%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWW097+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 03:09:59 PM UTC 2026
% Result : Theorem 171.00s 25.38s
% Output : CNFRefutation 171.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 53
% Number of leaves : 21
% Syntax : Number of formulae : 370 ( 114 unt; 0 def)
% Number of atoms : 845 ( 312 equ)
% Maximal formula atoms : 75 ( 2 avg)
% Number of connectives : 830 ( 355 ~; 410 |; 51 &)
% ( 6 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 7 con; 0-3 aty)
% Number of variables : 310 ( 58 sgn 64 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(def_lazy_and2,axiom,
! [X5,X6] :
? [X7] :
( ~ ? [X8] : forallprefers(f2(X5,X6,X8),f2(X5,X6,X7))
& lazy_and2(X5,X6) = phi(f2(X5,X6,X7)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',def_lazy_and2) ).
fof(def_f2,axiom,
! [X5,X6,X7] : f2(X5,X6,X7) = lazy_impl(prop(X7),impl(lazy_impl(X5,impl(X6,X7)),X7)),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',def_f2) ).
fof(def_false2,axiom,
? [X5] :
( ~ ? [X10] : forallprefers(f7(X10),f7(X5))
& false2 = phi(f7(X5)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',def_false2) ).
fof(def_f7,axiom,
! [X5] : f7(X5) = lazy_impl(prop(X5),X5),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',def_f7) ).
fof(prop_false,axiom,
! [X1] :
( prop(X1) = false
<=> ~ bool(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',prop_false) ).
fof(lazy_impl_axiom2,axiom,
! [X4] : lazy_impl(false,X4) = true,
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',lazy_impl_axiom2) ).
fof(def_phi,axiom,
! [X1] :
( ( phi(X1) = err
& ~ d(X1) )
| ( phi(X1) = X1
& d(X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',def_phi) ).
fof(prop_true,axiom,
! [X1] :
( prop(X1) = true
<=> bool(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',prop_true) ).
fof(lazy_impl_axiom3,axiom,
! [X4] : lazy_impl(true,X4) = phi(X4),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',lazy_impl_axiom3) ).
fof(def_forallprefers,axiom,
! [X1,X2] :
( forallprefers(X1,X2)
<=> ( ( X2 = true
& X1 = false )
| ( bool(X2)
& ~ bool(X1)
& d(X2)
& d(X1) )
| ( d(X2)
& ~ d(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',def_forallprefers) ).
fof(impl_axiom4,axiom,
! [X4] :
( bool(X4)
=> impl(true,X4) = X4 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',impl_axiom4) ).
fof(def_bool,axiom,
! [X1] :
( bool(X1)
<=> ( X1 = true
| X1 = false ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',def_bool) ).
fof(false_true_err_in_d,axiom,
( d(err)
& d(false)
& d(true) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',false_true_err_in_d) ).
fof(lazy_impl_axiom1,axiom,
! [X3,X4] :
( ~ bool(X3)
=> lazy_impl(X3,X4) = phi(X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',lazy_impl_axiom1) ).
fof(distinct_false_true_err,axiom,
( false != err
& true != err
& true != false ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',distinct_false_true_err) ).
fof(impl_axiom1,axiom,
! [X3,X4] :
( ~ bool(X3)
=> impl(X3,X4) = phi(X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',impl_axiom1) ).
fof(lazy_and1_lazy_and2,conjecture,
! [X5,X6] : lazy_and1(X5,X6) = lazy_and2(X5,X6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lazy_and1_lazy_and2) ).
fof(impl_axiom3,axiom,
! [X4] :
( bool(X4)
=> impl(false,X4) = true ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',impl_axiom3) ).
fof(lazy_and1_axiom1,axiom,
! [X3,X4] :
( ~ bool(X3)
=> lazy_and1(X3,X4) = phi(X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',lazy_and1_axiom1) ).
fof(lazy_and1_axiom2,axiom,
! [X4] : lazy_and1(false,X4) = false,
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',lazy_and1_axiom2) ).
fof(lazy_and1_axiom3,axiom,
! [X4] : lazy_and1(true,X4) = phi(X4),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',lazy_and1_axiom3) ).
fof(c_0_21,plain,
! [X49,X50,X52] :
( ~ forallprefers(f2(X49,X50,X52),f2(X49,X50,esk2_2(X49,X50)))
& lazy_and2(X49,X50) = phi(f2(X49,X50,esk2_2(X49,X50))) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[def_lazy_and2])])])])]) ).
fof(c_0_22,plain,
! [X46,X47,X48] : f2(X46,X47,X48) = lazy_impl(prop(X48),impl(lazy_impl(X46,impl(X47,X48)),X48)),
inference(variable_rename,[status(thm)],[def_f2]) ).
fof(c_0_23,plain,
! [X83] :
( ~ forallprefers(f7(X83),f7(esk7_0))
& false2 = phi(f7(esk7_0)) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[def_false2])])])])]) ).
fof(c_0_24,plain,
! [X81] : f7(X81) = lazy_impl(prop(X81),X81),
inference(variable_rename,[status(thm)],[def_f7]) ).
fof(c_0_25,plain,
! [X1] :
( prop(X1) = false
<=> ~ bool(X1) ),
inference(fof_simplification,[status(thm)],[prop_false]) ).
cnf(c_0_26,plain,
~ forallprefers(f2(X1,X2,X3),f2(X1,X2,esk2_2(X1,X2))),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_27,plain,
f2(X1,X2,X3) = lazy_impl(prop(X3),impl(lazy_impl(X1,impl(X2,X3)),X3)),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_28,plain,
! [X27] : lazy_impl(false,X27) = true,
inference(variable_rename,[status(thm)],[lazy_impl_axiom2]) ).
cnf(c_0_29,plain,
~ forallprefers(f7(X1),f7(esk7_0)),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_30,plain,
f7(X1) = lazy_impl(prop(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_31,plain,
! [X18] :
( ( prop(X18) = false
| bool(X18) )
& ( ~ bool(X18)
| prop(X18) != false ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_25])])]) ).
fof(c_0_32,plain,
! [X1] :
( ( phi(X1) = err
& ~ d(X1) )
| ( phi(X1) = X1
& d(X1) ) ),
inference(fof_simplification,[status(thm)],[def_phi]) ).
cnf(c_0_33,plain,
~ forallprefers(lazy_impl(prop(X3),impl(lazy_impl(X1,impl(X2,X3)),X3)),lazy_impl(prop(esk2_2(X1,X2)),impl(lazy_impl(X1,impl(X2,esk2_2(X1,X2))),esk2_2(X1,X2)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_27]),c_0_27]) ).
cnf(c_0_34,plain,
lazy_impl(false,X1) = true,
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_35,plain,
~ forallprefers(lazy_impl(prop(X1),X1),lazy_impl(prop(esk7_0),esk7_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_30]),c_0_30]) ).
cnf(c_0_36,plain,
( prop(X1) = false
| bool(X1) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
fof(c_0_37,plain,
! [X17] :
( ( prop(X17) = true
| ~ bool(X17) )
& ( bool(X17)
| prop(X17) != true ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[prop_true])])]) ).
fof(c_0_38,plain,
! [X16] :
( ( phi(X16) = X16
| phi(X16) = err )
& ( phi(X16) = X16
| ~ d(X16) )
& ( d(X16)
| phi(X16) = err )
& ( d(X16)
| ~ d(X16) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_32])])]) ).
fof(c_0_39,plain,
! [X28] : lazy_impl(true,X28) = phi(X28),
inference(variable_rename,[status(thm)],[lazy_impl_axiom3]) ).
fof(c_0_40,plain,
! [X1,X2] :
( forallprefers(X1,X2)
<=> ( ( X2 = true
& X1 = false )
| ( bool(X2)
& ~ bool(X1)
& d(X2)
& d(X1) )
| ( d(X2)
& ~ d(X1) ) ) ),
inference(fof_simplification,[status(thm)],[def_forallprefers]) ).
cnf(c_0_41,plain,
~ forallprefers(lazy_impl(prop(X1),impl(true,X1)),lazy_impl(prop(esk2_2(false,X2)),impl(true,esk2_2(false,X2)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_34]) ).
fof(c_0_42,plain,
! [X24] :
( impl(true,X24) = X24
| ~ bool(X24) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[impl_axiom4])])]) ).
cnf(c_0_43,plain,
( ~ forallprefers(lazy_impl(prop(X1),X1),true)
| bool(esk7_0) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_34]) ).
cnf(c_0_44,plain,
( ~ bool(X1)
| prop(X1) = true ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_45,plain,
( ~ d(X1)
| phi(X1) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_46,plain,
lazy_impl(true,X1) = phi(X1),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
fof(c_0_47,plain,
! [X12,X13] :
( ( forallprefers(X12,X13)
| X13 != true
| X12 != false )
& ( forallprefers(X12,X13)
| ~ bool(X13)
| bool(X12)
| ~ d(X13)
| ~ d(X12) )
& ( forallprefers(X12,X13)
| ~ d(X13)
| d(X12) )
& ( ~ forallprefers(X12,X13)
| d(X13)
| bool(X13)
| X13 = true )
& ( ~ forallprefers(X12,X13)
| d(X13)
| bool(X13)
| X12 = false )
& ( ~ forallprefers(X12,X13)
| d(X13)
| ~ bool(X12)
| X13 = true )
& ( ~ forallprefers(X12,X13)
| d(X13)
| ~ bool(X12)
| X12 = false )
& ( ~ forallprefers(X12,X13)
| d(X13)
| d(X13)
| X13 = true )
& ( ~ forallprefers(X12,X13)
| d(X13)
| d(X13)
| X12 = false )
& ( ~ forallprefers(X12,X13)
| d(X13)
| d(X12)
| X13 = true )
& ( ~ forallprefers(X12,X13)
| d(X13)
| d(X12)
| X12 = false )
& ( ~ forallprefers(X12,X13)
| ~ d(X12)
| bool(X13)
| X13 = true )
& ( ~ forallprefers(X12,X13)
| ~ d(X12)
| bool(X13)
| X12 = false )
& ( ~ forallprefers(X12,X13)
| ~ d(X12)
| ~ bool(X12)
| X13 = true )
& ( ~ forallprefers(X12,X13)
| ~ d(X12)
| ~ bool(X12)
| X12 = false )
& ( ~ forallprefers(X12,X13)
| ~ d(X12)
| d(X13)
| X13 = true )
& ( ~ forallprefers(X12,X13)
| ~ d(X12)
| d(X13)
| X12 = false )
& ( ~ forallprefers(X12,X13)
| ~ d(X12)
| d(X12)
| X13 = true )
& ( ~ forallprefers(X12,X13)
| ~ d(X12)
| d(X12)
| X12 = false ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_40])])])]) ).
fof(c_0_48,plain,
! [X11] :
( ( bool(X11)
| X11 != true )
& ( bool(X11)
| X11 != false )
& ( X11 = true
| X11 = false
| ~ bool(X11) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[def_bool])])])]) ).
cnf(c_0_49,plain,
( ~ forallprefers(lazy_impl(prop(X2),impl(true,X2)),true)
| bool(esk2_2(false,X1)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_36]),c_0_34]) ).
cnf(c_0_50,plain,
( ~ bool(X1)
| impl(true,X1) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_51,plain,
( ~ bool(X1)
| ~ forallprefers(lazy_impl(true,X1),true)
| bool(esk7_0) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_52,plain,
( ~ d(X1)
| lazy_impl(true,X1) = X1 ),
inference(rw,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_53,plain,
( X2 != true
| X1 != false
| forallprefers(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_54,plain,
( X1 != false
| bool(X1) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_55,plain,
( ~ bool(X2)
| ~ forallprefers(lazy_impl(prop(X2),X2),true)
| bool(esk2_2(false,X1)) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_56,plain,
( ~ bool(X1)
| ~ d(X1)
| ~ forallprefers(X1,true)
| bool(esk7_0) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_57,plain,
forallprefers(false,true),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_53])]) ).
cnf(c_0_58,plain,
d(false),
inference(split_conjunct,[status(thm)],[false_true_err_in_d]) ).
cnf(c_0_59,plain,
bool(false),
inference(er,[status(thm)],[c_0_54]) ).
cnf(c_0_60,plain,
( ~ bool(X2)
| ~ forallprefers(lazy_impl(true,X2),true)
| bool(esk2_2(false,X1)) ),
inference(spm,[status(thm)],[c_0_55,c_0_44]) ).
cnf(c_0_61,plain,
bool(esk7_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_58]),c_0_59])]) ).
cnf(c_0_62,plain,
( ~ bool(X2)
| ~ d(X2)
| ~ forallprefers(X2,true)
| bool(esk2_2(false,X1)) ),
inference(spm,[status(thm)],[c_0_60,c_0_52]) ).
cnf(c_0_63,plain,
( d(X1)
| phi(X1) = err ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_64,plain,
~ forallprefers(lazy_impl(prop(X1),X1),lazy_impl(true,esk7_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_44]),c_0_61])]) ).
cnf(c_0_65,plain,
bool(esk2_2(false,X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_57]),c_0_58]),c_0_59])]) ).
cnf(c_0_66,plain,
false2 = phi(f7(esk7_0)),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_67,plain,
( d(X1)
| lazy_impl(true,X1) = err ),
inference(rw,[status(thm)],[c_0_63,c_0_46]) ).
cnf(c_0_68,plain,
( ~ d(esk7_0)
| ~ forallprefers(lazy_impl(prop(X1),X1),esk7_0) ),
inference(spm,[status(thm)],[c_0_64,c_0_52]) ).
cnf(c_0_69,plain,
( ~ d(X2)
| forallprefers(X1,X2)
| d(X1) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_70,plain,
~ forallprefers(lazy_impl(prop(X1),impl(true,X1)),lazy_impl(prop(esk2_2(false,X2)),esk2_2(false,X2))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_50]),c_0_65])]) ).
cnf(c_0_71,plain,
false2 = lazy_impl(true,lazy_impl(prop(esk7_0),esk7_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_66,c_0_46]),c_0_30]) ).
cnf(c_0_72,plain,
( ~ forallprefers(lazy_impl(prop(X1),X1),err)
| d(esk7_0) ),
inference(spm,[status(thm)],[c_0_64,c_0_67]) ).
cnf(c_0_73,plain,
d(err),
inference(split_conjunct,[status(thm)],[false_true_err_in_d]) ).
cnf(c_0_74,plain,
( ~ d(esk7_0)
| d(lazy_impl(prop(X1),X1)) ),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_75,plain,
~ forallprefers(lazy_impl(prop(X1),impl(true,X1)),lazy_impl(true,esk2_2(false,X2))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_44]),c_0_65])]) ).
cnf(c_0_76,plain,
( ~ d(lazy_impl(prop(esk7_0),esk7_0))
| lazy_impl(prop(esk7_0),esk7_0) = false2 ),
inference(spm,[status(thm)],[c_0_52,c_0_71]) ).
cnf(c_0_77,plain,
d(lazy_impl(prop(X1),X1)),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_69]),c_0_73])]),c_0_74]) ).
cnf(c_0_78,plain,
( ~ bool(X1)
| ~ forallprefers(lazy_impl(prop(X1),X1),lazy_impl(true,esk2_2(false,X2))) ),
inference(spm,[status(thm)],[c_0_75,c_0_50]) ).
cnf(c_0_79,plain,
lazy_impl(prop(esk7_0),esk7_0) = false2,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_76,c_0_77])]) ).
fof(c_0_80,plain,
! [X3,X4] :
( ~ bool(X3)
=> lazy_impl(X3,X4) = phi(X3) ),
inference(fof_simplification,[status(thm)],[lazy_impl_axiom1]) ).
cnf(c_0_81,plain,
~ forallprefers(false2,lazy_impl(true,esk2_2(false,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_61])]) ).
cnf(c_0_82,plain,
( ~ bool(X2)
| ~ d(X2)
| ~ d(X1)
| forallprefers(X1,X2)
| bool(X1) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
fof(c_0_83,plain,
! [X25,X26] :
( lazy_impl(X25,X26) = phi(X25)
| bool(X25) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_80])]) ).
cnf(c_0_84,plain,
( ~ d(esk2_2(false,X1))
| ~ forallprefers(false2,esk2_2(false,X1)) ),
inference(spm,[status(thm)],[c_0_81,c_0_52]) ).
cnf(c_0_85,plain,
( ~ bool(X2)
| ~ d(X2)
| bool(X1)
| forallprefers(X1,X2) ),
inference(csr,[status(thm)],[c_0_82,c_0_69]) ).
cnf(c_0_86,plain,
( ~ bool(X1)
| X1 = true
| X1 = false ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_87,plain,
( lazy_impl(X1,X2) = phi(X1)
| bool(X1) ),
inference(split_conjunct,[status(thm)],[c_0_83]) ).
cnf(c_0_88,plain,
( ~ bool(X1)
| ~ forallprefers(lazy_impl(true,X1),lazy_impl(prop(esk7_0),esk7_0)) ),
inference(spm,[status(thm)],[c_0_35,c_0_44]) ).
cnf(c_0_89,plain,
( phi(X1) = X1
| phi(X1) = err ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_90,plain,
( ~ bool(esk7_0)
| lazy_impl(true,lazy_impl(true,esk7_0)) = false2 ),
inference(spm,[status(thm)],[c_0_71,c_0_44]) ).
cnf(c_0_91,plain,
( ~ d(esk2_2(false,X1))
| bool(false2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_65])]) ).
cnf(c_0_92,plain,
( esk2_2(false,X1) = false
| esk2_2(false,X1) = true ),
inference(spm,[status(thm)],[c_0_86,c_0_65]) ).
cnf(c_0_93,plain,
( bool(X1)
| lazy_impl(X1,X2) = lazy_impl(true,X1) ),
inference(rw,[status(thm)],[c_0_87,c_0_46]) ).
cnf(c_0_94,plain,
( ~ bool(X1)
| ~ forallprefers(lazy_impl(true,X1),false2) ),
inference(rw,[status(thm)],[c_0_88,c_0_79]) ).
cnf(c_0_95,plain,
( lazy_impl(true,X1) = err
| lazy_impl(true,X1) = X1 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_89,c_0_46]),c_0_46]) ).
cnf(c_0_96,plain,
~ forallprefers(lazy_impl(prop(X1),X1),false2),
inference(rw,[status(thm)],[c_0_35,c_0_79]) ).
cnf(c_0_97,plain,
lazy_impl(true,lazy_impl(true,esk7_0)) = false2,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_90,c_0_61])]) ).
cnf(c_0_98,plain,
( bool(false2)
| esk2_2(false,X1) = true ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_58])]) ).
cnf(c_0_99,plain,
d(true),
inference(split_conjunct,[status(thm)],[false_true_err_in_d]) ).
fof(c_0_100,plain,
( false != err
& true != err
& true != false ),
inference(fof_simplification,[status(thm)],[distinct_false_true_err]) ).
cnf(c_0_101,plain,
d(false2),
inference(spm,[status(thm)],[c_0_77,c_0_79]) ).
cnf(c_0_102,plain,
( bool(prop(esk7_0))
| lazy_impl(true,prop(esk7_0)) = false2 ),
inference(spm,[status(thm)],[c_0_93,c_0_79]) ).
cnf(c_0_103,plain,
( ~ bool(X1)
| ~ forallprefers(err,false2)
| lazy_impl(true,X1) = X1 ),
inference(spm,[status(thm)],[c_0_94,c_0_95]) ).
cnf(c_0_104,plain,
~ forallprefers(lazy_impl(true,prop(X1)),false2),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_93]),c_0_94]) ).
cnf(c_0_105,plain,
( false2 = err
| lazy_impl(true,esk7_0) = false2 ),
inference(spm,[status(thm)],[c_0_95,c_0_97]) ).
cnf(c_0_106,plain,
bool(false2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_98]),c_0_99])]) ).
fof(c_0_107,plain,
( false != err
& true != err
& true != false ),
inference(fof_nnf,[status(thm)],[c_0_100]) ).
fof(c_0_108,plain,
! [X3,X4] :
( ~ bool(X3)
=> impl(X3,X4) = phi(X3) ),
inference(fof_simplification,[status(thm)],[impl_axiom1]) ).
cnf(c_0_109,plain,
( ~ bool(X1)
| ~ bool(false2)
| bool(lazy_impl(true,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_85]),c_0_101])]) ).
cnf(c_0_110,plain,
( bool(prop(esk7_0))
| false2 = err
| prop(esk7_0) = false2 ),
inference(spm,[status(thm)],[c_0_95,c_0_102]) ).
cnf(c_0_111,plain,
( ~ bool(X1)
| ~ bool(false2)
| bool(err)
| lazy_impl(true,X1) = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_85]),c_0_101])]) ).
cnf(c_0_112,plain,
( ~ d(prop(X1))
| ~ forallprefers(prop(X1),false2) ),
inference(spm,[status(thm)],[c_0_104,c_0_52]) ).
cnf(c_0_113,plain,
( false2 = err
| false2 = esk7_0 ),
inference(spm,[status(thm)],[c_0_95,c_0_105]) ).
cnf(c_0_114,plain,
( false2 = false
| false2 = true ),
inference(spm,[status(thm)],[c_0_86,c_0_106]) ).
cnf(c_0_115,plain,
false != err,
inference(split_conjunct,[status(thm)],[c_0_107]) ).
fof(c_0_116,plain,
! [X19,X20] :
( impl(X19,X20) = phi(X19)
| bool(X19) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_108])]) ).
cnf(c_0_117,plain,
( ~ bool(X1)
| bool(lazy_impl(true,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_109,c_0_106])]) ).
cnf(c_0_118,plain,
( false2 = err
| prop(esk7_0) = false
| prop(esk7_0) = true
| prop(esk7_0) = false2 ),
inference(spm,[status(thm)],[c_0_86,c_0_110]) ).
cnf(c_0_119,plain,
lazy_impl(true,esk7_0) = false2,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_44]),c_0_61])]) ).
cnf(c_0_120,plain,
( ~ bool(X1)
| bool(err)
| lazy_impl(true,X1) = X1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_111,c_0_106])]) ).
cnf(c_0_121,plain,
( ~ forallprefers(false,false2)
| bool(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_36]),c_0_58])]) ).
cnf(c_0_122,plain,
( esk7_0 = false
| false2 = true ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_114]),c_0_115]) ).
cnf(c_0_123,plain,
( impl(X1,X2) = phi(X1)
| bool(X1) ),
inference(split_conjunct,[status(thm)],[c_0_116]) ).
cnf(c_0_124,plain,
( bool(X1)
| lazy_impl(X1,X2) = X1
| lazy_impl(X1,X2) = err ),
inference(spm,[status(thm)],[c_0_95,c_0_93]) ).
cnf(c_0_125,plain,
lazy_impl(true,err) = err,
inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_95])]) ).
cnf(c_0_126,plain,
( ~ bool(X1)
| lazy_impl(true,X1) = false
| lazy_impl(true,X1) = true ),
inference(spm,[status(thm)],[c_0_86,c_0_117]) ).
cnf(c_0_127,plain,
true != err,
inference(split_conjunct,[status(thm)],[c_0_107]) ).
cnf(c_0_128,plain,
( false2 != true
| false2 = err
| prop(esk7_0) = true
| prop(esk7_0) = false ),
inference(ef,[status(thm)],[c_0_118]) ).
cnf(c_0_129,plain,
( bool(err)
| false2 = esk7_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_120]),c_0_61])]) ).
cnf(c_0_130,plain,
( bool(X1)
| esk7_0 = false ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_122]),c_0_57])]) ).
cnf(c_0_131,plain,
( esk7_0 = false
| esk7_0 = true ),
inference(spm,[status(thm)],[c_0_86,c_0_61]) ).
cnf(c_0_132,plain,
( bool(X1)
| impl(X1,X2) = lazy_impl(true,X1) ),
inference(rw,[status(thm)],[c_0_123,c_0_46]) ).
cnf(c_0_133,plain,
( bool(err)
| lazy_impl(err,X1) = err ),
inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_124])]) ).
cnf(c_0_134,plain,
~ bool(err),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_126]),c_0_125]),c_0_115]),c_0_127]) ).
cnf(c_0_135,plain,
( ~ bool(X1)
| prop(X1) != false ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_136,plain,
( false2 = err
| prop(esk7_0) = true
| prop(esk7_0) = false ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_118]),c_0_61])]),c_0_128]) ).
cnf(c_0_137,plain,
( ~ bool(false2)
| bool(lazy_impl(true,prop(X1))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_85]),c_0_101])]) ).
cnf(c_0_138,plain,
false2 = esk7_0,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_129]),c_0_115]),c_0_127]) ).
cnf(c_0_139,plain,
( X1 = false
| X1 = true
| esk7_0 = false ),
inference(spm,[status(thm)],[c_0_86,c_0_130]) ).
cnf(c_0_140,plain,
( esk7_0 = true
| lazy_impl(true,lazy_impl(true,false)) = false2 ),
inference(spm,[status(thm)],[c_0_97,c_0_131]) ).
cnf(c_0_141,plain,
( ~ bool(X1)
| ~ forallprefers(err,lazy_impl(prop(esk7_0),esk7_0))
| d(X1) ),
inference(spm,[status(thm)],[c_0_88,c_0_67]) ).
cnf(c_0_142,plain,
( ~ forallprefers(lazy_impl(prop(X3),impl(lazy_impl(X1,impl(X2,X3)),X3)),lazy_impl(prop(esk2_2(X1,X2)),lazy_impl(true,lazy_impl(X1,impl(X2,esk2_2(X1,X2))))))
| bool(lazy_impl(X1,impl(X2,esk2_2(X1,X2)))) ),
inference(spm,[status(thm)],[c_0_33,c_0_132]) ).
cnf(c_0_143,plain,
lazy_impl(err,X1) = err,
inference(sr,[status(thm)],[c_0_133,c_0_134]) ).
cnf(c_0_144,plain,
( false2 = err
| prop(esk7_0) = true ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_136]),c_0_61])]) ).
cnf(c_0_145,plain,
bool(lazy_impl(true,prop(X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_137,c_0_106])]) ).
cnf(c_0_146,plain,
~ forallprefers(esk7_0,lazy_impl(true,esk2_2(false,X1))),
inference(rw,[status(thm)],[c_0_81,c_0_138]) ).
cnf(c_0_147,plain,
esk7_0 = false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_139]),c_0_125]),c_0_115]),c_0_127]) ).
cnf(c_0_148,plain,
( esk7_0 = true
| lazy_impl(true,false) = false2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_52]),c_0_58])]) ).
fof(c_0_149,negated_conjecture,
~ ! [X5,X6] : lazy_and1(X5,X6) = lazy_and2(X5,X6),
inference(assume_negation,[status(cth)],[lazy_and1_lazy_and2]) ).
cnf(c_0_150,plain,
( ~ forallprefers(lazy_impl(prop(X3),impl(lazy_impl(X1,impl(X2,X3)),X3)),true)
| bool(esk2_2(X1,X2)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_36]),c_0_34]) ).
cnf(c_0_151,plain,
( ~ bool(X1)
| ~ forallprefers(err,false2)
| d(X1) ),
inference(rw,[status(thm)],[c_0_141,c_0_79]) ).
cnf(c_0_152,plain,
~ forallprefers(lazy_impl(prop(X1),impl(err,X1)),lazy_impl(prop(esk2_2(err,X2)),err)),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_143]),c_0_143]),c_0_125]),c_0_134]) ).
cnf(c_0_153,plain,
( esk7_0 = err
| prop(esk7_0) = true ),
inference(rw,[status(thm)],[c_0_144,c_0_138]) ).
cnf(c_0_154,plain,
( lazy_impl(true,prop(X1)) = false
| lazy_impl(true,prop(X1)) = true ),
inference(spm,[status(thm)],[c_0_86,c_0_145]) ).
cnf(c_0_155,plain,
~ forallprefers(false,lazy_impl(true,esk2_2(false,X1))),
inference(rw,[status(thm)],[c_0_146,c_0_147]) ).
cnf(c_0_156,plain,
( ~ bool(X1)
| false = X1
| lazy_impl(true,X1) = true ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_126]),c_0_115]) ).
cnf(c_0_157,plain,
( esk7_0 = true
| lazy_impl(true,false) = esk7_0 ),
inference(rw,[status(thm)],[c_0_148,c_0_138]) ).
cnf(c_0_158,plain,
true != false,
inference(split_conjunct,[status(thm)],[c_0_107]) ).
fof(c_0_159,negated_conjecture,
lazy_and1(esk8_0,esk9_0) != lazy_and2(esk8_0,esk9_0),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_149])])])]) ).
cnf(c_0_160,plain,
lazy_and2(X1,X2) = phi(f2(X1,X2,esk2_2(X1,X2))),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_161,plain,
( ~ forallprefers(lazy_impl(prop(X3),lazy_impl(true,lazy_impl(X1,impl(X2,X3)))),true)
| bool(esk2_2(X1,X2))
| bool(lazy_impl(X1,impl(X2,X3))) ),
inference(spm,[status(thm)],[c_0_150,c_0_132]) ).
cnf(c_0_162,plain,
( ~ bool(X1)
| ~ bool(false2)
| bool(err)
| d(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_151,c_0_85]),c_0_101])]) ).
cnf(c_0_163,plain,
~ forallprefers(lazy_impl(prop(X1),err),lazy_impl(prop(esk2_2(err,X2)),err)),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_132]),c_0_125]),c_0_134]) ).
cnf(c_0_164,plain,
prop(false) = true,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_153,c_0_147]),c_0_147]),c_0_115]) ).
cnf(c_0_165,plain,
( prop(X1) = false
| lazy_impl(true,prop(X1)) = true ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_154]),c_0_115]) ).
cnf(c_0_166,plain,
esk2_2(false,X1) = false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_155,c_0_156]),c_0_57]),c_0_65])]) ).
cnf(c_0_167,plain,
lazy_impl(true,false) = false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_157,c_0_147]),c_0_147]),c_0_158]) ).
cnf(c_0_168,negated_conjecture,
lazy_and1(esk8_0,esk9_0) != lazy_and2(esk8_0,esk9_0),
inference(split_conjunct,[status(thm)],[c_0_159]) ).
cnf(c_0_169,plain,
lazy_and2(X1,X2) = lazy_impl(true,f2(X1,X2,esk2_2(X1,X2))),
inference(rw,[status(thm)],[c_0_160,c_0_46]) ).
cnf(c_0_170,plain,
( ~ bool(esk2_2(X2,X3))
| ~ forallprefers(lazy_impl(prop(X1),impl(lazy_impl(X2,impl(X3,X1)),X1)),lazy_impl(true,impl(lazy_impl(X2,impl(X3,esk2_2(X2,X3))),esk2_2(X2,X3)))) ),
inference(spm,[status(thm)],[c_0_33,c_0_44]) ).
cnf(c_0_171,plain,
( ~ forallprefers(lazy_impl(prop(X2),err),true)
| bool(esk2_2(err,X1)) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_143]),c_0_125]),c_0_134]) ).
cnf(c_0_172,plain,
( X1 != true
| bool(X1) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_173,plain,
( ~ bool(X1)
| bool(err)
| d(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_162,c_0_106])]) ).
cnf(c_0_174,plain,
~ forallprefers(err,lazy_impl(prop(esk2_2(err,X1)),err)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_163,c_0_164]),c_0_125]) ).
cnf(c_0_175,plain,
( prop(X1) = true
| prop(X1) = false ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_165]),c_0_127]) ).
cnf(c_0_176,plain,
~ forallprefers(lazy_impl(prop(X1),impl(true,X1)),false),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_166]),c_0_164]),c_0_167]) ).
cnf(c_0_177,negated_conjecture,
lazy_impl(true,lazy_impl(prop(esk2_2(esk8_0,esk9_0)),impl(lazy_impl(esk8_0,impl(esk9_0,esk2_2(esk8_0,esk9_0))),esk2_2(esk8_0,esk9_0)))) != lazy_and1(esk8_0,esk9_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_168,c_0_169]),c_0_27]) ).
cnf(c_0_178,plain,
( ~ bool(esk2_2(X1,X2))
| ~ forallprefers(lazy_impl(prop(X3),impl(lazy_impl(X1,impl(X2,X3)),X3)),lazy_impl(true,lazy_impl(true,lazy_impl(X1,impl(X2,esk2_2(X1,X2))))))
| bool(lazy_impl(X1,impl(X2,esk2_2(X1,X2)))) ),
inference(spm,[status(thm)],[c_0_170,c_0_132]) ).
cnf(c_0_179,plain,
( ~ forallprefers(err,true)
| bool(esk2_2(err,X1)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_171,c_0_164]),c_0_125]) ).
cnf(c_0_180,plain,
bool(true),
inference(er,[status(thm)],[c_0_172]) ).
cnf(c_0_181,plain,
( bool(X1)
| d(X1)
| lazy_impl(X1,X2) = err ),
inference(spm,[status(thm)],[c_0_67,c_0_93]) ).
cnf(c_0_182,plain,
( ~ bool(X1)
| d(X1) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_173]),c_0_115]),c_0_127]) ).
cnf(c_0_183,plain,
( ~ forallprefers(err,true)
| prop(esk2_2(err,X1)) = true ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_174,c_0_175]),c_0_34]) ).
cnf(c_0_184,plain,
~ forallprefers(lazy_impl(true,impl(true,false)),false),
inference(spm,[status(thm)],[c_0_176,c_0_164]) ).
cnf(c_0_185,negated_conjecture,
( ~ d(lazy_impl(prop(esk2_2(esk8_0,esk9_0)),impl(lazy_impl(esk8_0,impl(esk9_0,esk2_2(esk8_0,esk9_0))),esk2_2(esk8_0,esk9_0))))
| lazy_impl(prop(esk2_2(esk8_0,esk9_0)),impl(lazy_impl(esk8_0,impl(esk9_0,esk2_2(esk8_0,esk9_0))),esk2_2(esk8_0,esk9_0))) != lazy_and1(esk8_0,esk9_0) ),
inference(spm,[status(thm)],[c_0_177,c_0_52]) ).
cnf(c_0_186,plain,
( ~ bool(esk2_2(err,X2))
| ~ forallprefers(lazy_impl(prop(X1),impl(err,X1)),err) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_178,c_0_143]),c_0_143]),c_0_125]),c_0_125]),c_0_134]) ).
cnf(c_0_187,plain,
bool(esk2_2(err,X1)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_179,c_0_85]),c_0_99]),c_0_180])]),c_0_134]) ).
cnf(c_0_188,plain,
( ~ forallprefers(lazy_impl(prop(X3),err),true)
| bool(esk2_2(X1,X2))
| d(X1) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_181]),c_0_125]),c_0_134]),c_0_182]) ).
cnf(c_0_189,plain,
prop(esk2_2(err,X1)) = true,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_183,c_0_85]),c_0_99]),c_0_180])]),c_0_134]) ).
fof(c_0_190,plain,
! [X23] :
( impl(false,X23) = true
| ~ bool(X23) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[impl_axiom3])])]) ).
cnf(c_0_191,plain,
bool(lazy_impl(true,impl(true,false))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_184,c_0_85]),c_0_58]),c_0_59])]) ).
cnf(c_0_192,plain,
( ~ bool(X1)
| ~ forallprefers(lazy_impl(true,true),false2) ),
inference(spm,[status(thm)],[c_0_104,c_0_44]) ).
cnf(c_0_193,negated_conjecture,
( lazy_impl(true,lazy_impl(prop(esk2_2(esk8_0,esk9_0)),impl(lazy_impl(true,esk8_0),esk2_2(esk8_0,esk9_0)))) != lazy_and1(esk8_0,esk9_0)
| bool(esk8_0) ),
inference(spm,[status(thm)],[c_0_177,c_0_93]) ).
cnf(c_0_194,negated_conjecture,
( ~ d(lazy_impl(prop(esk2_2(esk8_0,esk9_0)),impl(lazy_impl(true,esk8_0),esk2_2(esk8_0,esk9_0))))
| lazy_impl(prop(esk2_2(esk8_0,esk9_0)),impl(lazy_impl(true,esk8_0),esk2_2(esk8_0,esk9_0))) != lazy_and1(esk8_0,esk9_0)
| bool(esk8_0) ),
inference(spm,[status(thm)],[c_0_185,c_0_93]) ).
cnf(c_0_195,plain,
~ forallprefers(lazy_impl(prop(X1),impl(err,X1)),err),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_186,c_0_187])]) ).
cnf(c_0_196,plain,
( ~ forallprefers(err,true)
| bool(esk2_2(X1,X2))
| d(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_188,c_0_189]),c_0_125]) ).
cnf(c_0_197,plain,
( ~ bool(X1)
| impl(false,X1) = true ),
inference(split_conjunct,[status(thm)],[c_0_190]) ).
cnf(c_0_198,plain,
( ~ d(impl(true,false))
| ~ forallprefers(impl(true,false),false) ),
inference(spm,[status(thm)],[c_0_184,c_0_52]) ).
cnf(c_0_199,plain,
d(impl(true,false)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_191,c_0_67]),c_0_134]) ).
cnf(c_0_200,plain,
( ~ bool(X1)
| ~ bool(false2)
| bool(lazy_impl(true,true)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_192,c_0_85]),c_0_101])]) ).
cnf(c_0_201,negated_conjecture,
( ~ d(esk8_0)
| lazy_impl(true,lazy_impl(prop(esk2_2(esk8_0,esk9_0)),impl(esk8_0,esk2_2(esk8_0,esk9_0)))) != lazy_and1(esk8_0,esk9_0)
| bool(esk8_0) ),
inference(spm,[status(thm)],[c_0_193,c_0_52]) ).
fof(c_0_202,plain,
! [X3,X4] :
( ~ bool(X3)
=> lazy_and1(X3,X4) = phi(X3) ),
inference(fof_simplification,[status(thm)],[lazy_and1_axiom1]) ).
cnf(c_0_203,negated_conjecture,
( ~ d(lazy_impl(prop(esk2_2(esk8_0,esk9_0)),impl(err,esk2_2(esk8_0,esk9_0))))
| lazy_impl(prop(esk2_2(esk8_0,esk9_0)),impl(err,esk2_2(esk8_0,esk9_0))) != lazy_and1(esk8_0,esk9_0)
| bool(esk8_0)
| d(esk8_0) ),
inference(spm,[status(thm)],[c_0_194,c_0_67]) ).
cnf(c_0_204,plain,
d(lazy_impl(prop(X1),impl(err,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_195,c_0_69]),c_0_73])]) ).
cnf(c_0_205,plain,
( ~ d(X1)
| bool(X1)
| lazy_impl(X1,X2) = X1 ),
inference(spm,[status(thm)],[c_0_52,c_0_93]) ).
cnf(c_0_206,plain,
( bool(esk2_2(X1,X2))
| d(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_196,c_0_85]),c_0_99]),c_0_180])]),c_0_134]) ).
cnf(c_0_207,plain,
( ~ bool(X1)
| ~ forallprefers(lazy_impl(prop(X1),impl(lazy_impl(X2,true),X1)),lazy_impl(prop(esk2_2(X2,false)),impl(lazy_impl(X2,impl(false,esk2_2(X2,false))),esk2_2(X2,false)))) ),
inference(spm,[status(thm)],[c_0_33,c_0_197]) ).
cnf(c_0_208,plain,
( ~ bool(X1)
| ~ forallprefers(lazy_impl(prop(X1),X1),lazy_impl(true,impl(true,false))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_50]),c_0_166]),c_0_164]),c_0_166]) ).
cnf(c_0_209,plain,
~ forallprefers(impl(true,false),false),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_198,c_0_199])]) ).
cnf(c_0_210,plain,
( ~ bool(X1)
| bool(lazy_impl(true,true)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_200,c_0_106])]) ).
cnf(c_0_211,plain,
( ~ bool(X1)
| ~ forallprefers(lazy_impl(true,impl(true,X1)),false) ),
inference(spm,[status(thm)],[c_0_176,c_0_44]) ).
cnf(c_0_212,negated_conjecture,
( ~ d(esk8_0)
| lazy_impl(true,lazy_impl(prop(esk2_2(esk8_0,esk9_0)),lazy_impl(true,esk8_0))) != lazy_and1(esk8_0,esk9_0)
| bool(esk8_0) ),
inference(spm,[status(thm)],[c_0_201,c_0_132]) ).
fof(c_0_213,plain,
! [X42,X43] :
( lazy_and1(X42,X43) = phi(X42)
| bool(X42) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_202])]) ).
cnf(c_0_214,negated_conjecture,
( lazy_impl(prop(esk2_2(esk8_0,esk9_0)),impl(err,esk2_2(esk8_0,esk9_0))) != lazy_and1(esk8_0,esk9_0)
| d(esk8_0) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_203,c_0_204])]),c_0_182]) ).
cnf(c_0_215,plain,
( ~ forallprefers(lazy_impl(prop(X3),impl(X1,X3)),true)
| bool(X1)
| bool(esk2_2(X1,X2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_205]),c_0_206]) ).
cnf(c_0_216,plain,
( ~ bool(X1)
| ~ forallprefers(lazy_impl(prop(X1),impl(true,X1)),lazy_impl(prop(esk2_2(true,false)),impl(lazy_impl(true,impl(false,esk2_2(true,false))),esk2_2(true,false)))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_207,c_0_52]),c_0_99])]) ).
cnf(c_0_217,plain,
~ forallprefers(false,lazy_impl(true,impl(true,false))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_208,c_0_164]),c_0_167]),c_0_59])]) ).
cnf(c_0_218,plain,
bool(impl(true,false)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_209,c_0_85]),c_0_58]),c_0_59])]) ).
cnf(c_0_219,plain,
bool(lazy_impl(true,true)),
inference(spm,[status(thm)],[c_0_210,c_0_65]) ).
cnf(c_0_220,plain,
( ~ bool(X2)
| ~ forallprefers(lazy_impl(prop(X2),impl(lazy_impl(X1,true),X2)),true)
| bool(esk2_2(X1,false)) ),
inference(spm,[status(thm)],[c_0_150,c_0_197]) ).
cnf(c_0_221,plain,
( ~ bool(X1)
| ~ forallprefers(err,false)
| d(impl(true,X1)) ),
inference(spm,[status(thm)],[c_0_211,c_0_67]) ).
cnf(c_0_222,negated_conjecture,
( ~ d(esk8_0)
| lazy_impl(true,lazy_impl(prop(esk2_2(esk8_0,esk9_0)),esk8_0)) != lazy_and1(esk8_0,esk9_0)
| bool(esk8_0) ),
inference(spm,[status(thm)],[c_0_212,c_0_52]) ).
cnf(c_0_223,plain,
( lazy_and1(X1,X2) = phi(X1)
| bool(X1) ),
inference(split_conjunct,[status(thm)],[c_0_213]) ).
cnf(c_0_224,negated_conjecture,
( lazy_impl(prop(esk2_2(esk8_0,esk9_0)),err) != lazy_and1(esk8_0,esk9_0)
| d(esk8_0) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_214,c_0_132]),c_0_125]),c_0_134]) ).
cnf(c_0_225,plain,
( ~ forallprefers(lazy_impl(true,impl(X1,false)),true)
| bool(X1)
| bool(esk2_2(X1,X2)) ),
inference(spm,[status(thm)],[c_0_215,c_0_164]) ).
cnf(c_0_226,plain,
( ~ bool(esk2_2(X2,false))
| ~ forallprefers(lazy_impl(prop(X1),impl(lazy_impl(X2,impl(false,X1)),X1)),lazy_impl(prop(esk2_2(X2,false)),impl(lazy_impl(X2,true),esk2_2(X2,false)))) ),
inference(spm,[status(thm)],[c_0_33,c_0_197]) ).
cnf(c_0_227,plain,
( ~ bool(X1)
| ~ forallprefers(lazy_impl(prop(X1),impl(true,X1)),true)
| prop(esk2_2(true,false)) = true ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_216,c_0_175]),c_0_34]) ).
cnf(c_0_228,plain,
impl(true,false) = false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_217,c_0_156]),c_0_57]),c_0_218])]) ).
cnf(c_0_229,plain,
( lazy_impl(true,true) = false
| lazy_impl(true,true) = true ),
inference(spm,[status(thm)],[c_0_86,c_0_219]) ).
cnf(c_0_230,plain,
( ~ forallprefers(lazy_impl(true,impl(lazy_impl(X1,true),false)),true)
| bool(esk2_2(X1,false)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_220,c_0_164]),c_0_59])]) ).
cnf(c_0_231,plain,
( ~ bool(X1)
| ~ d(impl(true,X1))
| ~ forallprefers(impl(true,X1),false) ),
inference(spm,[status(thm)],[c_0_211,c_0_52]) ).
cnf(c_0_232,plain,
( ~ bool(X1)
| d(impl(true,X1)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_221,c_0_85]),c_0_58]),c_0_59])]),c_0_134]) ).
cnf(c_0_233,negated_conjecture,
( ~ bool(esk2_2(esk8_0,esk9_0))
| ~ d(esk8_0)
| lazy_and1(esk8_0,esk9_0) != lazy_impl(true,lazy_impl(true,esk8_0))
| bool(esk8_0) ),
inference(spm,[status(thm)],[c_0_222,c_0_44]) ).
cnf(c_0_234,plain,
( bool(X1)
| lazy_and1(X1,X2) = lazy_impl(true,X1) ),
inference(rw,[status(thm)],[c_0_223,c_0_46]) ).
cnf(c_0_235,negated_conjecture,
( ~ bool(esk2_2(esk8_0,esk9_0))
| lazy_and1(esk8_0,esk9_0) != err
| d(esk8_0) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_224,c_0_44]),c_0_125]) ).
cnf(c_0_236,plain,
( ~ forallprefers(lazy_impl(true,lazy_impl(true,X1)),true)
| bool(X1)
| bool(esk2_2(X1,X2)) ),
inference(spm,[status(thm)],[c_0_225,c_0_132]) ).
cnf(c_0_237,plain,
( ~ bool(X1)
| ~ bool(esk2_2(X2,false))
| ~ forallprefers(lazy_impl(prop(X1),impl(lazy_impl(X2,true),X1)),lazy_impl(prop(esk2_2(X2,false)),impl(lazy_impl(X2,true),esk2_2(X2,false)))) ),
inference(spm,[status(thm)],[c_0_226,c_0_197]) ).
cnf(c_0_238,plain,
prop(esk2_2(true,false)) = true,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_227,c_0_228]),c_0_164]),c_0_167]),c_0_57]),c_0_59])]) ).
cnf(c_0_239,plain,
lazy_impl(true,true) = true,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_229]),c_0_99])]),c_0_158]) ).
cnf(c_0_240,plain,
bool(esk2_2(true,false)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_230,c_0_52]),c_0_228]),c_0_167]),c_0_57]),c_0_99])]) ).
cnf(c_0_241,plain,
( ~ bool(X1)
| bool(impl(true,X1)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_231,c_0_85]),c_0_58]),c_0_59])]),c_0_232]) ).
cnf(c_0_242,negated_conjecture,
( ~ bool(esk2_2(esk8_0,esk9_0))
| ~ d(esk8_0)
| lazy_impl(true,lazy_impl(true,esk8_0)) != lazy_impl(true,esk8_0)
| bool(esk8_0) ),
inference(spm,[status(thm)],[c_0_233,c_0_234]) ).
cnf(c_0_243,negated_conjecture,
( ~ bool(esk2_2(esk8_0,esk9_0))
| d(esk8_0) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_235,c_0_234]),c_0_67]),c_0_182]) ).
cnf(c_0_244,plain,
( ~ forallprefers(lazy_impl(true,X1),true)
| bool(X1)
| bool(esk2_2(X1,X2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_236,c_0_52]),c_0_206]) ).
cnf(c_0_245,plain,
( ~ forallprefers(lazy_impl(prop(X2),impl(err,X2)),lazy_impl(prop(esk2_2(true,X1)),impl(lazy_impl(true,impl(X1,esk2_2(true,X1))),esk2_2(true,X1))))
| d(impl(X1,X2)) ),
inference(spm,[status(thm)],[c_0_33,c_0_67]) ).
cnf(c_0_246,plain,
( ~ bool(X1)
| ~ forallprefers(lazy_impl(prop(X1),impl(true,X1)),lazy_impl(true,impl(true,esk2_2(true,false)))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_237,c_0_238]),c_0_239]),c_0_239]),c_0_240])]) ).
cnf(c_0_247,plain,
( ~ bool(X1)
| impl(true,X1) = false
| impl(true,X1) = true ),
inference(spm,[status(thm)],[c_0_86,c_0_241]) ).
cnf(c_0_248,negated_conjecture,
( ~ bool(esk2_2(esk8_0,esk9_0))
| ~ d(esk8_0)
| bool(esk8_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_242,c_0_52]),c_0_52]) ).
cnf(c_0_249,negated_conjecture,
d(esk8_0),
inference(spm,[status(thm)],[c_0_243,c_0_206]) ).
cnf(c_0_250,plain,
( ~ forallprefers(X1,true)
| bool(X1)
| bool(esk2_2(X1,X2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_244,c_0_52]),c_0_206]) ).
cnf(c_0_251,plain,
( ~ bool(esk2_2(true,false))
| ~ forallprefers(lazy_impl(prop(X1),impl(err,X1)),lazy_impl(prop(esk2_2(true,false)),impl(true,esk2_2(true,false))))
| d(impl(false,X1)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_245,c_0_197]),c_0_239]) ).
cnf(c_0_252,plain,
~ forallprefers(false,lazy_impl(true,impl(true,esk2_2(true,false)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_246,c_0_228]),c_0_164]),c_0_167]),c_0_59])]) ).
cnf(c_0_253,plain,
( ~ bool(X1)
| false = X1
| impl(true,X1) = true ),
inference(spm,[status(thm)],[c_0_50,c_0_247]) ).
cnf(c_0_254,plain,
( bool(lazy_impl(true,prop(X1)))
| false2 = err ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_113]),c_0_61])]) ).
cnf(c_0_255,negated_conjecture,
( ~ bool(esk2_2(esk8_0,esk9_0))
| bool(esk8_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_248,c_0_249])]) ).
cnf(c_0_256,plain,
( bool(X1)
| bool(esk2_2(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_250,c_0_85]),c_0_99]),c_0_180])]) ).
cnf(c_0_257,plain,
( ~ forallprefers(lazy_impl(prop(X2),impl(lazy_impl(X3,lazy_impl(true,X1)),X2)),lazy_impl(prop(esk2_2(X3,X1)),impl(lazy_impl(X3,impl(X1,esk2_2(X3,X1))),esk2_2(X3,X1))))
| bool(X1) ),
inference(spm,[status(thm)],[c_0_33,c_0_132]) ).
cnf(c_0_258,plain,
( ~ forallprefers(lazy_impl(prop(X1),impl(err,X1)),lazy_impl(prop(esk2_2(true,false)),impl(true,esk2_2(true,false))))
| d(impl(false,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_251,c_0_240])]) ).
cnf(c_0_259,plain,
esk2_2(true,false) = false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_252,c_0_253]),c_0_239]),c_0_57]),c_0_240])]) ).
cnf(c_0_260,plain,
( bool(lazy_impl(true,true))
| false2 = err ),
inference(spm,[status(thm)],[c_0_254,c_0_144]) ).
cnf(c_0_261,negated_conjecture,
bool(esk8_0),
inference(spm,[status(thm)],[c_0_255,c_0_256]) ).
fof(c_0_262,plain,
! [X44] : lazy_and1(false,X44) = false,
inference(variable_rename,[status(thm)],[lazy_and1_axiom2]) ).
fof(c_0_263,plain,
! [X45] : lazy_and1(true,X45) = phi(X45),
inference(variable_rename,[status(thm)],[lazy_and1_axiom3]) ).
cnf(c_0_264,plain,
( ~ forallprefers(lazy_impl(prop(X2),impl(err,X2)),true)
| bool(esk2_2(true,X1))
| d(impl(X1,X2)) ),
inference(spm,[status(thm)],[c_0_150,c_0_67]) ).
cnf(c_0_265,plain,
( ~ forallprefers(lazy_impl(prop(X2),impl(lazy_impl(X3,err),X2)),lazy_impl(prop(esk2_2(X3,X1)),impl(lazy_impl(X3,impl(X1,esk2_2(X3,X1))),esk2_2(X3,X1))))
| d(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_257,c_0_67]),c_0_182]) ).
cnf(c_0_266,plain,
( ~ forallprefers(lazy_impl(prop(X1),impl(err,X1)),false)
| d(impl(false,X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_258,c_0_259]),c_0_164]),c_0_228]),c_0_167]) ).
cnf(c_0_267,plain,
( false2 = err
| lazy_impl(true,true) = false
| lazy_impl(true,true) = true ),
inference(spm,[status(thm)],[c_0_86,c_0_260]) ).
cnf(c_0_268,plain,
( false2 = err
| lazy_impl(true,prop(X1)) = false
| lazy_impl(true,prop(X1)) = true ),
inference(spm,[status(thm)],[c_0_86,c_0_254]) ).
cnf(c_0_269,negated_conjecture,
( esk8_0 = false
| esk8_0 = true ),
inference(spm,[status(thm)],[c_0_86,c_0_261]) ).
cnf(c_0_270,plain,
lazy_and1(false,X1) = false,
inference(split_conjunct,[status(thm)],[c_0_262]) ).
cnf(c_0_271,plain,
lazy_and1(true,X1) = phi(X1),
inference(split_conjunct,[status(thm)],[c_0_263]) ).
cnf(c_0_272,plain,
( ~ forallprefers(lazy_impl(prop(X2),err),true)
| bool(esk2_2(true,X1))
| d(impl(X1,X2)) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_264,c_0_132]),c_0_125]),c_0_134]) ).
cnf(c_0_273,plain,
( ~ forallprefers(lazy_impl(prop(X3),impl(lazy_impl(X2,err),X3)),true)
| bool(esk2_2(X2,X1))
| d(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_265,c_0_36]),c_0_34]) ).
cnf(c_0_274,plain,
~ forallprefers(lazy_impl(prop(X1),impl(lazy_impl(true,impl(false,X1)),X1)),false),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_226,c_0_259]),c_0_164]),c_0_239]),c_0_228]),c_0_167]),c_0_59])]) ).
cnf(c_0_275,plain,
( ~ forallprefers(lazy_impl(prop(X1),err),false)
| d(impl(false,X1)) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_266,c_0_132]),c_0_125]),c_0_134]) ).
cnf(c_0_276,plain,
( ~ bool(X1)
| ~ forallprefers(lazy_impl(prop(X1),impl(lazy_impl(X2,X1),X1)),lazy_impl(prop(esk2_2(X2,true)),impl(lazy_impl(X2,impl(true,esk2_2(X2,true))),esk2_2(X2,true)))) ),
inference(spm,[status(thm)],[c_0_33,c_0_50]) ).
cnf(c_0_277,plain,
( false2 = err
| lazy_impl(true,true) = true ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_267]),c_0_99])]),c_0_158]) ).
cnf(c_0_278,plain,
( false2 = err
| prop(X1) = false
| lazy_impl(true,prop(X1)) = true ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_268]),c_0_115]) ).
cnf(c_0_279,negated_conjecture,
( lazy_impl(true,lazy_impl(prop(esk2_2(esk8_0,esk9_0)),impl(lazy_impl(esk8_0,lazy_impl(true,esk9_0)),esk2_2(esk8_0,esk9_0)))) != lazy_and1(esk8_0,esk9_0)
| bool(esk9_0) ),
inference(spm,[status(thm)],[c_0_177,c_0_132]) ).
cnf(c_0_280,negated_conjecture,
esk8_0 = true,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_177,c_0_269]),c_0_166]),c_0_164]),c_0_166]),c_0_34]),c_0_166]),c_0_228]),c_0_167]),c_0_167]),c_0_270])]) ).
cnf(c_0_281,plain,
lazy_and1(true,X1) = lazy_impl(true,X1),
inference(rw,[status(thm)],[c_0_271,c_0_46]) ).
cnf(c_0_282,plain,
( ~ forallprefers(err,true)
| bool(esk2_2(true,X1))
| d(impl(X1,false)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_272,c_0_164]),c_0_125]) ).
cnf(c_0_283,plain,
( ~ forallprefers(lazy_impl(prop(X2),impl(err,X2)),true)
| bool(esk2_2(true,X1))
| d(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_273,c_0_52]),c_0_73])]) ).
cnf(c_0_284,plain,
~ forallprefers(lazy_impl(true,impl(lazy_impl(true,impl(false,false)),false)),false),
inference(spm,[status(thm)],[c_0_274,c_0_164]) ).
cnf(c_0_285,plain,
( ~ forallprefers(err,false)
| d(impl(false,false)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_275,c_0_164]),c_0_125]) ).
cnf(c_0_286,plain,
( ~ forallprefers(lazy_impl(prop(true),impl(true,true)),lazy_impl(prop(esk2_2(true,true)),impl(lazy_impl(true,impl(true,esk2_2(true,true))),esk2_2(true,true))))
| false2 = err ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_276,c_0_277]),c_0_180])]) ).
cnf(c_0_287,plain,
( false2 = err
| prop(X1) = true
| prop(X1) = false ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_278]),c_0_127]) ).
cnf(c_0_288,negated_conjecture,
( lazy_impl(true,lazy_impl(prop(esk2_2(true,esk9_0)),impl(lazy_impl(true,lazy_impl(true,esk9_0)),esk2_2(true,esk9_0)))) != lazy_impl(true,esk9_0)
| bool(esk9_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_279,c_0_280]),c_0_280]),c_0_280]),c_0_280]),c_0_281]) ).
cnf(c_0_289,plain,
( ~ d(impl(X1,X2))
| ~ forallprefers(lazy_impl(prop(X2),impl(impl(X1,X2),X2)),true)
| bool(esk2_2(true,X1)) ),
inference(spm,[status(thm)],[c_0_150,c_0_52]) ).
cnf(c_0_290,plain,
( bool(esk2_2(true,X1))
| d(impl(X1,false)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_282,c_0_85]),c_0_99]),c_0_180])]),c_0_134]) ).
cnf(c_0_291,plain,
( ~ forallprefers(lazy_impl(prop(X2),err),true)
| bool(esk2_2(true,X1))
| d(X1) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_283,c_0_132]),c_0_125]),c_0_134]) ).
cnf(c_0_292,plain,
( ~ d(impl(false,false))
| ~ forallprefers(lazy_impl(true,impl(impl(false,false),false)),false) ),
inference(spm,[status(thm)],[c_0_284,c_0_52]) ).
cnf(c_0_293,plain,
d(impl(false,false)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_285,c_0_85]),c_0_58]),c_0_59])]),c_0_134]) ).
cnf(c_0_294,plain,
( ~ forallprefers(lazy_impl(prop(true),impl(true,true)),true)
| false2 = err
| prop(esk2_2(true,true)) = true ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_286,c_0_287]),c_0_34]) ).
cnf(c_0_295,negated_conjecture,
( ~ d(esk9_0)
| lazy_impl(true,lazy_impl(prop(esk2_2(true,esk9_0)),impl(lazy_impl(true,esk9_0),esk2_2(true,esk9_0)))) != esk9_0
| bool(esk9_0) ),
inference(spm,[status(thm)],[c_0_288,c_0_52]) ).
cnf(c_0_296,negated_conjecture,
( lazy_impl(true,lazy_impl(prop(esk2_2(esk8_0,esk9_0)),lazy_impl(true,lazy_impl(esk8_0,lazy_impl(true,esk9_0))))) != lazy_and1(esk8_0,esk9_0)
| bool(esk9_0)
| bool(lazy_impl(esk8_0,lazy_impl(true,esk9_0))) ),
inference(spm,[status(thm)],[c_0_279,c_0_132]) ).
cnf(c_0_297,plain,
( ~ forallprefers(lazy_impl(true,impl(impl(X1,false),false)),true)
| bool(esk2_2(true,X1)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_289,c_0_164]),c_0_290]) ).
cnf(c_0_298,plain,
( ~ forallprefers(err,true)
| bool(esk2_2(true,X1))
| d(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_291,c_0_189]),c_0_125]) ).
cnf(c_0_299,plain,
~ forallprefers(lazy_impl(true,impl(impl(false,false),false)),false),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_292,c_0_293])]) ).
cnf(c_0_300,plain,
( ~ forallprefers(lazy_impl(true,impl(true,true)),true)
| false2 = err
| prop(esk2_2(true,true)) = true ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_294,c_0_44]),c_0_180])]) ).
cnf(c_0_301,negated_conjecture,
( ~ d(esk9_0)
| lazy_impl(true,lazy_impl(prop(esk2_2(true,esk9_0)),impl(esk9_0,esk2_2(true,esk9_0)))) != esk9_0
| bool(esk9_0) ),
inference(spm,[status(thm)],[c_0_295,c_0_52]) ).
cnf(c_0_302,negated_conjecture,
( lazy_impl(true,lazy_impl(prop(esk2_2(esk8_0,esk9_0)),lazy_impl(true,lazy_impl(esk8_0,err)))) != lazy_and1(esk8_0,esk9_0)
| bool(lazy_impl(esk8_0,err))
| d(esk9_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_296,c_0_67]),c_0_182]) ).
cnf(c_0_303,plain,
( ~ forallprefers(lazy_impl(true,impl(lazy_impl(true,X1),false)),true)
| bool(X1)
| bool(esk2_2(true,X1)) ),
inference(spm,[status(thm)],[c_0_297,c_0_132]) ).
cnf(c_0_304,plain,
( bool(esk2_2(true,X1))
| d(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_298,c_0_85]),c_0_99]),c_0_180])]),c_0_134]) ).
cnf(c_0_305,plain,
( ~ forallprefers(err,false)
| d(impl(impl(false,false),false)) ),
inference(spm,[status(thm)],[c_0_299,c_0_67]) ).
cnf(c_0_306,plain,
( ~ d(impl(true,true))
| ~ forallprefers(impl(true,true),true)
| false2 = err
| prop(esk2_2(true,true)) = true ),
inference(spm,[status(thm)],[c_0_300,c_0_52]) ).
cnf(c_0_307,negated_conjecture,
( ~ d(esk9_0)
| lazy_impl(true,lazy_impl(prop(esk2_2(true,esk9_0)),lazy_impl(true,esk9_0))) != esk9_0
| bool(esk9_0) ),
inference(spm,[status(thm)],[c_0_301,c_0_132]) ).
cnf(c_0_308,negated_conjecture,
( lazy_impl(true,lazy_impl(prop(esk2_2(true,esk9_0)),err)) != lazy_impl(true,esk9_0)
| d(esk9_0) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_302,c_0_280]),c_0_125]),c_0_280]),c_0_280]),c_0_125]),c_0_125]),c_0_280]),c_0_281]),c_0_134]) ).
cnf(c_0_309,plain,
( ~ forallprefers(lazy_impl(true,impl(X1,false)),true)
| bool(X1)
| bool(esk2_2(true,X1)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_303,c_0_52]),c_0_304]) ).
cnf(c_0_310,plain,
( ~ d(impl(impl(false,false),false))
| ~ forallprefers(impl(impl(false,false),false),false) ),
inference(spm,[status(thm)],[c_0_299,c_0_52]) ).
cnf(c_0_311,plain,
d(impl(impl(false,false),false)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_305,c_0_85]),c_0_58]),c_0_59])]),c_0_134]) ).
cnf(c_0_312,plain,
( ~ bool(X1)
| ~ forallprefers(lazy_impl(true,X1),esk7_0) ),
inference(rw,[status(thm)],[c_0_94,c_0_138]) ).
cnf(c_0_313,plain,
( ~ d(impl(true,true))
| ~ forallprefers(impl(true,true),true)
| prop(esk2_2(true,true)) = true ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_306,c_0_138]),c_0_147]),c_0_115]) ).
cnf(c_0_314,plain,
( ~ bool(X1)
| lazy_impl(true,X1) = X1 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_95]),c_0_134]) ).
cnf(c_0_315,negated_conjecture,
( ~ d(esk9_0)
| lazy_impl(true,lazy_impl(prop(esk2_2(true,esk9_0)),esk9_0)) != esk9_0
| bool(esk9_0) ),
inference(spm,[status(thm)],[c_0_307,c_0_52]) ).
cnf(c_0_316,negated_conjecture,
( ~ bool(esk2_2(true,esk9_0))
| d(esk9_0) ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_308,c_0_44]),c_0_125]),c_0_125]),c_0_67]) ).
cnf(c_0_317,plain,
( ~ forallprefers(lazy_impl(true,lazy_impl(true,X1)),true)
| bool(X1)
| bool(esk2_2(true,X1)) ),
inference(spm,[status(thm)],[c_0_309,c_0_132]) ).
cnf(c_0_318,plain,
~ forallprefers(impl(impl(false,false),false),false),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_310,c_0_311])]) ).
cnf(c_0_319,plain,
( ~ bool(X1)
| ~ forallprefers(lazy_impl(true,X1),false) ),
inference(rw,[status(thm)],[c_0_312,c_0_147]) ).
cnf(c_0_320,plain,
bool(lazy_impl(prop(X1),impl(true,X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_176,c_0_85]),c_0_58]),c_0_59])]) ).
cnf(c_0_321,plain,
( impl(true,true) = true
| prop(esk2_2(true,true)) = true ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_313,c_0_247]),c_0_57]),c_0_58]),c_0_180])]) ).
cnf(c_0_322,negated_conjecture,
( ~ bool(lazy_impl(prop(esk2_2(esk8_0,esk9_0)),impl(lazy_impl(esk8_0,impl(esk9_0,esk2_2(esk8_0,esk9_0))),esk2_2(esk8_0,esk9_0))))
| lazy_impl(prop(esk2_2(esk8_0,esk9_0)),impl(lazy_impl(esk8_0,impl(esk9_0,esk2_2(esk8_0,esk9_0))),esk2_2(esk8_0,esk9_0))) != lazy_and1(esk8_0,esk9_0) ),
inference(spm,[status(thm)],[c_0_177,c_0_314]) ).
cnf(c_0_323,negated_conjecture,
( ~ bool(esk2_2(true,esk9_0))
| lazy_impl(true,lazy_impl(true,esk9_0)) != esk9_0
| bool(esk9_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_315,c_0_44]),c_0_316]) ).
cnf(c_0_324,plain,
( ~ forallprefers(lazy_impl(true,X1),true)
| bool(X1)
| bool(esk2_2(true,X1)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_317,c_0_52]),c_0_304]) ).
cnf(c_0_325,plain,
~ forallprefers(lazy_impl(true,impl(false,false)),false),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_318,c_0_132]),c_0_319]) ).
cnf(c_0_326,plain,
~ forallprefers(lazy_impl(prop(true),impl(true,true)),lazy_impl(prop(esk2_2(true,true)),impl(lazy_impl(true,impl(true,esk2_2(true,true))),esk2_2(true,true)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_276,c_0_239]),c_0_180])]) ).
cnf(c_0_327,plain,
( bool(lazy_impl(true,impl(true,esk2_2(true,true))))
| impl(true,true) = true ),
inference(spm,[status(thm)],[c_0_320,c_0_321]) ).
cnf(c_0_328,negated_conjecture,
( ~ bool(lazy_impl(prop(esk2_2(true,esk9_0)),impl(lazy_impl(true,impl(esk9_0,esk2_2(true,esk9_0))),esk2_2(true,esk9_0))))
| lazy_impl(prop(esk2_2(true,esk9_0)),impl(lazy_impl(true,impl(esk9_0,esk2_2(true,esk9_0))),esk2_2(true,esk9_0))) != lazy_impl(true,esk9_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_322,c_0_280]),c_0_280]),c_0_280]),c_0_280]),c_0_280]),c_0_281]),c_0_280]),c_0_280]),c_0_280]),c_0_280]) ).
cnf(c_0_329,negated_conjecture,
( ~ bool(esk2_2(true,esk9_0))
| lazy_impl(true,esk9_0) != esk9_0
| bool(esk9_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_323,c_0_52]),c_0_316]) ).
cnf(c_0_330,plain,
( ~ forallprefers(X1,true)
| bool(X1)
| bool(esk2_2(true,X1)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_324,c_0_52]),c_0_304]) ).
cnf(c_0_331,plain,
~ forallprefers(impl(false,false),false),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_325,c_0_52]),c_0_293])]) ).
cnf(c_0_332,plain,
~ forallprefers(lazy_impl(true,impl(true,true)),lazy_impl(prop(esk2_2(true,true)),impl(lazy_impl(true,impl(true,esk2_2(true,true))),esk2_2(true,true)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_326,c_0_44]),c_0_180])]) ).
cnf(c_0_333,plain,
( impl(true,true) = true
| lazy_impl(true,impl(true,esk2_2(true,true))) = false
| lazy_impl(true,impl(true,esk2_2(true,true))) = true ),
inference(spm,[status(thm)],[c_0_86,c_0_327]) ).
cnf(c_0_334,negated_conjecture,
( lazy_and1(esk8_0,esk9_0) != true
| prop(esk2_2(esk8_0,esk9_0)) = true ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_177,c_0_175]),c_0_34]),c_0_239]) ).
cnf(c_0_335,negated_conjecture,
( ~ bool(impl(esk9_0,esk2_2(true,esk9_0)))
| lazy_impl(prop(esk2_2(true,esk9_0)),impl(true,esk2_2(true,esk9_0))) != lazy_impl(true,esk9_0)
| impl(esk9_0,esk2_2(true,esk9_0)) = false ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_328,c_0_156]),c_0_320])]) ).
cnf(c_0_336,negated_conjecture,
( ~ bool(esk2_2(true,esk9_0))
| bool(esk9_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_329,c_0_52]),c_0_316]) ).
cnf(c_0_337,plain,
( bool(X1)
| bool(esk2_2(true,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_330,c_0_85]),c_0_99]),c_0_180])]) ).
cnf(c_0_338,plain,
bool(impl(false,false)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_331,c_0_85]),c_0_58]),c_0_59])]) ).
cnf(c_0_339,negated_conjecture,
( lazy_and1(esk8_0,esk9_0) != true
| bool(esk2_2(esk8_0,esk9_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_185,c_0_36]),c_0_34]),c_0_34]),c_0_99])]) ).
cnf(c_0_340,plain,
( ~ forallprefers(lazy_impl(true,impl(true,true)),lazy_impl(true,impl(lazy_impl(true,impl(true,esk2_2(true,true))),esk2_2(true,true))))
| impl(true,true) = true ),
inference(spm,[status(thm)],[c_0_332,c_0_321]) ).
cnf(c_0_341,plain,
( impl(true,true) = true
| impl(true,esk2_2(true,true)) = false
| lazy_impl(true,impl(true,esk2_2(true,true))) = true ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_333]),c_0_115]) ).
cnf(c_0_342,negated_conjecture,
( lazy_impl(true,esk9_0) != true
| prop(esk2_2(true,esk9_0)) = true ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_334,c_0_280]),c_0_280]),c_0_281]) ).
cnf(c_0_343,negated_conjecture,
( ~ bool(esk2_2(true,esk9_0))
| ~ bool(impl(esk9_0,esk2_2(true,esk9_0)))
| lazy_impl(true,impl(true,esk2_2(true,esk9_0))) != lazy_impl(true,esk9_0)
| impl(esk9_0,esk2_2(true,esk9_0)) = false ),
inference(spm,[status(thm)],[c_0_335,c_0_44]) ).
cnf(c_0_344,negated_conjecture,
bool(esk9_0),
inference(spm,[status(thm)],[c_0_336,c_0_337]) ).
cnf(c_0_345,plain,
( impl(false,false) = false
| impl(false,false) = true ),
inference(spm,[status(thm)],[c_0_86,c_0_338]) ).
cnf(c_0_346,negated_conjecture,
( lazy_impl(true,esk9_0) != true
| bool(esk2_2(true,esk9_0)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_339,c_0_280]),c_0_280]),c_0_281]) ).
cnf(c_0_347,plain,
( ~ forallprefers(lazy_impl(true,impl(true,true)),lazy_impl(true,impl(true,esk2_2(true,true))))
| impl(true,true) = true
| impl(true,esk2_2(true,true)) = false ),
inference(spm,[status(thm)],[c_0_340,c_0_341]) ).
cnf(c_0_348,negated_conjecture,
( ~ d(esk9_0)
| esk9_0 != true
| prop(esk2_2(true,esk9_0)) = true ),
inference(spm,[status(thm)],[c_0_342,c_0_52]) ).
cnf(c_0_349,negated_conjecture,
d(esk9_0),
inference(spm,[status(thm)],[c_0_316,c_0_304]) ).
cnf(c_0_350,negated_conjecture,
( ~ bool(esk2_2(true,esk9_0))
| ~ bool(impl(esk9_0,esk2_2(true,esk9_0)))
| lazy_impl(true,esk2_2(true,esk9_0)) != lazy_impl(true,esk9_0)
| impl(esk9_0,esk2_2(true,esk9_0)) = false ),
inference(spm,[status(thm)],[c_0_343,c_0_50]) ).
cnf(c_0_351,negated_conjecture,
( esk9_0 = false
| esk9_0 = true ),
inference(spm,[status(thm)],[c_0_86,c_0_344]) ).
cnf(c_0_352,plain,
impl(false,false) = true,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_197,c_0_345]),c_0_59])]),c_0_158]) ).
cnf(c_0_353,negated_conjecture,
( ~ d(esk9_0)
| esk9_0 != true
| bool(esk2_2(true,esk9_0)) ),
inference(spm,[status(thm)],[c_0_346,c_0_52]) ).
cnf(c_0_354,plain,
( ~ forallprefers(lazy_impl(true,impl(true,true)),true)
| impl(true,true) = true
| impl(true,esk2_2(true,true)) = false ),
inference(spm,[status(thm)],[c_0_347,c_0_341]) ).
cnf(c_0_355,negated_conjecture,
( esk9_0 != true
| prop(esk2_2(true,esk9_0)) = true ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_348,c_0_349])]) ).
cnf(c_0_356,negated_conjecture,
esk9_0 = true,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_350,c_0_351]),c_0_259]),c_0_352]),c_0_259]),c_0_167]),c_0_167]),c_0_259]),c_0_352]),c_0_180]),c_0_259]),c_0_59])]),c_0_158]) ).
cnf(c_0_357,negated_conjecture,
( esk9_0 != true
| bool(esk2_2(true,esk9_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_353,c_0_349])]) ).
cnf(c_0_358,plain,
( impl(true,true) = true
| impl(true,esk2_2(true,true)) = false ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_354,c_0_247]),c_0_167]),c_0_57]),c_0_180])]),c_0_158]) ).
cnf(c_0_359,negated_conjecture,
lazy_impl(true,lazy_impl(prop(esk2_2(true,esk9_0)),impl(lazy_impl(true,impl(esk9_0,esk2_2(true,esk9_0))),esk2_2(true,esk9_0)))) != lazy_impl(true,esk9_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_177,c_0_280]),c_0_280]),c_0_280]),c_0_280]),c_0_280]),c_0_281]) ).
cnf(c_0_360,negated_conjecture,
prop(esk2_2(true,true)) = true,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_355,c_0_356]),c_0_356])]) ).
cnf(c_0_361,negated_conjecture,
bool(esk2_2(true,true)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_357,c_0_356]),c_0_356])]) ).
cnf(c_0_362,plain,
( ~ forallprefers(lazy_impl(true,impl(true,true)),lazy_impl(true,impl(false,esk2_2(true,true))))
| impl(true,true) = true ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_340,c_0_358]),c_0_167]) ).
cnf(c_0_363,plain,
( ~ forallprefers(lazy_impl(true,impl(true,true)),true)
| bool(esk2_2(true,true)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_332,c_0_36]),c_0_34]) ).
cnf(c_0_364,negated_conjecture,
lazy_impl(true,lazy_impl(true,impl(lazy_impl(true,impl(true,esk2_2(true,true))),esk2_2(true,true)))) != true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_359,c_0_356]),c_0_356]),c_0_356]),c_0_356]),c_0_356]),c_0_239]),c_0_360]) ).
cnf(c_0_365,negated_conjecture,
( esk2_2(true,true) = false
| esk2_2(true,true) = true ),
inference(spm,[status(thm)],[c_0_86,c_0_361]) ).
cnf(c_0_366,plain,
( ~ forallprefers(lazy_impl(true,impl(true,true)),true)
| impl(true,true) = true ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_362,c_0_197]),c_0_239]),c_0_363]) ).
cnf(c_0_367,negated_conjecture,
esk2_2(true,true) = true,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_364,c_0_365]),c_0_228]),c_0_167]),c_0_352]),c_0_239]),c_0_239])]) ).
cnf(c_0_368,plain,
impl(true,true) = true,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_366,c_0_247]),c_0_167]),c_0_57]),c_0_180])]),c_0_158]) ).
cnf(c_0_369,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_364,c_0_367]),c_0_368]),c_0_239]),c_0_368]),c_0_239]),c_0_239])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWW097+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.18/0.44 % Computer : n016.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Mon Sep 21 09:44:08 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.25/0.51 Running first-order theorem proving
% 0.25/0.51 Running: /export/starexec/sandbox/solver/bin/eprover --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
% 171.00/25.38 % Version: 3.5.1
% 171.00/25.38 % Preprocessing class: FSMSSMSSSSSNFFN.
% 171.00/25.38 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 171.00/25.38 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 171.00/25.38 % Starting new_bool_3 with 300s (1) cores
% 171.00/25.38 % Starting new_bool_1 with 300s (1) cores
% 171.00/25.38 % Starting sh5l with 300s (1) cores
% 171.00/25.38 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2143639 completed with status 0
% 171.00/25.38 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 171.00/25.38 % Preprocessing class: FSMSSMSSSSSNFFN.
% 171.00/25.38 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 171.00/25.38 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 171.00/25.38 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 171.00/25.38 % No SInE strategy applied
% 171.00/25.38 % Search class: FGHSS-FFMM21-DFFFFFNN
% 171.00/25.38 % partial match(1): FGHSS-FFMM21-SFFFFFNN
% 171.00/25.38 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 171.00/25.38 % Starting SubtermCWHack with 136s (1) cores
% 171.00/25.38 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 171.00/25.38 % Starting G-E--_208_B07_F1_SE_CS_SP_PS_S4d with 136s (1) cores
% 171.00/25.38 % Starting new_bool_3 with 136s (1) cores
% 171.00/25.38 % Starting new_bool_1 with 136s (1) cores
% 171.00/25.38 % new_bool_1 with pid 2143650 completed with status 0
% 171.00/25.38 % Result found by new_bool_1
% 171.00/25.38 % Preprocessing class: FSMSSMSSSSSNFFN.
% 171.00/25.38 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 171.00/25.38 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 171.00/25.38 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 171.00/25.38 % No SInE strategy applied
% 171.00/25.38 % Search class: FGHSS-FFMM21-DFFFFFNN
% 171.00/25.38 % partial match(1): FGHSS-FFMM21-SFFFFFNN
% 171.00/25.38 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 171.00/25.38 % Starting SubtermCWHack with 136s (1) cores
% 171.00/25.38 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 171.00/25.38 % Starting G-E--_208_B07_F1_SE_CS_SP_PS_S4d with 136s (1) cores
% 171.00/25.38 % Starting new_bool_3 with 136s (1) cores
% 171.00/25.38 % Starting new_bool_1 with 136s (1) cores
% 171.00/25.38 % Preprocessing time : 0.003 s
% 171.00/25.38 % Presaturation interreduction done
% 171.00/25.38
% 171.00/25.38 % Proof found!
% 171.00/25.38 % SZS status Theorem
% 171.00/25.38 % SZS output start CNFRefutation
% See solution above
% 171.00/25.38 % Parsed axioms : 45
% 171.00/25.38 % Removed by relevancy pruning/SinE : 0
% 171.00/25.38 % Initial clauses : 99
% 171.00/25.38 % Removed in clause preprocessing : 19
% 171.00/25.38 % Initial clauses in saturation : 80
% 171.00/25.38 % Processed clauses : 41114
% 171.00/25.38 % ...of these trivial : 1754
% 171.00/25.38 % ...subsumed : 31967
% 171.00/25.38 % ...remaining for further processing : 7393
% 171.00/25.38 % Other redundant clauses eliminated : 13
% 171.00/25.38 % Clauses deleted for lack of memory : 0
% 171.00/25.38 % Backward-subsumed : 962
% 171.00/25.38 % Backward-rewritten : 2524
% 171.00/25.38 % Generated clauses : 721438
% 171.00/25.38 % ...of the previous two non-redundant : 414965
% 171.00/25.38 % ...aggressively subsumed : 0
% 171.00/25.38 % Contextual simplify-reflections : 631
% 171.00/25.38 % Paramodulations : 721215
% 171.00/25.38 % Factorizations : 211
% 171.00/25.38 % NegExts : 0
% 171.00/25.38 % Equation resolutions : 13
% 171.00/25.38 % Disequality decompositions : 0
% 171.00/25.38 % Total rewrite steps : 971876
% 171.00/25.38 % ...of those cached : 970119
% 171.00/25.38 % Propositional unsat checks : 1
% 171.00/25.38 % Propositional check models : 0
% 171.00/25.38 % Propositional check unsatisfiable : 0
% 171.00/25.38 % Propositional clauses : 0
% 171.00/25.38 % Propositional clauses after purity: 0
% 171.00/25.38 % Propositional unsat core size : 0
% 171.00/25.38 % Propositional preprocessing time : 0.000
% 171.00/25.38 % Propositional encoding time : 0.564
% 171.00/25.38 % Propositional solver time : 0.238
% 171.00/25.38 % Success case prop preproc time : 0.000
% 171.00/25.38 % Success case prop encoding time : 0.000
% 171.00/25.38 % Success case prop solver time : 0.000
% 171.00/25.38 % Current number of processed clauses : 3838
% 171.00/25.38 % Positive orientable unit clauses : 220
% 171.00/25.38 % Positive unorientable unit clauses: 0
% 171.00/25.38 % Negative unit clauses : 234
% 171.00/25.38 % Non-unit-clauses : 3384
% 171.00/25.38 % Current number of unprocessed clauses: 359330
% 171.00/25.38 % ...number of literals in the above : 1671262
% 171.00/25.38 % Current number of archived formulas : 0
% 171.00/25.38 % Current number of archived clauses : 3565
% 171.00/25.38 % Clause-clause subsumption calls (NU) : 2211708
% 171.00/25.38 % Rec. Clause-clause subsumption calls : 1171207
% 171.00/25.38 % Non-unit clause-clause subsumptions : 23876
% 171.00/25.38 % Unit Clause-clause subsumption calls : 122702
% 171.00/25.38 % Rewrite failures with RHS unbound : 0
% 171.00/25.38 % BW rewrite match attempts : 5555
% 171.00/25.38 % BW rewrite match successes : 132
% 171.00/25.38 % Condensation attempts : 0
% 171.00/25.38 % Condensation successes : 0
% 171.00/25.38 % Termbank termtop insertions : 21168481
% 171.00/25.38 % Search garbage collected termcells : 707
% 171.00/25.38
% 171.00/25.38 % -------------------------------------------------
% 171.00/25.38 % User time : 24.070 s
% 171.00/25.38 % System time : 0.459 s
% 171.00/25.38 % Total time : 24.529 s
% 171.00/25.38 % Maximum resident set size: 3944 pages
% 171.00/25.38
% 171.00/25.38 % -------------------------------------------------
% 171.00/25.38 % User time : 120.627 s
% 171.00/25.38 % System time : 2.349 s
% 171.00/25.38 % Total time : 122.976 s
% 171.00/25.38 % Maximum resident set size: 4864 pages
% 171.00/25.38 % E exiting
%------------------------------------------------------------------------------