| ~ ( epred1_1 @ ( esk8_1 @ X1 ) )
| ~ ( epred1_1 @ X1 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_84]) ).
thf(c_0_94,negated_conjecture,
! [X1: $i] :
( ( irel @ esk1_0 @ esk3_0 )
| ( epred1_1 @ X1 )
| ~ ( irel @ esk1_0 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
thf(c_0_95,plain,
! [X1: $i] :
( ( irel @ X1 @ ( esk8_1 @ X1 ) )
| ( a0 @ X1 )
| ~ ( epred1_1 @ X1 ) ),
inference(spm,[status(thm)],[c_0_85,c_0_71]) ).
thf(c_0_96,plain,
! [X3: $i,X2: $i,X1: $i] :
( ( irel @ X1 @ X2 )
| ( f @ X3 )
| ~ ( irel @ ( esk4_1 @ X1 ) @ X2 )
| ~ ( irel @ X1 @ X3 )
| ~ ( epred1_1 @ X1 ) ),
inference(spm,[status(thm)],[c_0_30,c_0_86]) ).
thf(c_0_97,negated_conjecture,
! [X2: $i,X1: $i] :
( ( irel @ esk1_0 @ esk2_0 )
| ~ ( a0 @ ( esk13_1 @ X1 ) )
| ~ ( irel @ X2 @ esk1_0 )
| ~ ( irel @ X1 @ X2 )
| ~ ( epred2_1 @ X1 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_89]) ).
thf(c_0_98,negated_conjecture,
! [X1: $i] :
( ( irel @ esk1_0 @ esk2_0 )
| ( a0 @ X1 )
| ~ ( irel @ esk1_0 @ ( esk10_1 @ X1 ) )
| ~ ( epred2_1 @ X1 ) ),
inference(spm,[status(thm)],[c_0_90,c_0_91]) ).
thf(c_0_99,plain,
! [X1: $i,X2: $i] :
( ( irel @ X1 @ ( esk10_1 @ X2 ) )
| ( a0 @ X2 )
| ~ ( irel @ X1 @ X2 )
| ~ ( epred2_1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_30,c_0_92]) ).
thf(c_0_100,plain,
! [X2: $i,X1: $i] :
( ( f @ X2 )
| ~ ( a0 @ ( esk4_1 @ X1 ) )
| ~ ( irel @ X1 @ X2 )
| ~ ( epred1_1 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_101,negated_conjecture,
! [X1: $i] :
( ( irel @ esk1_0 @ esk3_0 )
| ( a0 @ X1 )
| ~ ( irel @ esk1_0 @ ( esk8_1 @ X1 ) )
| ~ ( epred1_1 @ X1 ) ),
inference(spm,[status(thm)],[c_0_93,c_0_94]) ).
thf(c_0_102,plain,
! [X1: $i,X2: $i] :
( ( irel @ X1 @ ( esk8_1 @ X2 ) )
| ( a0 @ X2 )
| ~ ( irel @ X1 @ X2 )
| ~ ( epred1_1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_30,c_0_95]) ).
thf(c_0_103,plain,
! [X2: $i,X1: $i] :
( ( irel @ X1 @ X2 )
| ( f @ X1 )
| ~ ( irel @ ( esk4_1 @ X1 ) @ X2 )
| ~ ( epred1_1 @ X1 ) ),
inference(spm,[status(thm)],[c_0_96,c_0_29]) ).
thf(c_0_104,negated_conjecture,
! [X1: $i,X2: $i] :
( ( epred2_1 @ X1 )
| ( epred1_1 @ X2 )
| ~ ( irel @ esk1_0 @ X1 )
| ~ ( irel @ esk1_0 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
thf(c_0_105,negated_conjecture,
! [X1: $i] :
( ( irel @ esk1_0 @ esk2_0 )
| ~ ( a0 @ ( esk13_1 @ X1 ) )
| ~ ( irel @ X1 @ esk1_0 )
| ~ ( epred2_1 @ X1 ) ),
inference(spm,[status(thm)],[c_0_97,c_0_29]) ).
thf(c_0_106,plain,
! [X1: $i] :
( ( irel @ esk1_0 @ esk2_0 )
| ( a0 @ X1 )
| ~ ( irel @ esk1_0 @ X1 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_91]) ).
thf(c_0_107,plain,
! [X1: $i] :
( ( f @ X1 )
| ~ ( a0 @ ( esk4_1 @ X1 ) )
| ~ ( epred1_1 @ X1 ) ),
inference(spm,[status(thm)],[c_0_100,c_0_29]) ).
thf(c_0_108,plain,
! [X1: $i] :
( ( irel @ esk1_0 @ esk3_0 )
| ( a0 @ X1 )
| ~ ( irel @ esk1_0 @ X1 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_94]) ).
thf(c_0_109,plain,
! [X1: $i] :
( ( irel @ X1 @ ( esk4_1 @ X1 ) )
| ( f @ X1 )
| ~ ( epred1_1 @ X1 ) ),
inference(spm,[status(thm)],[c_0_103,c_0_29]) ).
thf(c_0_110,negated_conjecture,
! [X1: $i,X2: $i] :
( ( epred2_1 @ X1 )
| ( a0 @ X2 )
| ~ ( irel @ esk1_0 @ ( esk8_1 @ X2 ) )
| ~ ( irel @ esk1_0 @ X1 )
| ~ ( epred1_1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_93,c_0_104]) ).
thf(c_0_111,negated_conjecture,
! [X1: $i] :
( ( irel @ esk1_0 @ esk2_0 )
| ~ ( irel @ esk1_0 @ ( esk13_1 @ X1 ) )
| ~ ( irel @ X1 @ esk1_0 )
| ~ ( epred2_1 @ X1 ) ),
inference(spm,[status(thm)],[c_0_105,c_0_106]) ).
thf(c_0_112,plain,
! [X2: $i,X1: $i] :
( ( irel @ X1 @ ( esk13_1 @ X1 ) )
| ( f @ X2 )
| ~ ( irel @ X1 @ X2 )
| ~ ( epred2_1 @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_113,plain,
! [X1: $i] :
( ( irel @ esk1_0 @ esk3_0 )
| ( f @ X1 )
| ~ ( irel @ esk1_0 @ ( esk4_1 @ X1 ) )
| ~ ( epred1_1 @ X1 ) ),
inference(spm,[status(thm)],[c_0_107,c_0_108]) ).
thf(c_0_114,plain,
! [X1: $i,X2: $i] :
( ( irel @ X1 @ ( esk4_1 @ X2 ) )
| ( f @ X2 )
| ~ ( irel @ X1 @ X2 )
| ~ ( epred1_1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_30,c_0_109]) ).
thf(c_0_115,plain,
! [X2: $i,X1: $i] :
( ( a0 @ X1 )
| ( epred2_1 @ X2 )
| ~ ( irel @ esk1_0 @ X2 )
| ~ ( irel @ esk1_0 @ X1 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_102]),c_0_104]) ).
thf(c_0_116,plain,
! [X1: $i] :
( ( irel @ esk1_0 @ esk2_0 )
| ( f @ X1 )
| ~ ( irel @ esk1_0 @ X1 )
| ~ ( epred2_1 @ esk1_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_29])]) ).
thf(c_0_117,negated_conjecture,
( ( irel @ esk1_0 @ esk3_0 )
| ~ ( f @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
thf(c_0_118,plain,
! [X1: $i] :
( ( irel @ esk1_0 @ esk3_0 )
| ( f @ X1 )
| ~ ( irel @ esk1_0 @ X1 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_114]),c_0_94]) ).
thf(c_0_119,plain,
! [X1: $i,X2: $i] :
( ( epred2_1 @ X1 )
| ( f @ X2 )
| ~ ( irel @ esk1_0 @ ( esk4_1 @ X2 ) )
| ~ ( irel @ esk1_0 @ X1 )
| ~ ( epred1_1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_107,c_0_115]) ).
thf(c_0_120,negated_conjecture,
! [X1: $i] :
( ( irel @ esk1_0 @ esk2_0 )
| ( f @ X1 )
| ~ ( irel @ esk1_0 @ X1 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_91]),c_0_29])]) ).
thf(c_0_121,negated_conjecture,
irel @ esk1_0 @ esk3_0,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_118]),c_0_77]) ).
thf(c_0_122,negated_conjecture,
! [X1: $i] :
( ( epred2_1 @ X1 )
| ~ ( irel @ esk1_0 @ X1 )
| ~ ( f @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
thf(c_0_123,plain,
! [X2: $i,X1: $i] :
( ( f @ X1 )
| ( epred2_1 @ X2 )
| ~ ( irel @ esk1_0 @ X2 )
| ~ ( irel @ esk1_0 @ X1 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_114]),c_0_104]) ).
thf(c_0_124,negated_conjecture,
irel @ esk1_0 @ esk2_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_120]),c_0_121])]) ).
thf(c_0_125,negated_conjecture,
! [X1: $i] :
( ( irel @ X1 @ esk3_0 )
| ~ ( irel @ X1 @ esk1_0 ) ),
inference(spm,[status(thm)],[c_0_30,c_0_121]) ).
thf(c_0_126,negated_conjecture,
! [X1: $i] :
( ( epred2_1 @ X1 )
| ~ ( irel @ esk1_0 @ X1 ) ),
inference(condense,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_123]),c_0_124])])]) ).
thf(c_0_127,plain,
! [X2: $i,X1: $i] :
( ( f @ esk3_0 )
| ~ ( a0 @ ( esk13_1 @ X1 ) )
| ~ ( irel @ X2 @ esk1_0 )
| ~ ( irel @ X1 @ X2 )
| ~ ( epred2_1 @ X1 ) ),
inference(spm,[status(thm)],[c_0_87,c_0_125]) ).
thf(c_0_128,plain,
! [X1: $i] :
( ( a0 @ X1 )
| ~ ( irel @ esk1_0 @ ( esk10_1 @ X1 ) )
| ~ ( epred2_1 @ X1 ) ),
inference(spm,[status(thm)],[c_0_90,c_0_126]) ).
thf(c_0_129,plain,
! [X1: $i] :
( ( f @ esk3_0 )
| ~ ( a0 @ ( esk13_1 @ X1 ) )
| ~ ( irel @ X1 @ esk1_0 )
| ~ ( epred2_1 @ X1 ) ),
inference(spm,[status(thm)],[c_0_127,c_0_29]) ).
thf(c_0_130,plain,
! [X1: $i] :
( ( a0 @ X1 )
| ~ ( irel @ esk1_0 @ X1 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_99]),c_0_126]) ).
thf(c_0_131,plain,
! [X1: $i] :
( ( f @ esk3_0 )
| ~ ( irel @ esk1_0 @ ( esk13_1 @ X1 ) )
| ~ ( irel @ X1 @ esk1_0 )
| ~ ( epred2_1 @ X1 ) ),
inference(spm,[status(thm)],[c_0_129,c_0_130]) ).
thf(c_0_132,plain,
! [X3: $i,X2: $i,X1: $i] :
( ( irel @ X1 @ X2 )
| ( f @ X3 )
| ~ ( irel @ ( esk13_1 @ X1 ) @ X2 )
| ~ ( irel @ X1 @ X3 )
| ~ ( epred2_1 @ X1 ) ),
inference(spm,[status(thm)],[c_0_30,c_0_112]) ).
thf(c_0_133,plain,
! [X1: $i] :
( ( f @ esk3_0 )
| ( f @ X1 )
| ~ ( irel @ esk1_0 @ X1 )
| ~ ( epred2_1 @ esk1_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_112]),c_0_29])]) ).
thf(c_0_134,plain,
! [X2: $i,X1: $i] :
( ( irel @ X1 @ X2 )
| ( f @ X1 )
| ~ ( irel @ ( esk13_1 @ X1 ) @ X2 )
| ~ ( epred2_1 @ X1 ) ),
inference(spm,[status(thm)],[c_0_132,c_0_29]) ).
thf(c_0_135,negated_conjecture,
! [X1: $i] :
( ( f @ esk3_0 )
| ( f @ X1 )
| ~ ( irel @ esk1_0 @ X1 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_126]),c_0_29])]) ).
thf(c_0_136,plain,
! [X1: $i] :
( ( f @ X1 )
| ~ ( a0 @ ( esk13_1 @ X1 ) )
| ~ ( epred2_1 @ X1 ) ),
inference(spm,[status(thm)],[c_0_76,c_0_29]) ).
thf(c_0_137,plain,
! [X1: $i] :
( ( irel @ X1 @ ( esk13_1 @ X1 ) )
| ( f @ X1 )
| ~ ( epred2_1 @ X1 ) ),
inference(spm,[status(thm)],[c_0_134,c_0_29]) ).
thf(c_0_138,negated_conjecture,
( ~ ( f @ esk3_0 )
| ~ ( f @ esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
thf(c_0_139,negated_conjecture,
f @ esk3_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(ef,[status(thm)],[c_0_135]),c_0_121])]) ).
thf(c_0_140,plain,
! [X1: $i] :
( ( f @ X1 )
| ~ ( irel @ esk1_0 @ ( esk13_1 @ X1 ) )
| ~ ( epred2_1 @ X1 ) ),
inference(spm,[status(thm)],[c_0_136,c_0_130]) ).
thf(c_0_141,plain,
! [X1: $i,X2: $i] :
( ( irel @ X1 @ ( esk13_1 @ X2 ) )
| ( f @ X2 )
| ~ ( irel @ X1 @ X2 )
| ~ ( epred2_1 @ X2 ) ),
inference(spm,[status(thm)],[c_0_30,c_0_137]) ).
thf(c_0_142,negated_conjecture,
~ ( f @ esk2_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_138,c_0_139])]) ).
thf(c_0_143,plain,
! [X1: $i] :
( ( f @ X1 )
| ~ ( irel @ esk1_0 @ X1 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_141]),c_0_126]) ).
thf(c_0_144,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_143]),c_0_124])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : SYO069^4.001 : TPTP v8.2.0. Released v4.0.0.
% 0.00/0.09 % Command : run_E %s %d THM
% 0.08/0.29 % Computer : n021.cluster.edu
% 0.08/0.29 % Model : x86_64 x86_64
% 0.08/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.29 % Memory : 8042.1875MB
% 0.08/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.29 % CPULimit : 300
% 0.08/0.29 % WCLimit : 300
% 0.08/0.29 % DateTime : Mon May 20 08:44:37 EDT 2024
% 0.08/0.29 % CPUTime :
% 0.14/0.39 Running higher-order theorem proving
% 0.14/0.39 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
% 55.51/7.47 # Version: 3.1.0-ho
% 55.51/7.47 # Preprocessing class: HSMSSMSSMLSNHSN.
% 55.51/7.47 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 55.51/7.47 # Starting new_ho_10_cnf2 with 1500s (5) cores
% 55.51/7.47 # Starting post_as_ho3 with 300s (1) cores
% 55.51/7.47 # Starting post_as_ho11 with 300s (1) cores
% 55.51/7.47 # Starting full_lambda_8 with 300s (1) cores
% 55.51/7.47 # new_ho_10_cnf2 with pid 21921 completed with status 0
% 55.51/7.47 # Result found by new_ho_10_cnf2
% 55.51/7.47 # Preprocessing class: HSMSSMSSMLSNHSN.
% 55.51/7.47 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 55.51/7.47 # Starting new_ho_10_cnf2 with 1500s (5) cores
% 55.51/7.47 # No SInE strategy applied
% 55.51/7.47 # Search class: HGHNF-FFMF11-SHSSMFNN
% 55.51/7.47 # Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 55.51/7.47 # Starting new_ho_10_cnf2 with 901s (1) cores
% 55.51/7.47 # Starting post_as_ho11 with 151s (1) cores
% 55.51/7.47 # Starting new_ho_9 with 151s (1) cores
% 55.51/7.47 # Starting post_as_ho4 with 151s (1) cores
% 55.51/7.47 # Starting post_as_ho1 with 146s (1) cores
% 55.51/7.47 # post_as_ho11 with pid 21929 completed with status 0
% 55.51/7.47 # Result found by post_as_ho11
% 55.51/7.47 # Preprocessing class: HSMSSMSSMLSNHSN.
% 55.51/7.47 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 55.51/7.47 # Starting new_ho_10_cnf2 with 1500s (5) cores
% 55.51/7.47 # No SInE strategy applied
% 55.51/7.47 # Search class: HGHNF-FFMF11-SHSSMFNN
% 55.51/7.47 # Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 55.51/7.47 # Starting new_ho_10_cnf2 with 901s (1) cores
% 55.51/7.47 # Starting post_as_ho11 with 151s (1) cores
% 55.51/7.47 # Preprocessing time : 0.001 s
% 55.51/7.47
% 55.51/7.47 # Proof found!
% 55.51/7.47 # SZS status Theorem
% 55.51/7.47 # SZS output start CNFRefutation
% See solution above
% 55.51/7.47 # Parsed axioms : 47
% 55.51/7.47 # Removed by relevancy pruning/SinE : 0
% 55.51/7.47 # Initial clauses : 56
% 55.51/7.47 # Removed in clause preprocessing : 25
% 55.51/7.47 # Initial clauses in saturation : 31
% 55.51/7.47 # Processed clauses : 4100
% 55.51/7.47 # ...of these trivial : 0
% 55.51/7.47 # ...subsumed : 2465
% 55.51/7.47 # ...remaining for further processing : 1635
% 55.51/7.47 # Other redundant clauses eliminated : 0
% 55.51/7.47 # Clauses deleted for lack of memory : 0
% 55.51/7.47 # Backward-subsumed : 443
% 55.51/7.47 # Backward-rewritten : 222
% 55.51/7.47 # Generated clauses : 203045
% 55.51/7.47 # ...of the previous two non-redundant : 202955
% 55.51/7.47 # ...aggressively subsumed : 0
% 55.51/7.47 # Contextual simplify-reflections : 165
% 55.51/7.47 # Paramodulations : 203039
% 55.51/7.47 # Factorizations : 6
% 55.51/7.47 # NegExts : 0
% 55.51/7.47 # Equation resolutions : 0
% 55.51/7.47 # Disequality decompositions : 0
% 55.51/7.47 # Total rewrite steps : 596
% 55.51/7.47 # ...of those cached : 588
% 55.51/7.47 # Propositional unsat checks : 0
% 55.51/7.47 # Propositional check models : 0
% 55.51/7.47 # Propositional check unsatisfiable : 0
% 55.51/7.47 # Propositional clauses : 0
% 55.51/7.47 # Propositional clauses after purity: 0
% 55.51/7.47 # Propositional unsat core size : 0
% 55.51/7.47 # Propositional preprocessing time : 0.000
% 55.51/7.47 # Propositional encoding time : 0.000
% 55.51/7.47 # Propositional solver time : 0.000
% 55.51/7.47 # Success case prop preproc time : 0.000
% 55.51/7.47 # Success case prop encoding time : 0.000
% 55.51/7.47 # Success case prop solver time : 0.000
% 55.51/7.47 # Current number of processed clauses : 970
% 55.51/7.47 # Positive orientable unit clauses : 6
% 55.51/7.47 # Positive unorientable unit clauses: 0
% 55.51/7.47 # Negative unit clauses : 1
% 55.51/7.47 # Non-unit-clauses : 963
% 55.51/7.47 # Current number of unprocessed clauses: 198447
% 55.51/7.47 # ...number of literals in the above : 1668704
% 55.51/7.47 # Current number of archived formulas : 0
% 55.51/7.47 # Current number of archived clauses : 665
% 55.51/7.47 # Clause-clause subsumption calls (NU) : 179655
% 55.51/7.47 # Rec. Clause-clause subsumption calls : 29945
% 55.51/7.47 # Non-unit clause-clause subsumptions : 3129
% 55.51/7.47 # Unit Clause-clause subsumption calls : 210
% 55.51/7.47 # Rewrite failures with RHS unbound : 0
% 55.51/7.47 # BW rewrite match attempts : 8
% 55.51/7.47 # BW rewrite match successes : 5
% 55.51/7.47 # Condensation attempts : 4100
% 55.51/7.47 # Condensation successes : 60
% 55.51/7.47 # Termbank termtop insertions : 22540455
% 55.51/7.47 # Search garbage collected termcells : 1623
% 55.51/7.47
% 55.51/7.47 # -------------------------------------------------
% 55.51/7.47 # User time : 6.685 s
% 55.51/7.47 # System time : 0.143 s
% 55.51/7.47 # Total time : 6.828 s
% 55.51/7.47 # Maximum resident set size: 2044 pages
% 55.51/7.47
% 55.51/7.47 # -------------------------------------------------
% 55.51/7.47 # User time : 33.741 s
% 55.51/7.47 # System time : 0.775 s
% 55.51/7.47 # Total time : 34.516 s
% 55.51/7.47 # Maximum resident set size: 1784 pages
% 55.51/7.47 % E---3.1 exiting
% 55.51/7.47 % E exiting
%------------------------------------------------------------------------------