TSTP Solution File: SYO544^1 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SYO544^1 : TPTP v8.2.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n015.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 08:48:01 EDT 2024
% Result : Theorem 0.19s 0.52s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 46
% Syntax : Number of formulae : 140 ( 15 unt; 27 typ; 0 def)
% Number of atoms : 2675 ( 669 equ; 0 cnn)
% Maximal formula atoms : 453 ( 23 avg)
% Number of connectives : 4491 (1066 ~;1831 |; 378 &;1158 @)
% ( 56 <=>; 1 =>; 0 <=; 1 <~>)
% Maximal formula depth : 82 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 33 ( 33 >; 0 *; 0 +; 0 <<)
% Number of symbols : 31 ( 27 usr; 8 con; 0-5 aty)
% Number of variables : 155 ( 26 ^ 128 !; 1 ?; 155 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_22,type,
eps: ( $i > $o ) > $i ).
thf(decl_23,type,
case: ( $o > $o ) > $i > $i > $i > $i > $i ).
thf(decl_24,type,
f0: $o > $o ).
thf(decl_25,type,
f1: $o > $o ).
thf(decl_26,type,
f2: $o > $o ).
thf(decl_27,type,
f3: $o > $o ).
thf(decl_28,type,
esk1_0: $i ).
thf(decl_29,type,
esk2_0: $i ).
thf(decl_30,type,
esk3_0: $i ).
thf(decl_31,type,
esk4_0: $i ).
thf(decl_32,type,
epred1_0: $i > $o ).
thf(decl_33,type,
epred2_0: $i > $o ).
thf(decl_34,type,
epred3_0: $i > $o ).
thf(decl_35,type,
epred4_0: $i > $o ).
thf(decl_36,type,
epred5_1: $i > $o ).
thf(decl_37,type,
epred6_1: $i > $o ).
thf(decl_38,type,
epred7_1: $i > $o ).
thf(decl_39,type,
epred8_1: $i > $o ).
thf(decl_40,type,
epred9_1: $i > $o ).
thf(decl_41,type,
epred10_1: $i > $o ).
thf(decl_42,type,
epred11_1: $i > $o ).
thf(decl_43,type,
epred12_1: $i > $o ).
thf(decl_44,type,
epred13_1: $i > $o ).
thf(decl_45,type,
epred14_1: $i > $o ).
thf(decl_46,type,
epred15_1: $i > $o ).
thf(decl_47,type,
epred16_1: $i > $o ).
thf(decl_49,type,
esk6_0: $o ).
thf(f0f,axiom,
( ( f0 @ ~ $true )
<=> ~ $true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f0f) ).
thf(f3f,axiom,
( ( f3 @ ~ $true )
<=> $true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f3f) ).
thf(f0t,axiom,
( ( f0 @ $true )
<=> ~ $true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f0t) ).
thf(f3t,axiom,
( ( f3 @ $true )
<=> $true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f3t) ).
thf(f1f,axiom,
( ( f1 @ ~ $true )
<=> $true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f1f) ).
thf(f1t,axiom,
( ( f1 @ $true )
<=> ~ $true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f1t) ).
thf(f2f,axiom,
( ( f2 @ ~ $true )
<=> ~ $true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f2f) ).
thf(f2t,axiom,
( ( f2 @ $true )
<=> $true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f2t) ).
thf(caseood,axiom,
( case
= ( ^ [X3: $o > $o,X2: $i,X4: $i,X5: $i,X6: $i] :
( eps
@ ^ [X7: $i] :
( ( ( X3
= ( ^ [X8: $o] : ~ $true ) )
& ( X7 = X2 ) )
| ( ( X3 = $not )
& ( X7 = X4 ) )
| ( ( X3
= ( ^ [X8: $o] : X8 ) )
& ( X7 = X5 ) )
| ( ( X3
= ( ^ [X8: $o] : $true ) )
& ( X7 = X6 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',caseood) ).
thf(choiceax,axiom,
! [X1: $i > $o] :
( ? [X2: $i] : ( X1 @ X2 )
=> ( X1 @ ( eps @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',choiceax) ).
thf(conj,conjecture,
! [X2: $i,X4: $i,X5: $i,X6: $i] :
( ( ( case @ f0 @ X2 @ X4 @ X5 @ X6 )
= X2 )
& ( ( case @ f1 @ X2 @ X4 @ X5 @ X6 )
= X4 )
& ( ( case @ f2 @ X2 @ X4 @ X5 @ X6 )
= X5 )
& ( ( case @ f3 @ X2 @ X4 @ X5 @ X6 )
= X6 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(c_0_11,axiom,
( ( ( ~ ~ $true
| ( f0 @ $true ) )
& ( ~ $true
| ( f0 @ $false ) ) )
<=> ~ $true ),
inference(fool_unroll,[status(thm)],[f0f]) ).
thf(c_0_12,axiom,
( ( ( ~ ~ $true
| ( f3 @ $true ) )
& ( ~ $true
| ( f3 @ $false ) ) )
<=> $true ),
inference(fool_unroll,[status(thm)],[f3f]) ).
thf(c_0_13,plain,
( ( ~ ( f0 @ $true )
| ~ $true )
& ( $true
| ( f0 @ $true ) ) ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[f0t])]) ).
thf(c_0_14,plain,
! [X49: $i,X50: $o,X51: $o,X52: $o] :
( ( ~ ( f0 @ X52 )
| $true
| ~ ( f0 @ X51 )
| X51
| ( f0 = $not )
| ~ ( f0 @ X50 )
| ~ $true
| ~ ( epred1_0 @ X49 ) )
& ( ~ $true
| ( f0 @ X52 )
| ~ ( f0 @ X51 )
| X51
| ( f0 = $not )
| ~ ( f0 @ X50 )
| ~ $true
| ~ ( epred1_0 @ X49 ) )
& ( ( X49 = esk4_0 )
| ~ ( f0 @ X51 )
| X51
| ( f0 = $not )
| ~ ( f0 @ X50 )
| ~ $true
| ~ ( epred1_0 @ X49 ) )
& ( ~ ( f0 @ X52 )
| $true
| ~ X51
| ( f0 @ X51 )
| ( f0 = $not )
| ~ ( f0 @ X50 )
| ~ $true
| ~ ( epred1_0 @ X49 ) )
& ( ~ $true
| ( f0 @ X52 )
| ~ X51
| ( f0 @ X51 )
| ( f0 = $not )
| ~ ( f0 @ X50 )
| ~ $true
| ~ ( epred1_0 @ X49 ) )
& ( ( X49 = esk4_0 )
| ~ X51
| ( f0 @ X51 )
| ( f0 = $not )
| ~ ( f0 @ X50 )
| ~ $true
| ~ ( epred1_0 @ X49 ) )
& ( ~ ( f0 @ X52 )
| $true
| ( X49 = esk3_0 )
| ( f0 = $not )
| ~ ( f0 @ X50 )
| ~ $true
| ~ ( epred1_0 @ X49 ) )
& ( ~ $true
| ( f0 @ X52 )
| ( X49 = esk3_0 )
| ( f0 = $not )
| ~ ( f0 @ X50 )
| ~ $true
| ~ ( epred1_0 @ X49 ) )
& ( ( X49 = esk4_0 )
| ( X49 = esk3_0 )
| ( f0 = $not )
| ~ ( f0 @ X50 )
| ~ $true
| ~ ( epred1_0 @ X49 ) )
& ( ~ ( f0 @ X52 )
| $true
| ~ ( f0 @ X51 )
| X51
| ( X49 = esk2_0 )
| ~ ( f0 @ X50 )
| ~ $true
| ~ ( epred1_0 @ X49 ) )
& ( ~ $true
| ( f0 @ X52 )
| ~ ( f0 @ X51 )
| X51
| ( X49 = esk2_0 )
| ~ ( f0 @ X50 )
| ~ $true
| ~ ( epred1_0 @ X49 ) )
& ( ( X49 = esk4_0 )
| ~ ( f0 @ X51 )
| X51
| ( X49 = esk2_0 )
| ~ ( f0 @ X50 )
| ~ $true
| ~ ( epred1_0 @ X49 ) )
& ( ~ ( f0 @ X52 )
| $true
| ~ X51
| ( f0 @ X51 )
| ( X49 = esk2_0 )
| ~ ( f0 @ X50 )
| ~ $true
| ~ ( epred1_0 @ X49 ) )
& ( ~ $true
| ( f0 @ X52 )
| ~ X51
| ( f0 @ X51 )
| ( X49 = esk2_0 )
| ~ ( f0 @ X50 )
| ~ $true
| ~ ( epred1_0 @ X49 ) )
& ( ( X49 = esk4_0 )
| ~ X51
| ( f0 @ X51 )
| ( X49 = esk2_0 )
| ~ ( f0 @ X50 )
| ~ $true
| ~ ( epred1_0 @ X49 ) )
& ( ~ ( f0 @ X52 )
| $true
| ( X49 = esk3_0 )
| ( X49 = esk2_0 )
| ~ ( f0 @ X50 )
| ~ $true
| ~ ( epred1_0 @ X49 ) )
& ( ~ $true
| ( f0 @ X52 )
| ( X49 = esk3_0 )
| ( X49 = esk2_0 )
| ~ ( f0 @ X50 )
| ~ $true
| ~ ( epred1_0 @ X49 ) )
& ( ( X49 = esk4_0 )
| ( X49 = esk3_0 )
| ( X49 = esk2_0 )
| ~ ( f0 @ X50 )
| ~ $true
| ~ ( epred1_0 @ X49 ) )
& ( ~ ( f0 @ X52 )
| $true
| ~ ( f0 @ X51 )
| X51
| ( f0 = $not )
| $true
| ( f0 @ X50 )
| ~ ( epred1_0 @ X49 ) )
& ( ~ $true
| ( f0 @ X52 )
| ~ ( f0 @ X51 )
| X51
| ( f0 = $not )
| $true
| ( f0 @ X50 )
| ~ ( epred1_0 @ X49 ) )
& ( ( X49 = esk4_0 )
| ~ ( f0 @ X51 )
| X51
| ( f0 = $not )
| $true
| ( f0 @ X50 )
| ~ ( epred1_0 @ X49 ) )
& ( ~ ( f0 @ X52 )
| $true
| ~ X51
| ( f0 @ X51 )
| ( f0 = $not )
| $true
| ( f0 @ X50 )
| ~ ( epred1_0 @ X49 ) )
& ( ~ $true
| ( f0 @ X52 )
| ~ X51
| ( f0 @ X51 )
| ( f0 = $not )
| $true
| ( f0 @ X50 )
| ~ ( epred1_0 @ X49 ) )
& ( ( X49 = esk4_0 )
| ~ X51
| ( f0 @ X51 )
| ( f0 = $not )
| $true
| ( f0 @ X50 )
| ~ ( epred1_0 @ X49 ) )
& ( ~ ( f0 @ X52 )
| $true
| ( X49 = esk3_0 )
| ( f0 = $not )
| $true
| ( f0 @ X50 )
| ~ ( epred1_0 @ X49 ) )
& ( ~ $true
| ( f0 @ X52 )
| ( X49 = esk3_0 )
| ( f0 = $not )
| $true
| ( f0 @ X50 )
| ~ ( epred1_0 @ X49 ) )
& ( ( X49 = esk4_0 )
| ( X49 = esk3_0 )
| ( f0 = $not )
| $true
| ( f0 @ X50 )
| ~ ( epred1_0 @ X49 ) )
& ( ~ ( f0 @ X52 )
| $true
| ~ ( f0 @ X51 )
| X51
| ( X49 = esk2_0 )
| $true
| ( f0 @ X50 )
| ~ ( epred1_0 @ X49 ) )
& ( ~ $true
| ( f0 @ X52 )
| ~ ( f0 @ X51 )
| X51
| ( X49 = esk2_0 )
| $true
| ( f0 @ X50 )
| ~ ( epred1_0 @ X49 ) )
& ( ( X49 = esk4_0 )
| ~ ( f0 @ X51 )
| X51
| ( X49 = esk2_0 )
| $true
| ( f0 @ X50 )
| ~ ( epred1_0 @ X49 ) )
& ( ~ ( f0 @ X52 )
| $true
| ~ X51
| ( f0 @ X51 )
| ( X49 = esk2_0 )
| $true
| ( f0 @ X50 )
| ~ ( epred1_0 @ X49 ) )
& ( ~ $true
| ( f0 @ X52 )
| ~ X51
| ( f0 @ X51 )
| ( X49 = esk2_0 )
| $true
| ( f0 @ X50 )
| ~ ( epred1_0 @ X49 ) )
& ( ( X49 = esk4_0 )
| ~ X51
| ( f0 @ X51 )
| ( X49 = esk2_0 )
| $true
| ( f0 @ X50 )
| ~ ( epred1_0 @ X49 ) )
& ( ~ ( f0 @ X52 )
| $true
| ( X49 = esk3_0 )
| ( X49 = esk2_0 )
| $true
| ( f0 @ X50 )
| ~ ( epred1_0 @ X49 ) )
& ( ~ $true
| ( f0 @ X52 )
| ( X49 = esk3_0 )
| ( X49 = esk2_0 )
| $true
| ( f0 @ X50 )
| ~ ( epred1_0 @ X49 ) )
& ( ( X49 = esk4_0 )
| ( X49 = esk3_0 )
| ( X49 = esk2_0 )
| $true
| ( f0 @ X50 )
| ~ ( epred1_0 @ X49 ) )
& ( ~ ( f0 @ X52 )
| $true
| ~ ( f0 @ X51 )
| X51
| ( f0 = $not )
| ( X49 = esk1_0 )
| ~ ( epred1_0 @ X49 ) )
& ( ~ $true
| ( f0 @ X52 )
| ~ ( f0 @ X51 )
| X51
| ( f0 = $not )
| ( X49 = esk1_0 )
| ~ ( epred1_0 @ X49 ) )
& ( ( X49 = esk4_0 )
| ~ ( f0 @ X51 )
| X51
| ( f0 = $not )
| ( X49 = esk1_0 )
| ~ ( epred1_0 @ X49 ) )
& ( ~ ( f0 @ X52 )
| $true
| ~ X51
| ( f0 @ X51 )
| ( f0 = $not )
| ( X49 = esk1_0 )
| ~ ( epred1_0 @ X49 ) )
& ( ~ $true
| ( f0 @ X52 )
| ~ X51
| ( f0 @ X51 )
| ( f0 = $not )
| ( X49 = esk1_0 )
| ~ ( epred1_0 @ X49 ) )
& ( ( X49 = esk4_0 )
| ~ X51
| ( f0 @ X51 )
| ( f0 = $not )
| ( X49 = esk1_0 )
| ~ ( epred1_0 @ X49 ) )
& ( ~ ( f0 @ X52 )
| $true
| ( X49 = esk3_0 )
| ( f0 = $not )
| ( X49 = esk1_0 )
| ~ ( epred1_0 @ X49 ) )
& ( ~ $true
| ( f0 @ X52 )
| ( X49 = esk3_0 )
| ( f0 = $not )
| ( X49 = esk1_0 )
| ~ ( epred1_0 @ X49 ) )
& ( ( X49 = esk4_0 )
| ( X49 = esk3_0 )
| ( f0 = $not )
| ( X49 = esk1_0 )
| ~ ( epred1_0 @ X49 ) )
& ( ~ ( f0 @ X52 )
| $true
| ~ ( f0 @ X51 )
| X51
| ( X49 = esk2_0 )
| ( X49 = esk1_0 )
| ~ ( epred1_0 @ X49 ) )
& ( ~ $true
| ( f0 @ X52 )
| ~ ( f0 @ X51 )
| X51
| ( X49 = esk2_0 )
| ( X49 = esk1_0 )
| ~ ( epred1_0 @ X49 ) )
& ( ( X49 = esk4_0 )
| ~ ( f0 @ X51 )
| X51
| ( X49 = esk2_0 )
| ( X49 = esk1_0 )
| ~ ( epred1_0 @ X49 ) )
& ( ~ ( f0 @ X52 )
| $true
| ~ X51
| ( f0 @ X51 )
| ( X49 = esk2_0 )
| ( X49 = esk1_0 )
| ~ ( epred1_0 @ X49 ) )
& ( ~ $true
| ( f0 @ X52 )
| ~ X51
| ( f0 @ X51 )
| ( X49 = esk2_0 )
| ( X49 = esk1_0 )
| ~ ( epred1_0 @ X49 ) )
& ( ( X49 = esk4_0 )
| ~ X51
| ( f0 @ X51 )
| ( X49 = esk2_0 )
| ( X49 = esk1_0 )
| ~ ( epred1_0 @ X49 ) )
& ( ~ ( f0 @ X52 )
| $true
| ( X49 = esk3_0 )
| ( X49 = esk2_0 )
| ( X49 = esk1_0 )
| ~ ( epred1_0 @ X49 ) )
& ( ~ $true
| ( f0 @ X52 )
| ( X49 = esk3_0 )
| ( X49 = esk2_0 )
| ( X49 = esk1_0 )
| ~ ( epred1_0 @ X49 ) )
& ( ( X49 = esk4_0 )
| ( X49 = esk3_0 )
| ( X49 = esk2_0 )
| ( X49 = esk1_0 )
| ~ ( epred1_0 @ X49 ) )
& ( ~ ( epred5_1 @ X49 )
| ( epred5_1 @ X49 )
| $true
| ( X49 != esk1_0 )
| ( epred1_0 @ X49 ) )
& ( ~ ( f0 @ $false )
| ( epred5_1 @ X49 )
| $true
| ( X49 != esk1_0 )
| ( epred1_0 @ X49 ) )
& ( ~ ( epred5_1 @ X49 )
| ~ ( f0 @ $true )
| $true
| ( X49 != esk1_0 )
| ( epred1_0 @ X49 ) )
& ( ~ ( f0 @ $false )
| ~ ( f0 @ $true )
| $true
| ( X49 != esk1_0 )
| ( epred1_0 @ X49 ) )
& ( ~ ( epred5_1 @ X49 )
| ( f0 @ $true )
| ~ $true
| ( X49 != esk1_0 )
| ( epred1_0 @ X49 ) )
& ( ( epred5_1 @ X49 )
| ( f0 @ $false )
| ~ $true
| ( X49 != esk1_0 )
| ( epred1_0 @ X49 ) )
& ( ( f0 != $not )
| ( X49 != esk2_0 )
| ( epred1_0 @ X49 ) )
& ( ~ ( epred6_1 @ X49 )
| ( epred6_1 @ X49 )
| ~ ( epred6_1 @ X49 )
| ( X49 != esk3_0 )
| ( epred1_0 @ X49 ) )
& ( ~ ( f0 @ $false )
| ( epred6_1 @ X49 )
| ~ ( epred6_1 @ X49 )
| ( X49 != esk3_0 )
| ( epred1_0 @ X49 ) )
& ( ~ ( epred6_1 @ X49 )
| ~ ( f0 @ $true )
| ~ ( epred6_1 @ X49 )
| ( X49 != esk3_0 )
| ( epred1_0 @ X49 ) )
& ( ~ ( f0 @ $false )
| ~ ( f0 @ $true )
| ~ ( epred6_1 @ X49 )
| ( X49 != esk3_0 )
| ( epred1_0 @ X49 ) )
& ( ~ ( epred6_1 @ X49 )
| ( f0 @ $true )
| ( epred6_1 @ X49 )
| ( X49 != esk3_0 )
| ( epred1_0 @ X49 ) )
& ( ( epred6_1 @ X49 )
| ( f0 @ $false )
| ( epred6_1 @ X49 )
| ( X49 != esk3_0 )
| ( epred1_0 @ X49 ) )
& ( ~ ( epred7_1 @ X49 )
| ( epred7_1 @ X49 )
| ~ $true
| ( X49 != esk4_0 )
| ( epred1_0 @ X49 ) )
& ( ~ ( f0 @ $false )
| ( epred7_1 @ X49 )
| ~ $true
| ( X49 != esk4_0 )
| ( epred1_0 @ X49 ) )
& ( ~ ( epred7_1 @ X49 )
| ~ ( f0 @ $true )
| ~ $true
| ( X49 != esk4_0 )
| ( epred1_0 @ X49 ) )
& ( ~ ( f0 @ $false )
| ~ ( f0 @ $true )
| ~ $true
| ( X49 != esk4_0 )
| ( epred1_0 @ X49 ) )
& ( ~ ( epred7_1 @ X49 )
| ( f0 @ $true )
| $true
| ( X49 != esk4_0 )
| ( epred1_0 @ X49 ) )
& ( ( epred7_1 @ X49 )
| ( f0 @ $false )
| $true
| ( X49 != esk4_0 )
| ( epred1_0 @ X49 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[])])])])])])]) ).
thf(c_0_15,plain,
( ( $true
| ~ $true
| ~ $true )
& ( ~ ( f0 @ $false )
| ~ $true
| ~ $true )
& ( $true
| ~ ( f0 @ $true )
| ~ $true )
& ( ~ ( f0 @ $false )
| ~ ( f0 @ $true )
| ~ $true )
& ( $true
| ( f0 @ $true )
| $true )
& ( ~ $true
| ( f0 @ $false )
| $true ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])]) ).
thf(c_0_16,plain,
( ( $true
| ~ $true
| $true )
& ( ~ ( f3 @ $false )
| ~ $true
| $true )
& ( $true
| ~ ( f3 @ $true )
| $true )
& ( ~ ( f3 @ $false )
| ~ ( f3 @ $true )
| $true )
& ( $true
| ( f3 @ $true )
| ~ $true )
& ( ~ $true
| ( f3 @ $false )
| ~ $true ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])]) ).
thf(c_0_17,plain,
( ~ ( f0 @ $true )
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
thf(c_0_18,plain,
! [X2: $i] :
( ( epred5_1 @ X2 )
| ( f0 @ ~ $true )
| ( epred1_0 @ X2 )
| ~ $true
| ( X2 != esk1_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_19,plain,
( ~ ( f0 @ ~ $true )
| ~ $true
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_20,plain,
! [X70: $i,X71: $o,X72: $o,X73: $o] :
( ( ~ ( f3 @ X73 )
| $true
| ~ ( f3 @ X72 )
| X72
| ( f3 = $not )
| ~ ( f3 @ X71 )
| ~ $true
| ~ ( epred4_0 @ X70 ) )
& ( ~ $true
| ( f3 @ X73 )
| ~ ( f3 @ X72 )
| X72
| ( f3 = $not )
| ~ ( f3 @ X71 )
| ~ $true
| ~ ( epred4_0 @ X70 ) )
& ( ( X70 = esk4_0 )
| ~ ( f3 @ X72 )
| X72
| ( f3 = $not )
| ~ ( f3 @ X71 )
| ~ $true
| ~ ( epred4_0 @ X70 ) )
& ( ~ ( f3 @ X73 )
| $true
| ~ X72
| ( f3 @ X72 )
| ( f3 = $not )
| ~ ( f3 @ X71 )
| ~ $true
| ~ ( epred4_0 @ X70 ) )
& ( ~ $true
| ( f3 @ X73 )
| ~ X72
| ( f3 @ X72 )
| ( f3 = $not )
| ~ ( f3 @ X71 )
| ~ $true
| ~ ( epred4_0 @ X70 ) )
& ( ( X70 = esk4_0 )
| ~ X72
| ( f3 @ X72 )
| ( f3 = $not )
| ~ ( f3 @ X71 )
| ~ $true
| ~ ( epred4_0 @ X70 ) )
& ( ~ ( f3 @ X73 )
| $true
| ( X70 = esk3_0 )
| ( f3 = $not )
| ~ ( f3 @ X71 )
| ~ $true
| ~ ( epred4_0 @ X70 ) )
& ( ~ $true
| ( f3 @ X73 )
| ( X70 = esk3_0 )
| ( f3 = $not )
| ~ ( f3 @ X71 )
| ~ $true
| ~ ( epred4_0 @ X70 ) )
& ( ( X70 = esk4_0 )
| ( X70 = esk3_0 )
| ( f3 = $not )
| ~ ( f3 @ X71 )
| ~ $true
| ~ ( epred4_0 @ X70 ) )
& ( ~ ( f3 @ X73 )
| $true
| ~ ( f3 @ X72 )
| X72
| ( X70 = esk2_0 )
| ~ ( f3 @ X71 )
| ~ $true
| ~ ( epred4_0 @ X70 ) )
& ( ~ $true
| ( f3 @ X73 )
| ~ ( f3 @ X72 )
| X72
| ( X70 = esk2_0 )
| ~ ( f3 @ X71 )
| ~ $true
| ~ ( epred4_0 @ X70 ) )
& ( ( X70 = esk4_0 )
| ~ ( f3 @ X72 )
| X72
| ( X70 = esk2_0 )
| ~ ( f3 @ X71 )
| ~ $true
| ~ ( epred4_0 @ X70 ) )
& ( ~ ( f3 @ X73 )
| $true
| ~ X72
| ( f3 @ X72 )
| ( X70 = esk2_0 )
| ~ ( f3 @ X71 )
| ~ $true
| ~ ( epred4_0 @ X70 ) )
& ( ~ $true
| ( f3 @ X73 )
| ~ X72
| ( f3 @ X72 )
| ( X70 = esk2_0 )
| ~ ( f3 @ X71 )
| ~ $true
| ~ ( epred4_0 @ X70 ) )
& ( ( X70 = esk4_0 )
| ~ X72
| ( f3 @ X72 )
| ( X70 = esk2_0 )
| ~ ( f3 @ X71 )
| ~ $true
| ~ ( epred4_0 @ X70 ) )
& ( ~ ( f3 @ X73 )
| $true
| ( X70 = esk3_0 )
| ( X70 = esk2_0 )
| ~ ( f3 @ X71 )
| ~ $true
| ~ ( epred4_0 @ X70 ) )
& ( ~ $true
| ( f3 @ X73 )
| ( X70 = esk3_0 )
| ( X70 = esk2_0 )
| ~ ( f3 @ X71 )
| ~ $true
| ~ ( epred4_0 @ X70 ) )
& ( ( X70 = esk4_0 )
| ( X70 = esk3_0 )
| ( X70 = esk2_0 )
| ~ ( f3 @ X71 )
| ~ $true
| ~ ( epred4_0 @ X70 ) )
& ( ~ ( f3 @ X73 )
| $true
| ~ ( f3 @ X72 )
| X72
| ( f3 = $not )
| $true
| ( f3 @ X71 )
| ~ ( epred4_0 @ X70 ) )
& ( ~ $true
| ( f3 @ X73 )
| ~ ( f3 @ X72 )
| X72
| ( f3 = $not )
| $true
| ( f3 @ X71 )
| ~ ( epred4_0 @ X70 ) )
& ( ( X70 = esk4_0 )
| ~ ( f3 @ X72 )
| X72
| ( f3 = $not )
| $true
| ( f3 @ X71 )
| ~ ( epred4_0 @ X70 ) )
& ( ~ ( f3 @ X73 )
| $true
| ~ X72
| ( f3 @ X72 )
| ( f3 = $not )
| $true
| ( f3 @ X71 )
| ~ ( epred4_0 @ X70 ) )
& ( ~ $true
| ( f3 @ X73 )
| ~ X72
| ( f3 @ X72 )
| ( f3 = $not )
| $true
| ( f3 @ X71 )
| ~ ( epred4_0 @ X70 ) )
& ( ( X70 = esk4_0 )
| ~ X72
| ( f3 @ X72 )
| ( f3 = $not )
| $true
| ( f3 @ X71 )
| ~ ( epred4_0 @ X70 ) )
& ( ~ ( f3 @ X73 )
| $true
| ( X70 = esk3_0 )
| ( f3 = $not )
| $true
| ( f3 @ X71 )
| ~ ( epred4_0 @ X70 ) )
& ( ~ $true
| ( f3 @ X73 )
| ( X70 = esk3_0 )
| ( f3 = $not )
| $true
| ( f3 @ X71 )
| ~ ( epred4_0 @ X70 ) )
& ( ( X70 = esk4_0 )
| ( X70 = esk3_0 )
| ( f3 = $not )
| $true
| ( f3 @ X71 )
| ~ ( epred4_0 @ X70 ) )
& ( ~ ( f3 @ X73 )
| $true
| ~ ( f3 @ X72 )
| X72
| ( X70 = esk2_0 )
| $true
| ( f3 @ X71 )
| ~ ( epred4_0 @ X70 ) )
& ( ~ $true
| ( f3 @ X73 )
| ~ ( f3 @ X72 )
| X72
| ( X70 = esk2_0 )
| $true
| ( f3 @ X71 )
| ~ ( epred4_0 @ X70 ) )
& ( ( X70 = esk4_0 )
| ~ ( f3 @ X72 )
| X72
| ( X70 = esk2_0 )
| $true
| ( f3 @ X71 )
| ~ ( epred4_0 @ X70 ) )
& ( ~ ( f3 @ X73 )
| $true
| ~ X72
| ( f3 @ X72 )
| ( X70 = esk2_0 )
| $true
| ( f3 @ X71 )
| ~ ( epred4_0 @ X70 ) )
& ( ~ $true
| ( f3 @ X73 )
| ~ X72
| ( f3 @ X72 )
| ( X70 = esk2_0 )
| $true
| ( f3 @ X71 )
| ~ ( epred4_0 @ X70 ) )
& ( ( X70 = esk4_0 )
| ~ X72
| ( f3 @ X72 )
| ( X70 = esk2_0 )
| $true
| ( f3 @ X71 )
| ~ ( epred4_0 @ X70 ) )
& ( ~ ( f3 @ X73 )
| $true
| ( X70 = esk3_0 )
| ( X70 = esk2_0 )
| $true
| ( f3 @ X71 )
| ~ ( epred4_0 @ X70 ) )
& ( ~ $true
| ( f3 @ X73 )
| ( X70 = esk3_0 )
| ( X70 = esk2_0 )
| $true
| ( f3 @ X71 )
| ~ ( epred4_0 @ X70 ) )
& ( ( X70 = esk4_0 )
| ( X70 = esk3_0 )
| ( X70 = esk2_0 )
| $true
| ( f3 @ X71 )
| ~ ( epred4_0 @ X70 ) )
& ( ~ ( f3 @ X73 )
| $true
| ~ ( f3 @ X72 )
| X72
| ( f3 = $not )
| ( X70 = esk1_0 )
| ~ ( epred4_0 @ X70 ) )
& ( ~ $true
| ( f3 @ X73 )
| ~ ( f3 @ X72 )
| X72
| ( f3 = $not )
| ( X70 = esk1_0 )
| ~ ( epred4_0 @ X70 ) )
& ( ( X70 = esk4_0 )
| ~ ( f3 @ X72 )
| X72
| ( f3 = $not )
| ( X70 = esk1_0 )
| ~ ( epred4_0 @ X70 ) )
& ( ~ ( f3 @ X73 )
| $true
| ~ X72
| ( f3 @ X72 )
| ( f3 = $not )
| ( X70 = esk1_0 )
| ~ ( epred4_0 @ X70 ) )
& ( ~ $true
| ( f3 @ X73 )
| ~ X72
| ( f3 @ X72 )
| ( f3 = $not )
| ( X70 = esk1_0 )
| ~ ( epred4_0 @ X70 ) )
& ( ( X70 = esk4_0 )
| ~ X72
| ( f3 @ X72 )
| ( f3 = $not )
| ( X70 = esk1_0 )
| ~ ( epred4_0 @ X70 ) )
& ( ~ ( f3 @ X73 )
| $true
| ( X70 = esk3_0 )
| ( f3 = $not )
| ( X70 = esk1_0 )
| ~ ( epred4_0 @ X70 ) )
& ( ~ $true
| ( f3 @ X73 )
| ( X70 = esk3_0 )
| ( f3 = $not )
| ( X70 = esk1_0 )
| ~ ( epred4_0 @ X70 ) )
& ( ( X70 = esk4_0 )
| ( X70 = esk3_0 )
| ( f3 = $not )
| ( X70 = esk1_0 )
| ~ ( epred4_0 @ X70 ) )
& ( ~ ( f3 @ X73 )
| $true
| ~ ( f3 @ X72 )
| X72
| ( X70 = esk2_0 )
| ( X70 = esk1_0 )
| ~ ( epred4_0 @ X70 ) )
& ( ~ $true
| ( f3 @ X73 )
| ~ ( f3 @ X72 )
| X72
| ( X70 = esk2_0 )
| ( X70 = esk1_0 )
| ~ ( epred4_0 @ X70 ) )
& ( ( X70 = esk4_0 )
| ~ ( f3 @ X72 )
| X72
| ( X70 = esk2_0 )
| ( X70 = esk1_0 )
| ~ ( epred4_0 @ X70 ) )
& ( ~ ( f3 @ X73 )
| $true
| ~ X72
| ( f3 @ X72 )
| ( X70 = esk2_0 )
| ( X70 = esk1_0 )
| ~ ( epred4_0 @ X70 ) )
& ( ~ $true
| ( f3 @ X73 )
| ~ X72
| ( f3 @ X72 )
| ( X70 = esk2_0 )
| ( X70 = esk1_0 )
| ~ ( epred4_0 @ X70 ) )
& ( ( X70 = esk4_0 )
| ~ X72
| ( f3 @ X72 )
| ( X70 = esk2_0 )
| ( X70 = esk1_0 )
| ~ ( epred4_0 @ X70 ) )
& ( ~ ( f3 @ X73 )
| $true
| ( X70 = esk3_0 )
| ( X70 = esk2_0 )
| ( X70 = esk1_0 )
| ~ ( epred4_0 @ X70 ) )
& ( ~ $true
| ( f3 @ X73 )
| ( X70 = esk3_0 )
| ( X70 = esk2_0 )
| ( X70 = esk1_0 )
| ~ ( epred4_0 @ X70 ) )
& ( ( X70 = esk4_0 )
| ( X70 = esk3_0 )
| ( X70 = esk2_0 )
| ( X70 = esk1_0 )
| ~ ( epred4_0 @ X70 ) )
& ( ~ ( epred14_1 @ X70 )
| ( epred14_1 @ X70 )
| $true
| ( X70 != esk1_0 )
| ( epred4_0 @ X70 ) )
& ( ~ ( f3 @ $false )
| ( epred14_1 @ X70 )
| $true
| ( X70 != esk1_0 )
| ( epred4_0 @ X70 ) )
& ( ~ ( epred14_1 @ X70 )
| ~ ( f3 @ $true )
| $true
| ( X70 != esk1_0 )
| ( epred4_0 @ X70 ) )
& ( ~ ( f3 @ $false )
| ~ ( f3 @ $true )
| $true
| ( X70 != esk1_0 )
| ( epred4_0 @ X70 ) )
& ( ~ ( epred14_1 @ X70 )
| ( f3 @ $true )
| ~ $true
| ( X70 != esk1_0 )
| ( epred4_0 @ X70 ) )
& ( ( epred14_1 @ X70 )
| ( f3 @ $false )
| ~ $true
| ( X70 != esk1_0 )
| ( epred4_0 @ X70 ) )
& ( ( f3 != $not )
| ( X70 != esk2_0 )
| ( epred4_0 @ X70 ) )
& ( ~ ( epred15_1 @ X70 )
| ( epred15_1 @ X70 )
| ~ ( epred15_1 @ X70 )
| ( X70 != esk3_0 )
| ( epred4_0 @ X70 ) )
& ( ~ ( f3 @ $false )
| ( epred15_1 @ X70 )
| ~ ( epred15_1 @ X70 )
| ( X70 != esk3_0 )
| ( epred4_0 @ X70 ) )
& ( ~ ( epred15_1 @ X70 )
| ~ ( f3 @ $true )
| ~ ( epred15_1 @ X70 )
| ( X70 != esk3_0 )
| ( epred4_0 @ X70 ) )
& ( ~ ( f3 @ $false )
| ~ ( f3 @ $true )
| ~ ( epred15_1 @ X70 )
| ( X70 != esk3_0 )
| ( epred4_0 @ X70 ) )
& ( ~ ( epred15_1 @ X70 )
| ( f3 @ $true )
| ( epred15_1 @ X70 )
| ( X70 != esk3_0 )
| ( epred4_0 @ X70 ) )
& ( ( epred15_1 @ X70 )
| ( f3 @ $false )
| ( epred15_1 @ X70 )
| ( X70 != esk3_0 )
| ( epred4_0 @ X70 ) )
& ( ~ ( epred16_1 @ X70 )
| ( epred16_1 @ X70 )
| ~ $true
| ( X70 != esk4_0 )
| ( epred4_0 @ X70 ) )
& ( ~ ( f3 @ $false )
| ( epred16_1 @ X70 )
| ~ $true
| ( X70 != esk4_0 )
| ( epred4_0 @ X70 ) )
& ( ~ ( epred16_1 @ X70 )
| ~ ( f3 @ $true )
| ~ $true
| ( X70 != esk4_0 )
| ( epred4_0 @ X70 ) )
& ( ~ ( f3 @ $false )
| ~ ( f3 @ $true )
| ~ $true
| ( X70 != esk4_0 )
| ( epred4_0 @ X70 ) )
& ( ~ ( epred16_1 @ X70 )
| ( f3 @ $true )
| $true
| ( X70 != esk4_0 )
| ( epred4_0 @ X70 ) )
& ( ( epred16_1 @ X70 )
| ( f3 @ $false )
| $true
| ( X70 != esk4_0 )
| ( epred4_0 @ X70 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[])])])])])])]) ).
thf(c_0_21,plain,
( ( f3 @ ~ $true )
| ~ $true
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_22,plain,
! [X56: $i,X57: $o,X58: $o,X59: $o] :
( ( ~ ( f1 @ X59 )
| $true
| ~ ( f1 @ X58 )
| X58
| ( f1 = $not )
| ~ ( f1 @ X57 )
| ~ $true
| ~ ( epred2_0 @ X56 ) )
& ( ~ $true
| ( f1 @ X59 )
| ~ ( f1 @ X58 )
| X58
| ( f1 = $not )
| ~ ( f1 @ X57 )
| ~ $true
| ~ ( epred2_0 @ X56 ) )
& ( ( X56 = esk4_0 )
| ~ ( f1 @ X58 )
| X58
| ( f1 = $not )
| ~ ( f1 @ X57 )
| ~ $true
| ~ ( epred2_0 @ X56 ) )
& ( ~ ( f1 @ X59 )
| $true
| ~ X58
| ( f1 @ X58 )
| ( f1 = $not )
| ~ ( f1 @ X57 )
| ~ $true
| ~ ( epred2_0 @ X56 ) )
& ( ~ $true
| ( f1 @ X59 )
| ~ X58
| ( f1 @ X58 )
| ( f1 = $not )
| ~ ( f1 @ X57 )
| ~ $true
| ~ ( epred2_0 @ X56 ) )
& ( ( X56 = esk4_0 )
| ~ X58
| ( f1 @ X58 )
| ( f1 = $not )
| ~ ( f1 @ X57 )
| ~ $true
| ~ ( epred2_0 @ X56 ) )
& ( ~ ( f1 @ X59 )
| $true
| ( X56 = esk3_0 )
| ( f1 = $not )
| ~ ( f1 @ X57 )
| ~ $true
| ~ ( epred2_0 @ X56 ) )
& ( ~ $true
| ( f1 @ X59 )
| ( X56 = esk3_0 )
| ( f1 = $not )
| ~ ( f1 @ X57 )
| ~ $true
| ~ ( epred2_0 @ X56 ) )
& ( ( X56 = esk4_0 )
| ( X56 = esk3_0 )
| ( f1 = $not )
| ~ ( f1 @ X57 )
| ~ $true
| ~ ( epred2_0 @ X56 ) )
& ( ~ ( f1 @ X59 )
| $true
| ~ ( f1 @ X58 )
| X58
| ( X56 = esk2_0 )
| ~ ( f1 @ X57 )
| ~ $true
| ~ ( epred2_0 @ X56 ) )
& ( ~ $true
| ( f1 @ X59 )
| ~ ( f1 @ X58 )
| X58
| ( X56 = esk2_0 )
| ~ ( f1 @ X57 )
| ~ $true
| ~ ( epred2_0 @ X56 ) )
& ( ( X56 = esk4_0 )
| ~ ( f1 @ X58 )
| X58
| ( X56 = esk2_0 )
| ~ ( f1 @ X57 )
| ~ $true
| ~ ( epred2_0 @ X56 ) )
& ( ~ ( f1 @ X59 )
| $true
| ~ X58
| ( f1 @ X58 )
| ( X56 = esk2_0 )
| ~ ( f1 @ X57 )
| ~ $true
| ~ ( epred2_0 @ X56 ) )
& ( ~ $true
| ( f1 @ X59 )
| ~ X58
| ( f1 @ X58 )
| ( X56 = esk2_0 )
| ~ ( f1 @ X57 )
| ~ $true
| ~ ( epred2_0 @ X56 ) )
& ( ( X56 = esk4_0 )
| ~ X58
| ( f1 @ X58 )
| ( X56 = esk2_0 )
| ~ ( f1 @ X57 )
| ~ $true
| ~ ( epred2_0 @ X56 ) )
& ( ~ ( f1 @ X59 )
| $true
| ( X56 = esk3_0 )
| ( X56 = esk2_0 )
| ~ ( f1 @ X57 )
| ~ $true
| ~ ( epred2_0 @ X56 ) )
& ( ~ $true
| ( f1 @ X59 )
| ( X56 = esk3_0 )
| ( X56 = esk2_0 )
| ~ ( f1 @ X57 )
| ~ $true
| ~ ( epred2_0 @ X56 ) )
& ( ( X56 = esk4_0 )
| ( X56 = esk3_0 )
| ( X56 = esk2_0 )
| ~ ( f1 @ X57 )
| ~ $true
| ~ ( epred2_0 @ X56 ) )
& ( ~ ( f1 @ X59 )
| $true
| ~ ( f1 @ X58 )
| X58
| ( f1 = $not )
| $true
| ( f1 @ X57 )
| ~ ( epred2_0 @ X56 ) )
& ( ~ $true
| ( f1 @ X59 )
| ~ ( f1 @ X58 )
| X58
| ( f1 = $not )
| $true
| ( f1 @ X57 )
| ~ ( epred2_0 @ X56 ) )
& ( ( X56 = esk4_0 )
| ~ ( f1 @ X58 )
| X58
| ( f1 = $not )
| $true
| ( f1 @ X57 )
| ~ ( epred2_0 @ X56 ) )
& ( ~ ( f1 @ X59 )
| $true
| ~ X58
| ( f1 @ X58 )
| ( f1 = $not )
| $true
| ( f1 @ X57 )
| ~ ( epred2_0 @ X56 ) )
& ( ~ $true
| ( f1 @ X59 )
| ~ X58
| ( f1 @ X58 )
| ( f1 = $not )
| $true
| ( f1 @ X57 )
| ~ ( epred2_0 @ X56 ) )
& ( ( X56 = esk4_0 )
| ~ X58
| ( f1 @ X58 )
| ( f1 = $not )
| $true
| ( f1 @ X57 )
| ~ ( epred2_0 @ X56 ) )
& ( ~ ( f1 @ X59 )
| $true
| ( X56 = esk3_0 )
| ( f1 = $not )
| $true
| ( f1 @ X57 )
| ~ ( epred2_0 @ X56 ) )
& ( ~ $true
| ( f1 @ X59 )
| ( X56 = esk3_0 )
| ( f1 = $not )
| $true
| ( f1 @ X57 )
| ~ ( epred2_0 @ X56 ) )
& ( ( X56 = esk4_0 )
| ( X56 = esk3_0 )
| ( f1 = $not )
| $true
| ( f1 @ X57 )
| ~ ( epred2_0 @ X56 ) )
& ( ~ ( f1 @ X59 )
| $true
| ~ ( f1 @ X58 )
| X58
| ( X56 = esk2_0 )
| $true
| ( f1 @ X57 )
| ~ ( epred2_0 @ X56 ) )
& ( ~ $true
| ( f1 @ X59 )
| ~ ( f1 @ X58 )
| X58
| ( X56 = esk2_0 )
| $true
| ( f1 @ X57 )
| ~ ( epred2_0 @ X56 ) )
& ( ( X56 = esk4_0 )
| ~ ( f1 @ X58 )
| X58
| ( X56 = esk2_0 )
| $true
| ( f1 @ X57 )
| ~ ( epred2_0 @ X56 ) )
& ( ~ ( f1 @ X59 )
| $true
| ~ X58
| ( f1 @ X58 )
| ( X56 = esk2_0 )
| $true
| ( f1 @ X57 )
| ~ ( epred2_0 @ X56 ) )
& ( ~ $true
| ( f1 @ X59 )
| ~ X58
| ( f1 @ X58 )
| ( X56 = esk2_0 )
| $true
| ( f1 @ X57 )
| ~ ( epred2_0 @ X56 ) )
& ( ( X56 = esk4_0 )
| ~ X58
| ( f1 @ X58 )
| ( X56 = esk2_0 )
| $true
| ( f1 @ X57 )
| ~ ( epred2_0 @ X56 ) )
& ( ~ ( f1 @ X59 )
| $true
| ( X56 = esk3_0 )
| ( X56 = esk2_0 )
| $true
| ( f1 @ X57 )
| ~ ( epred2_0 @ X56 ) )
& ( ~ $true
| ( f1 @ X59 )
| ( X56 = esk3_0 )
| ( X56 = esk2_0 )
| $true
| ( f1 @ X57 )
| ~ ( epred2_0 @ X56 ) )
& ( ( X56 = esk4_0 )
| ( X56 = esk3_0 )
| ( X56 = esk2_0 )
| $true
| ( f1 @ X57 )
| ~ ( epred2_0 @ X56 ) )
& ( ~ ( f1 @ X59 )
| $true
| ~ ( f1 @ X58 )
| X58
| ( f1 = $not )
| ( X56 = esk1_0 )
| ~ ( epred2_0 @ X56 ) )
& ( ~ $true
| ( f1 @ X59 )
| ~ ( f1 @ X58 )
| X58
| ( f1 = $not )
| ( X56 = esk1_0 )
| ~ ( epred2_0 @ X56 ) )
& ( ( X56 = esk4_0 )
| ~ ( f1 @ X58 )
| X58
| ( f1 = $not )
| ( X56 = esk1_0 )
| ~ ( epred2_0 @ X56 ) )
& ( ~ ( f1 @ X59 )
| $true
| ~ X58
| ( f1 @ X58 )
| ( f1 = $not )
| ( X56 = esk1_0 )
| ~ ( epred2_0 @ X56 ) )
& ( ~ $true
| ( f1 @ X59 )
| ~ X58
| ( f1 @ X58 )
| ( f1 = $not )
| ( X56 = esk1_0 )
| ~ ( epred2_0 @ X56 ) )
& ( ( X56 = esk4_0 )
| ~ X58
| ( f1 @ X58 )
| ( f1 = $not )
| ( X56 = esk1_0 )
| ~ ( epred2_0 @ X56 ) )
& ( ~ ( f1 @ X59 )
| $true
| ( X56 = esk3_0 )
| ( f1 = $not )
| ( X56 = esk1_0 )
| ~ ( epred2_0 @ X56 ) )
& ( ~ $true
| ( f1 @ X59 )
| ( X56 = esk3_0 )
| ( f1 = $not )
| ( X56 = esk1_0 )
| ~ ( epred2_0 @ X56 ) )
& ( ( X56 = esk4_0 )
| ( X56 = esk3_0 )
| ( f1 = $not )
| ( X56 = esk1_0 )
| ~ ( epred2_0 @ X56 ) )
& ( ~ ( f1 @ X59 )
| $true
| ~ ( f1 @ X58 )
| X58
| ( X56 = esk2_0 )
| ( X56 = esk1_0 )
| ~ ( epred2_0 @ X56 ) )
& ( ~ $true
| ( f1 @ X59 )
| ~ ( f1 @ X58 )
| X58
| ( X56 = esk2_0 )
| ( X56 = esk1_0 )
| ~ ( epred2_0 @ X56 ) )
& ( ( X56 = esk4_0 )
| ~ ( f1 @ X58 )
| X58
| ( X56 = esk2_0 )
| ( X56 = esk1_0 )
| ~ ( epred2_0 @ X56 ) )
& ( ~ ( f1 @ X59 )
| $true
| ~ X58
| ( f1 @ X58 )
| ( X56 = esk2_0 )
| ( X56 = esk1_0 )
| ~ ( epred2_0 @ X56 ) )
& ( ~ $true
| ( f1 @ X59 )
| ~ X58
| ( f1 @ X58 )
| ( X56 = esk2_0 )
| ( X56 = esk1_0 )
| ~ ( epred2_0 @ X56 ) )
& ( ( X56 = esk4_0 )
| ~ X58
| ( f1 @ X58 )
| ( X56 = esk2_0 )
| ( X56 = esk1_0 )
| ~ ( epred2_0 @ X56 ) )
& ( ~ ( f1 @ X59 )
| $true
| ( X56 = esk3_0 )
| ( X56 = esk2_0 )
| ( X56 = esk1_0 )
| ~ ( epred2_0 @ X56 ) )
& ( ~ $true
| ( f1 @ X59 )
| ( X56 = esk3_0 )
| ( X56 = esk2_0 )
| ( X56 = esk1_0 )
| ~ ( epred2_0 @ X56 ) )
& ( ( X56 = esk4_0 )
| ( X56 = esk3_0 )
| ( X56 = esk2_0 )
| ( X56 = esk1_0 )
| ~ ( epred2_0 @ X56 ) )
& ( ~ ( epred8_1 @ X56 )
| ( epred8_1 @ X56 )
| $true
| ( X56 != esk1_0 )
| ( epred2_0 @ X56 ) )
& ( ~ ( f1 @ $false )
| ( epred8_1 @ X56 )
| $true
| ( X56 != esk1_0 )
| ( epred2_0 @ X56 ) )
& ( ~ ( epred8_1 @ X56 )
| ~ ( f1 @ $true )
| $true
| ( X56 != esk1_0 )
| ( epred2_0 @ X56 ) )
& ( ~ ( f1 @ $false )
| ~ ( f1 @ $true )
| $true
| ( X56 != esk1_0 )
| ( epred2_0 @ X56 ) )
& ( ~ ( epred8_1 @ X56 )
| ( f1 @ $true )
| ~ $true
| ( X56 != esk1_0 )
| ( epred2_0 @ X56 ) )
& ( ( epred8_1 @ X56 )
| ( f1 @ $false )
| ~ $true
| ( X56 != esk1_0 )
| ( epred2_0 @ X56 ) )
& ( ( f1 != $not )
| ( X56 != esk2_0 )
| ( epred2_0 @ X56 ) )
& ( ~ ( epred9_1 @ X56 )
| ( epred9_1 @ X56 )
| ~ ( epred9_1 @ X56 )
| ( X56 != esk3_0 )
| ( epred2_0 @ X56 ) )
& ( ~ ( f1 @ $false )
| ( epred9_1 @ X56 )
| ~ ( epred9_1 @ X56 )
| ( X56 != esk3_0 )
| ( epred2_0 @ X56 ) )
& ( ~ ( epred9_1 @ X56 )
| ~ ( f1 @ $true )
| ~ ( epred9_1 @ X56 )
| ( X56 != esk3_0 )
| ( epred2_0 @ X56 ) )
& ( ~ ( f1 @ $false )
| ~ ( f1 @ $true )
| ~ ( epred9_1 @ X56 )
| ( X56 != esk3_0 )
| ( epred2_0 @ X56 ) )
& ( ~ ( epred9_1 @ X56 )
| ( f1 @ $true )
| ( epred9_1 @ X56 )
| ( X56 != esk3_0 )
| ( epred2_0 @ X56 ) )
& ( ( epred9_1 @ X56 )
| ( f1 @ $false )
| ( epred9_1 @ X56 )
| ( X56 != esk3_0 )
| ( epred2_0 @ X56 ) )
& ( ~ ( epred10_1 @ X56 )
| ( epred10_1 @ X56 )
| ~ $true
| ( X56 != esk4_0 )
| ( epred2_0 @ X56 ) )
& ( ~ ( f1 @ $false )
| ( epred10_1 @ X56 )
| ~ $true
| ( X56 != esk4_0 )
| ( epred2_0 @ X56 ) )
& ( ~ ( epred10_1 @ X56 )
| ~ ( f1 @ $true )
| ~ $true
| ( X56 != esk4_0 )
| ( epred2_0 @ X56 ) )
& ( ~ ( f1 @ $false )
| ~ ( f1 @ $true )
| ~ $true
| ( X56 != esk4_0 )
| ( epred2_0 @ X56 ) )
& ( ~ ( epred10_1 @ X56 )
| ( f1 @ $true )
| $true
| ( X56 != esk4_0 )
| ( epred2_0 @ X56 ) )
& ( ( epred10_1 @ X56 )
| ( f1 @ $false )
| $true
| ( X56 != esk4_0 )
| ( epred2_0 @ X56 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[])])])])])])]) ).
thf(c_0_23,plain,
! [X8: $o,X2: $i] :
( ( f0 @ X8 )
| ( f0 @ $true )
| ( f0 = $not )
| ( X2 = esk1_0 )
| ~ ( epred1_0 @ X2 ) ),
inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_14])])]) ).
thf(c_0_24,plain,
~ ( f0 @ $true ),
inference(cn,[status(thm)],[c_0_17]) ).
thf(c_0_25,plain,
! [X2: $i] :
( ( f0 @ $true )
| ( epred1_0 @ X2 )
| ~ ( epred5_1 @ X2 )
| ~ $true
| ( X2 != esk1_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
thf(c_0_26,plain,
! [X2: $i] :
( ( epred1_0 @ X2 )
| ( epred5_1 @ X2 )
| ( f0 @ ~ $true )
| ( X2 != esk1_0 ) ),
inference(cn,[status(thm)],[c_0_18]) ).
thf(c_0_27,plain,
~ ( f0 @ ~ $true ),
inference(cn,[status(thm)],[c_0_19]) ).
thf(c_0_28,plain,
! [X15: $o,X2: $i] :
( ( X2 = esk4_0 )
| ( f3 = $not )
| ~ ( f3 @ ~ $true )
| ~ ( f3 @ X15 )
| ~ ( epred4_0 @ X2 ) ),
inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_20])])]) ).
thf(c_0_29,plain,
f3 @ ~ $true,
inference(cn,[status(thm)],[c_0_21]) ).
thf(c_0_30,plain,
( ( ~ ( f3 @ $true )
| $true )
& ( ~ $true
| ( f3 @ $true ) ) ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[f3t])]) ).
thf(c_0_31,axiom,
( ( ( ~ ~ $true
| ( f1 @ $true ) )
& ( ~ $true
| ( f1 @ $false ) ) )
<=> $true ),
inference(fool_unroll,[status(thm)],[f1f]) ).
thf(c_0_32,plain,
! [X2: $i] :
( ( epred2_0 @ X2 )
| ( f1 != $not )
| ( X2 != esk2_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
thf(c_0_33,plain,
( ( ~ ( f1 @ $true )
| ~ $true )
& ( $true
| ( f1 @ $true ) ) ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[f1t])]) ).
thf(c_0_34,plain,
! [X63: $i,X64: $o,X65: $o,X66: $o] :
( ( ~ ( f2 @ X66 )
| $true
| ~ ( f2 @ X65 )
| X65
| ( f2 = $not )
| ~ ( f2 @ X64 )
| ~ $true
| ~ ( epred3_0 @ X63 ) )
& ( ~ $true
| ( f2 @ X66 )
| ~ ( f2 @ X65 )
| X65
| ( f2 = $not )
| ~ ( f2 @ X64 )
| ~ $true
| ~ ( epred3_0 @ X63 ) )
& ( ( X63 = esk4_0 )
| ~ ( f2 @ X65 )
| X65
| ( f2 = $not )
| ~ ( f2 @ X64 )
| ~ $true
| ~ ( epred3_0 @ X63 ) )
& ( ~ ( f2 @ X66 )
| $true
| ~ X65
| ( f2 @ X65 )
| ( f2 = $not )
| ~ ( f2 @ X64 )
| ~ $true
| ~ ( epred3_0 @ X63 ) )
& ( ~ $true
| ( f2 @ X66 )
| ~ X65
| ( f2 @ X65 )
| ( f2 = $not )
| ~ ( f2 @ X64 )
| ~ $true
| ~ ( epred3_0 @ X63 ) )
& ( ( X63 = esk4_0 )
| ~ X65
| ( f2 @ X65 )
| ( f2 = $not )
| ~ ( f2 @ X64 )
| ~ $true
| ~ ( epred3_0 @ X63 ) )
& ( ~ ( f2 @ X66 )
| $true
| ( X63 = esk3_0 )
| ( f2 = $not )
| ~ ( f2 @ X64 )
| ~ $true
| ~ ( epred3_0 @ X63 ) )
& ( ~ $true
| ( f2 @ X66 )
| ( X63 = esk3_0 )
| ( f2 = $not )
| ~ ( f2 @ X64 )
| ~ $true
| ~ ( epred3_0 @ X63 ) )
& ( ( X63 = esk4_0 )
| ( X63 = esk3_0 )
| ( f2 = $not )
| ~ ( f2 @ X64 )
| ~ $true
| ~ ( epred3_0 @ X63 ) )
& ( ~ ( f2 @ X66 )
| $true
| ~ ( f2 @ X65 )
| X65
| ( X63 = esk2_0 )
| ~ ( f2 @ X64 )
| ~ $true
| ~ ( epred3_0 @ X63 ) )
& ( ~ $true
| ( f2 @ X66 )
| ~ ( f2 @ X65 )
| X65
| ( X63 = esk2_0 )
| ~ ( f2 @ X64 )
| ~ $true
| ~ ( epred3_0 @ X63 ) )
& ( ( X63 = esk4_0 )
| ~ ( f2 @ X65 )
| X65
| ( X63 = esk2_0 )
| ~ ( f2 @ X64 )
| ~ $true
| ~ ( epred3_0 @ X63 ) )
& ( ~ ( f2 @ X66 )
| $true
| ~ X65
| ( f2 @ X65 )
| ( X63 = esk2_0 )
| ~ ( f2 @ X64 )
| ~ $true
| ~ ( epred3_0 @ X63 ) )
& ( ~ $true
| ( f2 @ X66 )
| ~ X65
| ( f2 @ X65 )
| ( X63 = esk2_0 )
| ~ ( f2 @ X64 )
| ~ $true
| ~ ( epred3_0 @ X63 ) )
& ( ( X63 = esk4_0 )
| ~ X65
| ( f2 @ X65 )
| ( X63 = esk2_0 )
| ~ ( f2 @ X64 )
| ~ $true
| ~ ( epred3_0 @ X63 ) )
& ( ~ ( f2 @ X66 )
| $true
| ( X63 = esk3_0 )
| ( X63 = esk2_0 )
| ~ ( f2 @ X64 )
| ~ $true
| ~ ( epred3_0 @ X63 ) )
& ( ~ $true
| ( f2 @ X66 )
| ( X63 = esk3_0 )
| ( X63 = esk2_0 )
| ~ ( f2 @ X64 )
| ~ $true
| ~ ( epred3_0 @ X63 ) )
& ( ( X63 = esk4_0 )
| ( X63 = esk3_0 )
| ( X63 = esk2_0 )
| ~ ( f2 @ X64 )
| ~ $true
| ~ ( epred3_0 @ X63 ) )
& ( ~ ( f2 @ X66 )
| $true
| ~ ( f2 @ X65 )
| X65
| ( f2 = $not )
| $true
| ( f2 @ X64 )
| ~ ( epred3_0 @ X63 ) )
& ( ~ $true
| ( f2 @ X66 )
| ~ ( f2 @ X65 )
| X65
| ( f2 = $not )
| $true
| ( f2 @ X64 )
| ~ ( epred3_0 @ X63 ) )
& ( ( X63 = esk4_0 )
| ~ ( f2 @ X65 )
| X65
| ( f2 = $not )
| $true
| ( f2 @ X64 )
| ~ ( epred3_0 @ X63 ) )
& ( ~ ( f2 @ X66 )
| $true
| ~ X65
| ( f2 @ X65 )
| ( f2 = $not )
| $true
| ( f2 @ X64 )
| ~ ( epred3_0 @ X63 ) )
& ( ~ $true
| ( f2 @ X66 )
| ~ X65
| ( f2 @ X65 )
| ( f2 = $not )
| $true
| ( f2 @ X64 )
| ~ ( epred3_0 @ X63 ) )
& ( ( X63 = esk4_0 )
| ~ X65
| ( f2 @ X65 )
| ( f2 = $not )
| $true
| ( f2 @ X64 )
| ~ ( epred3_0 @ X63 ) )
& ( ~ ( f2 @ X66 )
| $true
| ( X63 = esk3_0 )
| ( f2 = $not )
| $true
| ( f2 @ X64 )
| ~ ( epred3_0 @ X63 ) )
& ( ~ $true
| ( f2 @ X66 )
| ( X63 = esk3_0 )
| ( f2 = $not )
| $true
| ( f2 @ X64 )
| ~ ( epred3_0 @ X63 ) )
& ( ( X63 = esk4_0 )
| ( X63 = esk3_0 )
| ( f2 = $not )
| $true
| ( f2 @ X64 )
| ~ ( epred3_0 @ X63 ) )
& ( ~ ( f2 @ X66 )
| $true
| ~ ( f2 @ X65 )
| X65
| ( X63 = esk2_0 )
| $true
| ( f2 @ X64 )
| ~ ( epred3_0 @ X63 ) )
& ( ~ $true
| ( f2 @ X66 )
| ~ ( f2 @ X65 )
| X65
| ( X63 = esk2_0 )
| $true
| ( f2 @ X64 )
| ~ ( epred3_0 @ X63 ) )
& ( ( X63 = esk4_0 )
| ~ ( f2 @ X65 )
| X65
| ( X63 = esk2_0 )
| $true
| ( f2 @ X64 )
| ~ ( epred3_0 @ X63 ) )
& ( ~ ( f2 @ X66 )
| $true
| ~ X65
| ( f2 @ X65 )
| ( X63 = esk2_0 )
| $true
| ( f2 @ X64 )
| ~ ( epred3_0 @ X63 ) )
& ( ~ $true
| ( f2 @ X66 )
| ~ X65
| ( f2 @ X65 )
| ( X63 = esk2_0 )
| $true
| ( f2 @ X64 )
| ~ ( epred3_0 @ X63 ) )
& ( ( X63 = esk4_0 )
| ~ X65
| ( f2 @ X65 )
| ( X63 = esk2_0 )
| $true
| ( f2 @ X64 )
| ~ ( epred3_0 @ X63 ) )
& ( ~ ( f2 @ X66 )
| $true
| ( X63 = esk3_0 )
| ( X63 = esk2_0 )
| $true
| ( f2 @ X64 )
| ~ ( epred3_0 @ X63 ) )
& ( ~ $true
| ( f2 @ X66 )
| ( X63 = esk3_0 )
| ( X63 = esk2_0 )
| $true
| ( f2 @ X64 )
| ~ ( epred3_0 @ X63 ) )
& ( ( X63 = esk4_0 )
| ( X63 = esk3_0 )
| ( X63 = esk2_0 )
| $true
| ( f2 @ X64 )
| ~ ( epred3_0 @ X63 ) )
& ( ~ ( f2 @ X66 )
| $true
| ~ ( f2 @ X65 )
| X65
| ( f2 = $not )
| ( X63 = esk1_0 )
| ~ ( epred3_0 @ X63 ) )
& ( ~ $true
| ( f2 @ X66 )
| ~ ( f2 @ X65 )
| X65
| ( f2 = $not )
| ( X63 = esk1_0 )
| ~ ( epred3_0 @ X63 ) )
& ( ( X63 = esk4_0 )
| ~ ( f2 @ X65 )
| X65
| ( f2 = $not )
| ( X63 = esk1_0 )
| ~ ( epred3_0 @ X63 ) )
& ( ~ ( f2 @ X66 )
| $true
| ~ X65
| ( f2 @ X65 )
| ( f2 = $not )
| ( X63 = esk1_0 )
| ~ ( epred3_0 @ X63 ) )
& ( ~ $true
| ( f2 @ X66 )
| ~ X65
| ( f2 @ X65 )
| ( f2 = $not )
| ( X63 = esk1_0 )
| ~ ( epred3_0 @ X63 ) )
& ( ( X63 = esk4_0 )
| ~ X65
| ( f2 @ X65 )
| ( f2 = $not )
| ( X63 = esk1_0 )
| ~ ( epred3_0 @ X63 ) )
& ( ~ ( f2 @ X66 )
| $true
| ( X63 = esk3_0 )
| ( f2 = $not )
| ( X63 = esk1_0 )
| ~ ( epred3_0 @ X63 ) )
& ( ~ $true
| ( f2 @ X66 )
| ( X63 = esk3_0 )
| ( f2 = $not )
| ( X63 = esk1_0 )
| ~ ( epred3_0 @ X63 ) )
& ( ( X63 = esk4_0 )
| ( X63 = esk3_0 )
| ( f2 = $not )
| ( X63 = esk1_0 )
| ~ ( epred3_0 @ X63 ) )
& ( ~ ( f2 @ X66 )
| $true
| ~ ( f2 @ X65 )
| X65
| ( X63 = esk2_0 )
| ( X63 = esk1_0 )
| ~ ( epred3_0 @ X63 ) )
& ( ~ $true
| ( f2 @ X66 )
| ~ ( f2 @ X65 )
| X65
| ( X63 = esk2_0 )
| ( X63 = esk1_0 )
| ~ ( epred3_0 @ X63 ) )
& ( ( X63 = esk4_0 )
| ~ ( f2 @ X65 )
| X65
| ( X63 = esk2_0 )
| ( X63 = esk1_0 )
| ~ ( epred3_0 @ X63 ) )
& ( ~ ( f2 @ X66 )
| $true
| ~ X65
| ( f2 @ X65 )
| ( X63 = esk2_0 )
| ( X63 = esk1_0 )
| ~ ( epred3_0 @ X63 ) )
& ( ~ $true
| ( f2 @ X66 )
| ~ X65
| ( f2 @ X65 )
| ( X63 = esk2_0 )
| ( X63 = esk1_0 )
| ~ ( epred3_0 @ X63 ) )
& ( ( X63 = esk4_0 )
| ~ X65
| ( f2 @ X65 )
| ( X63 = esk2_0 )
| ( X63 = esk1_0 )
| ~ ( epred3_0 @ X63 ) )
& ( ~ ( f2 @ X66 )
| $true
| ( X63 = esk3_0 )
| ( X63 = esk2_0 )
| ( X63 = esk1_0 )
| ~ ( epred3_0 @ X63 ) )
& ( ~ $true
| ( f2 @ X66 )
| ( X63 = esk3_0 )
| ( X63 = esk2_0 )
| ( X63 = esk1_0 )
| ~ ( epred3_0 @ X63 ) )
& ( ( X63 = esk4_0 )
| ( X63 = esk3_0 )
| ( X63 = esk2_0 )
| ( X63 = esk1_0 )
| ~ ( epred3_0 @ X63 ) )
& ( ~ ( epred11_1 @ X63 )
| ( epred11_1 @ X63 )
| $true
| ( X63 != esk1_0 )
| ( epred3_0 @ X63 ) )
& ( ~ ( f2 @ $false )
| ( epred11_1 @ X63 )
| $true
| ( X63 != esk1_0 )
| ( epred3_0 @ X63 ) )
& ( ~ ( epred11_1 @ X63 )
| ~ ( f2 @ $true )
| $true
| ( X63 != esk1_0 )
| ( epred3_0 @ X63 ) )
& ( ~ ( f2 @ $false )
| ~ ( f2 @ $true )
| $true
| ( X63 != esk1_0 )
| ( epred3_0 @ X63 ) )
& ( ~ ( epred11_1 @ X63 )
| ( f2 @ $true )
| ~ $true
| ( X63 != esk1_0 )
| ( epred3_0 @ X63 ) )
& ( ( epred11_1 @ X63 )
| ( f2 @ $false )
| ~ $true
| ( X63 != esk1_0 )
| ( epred3_0 @ X63 ) )
& ( ( f2 != $not )
| ( X63 != esk2_0 )
| ( epred3_0 @ X63 ) )
& ( ~ ( epred12_1 @ X63 )
| ( epred12_1 @ X63 )
| ~ ( epred12_1 @ X63 )
| ( X63 != esk3_0 )
| ( epred3_0 @ X63 ) )
& ( ~ ( f2 @ $false )
| ( epred12_1 @ X63 )
| ~ ( epred12_1 @ X63 )
| ( X63 != esk3_0 )
| ( epred3_0 @ X63 ) )
& ( ~ ( epred12_1 @ X63 )
| ~ ( f2 @ $true )
| ~ ( epred12_1 @ X63 )
| ( X63 != esk3_0 )
| ( epred3_0 @ X63 ) )
& ( ~ ( f2 @ $false )
| ~ ( f2 @ $true )
| ~ ( epred12_1 @ X63 )
| ( X63 != esk3_0 )
| ( epred3_0 @ X63 ) )
& ( ~ ( epred12_1 @ X63 )
| ( f2 @ $true )
| ( epred12_1 @ X63 )
| ( X63 != esk3_0 )
| ( epred3_0 @ X63 ) )
& ( ( epred12_1 @ X63 )
| ( f2 @ $false )
| ( epred12_1 @ X63 )
| ( X63 != esk3_0 )
| ( epred3_0 @ X63 ) )
& ( ~ ( epred13_1 @ X63 )
| ( epred13_1 @ X63 )
| ~ $true
| ( X63 != esk4_0 )
| ( epred3_0 @ X63 ) )
& ( ~ ( f2 @ $false )
| ( epred13_1 @ X63 )
| ~ $true
| ( X63 != esk4_0 )
| ( epred3_0 @ X63 ) )
& ( ~ ( epred13_1 @ X63 )
| ~ ( f2 @ $true )
| ~ $true
| ( X63 != esk4_0 )
| ( epred3_0 @ X63 ) )
& ( ~ ( f2 @ $false )
| ~ ( f2 @ $true )
| ~ $true
| ( X63 != esk4_0 )
| ( epred3_0 @ X63 ) )
& ( ~ ( epred13_1 @ X63 )
| ( f2 @ $true )
| $true
| ( X63 != esk4_0 )
| ( epred3_0 @ X63 ) )
& ( ( epred13_1 @ X63 )
| ( f2 @ $false )
| $true
| ( X63 != esk4_0 )
| ( epred3_0 @ X63 ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[])])])])])])]) ).
thf(c_0_35,axiom,
( ( ( ~ ~ $true
| ( f2 @ $true ) )
& ( ~ $true
| ( f2 @ $false ) ) )
<=> ~ $true ),
inference(fool_unroll,[status(thm)],[f2f]) ).
thf(c_0_36,plain,
( ( ~ ( f2 @ $true )
| $true )
& ( ~ $true
| ( f2 @ $true ) ) ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[f2t])]) ).
thf(c_0_37,plain,
( case
= ( ^ [Z0: $o > $o,Z1: $i,Z2: $i,Z3: $i,Z4: $i] :
( eps
@ ^ [Z5: $i] :
( ( ( Z0
= ( ^ [Z6: $o] : ~ $true ) )
& ( Z5 = Z1 ) )
| ( ( Z0 = $not )
& ( Z5 = Z2 ) )
| ( ( Z0
= ( ^ [Z6: $o] : Z6 ) )
& ( Z5 = Z3 ) )
| ( ( Z0
= ( ^ [Z6: $o] : $true ) )
& Z5 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[caseood]) ).
thf(c_0_38,plain,
! [X2: $i] :
( ( $not = f0 )
| ( X2 = esk1_0 )
| ~ ( epred1_0 @ X2 ) ),
inference(sr,[status(thm)],[inference(condense,[status(thm)],[c_0_23]),c_0_24]) ).
thf(c_0_39,plain,
! [X31: $i > $o,X32: $i] :
( ~ ( X31 @ X32 )
| ( X31 @ ( eps @ X31 ) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[choiceax])])])]) ).
thf(c_0_40,plain,
! [X2: $i] :
( ( epred1_0 @ X2 )
| ( f0 @ $true )
| ( X2 != esk1_0 )
| ~ ( epred5_1 @ X2 ) ),
inference(cn,[status(thm)],[c_0_25]) ).
thf(c_0_41,plain,
( ( epred1_0 @ esk1_0 )
| ( epred5_1 @ esk1_0 ) ),
inference(er,[status(thm)],[inference(sr,[status(thm)],[c_0_26,c_0_27])]) ).
thf(c_0_42,plain,
! [X8: $o,X2: $i] :
( ( $not = f3 )
| ( X2 = esk4_0 )
| ~ ( f3 @ X8 )
| ~ ( epred4_0 @ X2 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_29])]) ).
thf(c_0_43,plain,
( ( f3 @ $true )
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_44,plain,
! [X2: $i] :
( ( epred4_0 @ X2 )
| ~ ( f3 @ ~ $true )
| ~ ( f3 @ $true )
| ~ $true
| ( X2 != esk4_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_45,plain,
( ( $true
| ~ $true
| $true )
& ( ~ ( f1 @ $false )
| ~ $true
| $true )
& ( $true
| ~ ( f1 @ $true )
| $true )
& ( ~ ( f1 @ $false )
| ~ ( f1 @ $true )
| $true )
& ( $true
| ( f1 @ $true )
| ~ $true )
& ( ~ $true
| ( f1 @ $false )
| ~ $true ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_31])])]) ).
thf(c_0_46,plain,
( ( epred2_0 @ esk2_0 )
| ( $not != f1 ) ),
inference(er,[status(thm)],[c_0_32]) ).
thf(c_0_47,plain,
( ~ ( f1 @ $true )
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
thf(c_0_48,plain,
! [X8: $o,X2: $i] :
( ( X2 = esk4_0 )
| ( X2 = esk3_0 )
| ( f2 = $not )
| ~ ( f2 @ X8 )
| ~ $true
| ~ ( epred3_0 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
thf(c_0_49,plain,
( ( $true
| ~ $true
| ~ $true )
& ( ~ ( f2 @ $false )
| ~ $true
| ~ $true )
& ( $true
| ~ ( f2 @ $true )
| ~ $true )
& ( ~ ( f2 @ $false )
| ~ ( f2 @ $true )
| ~ $true )
& ( $true
| ( f2 @ $true )
| $true )
& ( ~ $true
| ( f2 @ $false )
| $true ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_35])])]) ).
thf(c_0_50,plain,
! [X2: $i] :
( ( epred3_0 @ X2 )
| ~ ( epred12_1 @ X2 )
| ~ ( f2 @ $true )
| ~ ( epred12_1 @ X2 )
| ( X2 != esk3_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
thf(c_0_51,plain,
( ( f2 @ $true )
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
thf(c_0_52,negated_conjecture,
~ ! [X2: $i,X4: $i,X5: $i,X6: $i] :
( ( ( eps
@ ^ [Z0: $i] :
( ( ! [X15: $o] :
( ( f0 @ X15 )
<=> ~ $true )
& ( Z0 = X2 ) )
| ( ( f0 = $not )
& ( Z0 = X4 ) )
| ( ! [X16: $o] :
( ( f0 @ X16 )
<=> X16 )
& ( Z0 = X5 ) )
| ( ! [X17: $o] :
( ( f0 @ X17 )
<=> $true )
& ( Z0 = X6 ) ) ) )
= X2 )
& ( ( eps
@ ^ [Z0: $i] :
( ( ! [X18: $o] :
( ( f1 @ X18 )
<=> ~ $true )
& ( Z0 = X2 ) )
| ( ( f1 = $not )
& ( Z0 = X4 ) )
| ( ! [X19: $o] :
( ( f1 @ X19 )
<=> X19 )
& ( Z0 = X5 ) )
| ( ! [X20: $o] :
( ( f1 @ X20 )
<=> $true )
& ( Z0 = X6 ) ) ) )
= X4 )
& ( ( eps
@ ^ [Z0: $i] :
( ( ! [X21: $o] :
( ( f2 @ X21 )
<=> ~ $true )
& ( Z0 = X2 ) )
| ( ( f2 = $not )
& ( Z0 = X4 ) )
| ( ! [X22: $o] :
( ( f2 @ X22 )
<=> X22 )
& ( Z0 = X5 ) )
| ( ! [X23: $o] :
( ( f2 @ X23 )
<=> $true )
& ( Z0 = X6 ) ) ) )
= X5 )
& ( ( eps
@ ^ [Z0: $i] :
( ( ! [X24: $o] :
( ( f3 @ X24 )
<=> ~ $true )
& ( Z0 = X2 ) )
| ( ( f3 = $not )
& ( Z0 = X4 ) )
| ( ! [X25: $o] :
( ( f3 @ X25 )
<=> X25 )
& ( Z0 = X5 ) )
| ( ! [X26: $o] :
( ( f3 @ X26 )
<=> $true )
& ( Z0 = X6 ) ) ) )
= X6 ) ),
inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[conj]),c_0_37])]) ).
thf(c_0_53,plain,
! [X77: $o,X2: $i] :
( ( ~ X77
<=> ( f0 @ X77 ) )
| ( X2 = esk1_0 )
| ~ ( epred1_0 @ X2 ) ),
inference(arg_cong,[status(thm)],[c_0_38]) ).
thf(c_0_54,plain,
! [X1: $i > $o,X2: $i] :
( ( X1 @ ( eps @ X1 ) )
| ~ ( X1 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
thf(c_0_55,plain,
epred1_0 @ esk1_0,
inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(sr,[status(thm)],[c_0_40,c_0_24])]),c_0_41]) ).
thf(c_0_56,plain,
! [X94: $o,X8: $o,X2: $i] :
( ( ~ X94
<=> ( f3 @ X94 ) )
| ( X2 = esk4_0 )
| ~ ( f3 @ X8 )
| ~ ( epred4_0 @ X2 ) ),
inference(arg_cong,[status(thm)],[c_0_42]) ).
thf(c_0_57,plain,
f3 @ $true,
inference(cn,[status(thm)],[c_0_43]) ).
thf(c_0_58,plain,
! [X2: $i] :
( ( epred4_0 @ X2 )
| ( X2 != esk4_0 )
| ~ ( f3 @ $true )
| ~ ( f3 @ ~ $true ) ),
inference(cn,[status(thm)],[c_0_44]) ).
thf(c_0_59,plain,
( ( f1 @ ~ $true )
| ~ $true
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
thf(c_0_60,plain,
( ( epred2_0 @ esk2_0 )
| ( ~ esk6_0
<~> ( f1 @ esk6_0 ) ) ),
inference(neg_ext,[status(thm)],[c_0_46]) ).
thf(c_0_61,plain,
~ ( f1 @ $true ),
inference(cn,[status(thm)],[c_0_47]) ).
thf(c_0_62,plain,
! [X8: $o,X2: $i] :
( ( X2 = esk3_0 )
| ( X2 = esk4_0 )
| ( f2 = $not )
| ~ ( f2 @ X8 )
| ~ ( epred3_0 @ X2 ) ),
inference(cn,[status(thm)],[c_0_48]) ).
thf(c_0_63,plain,
! [X2: $i] :
( ( epred12_1 @ X2 )
| ( f2 @ ~ $true )
| ( epred12_1 @ X2 )
| ( epred3_0 @ X2 )
| ( X2 != esk3_0 ) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
thf(c_0_64,plain,
( ~ ( f2 @ ~ $true )
| ~ $true
| ~ $true ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
thf(c_0_65,plain,
! [X2: $i] :
( ( epred3_0 @ X2 )
| ( X2 != esk3_0 )
| ~ ( epred12_1 @ X2 )
| ~ ( f2 @ $true ) ),
inference(cn,[status(thm)],[c_0_50]) ).
thf(c_0_66,plain,
f2 @ $true,
inference(cn,[status(thm)],[c_0_51]) ).
thf(c_0_67,negated_conjecture,
( ( ( eps
@ ^ [Z0: $i] :
( ( ! [X15: $o] :
( ( f0 @ X15 )
<=> ~ $true )
& ( Z0 = esk1_0 ) )
| ( ( f0 = $not )
& ( Z0 = esk2_0 ) )
| ( ! [X16: $o] :
( ( f0 @ X16 )
<=> X16 )
& ( Z0 = esk3_0 ) )
| ( ! [X17: $o] :
( ( f0 @ X17 )
<=> $true )
& ( Z0 = esk4_0 ) ) ) )
!= esk1_0 )
| ( ( eps
@ ^ [Z0: $i] :
( ( ! [X18: $o] :
( ( f1 @ X18 )
<=> ~ $true )
& ( Z0 = esk1_0 ) )
| ( ( f1 = $not )
& ( Z0 = esk2_0 ) )
| ( ! [X19: $o] :
( ( f1 @ X19 )
<=> X19 )
& ( Z0 = esk3_0 ) )
| ( ! [X20: $o] :
( ( f1 @ X20 )
<=> $true )
& ( Z0 = esk4_0 ) ) ) )
!= esk2_0 )
| ( ( eps
@ ^ [Z0: $i] :
( ( ! [X21: $o] :
( ( f2 @ X21 )
<=> ~ $true )
& ( Z0 = esk1_0 ) )
| ( ( f2 = $not )
& ( Z0 = esk2_0 ) )
| ( ! [X22: $o] :
( ( f2 @ X22 )
<=> X22 )
& ( Z0 = esk3_0 ) )
| ( ! [X23: $o] :
( ( f2 @ X23 )
<=> $true )
& ( Z0 = esk4_0 ) ) ) )
!= esk3_0 )
| ( ( eps
@ ^ [Z0: $i] :
( ( ! [X24: $o] :
( ( f3 @ X24 )
<=> ~ $true )
& ( Z0 = esk1_0 ) )
| ( ( f3 = $not )
& ( Z0 = esk2_0 ) )
| ( ! [X25: $o] :
( ( f3 @ X25 )
<=> X25 )
& ( Z0 = esk3_0 ) )
| ( ! [X26: $o] :
( ( f3 @ X26 )
<=> $true )
& ( Z0 = esk4_0 ) ) ) )
!= esk4_0 ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_52])])])]) ).
thf(c_0_68,plain,
! [X48: $i] :
( ( epred4_0 @ X48 )
<=> ( ( ! [X45: $o] :
( ( f3 @ X45 )
<=> ~ $true )
& ( X48 = esk1_0 ) )
| ( ( f3 = $not )
& ( X48 = esk2_0 ) )
| ( ! [X46: $o] :
( ( f3 @ X46 )
<=> X46 )
& ( X48 = esk3_0 ) )
| ( ! [X47: $o] :
( ( f3 @ X47 )
<=> $true )
& ( X48 = esk4_0 ) ) ) ),
introduced(definition) ).
thf(c_0_69,plain,
! [X44: $i] :
( ( epred3_0 @ X44 )
<=> ( ( ! [X41: $o] :
( ( f2 @ X41 )
<=> ~ $true )
& ( X44 = esk1_0 ) )
| ( ( f2 = $not )
& ( X44 = esk2_0 ) )
| ( ! [X42: $o] :
( ( f2 @ X42 )
<=> X42 )
& ( X44 = esk3_0 ) )
| ( ! [X43: $o] :
( ( f2 @ X43 )
<=> $true )
& ( X44 = esk4_0 ) ) ) ),
introduced(definition) ).
thf(c_0_70,plain,
! [X40: $i] :
( ( epred2_0 @ X40 )
<=> ( ( ! [X37: $o] :
( ( f1 @ X37 )
<=> ~ $true )
& ( X40 = esk1_0 ) )
| ( ( f1 = $not )
& ( X40 = esk2_0 ) )
| ( ! [X38: $o] :
( ( f1 @ X38 )
<=> X38 )
& ( X40 = esk3_0 ) )
| ( ! [X39: $o] :
( ( f1 @ X39 )
<=> $true )
& ( X40 = esk4_0 ) ) ) ),
introduced(definition) ).
thf(c_0_71,plain,
! [X36: $i] :
( ( epred1_0 @ X36 )
<=> ( ( ! [X33: $o] :
( ( f0 @ X33 )
<=> ~ $true )
& ( X36 = esk1_0 ) )
| ( ( f0 = $not )
& ( X36 = esk2_0 ) )
| ( ! [X34: $o] :
( ( f0 @ X34 )
<=> X34 )
& ( X36 = esk3_0 ) )
| ( ! [X35: $o] :
( ( f0 @ X35 )
<=> $true )
& ( X36 = esk4_0 ) ) ) ),
introduced(definition) ).
thf(c_0_72,plain,
! [X2: $i] :
( ( X2 = esk1_0 )
| ~ ( epred1_0 @ X2 ) ),
inference(sr,[status(thm)],[inference(dynamic_cnf,[status(thm)],[c_0_53]),c_0_27]) ).
thf(c_0_73,plain,
epred1_0 @ ( eps @ epred1_0 ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
thf(c_0_74,plain,
! [X8: $o,X2: $i] :
( ( X2 = esk4_0 )
| ~ ( f3 @ X8 )
| ~ ( epred4_0 @ X2 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(dynamic_cnf,[status(thm)],[c_0_56]),c_0_57])]) ).
thf(c_0_75,plain,
epred4_0 @ esk4_0,
inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_57]),c_0_29])])]) ).
thf(c_0_76,plain,
! [X16: $o,X8: $o,X2: $i] :
( ( f1 @ X8 )
| ( f1 @ $true )
| ( X2 = esk2_0 )
| ~ ( f1 @ X16 )
| ~ ( epred2_0 @ X2 ) ),
inference(cn,[status(thm)],[inference(cn,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_22])])]) ).
thf(c_0_77,plain,
f1 @ ~ $true,
inference(cn,[status(thm)],[c_0_59]) ).
thf(c_0_78,plain,
( ( epred2_0 @ esk2_0 )
| ~ esk6_0 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(dynamic_cnf,[status(thm)],[c_0_60])]),c_0_61]) ).
thf(c_0_79,plain,
! [X100: $o,X8: $o,X2: $i] :
( ( ~ X100
<=> ( f2 @ X100 ) )
| ( X2 = esk4_0 )
| ( X2 = esk3_0 )
| ~ ( f2 @ X8 )
| ~ ( epred3_0 @ X2 ) ),
inference(arg_cong,[status(thm)],[c_0_62]) ).
thf(c_0_80,plain,
! [X2: $i] :
( ( epred3_0 @ X2 )
| ( epred12_1 @ X2 )
| ( f2 @ ~ $true )
| ( X2 != esk3_0 ) ),
inference(cn,[status(thm)],[c_0_63]) ).
thf(c_0_81,plain,
~ ( f2 @ ~ $true ),
inference(cn,[status(thm)],[c_0_64]) ).
thf(c_0_82,plain,
( ( epred3_0 @ esk3_0 )
| ~ ( epred12_1 @ esk3_0 ) ),
inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_65,c_0_66])])]) ).
thf(c_0_83,negated_conjecture,
( ( ( eps @ epred1_0 )
!= esk1_0 )
| ( ( eps @ epred2_0 )
!= esk2_0 )
| ( ( eps @ epred3_0 )
!= esk3_0 )
| ( ( eps @ epred4_0 )
!= esk4_0 ) ),
inference(lift_lambdas,[status(thm)],[inference(lift_lambdas,[status(thm)],[inference(lift_lambdas,[status(thm)],[inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_67]),c_0_68]),c_0_69]),c_0_70]),c_0_71]) ).
thf(c_0_84,plain,
( ( eps @ epred1_0 )
= esk1_0 ),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
thf(c_0_85,plain,
! [X2: $i] :
( ( X2 = esk4_0 )
| ~ ( epred4_0 @ X2 ) ),
inference(spm,[status(thm)],[c_0_74,c_0_29]) ).
thf(c_0_86,plain,
epred4_0 @ ( eps @ epred4_0 ),
inference(spm,[status(thm)],[c_0_54,c_0_75]) ).
thf(c_0_87,plain,
! [X8: $o,X2: $i] :
( ( X2 = esk2_0 )
| ~ ( f1 @ X8 )
| ~ ( epred2_0 @ X2 ) ),
inference(sr,[status(thm)],[inference(condense,[status(thm)],[c_0_76]),c_0_61]) ).
thf(c_0_88,plain,
epred2_0 @ esk2_0,
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(dynamic_cnf,[status(thm)],[c_0_60]),c_0_77])]),c_0_78]) ).
thf(c_0_89,plain,
! [X8: $o,X2: $i] :
( ( X2 = esk3_0 )
| ( X2 = esk4_0 )
| ~ ( f2 @ X8 )
| ~ ( epred3_0 @ X2 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(dynamic_cnf,[status(thm)],[c_0_79]),c_0_66])]) ).
thf(c_0_90,plain,
epred3_0 @ esk3_0,
inference(csr,[status(thm)],[inference(er,[status(thm)],[inference(sr,[status(thm)],[c_0_80,c_0_81])]),c_0_82]) ).
thf(c_0_91,negated_conjecture,
( ( ( eps @ epred2_0 )
!= esk2_0 )
| ( ( eps @ epred3_0 )
!= esk3_0 )
| ( ( eps @ epred4_0 )
!= esk4_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_83,c_0_84])]) ).
thf(c_0_92,plain,
( ( eps @ epred4_0 )
= esk4_0 ),
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
thf(c_0_93,plain,
! [X2: $i] :
( ( X2 = esk2_0 )
| ~ ( epred2_0 @ X2 ) ),
inference(spm,[status(thm)],[c_0_87,c_0_77]) ).
thf(c_0_94,plain,
epred2_0 @ ( eps @ epred2_0 ),
inference(spm,[status(thm)],[c_0_54,c_0_88]) ).
thf(c_0_95,plain,
! [X2: $i] :
( ( X2 = esk4_0 )
| ( X2 = esk3_0 )
| ~ ( epred3_0 @ X2 ) ),
inference(spm,[status(thm)],[c_0_89,c_0_66]) ).
thf(c_0_96,plain,
epred3_0 @ ( eps @ epred3_0 ),
inference(spm,[status(thm)],[c_0_54,c_0_90]) ).
thf(c_0_97,plain,
! [X15: $o,X8: $o,X2: $i] :
( ( f2 @ X8 )
| ( X2 = esk3_0 )
| ( f2 = $not )
| ~ $true
| ~ ( f2 @ X15 )
| ~ $true
| ~ ( epred3_0 @ X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
thf(c_0_98,negated_conjecture,
( ( ( eps @ epred2_0 )
!= esk2_0 )
| ( ( eps @ epred3_0 )
!= esk3_0 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_91,c_0_92])]) ).
thf(c_0_99,plain,
( ( eps @ epred2_0 )
= esk2_0 ),
inference(spm,[status(thm)],[c_0_93,c_0_94]) ).
thf(c_0_100,plain,
( ( ( eps @ epred3_0 )
= esk3_0 )
| ( ( eps @ epred3_0 )
= esk4_0 ) ),
inference(spm,[status(thm)],[c_0_95,c_0_96]) ).
thf(c_0_101,plain,
! [X15: $o,X8: $o,X2: $i] :
( ( X2 = esk3_0 )
| ( f2 = $not )
| ( f2 @ X8 )
| ~ ( f2 @ X15 )
| ~ ( epred3_0 @ X2 ) ),
inference(cn,[status(thm)],[c_0_97]) ).
thf(c_0_102,negated_conjecture,
( ( eps @ epred3_0 )
!= esk3_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_98,c_0_99])]) ).
thf(c_0_103,plain,
( ( ( eps @ epred3_0 )
= esk4_0 )
| ( esk3_0 != esk4_0 ) ),
inference(ef,[status(thm)],[c_0_100]) ).
thf(c_0_104,plain,
! [X121: $o,X15: $o,X8: $o,X2: $i] :
( ( ~ X121
<=> ( f2 @ X121 ) )
| ( X2 = esk3_0 )
| ( f2 @ X8 )
| ~ ( f2 @ X15 )
| ~ ( epred3_0 @ X2 ) ),
inference(arg_cong,[status(thm)],[c_0_101]) ).
thf(c_0_105,plain,
( ( eps @ epred3_0 )
= esk4_0 ),
inference(sr,[status(thm)],[c_0_100,c_0_102]) ).
thf(c_0_106,negated_conjecture,
( ( ( eps @ epred2_0 )
!= esk2_0 )
| ( esk3_0 != esk4_0 ) ),
inference(spm,[status(thm)],[c_0_98,c_0_103]) ).
thf(c_0_107,plain,
! [X15: $o,X8: $o,X2: $i] :
( ( X2 = esk3_0 )
| ( f2 @ X8 )
| ~ ( f2 @ X15 )
| ~ ( epred3_0 @ X2 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(dynamic_cnf,[status(thm)],[c_0_104]),c_0_66])]) ).
thf(c_0_108,plain,
epred3_0 @ esk4_0,
inference(rw,[status(thm)],[c_0_96,c_0_105]) ).
thf(c_0_109,negated_conjecture,
esk3_0 != esk4_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_106,c_0_99])]) ).
thf(c_0_110,plain,
! [X8: $o,X15: $o] :
( ( f2 @ X8 )
| ~ ( f2 @ X15 ) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_109]) ).
thf(c_0_111,plain,
! [X8: $o] : ( f2 @ X8 ),
inference(spm,[status(thm)],[c_0_110,c_0_66]) ).
thf(c_0_112,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_81,c_0_111])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SYO544^1 : TPTP v8.2.0. Released v5.2.0.
% 0.04/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n015.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon May 20 10:31:08 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.19/0.47 Running higher-order theorem proving
% 0.19/0.47 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 0.19/0.52 # Version: 3.1.0-ho
% 0.19/0.52 # partial match(1): HSLSSMSSSSMCHSA
% 0.19/0.52 # Preprocessing class: HSMSSMSSSSMCHSA.
% 0.19/0.52 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.52 # Starting post_as_ho6 with 1500s (5) cores
% 0.19/0.52 # Starting post_as_ho7 with 300s (1) cores
% 0.19/0.52 # Starting post_as_ho8 with 300s (1) cores
% 0.19/0.52 # Starting lpo8_s with 300s (1) cores
% 0.19/0.52 # lpo8_s with pid 8406 completed with status 0
% 0.19/0.52 # Result found by lpo8_s
% 0.19/0.52 # partial match(1): HSLSSMSSSSMCHSA
% 0.19/0.52 # Preprocessing class: HSMSSMSSSSMCHSA.
% 0.19/0.52 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.52 # Starting post_as_ho6 with 1500s (5) cores
% 0.19/0.52 # Starting post_as_ho7 with 300s (1) cores
% 0.19/0.52 # Starting post_as_ho8 with 300s (1) cores
% 0.19/0.52 # Starting lpo8_s with 300s (1) cores
% 0.19/0.52 # SinE strategy is GSinE(CountFormulas,hypos,4.0,,6,20000,1.0)
% 0.19/0.52 # Search class: HGHSF-FSLS11-SHSFFFBC
% 0.19/0.52 # partial match(4): HGHSM-FSLM32-SHSFFFBC
% 0.19/0.52 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.19/0.52 # Starting new_ho_10 with 163s (1) cores
% 0.19/0.52 # new_ho_10 with pid 8414 completed with status 0
% 0.19/0.52 # Result found by new_ho_10
% 0.19/0.52 # partial match(1): HSLSSMSSSSMCHSA
% 0.19/0.52 # Preprocessing class: HSMSSMSSSSMCHSA.
% 0.19/0.52 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.52 # Starting post_as_ho6 with 1500s (5) cores
% 0.19/0.52 # Starting post_as_ho7 with 300s (1) cores
% 0.19/0.52 # Starting post_as_ho8 with 300s (1) cores
% 0.19/0.52 # Starting lpo8_s with 300s (1) cores
% 0.19/0.52 # SinE strategy is GSinE(CountFormulas,hypos,4.0,,6,20000,1.0)
% 0.19/0.52 # Search class: HGHSF-FSLS11-SHSFFFBC
% 0.19/0.52 # partial match(4): HGHSM-FSLM32-SHSFFFBC
% 0.19/0.52 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.19/0.52 # Starting new_ho_10 with 163s (1) cores
% 0.19/0.52 # Preprocessing time : 0.003 s
% 0.19/0.52 # Presaturation interreduction done
% 0.19/0.52
% 0.19/0.52 # Proof found!
% 0.19/0.52 # SZS status Theorem
% 0.19/0.52 # SZS output start CNFRefutation
% See solution above
% 0.19/0.52 # Parsed axioms : 17
% 0.19/0.52 # Removed by relevancy pruning/SinE : 6
% 0.19/0.52 # Initial clauses : 326
% 0.19/0.52 # Removed in clause preprocessing : 182
% 0.19/0.52 # Initial clauses in saturation : 144
% 0.19/0.52 # Processed clauses : 348
% 0.19/0.52 # ...of these trivial : 25
% 0.19/0.52 # ...subsumed : 80
% 0.19/0.52 # ...remaining for further processing : 243
% 0.19/0.52 # Other redundant clauses eliminated : 18
% 0.19/0.52 # Clauses deleted for lack of memory : 0
% 0.19/0.52 # Backward-subsumed : 78
% 0.19/0.52 # Backward-rewritten : 28
% 0.19/0.52 # Generated clauses : 362
% 0.19/0.52 # ...of the previous two non-redundant : 264
% 0.19/0.52 # ...aggressively subsumed : 0
% 0.19/0.52 # Contextual simplify-reflections : 3
% 0.19/0.52 # Paramodulations : 202
% 0.19/0.52 # Factorizations : 9
% 0.19/0.52 # NegExts : 14
% 0.19/0.52 # Equation resolutions : 18
% 0.19/0.52 # Disequality decompositions : 0
% 0.19/0.52 # Total rewrite steps : 193
% 0.19/0.52 # ...of those cached : 163
% 0.19/0.52 # Propositional unsat checks : 0
% 0.19/0.52 # Propositional check models : 0
% 0.19/0.52 # Propositional check unsatisfiable : 0
% 0.19/0.52 # Propositional clauses : 0
% 0.19/0.52 # Propositional clauses after purity: 0
% 0.19/0.52 # Propositional unsat core size : 0
% 0.19/0.52 # Propositional preprocessing time : 0.000
% 0.19/0.52 # Propositional encoding time : 0.000
% 0.19/0.52 # Propositional solver time : 0.000
% 0.19/0.52 # Success case prop preproc time : 0.000
% 0.19/0.52 # Success case prop encoding time : 0.000
% 0.19/0.52 # Success case prop solver time : 0.000
% 0.19/0.52 # Current number of processed clauses : 53
% 0.19/0.52 # Positive orientable unit clauses : 13
% 0.19/0.52 # Positive unorientable unit clauses: 0
% 0.19/0.52 # Negative unit clauses : 4
% 0.19/0.52 # Non-unit-clauses : 36
% 0.19/0.52 # Current number of unprocessed clauses: 85
% 0.19/0.52 # ...number of literals in the above : 253
% 0.19/0.52 # Current number of archived formulas : 0
% 0.19/0.52 # Current number of archived clauses : 172
% 0.19/0.52 # Clause-clause subsumption calls (NU) : 1254
% 0.19/0.52 # Rec. Clause-clause subsumption calls : 565
% 0.19/0.52 # Non-unit clause-clause subsumptions : 120
% 0.19/0.52 # Unit Clause-clause subsumption calls : 207
% 0.19/0.52 # Rewrite failures with RHS unbound : 0
% 0.19/0.52 # BW rewrite match attempts : 18
% 0.19/0.52 # BW rewrite match successes : 17
% 0.19/0.52 # Condensation attempts : 348
% 0.19/0.52 # Condensation successes : 18
% 0.19/0.52 # Termbank termtop insertions : 23643
% 0.19/0.52 # Search garbage collected termcells : 3768
% 0.19/0.52
% 0.19/0.52 # -------------------------------------------------
% 0.19/0.52 # User time : 0.031 s
% 0.19/0.52 # System time : 0.007 s
% 0.19/0.52 # Total time : 0.038 s
% 0.19/0.52 # Maximum resident set size: 3288 pages
% 0.19/0.52
% 0.19/0.52 # -------------------------------------------------
% 0.19/0.52 # User time : 0.033 s
% 0.19/0.52 # System time : 0.009 s
% 0.19/0.52 # Total time : 0.041 s
% 0.19/0.52 # Maximum resident set size: 1772 pages
% 0.19/0.52 % E---3.1 exiting
% 0.19/0.52 % E exiting
%------------------------------------------------------------------------------