%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM639+4 : TPTP v9.2.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n002.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 04:58:14 PM UTC 2026
% Result : Theorem 156.64s 65.70s
% Output : CNFRefutation 156.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 15
% Syntax : Number of formulae : 59 ( 28 unt; 0 def)
% Number of atoms : 120 ( 27 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 103 ( 42 ~; 46 |; 7 &)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 12 con; 0-2 aty)
% Number of variables : 70 ( 5 sgn 36 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(help_fequal_1_1_fequal_001t__TPTP____Interpret__Oind_T,axiom,
! [X34,X35] :
( ( gg_TPTP_ind(X34)
& gg_TPTP_ind(X35) )
=> ( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X34),X35))
| X34 = X35 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_fequal_001t__TPTP____Interpret__Oind_T) ).
fof(fact_def__e__is,axiom,
! [X4] : scratc1770836270d_e_is(X4) = fequal_TPTP_ind,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_def__e__is) ).
fof(fact_def__n__is,axiom,
scratc1289496631d_n_is = scratc1770836270d_e_is(scratc1472361728nd_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_def__n__is) ).
fof(fact_ATP_Olambda__3,axiom,
! [X25] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bu,X25))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1289496631d_n_is,aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(X25),scratc214542084nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,X25))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ATP_Olambda__3) ).
fof(fact_def__n__pl,axiom,
! [X4] : scratc1289955817d_n_pl(X4) = aa_TPT1424761345TP_ind(scratc932095312bnd_ap,aa_TPTP_ind_TPTP_ind(scratc1884559291d_plus,X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_def__n__pl) ).
fof(fact_ATP_Olambda__7,axiom,
! [X25] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,X25))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1289496631d_n_is,aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,X25)),aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(X25),scratc214542084nd_n_1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ATP_Olambda__7) ).
fof(gsy_c_aa_001t__TPTP____Interpret__Oind_001t__TPTP____Interpret__Oind,axiom,
! [X1,X2] : gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_aa_001t__TPTP____Interpret__Oind_001t__TPTP____Interpret__Oind) ).
fof(help_fequal_2_1_fequal_001t__TPTP____Interpret__Oind_T,axiom,
! [X34,X35] :
( X34 != X35
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X34),X35)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_fequal_001t__TPTP____Interpret__Oind_T) ).
fof(fact_def__all__of,axiom,
! [X4,X5] :
( pp(aa_fun171081125l_bool(scratc1153622423all_of(X4),X5))
<=> ! [X12] :
( gg_TPTP_ind(X12)
=> ( scratc1829621698_is_of(X12,X4)
=> pp(aa_TPTP_ind_bool(X5,X12)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_def__all__of) ).
fof(help_fFalse_1_1_T,axiom,
! [X32] :
( gg_bool(X32)
=> ( X32 = fTrue
| X32 = fFalse ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_T) ).
fof(gsy_c_aa_001t__fun_It__TPTP____Interpret__Oind_Mt__HOL__Obool_J_001t__HOL__Obool,hypothesis,
! [X1,X2] : gg_bool(aa_fun171081125l_bool(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_aa_001t__fun_It__TPTP____Interpret__Oind_Mt__HOL__Obool_J_001t__HOL__Obool) ).
fof(fact_satz4a,axiom,
pp(aa_fun171081125l_bool(scratc1153622423all_of(aTP_Lamm_a),aTP_Lamm_bu)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_satz4a) ).
fof(conj_0,conjecture,
pp(aa_fun171081125l_bool(scratc1153622423all_of(aTP_Lamm_a),aTP_Lamm_aa)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(help_pp_2_1_U,axiom,
pp(fTrue),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).
fof(help_fFalse_1_1_U,axiom,
~ pp(fFalse),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).
fof(c_0_15,plain,
! [X34,X35] :
( ( gg_TPTP_ind(X34)
& gg_TPTP_ind(X35) )
=> ( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X34),X35))
| X34 = X35 ) ),
inference(fof_simplification,[status(thm)],[help_fequal_1_1_fequal_001t__TPTP____Interpret__Oind_T]) ).
fof(c_0_16,plain,
! [X920] : scratc1770836270d_e_is(X920) = fequal_TPTP_ind,
inference(variable_rename,[status(thm)],[fact_def__e__is]) ).
fof(c_0_17,plain,
! [X1445,X1446] :
( ~ gg_TPTP_ind(X1445)
| ~ gg_TPTP_ind(X1446)
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X1445),X1446))
| X1445 = X1446 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])]) ).
cnf(c_0_18,plain,
scratc1289496631d_n_is = scratc1770836270d_e_is(scratc1472361728nd_nat),
inference(split_conjunct,[status(thm)],[fact_def__n__is]) ).
cnf(c_0_19,plain,
scratc1770836270d_e_is(X1) = fequal_TPTP_ind,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_20,plain,
! [X1181] :
( ( ~ pp(aa_TPTP_ind_bool(aTP_Lamm_bu,X1181))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1289496631d_n_is,aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(X1181),scratc214542084nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,X1181))) )
& ( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1289496631d_n_is,aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(X1181),scratc214542084nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,X1181)))
| pp(aa_TPTP_ind_bool(aTP_Lamm_bu,X1181)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ATP_Olambda__3])]) ).
fof(c_0_21,plain,
! [X760] : scratc1289955817d_n_pl(X760) = aa_TPT1424761345TP_ind(scratc932095312bnd_ap,aa_TPTP_ind_TPTP_ind(scratc1884559291d_plus,X760)),
inference(variable_rename,[status(thm)],[fact_def__n__pl]) ).
fof(c_0_22,plain,
! [X1185] :
( ( ~ pp(aa_TPTP_ind_bool(aTP_Lamm_aa,X1185))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1289496631d_n_is,aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,X1185)),aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(X1185),scratc214542084nd_n_1))) )
& ( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1289496631d_n_is,aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,X1185)),aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(X1185),scratc214542084nd_n_1)))
| pp(aa_TPTP_ind_bool(aTP_Lamm_aa,X1185)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ATP_Olambda__7])]) ).
cnf(c_0_23,plain,
( X1 = X2
| ~ gg_TPTP_ind(X1)
| ~ gg_TPTP_ind(X2)
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_24,plain,
fequal_TPTP_ind = scratc1289496631d_n_is,
inference(rw,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_25,plain,
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1289496631d_n_is,aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(X1),scratc214542084nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,X1)))
| ~ pp(aa_TPTP_ind_bool(aTP_Lamm_bu,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_26,plain,
scratc1289955817d_n_pl(X1) = aa_TPT1424761345TP_ind(scratc932095312bnd_ap,aa_TPTP_ind_TPTP_ind(scratc1884559291d_plus,X1)),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_27,plain,
! [X751,X752] : gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(X751,X752)),
inference(variable_rename,[status(thm)],[gsy_c_aa_001t__TPTP____Interpret__Oind_001t__TPTP____Interpret__Oind]) ).
fof(c_0_28,plain,
! [X1443,X1444] :
( X1443 != X1444
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X1443),X1444)) ),
inference(variable_rename,[status(thm)],[help_fequal_2_1_fequal_001t__TPTP____Interpret__Oind_T]) ).
cnf(c_0_29,plain,
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,X1))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1289496631d_n_is,aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,X1)),aa_TPTP_ind_TPTP_ind(scratc1289955817d_n_pl(X1),scratc214542084nd_n_1))) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_30,plain,
( X1 = X2
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1289496631d_n_is,X1),X2))
| ~ gg_TPTP_ind(X2)
| ~ gg_TPTP_ind(X1) ),
inference(rw,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_31,plain,
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1289496631d_n_is,aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc932095312bnd_ap,aa_TPTP_ind_TPTP_ind(scratc1884559291d_plus,X1)),scratc214542084nd_n_1)),aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,X1)))
| ~ pp(aa_TPTP_ind_bool(aTP_Lamm_bu,X1)) ),
inference(rw,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_32,plain,
gg_TPTP_ind(aa_TPTP_ind_TPTP_ind(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_33,plain,
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(fequal_TPTP_ind,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
fof(c_0_34,plain,
! [X1028,X1029,X1030,X1031,X1032] :
( ( ~ pp(aa_fun171081125l_bool(scratc1153622423all_of(X1028),X1029))
| ~ gg_TPTP_ind(X1030)
| ~ scratc1829621698_is_of(X1030,X1028)
| pp(aa_TPTP_ind_bool(X1029,X1030)) )
& ( gg_TPTP_ind(esk13_2(X1031,X1032))
| pp(aa_fun171081125l_bool(scratc1153622423all_of(X1031),X1032)) )
& ( scratc1829621698_is_of(esk13_2(X1031,X1032),X1031)
| pp(aa_fun171081125l_bool(scratc1153622423all_of(X1031),X1032)) )
& ( ~ pp(aa_TPTP_ind_bool(X1032,esk13_2(X1031,X1032)))
| pp(aa_fun171081125l_bool(scratc1153622423all_of(X1031),X1032)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_def__all__of])])])])])]) ).
fof(c_0_35,plain,
! [X1434] :
( ~ gg_bool(X1434)
| X1434 = fTrue
| X1434 = fFalse ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[help_fFalse_1_1_T])]) ).
fof(c_0_36,hypothesis,
! [X753,X754] : gg_bool(aa_fun171081125l_bool(X753,X754)),
inference(variable_rename,[status(thm)],[gsy_c_aa_001t__fun_It__TPTP____Interpret__Oind_Mt__HOL__Obool_J_001t__HOL__Obool]) ).
cnf(c_0_37,plain,
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,X1))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1289496631d_n_is,aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,X1)),aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc932095312bnd_ap,aa_TPTP_ind_TPTP_ind(scratc1884559291d_plus,X1)),scratc214542084nd_n_1))) ),
inference(rw,[status(thm)],[c_0_29,c_0_26]) ).
cnf(c_0_38,plain,
( aa_TPTP_ind_TPTP_ind(aa_TPT1424761345TP_ind(scratc932095312bnd_ap,aa_TPTP_ind_TPTP_ind(scratc1884559291d_plus,X1)),scratc214542084nd_n_1) = aa_TPTP_ind_TPTP_ind(scratc236248354rdsucc,X1)
| ~ pp(aa_TPTP_ind_bool(aTP_Lamm_bu,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]),c_0_32])]) ).
cnf(c_0_39,plain,
pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1289496631d_n_is,X1),X1)),
inference(er,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_24])]) ).
cnf(c_0_40,plain,
( pp(aa_TPTP_ind_bool(X2,X3))
| ~ pp(aa_fun171081125l_bool(scratc1153622423all_of(X1),X2))
| ~ gg_TPTP_ind(X3)
| ~ scratc1829621698_is_of(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_41,plain,
pp(aa_fun171081125l_bool(scratc1153622423all_of(aTP_Lamm_a),aTP_Lamm_bu)),
inference(split_conjunct,[status(thm)],[fact_satz4a]) ).
fof(c_0_42,negated_conjecture,
~ pp(aa_fun171081125l_bool(scratc1153622423all_of(aTP_Lamm_a),aTP_Lamm_aa)),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])]) ).
cnf(c_0_43,plain,
( X1 = fTrue
| X1 = fFalse
| ~ gg_bool(X1) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_44,hypothesis,
gg_bool(aa_fun171081125l_bool(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_45,plain,
( pp(aa_fun171081125l_bool(scratc1153622423all_of(X2),X1))
| ~ pp(aa_TPTP_ind_bool(X1,esk13_2(X2,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_46,plain,
( pp(aa_TPTP_ind_bool(aTP_Lamm_aa,X1))
| ~ pp(aa_TPTP_ind_bool(aTP_Lamm_bu,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39])]) ).
cnf(c_0_47,plain,
( pp(aa_TPTP_ind_bool(aTP_Lamm_bu,X1))
| ~ scratc1829621698_is_of(X1,aTP_Lamm_a)
| ~ gg_TPTP_ind(X1) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_48,plain,
( scratc1829621698_is_of(esk13_2(X1,X2),X1)
| pp(aa_fun171081125l_bool(scratc1153622423all_of(X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_49,plain,
( gg_TPTP_ind(esk13_2(X1,X2))
| pp(aa_fun171081125l_bool(scratc1153622423all_of(X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_50,negated_conjecture,
~ pp(aa_fun171081125l_bool(scratc1153622423all_of(aTP_Lamm_a),aTP_Lamm_aa)),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_51,hypothesis,
( aa_fun171081125l_bool(X1,X2) = fTrue
| aa_fun171081125l_bool(X1,X2) = fFalse ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_52,plain,
pp(fTrue),
inference(split_conjunct,[status(thm)],[help_pp_2_1_U]) ).
fof(c_0_53,plain,
~ pp(fFalse),
inference(fof_simplification,[status(thm)],[help_fFalse_1_1_U]) ).
cnf(c_0_54,plain,
( pp(aa_fun171081125l_bool(scratc1153622423all_of(X1),aTP_Lamm_aa))
| ~ pp(aa_TPTP_ind_bool(aTP_Lamm_bu,esk13_2(X1,aTP_Lamm_aa))) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_55,plain,
( pp(aa_TPTP_ind_bool(aTP_Lamm_bu,esk13_2(aTP_Lamm_a,X1)))
| pp(aa_fun171081125l_bool(scratc1153622423all_of(aTP_Lamm_a),X1)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49]) ).
cnf(c_0_56,negated_conjecture,
aa_fun171081125l_bool(scratc1153622423all_of(aTP_Lamm_a),aTP_Lamm_aa) = fFalse,
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,plain,
~ pp(fFalse),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_58,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_56]),c_0_57]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM639+4 : TPTP v9.2.1. Released v7.3.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.32 % Computer : n002.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 00:55:01 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 156.64/65.70 % Version : CSE_E---1.7
% 156.64/65.70 % Problem : theBenchmark.p
% 156.64/65.70 % SZS status Theorem for theBenchmark.p
% 156.64/65.70 % SZS output start CNFRefutation
% See solution above
% 156.83/65.97 % Total time : 55.653s
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