%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM694+4 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 01:50:11 PM UTC 2026
% Result : Theorem 11.23s 2.42s
% Output : CNFRefutation 11.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 30
% Syntax : Number of formulae : 144 ( 66 unt; 0 def)
% Number of atoms : 286 ( 29 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 230 ( 88 ~; 104 |; 18 &)
% ( 12 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 29 ( 29 usr; 19 con; 0-2 aty)
% Number of variables : 127 ( 17 sgn 62 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_def__all__of,axiom,
! [X4,X5] :
( pp(aa_fun171081125l_bool(scratc2055738343all_of(X4),X5))
<=> ! [X12] :
( gg_TPTP_ind(X12)
=> ( scratc2135361906_is_of(X12,X4)
=> pp(aa_TPTP_ind_bool(X5,X12)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_def__all__of) ).
fof(fact_satz10c,axiom,
pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aTP_Lamm_gu)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_satz10c) ).
fof(fact_satz24,axiom,
pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aTP_Lamm_bo)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_satz24) ).
fof(fact_ATP_Olambda__39,axiom,
! [X25] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_gu,X25))
<=> pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gt,X25))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ATP_Olambda__39) ).
fof(fact_n__1__p,axiom,
scratc2135361906_is_of(scratc2094053556nd_n_1,aTP_Lamm_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__1__p) ).
fof(gsy_c_Scratch__tptp__translate__50151__9814_ONUM694__thf__4__p_Obnd__n__1,hypothesis,
gg_TPTP_ind(scratc2094053556nd_n_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Scratch__tptp__translate__50151__9814_ONUM694__thf__4__p_Obnd__n__1) ).
fof(help_fimplies_1_1_U,axiom,
! [X32,X33] :
( pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,X32),X33))
| pp(X32) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fimplies_1_1_U) ).
fof(fact_ATP_Olambda__15,axiom,
! [X25] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_bo,X25))
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,X25),scratc2094053556nd_n_1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ATP_Olambda__15) ).
fof(help_fFalse_1_1_U,axiom,
~ pp(fFalse),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).
fof(help_fFalse_1_1_T,axiom,
! [X32] :
( gg_bool(X32)
=> ( X32 = fFalse
| X32 = fTrue ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_T) ).
fof(gsy_c_Scratch__tptp__translate__50151__9814_ONUM694__thf__4__p_Obnd__d__not,axiom,
! [X1] : gg_bool(scratc1230282688_d_not(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Scratch__tptp__translate__50151__9814_ONUM694__thf__4__p_Obnd__d__not) ).
fof(fact_def__d__not,axiom,
! [X4] :
( pp(scratc1230282688_d_not(X4))
<=> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc302099643nd_imp,X4),fFalse)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_def__d__not) ).
fof(fact_def__imp,axiom,
scratc302099643nd_imp = fimplies,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_def__imp) ).
fof(fact_satz10j,axiom,
pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aTP_Lamm_gi)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_satz10j) ).
fof(fact_ATP_Olambda__107,axiom,
! [X25,X26] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gt,X25),X26))
<=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,X25),X26))
=> pp(scratc1230282688_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc301837240nd_iii,X25),X26))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ATP_Olambda__107) ).
fof(fact_l__et,axiom,
! [X17] :
( scratc417235917nd_wel(X17)
=> pp(X17) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_l__et) ).
fof(fact_def__wel,axiom,
! [X4] :
( scratc417235917nd_wel(X4)
<=> pp(scratc1230282688_d_not(scratc1230282688_d_not(X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_def__wel) ).
fof(fact_def__r__ec,axiom,
! [X4,X5] :
( scratc2146893183d_r_ec(X4,X5)
<=> ( pp(X4)
=> pp(scratc1230282688_d_not(X5)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_def__r__ec) ).
fof(conj_0,conjecture,
pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(fact_ATP_Olambda__45,axiom,
! [X25] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_gi,X25))
<=> pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gh,X25))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ATP_Olambda__45) ).
fof(gsy_c_aa_001t__TPTP____Interpret__Oind_001t__HOL__Obool,axiom,
! [X1,X2] : gg_bool(aa_TPTP_ind_bool(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_aa_001t__TPTP____Interpret__Oind_001t__HOL__Obool) ).
fof(help_pp_2_1_U,axiom,
pp(fTrue),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).
fof(help_fEx_1_1_fEx_001t__TPTP____Interpret__Oind_U,axiom,
! [X32,X34] :
( pp(fEx_TPTP_ind(X32))
| ~ pp(aa_TPTP_ind_bool(X32,X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fEx_1_1_fEx_001t__TPTP____Interpret__Oind_U) ).
fof(fact_ATP_Olambda__11,axiom,
! [X25] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_jf,X25))
<=> scratc2135361906_is_of(aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,X25),aTP_Lamm_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ATP_Olambda__11) ).
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_def__n__1,axiom,
scratc2094053556nd_n_1 = aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_def__n__1) ).
fof(fact_ATP_Olambda__116,axiom,
! [X25,X26] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gh,X25),X26))
<=> ( pp(scratc1230282688_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,X25),X26)))
=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc301837240nd_iii,X25),X26)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ATP_Olambda__116) ).
fof(fact_satz13,axiom,
pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aTP_Lamm_gy)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_satz13) ).
fof(fact_ATP_Olambda__103,axiom,
! [X25,X26] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,X25),X26))
<=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,X25),X26))
=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,X26),X25)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ATP_Olambda__103) ).
fof(fact_ATP_Olambda__37,axiom,
! [X25] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_gy,X25))
<=> pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,X25))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ATP_Olambda__37) ).
fof(c_0_30,plain,
! [X359,X360,X361,X362,X363] :
( ( pp(aa_fun171081125l_bool(scratc2055738343all_of(X362),X363))
| ~ pp(aa_TPTP_ind_bool(X363,esk13_2(X362,X363))) )
& ( pp(aa_fun171081125l_bool(scratc2055738343all_of(X362),X363))
| scratc2135361906_is_of(esk13_2(X362,X363),X362) )
& ( pp(aa_fun171081125l_bool(scratc2055738343all_of(X362),X363))
| gg_TPTP_ind(esk13_2(X362,X363)) )
& ( pp(aa_TPTP_ind_bool(X360,X361))
| ~ scratc2135361906_is_of(X361,X359)
| ~ gg_TPTP_ind(X361)
| ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(X359),X360)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[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])])])])])])]) ).
cnf(c_0_31,plain,
( ~ scratc2135361906_is_of(X3,X1)
| ~ gg_TPTP_ind(X3)
| ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(X1),X2))
| pp(aa_TPTP_ind_bool(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_32,plain,
pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aTP_Lamm_gu)),
inference(split_conjunct,[status(thm)],[fact_satz10c]) ).
cnf(c_0_33,plain,
pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aTP_Lamm_bo)),
inference(split_conjunct,[status(thm)],[fact_satz24]) ).
fof(c_0_34,plain,
! [X548] :
( ( pp(aa_TPTP_ind_bool(aTP_Lamm_gu,X548))
| ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gt,X548))) )
& ( pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gt,X548)))
| ~ pp(aa_TPTP_ind_bool(aTP_Lamm_gu,X548)) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ATP_Olambda__39])])]) ).
cnf(c_0_35,plain,
( ~ gg_TPTP_ind(X1)
| ~ scratc2135361906_is_of(X1,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aTP_Lamm_gu,X1)) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_36,plain,
scratc2135361906_is_of(scratc2094053556nd_n_1,aTP_Lamm_a),
inference(split_conjunct,[status(thm)],[fact_n__1__p]) ).
cnf(c_0_37,hypothesis,
gg_TPTP_ind(scratc2094053556nd_n_1),
inference(split_conjunct,[status(thm)],[gsy_c_Scratch__tptp__translate__50151__9814_ONUM694__thf__4__p_Obnd__n__1]) ).
fof(c_0_38,plain,
! [X1125,X1126] :
( pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,X1125),X1126))
| pp(X1125) ),
inference(variable_rename,[status(thm)],[help_fimplies_1_1_U]) ).
fof(c_0_39,plain,
! [X524] :
( ( pp(aa_TPTP_ind_bool(aTP_Lamm_bo,X524))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,X524),scratc2094053556nd_n_1)) )
& ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,X524),scratc2094053556nd_n_1))
| ~ pp(aa_TPTP_ind_bool(aTP_Lamm_bo,X524)) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ATP_Olambda__15])])]) ).
cnf(c_0_40,plain,
( ~ gg_TPTP_ind(X1)
| ~ scratc2135361906_is_of(X1,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aTP_Lamm_bo,X1)) ),
inference(spm,[status(thm)],[c_0_31,c_0_33]) ).
cnf(c_0_41,plain,
( ~ pp(aa_TPTP_ind_bool(aTP_Lamm_gu,X1))
| pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gt,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_42,plain,
pp(aa_TPTP_ind_bool(aTP_Lamm_gu,scratc2094053556nd_n_1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37])]) ).
fof(c_0_43,plain,
~ pp(fFalse),
inference(fof_simplification,[status(thm)],[help_fFalse_1_1_U]) ).
fof(c_0_44,plain,
! [X1120] :
( X1120 = fFalse
| X1120 = fTrue
| ~ gg_bool(X1120) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[help_fFalse_1_1_T])])]) ).
fof(c_0_45,plain,
! [X41] : gg_bool(scratc1230282688_d_not(X41)),
inference(variable_rename,[status(thm)],[gsy_c_Scratch__tptp__translate__50151__9814_ONUM694__thf__4__p_Obnd__d__not]) ).
fof(c_0_46,plain,
! [X280] :
( ( pp(scratc1230282688_d_not(X280))
| ~ pp(aa_bool_bool(aa_boo1142376798l_bool(scratc302099643nd_imp,X280),fFalse)) )
& ( pp(aa_bool_bool(aa_boo1142376798l_bool(scratc302099643nd_imp,X280),fFalse))
| ~ pp(scratc1230282688_d_not(X280)) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_def__d__not])])]) ).
cnf(c_0_47,plain,
( pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,X1),X2))
| pp(X1) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_48,plain,
scratc302099643nd_imp = fimplies,
inference(split_conjunct,[status(thm)],[fact_def__imp]) ).
cnf(c_0_49,plain,
pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aTP_Lamm_gi)),
inference(split_conjunct,[status(thm)],[fact_satz10j]) ).
fof(c_0_50,plain,
! [X640,X641] :
( ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gt,X640),X641))
| ~ pp(scratc1230282688_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc301837240nd_iii,X640),X641))) )
& ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gt,X640),X641))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,X640),X641)) )
& ( pp(scratc1230282688_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc301837240nd_iii,X640),X641)))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,X640),X641))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gt,X640),X641)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ATP_Olambda__107])])])]) ).
cnf(c_0_51,plain,
( ~ pp(aa_TPTP_ind_bool(aTP_Lamm_bo,X1))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,X1),scratc2094053556nd_n_1)) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_52,plain,
pp(aa_TPTP_ind_bool(aTP_Lamm_bo,scratc2094053556nd_n_1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_36]),c_0_37])]) ).
cnf(c_0_53,plain,
pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gt,scratc2094053556nd_n_1))),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
fof(c_0_54,plain,
~ pp(fFalse),
inference(fof_nnf,[status(thm)],[c_0_43]) ).
fof(c_0_55,plain,
! [X403] :
( pp(X403)
| ~ scratc417235917nd_wel(X403) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_l__et])])]) ).
fof(c_0_56,plain,
! [X279] :
( ( scratc417235917nd_wel(X279)
| ~ pp(scratc1230282688_d_not(scratc1230282688_d_not(X279))) )
& ( pp(scratc1230282688_d_not(scratc1230282688_d_not(X279)))
| ~ scratc417235917nd_wel(X279) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_def__wel])])]) ).
cnf(c_0_57,plain,
( ~ gg_bool(X1)
| X1 = fFalse
| X1 = fTrue ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_58,plain,
gg_bool(scratc1230282688_d_not(X1)),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
fof(c_0_59,plain,
! [X177,X178] :
( ( scratc2146893183d_r_ec(X177,X178)
| ~ pp(scratc1230282688_d_not(X178)) )
& ( scratc2146893183d_r_ec(X177,X178)
| pp(X177) )
& ( pp(scratc1230282688_d_not(X178))
| ~ pp(X177)
| ~ scratc2146893183d_r_ec(X177,X178) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_def__r__ec])])])]) ).
cnf(c_0_60,plain,
( ~ pp(aa_bool_bool(aa_boo1142376798l_bool(scratc302099643nd_imp,X1),fFalse))
| pp(scratc1230282688_d_not(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_61,plain,
( pp(X1)
| pp(aa_bool_bool(aa_boo1142376798l_bool(scratc302099643nd_imp,X1),X2)) ),
inference(rw,[status(thm)],[c_0_47,c_0_48]) ).
fof(c_0_62,negated_conjecture,
~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1))),
inference(assume_negation,[status(cth)],[conj_0]) ).
fof(c_0_63,plain,
! [X554] :
( ( pp(aa_TPTP_ind_bool(aTP_Lamm_gi,X554))
| ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gh,X554))) )
& ( pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gh,X554)))
| ~ pp(aa_TPTP_ind_bool(aTP_Lamm_gi,X554)) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ATP_Olambda__45])])]) ).
cnf(c_0_64,plain,
( ~ gg_TPTP_ind(X1)
| ~ scratc2135361906_is_of(X1,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aTP_Lamm_gi,X1)) ),
inference(spm,[status(thm)],[c_0_31,c_0_49]) ).
cnf(c_0_65,plain,
( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,X1),X2))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gt,X1),X2))
| pp(scratc1230282688_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc301837240nd_iii,X1),X2))) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_66,plain,
pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,scratc2094053556nd_n_1),scratc2094053556nd_n_1)),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_67,plain,
( ~ gg_TPTP_ind(X1)
| ~ scratc2135361906_is_of(X1,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gt,scratc2094053556nd_n_1),X1)) ),
inference(spm,[status(thm)],[c_0_31,c_0_53]) ).
fof(c_0_68,plain,
! [X57,X58] : gg_bool(aa_TPTP_ind_bool(X57,X58)),
inference(variable_rename,[status(thm)],[gsy_c_aa_001t__TPTP____Interpret__Oind_001t__HOL__Obool]) ).
cnf(c_0_69,plain,
~ pp(fFalse),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_70,plain,
( ~ scratc417235917nd_wel(X1)
| pp(X1) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_71,plain,
( ~ pp(scratc1230282688_d_not(scratc1230282688_d_not(X1)))
| scratc417235917nd_wel(X1) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_72,plain,
( scratc1230282688_d_not(X1) = fTrue
| scratc1230282688_d_not(X1) = fFalse ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_73,plain,
pp(fTrue),
inference(split_conjunct,[status(thm)],[help_pp_2_1_U]) ).
cnf(c_0_74,plain,
( ~ pp(scratc1230282688_d_not(X1))
| scratc2146893183d_r_ec(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_75,plain,
( pp(X1)
| pp(scratc1230282688_d_not(X1)) ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
fof(c_0_76,plain,
! [X32,X34] :
( pp(fEx_TPTP_ind(X32))
| ~ pp(aa_TPTP_ind_bool(X32,X34)) ),
inference(fof_simplification,[status(thm)],[help_fEx_1_1_fEx_001t__TPTP____Interpret__Oind_U]) ).
fof(c_0_77,plain,
! [X520] :
( ( pp(aa_TPTP_ind_bool(aTP_Lamm_jf,X520))
| ~ scratc2135361906_is_of(aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,X520),aTP_Lamm_a) )
& ( scratc2135361906_is_of(aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,X520),aTP_Lamm_a)
| ~ pp(aa_TPTP_ind_bool(aTP_Lamm_jf,X520)) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ATP_Olambda__11])])]) ).
fof(c_0_78,negated_conjecture,
~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1))),
inference(fof_simplification,[status(thm)],[c_0_62]) ).
fof(c_0_79,hypothesis,
! [X61,X62] : gg_bool(aa_fun171081125l_bool(X61,X62)),
inference(variable_rename,[status(thm)],[gsy_c_aa_001t__fun_It__TPTP____Interpret__Oind_Mt__HOL__Obool_J_001t__HOL__Obool]) ).
cnf(c_0_80,plain,
( ~ pp(aa_TPTP_ind_bool(aTP_Lamm_gi,X1))
| pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gh,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_81,plain,
pp(aa_TPTP_ind_bool(aTP_Lamm_gi,scratc2094053556nd_n_1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_36]),c_0_37])]) ).
cnf(c_0_82,plain,
( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gt,scratc2094053556nd_n_1),scratc2094053556nd_n_1))
| pp(scratc1230282688_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc301837240nd_iii,scratc2094053556nd_n_1),scratc2094053556nd_n_1))) ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_83,plain,
pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gt,scratc2094053556nd_n_1),scratc2094053556nd_n_1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_36]),c_0_37])]) ).
cnf(c_0_84,plain,
gg_bool(aa_TPTP_ind_bool(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_85,plain,
~ scratc417235917nd_wel(fFalse),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_86,plain,
( scratc417235917nd_wel(X1)
| scratc1230282688_d_not(scratc1230282688_d_not(X1)) = fFalse ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_73])]) ).
cnf(c_0_87,plain,
( pp(X2)
| scratc2146893183d_r_ec(X1,X2) ),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
fof(c_0_88,plain,
! [X1127,X1128] :
( pp(fEx_TPTP_ind(X1127))
| ~ pp(aa_TPTP_ind_bool(X1127,X1128)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_76])]) ).
cnf(c_0_89,plain,
( ~ scratc2135361906_is_of(aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,X1),aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aTP_Lamm_jf,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
cnf(c_0_90,plain,
scratc2094053556nd_n_1 = aa_TPTP_ind_TPTP_ind(scratc1138364274rdsucc,scratc1150508294ptyset),
inference(split_conjunct,[status(thm)],[fact_def__n__1]) ).
fof(c_0_91,negated_conjecture,
~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1))),
inference(fof_nnf,[status(thm)],[c_0_78]) ).
cnf(c_0_92,hypothesis,
gg_bool(aa_fun171081125l_bool(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_93,plain,
pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gh,scratc2094053556nd_n_1))),
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_94,plain,
pp(scratc1230282688_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc301837240nd_iii,scratc2094053556nd_n_1),scratc2094053556nd_n_1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_82,c_0_83])]) ).
cnf(c_0_95,plain,
( aa_TPTP_ind_bool(X1,X2) = fTrue
| aa_TPTP_ind_bool(X1,X2) = fFalse ),
inference(spm,[status(thm)],[c_0_57,c_0_84]) ).
cnf(c_0_96,plain,
scratc1230282688_d_not(scratc1230282688_d_not(fFalse)) = fFalse,
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_97,plain,
( ~ pp(X1)
| ~ scratc2146893183d_r_ec(X1,X2)
| pp(scratc1230282688_d_not(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_98,plain,
scratc2146893183d_r_ec(X1,fFalse),
inference(spm,[status(thm)],[c_0_69,c_0_87]) ).
cnf(c_0_99,plain,
( ~ pp(aa_TPTP_ind_bool(X1,X2))
| pp(fEx_TPTP_ind(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_88]) ).
cnf(c_0_100,plain,
pp(aa_TPTP_ind_bool(aTP_Lamm_jf,scratc1150508294ptyset)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_36])]) ).
cnf(c_0_101,plain,
( ~ pp(aa_TPTP_ind_bool(X1,esk13_2(X2,X1)))
| pp(aa_fun171081125l_bool(scratc2055738343all_of(X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_102,plain,
( scratc2146893183d_r_ec(X1,X2)
| pp(X1) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_103,negated_conjecture,
~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1))),
inference(split_conjunct,[status(thm)],[c_0_91]) ).
cnf(c_0_104,hypothesis,
( aa_fun171081125l_bool(X1,X2) = fTrue
| aa_fun171081125l_bool(X1,X2) = fFalse ),
inference(spm,[status(thm)],[c_0_57,c_0_92]) ).
fof(c_0_105,plain,
! [X658,X659] :
( ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gh,X658),X659))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc301837240nd_iii,X658),X659)) )
& ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gh,X658),X659))
| pp(scratc1230282688_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,X658),X659))) )
& ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc301837240nd_iii,X658),X659))
| ~ pp(scratc1230282688_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,X658),X659)))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gh,X658),X659)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ATP_Olambda__116])])])]) ).
cnf(c_0_106,plain,
( ~ gg_TPTP_ind(X1)
| ~ scratc2135361906_is_of(X1,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gh,scratc2094053556nd_n_1),X1)) ),
inference(spm,[status(thm)],[c_0_31,c_0_93]) ).
cnf(c_0_107,plain,
( pp(scratc1230282688_d_not(fTrue))
| aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc301837240nd_iii,scratc2094053556nd_n_1),scratc2094053556nd_n_1) = fFalse ),
inference(spm,[status(thm)],[c_0_94,c_0_95]) ).
cnf(c_0_108,plain,
( scratc1230282688_d_not(fTrue) = fFalse
| scratc1230282688_d_not(fFalse) = fFalse ),
inference(spm,[status(thm)],[c_0_96,c_0_72]) ).
cnf(c_0_109,plain,
( ~ pp(X1)
| pp(scratc1230282688_d_not(fFalse)) ),
inference(spm,[status(thm)],[c_0_97,c_0_98]) ).
cnf(c_0_110,plain,
pp(fEx_TPTP_ind(aTP_Lamm_jf)),
inference(spm,[status(thm)],[c_0_99,c_0_100]) ).
cnf(c_0_111,plain,
( pp(aa_fun171081125l_bool(scratc2055738343all_of(X1),X2))
| scratc2135361906_is_of(esk13_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_112,plain,
( pp(aa_fun171081125l_bool(scratc2055738343all_of(X1),X2))
| gg_TPTP_ind(esk13_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_113,plain,
( pp(aa_fun171081125l_bool(scratc2055738343all_of(X2),X1))
| scratc2146893183d_r_ec(aa_TPTP_ind_bool(X1,esk13_2(X2,X1)),X3) ),
inference(spm,[status(thm)],[c_0_101,c_0_102]) ).
cnf(c_0_114,negated_conjecture,
aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1)) = fFalse,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_73])]) ).
cnf(c_0_115,plain,
( ~ pp(scratc1230282688_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,X1),X2)))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gh,X1),X2))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc301837240nd_iii,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_105]) ).
cnf(c_0_116,plain,
pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gh,scratc2094053556nd_n_1),scratc2094053556nd_n_1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_36]),c_0_37])]) ).
cnf(c_0_117,plain,
( scratc1230282688_d_not(fFalse) = fFalse
| aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc301837240nd_iii,scratc2094053556nd_n_1),scratc2094053556nd_n_1) = fFalse ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_69]) ).
cnf(c_0_118,plain,
pp(scratc1230282688_d_not(fFalse)),
inference(spm,[status(thm)],[c_0_109,c_0_110]) ).
cnf(c_0_119,negated_conjecture,
scratc2135361906_is_of(esk13_2(aTP_Lamm_a,aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1)),aTP_Lamm_a),
inference(spm,[status(thm)],[c_0_103,c_0_111]) ).
cnf(c_0_120,negated_conjecture,
gg_TPTP_ind(esk13_2(aTP_Lamm_a,aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1))),
inference(spm,[status(thm)],[c_0_103,c_0_112]) ).
cnf(c_0_121,negated_conjecture,
scratc2146893183d_r_ec(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),esk13_2(aTP_Lamm_a,aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1))),X1),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_114]),c_0_69]) ).
cnf(c_0_122,plain,
( ~ pp(scratc1230282688_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,scratc2094053556nd_n_1),scratc2094053556nd_n_1)))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc301837240nd_iii,scratc2094053556nd_n_1),scratc2094053556nd_n_1)) ),
inference(spm,[status(thm)],[c_0_115,c_0_116]) ).
cnf(c_0_123,plain,
aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc301837240nd_iii,scratc2094053556nd_n_1),scratc2094053556nd_n_1) = fFalse,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_117]),c_0_118])]),c_0_85]) ).
cnf(c_0_124,plain,
pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aTP_Lamm_gy)),
inference(split_conjunct,[status(thm)],[fact_satz13]) ).
fof(c_0_125,plain,
! [X632,X633] :
( ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,X632),X633))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,X633),X632)) )
& ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,X632),X633))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,X632),X633)) )
& ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,X633),X632))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,X632),X633))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,X632),X633)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ATP_Olambda__103])])])]) ).
cnf(c_0_126,negated_conjecture,
pp(aa_TPTP_ind_bool(aTP_Lamm_bo,esk13_2(aTP_Lamm_a,aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_119]),c_0_120])]) ).
cnf(c_0_127,negated_conjecture,
( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),esk13_2(aTP_Lamm_a,aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1))))
| pp(scratc1230282688_d_not(X1)) ),
inference(spm,[status(thm)],[c_0_97,c_0_121]) ).
cnf(c_0_128,plain,
~ pp(scratc1230282688_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,scratc2094053556nd_n_1),scratc2094053556nd_n_1))),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_122,c_0_123]),c_0_69]) ).
fof(c_0_129,plain,
! [X546] :
( ( pp(aa_TPTP_ind_bool(aTP_Lamm_gy,X546))
| ~ pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,X546))) )
& ( pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,X546)))
| ~ pp(aa_TPTP_ind_bool(aTP_Lamm_gy,X546)) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ATP_Olambda__37])])]) ).
cnf(c_0_130,plain,
( ~ gg_TPTP_ind(X1)
| ~ scratc2135361906_is_of(X1,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aTP_Lamm_gy,X1)) ),
inference(spm,[status(thm)],[c_0_31,c_0_124]) ).
cnf(c_0_131,plain,
( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,X1),X2))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,X1),X2))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_125]) ).
cnf(c_0_132,negated_conjecture,
pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,esk13_2(aTP_Lamm_a,aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1))),scratc2094053556nd_n_1)),
inference(spm,[status(thm)],[c_0_51,c_0_126]) ).
cnf(c_0_133,negated_conjecture,
( pp(scratc1230282688_d_not(X1))
| aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),esk13_2(aTP_Lamm_a,aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1))) = fFalse ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_95]),c_0_73])]) ).
cnf(c_0_134,plain,
scratc1230282688_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc1060564016moreis,scratc2094053556nd_n_1),scratc2094053556nd_n_1)) = fFalse,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_72]),c_0_73])]) ).
cnf(c_0_135,plain,
( ~ pp(aa_TPTP_ind_bool(aTP_Lamm_gy,X1))
| pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_129]) ).
cnf(c_0_136,negated_conjecture,
pp(aa_TPTP_ind_bool(aTP_Lamm_gy,esk13_2(aTP_Lamm_a,aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_119]),c_0_120])]) ).
cnf(c_0_137,negated_conjecture,
( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,esk13_2(aTP_Lamm_a,aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1))),scratc2094053556nd_n_1))
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),esk13_2(aTP_Lamm_a,aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1)))) ),
inference(spm,[status(thm)],[c_0_131,c_0_132]) ).
cnf(c_0_138,negated_conjecture,
aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1),esk13_2(aTP_Lamm_a,aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1))) = fFalse,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_134]),c_0_69]) ).
cnf(c_0_139,negated_conjecture,
pp(aa_fun171081125l_bool(scratc2055738343all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_gx,esk13_2(aTP_Lamm_a,aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1))))),
inference(spm,[status(thm)],[c_0_135,c_0_136]) ).
cnf(c_0_140,negated_conjecture,
~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,esk13_2(aTP_Lamm_a,aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1))),scratc2094053556nd_n_1)),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_137,c_0_138]),c_0_69]) ).
cnf(c_0_141,negated_conjecture,
( ~ gg_TPTP_ind(X1)
| ~ scratc2135361906_is_of(X1,aTP_Lamm_a)
| pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,esk13_2(aTP_Lamm_a,aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1))),X1)) ),
inference(spm,[status(thm)],[c_0_31,c_0_139]) ).
cnf(c_0_142,negated_conjecture,
aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_gx,esk13_2(aTP_Lamm_a,aa_TPT43085870d_bool(scratc926580404lessis,scratc2094053556nd_n_1))),scratc2094053556nd_n_1) = fFalse,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_95]),c_0_73])]) ).
cnf(c_0_143,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_36]),c_0_142]),c_0_37])]),c_0_69]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM694+4 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/0.44 % Computer : n026.cluster.edu
% 0.16/0.44 % Model : x86_64 x86_64
% 0.16/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.44 % Memory : 8046.5625MB
% 0.16/0.44 % OS : Linux 6.8.0-71-generic
% 0.16/0.44 % CPULimit : 300
% 0.16/0.44 % WCLimit : 300
% 0.16/0.44 % DateTime : Mon Sep 21 02:58:22 UTC 2026
% 0.16/0.44 % CPUTime :
% 0.16/0.44 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/0.48 Running first-order theorem proving
% 0.16/0.48 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
% 11.23/2.42 % Version: 3.5.1
% 11.23/2.42 % Preprocessing class: FSLMSMSLSSSNFFN.
% 11.23/2.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 11.23/2.42 % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 900s (3) cores
% 11.23/2.42 % Starting new_bool_3 with 600s (2) cores
% 11.23/2.42 % Starting new_bool_1 with 600s (2) cores
% 11.23/2.42 % Starting sh5l with 300s (1) cores
% 11.23/2.42 % G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with pid 1216978 completed with status 0
% 11.23/2.42 % Result found by G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI
% 11.23/2.42 % Preprocessing class: FSLMSMSLSSSNFFN.
% 11.23/2.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 11.23/2.42 % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 900s (3) cores
% 11.23/2.42 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 11.23/2.42 % No SInE strategy applied
% 11.23/2.42 % Search class: FGHSM-SSLM31-DFFFFFNN
% 11.23/2.42 % Scheduled 7 strats onto 3 cores with 900 seconds (900 total)
% 11.23/2.42 % Starting SubtermCWHack with 82s (1) cores
% 11.23/2.42 % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 91s (1) cores
% 11.23/2.42 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_RG_S2S with 82s (1) cores
% 11.23/2.42 % G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with pid 1216988 completed with status 0
% 11.23/2.42 % Result found by G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI
% 11.23/2.42 % Preprocessing class: FSLMSMSLSSSNFFN.
% 11.23/2.42 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 11.23/2.42 % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 900s (3) cores
% 11.23/2.42 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 11.23/2.42 % No SInE strategy applied
% 11.23/2.42 % Search class: FGHSM-SSLM31-DFFFFFNN
% 11.23/2.42 % Scheduled 7 strats onto 3 cores with 900 seconds (900 total)
% 11.23/2.42 % Starting SubtermCWHack with 82s (1) cores
% 11.23/2.42 % Starting G-E--_008_C45_F1_PI_SE_Q4_CS_SP_S4SI with 91s (1) cores
% 11.23/2.42 % Preprocessing time : 0.015 s
% 11.23/2.42
% 11.23/2.42 % Proof found!
% 11.23/2.42 % SZS status Theorem
% 11.23/2.42 % SZS output start CNFRefutation
% See solution above
% 11.23/2.42 % Parsed axioms : 573
% 11.23/2.42 % Removed by relevancy pruning/SinE : 0
% 11.23/2.42 % Initial clauses : 1035
% 11.23/2.42 % Removed in clause preprocessing : 18
% 11.23/2.42 % Initial clauses in saturation : 1017
% 11.23/2.42 % Processed clauses : 6470
% 11.23/2.42 % ...of these trivial : 79
% 11.23/2.42 % ...subsumed : 612
% 11.23/2.42 % ...remaining for further processing : 5779
% 11.23/2.42 % Other redundant clauses eliminated : 8
% 11.23/2.42 % Clauses deleted for lack of memory : 0
% 11.23/2.42 % Backward-subsumed : 26
% 11.23/2.42 % Backward-rewritten : 188
% 11.23/2.42 % Generated clauses : 56513
% 11.23/2.42 % ...of the previous two non-redundant : 49493
% 11.23/2.42 % ...aggressively subsumed : 0
% 11.23/2.42 % Contextual simplify-reflections : 1
% 11.23/2.42 % Paramodulations : 56490
% 11.23/2.42 % Factorizations : 13
% 11.23/2.42 % NegExts : 0
% 11.23/2.42 % Equation resolutions : 10
% 11.23/2.42 % Disequality decompositions : 0
% 11.23/2.42 % Total rewrite steps : 15268
% 11.23/2.42 % ...of those cached : 12789
% 11.23/2.42 % Propositional unsat checks : 0
% 11.23/2.42 % Propositional check models : 0
% 11.23/2.42 % Propositional check unsatisfiable : 0
% 11.23/2.42 % Propositional clauses : 0
% 11.23/2.42 % Propositional clauses after purity: 0
% 11.23/2.42 % Propositional unsat core size : 0
% 11.23/2.42 % Propositional preprocessing time : 0.000
% 11.23/2.42 % Propositional encoding time : 0.000
% 11.23/2.42 % Propositional solver time : 0.000
% 11.23/2.42 % Success case prop preproc time : 0.000
% 11.23/2.42 % Success case prop encoding time : 0.000
% 11.23/2.42 % Success case prop solver time : 0.000
% 11.23/2.42 % Current number of processed clauses : 5557
% 11.23/2.42 % Positive orientable unit clauses : 3312
% 11.23/2.42 % Positive unorientable unit clauses: 3
% 11.23/2.42 % Negative unit clauses : 12
% 11.23/2.42 % Non-unit-clauses : 2230
% 11.23/2.42 % Current number of unprocessed clauses: 41904
% 11.23/2.42 % ...number of literals in the above : 105127
% 11.23/2.42 % Current number of archived formulas : 0
% 11.23/2.42 % Current number of archived clauses : 230
% 11.23/2.42 % Clause-clause subsumption calls (NU) : 490161
% 11.23/2.42 % Rec. Clause-clause subsumption calls : 413692
% 11.23/2.42 % Non-unit clause-clause subsumptions : 414
% 11.23/2.42 % Unit Clause-clause subsumption calls : 630633
% 11.23/2.42 % Rewrite failures with RHS unbound : 0
% 11.23/2.42 % BW rewrite match attempts : 311476
% 11.23/2.42 % BW rewrite match successes : 152
% 11.23/2.42 % Condensation attempts : 0
% 11.23/2.42 % Condensation successes : 0
% 11.23/2.42 % Termbank termtop insertions : 1032058
% 11.23/2.42 % Search garbage collected termcells : 10456
% 11.23/2.42
% 11.23/2.42 % -------------------------------------------------
% 11.23/2.42 % User time : 1.780 s
% 11.23/2.42 % System time : 0.092 s
% 11.23/2.42 % Total time : 1.872 s
% 11.23/2.42 % Maximum resident set size: 7344 pages
% 11.23/2.42
% 11.23/2.42 % -------------------------------------------------
% 11.23/2.42 % User time : 5.276 s
% 11.23/2.42 % System time : 0.270 s
% 11.23/2.42 % Total time : 5.546 s
% 11.23/2.42 % Maximum resident set size: 5376 pages
% 11.23/2.42 % E exiting
%------------------------------------------------------------------------------