%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWW102+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 : n002.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 03:10:01 PM UTC 2026
% Result : Theorem 0.14s 0.44s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 19
% Syntax : Number of formulae : 108 ( 41 unt; 0 def)
% Number of atoms : 298 ( 145 equ)
% Maximal formula atoms : 75 ( 2 avg)
% Number of connectives : 296 ( 106 ~; 129 |; 49 &)
% ( 6 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-2 aty)
% Number of variables : 72 ( 4 sgn 40 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
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(not1_not2,conjecture,
! [X5] : not1(X5) = not2(X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not1_not2) ).
fof(not1_axiom1,axiom,
! [X3] :
( ~ bool(X3)
=> not1(X3) = phi(X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',not1_axiom1) ).
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] :
( ( phi(X1) = err
& ~ d(X1) )
| ( phi(X1) = X1
& d(X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',def_phi) ).
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_not2,axiom,
! [X5] : not2(X5) = impl(X5,false2),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',def_not2) ).
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(prop_true,axiom,
! [X1] :
( prop(X1) = true
<=> bool(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',prop_true) ).
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(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(not1_axiom2,axiom,
not1(false) = true,
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',not1_axiom2) ).
fof(impl_axiom3,axiom,
! [X4] :
( bool(X4)
=> impl(false,X4) = true ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',impl_axiom3) ).
fof(not1_axiom3,axiom,
not1(true) = false,
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',not1_axiom3) ).
fof(impl_axiom4,axiom,
! [X4] :
( bool(X4)
=> impl(true,X4) = X4 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',impl_axiom4) ).
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(c_0_19,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_20,plain,
! [X81] : f7(X81) = lazy_impl(prop(X81),X81),
inference(variable_rename,[status(thm)],[def_f7]) ).
fof(c_0_21,plain,
! [X1] :
( prop(X1) = false
<=> ~ bool(X1) ),
inference(fof_simplification,[status(thm)],[prop_false]) ).
fof(c_0_22,negated_conjecture,
~ ! [X5] : not1(X5) = not2(X5),
inference(assume_negation,[status(cth)],[not1_not2]) ).
fof(c_0_23,plain,
! [X3] :
( ~ bool(X3)
=> not1(X3) = phi(X3) ),
inference(fof_simplification,[status(thm)],[not1_axiom1]) ).
fof(c_0_24,plain,
! [X28] : lazy_impl(true,X28) = phi(X28),
inference(variable_rename,[status(thm)],[lazy_impl_axiom3]) ).
fof(c_0_25,plain,
! [X1] :
( ( phi(X1) = err
& ~ d(X1) )
| ( phi(X1) = X1
& d(X1) ) ),
inference(fof_simplification,[status(thm)],[def_phi]) ).
cnf(c_0_26,plain,
~ forallprefers(f7(X1),f7(esk7_0)),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_27,plain,
f7(X1) = lazy_impl(prop(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_28,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_21])])]) ).
fof(c_0_29,plain,
! [X27] : lazy_impl(false,X27) = true,
inference(variable_rename,[status(thm)],[lazy_impl_axiom2]) ).
fof(c_0_30,negated_conjecture,
not1(esk8_0) != not2(esk8_0),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_22])])])]) ).
fof(c_0_31,plain,
! [X85] : not2(X85) = impl(X85,false2),
inference(variable_rename,[status(thm)],[def_not2]) ).
fof(c_0_32,plain,
! [X84] :
( not1(X84) = phi(X84)
| bool(X84) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])]) ).
fof(c_0_33,plain,
! [X3,X4] :
( ~ bool(X3)
=> impl(X3,X4) = phi(X3) ),
inference(fof_simplification,[status(thm)],[impl_axiom1]) ).
cnf(c_0_34,plain,
false2 = phi(f7(esk7_0)),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_35,plain,
lazy_impl(true,X1) = phi(X1),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_36,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_25])])]) ).
cnf(c_0_37,plain,
~ forallprefers(lazy_impl(prop(X1),X1),lazy_impl(prop(esk7_0),esk7_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_27]),c_0_27]) ).
cnf(c_0_38,plain,
( prop(X1) = false
| bool(X1) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_39,plain,
lazy_impl(false,X1) = true,
inference(split_conjunct,[status(thm)],[c_0_29]) ).
fof(c_0_40,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_41,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_42,negated_conjecture,
not1(esk8_0) != not2(esk8_0),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_43,plain,
not2(X1) = impl(X1,false2),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_44,plain,
( not1(X1) = phi(X1)
| bool(X1) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
fof(c_0_45,plain,
! [X19,X20] :
( impl(X19,X20) = phi(X19)
| bool(X19) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_33])]) ).
cnf(c_0_46,plain,
false2 = lazy_impl(true,lazy_impl(prop(esk7_0),esk7_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_35]),c_0_27]) ).
cnf(c_0_47,plain,
( ~ d(X1)
| phi(X1) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_48,plain,
( ~ forallprefers(lazy_impl(prop(X1),X1),true)
| bool(esk7_0) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]) ).
cnf(c_0_49,plain,
( ~ bool(X1)
| prop(X1) = true ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
fof(c_0_50,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_41])])])]) ).
fof(c_0_51,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_52,negated_conjecture,
impl(esk8_0,false2) != not1(esk8_0),
inference(rw,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_53,plain,
( bool(X1)
| not1(X1) = lazy_impl(true,X1) ),
inference(rw,[status(thm)],[c_0_44,c_0_35]) ).
cnf(c_0_54,plain,
( impl(X1,X2) = phi(X1)
| bool(X1) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_55,plain,
( bool(esk7_0)
| lazy_impl(true,true) = false2 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_38]),c_0_39]) ).
cnf(c_0_56,plain,
( ~ d(X1)
| lazy_impl(true,X1) = X1 ),
inference(rw,[status(thm)],[c_0_47,c_0_35]) ).
cnf(c_0_57,plain,
d(true),
inference(split_conjunct,[status(thm)],[false_true_err_in_d]) ).
cnf(c_0_58,plain,
( ~ bool(X1)
| ~ forallprefers(lazy_impl(true,X1),true)
| bool(esk7_0) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_59,plain,
( X2 != true
| X1 != false
| forallprefers(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_60,plain,
( X1 != false
| bool(X1) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_61,negated_conjecture,
( impl(esk8_0,false2) != lazy_impl(true,esk8_0)
| bool(esk8_0) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_62,plain,
( bool(X1)
| impl(X1,X2) = lazy_impl(true,X1) ),
inference(rw,[status(thm)],[c_0_54,c_0_35]) ).
cnf(c_0_63,plain,
( ~ bool(esk7_0)
| lazy_impl(true,lazy_impl(true,esk7_0)) = false2 ),
inference(spm,[status(thm)],[c_0_46,c_0_49]) ).
cnf(c_0_64,plain,
( bool(esk7_0)
| false2 = true ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_57])]) ).
cnf(c_0_65,plain,
( ~ bool(X1)
| ~ d(X1)
| ~ forallprefers(X1,true)
| bool(esk7_0) ),
inference(spm,[status(thm)],[c_0_58,c_0_56]) ).
cnf(c_0_66,plain,
forallprefers(false,true),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_59])]) ).
cnf(c_0_67,plain,
d(false),
inference(split_conjunct,[status(thm)],[false_true_err_in_d]) ).
cnf(c_0_68,plain,
bool(false),
inference(er,[status(thm)],[c_0_60]) ).
cnf(c_0_69,plain,
( ~ bool(X1)
| X1 = true
| X1 = false ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_70,negated_conjecture,
bool(esk8_0),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_71,plain,
( false2 = true
| lazy_impl(true,lazy_impl(true,esk7_0)) = false2 ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_72,plain,
bool(esk7_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_67]),c_0_68])]) ).
cnf(c_0_73,negated_conjecture,
( esk8_0 = false
| esk8_0 = true ),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_74,plain,
not1(false) = true,
inference(split_conjunct,[status(thm)],[not1_axiom2]) ).
fof(c_0_75,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_76,plain,
( ~ d(esk7_0)
| false2 = true
| lazy_impl(true,esk7_0) = false2 ),
inference(spm,[status(thm)],[c_0_71,c_0_56]) ).
cnf(c_0_77,plain,
( esk7_0 = false
| esk7_0 = true ),
inference(spm,[status(thm)],[c_0_69,c_0_72]) ).
cnf(c_0_78,negated_conjecture,
( impl(false,false2) != true
| esk8_0 = true ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_73]),c_0_74]) ).
cnf(c_0_79,plain,
( ~ bool(X1)
| impl(false,X1) = true ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_80,plain,
( false2 = true
| esk7_0 = true
| lazy_impl(true,false) = false2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_67])]) ).
cnf(c_0_81,negated_conjecture,
( ~ bool(false2)
| esk8_0 = true ),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_82,plain,
( false2 = false
| esk7_0 = true
| false2 = true ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_80]),c_0_67])]) ).
cnf(c_0_83,negated_conjecture,
( esk8_0 = true
| false2 = true
| esk7_0 = true ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_68])]) ).
cnf(c_0_84,plain,
not1(true) = false,
inference(split_conjunct,[status(thm)],[not1_axiom3]) ).
fof(c_0_85,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])])]) ).
fof(c_0_86,plain,
( false != err
& true != err
& true != false ),
inference(fof_simplification,[status(thm)],[distinct_false_true_err]) ).
cnf(c_0_87,plain,
lazy_impl(true,lazy_impl(true,esk7_0)) = false2,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_63,c_0_72])]) ).
cnf(c_0_88,negated_conjecture,
( impl(true,false2) != false
| esk7_0 = true
| false2 = true ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_83]),c_0_84]) ).
cnf(c_0_89,plain,
( ~ bool(X1)
| impl(true,X1) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_85]) ).
fof(c_0_90,plain,
( false != err
& true != err
& true != false ),
inference(fof_nnf,[status(thm)],[c_0_86]) ).
cnf(c_0_91,plain,
( ~ d(esk7_0)
| lazy_impl(true,esk7_0) = false2 ),
inference(spm,[status(thm)],[c_0_87,c_0_56]) ).
cnf(c_0_92,negated_conjecture,
( ~ bool(false2)
| false2 = true
| esk7_0 = true ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_69]) ).
cnf(c_0_93,plain,
true != false,
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_94,plain,
( esk7_0 = true
| lazy_impl(true,false) = false2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_77]),c_0_67])]) ).
cnf(c_0_95,negated_conjecture,
( esk7_0 = true
| false2 = true ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_82]),c_0_68])]),c_0_93]) ).
cnf(c_0_96,plain,
( false2 = false
| esk7_0 = true ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_94]),c_0_67])]) ).
cnf(c_0_97,negated_conjecture,
esk7_0 = true,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_93]) ).
cnf(c_0_98,plain,
lazy_impl(true,true) = false2,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_91,c_0_97]),c_0_97]),c_0_57])]) ).
cnf(c_0_99,plain,
false2 = true,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_98]),c_0_57])]) ).
cnf(c_0_100,plain,
( X1 != true
| bool(X1) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_101,negated_conjecture,
~ forallprefers(lazy_impl(prop(X1),X1),lazy_impl(prop(true),true)),
inference(spm,[status(thm)],[c_0_37,c_0_97]) ).
cnf(c_0_102,plain,
lazy_impl(true,true) = true,
inference(rw,[status(thm)],[c_0_98,c_0_99]) ).
cnf(c_0_103,plain,
bool(true),
inference(er,[status(thm)],[c_0_100]) ).
cnf(c_0_104,negated_conjecture,
~ forallprefers(lazy_impl(prop(X1),X1),true),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_49]),c_0_102]),c_0_103])]) ).
cnf(c_0_105,negated_conjecture,
( ~ bool(X1)
| ~ forallprefers(lazy_impl(true,X1),true) ),
inference(spm,[status(thm)],[c_0_104,c_0_49]) ).
cnf(c_0_106,negated_conjecture,
( ~ bool(X1)
| ~ d(X1)
| ~ forallprefers(X1,true) ),
inference(spm,[status(thm)],[c_0_105,c_0_56]) ).
cnf(c_0_107,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_66]),c_0_67]),c_0_68])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW102+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.35 % Computer : n002.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Mon Sep 21 09:41:47 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 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
% 0.14/0.44 % Version: 3.5.1
% 0.14/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.44 % Starting sh5l with 300s (1) cores
% 0.14/0.44 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2991890 completed with status 0
% 0.14/0.44 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.14/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.44 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/0.44 % No SInE strategy applied
% 0.14/0.44 % Search class: FGHSS-FFMM21-DFFFFFNN
% 0.14/0.44 % partial match(1): FGHSS-FFMM21-SFFFFFNN
% 0.14/0.44 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.44 % Starting SubtermCWHack with 136s (1) cores
% 0.14/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.14/0.44 % Starting G-E--_208_B07_F1_SE_CS_SP_PS_S4d with 136s (1) cores
% 0.14/0.44 % Starting new_bool_3 with 136s (1) cores
% 0.14/0.44 % Starting new_bool_1 with 136s (1) cores
% 0.14/0.44 % new_bool_3 with pid 2991903 completed with status 0
% 0.14/0.44 % Result found by new_bool_3
% 0.14/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.44 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/0.44 % No SInE strategy applied
% 0.14/0.44 % Search class: FGHSS-FFMM21-DFFFFFNN
% 0.14/0.44 % partial match(1): FGHSS-FFMM21-SFFFFFNN
% 0.14/0.44 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.44 % Starting SubtermCWHack with 136s (1) cores
% 0.14/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.14/0.44 % Starting G-E--_208_B07_F1_SE_CS_SP_PS_S4d with 136s (1) cores
% 0.14/0.44 % Starting new_bool_3 with 136s (1) cores
% 0.14/0.44 % Preprocessing time : 0.001 s
% 0.14/0.44 % Presaturation interreduction done
% 0.14/0.44
% 0.14/0.44 % Proof found!
% 0.14/0.44 % SZS status Theorem
% 0.14/0.44 % SZS output start CNFRefutation
% See solution above
% 0.14/0.44 % Parsed axioms : 45
% 0.14/0.44 % Removed by relevancy pruning/SinE : 0
% 0.14/0.44 % Initial clauses : 99
% 0.14/0.44 % Removed in clause preprocessing : 19
% 0.14/0.44 % Initial clauses in saturation : 80
% 0.14/0.44 % Processed clauses : 206
% 0.14/0.44 % ...of these trivial : 3
% 0.14/0.44 % ...subsumed : 27
% 0.14/0.44 % ...remaining for further processing : 176
% 0.14/0.44 % Other redundant clauses eliminated : 8
% 0.14/0.44 % Clauses deleted for lack of memory : 0
% 0.14/0.44 % Backward-subsumed : 11
% 0.14/0.44 % Backward-rewritten : 27
% 0.14/0.44 % Generated clauses : 245
% 0.14/0.44 % ...of the previous two non-redundant : 197
% 0.14/0.44 % ...aggressively subsumed : 0
% 0.14/0.44 % Contextual simplify-reflections : 3
% 0.14/0.44 % Paramodulations : 234
% 0.14/0.44 % Factorizations : 5
% 0.14/0.44 % NegExts : 0
% 0.14/0.44 % Equation resolutions : 8
% 0.14/0.44 % Disequality decompositions : 0
% 0.14/0.44 % Total rewrite steps : 136
% 0.14/0.44 % ...of those cached : 108
% 0.14/0.44 % Propositional unsat checks : 0
% 0.14/0.44 % Propositional check models : 0
% 0.14/0.44 % Propositional check unsatisfiable : 0
% 0.14/0.44 % Propositional clauses : 0
% 0.14/0.44 % Propositional clauses after purity: 0
% 0.14/0.44 % Propositional unsat core size : 0
% 0.14/0.44 % Propositional preprocessing time : 0.000
% 0.14/0.44 % Propositional encoding time : 0.000
% 0.14/0.44 % Propositional solver time : 0.000
% 0.14/0.44 % Success case prop preproc time : 0.000
% 0.14/0.44 % Success case prop encoding time : 0.000
% 0.14/0.44 % Success case prop solver time : 0.000
% 0.14/0.44 % Current number of processed clauses : 70
% 0.14/0.44 % Positive orientable unit clauses : 19
% 0.14/0.44 % Positive unorientable unit clauses: 0
% 0.14/0.44 % Negative unit clauses : 14
% 0.14/0.44 % Non-unit-clauses : 37
% 0.14/0.44 % Current number of unprocessed clauses: 113
% 0.14/0.44 % ...number of literals in the above : 244
% 0.14/0.44 % Current number of archived formulas : 0
% 0.14/0.44 % Current number of archived clauses : 116
% 0.14/0.44 % Clause-clause subsumption calls (NU) : 610
% 0.14/0.44 % Rec. Clause-clause subsumption calls : 443
% 0.14/0.44 % Non-unit clause-clause subsumptions : 29
% 0.14/0.44 % Unit Clause-clause subsumption calls : 71
% 0.14/0.44 % Rewrite failures with RHS unbound : 0
% 0.14/0.44 % BW rewrite match attempts : 6
% 0.14/0.44 % BW rewrite match successes : 6
% 0.14/0.44 % Condensation attempts : 0
% 0.14/0.44 % Condensation successes : 0
% 0.14/0.44 % Termbank termtop insertions : 8022
% 0.14/0.44 % Search garbage collected termcells : 703
% 0.14/0.44
% 0.14/0.44 % -------------------------------------------------
% 0.14/0.44 % User time : 0.018 s
% 0.14/0.44 % System time : 0.003 s
% 0.14/0.44 % Total time : 0.021 s
% 0.14/0.44 % Maximum resident set size: 3636 pages
% 0.14/0.44
% 0.14/0.44 % -------------------------------------------------
% 0.14/0.44 % User time : 0.054 s
% 0.14/0.44 % System time : 0.023 s
% 0.14/0.44 % Total time : 0.077 s
% 0.14/0.44 % Maximum resident set size: 4864 pages
% 0.14/0.44 % E exiting
%------------------------------------------------------------------------------