TSTP Solution File: SWW096+1 by E---3.1.00
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- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SWW096+1 : TPTP v8.2.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n023.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 06:41:18 EDT 2024
% Result : Theorem 42.67s 5.86s
% Output : CNFRefutation 42.67s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats ran out of CPU time)
% Comments :
%------------------------------------------------------------------------------
fof(prop_false,axiom,
! [X1] :
( prop(X1) = false
<=> ~ bool(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',prop_false) ).
fof(def_f7,axiom,
! [X5] : f7(X5) = lazy_impl(prop(X5),X5),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',def_f7) ).
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_forallprefers,axiom,
! [X1,X2] :
( forallprefers(X1,X2)
<=> ( ( ~ d(X1)
& d(X2) )
| ( d(X1)
& d(X2)
& ~ bool(X1)
& bool(X2) )
| ( X1 = false
& X2 = true ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',def_forallprefers) ).
fof(def_false2,axiom,
? [X5] :
( false2 = phi(f7(X5))
& ~ ? [X10] : forallprefers(f7(X10),f7(X5)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',def_false2) ).
fof(def_bool,axiom,
! [X1] :
( bool(X1)
<=> ( X1 = false
| X1 = true ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',def_bool) ).
fof(false_true_err_in_d,axiom,
( d(true)
& d(false)
& d(err) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',false_true_err_in_d) ).
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_phi,axiom,
! [X1] :
( ( d(X1)
& phi(X1) = X1 )
| ( ~ d(X1)
& phi(X1) = err ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',def_phi) ).
fof(distinct_false_true_err,axiom,
( true != false
& true != err
& false != err ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',distinct_false_true_err) ).
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_lazy_and2,axiom,
! [X5,X6] :
? [X7] :
( lazy_and2(X5,X6) = phi(f2(X5,X6,X7))
& ~ ? [X8] : forallprefers(f2(X5,X6,X8),f2(X5,X6,X7)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',def_lazy_and2) ).
fof(impl_axiom4,axiom,
! [X4] :
( bool(X4)
=> impl(true,X4) = X4 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',impl_axiom4) ).
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(impl_axiom1,axiom,
! [X3,X4] :
( ~ bool(X3)
=> impl(X3,X4) = phi(X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',impl_axiom1) ).
fof(def_and2,axiom,
! [X5,X6] :
? [X7] :
( and2(X5,X6) = phi(f1(X5,X6,X7))
& ~ ? [X8] : forallprefers(f1(X5,X6,X8),f1(X5,X6,X7)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',def_and2) ).
fof(def_f1,axiom,
! [X5,X6,X7] : f1(X5,X6,X7) = lazy_impl(prop(X7),impl(impl(X5,impl(X6,X7)),X7)),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',def_f1) ).
fof(and1_and2,conjecture,
! [X5,X6] : and1(X5,X6) = and2(X5,X6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and1_and2) ).
fof(and1_axiom1,axiom,
! [X3,X4] :
( ~ bool(X3)
=> and1(X3,X4) = phi(X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',and1_axiom1) ).
fof(def_f3,axiom,
! [X5,X6,X7] : f3(X5,X6,X7) = lazy_impl(prop(X7),impl(impl(X5,X7),impl(impl(X6,X7),X7))),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',def_f3) ).
fof(def_or2,axiom,
! [X5,X6] :
? [X7] :
( or2(X5,X6) = phi(f3(X5,X6,X7))
& ~ ? [X8] : forallprefers(f3(X5,X6,X8),f3(X5,X6,X7)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',def_or2) ).
fof(impl_axiom3,axiom,
! [X4] :
( bool(X4)
=> impl(false,X4) = true ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',impl_axiom3) ).
fof(impl_axiom2,axiom,
! [X3,X4] :
( ( bool(X3)
& ~ bool(X4) )
=> impl(X3,X4) = phi(X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',impl_axiom2) ).
fof(and1_axiom2,axiom,
! [X3,X4] :
( ( bool(X3)
& ~ bool(X4) )
=> and1(X3,X4) = phi(X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',and1_axiom2) ).
fof(and1_axiom3,axiom,
! [X4] :
( bool(X4)
=> and1(false,X4) = false ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',and1_axiom3) ).
fof(and1_axiom4,axiom,
! [X4] :
( bool(X4)
=> and1(true,X4) = X4 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',and1_axiom4) ).
fof(c_0_27,plain,
! [X1] :
( prop(X1) = false
<=> ~ bool(X1) ),
inference(fof_simplification,[status(thm)],[prop_false]) ).
fof(c_0_28,plain,
! [X63] : f7(X63) = lazy_impl(prop(X63),X63),
inference(variable_rename,[status(thm)],[def_f7]) ).
fof(c_0_29,plain,
! [X47] :
( ( prop(X47) != false
| ~ bool(X47) )
& ( bool(X47)
| prop(X47) = false ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_27])])]) ).
fof(c_0_30,plain,
! [X52] : lazy_impl(false,X52) = true,
inference(variable_rename,[status(thm)],[lazy_impl_axiom2]) ).
fof(c_0_31,plain,
! [X1,X2] :
( forallprefers(X1,X2)
<=> ( ( ~ d(X1)
& d(X2) )
| ( d(X1)
& d(X2)
& ~ bool(X1)
& bool(X2) )
| ( X1 = false
& X2 = true ) ) ),
inference(fof_simplification,[status(thm)],[def_forallprefers]) ).
fof(c_0_32,plain,
! [X30] :
( false2 = phi(f7(esk5_0))
& ~ forallprefers(f7(X30),f7(esk5_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])])])])]) ).
cnf(c_0_33,plain,
f7(X1) = lazy_impl(prop(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_34,plain,
( bool(X1)
| prop(X1) = false ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_35,plain,
lazy_impl(false,X1) = true,
inference(split_conjunct,[status(thm)],[c_0_30]) ).
fof(c_0_36,plain,
! [X23,X24] :
( ( X23 = false
| d(X23)
| ~ d(X23)
| ~ forallprefers(X23,X24) )
& ( X24 = true
| d(X23)
| ~ d(X23)
| ~ forallprefers(X23,X24) )
& ( X23 = false
| d(X24)
| ~ d(X23)
| ~ forallprefers(X23,X24) )
& ( X24 = true
| d(X24)
| ~ d(X23)
| ~ forallprefers(X23,X24) )
& ( X23 = false
| ~ bool(X23)
| ~ d(X23)
| ~ forallprefers(X23,X24) )
& ( X24 = true
| ~ bool(X23)
| ~ d(X23)
| ~ forallprefers(X23,X24) )
& ( X23 = false
| bool(X24)
| ~ d(X23)
| ~ forallprefers(X23,X24) )
& ( X24 = true
| bool(X24)
| ~ d(X23)
| ~ forallprefers(X23,X24) )
& ( X23 = false
| d(X23)
| d(X24)
| ~ forallprefers(X23,X24) )
& ( X24 = true
| d(X23)
| d(X24)
| ~ forallprefers(X23,X24) )
& ( X23 = false
| d(X24)
| d(X24)
| ~ forallprefers(X23,X24) )
& ( X24 = true
| d(X24)
| d(X24)
| ~ forallprefers(X23,X24) )
& ( X23 = false
| ~ bool(X23)
| d(X24)
| ~ forallprefers(X23,X24) )
& ( X24 = true
| ~ bool(X23)
| d(X24)
| ~ forallprefers(X23,X24) )
& ( X23 = false
| bool(X24)
| d(X24)
| ~ forallprefers(X23,X24) )
& ( X24 = true
| bool(X24)
| d(X24)
| ~ forallprefers(X23,X24) )
& ( d(X23)
| ~ d(X24)
| forallprefers(X23,X24) )
& ( ~ d(X23)
| ~ d(X24)
| bool(X23)
| ~ bool(X24)
| forallprefers(X23,X24) )
& ( X23 != false
| X24 != true
| forallprefers(X23,X24) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_31])])])]) ).
fof(c_0_37,plain,
! [X45] :
( ( ~ bool(X45)
| X45 = false
| X45 = true )
& ( X45 != false
| bool(X45) )
& ( X45 != true
| bool(X45) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[def_bool])])])]) ).
cnf(c_0_38,plain,
~ forallprefers(f7(X1),f7(esk5_0)),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_39,plain,
( f7(X1) = true
| bool(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35]) ).
cnf(c_0_40,plain,
( bool(X1)
| forallprefers(X1,X2)
| ~ d(X1)
| ~ d(X2)
| ~ bool(X2) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_41,plain,
( d(X1)
| forallprefers(X1,X2)
| ~ d(X2) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_42,plain,
( bool(X1)
| X1 != true ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_43,plain,
( bool(esk5_0)
| ~ forallprefers(f7(X1),true) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_44,plain,
( forallprefers(X1,X2)
| bool(X1)
| ~ d(X2)
| ~ bool(X2) ),
inference(csr,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_45,plain,
d(true),
inference(split_conjunct,[status(thm)],[false_true_err_in_d]) ).
cnf(c_0_46,plain,
bool(true),
inference(er,[status(thm)],[c_0_42]) ).
cnf(c_0_47,plain,
( forallprefers(X1,X2)
| X1 != false
| X2 != true ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
fof(c_0_48,plain,
! [X46] :
( ( prop(X46) != true
| bool(X46) )
& ( ~ bool(X46)
| prop(X46) = true ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[prop_true])])]) ).
fof(c_0_49,plain,
! [X40] : lazy_impl(true,X40) = phi(X40),
inference(variable_rename,[status(thm)],[lazy_impl_axiom3]) ).
cnf(c_0_50,plain,
( X1 = false
| X1 = true
| ~ bool(X1) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_51,plain,
( bool(f7(X1))
| bool(esk5_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]),c_0_46])]) ).
cnf(c_0_52,plain,
( forallprefers(X1,true)
| X1 != false ),
inference(er,[status(thm)],[c_0_47]) ).
fof(c_0_53,plain,
! [X1] :
( ( d(X1)
& phi(X1) = X1 )
| ( ~ d(X1)
& phi(X1) = err ) ),
inference(fof_simplification,[status(thm)],[def_phi]) ).
cnf(c_0_54,plain,
( prop(X1) = true
| ~ bool(X1) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_55,plain,
lazy_impl(true,X1) = phi(X1),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_56,plain,
( f7(X1) = true
| f7(X1) = false
| bool(esk5_0) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_57,plain,
forallprefers(false,true),
inference(er,[status(thm)],[c_0_52]) ).
fof(c_0_58,plain,
( true != false
& true != err
& false != err ),
inference(fof_simplification,[status(thm)],[distinct_false_true_err]) ).
fof(c_0_59,plain,
! [X57] :
( ( ~ d(X57)
| d(X57) )
& ( phi(X57) = err
| d(X57) )
& ( ~ d(X57)
| phi(X57) = X57 )
& ( phi(X57) = err
| phi(X57) = X57 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_53])])]) ).
cnf(c_0_60,plain,
( f7(X1) = phi(X1)
| ~ bool(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_54]),c_0_55]) ).
cnf(c_0_61,plain,
( f7(X1) = true
| bool(esk5_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_56]),c_0_57])]) ).
fof(c_0_62,plain,
( true != false
& true != err
& false != err ),
inference(fof_nnf,[status(thm)],[c_0_58]) ).
cnf(c_0_63,plain,
( phi(X1) = err
| phi(X1) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_64,plain,
( phi(X1) = true
| bool(esk5_0)
| ~ bool(X1) ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_65,plain,
true != err,
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_66,plain,
( true = X1
| bool(esk5_0)
| ~ bool(X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_65]) ).
cnf(c_0_67,plain,
( bool(X1)
| X1 != false ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_68,plain,
( esk5_0 = true
| esk5_0 = false
| true = X1
| ~ bool(X1) ),
inference(spm,[status(thm)],[c_0_50,c_0_66]) ).
cnf(c_0_69,plain,
bool(false),
inference(er,[status(thm)],[c_0_67]) ).
cnf(c_0_70,plain,
true != false,
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_71,plain,
false2 = phi(f7(esk5_0)),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_72,plain,
( esk5_0 = false
| esk5_0 = true ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_70]) ).
cnf(c_0_73,plain,
( phi(f7(false)) = false2
| esk5_0 = true ),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_74,plain,
( phi(X1) = X1
| err != X1 ),
inference(ef,[status(thm)],[c_0_63]) ).
cnf(c_0_75,plain,
( bool(phi(X1))
| bool(esk5_0)
| ~ bool(X1) ),
inference(spm,[status(thm)],[c_0_51,c_0_60]) ).
cnf(c_0_76,plain,
( phi(phi(false)) = false2
| esk5_0 = true ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_60]),c_0_69])]) ).
cnf(c_0_77,plain,
( phi(X1) = X1
| ~ d(X1) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_78,plain,
d(false),
inference(split_conjunct,[status(thm)],[false_true_err_in_d]) ).
cnf(c_0_79,plain,
phi(err) = err,
inference(er,[status(thm)],[c_0_74]) ).
cnf(c_0_80,plain,
( phi(X1) = true
| phi(X1) = false
| bool(esk5_0)
| ~ bool(X1) ),
inference(spm,[status(thm)],[c_0_50,c_0_75]) ).
cnf(c_0_81,plain,
false != err,
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_82,plain,
( phi(false) = false2
| esk5_0 = true ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_78])]) ).
cnf(c_0_83,plain,
( bool(esk5_0)
| ~ bool(err) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_79]),c_0_81]),c_0_65]) ).
cnf(c_0_84,plain,
( esk5_0 = true
| false2 = false ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_82]),c_0_78])]) ).
cnf(c_0_85,plain,
( bool(esk5_0)
| ~ forallprefers(phi(X1),true)
| ~ bool(X1) ),
inference(spm,[status(thm)],[c_0_43,c_0_60]) ).
cnf(c_0_86,plain,
( phi(X1) = X1
| bool(esk5_0)
| ~ bool(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_63]),c_0_83]) ).
cnf(c_0_87,plain,
( phi(f7(true)) = false2
| false2 = false ),
inference(spm,[status(thm)],[c_0_71,c_0_84]) ).
cnf(c_0_88,plain,
( bool(esk5_0)
| ~ forallprefers(X1,true)
| ~ bool(X1) ),
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_89,plain,
( phi(phi(true)) = false2
| false2 = false ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_60]),c_0_46])]) ).
cnf(c_0_90,plain,
( ~ forallprefers(f7(X1),phi(esk5_0))
| ~ bool(esk5_0) ),
inference(spm,[status(thm)],[c_0_38,c_0_60]) ).
cnf(c_0_91,plain,
bool(esk5_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_57]),c_0_69])]) ).
cnf(c_0_92,plain,
( f7(esk5_0) = false2
| false2 = err ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_63]),c_0_71]) ).
cnf(c_0_93,plain,
( phi(true) = false2
| false2 = false ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_77]),c_0_45])]) ).
cnf(c_0_94,plain,
~ forallprefers(f7(X1),phi(esk5_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_90,c_0_91])]) ).
cnf(c_0_95,plain,
( phi(X1) = err
| d(X1) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_96,plain,
( false2 = err
| ~ forallprefers(f7(X1),false2) ),
inference(spm,[status(thm)],[c_0_38,c_0_92]) ).
cnf(c_0_97,plain,
( false2 = false
| false2 = true ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_93]),c_0_45])]) ).
cnf(c_0_98,plain,
( d(esk5_0)
| ~ forallprefers(f7(X1),err) ),
inference(spm,[status(thm)],[c_0_94,c_0_95]) ).
cnf(c_0_99,plain,
d(err),
inference(split_conjunct,[status(thm)],[false_true_err_in_d]) ).
cnf(c_0_100,plain,
( false2 = true
| ~ forallprefers(f7(X1),false) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_81]) ).
cnf(c_0_101,plain,
( d(f7(X1))
| ~ d(phi(esk5_0)) ),
inference(spm,[status(thm)],[c_0_94,c_0_41]) ).
cnf(c_0_102,plain,
( d(f7(X1))
| d(esk5_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_41]),c_0_99])]) ).
cnf(c_0_103,plain,
( f7(esk5_0) = false2
| ~ d(f7(esk5_0)) ),
inference(spm,[status(thm)],[c_0_71,c_0_77]) ).
cnf(c_0_104,plain,
( false2 = true
| d(f7(X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_41]),c_0_78])]) ).
cnf(c_0_105,plain,
( bool(f7(X1))
| ~ d(f7(esk5_0))
| ~ bool(f7(esk5_0)) ),
inference(spm,[status(thm)],[c_0_38,c_0_44]) ).
cnf(c_0_106,plain,
d(f7(X1)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_77]),c_0_102]) ).
cnf(c_0_107,plain,
( false2 = true
| bool(f7(X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_44]),c_0_78]),c_0_69])]) ).
cnf(c_0_108,plain,
( f7(esk5_0) = false2
| false2 = true ),
inference(spm,[status(thm)],[c_0_103,c_0_104]) ).
cnf(c_0_109,plain,
( bool(f7(X1))
| ~ bool(f7(esk5_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_105,c_0_106])]) ).
cnf(c_0_110,plain,
f7(esk5_0) = false2,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_103,c_0_106])]) ).
cnf(c_0_111,plain,
bool(false2),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_42]) ).
cnf(c_0_112,plain,
bool(f7(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_109,c_0_110]),c_0_111])]) ).
cnf(c_0_113,plain,
( bool(phi(X1))
| ~ bool(X1) ),
inference(spm,[status(thm)],[c_0_112,c_0_60]) ).
fof(c_0_114,plain,
! [X65,X66,X67] : f2(X65,X66,X67) = lazy_impl(prop(X67),impl(lazy_impl(X65,impl(X66,X67)),X67)),
inference(variable_rename,[status(thm)],[def_f2]) ).
fof(c_0_115,plain,
! [X80,X81,X83] :
( lazy_and2(X80,X81) = phi(f2(X80,X81,esk8_2(X80,X81)))
& ~ forallprefers(f2(X80,X81,X83),f2(X80,X81,esk8_2(X80,X81))) ),
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])])])])]) ).
cnf(c_0_116,plain,
( phi(X1) = true
| phi(X1) = false
| ~ bool(X1) ),
inference(spm,[status(thm)],[c_0_50,c_0_113]) ).
cnf(c_0_117,plain,
f2(X1,X2,X3) = lazy_impl(prop(X3),impl(lazy_impl(X1,impl(X2,X3)),X3)),
inference(split_conjunct,[status(thm)],[c_0_114]) ).
fof(c_0_118,plain,
! [X49] :
( ~ bool(X49)
| impl(true,X49) = X49 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[impl_axiom4])])]) ).
cnf(c_0_119,plain,
~ forallprefers(f2(X1,X2,X3),f2(X1,X2,esk8_2(X1,X2))),
inference(split_conjunct,[status(thm)],[c_0_115]) ).
cnf(c_0_120,plain,
~ bool(err),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_116]),c_0_79]),c_0_81]),c_0_65]) ).
cnf(c_0_121,plain,
lazy_impl(prop(X1),impl(true,X1)) = f2(false,X2,X1),
inference(spm,[status(thm)],[c_0_117,c_0_35]) ).
cnf(c_0_122,plain,
( impl(true,X1) = X1
| ~ bool(X1) ),
inference(split_conjunct,[status(thm)],[c_0_118]) ).
cnf(c_0_123,plain,
( bool(f2(X1,X2,X3))
| ~ d(f2(X1,X2,esk8_2(X1,X2)))
| ~ bool(f2(X1,X2,esk8_2(X1,X2))) ),
inference(spm,[status(thm)],[c_0_119,c_0_44]) ).
cnf(c_0_124,plain,
( f2(X1,X2,X3) = true
| bool(X3) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_34]),c_0_35]) ).
fof(c_0_125,plain,
! [X3,X4] :
( ~ bool(X3)
=> lazy_impl(X3,X4) = phi(X3) ),
inference(fof_simplification,[status(thm)],[lazy_impl_axiom1]) ).
cnf(c_0_126,plain,
( d(phi(X1))
| ~ bool(X1) ),
inference(spm,[status(thm)],[c_0_106,c_0_60]) ).
cnf(c_0_127,plain,
( phi(X1) = X1
| ~ bool(X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_63]),c_0_120]) ).
cnf(c_0_128,plain,
( f2(false,X1,X2) = f7(X2)
| ~ bool(X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_122]),c_0_33]) ).
cnf(c_0_129,plain,
( bool(f2(X1,X2,X3))
| bool(esk8_2(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_124]),c_0_45]),c_0_46])]) ).
fof(c_0_130,plain,
! [X38,X39] :
( bool(X38)
| lazy_impl(X38,X39) = phi(X38) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_125])]) ).
cnf(c_0_131,plain,
lazy_and2(X1,X2) = phi(f2(X1,X2,esk8_2(X1,X2))),
inference(split_conjunct,[status(thm)],[c_0_115]) ).
cnf(c_0_132,plain,
( d(X1)
| ~ bool(X1) ),
inference(spm,[status(thm)],[c_0_126,c_0_127]) ).
cnf(c_0_133,plain,
bool(f2(false,X1,X2)),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_128]),c_0_106]),c_0_112])]),c_0_129]) ).
cnf(c_0_134,plain,
( bool(X1)
| lazy_impl(X1,X2) = phi(X1) ),
inference(split_conjunct,[status(thm)],[c_0_130]) ).
cnf(c_0_135,plain,
( f2(X1,X2,esk8_2(X1,X2)) = lazy_and2(X1,X2)
| ~ d(f2(X1,X2,esk8_2(X1,X2))) ),
inference(spm,[status(thm)],[c_0_77,c_0_131]) ).
cnf(c_0_136,plain,
d(f2(false,X1,X2)),
inference(spm,[status(thm)],[c_0_132,c_0_133]) ).
cnf(c_0_137,plain,
( f7(X1) = phi(prop(X1))
| bool(prop(X1)) ),
inference(spm,[status(thm)],[c_0_33,c_0_134]) ).
cnf(c_0_138,plain,
f2(false,X1,X2) = f2(false,X3,X2),
inference(spm,[status(thm)],[c_0_121,c_0_121]) ).
cnf(c_0_139,plain,
f2(false,X1,esk8_2(false,X1)) = lazy_and2(false,X1),
inference(spm,[status(thm)],[c_0_135,c_0_136]) ).
fof(c_0_140,plain,
! [X3,X4] :
( ~ bool(X3)
=> impl(X3,X4) = phi(X3) ),
inference(fof_simplification,[status(thm)],[impl_axiom1]) ).
cnf(c_0_141,plain,
bool(phi(prop(X1))),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_137]),c_0_113]) ).
cnf(c_0_142,plain,
f2(false,X1,esk8_2(false,X2)) = lazy_and2(false,X2),
inference(spm,[status(thm)],[c_0_138,c_0_139]) ).
fof(c_0_143,plain,
! [X13,X14,X16] :
( and2(X13,X14) = phi(f1(X13,X14,esk3_2(X13,X14)))
& ~ forallprefers(f1(X13,X14,X16),f1(X13,X14,esk3_2(X13,X14))) ),
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_and2])])])])]) ).
fof(c_0_144,plain,
! [X31,X32,X33] : f1(X31,X32,X33) = lazy_impl(prop(X33),impl(impl(X31,impl(X32,X33)),X33)),
inference(variable_rename,[status(thm)],[def_f1]) ).
fof(c_0_145,plain,
! [X34,X35] :
( bool(X34)
| impl(X34,X35) = phi(X34) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_140])]) ).
cnf(c_0_146,plain,
d(prop(X1)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_95]),c_0_120]) ).
cnf(c_0_147,plain,
~ forallprefers(f2(false,X1,X2),lazy_and2(false,X1)),
inference(spm,[status(thm)],[c_0_119,c_0_142]) ).
cnf(c_0_148,plain,
( bool(phi(true))
| ~ bool(X1) ),
inference(spm,[status(thm)],[c_0_141,c_0_54]) ).
fof(c_0_149,negated_conjecture,
~ ! [X5,X6] : and1(X5,X6) = and2(X5,X6),
inference(assume_negation,[status(cth)],[and1_and2]) ).
cnf(c_0_150,plain,
~ forallprefers(f1(X1,X2,X3),f1(X1,X2,esk3_2(X1,X2))),
inference(split_conjunct,[status(thm)],[c_0_143]) ).
cnf(c_0_151,plain,
and2(X1,X2) = phi(f1(X1,X2,esk3_2(X1,X2))),
inference(split_conjunct,[status(thm)],[c_0_143]) ).
cnf(c_0_152,plain,
f1(X1,X2,X3) = lazy_impl(prop(X3),impl(impl(X1,impl(X2,X3)),X3)),
inference(split_conjunct,[status(thm)],[c_0_144]) ).
cnf(c_0_153,plain,
( bool(X1)
| impl(X1,X2) = phi(X1) ),
inference(split_conjunct,[status(thm)],[c_0_145]) ).
cnf(c_0_154,plain,
bool(prop(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_77]),c_0_146])]) ).
cnf(c_0_155,plain,
~ forallprefers(f2(false,X1,X2),lazy_and2(false,X3)),
inference(spm,[status(thm)],[c_0_147,c_0_138]) ).
cnf(c_0_156,plain,
( bool(phi(false))
| bool(X1) ),
inference(spm,[status(thm)],[c_0_141,c_0_34]) ).
cnf(c_0_157,plain,
( f2(false,X1,X2) = true
| f2(false,X1,X2) = false ),
inference(spm,[status(thm)],[c_0_50,c_0_133]) ).
cnf(c_0_158,plain,
bool(phi(true)),
inference(spm,[status(thm)],[c_0_148,c_0_112]) ).
fof(c_0_159,negated_conjecture,
and1(esk1_0,esk2_0) != and2(esk1_0,esk2_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,
( d(f1(X1,X2,X3))
| ~ d(f1(X1,X2,esk3_2(X1,X2))) ),
inference(spm,[status(thm)],[c_0_150,c_0_41]) ).
cnf(c_0_161,plain,
( and2(X1,X2) = err
| d(f1(X1,X2,esk3_2(X1,X2))) ),
inference(spm,[status(thm)],[c_0_95,c_0_151]) ).
fof(c_0_162,plain,
! [X3,X4] :
( ~ bool(X3)
=> and1(X3,X4) = phi(X3) ),
inference(fof_simplification,[status(thm)],[and1_axiom1]) ).
cnf(c_0_163,plain,
( lazy_impl(prop(X1),impl(phi(X2),X1)) = f1(X2,X3,X1)
| bool(X2) ),
inference(spm,[status(thm)],[c_0_152,c_0_153]) ).
cnf(c_0_164,plain,
( prop(X1) = true
| prop(X1) = false ),
inference(spm,[status(thm)],[c_0_50,c_0_154]) ).
cnf(c_0_165,plain,
( ~ forallprefers(f7(X1),lazy_and2(false,X2))
| ~ bool(X1) ),
inference(spm,[status(thm)],[c_0_155,c_0_128]) ).
cnf(c_0_166,plain,
bool(phi(false)),
inference(ef,[status(thm)],[c_0_156]) ).
cnf(c_0_167,plain,
( f7(X1) = true
| f7(X1) = false ),
inference(spm,[status(thm)],[c_0_50,c_0_112]) ).
cnf(c_0_168,plain,
( f2(false,X1,X2) = true
| f7(X2) = false ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_157]),c_0_124]) ).
cnf(c_0_169,plain,
phi(true) = true,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_158,c_0_63]),c_0_120]) ).
cnf(c_0_170,negated_conjecture,
and1(esk1_0,esk2_0) != and2(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_159]) ).
cnf(c_0_171,plain,
( and2(X1,X2) = err
| d(f1(X1,X2,X3)) ),
inference(spm,[status(thm)],[c_0_160,c_0_161]) ).
fof(c_0_172,plain,
! [X17,X18] :
( bool(X17)
| and1(X17,X18) = phi(X17) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_162])]) ).
cnf(c_0_173,plain,
( lazy_impl(prop(X1),phi(phi(X2))) = f1(X2,X3,X1)
| bool(phi(X2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_163,c_0_153]),c_0_113]) ).
cnf(c_0_174,plain,
( f1(X1,X2,X3) = true
| prop(X3) = true ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_164]),c_0_35]) ).
cnf(c_0_175,plain,
( ~ forallprefers(phi(X1),lazy_and2(false,X2))
| ~ bool(X1) ),
inference(spm,[status(thm)],[c_0_165,c_0_60]) ).
cnf(c_0_176,plain,
phi(false) = false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_166,c_0_63]),c_0_120]) ).
cnf(c_0_177,plain,
( f7(X1) = true
| phi(X1) = false ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_167]),c_0_39]) ).
cnf(c_0_178,plain,
( f7(esk8_2(false,X1)) = false
| lazy_and2(false,X1) = true ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_168]),c_0_169]) ).
cnf(c_0_179,negated_conjecture,
( d(f1(esk1_0,esk2_0,X1))
| and1(esk1_0,esk2_0) != err ),
inference(spm,[status(thm)],[c_0_170,c_0_171]) ).
cnf(c_0_180,plain,
( bool(X1)
| and1(X1,X2) = phi(X1) ),
inference(split_conjunct,[status(thm)],[c_0_172]) ).
cnf(c_0_181,plain,
( f1(X1,X2,X3) = phi(phi(phi(X1)))
| bool(phi(X1))
| ~ bool(X3) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_173,c_0_54]),c_0_55]) ).
cnf(c_0_182,plain,
( prop(esk3_2(X1,X2)) = true
| and2(X1,X2) = true ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_151,c_0_174]),c_0_169]) ).
cnf(c_0_183,plain,
~ forallprefers(false,lazy_and2(false,X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_175,c_0_176]),c_0_69])]) ).
cnf(c_0_184,plain,
( phi(esk8_2(false,X1)) = false
| lazy_and2(false,X1) = true ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_177,c_0_178]),c_0_70]) ).
cnf(c_0_185,negated_conjecture,
( d(f1(esk1_0,esk2_0,X1))
| bool(esk1_0)
| phi(esk1_0) != err ),
inference(spm,[status(thm)],[c_0_179,c_0_180]) ).
cnf(c_0_186,plain,
( and2(X1,X2) = phi(phi(phi(phi(X1))))
| bool(phi(X1))
| ~ bool(esk3_2(X1,X2)) ),
inference(spm,[status(thm)],[c_0_151,c_0_181]) ).
cnf(c_0_187,plain,
( and2(X1,X2) = true
| bool(esk3_2(X1,X2)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_182]),c_0_70]) ).
cnf(c_0_188,plain,
phi(esk8_2(false,X1)) = false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_183,c_0_184]),c_0_57])]) ).
cnf(c_0_189,negated_conjecture,
( d(f1(esk1_0,esk2_0,X1))
| d(esk1_0)
| bool(esk1_0) ),
inference(spm,[status(thm)],[c_0_185,c_0_95]) ).
cnf(c_0_190,plain,
( f1(X1,X2,X3) = f1(X1,X4,X3)
| bool(X1) ),
inference(spm,[status(thm)],[c_0_163,c_0_163]) ).
cnf(c_0_191,plain,
( and2(X1,X2) = phi(phi(phi(phi(X1))))
| and2(X1,X2) = true
| bool(phi(X1)) ),
inference(spm,[status(thm)],[c_0_186,c_0_187]) ).
cnf(c_0_192,plain,
esk8_2(false,X1) = false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_188]),c_0_81]) ).
cnf(c_0_193,plain,
( f1(X1,X2,esk3_2(X1,X2)) = and2(X1,X2)
| ~ d(f1(X1,X2,esk3_2(X1,X2))) ),
inference(spm,[status(thm)],[c_0_77,c_0_151]) ).
cnf(c_0_194,negated_conjecture,
( d(f1(esk1_0,X1,X2))
| d(esk1_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_189,c_0_190]),c_0_132]) ).
cnf(c_0_195,negated_conjecture,
( and2(esk1_0,esk2_0) = true
| bool(phi(esk1_0))
| phi(phi(phi(phi(esk1_0)))) != and1(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_170,c_0_191]) ).
cnf(c_0_196,plain,
lazy_impl(prop(X1),impl(err,X1)) = f1(err,X2,X1),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_163,c_0_79]),c_0_120]) ).
cnf(c_0_197,plain,
( lazy_and2(false,X1) = true
| f7(false) = false ),
inference(rw,[status(thm)],[c_0_178,c_0_192]) ).
cnf(c_0_198,negated_conjecture,
( f1(esk1_0,X1,esk3_2(esk1_0,X1)) = and2(esk1_0,X1)
| d(esk1_0) ),
inference(spm,[status(thm)],[c_0_193,c_0_194]) ).
cnf(c_0_199,plain,
( bool(f1(X1,X2,X3))
| ~ d(f1(X1,X2,esk3_2(X1,X2)))
| ~ bool(f1(X1,X2,esk3_2(X1,X2))) ),
inference(spm,[status(thm)],[c_0_150,c_0_44]) ).
cnf(c_0_200,plain,
( f1(X1,X2,esk3_2(X1,X2)) = and2(X1,X2)
| and2(X1,X2) = err ),
inference(spm,[status(thm)],[c_0_63,c_0_151]) ).
cnf(c_0_201,negated_conjecture,
( and2(esk1_0,esk2_0) = true
| d(esk1_0)
| and1(esk1_0,esk2_0) != err ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_195,c_0_95]),c_0_79]),c_0_79]),c_0_79]),c_0_120]) ).
cnf(c_0_202,plain,
f1(err,X1,X2) = lazy_impl(prop(X2),err),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_196,c_0_153]),c_0_79]),c_0_120]) ).
cnf(c_0_203,plain,
( prop(X1) = true
| f7(X1) = true ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_164]),c_0_35]) ).
cnf(c_0_204,plain,
f7(false) = false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_183,c_0_197]),c_0_57])]) ).
cnf(c_0_205,negated_conjecture,
( f1(esk1_0,X1,esk3_2(esk1_0,X2)) = and2(esk1_0,X2)
| d(esk1_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_190,c_0_198]),c_0_132]) ).
cnf(c_0_206,plain,
( and2(X1,X2) = err
| bool(f1(X1,X2,X3))
| ~ bool(and2(X1,X2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_199,c_0_200]),c_0_132]) ).
cnf(c_0_207,negated_conjecture,
( and2(esk1_0,esk2_0) = true
| d(esk1_0) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_201,c_0_180]),c_0_95]),c_0_132]) ).
fof(c_0_208,plain,
! [X68,X69,X70] : f3(X68,X69,X70) = lazy_impl(prop(X70),impl(impl(X68,X70),impl(impl(X69,X70),X70))),
inference(variable_rename,[status(thm)],[def_f3]) ).
cnf(c_0_209,plain,
lazy_impl(prop(X1),impl(err,X1)) = lazy_impl(prop(X1),err),
inference(rw,[status(thm)],[c_0_196,c_0_202]) ).
cnf(c_0_210,plain,
prop(false) = true,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_203,c_0_204]),c_0_70]) ).
cnf(c_0_211,negated_conjecture,
( d(esk1_0)
| ~ forallprefers(f1(esk1_0,X1,X2),and2(esk1_0,X1)) ),
inference(spm,[status(thm)],[c_0_150,c_0_205]) ).
cnf(c_0_212,negated_conjecture,
( d(esk1_0)
| bool(f1(esk1_0,esk2_0,X1)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_206,c_0_207]),c_0_46])]),c_0_65]) ).
cnf(c_0_213,plain,
f3(X1,X2,X3) = lazy_impl(prop(X3),impl(impl(X1,X3),impl(impl(X2,X3),X3))),
inference(split_conjunct,[status(thm)],[c_0_208]) ).
cnf(c_0_214,plain,
phi(impl(err,false)) = err,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_209,c_0_210]),c_0_55]),c_0_55]),c_0_79]) ).
cnf(c_0_215,negated_conjecture,
( d(esk1_0)
| ~ forallprefers(and2(esk1_0,X1),and2(esk1_0,X2)) ),
inference(spm,[status(thm)],[c_0_211,c_0_205]) ).
cnf(c_0_216,negated_conjecture,
( d(esk1_0)
| bool(and2(esk1_0,X1)) ),
inference(spm,[status(thm)],[c_0_212,c_0_205]) ).
fof(c_0_217,plain,
! [X84,X85,X87] :
( or2(X84,X85) = phi(f3(X84,X85,esk9_2(X84,X85)))
& ~ forallprefers(f3(X84,X85,X87),f3(X84,X85,esk9_2(X84,X85))) ),
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_or2])])])])]) ).
cnf(c_0_218,plain,
( lazy_impl(prop(X1),phi(impl(X2,X1))) = f3(X2,X3,X1)
| bool(impl(X2,X1)) ),
inference(spm,[status(thm)],[c_0_213,c_0_153]) ).
cnf(c_0_219,plain,
~ bool(impl(err,false)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_214]),c_0_120]) ).
cnf(c_0_220,negated_conjecture,
( d(esk1_0)
| ~ forallprefers(and2(esk1_0,X1),true) ),
inference(spm,[status(thm)],[c_0_215,c_0_207]) ).
cnf(c_0_221,negated_conjecture,
( and2(esk1_0,X1) = true
| and2(esk1_0,X1) = false
| d(esk1_0) ),
inference(spm,[status(thm)],[c_0_50,c_0_216]) ).
cnf(c_0_222,plain,
~ forallprefers(f3(X1,X2,X3),f3(X1,X2,esk9_2(X1,X2))),
inference(split_conjunct,[status(thm)],[c_0_217]) ).
cnf(c_0_223,plain,
f3(err,X1,false) = err,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_218,c_0_214]),c_0_210]),c_0_55]),c_0_79]),c_0_219]) ).
cnf(c_0_224,negated_conjecture,
( and2(esk1_0,X1) = true
| d(esk1_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_220,c_0_221]),c_0_57])]) ).
cnf(c_0_225,plain,
( lazy_impl(prop(X1),impl(err,X1)) = f1(X2,X3,X1)
| d(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_163,c_0_95]),c_0_132]) ).
cnf(c_0_226,plain,
~ forallprefers(err,f3(err,X1,esk9_2(err,X1))),
inference(spm,[status(thm)],[c_0_222,c_0_223]) ).
cnf(c_0_227,plain,
( f3(X1,X2,X3) = true
| prop(X3) = true ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_213,c_0_164]),c_0_35]) ).
fof(c_0_228,plain,
! [X48] :
( ~ bool(X48)
| impl(false,X48) = true ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[impl_axiom3])])]) ).
cnf(c_0_229,negated_conjecture,
( d(esk1_0)
| bool(f1(esk1_0,X1,X2)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_206,c_0_224]),c_0_46])]),c_0_65]) ).
cnf(c_0_230,plain,
( f1(X1,X2,X3) = lazy_impl(prop(X3),err)
| d(X1) ),
inference(rw,[status(thm)],[c_0_225,c_0_209]) ).
cnf(c_0_231,plain,
( prop(esk9_2(err,X1)) = true
| ~ forallprefers(err,true) ),
inference(spm,[status(thm)],[c_0_226,c_0_227]) ).
cnf(c_0_232,plain,
( impl(false,X1) = true
| ~ bool(X1) ),
inference(split_conjunct,[status(thm)],[c_0_228]) ).
cnf(c_0_233,negated_conjecture,
( d(esk1_0)
| bool(lazy_impl(prop(X1),err)) ),
inference(spm,[status(thm)],[c_0_229,c_0_230]) ).
cnf(c_0_234,plain,
prop(esk9_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_231,c_0_44]),c_0_45]),c_0_46])]),c_0_120]) ).
cnf(c_0_235,plain,
( lazy_impl(prop(X1),impl(impl(X2,X1),X1)) = f1(X2,true,X1)
| ~ bool(X1) ),
inference(spm,[status(thm)],[c_0_152,c_0_122]) ).
cnf(c_0_236,plain,
( lazy_impl(prop(X1),impl(impl(X2,true),X1)) = f1(X2,false,X1)
| ~ bool(X1) ),
inference(spm,[status(thm)],[c_0_152,c_0_232]) ).
cnf(c_0_237,negated_conjecture,
d(esk1_0),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_233,c_0_234]),c_0_55]),c_0_79]),c_0_120]) ).
cnf(c_0_238,plain,
f1(X1,false,true) = f1(X1,true,true),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_235,c_0_236]),c_0_46])]) ).
cnf(c_0_239,negated_conjecture,
( and2(esk1_0,esk2_0) = true
| bool(esk1_0)
| phi(phi(phi(esk1_0))) != and1(esk1_0,esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_195,c_0_77]),c_0_237])]) ).
cnf(c_0_240,plain,
( f1(X1,X2,X3) = f1(X1,X4,X3)
| bool(phi(X1)) ),
inference(spm,[status(thm)],[c_0_173,c_0_173]) ).
cnf(c_0_241,plain,
( f1(X1,true,true) = phi(phi(phi(X1)))
| bool(phi(X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_238,c_0_181]),c_0_46])]) ).
cnf(c_0_242,negated_conjecture,
( and2(esk1_0,esk2_0) = true
| bool(esk1_0)
| and1(esk1_0,esk2_0) != phi(phi(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_239,c_0_77]),c_0_237])]) ).
cnf(c_0_243,plain,
( lazy_impl(prop(X1),impl(lazy_impl(X2,X1),X1)) = f2(X2,true,X1)
| ~ bool(X1) ),
inference(spm,[status(thm)],[c_0_117,c_0_122]) ).
cnf(c_0_244,plain,
( lazy_impl(prop(X1),impl(lazy_impl(X2,true),X1)) = f2(X2,false,X1)
| ~ bool(X1) ),
inference(spm,[status(thm)],[c_0_117,c_0_232]) ).
cnf(c_0_245,plain,
( f1(X1,X2,true) = phi(phi(phi(X1)))
| bool(phi(X1)) ),
inference(spm,[status(thm)],[c_0_240,c_0_241]) ).
cnf(c_0_246,plain,
( lazy_impl(prop(X1),impl(X1,X1)) = f1(true,true,X1)
| ~ bool(X1) ),
inference(spm,[status(thm)],[c_0_235,c_0_122]) ).
cnf(c_0_247,negated_conjecture,
( and2(esk1_0,esk2_0) = true
| bool(esk1_0)
| phi(phi(esk1_0)) != phi(esk1_0) ),
inference(spm,[status(thm)],[c_0_242,c_0_180]) ).
cnf(c_0_248,plain,
f2(X1,false,true) = f2(X1,true,true),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_243,c_0_244]),c_0_46])]) ).
cnf(c_0_249,plain,
( lazy_impl(prop(X1),err) = true
| prop(X1) = true ),
inference(spm,[status(thm)],[c_0_174,c_0_202]) ).
cnf(c_0_250,plain,
lazy_impl(prop(true),err) = err,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_202,c_0_245]),c_0_79]),c_0_79]),c_0_79]),c_0_79]),c_0_120]) ).
cnf(c_0_251,plain,
f1(true,true,false) = lazy_impl(prop(false),true),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_246,c_0_232]),c_0_69])]) ).
cnf(c_0_252,negated_conjecture,
( and2(esk1_0,esk2_0) = true
| bool(esk1_0)
| phi(esk1_0) != esk1_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_247,c_0_77]),c_0_237])]) ).
cnf(c_0_253,plain,
f2(false,true,true) = f7(true),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_248,c_0_128]),c_0_46])]) ).
cnf(c_0_254,plain,
prop(true) = true,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_249,c_0_250]),c_0_65]) ).
cnf(c_0_255,plain,
( lazy_impl(prop(X1),phi(impl(X2,impl(X3,X1)))) = f1(X2,X3,X1)
| bool(impl(X2,impl(X3,X1))) ),
inference(spm,[status(thm)],[c_0_152,c_0_153]) ).
cnf(c_0_256,plain,
phi(impl(false,false)) = 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(spm,[status(thm)],[c_0_246,c_0_210]),c_0_55]),c_0_251]),c_0_210]),c_0_55]),c_0_169]),c_0_69])]) ).
cnf(c_0_257,negated_conjecture,
( and2(esk1_0,esk2_0) = true
| bool(esk1_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_252,c_0_77]),c_0_237])]) ).
cnf(c_0_258,plain,
f2(false,X1,true) = f7(true),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_248,c_0_138]),c_0_253]) ).
cnf(c_0_259,plain,
f7(true) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_254]),c_0_55]),c_0_169]) ).
cnf(c_0_260,plain,
( lazy_impl(prop(X1),impl(true,X1)) = f1(true,false,X1)
| ~ bool(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_236,c_0_122]),c_0_46])]) ).
cnf(c_0_261,plain,
( f1(X1,X2,X3) = lazy_impl(prop(X3),err)
| d(impl(X1,impl(X2,X3))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_255,c_0_95]),c_0_132]) ).
cnf(c_0_262,plain,
impl(false,false) = true,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_256]),c_0_65]) ).
cnf(c_0_263,negated_conjecture,
( bool(f1(esk1_0,esk2_0,X1))
| bool(esk1_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_206,c_0_257]),c_0_46])]),c_0_65]) ).
cnf(c_0_264,plain,
( lazy_impl(prop(X1),impl(phi(X2),X1)) = f2(X2,X3,X1)
| bool(X2) ),
inference(spm,[status(thm)],[c_0_117,c_0_134]) ).
cnf(c_0_265,plain,
f2(false,X1,true) = true,
inference(rw,[status(thm)],[c_0_258,c_0_259]) ).
cnf(c_0_266,plain,
( f1(true,false,X1) = f7(X1)
| ~ bool(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_260,c_0_122]),c_0_33]) ).
cnf(c_0_267,plain,
( f1(X1,false,false) = err
| d(impl(X1,true)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_261,c_0_262]),c_0_210]),c_0_55]),c_0_79]) ).
fof(c_0_268,plain,
! [X3,X4] :
( ( bool(X3)
& ~ bool(X4) )
=> impl(X3,X4) = phi(X4) ),
inference(fof_simplification,[status(thm)],[impl_axiom2]) ).
cnf(c_0_269,negated_conjecture,
( bool(f1(esk1_0,X1,X2))
| bool(esk1_0) ),
inference(spm,[status(thm)],[c_0_263,c_0_190]) ).
cnf(c_0_270,plain,
( f2(X1,X2,X3) = f1(X1,X4,X3)
| bool(X1) ),
inference(spm,[status(thm)],[c_0_163,c_0_264]) ).
cnf(c_0_271,plain,
( f2(X1,X2,X3) = lazy_impl(prop(X3),err)
| phi(X1) = X1 ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_264,c_0_63]),c_0_209]),c_0_127]) ).
cnf(c_0_272,plain,
phi(impl(true,true)) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_265]),c_0_254]),c_0_55]) ).
cnf(c_0_273,plain,
d(impl(true,true)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_266,c_0_267]),c_0_204]),c_0_69])]),c_0_81]) ).
fof(c_0_274,plain,
! [X36,X37] :
( ~ bool(X36)
| bool(X37)
| impl(X36,X37) = phi(X37) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_268])])]) ).
cnf(c_0_275,negated_conjecture,
( bool(f2(esk1_0,X1,X2))
| bool(esk1_0) ),
inference(spm,[status(thm)],[c_0_269,c_0_270]) ).
cnf(c_0_276,plain,
( f2(X1,true,true) = err
| phi(X1) = X1 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_248,c_0_271]),c_0_254]),c_0_55]),c_0_79]) ).
cnf(c_0_277,plain,
( phi(impl(impl(X1,true),X2)) = f1(X1,false,X2)
| ~ bool(X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_236,c_0_54]),c_0_55]) ).
cnf(c_0_278,plain,
impl(true,true) = true,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_272]),c_0_273])]) ).
cnf(c_0_279,plain,
( bool(X2)
| impl(X1,X2) = phi(X2)
| ~ bool(X1) ),
inference(split_conjunct,[status(thm)],[c_0_274]) ).
cnf(c_0_280,negated_conjecture,
phi(esk1_0) = esk1_0,
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_275,c_0_276]),c_0_120]),c_0_127]) ).
cnf(c_0_281,plain,
( f1(true,false,X1) = phi(impl(true,X1))
| ~ bool(X1) ),
inference(spm,[status(thm)],[c_0_277,c_0_278]) ).
cnf(c_0_282,plain,
( lazy_impl(prop(X1),phi(X1)) = f2(false,X2,X1)
| bool(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_279]),c_0_46])]) ).
cnf(c_0_283,negated_conjecture,
( f1(esk1_0,X1,X2) = lazy_impl(prop(X2),esk1_0)
| bool(esk1_0) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_173,c_0_280]),c_0_280]) ).
cnf(c_0_284,plain,
( phi(impl(true,X1)) = f7(X1)
| ~ bool(X1) ),
inference(spm,[status(thm)],[c_0_266,c_0_281]) ).
cnf(c_0_285,negated_conjecture,
f2(false,X1,esk1_0) = f7(esk1_0),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_282,c_0_280]),c_0_33]),c_0_128]) ).
cnf(c_0_286,negated_conjecture,
( f1(esk1_0,true,true) = esk1_0
| bool(esk1_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_238,c_0_283]),c_0_254]),c_0_55]),c_0_280]) ).
cnf(c_0_287,plain,
( f7(X1) = impl(true,X1)
| f7(X1) = err
| ~ bool(X1) ),
inference(spm,[status(thm)],[c_0_63,c_0_284]) ).
cnf(c_0_288,negated_conjecture,
lazy_impl(prop(esk1_0),impl(true,esk1_0)) = f7(esk1_0),
inference(spm,[status(thm)],[c_0_121,c_0_285]) ).
cnf(c_0_289,negated_conjecture,
bool(esk1_0),
inference(spm,[status(thm)],[c_0_269,c_0_286]) ).
cnf(c_0_290,plain,
( and2(X1,X2) = true
| esk3_2(X1,X2) = true
| esk3_2(X1,X2) = false ),
inference(spm,[status(thm)],[c_0_50,c_0_187]) ).
cnf(c_0_291,plain,
( impl(true,X1) = phi(X1)
| f7(X1) = err
| ~ bool(X1) ),
inference(spm,[status(thm)],[c_0_60,c_0_287]) ).
cnf(c_0_292,negated_conjecture,
phi(impl(true,esk1_0)) = f7(esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_288,c_0_54]),c_0_55]),c_0_289])]) ).
cnf(c_0_293,plain,
( lazy_impl(prop(X1),impl(impl(X2,phi(X3)),X1)) = f1(X2,X3,X1)
| bool(X3) ),
inference(spm,[status(thm)],[c_0_152,c_0_153]) ).
cnf(c_0_294,plain,
( and2(X1,X2) = f1(X1,X2,false)
| esk3_2(X1,X2) = true
| and2(X1,X2) = true
| ~ d(f1(X1,X2,false)) ),
inference(spm,[status(thm)],[c_0_193,c_0_290]) ).
cnf(c_0_295,plain,
f1(true,true,false) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_251,c_0_210]),c_0_55]),c_0_169]) ).
cnf(c_0_296,plain,
( impl(true,X1) = phi(X1)
| ~ bool(X1) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_167,c_0_291]),c_0_65]),c_0_81]) ).
cnf(c_0_297,plain,
lazy_impl(prop(X1),impl(phi(impl(X2,X1)),X1)) = f2(true,X2,X1),
inference(spm,[status(thm)],[c_0_117,c_0_55]) ).
cnf(c_0_298,negated_conjecture,
f7(esk1_0) = esk1_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_292,c_0_122]),c_0_280]),c_0_289])]) ).
cnf(c_0_299,plain,
( and2(X1,X2) = phi(f1(X1,X2,false))
| esk3_2(X1,X2) = true
| and2(X1,X2) = true ),
inference(spm,[status(thm)],[c_0_151,c_0_290]) ).
cnf(c_0_300,plain,
lazy_impl(prop(X1),impl(impl(X2,err),X1)) = f1(X2,err,X1),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_293,c_0_79]),c_0_120]) ).
cnf(c_0_301,plain,
( lazy_impl(prop(X1),phi(phi(impl(X2,X1)))) = f1(X3,X2,X1)
| bool(phi(impl(X2,X1)))
| ~ bool(X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_255,c_0_279]),c_0_113]) ).
cnf(c_0_302,plain,
( esk3_2(true,true) = true
| and2(true,true) = true ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_294,c_0_295]),c_0_45])]) ).
cnf(c_0_303,plain,
f1(true,true,true) = f7(true),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_246]),c_0_258]),c_0_46])]) ).
cnf(c_0_304,plain,
( f2(true,X1,X2) = f1(true,X1,X2)
| ~ bool(impl(X1,X2)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_296]),c_0_297]) ).
cnf(c_0_305,plain,
( phi(impl(phi(impl(X1,X2)),X2)) = f2(true,X1,X2)
| ~ bool(X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_297,c_0_54]),c_0_55]) ).
cnf(c_0_306,negated_conjecture,
phi(impl(true,esk1_0)) = esk1_0,
inference(rw,[status(thm)],[c_0_292,c_0_298]) ).
cnf(c_0_307,plain,
( and2(X1,X2) = phi(f1(X1,X2,false))
| and2(X1,X2) = phi(f1(X1,X2,true))
| and2(X1,X2) = true ),
inference(spm,[status(thm)],[c_0_151,c_0_299]) ).
cnf(c_0_308,plain,
( f1(X1,err,X2) = f1(X1,X3,X2)
| phi(X3) = X3 ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_293,c_0_63]),c_0_300]),c_0_127]) ).
cnf(c_0_309,plain,
( f1(X1,err,false) = err
| ~ bool(X1) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_301,c_0_214]),c_0_210]),c_0_79]),c_0_55]),c_0_79]),c_0_120]) ).
cnf(c_0_310,plain,
and2(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_151,c_0_302]),c_0_303]),c_0_259]),c_0_169])]) ).
cnf(c_0_311,plain,
( f2(true,true,X1) = f1(true,true,X1)
| ~ bool(X1) ),
inference(spm,[status(thm)],[c_0_304,c_0_122]) ).
cnf(c_0_312,negated_conjecture,
f2(true,true,esk1_0) = phi(impl(esk1_0,esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_305,c_0_306]),c_0_289])]) ).
cnf(c_0_313,negated_conjecture,
( and2(esk1_0,esk2_0) = phi(f1(esk1_0,esk2_0,true))
| and2(esk1_0,esk2_0) = true
| phi(f1(esk1_0,esk2_0,false)) != and1(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_170,c_0_307]) ).
cnf(c_0_314,plain,
( f1(X1,X2,false) = err
| phi(X2) = X2
| ~ bool(X1) ),
inference(spm,[status(thm)],[c_0_308,c_0_309]) ).
fof(c_0_315,plain,
! [X3,X4] :
( ( bool(X3)
& ~ bool(X4) )
=> and1(X3,X4) = phi(X4) ),
inference(fof_simplification,[status(thm)],[and1_axiom2]) ).
cnf(c_0_316,plain,
( f7(X1) = err
| bool(impl(true,X1))
| ~ bool(X1) ),
inference(spm,[status(thm)],[c_0_112,c_0_287]) ).
cnf(c_0_317,plain,
( and2(X1,X2) = err
| ~ forallprefers(f1(X1,X2,X3),and2(X1,X2)) ),
inference(spm,[status(thm)],[c_0_150,c_0_200]) ).
cnf(c_0_318,plain,
bool(f1(true,true,X1)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_206,c_0_310]),c_0_46])]),c_0_65]) ).
cnf(c_0_319,negated_conjecture,
f1(true,true,esk1_0) = phi(impl(esk1_0,esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_311,c_0_312]),c_0_289])]) ).
cnf(c_0_320,negated_conjecture,
( and2(esk1_0,esk2_0) = phi(f1(esk1_0,esk2_0,true))
| and2(esk1_0,esk2_0) = true
| phi(esk2_0) = esk2_0
| and1(esk1_0,esk2_0) != err
| ~ bool(esk1_0) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_313,c_0_314]),c_0_79]) ).
fof(c_0_321,plain,
! [X19,X20] :
( ~ bool(X19)
| bool(X20)
| and1(X19,X20) = phi(X20) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_315])])]) ).
cnf(c_0_322,negated_conjecture,
( impl(true,esk1_0) = esk1_0
| ~ bool(impl(true,esk1_0)) ),
inference(spm,[status(thm)],[c_0_127,c_0_306]) ).
cnf(c_0_323,plain,
( bool(impl(true,X1))
| ~ bool(X1) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_167,c_0_316]),c_0_65]),c_0_81]) ).
cnf(c_0_324,plain,
~ forallprefers(f1(true,true,X1),true),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_317,c_0_310]),c_0_65]) ).
cnf(c_0_325,negated_conjecture,
bool(phi(impl(esk1_0,esk1_0))),
inference(spm,[status(thm)],[c_0_318,c_0_319]) ).
cnf(c_0_326,negated_conjecture,
( and2(esk1_0,esk2_0) = phi(f1(esk1_0,esk2_0,true))
| and2(esk1_0,esk2_0) = true
| phi(esk2_0) = esk2_0
| and1(esk1_0,esk2_0) != err ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_320,c_0_289])]) ).
cnf(c_0_327,plain,
( bool(X2)
| and1(X1,X2) = phi(X2)
| ~ bool(X1) ),
inference(split_conjunct,[status(thm)],[c_0_321]) ).
cnf(c_0_328,plain,
phi(impl(err,true)) = err,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_209,c_0_254]),c_0_55]),c_0_55]),c_0_79]) ).
cnf(c_0_329,plain,
( phi(impl(impl(X1,impl(X2,X3)),X3)) = f1(X1,X2,X3)
| ~ bool(X3) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_54]),c_0_55]) ).
cnf(c_0_330,negated_conjecture,
impl(true,esk1_0) = esk1_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_322,c_0_323]),c_0_289])]) ).
cnf(c_0_331,negated_conjecture,
~ forallprefers(phi(impl(esk1_0,esk1_0)),true),
inference(spm,[status(thm)],[c_0_324,c_0_319]) ).
cnf(c_0_332,negated_conjecture,
d(impl(esk1_0,esk1_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_325,c_0_95]),c_0_120]) ).
cnf(c_0_333,negated_conjecture,
( and2(esk1_0,esk2_0) = phi(f1(esk1_0,esk2_0,true))
| and2(esk1_0,esk2_0) = true
| phi(esk2_0) = esk2_0 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_326,c_0_327]),c_0_289])]),c_0_63]),c_0_127]) ).
cnf(c_0_334,plain,
( f1(X1,err,true) = err
| ~ bool(X1) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_301,c_0_328]),c_0_254]),c_0_79]),c_0_55]),c_0_79]),c_0_120]) ).
cnf(c_0_335,negated_conjecture,
phi(impl(impl(X1,esk1_0),esk1_0)) = f1(X1,true,esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_329,c_0_330]),c_0_289])]) ).
cnf(c_0_336,negated_conjecture,
~ forallprefers(impl(esk1_0,esk1_0),true),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_331,c_0_77]),c_0_332])]) ).
cnf(c_0_337,negated_conjecture,
( and2(esk1_0,esk2_0) = true
| phi(esk2_0) = esk2_0
| phi(f1(esk1_0,esk2_0,true)) != and1(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_170,c_0_333]) ).
cnf(c_0_338,plain,
( f1(X1,X2,true) = err
| phi(X2) = X2
| ~ bool(X1) ),
inference(spm,[status(thm)],[c_0_308,c_0_334]) ).
cnf(c_0_339,negated_conjecture,
( f1(X1,true,esk1_0) = phi(impl(phi(X1),esk1_0))
| bool(X1) ),
inference(spm,[status(thm)],[c_0_335,c_0_153]) ).
cnf(c_0_340,negated_conjecture,
bool(impl(esk1_0,esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_336,c_0_44]),c_0_45]),c_0_46])]) ).
cnf(c_0_341,negated_conjecture,
( and2(esk1_0,esk2_0) = true
| phi(esk2_0) = esk2_0
| and1(esk1_0,esk2_0) != err ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_337,c_0_338]),c_0_79]),c_0_289])]) ).
cnf(c_0_342,negated_conjecture,
( f1(X1,X2,esk1_0) = phi(impl(phi(X1),esk1_0))
| bool(X1) ),
inference(spm,[status(thm)],[c_0_190,c_0_339]) ).
cnf(c_0_343,negated_conjecture,
( impl(esk1_0,esk1_0) = true
| impl(esk1_0,esk1_0) = false ),
inference(spm,[status(thm)],[c_0_50,c_0_340]) ).
cnf(c_0_344,negated_conjecture,
( and2(esk1_0,esk2_0) = true
| phi(esk2_0) = esk2_0 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_341,c_0_327]),c_0_289])]),c_0_63]),c_0_127]) ).
cnf(c_0_345,plain,
( lazy_impl(prop(X1),err) = err
| ~ bool(X1) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_202,c_0_181]),c_0_79]),c_0_79]),c_0_79]),c_0_79]),c_0_120]) ).
cnf(c_0_346,negated_conjecture,
lazy_impl(prop(esk1_0),err) = phi(impl(err,esk1_0)),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_202,c_0_342]),c_0_79]),c_0_120]) ).
cnf(c_0_347,negated_conjecture,
impl(esk1_0,esk1_0) = true,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_331,c_0_343]),c_0_176]),c_0_57])]) ).
cnf(c_0_348,negated_conjecture,
( phi(esk2_0) = esk2_0
| bool(f1(esk1_0,esk2_0,X1)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_206,c_0_344]),c_0_46])]),c_0_65]) ).
cnf(c_0_349,negated_conjecture,
phi(impl(err,esk1_0)) = err,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_345,c_0_346]),c_0_289])]) ).
cnf(c_0_350,negated_conjecture,
phi(impl(impl(X1,true),esk1_0)) = f1(X1,esk1_0,esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_329,c_0_347]),c_0_289])]) ).
cnf(c_0_351,negated_conjecture,
phi(esk2_0) = esk2_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_348,c_0_338]),c_0_289])]),c_0_120]) ).
cnf(c_0_352,negated_conjecture,
lazy_impl(prop(esk1_0),err) = err,
inference(rw,[status(thm)],[c_0_346,c_0_349]) ).
cnf(c_0_353,plain,
( f1(X1,X2,X3) = true
| bool(X3) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_34]),c_0_35]) ).
cnf(c_0_354,negated_conjecture,
f1(X1,esk1_0,esk1_0) = f1(X1,false,esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_277,c_0_350]),c_0_289])]) ).
cnf(c_0_355,negated_conjecture,
( f1(esk2_0,X1,X2) = lazy_impl(prop(X2),esk2_0)
| bool(esk2_0) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_173,c_0_351]),c_0_351]) ).
cnf(c_0_356,negated_conjecture,
prop(esk1_0) = true,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_249,c_0_352]),c_0_65]) ).
cnf(c_0_357,plain,
phi(and2(X1,X2)) = and2(X1,X2),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_151,c_0_200]),c_0_74]) ).
cnf(c_0_358,plain,
( bool(f1(X1,X2,X3))
| bool(esk3_2(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_199,c_0_353]),c_0_45]),c_0_46])]) ).
cnf(c_0_359,negated_conjecture,
( f1(esk2_0,false,esk1_0) = esk2_0
| bool(esk2_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_354,c_0_355]),c_0_356]),c_0_55]),c_0_351]) ).
cnf(c_0_360,plain,
( f1(X1,X2,false) = phi(phi(phi(X1)))
| bool(phi(X1)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_173,c_0_210]),c_0_55]) ).
cnf(c_0_361,plain,
( lazy_impl(prop(X1),impl(and2(X2,X3),X1)) = f1(and2(X2,X3),X4,X1)
| bool(and2(X2,X3)) ),
inference(spm,[status(thm)],[c_0_163,c_0_357]) ).
cnf(c_0_362,plain,
( bool(f1(X1,X2,X3))
| bool(esk3_2(X1,X4))
| bool(X1) ),
inference(spm,[status(thm)],[c_0_358,c_0_190]) ).
cnf(c_0_363,negated_conjecture,
( f1(esk2_0,X1,esk1_0) = esk2_0
| bool(esk2_0) ),
inference(spm,[status(thm)],[c_0_190,c_0_359]) ).
cnf(c_0_364,plain,
f2(false,X1,false) = lazy_and2(false,X2),
inference(rw,[status(thm)],[c_0_142,c_0_192]) ).
cnf(c_0_365,plain,
( phi(impl(and2(X1,X2),false)) = and2(X1,X2)
| bool(and2(X1,X2)) ),
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(spm,[status(thm)],[c_0_360,c_0_361]),c_0_210]),c_0_55]),c_0_357]),c_0_357]),c_0_357]),c_0_357])]) ).
cnf(c_0_366,negated_conjecture,
( bool(esk3_2(esk2_0,X1))
| bool(esk2_0) ),
inference(spm,[status(thm)],[c_0_362,c_0_363]) ).
cnf(c_0_367,plain,
lazy_and2(false,X1) = false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_364]),c_0_204]),c_0_69])]) ).
cnf(c_0_368,plain,
( f1(X1,and2(X2,X3),false) = and2(X2,X3)
| bool(and2(X2,X3))
| ~ bool(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_301,c_0_365]),c_0_210]),c_0_357]),c_0_55]),c_0_357]) ).
cnf(c_0_369,negated_conjecture,
( and2(esk2_0,X1) = esk2_0
| bool(esk2_0) ),
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_186,c_0_366]),c_0_351]),c_0_351]),c_0_351]),c_0_351]),c_0_351])]) ).
cnf(c_0_370,plain,
f2(false,X1,false) = false,
inference(rw,[status(thm)],[c_0_364,c_0_367]) ).
cnf(c_0_371,negated_conjecture,
( f1(X1,esk2_0,false) = esk2_0
| bool(esk2_0)
| ~ bool(X1) ),
inference(spm,[status(thm)],[c_0_368,c_0_369]) ).
cnf(c_0_372,plain,
phi(impl(true,false)) = false,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_370]),c_0_210]),c_0_55]) ).
cnf(c_0_373,negated_conjecture,
( and2(esk1_0,esk2_0) = phi(f1(esk1_0,esk2_0,true))
| and2(esk1_0,esk2_0) = true
| bool(esk2_0)
| and1(esk1_0,esk2_0) != esk2_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_313,c_0_371]),c_0_351]),c_0_289])]) ).
cnf(c_0_374,plain,
( phi(impl(and2(X1,X2),true)) = and2(X1,X2)
| bool(and2(X1,X2)) ),
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(spm,[status(thm)],[c_0_245,c_0_361]),c_0_254]),c_0_55]),c_0_357]),c_0_357]),c_0_357]),c_0_357])]) ).
cnf(c_0_375,plain,
bool(lazy_impl(prop(X1),impl(true,X1))),
inference(spm,[status(thm)],[c_0_133,c_0_121]) ).
cnf(c_0_376,plain,
( lazy_impl(prop(X1),impl(true,X1)) = f1(false,false,X1)
| ~ bool(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_236,c_0_232]),c_0_46])]) ).
cnf(c_0_377,plain,
( bool(and2(X1,X2))
| ~ bool(f1(X1,X2,esk3_2(X1,X2))) ),
inference(spm,[status(thm)],[c_0_113,c_0_151]) ).
cnf(c_0_378,plain,
impl(true,false) = false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_372]),c_0_81]) ).
cnf(c_0_379,negated_conjecture,
( and2(esk1_0,esk2_0) = phi(f1(esk1_0,esk2_0,true))
| and2(esk1_0,esk2_0) = true
| bool(esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_373,c_0_327]),c_0_351]),c_0_289])]) ).
cnf(c_0_380,plain,
( f1(X1,and2(X2,X3),true) = and2(X2,X3)
| bool(and2(X2,X3))
| ~ bool(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_301,c_0_374]),c_0_254]),c_0_357]),c_0_55]),c_0_357]) ).
cnf(c_0_381,plain,
( bool(f1(false,false,X1))
| ~ bool(X1) ),
inference(spm,[status(thm)],[c_0_375,c_0_376]) ).
cnf(c_0_382,plain,
( bool(esk3_2(X1,X2))
| bool(and2(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_377,c_0_353]),c_0_46])]) ).
cnf(c_0_383,plain,
( bool(esk3_2(X1,X2))
| ~ forallprefers(f1(X1,X2,X3),true) ),
inference(spm,[status(thm)],[c_0_150,c_0_353]) ).
cnf(c_0_384,plain,
f1(false,false,false) = false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_376,c_0_378]),c_0_33]),c_0_204]),c_0_69])]) ).
cnf(c_0_385,negated_conjecture,
( and2(esk1_0,esk2_0) = true
| bool(esk2_0)
| phi(f1(esk1_0,esk2_0,true)) != and1(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_170,c_0_379]) ).
cnf(c_0_386,negated_conjecture,
( f1(X1,esk2_0,true) = esk2_0
| bool(esk2_0)
| ~ bool(X1) ),
inference(spm,[status(thm)],[c_0_380,c_0_369]) ).
cnf(c_0_387,plain,
bool(and2(false,false)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_377,c_0_381]),c_0_382]) ).
cnf(c_0_388,plain,
bool(esk3_2(false,false)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_383,c_0_384]),c_0_57])]) ).
cnf(c_0_389,plain,
( lazy_impl(prop(X1),impl(true,X1)) = f1(false,true,X1)
| ~ bool(X1) ),
inference(spm,[status(thm)],[c_0_235,c_0_232]) ).
cnf(c_0_390,plain,
( lazy_impl(prop(X1),impl(true,X1)) = f1(false,X2,X1)
| ~ bool(impl(X2,X1)) ),
inference(spm,[status(thm)],[c_0_152,c_0_232]) ).
cnf(c_0_391,negated_conjecture,
( and2(esk1_0,esk2_0) = true
| bool(esk2_0)
| and1(esk1_0,esk2_0) != esk2_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_385,c_0_386]),c_0_351]),c_0_289])]) ).
cnf(c_0_392,plain,
d(f1(false,false,X1)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_387,c_0_171]),c_0_120]) ).
cnf(c_0_393,plain,
( esk3_2(false,false) = true
| esk3_2(false,false) = false ),
inference(spm,[status(thm)],[c_0_50,c_0_388]) ).
cnf(c_0_394,plain,
( bool(f1(false,true,X1))
| ~ bool(X1) ),
inference(spm,[status(thm)],[c_0_375,c_0_389]) ).
cnf(c_0_395,plain,
f1(false,true,false) = 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_390,c_0_378]),c_0_210]),c_0_378]),c_0_55]),c_0_176]),c_0_69])]) ).
cnf(c_0_396,negated_conjecture,
( and2(esk1_0,esk2_0) = true
| bool(esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_391,c_0_327]),c_0_351]),c_0_289])]) ).
cnf(c_0_397,plain,
f1(false,false,esk3_2(false,false)) = and2(false,false),
inference(spm,[status(thm)],[c_0_193,c_0_392]) ).
cnf(c_0_398,plain,
( esk3_2(false,false) = true
| and2(false,false) = false ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_151,c_0_393]),c_0_384]),c_0_176]) ).
cnf(c_0_399,plain,
f1(false,true,true) = f7(true),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_246,c_0_389]),c_0_303]),c_0_46])]) ).
cnf(c_0_400,plain,
bool(and2(false,true)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_377,c_0_394]),c_0_382]) ).
cnf(c_0_401,plain,
bool(esk3_2(false,true)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_383,c_0_395]),c_0_57])]) ).
cnf(c_0_402,negated_conjecture,
( bool(f1(esk1_0,esk2_0,X1))
| bool(esk2_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_206,c_0_396]),c_0_46])]),c_0_65]) ).
cnf(c_0_403,plain,
~ forallprefers(false,and2(false,false)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_384]),c_0_397]) ).
cnf(c_0_404,plain,
( and2(false,false) = f7(true)
| and2(false,false) = 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_193,c_0_398]),c_0_238]),c_0_399]),c_0_238]),c_0_399]),c_0_106])]) ).
cnf(c_0_405,plain,
d(f1(false,true,X1)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_400,c_0_171]),c_0_120]) ).
cnf(c_0_406,plain,
( esk3_2(false,true) = true
| esk3_2(false,true) = false ),
inference(spm,[status(thm)],[c_0_50,c_0_401]) ).
cnf(c_0_407,plain,
( bool(f1(true,false,X1))
| ~ bool(X1) ),
inference(spm,[status(thm)],[c_0_375,c_0_260]) ).
cnf(c_0_408,plain,
f1(true,false,false) = false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_260,c_0_378]),c_0_33]),c_0_204]),c_0_69])]) ).
cnf(c_0_409,negated_conjecture,
( esk1_0 = true
| esk1_0 = false ),
inference(spm,[status(thm)],[c_0_50,c_0_289]) ).
cnf(c_0_410,negated_conjecture,
bool(esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_402,c_0_371]),c_0_289])]) ).
cnf(c_0_411,plain,
( and2(false,false) = false
| ~ forallprefers(false,f7(true)) ),
inference(spm,[status(thm)],[c_0_403,c_0_404]) ).
cnf(c_0_412,plain,
f1(false,true,esk3_2(false,true)) = and2(false,true),
inference(spm,[status(thm)],[c_0_193,c_0_405]) ).
cnf(c_0_413,plain,
( esk3_2(false,true) = true
| and2(false,true) = false ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_151,c_0_406]),c_0_395]),c_0_176]) ).
cnf(c_0_414,plain,
bool(and2(true,false)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_377,c_0_407]),c_0_382]) ).
cnf(c_0_415,plain,
bool(esk3_2(true,false)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_383,c_0_408]),c_0_57])]) ).
cnf(c_0_416,negated_conjecture,
( esk1_0 = true
| and2(false,esk2_0) != and1(false,esk2_0) ),
inference(spm,[status(thm)],[c_0_170,c_0_409]) ).
cnf(c_0_417,negated_conjecture,
( esk2_0 = true
| esk2_0 = false ),
inference(spm,[status(thm)],[c_0_50,c_0_410]) ).
cnf(c_0_418,plain,
and2(false,false) = false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_411,c_0_60]),c_0_169]),c_0_57]),c_0_46])]) ).
fof(c_0_419,plain,
! [X21] :
( ~ bool(X21)
| and1(false,X21) = false ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[and1_axiom3])])]) ).
cnf(c_0_420,plain,
~ forallprefers(false,and2(false,true)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_395]),c_0_412]) ).
cnf(c_0_421,plain,
( and2(false,true) = f7(true)
| and2(false,true) = false ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_193,c_0_413]),c_0_399]),c_0_399]),c_0_106])]) ).
cnf(c_0_422,plain,
d(f1(true,false,X1)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_414,c_0_171]),c_0_120]) ).
cnf(c_0_423,plain,
( esk3_2(true,false) = true
| esk3_2(true,false) = false ),
inference(spm,[status(thm)],[c_0_50,c_0_415]) ).
cnf(c_0_424,negated_conjecture,
( esk2_0 = true
| esk1_0 = true
| and1(false,false) != false ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_416,c_0_417]),c_0_418]) ).
cnf(c_0_425,plain,
( and1(false,X1) = false
| ~ bool(X1) ),
inference(split_conjunct,[status(thm)],[c_0_419]) ).
cnf(c_0_426,plain,
( and2(false,true) = false
| ~ forallprefers(false,f7(true)) ),
inference(spm,[status(thm)],[c_0_420,c_0_421]) ).
cnf(c_0_427,plain,
f1(true,false,esk3_2(true,false)) = and2(true,false),
inference(spm,[status(thm)],[c_0_193,c_0_422]) ).
cnf(c_0_428,plain,
( esk3_2(true,false) = true
| and2(true,false) = false ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_151,c_0_423]),c_0_408]),c_0_176]) ).
cnf(c_0_429,negated_conjecture,
( esk1_0 = true
| esk2_0 = true ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_424,c_0_425]),c_0_69])]) ).
cnf(c_0_430,plain,
and2(false,true) = false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_426,c_0_60]),c_0_169]),c_0_57]),c_0_46])]) ).
cnf(c_0_431,plain,
~ forallprefers(false,and2(true,false)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_408]),c_0_427]) ).
cnf(c_0_432,plain,
( and2(true,false) = f7(true)
| and2(true,false) = 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_193,c_0_428]),c_0_238]),c_0_303]),c_0_238]),c_0_303]),c_0_106])]) ).
cnf(c_0_433,negated_conjecture,
( esk1_0 = true
| and1(false,true) != false ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_416,c_0_429]),c_0_430]) ).
cnf(c_0_434,plain,
( and2(true,false) = false
| ~ forallprefers(false,f7(true)) ),
inference(spm,[status(thm)],[c_0_431,c_0_432]) ).
cnf(c_0_435,negated_conjecture,
( esk2_0 = true
| and2(esk1_0,false) != and1(esk1_0,false) ),
inference(spm,[status(thm)],[c_0_170,c_0_417]) ).
cnf(c_0_436,negated_conjecture,
esk1_0 = true,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_433,c_0_425]),c_0_46])]) ).
cnf(c_0_437,plain,
and2(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_434,c_0_60]),c_0_169]),c_0_57]),c_0_46])]) ).
fof(c_0_438,plain,
! [X22] :
( ~ bool(X22)
| and1(true,X22) = X22 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[and1_axiom4])])]) ).
cnf(c_0_439,negated_conjecture,
( esk2_0 = true
| and1(true,false) != false ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_435,c_0_436]),c_0_437]),c_0_436]) ).
cnf(c_0_440,plain,
( and1(true,X1) = X1
| ~ bool(X1) ),
inference(split_conjunct,[status(thm)],[c_0_438]) ).
cnf(c_0_441,negated_conjecture,
esk2_0 = true,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_439,c_0_440]),c_0_69])]) ).
cnf(c_0_442,negated_conjecture,
and1(true,true) != true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_170,c_0_436]),c_0_436]),c_0_441]),c_0_310]),c_0_441]) ).
cnf(c_0_443,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_442,c_0_440]),c_0_46])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW096+1 : TPTP v8.2.0. Released v5.2.0.
% 0.07/0.14 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n023.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat May 18 19:30:38 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.20/0.49 Running first-order theorem proving
% 0.20/0.49 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
% 42.67/5.86 # Version: 3.1.0
% 42.67/5.86 # Preprocessing class: FSMSSMSSSSSNFFN.
% 42.67/5.86 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 42.67/5.86 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 42.67/5.86 # Starting new_bool_3 with 300s (1) cores
% 42.67/5.86 # Starting new_bool_1 with 300s (1) cores
% 42.67/5.86 # Starting sh5l with 300s (1) cores
% 42.67/5.86 # sh5l with pid 16673 completed with status 0
% 42.67/5.86 # Result found by sh5l
% 42.67/5.86 # Preprocessing class: FSMSSMSSSSSNFFN.
% 42.67/5.86 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 42.67/5.86 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 42.67/5.86 # Starting new_bool_3 with 300s (1) cores
% 42.67/5.86 # Starting new_bool_1 with 300s (1) cores
% 42.67/5.86 # Starting sh5l with 300s (1) cores
% 42.67/5.86 # SinE strategy is gf500_gu_R04_F100_L20000
% 42.67/5.86 # Search class: FGHSM-FFMM31-MFFFFFNN
% 42.67/5.86 # Scheduled 13 strats onto 1 cores with 300 seconds (300 total)
% 42.67/5.86 # Starting G-E--_107_C41_F1_PI_AE_CS_SP_PS_S4S with 23s (1) cores
% 42.67/5.86 # G-E--_107_C41_F1_PI_AE_CS_SP_PS_S4S with pid 16676 completed with status 0
% 42.67/5.86 # Result found by G-E--_107_C41_F1_PI_AE_CS_SP_PS_S4S
% 42.67/5.86 # Preprocessing class: FSMSSMSSSSSNFFN.
% 42.67/5.86 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 42.67/5.86 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 42.67/5.86 # Starting new_bool_3 with 300s (1) cores
% 42.67/5.86 # Starting new_bool_1 with 300s (1) cores
% 42.67/5.86 # Starting sh5l with 300s (1) cores
% 42.67/5.86 # SinE strategy is gf500_gu_R04_F100_L20000
% 42.67/5.86 # Search class: FGHSM-FFMM31-MFFFFFNN
% 42.67/5.86 # Scheduled 13 strats onto 1 cores with 300 seconds (300 total)
% 42.67/5.86 # Starting G-E--_107_C41_F1_PI_AE_CS_SP_PS_S4S with 23s (1) cores
% 42.67/5.86 # Preprocessing time : 0.002 s
% 42.67/5.86 # Presaturation interreduction done
% 42.67/5.86
% 42.67/5.86 # Proof found!
% 42.67/5.86 # SZS status Theorem
% 42.67/5.86 # SZS output start CNFRefutation
% See solution above
% 42.67/5.86 # Parsed axioms : 45
% 42.67/5.86 # Removed by relevancy pruning/SinE : 1
% 42.67/5.86 # Initial clauses : 98
% 42.67/5.86 # Removed in clause preprocessing : 5
% 42.67/5.86 # Initial clauses in saturation : 93
% 42.67/5.86 # Processed clauses : 19856
% 42.67/5.86 # ...of these trivial : 547
% 42.67/5.86 # ...subsumed : 14470
% 42.67/5.86 # ...remaining for further processing : 4839
% 42.67/5.86 # Other redundant clauses eliminated : 0
% 42.67/5.86 # Clauses deleted for lack of memory : 0
% 42.67/5.86 # Backward-subsumed : 610
% 42.67/5.86 # Backward-rewritten : 1420
% 42.67/5.86 # Generated clauses : 471404
% 42.67/5.86 # ...of the previous two non-redundant : 331113
% 42.67/5.86 # ...aggressively subsumed : 0
% 42.67/5.86 # Contextual simplify-reflections : 240
% 42.67/5.86 # Paramodulations : 471215
% 42.67/5.86 # Factorizations : 180
% 42.67/5.86 # NegExts : 0
% 42.67/5.86 # Equation resolutions : 9
% 42.67/5.86 # Disequality decompositions : 0
% 42.67/5.86 # Total rewrite steps : 627031
% 42.67/5.86 # ...of those cached : 611046
% 42.67/5.86 # Propositional unsat checks : 0
% 42.67/5.86 # Propositional check models : 0
% 42.67/5.86 # Propositional check unsatisfiable : 0
% 42.67/5.86 # Propositional clauses : 0
% 42.67/5.86 # Propositional clauses after purity: 0
% 42.67/5.86 # Propositional unsat core size : 0
% 42.67/5.86 # Propositional preprocessing time : 0.000
% 42.67/5.86 # Propositional encoding time : 0.000
% 42.67/5.86 # Propositional solver time : 0.000
% 42.67/5.86 # Success case prop preproc time : 0.000
% 42.67/5.86 # Success case prop encoding time : 0.000
% 42.67/5.86 # Success case prop solver time : 0.000
% 42.67/5.86 # Current number of processed clauses : 2734
% 42.67/5.86 # Positive orientable unit clauses : 335
% 42.67/5.86 # Positive unorientable unit clauses: 6
% 42.67/5.86 # Negative unit clauses : 114
% 42.67/5.86 # Non-unit-clauses : 2279
% 42.67/5.86 # Current number of unprocessed clauses: 306656
% 42.67/5.86 # ...number of literals in the above : 1191917
% 42.67/5.86 # Current number of archived formulas : 0
% 42.67/5.86 # Current number of archived clauses : 2105
% 42.67/5.86 # Clause-clause subsumption calls (NU) : 854730
% 42.67/5.86 # Rec. Clause-clause subsumption calls : 475831
% 42.67/5.86 # Non-unit clause-clause subsumptions : 11021
% 42.67/5.86 # Unit Clause-clause subsumption calls : 78226
% 42.67/5.86 # Rewrite failures with RHS unbound : 171
% 42.67/5.86 # BW rewrite match attempts : 1348
% 42.67/5.86 # BW rewrite match successes : 252
% 42.67/5.86 # Condensation attempts : 0
% 42.67/5.86 # Condensation successes : 0
% 42.67/5.86 # Termbank termtop insertions : 9270470
% 42.67/5.86 # Search garbage collected termcells : 710
% 42.67/5.86
% 42.67/5.86 # -------------------------------------------------
% 42.67/5.86 # User time : 5.127 s
% 42.67/5.86 # System time : 0.178 s
% 42.67/5.86 # Total time : 5.305 s
% 42.67/5.86 # Maximum resident set size: 1920 pages
% 42.67/5.86
% 42.67/5.86 # -------------------------------------------------
% 42.67/5.86 # User time : 5.128 s
% 42.67/5.86 # System time : 0.181 s
% 42.67/5.86 # Total time : 5.309 s
% 42.67/5.86 # Maximum resident set size: 1744 pages
% 42.67/5.86 % E---3.1 exiting
% 42.67/5.86 % E exiting
%------------------------------------------------------------------------------