%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : ITP021+2 : TPTP v9.2.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n018.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 5 04:32:42 PM UTC 2026
% Result : Theorem 11.59s 7.49s
% Output : CNFRefutation 11.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 19
% Syntax : Number of formulae : 137 ( 38 unt; 0 def)
% Number of atoms : 408 ( 81 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 446 ( 175 ~; 223 |; 14 &)
% ( 6 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 10 con; 0-2 aty)
% Number of variables : 125 ( 0 sgn 49 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(ax_false_p,axiom,
~ p(c_2Ebool_2EF),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_false_p) ).
fof(ax_all_p,axiom,
! [X1] :
( ne(X1)
=> ! [X5] :
( mem(X5,arr(X1,bool))
=> ( p(ap(c_2Ebool_2E_21(X1),X5))
<=> ! [X4] :
( mem(X4,X1)
=> p(ap(X5,X4)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_all_p) ).
fof(mem_c_2Ebool_2EF,axiom,
mem(c_2Ebool_2EF,bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Ebool_2EF) ).
fof(mem_c_2Ebool_2E_7E,axiom,
mem(c_2Ebool_2E_7E,arr(bool,bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Ebool_2E_7E) ).
fof(bool_ne,axiom,
ne(bool),
file('/export/starexec/sandbox2/benchmark/Axioms/ITP001/ITP001+2.ax',bool_ne) ).
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(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,X23),X22))
& p(ap(ap(c_2Eextreal_2Eextreal__le,X24),X22)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Eextreal_2Emax__le) ).
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,X13),X14))
| p(ap(ap(c_2Eextreal_2Eextreal__le,X14),X13)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Eextreal_2Ele__total) ).
fof(ax_neg_p,axiom,
! [X5] :
( mem(X5,bool)
=> ( p(ap(c_2Ebool_2E_7E,X5))
<=> ~ p(X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_neg_p) ).
fof(mem_c_2Ebool_2E_21,axiom,
! [X9] :
( ne(X9)
=> mem(c_2Ebool_2E_21(X9),arr(arr(X9,bool),bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Ebool_2E_21) ).
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(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_2ET),X10),X11) = X10
& ap(ap(ap(c_2Ebool_2ECOND(X9),c_2Ebool_2EF),X10),X11) = X11 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Ebool_2ECOND__CLAUSES) ).
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,X13),X14))
& p(ap(ap(c_2Eextreal_2Eextreal__le,X14),X18)) )
=> p(ap(ap(c_2Eextreal_2Eextreal__le,X13),X18)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Eextreal_2Ele__trans) ).
fof(ne_ty_2Eextreal_2Eextreal,axiom,
ne(ty_2Eextreal_2Eextreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ne_ty_2Eextreal_2Eextreal) ).
fof(mem_c_2Eextreal_2Eextreal__max,axiom,
mem(c_2Eextreal_2Eextreal__max,arr(ty_2Eextreal_2Eextreal,arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Eextreal_2Eextreal__max) ).
fof(c_0_19,plain,
! [X118,X119] :
( ( ~ p(X118)
| ~ p(X119)
| X118 = X119
| ~ mem(X119,bool)
| ~ mem(X118,bool) )
& ( p(X118)
| p(X119)
| X118 = X119
| ~ mem(X119,bool)
| ~ mem(X118,bool) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[boolext])])])]) ).
fof(c_0_20,plain,
~ p(c_2Ebool_2EF),
inference(fof_simplification,[status(thm)],[ax_false_p]) ).
fof(c_0_21,plain,
! [X143,X144,X145] :
( ( ~ p(ap(c_2Ebool_2E_21(X143),X144))
| ~ mem(X145,X143)
| p(ap(X144,X145))
| ~ mem(X144,arr(X143,bool))
| ~ ne(X143) )
& ( mem(esk2_2(X143,X144),X143)
| p(ap(c_2Ebool_2E_21(X143),X144))
| ~ mem(X144,arr(X143,bool))
| ~ ne(X143) )
& ( ~ p(ap(X144,esk2_2(X143,X144)))
| p(ap(c_2Ebool_2E_21(X143),X144))
| ~ mem(X144,arr(X143,bool))
| ~ ne(X143) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax_all_p])])])])]) ).
cnf(c_0_22,plain,
( p(X1)
| p(X2)
| X1 = X2
| ~ mem(X2,bool)
| ~ mem(X1,bool) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_23,plain,
mem(c_2Ebool_2EF,bool),
inference(split_conjunct,[status(thm)],[mem_c_2Ebool_2EF]) ).
cnf(c_0_24,plain,
~ p(c_2Ebool_2EF),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_25,plain,
( mem(esk2_2(X1,X2),X1)
| p(ap(c_2Ebool_2E_21(X1),X2))
| ~ mem(X2,arr(X1,bool))
| ~ ne(X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_26,plain,
mem(c_2Ebool_2E_7E,arr(bool,bool)),
inference(split_conjunct,[status(thm)],[mem_c_2Ebool_2E_7E]) ).
cnf(c_0_27,plain,
ne(bool),
inference(split_conjunct,[status(thm)],[bool_ne]) ).
fof(c_0_28,plain,
! [X114,X115,X116,X117] :
( ~ mem(X116,arr(X114,X115))
| ~ mem(X117,X114)
| mem(ap(X116,X117),X115) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ap_tp])])]) ).
cnf(c_0_29,plain,
( X1 = c_2Ebool_2EF
| p(X1)
| ~ mem(X1,bool) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]) ).
cnf(c_0_30,plain,
( p(ap(c_2Ebool_2E_21(bool),c_2Ebool_2E_7E))
| mem(esk2_2(bool,c_2Ebool_2E_7E),bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27])]) ).
fof(c_0_31,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,X23),X22))
& p(ap(ap(c_2Eextreal_2Eextreal__le,X24),X22)) ) ) ) ) ),
inference(assume_negation,[status(cth)],[conj_thm_2Eextreal_2Emax__le]) ).
cnf(c_0_32,plain,
( mem(ap(X1,X4),X3)
| ~ mem(X1,arr(X2,X3))
| ~ mem(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_33,plain,
( p(ap(X2,X3))
| ~ p(ap(c_2Ebool_2E_21(X1),X2))
| ~ mem(X3,X1)
| ~ mem(X2,arr(X1,bool))
| ~ ne(X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_34,plain,
( esk2_2(bool,c_2Ebool_2E_7E) = c_2Ebool_2EF
| p(ap(c_2Ebool_2E_21(bool),c_2Ebool_2E_7E))
| p(esk2_2(bool,c_2Ebool_2E_7E)) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_35,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_36,plain,
! [X163,X164] :
( ~ mem(X163,ty_2Eextreal_2Eextreal)
| ~ mem(X164,ty_2Eextreal_2Eextreal)
| p(ap(ap(c_2Eextreal_2Eextreal__le,X163),X164))
| p(ap(ap(c_2Eextreal_2Eextreal__le,X164),X163)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_thm_2Eextreal_2Ele__total])])]) ).
fof(c_0_37,negated_conjecture,
( mem(esk3_0,ty_2Eextreal_2Eextreal)
& mem(esk4_0,ty_2Eextreal_2Eextreal)
& mem(esk5_0,ty_2Eextreal_2Eextreal)
& ( ~ p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__max,esk4_0),esk5_0)),esk3_0))
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,esk4_0),esk3_0))
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,esk5_0),esk3_0)) )
& ( p(ap(ap(c_2Eextreal_2Eextreal__le,esk4_0),esk3_0))
| p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__max,esk4_0),esk5_0)),esk3_0)) )
& ( p(ap(ap(c_2Eextreal_2Eextreal__le,esk5_0),esk3_0))
| p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__max,esk4_0),esk5_0)),esk3_0)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_31])])])]) ).
fof(c_0_38,plain,
! [X5] :
( mem(X5,bool)
=> ( p(ap(c_2Ebool_2E_7E,X5))
<=> ~ p(X5) ) ),
inference(fof_simplification,[status(thm)],[ax_neg_p]) ).
cnf(c_0_39,plain,
( mem(ap(c_2Ebool_2E_7E,X1),bool)
| ~ mem(X1,bool) ),
inference(spm,[status(thm)],[c_0_32,c_0_26]) ).
fof(c_0_40,plain,
! [X142] :
( ~ ne(X142)
| mem(c_2Ebool_2E_21(X142),arr(arr(X142,bool),bool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mem_c_2Ebool_2E_21])]) ).
cnf(c_0_41,plain,
( X1 = X2
| ~ p(X1)
| ~ p(X2)
| ~ mem(X2,bool)
| ~ mem(X1,bool) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_42,plain,
( esk2_2(bool,c_2Ebool_2E_7E) = c_2Ebool_2EF
| p(esk2_2(bool,c_2Ebool_2E_7E))
| p(ap(c_2Ebool_2E_7E,X1))
| ~ mem(X1,bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_26]),c_0_27])]) ).
cnf(c_0_43,plain,
mem(c_2Ebool_2ET,bool),
inference(split_conjunct,[status(thm)],[mem_c_2Ebool_2ET]) ).
cnf(c_0_44,plain,
( mem(ap(c_2Eextreal_2Eextreal__le,X1),arr(ty_2Eextreal_2Eextreal,bool))
| ~ mem(X1,ty_2Eextreal_2Eextreal) ),
inference(spm,[status(thm)],[c_0_32,c_0_35]) ).
cnf(c_0_45,plain,
( p(ap(ap(c_2Eextreal_2Eextreal__le,X1),X2))
| p(ap(ap(c_2Eextreal_2Eextreal__le,X2),X1))
| ~ mem(X1,ty_2Eextreal_2Eextreal)
| ~ mem(X2,ty_2Eextreal_2Eextreal) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_46,negated_conjecture,
mem(esk4_0,ty_2Eextreal_2Eextreal),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_47,plain,
p(c_2Ebool_2ET),
inference(split_conjunct,[status(thm)],[ax_true_p]) ).
fof(c_0_48,plain,
! [X137] :
( ( ~ p(ap(c_2Ebool_2E_7E,X137))
| ~ p(X137)
| ~ mem(X137,bool) )
& ( p(X137)
| p(ap(c_2Ebool_2E_7E,X137))
| ~ mem(X137,bool) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_38])])]) ).
cnf(c_0_49,plain,
( ap(c_2Ebool_2E_7E,X1) = c_2Ebool_2EF
| p(ap(c_2Ebool_2E_7E,X1))
| ~ mem(X1,bool) ),
inference(spm,[status(thm)],[c_0_29,c_0_39]) ).
cnf(c_0_50,plain,
( mem(c_2Ebool_2E_21(X1),arr(arr(X1,bool),bool))
| ~ ne(X1) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_51,plain,
( X1 = esk2_2(bool,c_2Ebool_2E_7E)
| p(ap(c_2Ebool_2E_21(bool),c_2Ebool_2E_7E))
| ~ p(esk2_2(bool,c_2Ebool_2E_7E))
| ~ p(X1)
| ~ mem(X1,bool) ),
inference(spm,[status(thm)],[c_0_41,c_0_30]) ).
cnf(c_0_52,plain,
( esk2_2(bool,c_2Ebool_2E_7E) = c_2Ebool_2EF
| p(ap(c_2Ebool_2E_7E,c_2Ebool_2ET))
| p(esk2_2(bool,c_2Ebool_2E_7E)) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_53,plain,
( mem(ap(ap(c_2Eextreal_2Eextreal__le,X1),X2),bool)
| ~ mem(X2,ty_2Eextreal_2Eextreal)
| ~ mem(X1,ty_2Eextreal_2Eextreal) ),
inference(spm,[status(thm)],[c_0_32,c_0_44]) ).
cnf(c_0_54,negated_conjecture,
( p(ap(ap(c_2Eextreal_2Eextreal__le,esk4_0),X1))
| p(ap(ap(c_2Eextreal_2Eextreal__le,X1),esk4_0))
| ~ mem(X1,ty_2Eextreal_2Eextreal) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_55,plain,
( X1 = c_2Ebool_2ET
| ~ p(X1)
| ~ mem(X1,bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_43]),c_0_47])]) ).
cnf(c_0_56,plain,
( ~ p(ap(c_2Ebool_2E_7E,X1))
| ~ p(X1)
| ~ mem(X1,bool) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_57,plain,
( ap(c_2Ebool_2E_7E,c_2Ebool_2ET) = c_2Ebool_2EF
| p(ap(c_2Ebool_2E_7E,c_2Ebool_2ET)) ),
inference(spm,[status(thm)],[c_0_49,c_0_43]) ).
cnf(c_0_58,plain,
( mem(ap(c_2Ebool_2E_21(X1),X2),bool)
| ~ mem(X2,arr(X1,bool))
| ~ ne(X1) ),
inference(spm,[status(thm)],[c_0_32,c_0_50]) ).
cnf(c_0_59,plain,
( esk2_2(bool,c_2Ebool_2E_7E) = c_2Ebool_2EF
| X1 = esk2_2(bool,c_2Ebool_2E_7E)
| p(ap(c_2Ebool_2E_21(bool),c_2Ebool_2E_7E))
| p(ap(c_2Ebool_2E_7E,c_2Ebool_2ET))
| ~ p(X1)
| ~ mem(X1,bool) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_60,plain,
( X1 = ap(ap(c_2Eextreal_2Eextreal__le,X2),X3)
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,X2),X3))
| ~ p(X1)
| ~ mem(X1,bool)
| ~ mem(X3,ty_2Eextreal_2Eextreal)
| ~ mem(X2,ty_2Eextreal_2Eextreal) ),
inference(spm,[status(thm)],[c_0_41,c_0_53]) ).
cnf(c_0_61,negated_conjecture,
p(ap(ap(c_2Eextreal_2Eextreal__le,esk4_0),esk4_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(ef,[status(thm)],[c_0_54]),c_0_46])]) ).
cnf(c_0_62,plain,
( esk2_2(bool,c_2Ebool_2E_7E) = c_2Ebool_2ET
| p(ap(c_2Ebool_2E_21(bool),c_2Ebool_2E_7E))
| ~ p(esk2_2(bool,c_2Ebool_2E_7E)) ),
inference(spm,[status(thm)],[c_0_55,c_0_30]) ).
cnf(c_0_63,plain,
ap(c_2Ebool_2E_7E,c_2Ebool_2ET) = c_2Ebool_2EF,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_47]),c_0_43])]) ).
cnf(c_0_64,plain,
( ap(c_2Ebool_2E_21(X1),X2) = c_2Ebool_2EF
| p(ap(c_2Ebool_2E_21(X1),X2))
| ~ mem(X2,arr(X1,bool))
| ~ ne(X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_58]) ).
cnf(c_0_65,plain,
( esk2_2(bool,c_2Ebool_2E_7E) = c_2Ebool_2EF
| p(ap(c_2Ebool_2E_21(bool),c_2Ebool_2E_7E))
| p(ap(c_2Ebool_2E_7E,c_2Ebool_2ET))
| X1 != c_2Ebool_2EF
| ~ p(X1)
| ~ mem(X1,bool) ),
inference(ef,[status(thm)],[c_0_59]) ).
cnf(c_0_66,negated_conjecture,
( X1 = ap(ap(c_2Eextreal_2Eextreal__le,esk4_0),esk4_0)
| ~ p(X1)
| ~ mem(X1,bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_46])]) ).
cnf(c_0_67,plain,
( ap(ap(c_2Eextreal_2Eextreal__le,X1),X2) = c_2Ebool_2EF
| p(ap(ap(c_2Eextreal_2Eextreal__le,X1),X2))
| ~ mem(X2,ty_2Eextreal_2Eextreal)
| ~ mem(X1,ty_2Eextreal_2Eextreal) ),
inference(spm,[status(thm)],[c_0_29,c_0_53]) ).
cnf(c_0_68,negated_conjecture,
mem(esk5_0,ty_2Eextreal_2Eextreal),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_69,plain,
( esk2_2(bool,c_2Ebool_2E_7E) = c_2Ebool_2EF
| esk2_2(bool,c_2Ebool_2E_7E) = c_2Ebool_2ET
| p(ap(c_2Ebool_2E_21(bool),c_2Ebool_2E_7E))
| p(ap(c_2Ebool_2E_7E,c_2Ebool_2ET)) ),
inference(spm,[status(thm)],[c_0_62,c_0_52]) ).
cnf(c_0_70,plain,
( ~ p(ap(c_2Ebool_2E_21(X1),c_2Ebool_2E_7E))
| ~ mem(c_2Ebool_2E_7E,arr(X1,bool))
| ~ mem(c_2Ebool_2ET,X1)
| ~ ne(X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_63]),c_0_24]) ).
cnf(c_0_71,plain,
( ap(c_2Ebool_2E_21(bool),c_2Ebool_2E_7E) = c_2Ebool_2EF
| p(ap(c_2Ebool_2E_21(bool),c_2Ebool_2E_7E)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_26]),c_0_27])]) ).
cnf(c_0_72,plain,
( p(X1)
| p(ap(c_2Ebool_2E_7E,X1))
| ~ mem(X1,bool) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_73,plain,
( esk2_2(bool,c_2Ebool_2E_7E) = c_2Ebool_2EF
| p(ap(c_2Ebool_2E_21(bool),c_2Ebool_2E_7E))
| p(ap(c_2Ebool_2E_7E,c_2Ebool_2ET))
| c_2Ebool_2EF != c_2Ebool_2ET ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_43]),c_0_47])]) ).
cnf(c_0_74,negated_conjecture,
( ap(ap(c_2Eextreal_2Eextreal__le,X1),X2) = ap(ap(c_2Eextreal_2Eextreal__le,esk4_0),esk4_0)
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,X1),X2))
| ~ mem(X2,ty_2Eextreal_2Eextreal)
| ~ mem(X1,ty_2Eextreal_2Eextreal) ),
inference(spm,[status(thm)],[c_0_66,c_0_53]) ).
cnf(c_0_75,negated_conjecture,
ap(ap(c_2Eextreal_2Eextreal__le,esk4_0),esk4_0) = c_2Ebool_2ET,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_43]),c_0_47])]) ).
cnf(c_0_76,negated_conjecture,
( ap(ap(c_2Eextreal_2Eextreal__le,X1),esk5_0) = c_2Ebool_2EF
| p(ap(ap(c_2Eextreal_2Eextreal__le,X1),esk5_0))
| ~ mem(X1,ty_2Eextreal_2Eextreal) ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_77,plain,
( esk2_2(bool,c_2Ebool_2E_7E) = c_2Ebool_2ET
| esk2_2(bool,c_2Ebool_2E_7E) = c_2Ebool_2EF
| p(ap(c_2Ebool_2E_21(bool),c_2Ebool_2E_7E)) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_69,c_0_63]),c_0_24]) ).
cnf(c_0_78,plain,
ap(c_2Ebool_2E_21(bool),c_2Ebool_2E_7E) = c_2Ebool_2EF,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_26]),c_0_43]),c_0_27])]) ).
cnf(c_0_79,plain,
( ap(c_2Ebool_2E_7E,X1) = c_2Ebool_2ET
| ~ p(ap(c_2Ebool_2E_7E,X1))
| ~ mem(X1,bool) ),
inference(spm,[status(thm)],[c_0_55,c_0_39]) ).
cnf(c_0_80,plain,
p(ap(c_2Ebool_2E_7E,c_2Ebool_2EF)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_23]),c_0_24]) ).
cnf(c_0_81,plain,
( esk2_2(bool,c_2Ebool_2E_7E) = c_2Ebool_2EF
| p(ap(c_2Ebool_2E_21(bool),c_2Ebool_2E_7E))
| c_2Ebool_2EF != c_2Ebool_2ET ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_73,c_0_63]),c_0_24]) ).
cnf(c_0_82,negated_conjecture,
( p(ap(ap(c_2Eextreal_2Eextreal__le,esk5_0),X1))
| p(ap(ap(c_2Eextreal_2Eextreal__le,X1),esk5_0))
| ~ mem(X1,ty_2Eextreal_2Eextreal) ),
inference(spm,[status(thm)],[c_0_45,c_0_68]) ).
cnf(c_0_83,negated_conjecture,
mem(esk3_0,ty_2Eextreal_2Eextreal),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
fof(c_0_84,plain,
! [X165,X166] :
( ~ mem(X165,ty_2Eextreal_2Eextreal)
| ~ mem(X166,ty_2Eextreal_2Eextreal)
| ap(ap(c_2Eextreal_2Eextreal__max,X165),X166) = ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),ap(ap(c_2Eextreal_2Eextreal__le,X165),X166)),X166),X165) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax_thm_2Eextreal_2Eextreal__max__def])])]) ).
cnf(c_0_85,negated_conjecture,
( ap(ap(c_2Eextreal_2Eextreal__le,X1),X2) = c_2Ebool_2ET
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,X1),X2))
| ~ mem(X2,ty_2Eextreal_2Eextreal)
| ~ mem(X1,ty_2Eextreal_2Eextreal) ),
inference(rw,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_86,negated_conjecture,
( ap(ap(c_2Eextreal_2Eextreal__le,esk4_0),esk5_0) = c_2Ebool_2EF
| p(ap(ap(c_2Eextreal_2Eextreal__le,esk4_0),esk5_0)) ),
inference(spm,[status(thm)],[c_0_76,c_0_46]) ).
cnf(c_0_87,plain,
( p(ap(c_2Ebool_2E_21(X2),X1))
| ~ p(ap(X1,esk2_2(X2,X1)))
| ~ mem(X1,arr(X2,bool))
| ~ ne(X2) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_88,plain,
( esk2_2(bool,c_2Ebool_2E_7E) = c_2Ebool_2EF
| esk2_2(bool,c_2Ebool_2E_7E) = c_2Ebool_2ET ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_77,c_0_78]),c_0_24]) ).
cnf(c_0_89,plain,
ap(c_2Ebool_2E_7E,c_2Ebool_2EF) = c_2Ebool_2ET,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_23])]) ).
cnf(c_0_90,plain,
( esk2_2(bool,c_2Ebool_2E_7E) = c_2Ebool_2EF
| c_2Ebool_2EF != c_2Ebool_2ET ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_81,c_0_78]),c_0_24]) ).
cnf(c_0_91,negated_conjecture,
( p(ap(ap(c_2Eextreal_2Eextreal__le,esk3_0),esk5_0))
| p(ap(ap(c_2Eextreal_2Eextreal__le,esk5_0),esk3_0)) ),
inference(spm,[status(thm)],[c_0_82,c_0_83]) ).
fof(c_0_92,plain,
! [X153,X154,X155] :
( ( ap(ap(ap(c_2Ebool_2ECOND(X153),c_2Ebool_2ET),X154),X155) = X154
| ~ mem(X155,X153)
| ~ mem(X154,X153)
| ~ ne(X153) )
& ( ap(ap(ap(c_2Ebool_2ECOND(X153),c_2Ebool_2EF),X154),X155) = X155
| ~ mem(X155,X153)
| ~ mem(X154,X153)
| ~ ne(X153) ) ),
inference(distribute,[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_93,plain,
( 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)
| ~ mem(X1,ty_2Eextreal_2Eextreal)
| ~ mem(X2,ty_2Eextreal_2Eextreal) ),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
cnf(c_0_94,negated_conjecture,
( ap(ap(c_2Eextreal_2Eextreal__le,esk4_0),esk5_0) = c_2Ebool_2EF
| ap(ap(c_2Eextreal_2Eextreal__le,esk4_0),esk5_0) = c_2Ebool_2ET ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_68]),c_0_46])]) ).
cnf(c_0_95,plain,
( esk2_2(bool,c_2Ebool_2E_7E) = c_2Ebool_2EF
| p(ap(c_2Ebool_2E_21(bool),c_2Ebool_2E_7E))
| X1 != c_2Ebool_2EF
| ~ p(X1)
| ~ mem(X1,bool) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_65,c_0_63]),c_0_24]) ).
cnf(c_0_96,plain,
esk2_2(bool,c_2Ebool_2E_7E) = c_2Ebool_2ET,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_78]),c_0_89]),c_0_47]),c_0_26]),c_0_27])]),c_0_24]) ).
cnf(c_0_97,plain,
c_2Ebool_2EF != c_2Ebool_2ET,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_90]),c_0_78]),c_0_89]),c_0_47]),c_0_26]),c_0_27])]),c_0_24]) ).
cnf(c_0_98,negated_conjecture,
( X1 = ap(ap(c_2Eextreal_2Eextreal__le,esk5_0),esk3_0)
| p(ap(ap(c_2Eextreal_2Eextreal__le,esk3_0),esk5_0))
| ~ p(X1)
| ~ mem(X1,bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_91]),c_0_83]),c_0_68])]) ).
fof(c_0_99,plain,
! [X160,X161,X162] :
( ~ mem(X160,ty_2Eextreal_2Eextreal)
| ~ mem(X161,ty_2Eextreal_2Eextreal)
| ~ mem(X162,ty_2Eextreal_2Eextreal)
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,X160),X161))
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,X161),X162))
| p(ap(ap(c_2Eextreal_2Eextreal__le,X160),X162)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_thm_2Eextreal_2Ele__trans])])]) ).
cnf(c_0_100,plain,
( ap(ap(ap(c_2Ebool_2ECOND(X1),c_2Ebool_2EF),X2),X3) = X3
| ~ mem(X3,X1)
| ~ mem(X2,X1)
| ~ ne(X1) ),
inference(split_conjunct,[status(thm)],[c_0_92]) ).
cnf(c_0_101,negated_conjecture,
( ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2EF),esk5_0),esk4_0) = ap(ap(c_2Eextreal_2Eextreal__max,esk4_0),esk5_0)
| ap(ap(c_2Eextreal_2Eextreal__le,esk4_0),esk5_0) = c_2Ebool_2ET ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_68]),c_0_46])]) ).
cnf(c_0_102,plain,
ne(ty_2Eextreal_2Eextreal),
inference(split_conjunct,[status(thm)],[ne_ty_2Eextreal_2Eextreal]) ).
cnf(c_0_103,plain,
( X1 != c_2Ebool_2EF
| ~ p(X1)
| ~ mem(X1,bool) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_95,c_0_78]),c_0_24]),c_0_96]),c_0_97]) ).
cnf(c_0_104,negated_conjecture,
( ap(c_2Ebool_2E_7E,X1) = ap(ap(c_2Eextreal_2Eextreal__le,esk5_0),esk3_0)
| p(ap(ap(c_2Eextreal_2Eextreal__le,esk3_0),esk5_0))
| ~ p(ap(c_2Ebool_2E_7E,X1))
| ~ mem(X1,bool) ),
inference(spm,[status(thm)],[c_0_98,c_0_39]) ).
cnf(c_0_105,plain,
( p(ap(ap(c_2Eextreal_2Eextreal__le,X1),X3))
| ~ mem(X1,ty_2Eextreal_2Eextreal)
| ~ mem(X2,ty_2Eextreal_2Eextreal)
| ~ mem(X3,ty_2Eextreal_2Eextreal)
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,X1),X2))
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_99]) ).
cnf(c_0_106,negated_conjecture,
( ap(ap(c_2Eextreal_2Eextreal__le,esk3_0),esk5_0) = c_2Ebool_2EF
| p(ap(ap(c_2Eextreal_2Eextreal__le,esk3_0),esk5_0)) ),
inference(spm,[status(thm)],[c_0_76,c_0_83]) ).
cnf(c_0_107,negated_conjecture,
( ~ p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__max,esk4_0),esk5_0)),esk3_0))
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,esk4_0),esk3_0))
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,esk5_0),esk3_0)) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_108,negated_conjecture,
( ap(ap(c_2Eextreal_2Eextreal__le,esk4_0),esk5_0) = c_2Ebool_2ET
| ap(ap(c_2Eextreal_2Eextreal__max,esk4_0),esk5_0) = esk4_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_46]),c_0_68]),c_0_102])]) ).
cnf(c_0_109,plain,
( ap(ap(c_2Eextreal_2Eextreal__le,X1),X2) != c_2Ebool_2EF
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,X1),X2))
| ~ mem(X2,ty_2Eextreal_2Eextreal)
| ~ mem(X1,ty_2Eextreal_2Eextreal) ),
inference(spm,[status(thm)],[c_0_103,c_0_53]) ).
cnf(c_0_110,negated_conjecture,
( ap(ap(c_2Eextreal_2Eextreal__le,esk5_0),esk3_0) = c_2Ebool_2ET
| p(ap(ap(c_2Eextreal_2Eextreal__le,esk3_0),esk5_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_89]),c_0_47]),c_0_23])]) ).
cnf(c_0_111,negated_conjecture,
( ap(ap(c_2Eextreal_2Eextreal__le,esk3_0),esk5_0) = c_2Ebool_2EF
| p(ap(ap(c_2Eextreal_2Eextreal__le,X1),esk5_0))
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,X1),esk3_0))
| ~ mem(X1,ty_2Eextreal_2Eextreal) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_68]),c_0_83])]) ).
cnf(c_0_112,plain,
mem(c_2Eextreal_2Eextreal__max,arr(ty_2Eextreal_2Eextreal,arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal))),
inference(split_conjunct,[status(thm)],[mem_c_2Eextreal_2Eextreal__max]) ).
cnf(c_0_113,negated_conjecture,
( ap(ap(c_2Eextreal_2Eextreal__le,esk4_0),esk5_0) = c_2Ebool_2ET
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,esk4_0),esk3_0))
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,esk5_0),esk3_0)) ),
inference(spm,[status(thm)],[c_0_107,c_0_108]) ).
cnf(c_0_114,negated_conjecture,
( ap(ap(c_2Eextreal_2Eextreal__le,esk5_0),esk3_0) = c_2Ebool_2ET
| ap(ap(c_2Eextreal_2Eextreal__le,esk3_0),esk5_0) != c_2Ebool_2EF ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_110]),c_0_68]),c_0_83])]) ).
cnf(c_0_115,negated_conjecture,
( ap(ap(c_2Eextreal_2Eextreal__le,esk4_0),esk5_0) = c_2Ebool_2ET
| ap(ap(c_2Eextreal_2Eextreal__le,esk3_0),esk5_0) = c_2Ebool_2EF
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,esk4_0),esk3_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_94]),c_0_46])]),c_0_24]) ).
cnf(c_0_116,negated_conjecture,
( p(ap(ap(c_2Eextreal_2Eextreal__le,esk5_0),esk3_0))
| p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__max,esk4_0),esk5_0)),esk3_0)) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_117,plain,
( mem(ap(c_2Eextreal_2Eextreal__max,X1),arr(ty_2Eextreal_2Eextreal,ty_2Eextreal_2Eextreal))
| ~ mem(X1,ty_2Eextreal_2Eextreal) ),
inference(spm,[status(thm)],[c_0_32,c_0_112]) ).
cnf(c_0_118,negated_conjecture,
( p(ap(ap(c_2Eextreal_2Eextreal__le,esk4_0),esk3_0))
| p(ap(ap(c_2Eextreal_2Eextreal__le,ap(ap(c_2Eextreal_2Eextreal__max,esk4_0),esk5_0)),esk3_0)) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_119,negated_conjecture,
( ap(ap(c_2Eextreal_2Eextreal__le,esk4_0),esk5_0) = c_2Ebool_2ET
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,esk4_0),esk3_0)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_114]),c_0_47])]),c_0_115]) ).
cnf(c_0_120,negated_conjecture,
( p(ap(ap(c_2Eextreal_2Eextreal__le,esk5_0),esk3_0))
| p(ap(ap(c_2Eextreal_2Eextreal__le,X1),esk3_0))
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,X1),ap(ap(c_2Eextreal_2Eextreal__max,esk4_0),esk5_0)))
| ~ mem(ap(ap(c_2Eextreal_2Eextreal__max,esk4_0),esk5_0),ty_2Eextreal_2Eextreal)
| ~ mem(X1,ty_2Eextreal_2Eextreal) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_116]),c_0_83])]) ).
cnf(c_0_121,plain,
( mem(ap(ap(c_2Eextreal_2Eextreal__max,X1),X2),ty_2Eextreal_2Eextreal)
| ~ mem(X2,ty_2Eextreal_2Eextreal)
| ~ mem(X1,ty_2Eextreal_2Eextreal) ),
inference(spm,[status(thm)],[c_0_32,c_0_117]) ).
cnf(c_0_122,negated_conjecture,
ap(ap(c_2Eextreal_2Eextreal__le,esk4_0),esk5_0) = c_2Ebool_2ET,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_108]),c_0_119]) ).
cnf(c_0_123,negated_conjecture,
p(ap(ap(c_2Eextreal_2Eextreal__le,esk5_0),esk5_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(ef,[status(thm)],[c_0_82]),c_0_68])]) ).
cnf(c_0_124,negated_conjecture,
( p(ap(ap(c_2Eextreal_2Eextreal__le,esk5_0),esk3_0))
| p(ap(ap(c_2Eextreal_2Eextreal__le,X1),esk3_0))
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,X1),ap(ap(c_2Eextreal_2Eextreal__max,esk4_0),esk5_0)))
| ~ mem(X1,ty_2Eextreal_2Eextreal) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_121]),c_0_68]),c_0_46])]) ).
cnf(c_0_125,plain,
( ap(ap(ap(c_2Ebool_2ECOND(X1),c_2Ebool_2ET),X2),X3) = X2
| ~ mem(X3,X1)
| ~ mem(X2,X1)
| ~ ne(X1) ),
inference(split_conjunct,[status(thm)],[c_0_92]) ).
cnf(c_0_126,negated_conjecture,
ap(ap(ap(c_2Ebool_2ECOND(ty_2Eextreal_2Eextreal),c_2Ebool_2ET),esk5_0),esk4_0) = ap(ap(c_2Eextreal_2Eextreal__max,esk4_0),esk5_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_122]),c_0_68]),c_0_46])]) ).
cnf(c_0_127,negated_conjecture,
( X1 = ap(ap(c_2Eextreal_2Eextreal__le,esk5_0),esk5_0)
| ~ p(X1)
| ~ mem(X1,bool) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_123]),c_0_68])]) ).
cnf(c_0_128,negated_conjecture,
( p(ap(ap(c_2Eextreal_2Eextreal__le,esk4_0),esk3_0))
| p(ap(ap(c_2Eextreal_2Eextreal__le,X1),esk3_0))
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,X1),ap(ap(c_2Eextreal_2Eextreal__max,esk4_0),esk5_0)))
| ~ mem(ap(ap(c_2Eextreal_2Eextreal__max,esk4_0),esk5_0),ty_2Eextreal_2Eextreal)
| ~ mem(X1,ty_2Eextreal_2Eextreal) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_118]),c_0_83])]) ).
cnf(c_0_129,negated_conjecture,
( p(ap(ap(c_2Eextreal_2Eextreal__le,esk5_0),esk3_0))
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,esk5_0),ap(ap(c_2Eextreal_2Eextreal__max,esk4_0),esk5_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(ef,[status(thm)],[c_0_124]),c_0_68])]) ).
cnf(c_0_130,negated_conjecture,
ap(ap(c_2Eextreal_2Eextreal__max,esk4_0),esk5_0) = esk5_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_126]),c_0_46]),c_0_68]),c_0_102])]) ).
cnf(c_0_131,negated_conjecture,
ap(ap(c_2Eextreal_2Eextreal__le,esk5_0),esk5_0) = c_2Ebool_2ET,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_43]),c_0_47])]) ).
cnf(c_0_132,negated_conjecture,
( p(ap(ap(c_2Eextreal_2Eextreal__le,esk4_0),esk3_0))
| p(ap(ap(c_2Eextreal_2Eextreal__le,X1),esk3_0))
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,X1),ap(ap(c_2Eextreal_2Eextreal__max,esk4_0),esk5_0)))
| ~ mem(X1,ty_2Eextreal_2Eextreal) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_121]),c_0_68]),c_0_46])]) ).
cnf(c_0_133,negated_conjecture,
p(ap(ap(c_2Eextreal_2Eextreal__le,esk5_0),esk3_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_129,c_0_130]),c_0_131]),c_0_47])]) ).
cnf(c_0_134,negated_conjecture,
( p(ap(ap(c_2Eextreal_2Eextreal__le,esk4_0),esk3_0))
| ~ p(ap(ap(c_2Eextreal_2Eextreal__le,esk4_0),ap(ap(c_2Eextreal_2Eextreal__max,esk4_0),esk5_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(ef,[status(thm)],[c_0_132]),c_0_46])]) ).
cnf(c_0_135,negated_conjecture,
~ p(ap(ap(c_2Eextreal_2Eextreal__le,esk4_0),esk3_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_107,c_0_130])]),c_0_133])]) ).
cnf(c_0_136,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_134,c_0_130]),c_0_122]),c_0_47])]),c_0_135]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP021+2 : TPTP v9.2.1. Bugfixed v7.5.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n018.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Mon May 4 19:45:17 EDT 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 11.59/7.49 % Version : CSE_E---1.7
% 11.59/7.49 % Problem : theBenchmark.p
% 11.59/7.49 % SZS status Theorem for theBenchmark.p
% 11.59/7.49 % SZS output start CNFRefutation
% See solution above
% 11.69/7.53 % Total time : 5.374s
%------------------------------------------------------------------------------