%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP021+2 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 12:53:50 PM UTC 2026
% Result : Theorem 0.38s 0.49s
% Output : CNFRefutation 0.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 13
% Syntax : Number of formulae : 75 ( 27 unt; 0 def)
% Number of atoms : 219 ( 42 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 233 ( 89 ~; 108 |; 11 &)
% ( 3 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 83 ( 0 sgn 38 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ap_tp,axiom,
! [X1,X2,X3] :
( mem(X3,arr(X1,X2))
=> ! [X4] :
( mem(X4,X1)
=> mem(ap(X3,X4),X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/ITP001/ITP001+2.ax',ap_tp) ).
fof(ax_false_p,axiom,
~ p(c_2Ebool_2EF),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_false_p) ).
fof(conj_thm_2Eextreal_2Emax__le,conjecture,
! [X22] :
( mem(X22,ty_2Eextreal_2Eextreal)
=> ! [X23] :
( mem(X23,ty_2Eextreal_2Eextreal)
=> ! [X24] :
( mem(X24,ty_2Eextreal_2Eextreal)
=> ( p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__max,X23),X24)),X22))
<=> ( p(ap(ap(c_2Eextreal_2Eextreal__le,X24),X22))
& p(ap(ap(c_2Eextreal_2Eextreal__le,X23),X22)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Eextreal_2Emax__le) ).
fof(boolext,axiom,
! [X5] :
( mem(X5,bool)
=> ! [X6] :
( mem(X6,bool)
=> ( ( p(X5)
<=> p(X6) )
=> X5 = X6 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/ITP001/ITP001+2.ax',boolext) ).
fof(mem_c_2Eextreal_2Eextreal__le,axiom,
mem(c_2Eextreal_2Eextreal__le,arr(ty_2Eextreal_2Eextreal,arr(ty_2Eextreal_2Eextreal,bool))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Eextreal_2Eextreal__le) ).
fof(conj_thm_2Eextreal_2Ele__total,axiom,
! [X13] :
( mem(X13,ty_2Eextreal_2Eextreal)
=> ! [X14] :
( mem(X14,ty_2Eextreal_2Eextreal)
=> ( p(ap(ap(c_2Eextreal_2Eextreal__le,X14),X13))
| p(ap(ap(c_2Eextreal_2Eextreal__le,X13),X14)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Eextreal_2Ele__total) ).
fof(mem_c_2Ebool_2ET,axiom,
mem(c_2Ebool_2ET,bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Ebool_2ET) ).
fof(ax_true_p,axiom,
p(c_2Ebool_2ET),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_true_p) ).
fof(mem_c_2Ebool_2EF,axiom,
mem(c_2Ebool_2EF,bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Ebool_2EF) ).
fof(conj_thm_2Eextreal_2Ele__trans,axiom,
! [X13] :
( mem(X13,ty_2Eextreal_2Eextreal)
=> ! [X14] :
( mem(X14,ty_2Eextreal_2Eextreal)
=> ! [X18] :
( mem(X18,ty_2Eextreal_2Eextreal)
=> ( ( p(ap(ap(c_2Eextreal_2Eextreal__le,X14),X18))
& p(ap(ap(c_2Eextreal_2Eextreal__le,X13),X14)) )
=> p(ap(ap(c_2Eextreal_2Eextreal__le,X13),X18)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Eextreal_2Ele__trans) ).
fof(ax_thm_2Eextreal_2Eextreal__max__def,axiom,
! [X13] :
( mem(X13,ty_2Eextreal_2Eextreal)
=> ! [X14] :
( mem(X14,ty_2Eextreal_2Eextreal)
=> ap(ap(c_2Eextreal_2Eextreal__max,X13),X14) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),ap(ap(c_2Eextreal_2Eextreal__le,X13),X14)),X14),X13) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_thm_2Eextreal_2Eextreal__max__def) ).
fof(conj_thm_2Ebool_2ECOND__CLAUSES,axiom,
! [X9] :
( ne(X9)
=> ! [X10] :
( mem(X10,X9)
=> ! [X11] :
( mem(X11,X9)
=> ( ap(ap(ap(c_2Ebool_2ECOND(X9),c_2Ebool_2EF),X10),X11) = X11
& ap(ap(ap(c_2Ebool_2ECOND(X9),c_2Ebool_2ET),X10),X11) = X10 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Ebool_2ECOND__CLAUSES) ).
fof(ne_ty_2Eextreal_2Eextreal,axiom,
ne(ty_2Eextreal_2Eextreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ne_ty_2Eextreal_2Eextreal) ).
fof(c_0_13,plain,
! [X62,X63,X64,X65] :
( mem(ap(X64,X65),X63)
| ~ mem(X65,X62)
| ~ mem(X64,arr(X62,X63)) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ap_tp])])])]) ).
fof(c_0_14,plain,
~ p(c_2Ebool_2EF),
inference(fof_simplification,[status(thm)],[ax_false_p]) ).
fof(c_0_15,negated_conjecture,
~ ! [X22] :
( mem(X22,ty_2Eextreal_2Eextreal)
=> ! [X23] :
( mem(X23,ty_2Eextreal_2Eextreal)
=> ! [X24] :
( mem(X24,ty_2Eextreal_2Eextreal)
=> ( p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__max,X23),X24)),X22))
<=> ( p(ap(ap(c_2Eextreal_2Eextreal__le,X24),X22))
& p(ap(ap(c_2Eextreal_2Eextreal__le,X23),X22)) ) ) ) ) ),
inference(assume_negation,[status(cth)],[conj_thm_2Eextreal_2Emax__le]) ).
fof(c_0_16,plain,
! [X28,X29] :
( ( ~ mem(X28,bool)
| ~ mem(X29,bool)
| X28 = X29
| p(X29)
| p(X28) )
& ( ~ mem(X28,bool)
| ~ mem(X29,bool)
| X28 = X29
| ~ p(X29)
| ~ p(X28) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[boolext])])])])]) ).
cnf(c_0_17,plain,
( ~ mem(X4,X2)
| ~ mem(X1,arr(X2,X3))
| mem(ap(X1,X4),X3) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,plain,
mem(c_2Eextreal_2Eextreal__le,arr(ty_2Eextreal_2Eextreal,arr(ty_2Eextreal_2Eextreal,bool))),
inference(split_conjunct,[status(thm)],[mem_c_2Eextreal_2Eextreal__le]) ).
fof(c_0_19,plain,
~ p(c_2Ebool_2EF),
inference(fof_nnf,[status(thm)],[c_0_14]) ).
fof(c_0_20,plain,
! [X74,X75] :
( p(ap(ap(c_2Eextreal_2Eextreal__le,X75),X74))
| p(ap(ap(c_2Eextreal_2Eextreal__le,X74),X75))
| ~ mem(X75,ty_2Eextreal_2Eextreal)
| ~ mem(X74,ty_2Eextreal_2Eextreal) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_thm_2Eextreal_2Ele__total])])])]) ).
fof(c_0_21,negated_conjecture,
( ( p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__max,esk2_0),esk3_0)),esk1_0))
| p(ap(ap(c_2Eextreal_2Eextreal__le,esk3_0),esk1_0)) )
& ( p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__max,esk2_0),esk3_0)),esk1_0))
| p(ap(ap(c_2Eextreal_2Eextreal__le,esk2_0),esk1_0)) )
& ( ~ p(ap(ap(c_2Eextreal_2Eextreal__le,esk3_0),esk1_0))
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,esk2_0),esk1_0))
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__max,esk2_0),esk3_0)),esk1_0)) )
& mem(esk3_0,ty_2Eextreal_2Eextreal)
& mem(esk2_0,ty_2Eextreal_2Eextreal)
& mem(esk1_0,ty_2Eextreal_2Eextreal) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])])])]) ).
cnf(c_0_22,plain,
( ~ mem(X1,bool)
| ~ mem(X2,bool)
| ~ p(X2)
| ~ p(X1)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,plain,
mem(c_2Ebool_2ET,bool),
inference(split_conjunct,[status(thm)],[mem_c_2Ebool_2ET]) ).
cnf(c_0_24,plain,
p(c_2Ebool_2ET),
inference(split_conjunct,[status(thm)],[ax_true_p]) ).
cnf(c_0_25,plain,
( ~ mem(X1,ty_2Eextreal_2Eextreal)
| mem(ap(c_2Eextreal_2Eextreal__le,X1),arr(ty_2Eextreal_2Eextreal,bool)) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_26,plain,
( ~ mem(X1,bool)
| ~ mem(X2,bool)
| X1 = X2
| p(X2)
| p(X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_27,plain,
mem(c_2Ebool_2EF,bool),
inference(split_conjunct,[status(thm)],[mem_c_2Ebool_2EF]) ).
cnf(c_0_28,plain,
~ p(c_2Ebool_2EF),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_29,plain,
( ~ mem(X2,ty_2Eextreal_2Eextreal)
| ~ mem(X1,ty_2Eextreal_2Eextreal)
| p(ap(ap(c_2Eextreal_2Eextreal__le,X2),X1))
| p(ap(ap(c_2Eextreal_2Eextreal__le,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_30,negated_conjecture,
mem(esk2_0,ty_2Eextreal_2Eextreal),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_31,plain,
( ~ mem(X1,bool)
| ~ p(X1)
| X1 = c_2Ebool_2ET ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24])]) ).
cnf(c_0_32,plain,
( ~ mem(X1,ty_2Eextreal_2Eextreal)
| ~ mem(X2,ty_2Eextreal_2Eextreal)
| mem(ap(ap(c_2Eextreal_2Eextreal__le,X1),X2),bool) ),
inference(spm,[status(thm)],[c_0_17,c_0_25]) ).
cnf(c_0_33,plain,
( ~ mem(X1,bool)
| p(X1)
| X1 = c_2Ebool_2EF ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]) ).
cnf(c_0_34,negated_conjecture,
mem(esk3_0,ty_2Eextreal_2Eextreal),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_35,plain,
! [X71,X72,X73] :
( p(ap(ap(c_2Eextreal_2Eextreal__le,X71),X73))
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,X72),X73))
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,X71),X72))
| ~ mem(X73,ty_2Eextreal_2Eextreal)
| ~ mem(X72,ty_2Eextreal_2Eextreal)
| ~ mem(X71,ty_2Eextreal_2Eextreal) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_thm_2Eextreal_2Ele__trans])])])]) ).
cnf(c_0_36,negated_conjecture,
( ~ mem(X1,ty_2Eextreal_2Eextreal)
| p(ap(ap(c_2Eextreal_2Eextreal__le,X1),esk2_0))
| p(ap(ap(c_2Eextreal_2Eextreal__le,esk2_0),X1)) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
fof(c_0_37,plain,
! [X76,X77] :
( ap(ap(c_2Eextreal_2Eextreal__max,X76),X77) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),ap(ap(c_2Eextreal_2Eextreal__le,X76),X77)),X77),X76)
| ~ mem(X77,ty_2Eextreal_2Eextreal)
| ~ mem(X76,ty_2Eextreal_2Eextreal) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax_thm_2Eextreal_2Eextreal__max__def])])])]) ).
cnf(c_0_38,plain,
( ~ mem(X1,ty_2Eextreal_2Eextreal)
| ~ mem(X2,ty_2Eextreal_2Eextreal)
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,X1),X2))
| ap(ap(c_2Eextreal_2Eextreal__le,X1),X2) = c_2Ebool_2ET ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_39,plain,
( ~ mem(X1,ty_2Eextreal_2Eextreal)
| ~ mem(X2,ty_2Eextreal_2Eextreal)
| p(ap(ap(c_2Eextreal_2Eextreal__le,X1),X2))
| ap(ap(c_2Eextreal_2Eextreal__le,X1),X2) = c_2Ebool_2EF ),
inference(spm,[status(thm)],[c_0_33,c_0_32]) ).
cnf(c_0_40,negated_conjecture,
( ~ mem(X1,ty_2Eextreal_2Eextreal)
| p(ap(ap(c_2Eextreal_2Eextreal__le,X1),esk3_0))
| p(ap(ap(c_2Eextreal_2Eextreal__le,esk3_0),X1)) ),
inference(spm,[status(thm)],[c_0_29,c_0_34]) ).
cnf(c_0_41,negated_conjecture,
mem(esk1_0,ty_2Eextreal_2Eextreal),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_42,plain,
( ~ p(ap(ap(c_2Eextreal_2Eextreal__le,X2),X3))
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,X1),X2))
| ~ mem(X3,ty_2Eextreal_2Eextreal)
| ~ mem(X2,ty_2Eextreal_2Eextreal)
| ~ mem(X1,ty_2Eextreal_2Eextreal)
| p(ap(ap(c_2Eextreal_2Eextreal__le,X1),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_43,negated_conjecture,
p(ap(ap(c_2Eextreal_2Eextreal__le,esk2_0),esk2_0)),
inference(spm,[status(thm)],[c_0_36,c_0_30]) ).
fof(c_0_44,plain,
! [X81,X82,X83] :
( ( ~ ne(X81)
| ~ mem(X82,X81)
| ~ mem(X83,X81)
| ap(ap(ap(c_2Ebool_2ECOND(X81),c_2Ebool_2EF),X82),X83) = X83 )
& ( ~ ne(X81)
| ~ mem(X82,X81)
| ~ mem(X83,X81)
| ap(ap(ap(c_2Ebool_2ECOND(X81),c_2Ebool_2ET),X82),X83) = X82 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_thm_2Ebool_2ECOND__CLAUSES])])])])]) ).
cnf(c_0_45,plain,
( ~ mem(X2,ty_2Eextreal_2Eextreal)
| ~ mem(X1,ty_2Eextreal_2Eextreal)
| ap(ap(c_2Eextreal_2Eextreal__max,X1),X2) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),ap(ap(c_2Eextreal_2Eextreal__le,X1),X2)),X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_46,plain,
( ~ mem(X1,ty_2Eextreal_2Eextreal)
| ~ mem(X2,ty_2Eextreal_2Eextreal)
| ap(ap(c_2Eextreal_2Eextreal__le,X1),X2) = c_2Ebool_2ET
| ap(ap(c_2Eextreal_2Eextreal__le,X1),X2) = c_2Ebool_2EF ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_47,negated_conjecture,
( p(ap(ap(c_2Eextreal_2Eextreal__le,esk3_0),esk1_0))
| p(ap(ap(c_2Eextreal_2Eextreal__le,esk1_0),esk3_0)) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_48,plain,
( ~ mem(X3,ty_2Eextreal_2Eextreal)
| ~ mem(X1,ty_2Eextreal_2Eextreal)
| ~ mem(X2,ty_2Eextreal_2Eextreal)
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,X3),X1))
| p(ap(ap(c_2Eextreal_2Eextreal__le,X3),X2))
| ap(ap(c_2Eextreal_2Eextreal__le,X1),X2) = c_2Ebool_2EF ),
inference(spm,[status(thm)],[c_0_42,c_0_39]) ).
cnf(c_0_49,negated_conjecture,
ap(ap(c_2Eextreal_2Eextreal__le,esk2_0),esk2_0) = c_2Ebool_2ET,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_43]),c_0_30])]) ).
cnf(c_0_50,plain,
( ~ ne(X1)
| ~ mem(X2,X1)
| ~ mem(X3,X1)
| ap(ap(ap(c_2Ebool_2ECOND(X1),c_2Ebool_2EF),X2),X3) = X3 ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_51,plain,
( ~ mem(X2,ty_2Eextreal_2Eextreal)
| ~ mem(X1,ty_2Eextreal_2Eextreal)
| ap(ap(c_2Eextreal_2Eextreal__le,X2),X1) = c_2Ebool_2ET
| ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2EF),X1),X2) = ap(ap(c_2Eextreal_2Eextreal__max,X2),X1) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_52,plain,
ne(ty_2Eextreal_2Eextreal),
inference(split_conjunct,[status(thm)],[ne_ty_2Eextreal_2Eextreal]) ).
cnf(c_0_53,negated_conjecture,
( p(ap(ap(c_2Eextreal_2Eextreal__le,esk1_0),esk3_0))
| ap(ap(c_2Eextreal_2Eextreal__le,esk3_0),esk1_0) = c_2Ebool_2ET ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_47]),c_0_41]),c_0_34])]) ).
cnf(c_0_54,negated_conjecture,
( ~ mem(X1,ty_2Eextreal_2Eextreal)
| p(ap(ap(c_2Eextreal_2Eextreal__le,esk2_0),X1))
| ap(ap(c_2Eextreal_2Eextreal__le,esk2_0),X1) = c_2Ebool_2EF ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_24]),c_0_30])]) ).
cnf(c_0_55,negated_conjecture,
( p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__max,esk2_0),esk3_0)),esk1_0))
| p(ap(ap(c_2Eextreal_2Eextreal__le,esk2_0),esk1_0)) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_56,plain,
( ~ mem(X2,ty_2Eextreal_2Eextreal)
| ~ mem(X1,ty_2Eextreal_2Eextreal)
| ap(ap(c_2Eextreal_2Eextreal__max,X1),X2) = X1
| ap(ap(c_2Eextreal_2Eextreal__le,X1),X2) = c_2Ebool_2ET ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52])]) ).
cnf(c_0_57,negated_conjecture,
( ~ mem(X1,ty_2Eextreal_2Eextreal)
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,X1),esk1_0))
| p(ap(ap(c_2Eextreal_2Eextreal__le,X1),esk3_0))
| ap(ap(c_2Eextreal_2Eextreal__le,esk3_0),esk1_0) = c_2Ebool_2ET ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_53]),c_0_34]),c_0_41])]) ).
cnf(c_0_58,negated_conjecture,
( ~ mem(X1,ty_2Eextreal_2Eextreal)
| ap(ap(c_2Eextreal_2Eextreal__le,esk2_0),X1) = c_2Ebool_2ET
| ap(ap(c_2Eextreal_2Eextreal__le,esk2_0),X1) = c_2Ebool_2EF ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_54]),c_0_30])]) ).
cnf(c_0_59,negated_conjecture,
( ~ p(ap(ap(c_2Eextreal_2Eextreal__le,esk3_0),esk1_0))
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,esk2_0),esk1_0))
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__max,esk2_0),esk3_0)),esk1_0)) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_60,negated_conjecture,
( p(ap(ap(c_2Eextreal_2Eextreal__le,esk2_0),esk1_0))
| ap(ap(c_2Eextreal_2Eextreal__le,esk2_0),esk3_0) = c_2Ebool_2ET ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_30]),c_0_34])]) ).
cnf(c_0_61,negated_conjecture,
( ~ p(ap(ap(c_2Eextreal_2Eextreal__le,esk2_0),esk1_0))
| ap(ap(c_2Eextreal_2Eextreal__le,esk3_0),esk1_0) = c_2Ebool_2ET
| ap(ap(c_2Eextreal_2Eextreal__le,esk2_0),esk3_0) = c_2Ebool_2ET ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_30]),c_0_34])]),c_0_28]) ).
cnf(c_0_62,negated_conjecture,
( ~ p(ap(ap(c_2Eextreal_2Eextreal__le,esk3_0),esk1_0))
| ap(ap(c_2Eextreal_2Eextreal__le,esk2_0),esk3_0) = c_2Ebool_2ET ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_56]),c_0_30]),c_0_34])]),c_0_60]) ).
cnf(c_0_63,negated_conjecture,
( ap(ap(c_2Eextreal_2Eextreal__le,esk2_0),esk3_0) = c_2Ebool_2ET
| ap(ap(c_2Eextreal_2Eextreal__le,esk3_0),esk1_0) = c_2Ebool_2ET ),
inference(spm,[status(thm)],[c_0_61,c_0_60]) ).
cnf(c_0_64,negated_conjecture,
ap(ap(c_2Eextreal_2Eextreal__le,esk2_0),esk3_0) = c_2Ebool_2ET,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_24])]) ).
cnf(c_0_65,plain,
( ~ ne(X1)
| ~ mem(X2,X1)
| ~ mem(X3,X1)
| ap(ap(ap(c_2Ebool_2ECOND(X1),c_2Ebool_2ET),X2),X3) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_66,negated_conjecture,
ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2ET),esk3_0),esk2_0) = ap(ap(c_2Eextreal_2Eextreal__max,esk2_0),esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_64]),c_0_34]),c_0_30])]) ).
cnf(c_0_67,negated_conjecture,
( p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__max,esk2_0),esk3_0)),esk1_0))
| p(ap(ap(c_2Eextreal_2Eextreal__le,esk3_0),esk1_0)) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_68,negated_conjecture,
ap(ap(c_2Eextreal_2Eextreal__max,esk2_0),esk3_0) = esk3_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_30]),c_0_34]),c_0_52])]) ).
cnf(c_0_69,negated_conjecture,
p(ap(ap(c_2Eextreal_2Eextreal__le,esk3_0),esk1_0)),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_70,negated_conjecture,
ap(ap(c_2Eextreal_2Eextreal__le,esk3_0),esk1_0) = c_2Ebool_2ET,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_69]),c_0_41]),c_0_34])]) ).
cnf(c_0_71,negated_conjecture,
~ p(ap(ap(c_2Eextreal_2Eextreal__le,esk2_0),esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_59,c_0_68]),c_0_69]),c_0_69])]) ).
cnf(c_0_72,negated_conjecture,
( ~ mem(X1,ty_2Eextreal_2Eextreal)
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,X1),esk3_0))
| p(ap(ap(c_2Eextreal_2Eextreal__le,X1),esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_70]),c_0_24]),c_0_41]),c_0_34])]) ).
cnf(c_0_73,negated_conjecture,
ap(ap(c_2Eextreal_2Eextreal__le,esk2_0),esk1_0) = c_2Ebool_2EF,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_54]),c_0_41])]) ).
cnf(c_0_74,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_64]),c_0_73]),c_0_24]),c_0_30])]),c_0_28]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP021+2 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n018.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 20 21:55:15 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 0.38/0.49 % Version: 3.5.1
% 0.38/0.49 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.38/0.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.38/0.49 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.38/0.49 % Starting new_bool_3 with 300s (1) cores
% 0.38/0.49 % Starting new_bool_1 with 300s (1) cores
% 0.38/0.49 % Starting sh5l with 300s (1) cores
% 0.38/0.49 % new_bool_3 with pid 253325 completed with status 0
% 0.38/0.49 % Result found by new_bool_3
% 0.38/0.49 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.38/0.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.38/0.49 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.38/0.49 % Starting new_bool_3 with 300s (1) cores
% 0.38/0.49 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.38/0.49 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.38/0.49 % Search class: FGHSF-FFMM32-MFFFFFNN
% 0.38/0.49 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.38/0.49 % Starting SubtermCWHack with 31s (1) cores
% 0.38/0.49 % SubtermCWHack with pid 253333 completed with status 0
% 0.38/0.49 % Result found by SubtermCWHack
% 0.38/0.49 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.38/0.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.38/0.49 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.38/0.49 % Starting new_bool_3 with 300s (1) cores
% 0.38/0.49 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.38/0.49 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.38/0.49 % Search class: FGHSF-FFMM32-MFFFFFNN
% 0.38/0.49 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.38/0.49 % Starting SubtermCWHack with 31s (1) cores
% 0.38/0.49 % Preprocessing time : 0.002 s
% 0.38/0.49
% 0.38/0.49 % Proof found!
% 0.38/0.49 % SZS status Theorem
% 0.38/0.49 % SZS output start CNFRefutation
% See solution above
% 0.38/0.49 % Parsed axioms : 56
% 0.38/0.49 % Removed by relevancy pruning/SinE : 16
% 0.38/0.49 % Initial clauses : 307
% 0.38/0.49 % Removed in clause preprocessing : 252
% 0.38/0.49 % Initial clauses in saturation : 55
% 0.38/0.49 % Processed clauses : 500
% 0.38/0.49 % ...of these trivial : 4
% 0.38/0.49 % ...subsumed : 247
% 0.38/0.49 % ...remaining for further processing : 249
% 0.38/0.49 % Other redundant clauses eliminated : 0
% 0.38/0.49 % Clauses deleted for lack of memory : 0
% 0.38/0.49 % Backward-subsumed : 60
% 0.38/0.49 % Backward-rewritten : 72
% 0.38/0.49 % Generated clauses : 1740
% 0.38/0.49 % ...of the previous two non-redundant : 1180
% 0.38/0.49 % ...aggressively subsumed : 0
% 0.38/0.49 % Contextual simplify-reflections : 3
% 0.38/0.49 % Paramodulations : 1730
% 0.38/0.49 % Factorizations : 4
% 0.38/0.49 % NegExts : 0
% 0.38/0.49 % Equation resolutions : 1
% 0.38/0.49 % Disequality decompositions : 0
% 0.38/0.49 % Total rewrite steps : 2971
% 0.38/0.49 % ...of those cached : 2942
% 0.38/0.49 % Propositional unsat checks : 0
% 0.38/0.49 % Propositional check models : 0
% 0.38/0.49 % Propositional check unsatisfiable : 0
% 0.38/0.49 % Propositional clauses : 0
% 0.38/0.49 % Propositional clauses after purity: 0
% 0.38/0.49 % Propositional unsat core size : 0
% 0.38/0.49 % Propositional preprocessing time : 0.000
% 0.38/0.49 % Propositional encoding time : 0.000
% 0.38/0.49 % Propositional solver time : 0.000
% 0.38/0.49 % Success case prop preproc time : 0.000
% 0.38/0.49 % Success case prop encoding time : 0.000
% 0.38/0.49 % Success case prop solver time : 0.000
% 0.38/0.49 % Current number of processed clauses : 112
% 0.38/0.49 % Positive orientable unit clauses : 37
% 0.38/0.49 % Positive unorientable unit clauses: 0
% 0.38/0.49 % Negative unit clauses : 2
% 0.38/0.49 % Non-unit-clauses : 73
% 0.38/0.49 % Current number of unprocessed clauses: 660
% 0.38/0.49 % ...number of literals in the above : 3338
% 0.38/0.49 % Current number of archived formulas : 0
% 0.38/0.49 % Current number of archived clauses : 137
% 0.38/0.49 % Clause-clause subsumption calls (NU) : 3213
% 0.38/0.49 % Rec. Clause-clause subsumption calls : 1044
% 0.38/0.49 % Non-unit clause-clause subsumptions : 241
% 0.38/0.49 % Unit Clause-clause subsumption calls : 265
% 0.38/0.49 % Rewrite failures with RHS unbound : 0
% 0.38/0.49 % BW rewrite match attempts : 42
% 0.38/0.49 % BW rewrite match successes : 21
% 0.38/0.49 % Condensation attempts : 0
% 0.38/0.49 % Condensation successes : 0
% 0.38/0.49 % Termbank termtop insertions : 54015
% 0.38/0.49 % Search garbage collected termcells : 3426
% 0.38/0.49
% 0.38/0.49 % -------------------------------------------------
% 0.38/0.49 % User time : 0.055 s
% 0.38/0.49 % System time : 0.008 s
% 0.38/0.49 % Total time : 0.062 s
% 0.38/0.49 % Maximum resident set size: 4232 pages
% 0.38/0.49
% 0.38/0.49 % -------------------------------------------------
% 0.38/0.49 % User time : 0.058 s
% 0.38/0.49 % System time : 0.013 s
% 0.38/0.49 % Total time : 0.071 s
% 0.38/0.49 % Maximum resident set size: 4864 pages
% 0.38/0.49 % E exiting
%------------------------------------------------------------------------------