%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWW470+5 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 03:10:46 PM UTC 2026
% Result : Theorem 87.56s 13.16s
% Output : CNFRefutation 87.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 20
% Syntax : Number of formulae : 91 ( 60 unt; 0 def)
% Number of atoms : 129 ( 61 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 66 ( 28 ~; 29 |; 3 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 14 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 30 ( 30 usr; 12 con; 0-5 aty)
% Number of variables : 183 ( 7 sgn 82 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(help_fFalse_1_1_T,axiom,
! [X65] :
( ti(bool,X65) = fFalse
| ti(bool,X65) = fTrue ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_T) ).
fof(fact_54_the__sym__eq__trivial,axiom,
! [X1,X32] : hAPP(fun(X1,bool),X1,the(X1),hAPP(X1,fun(X1,bool),fequal(X1),X32)) = ti(X1,X32),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_the__sym__eq__trivial) ).
fof(tsy_c_hAPP_res,axiom,
! [X2,X3,X4,X5] : ti(X2,hAPP(X3,X2,X4,X5)) = hAPP(X3,X2,X4,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_hAPP_res) ).
fof(help_fFalse_1_1_U,axiom,
~ hBOOL(fFalse),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).
fof(help_fNot_2_1_U,axiom,
! [X65] :
( hBOOL(hAPP(bool,bool,fNot,X65))
| hBOOL(X65) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_2_1_U) ).
fof(tsy_c_hAPP_arg2,axiom,
! [X3,X2,X4,X5] : hAPP(X3,X2,X4,ti(X3,X5)) = hAPP(X3,X2,X4,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_hAPP_arg2) ).
fof(fact_11_emptyE,axiom,
! [X1,X26] : ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),bot_bot(fun(X1,bool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_emptyE) ).
fof(fact_77_Collect__def,axiom,
! [X1,X16] : hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X16) = ti(fun(X1,bool),X16),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_Collect__def) ).
fof(tsy_c_hBOOL_arg1,hypothesis,
! [X4] :
( hBOOL(ti(bool,X4))
<=> hBOOL(X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_hBOOL_arg1) ).
fof(fact_66_bot__empty__eq,axiom,
! [X1,X31] :
( hBOOL(hAPP(X1,bool,bot_bot(fun(X1,bool)),X31))
<=> hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X31),bot_bot(fun(X1,bool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_bot__empty__eq) ).
fof(fact_43_bot__apply,axiom,
! [X2,X1] :
( bot(X1)
=> ! [X32] : hAPP(X2,X1,bot_bot(fun(X2,X1)),X32) = bot_bot(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_bot__apply) ).
fof(conj_0,conjecture,
hBOOL(hAPP(fun(hoare_509422987triple(x_a),bool),bool,hAPP(fun(hoare_509422987triple(x_a),bool),fun(fun(hoare_509422987triple(x_a),bool),bool),hoare_122391849derivs(x_a),g),hAPP(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool),hAPP(hoare_509422987triple(x_a),fun(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool)),insert(hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse))),c),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)))),bot_bot(fun(hoare_509422987triple(x_a),bool))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(fact_5_escape,axiom,
! [X1,X6,X17,X18,X16] :
( ! [X20,X21] :
( hBOOL(hAPP(state,bool,hAPP(X1,fun(state,bool),X16,X20),X21))
=> hBOOL(hAPP(fun(hoare_509422987triple(X1),bool),bool,hAPP(fun(hoare_509422987triple(X1),bool),fun(fun(hoare_509422987triple(X1),bool),bool),hoare_122391849derivs(X1),X6),hAPP(fun(hoare_509422987triple(X1),bool),fun(hoare_509422987triple(X1),bool),hAPP(hoare_509422987triple(X1),fun(fun(hoare_509422987triple(X1),bool),fun(hoare_509422987triple(X1),bool)),insert(hoare_509422987triple(X1)),hAPP(fun(X1,fun(state,bool)),hoare_509422987triple(X1),hAPP(com,fun(fun(X1,fun(state,bool)),hoare_509422987triple(X1)),hAPP(fun(X1,fun(state,bool)),fun(com,fun(fun(X1,fun(state,bool)),hoare_509422987triple(X1))),hoare_1008221573triple(X1),hAPP(fun(state,bool),fun(X1,fun(state,bool)),combk(fun(state,bool),X1),hAPP(state,fun(state,bool),hAPP(fun(state,fun(state,bool)),fun(state,fun(state,bool)),combc(state,state,bool),fequal(state)),X21))),X17),hAPP(fun(state,bool),fun(X1,fun(state,bool)),combk(fun(state,bool),X1),hAPP(X1,fun(state,bool),X18,X20)))),bot_bot(fun(hoare_509422987triple(X1),bool))))) )
=> hBOOL(hAPP(fun(hoare_509422987triple(X1),bool),bool,hAPP(fun(hoare_509422987triple(X1),bool),fun(fun(hoare_509422987triple(X1),bool),bool),hoare_122391849derivs(X1),X6),hAPP(fun(hoare_509422987triple(X1),bool),fun(hoare_509422987triple(X1),bool),hAPP(hoare_509422987triple(X1),fun(fun(hoare_509422987triple(X1),bool),fun(hoare_509422987triple(X1),bool)),insert(hoare_509422987triple(X1)),hAPP(fun(X1,fun(state,bool)),hoare_509422987triple(X1),hAPP(com,fun(fun(X1,fun(state,bool)),hoare_509422987triple(X1)),hAPP(fun(X1,fun(state,bool)),fun(com,fun(fun(X1,fun(state,bool)),hoare_509422987triple(X1))),hoare_1008221573triple(X1),X16),X17),X18)),bot_bot(fun(hoare_509422987triple(X1),bool))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_escape) ).
fof(fact_12_singleton__conv2,axiom,
! [X1,X26] : hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(X1,fun(X1,bool),fequal(X1),X26)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X26),bot_bot(fun(X1,bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_singleton__conv2) ).
fof(tsy_c_hAPP_arg1,axiom,
! [X3,X2,X4,X5] : hAPP(X3,X2,ti(fun(X3,X2),X4),X5) = hAPP(X3,X2,X4,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_hAPP_arg1) ).
fof(tsy_c_Orderings_Obot__class_Obot_res,axiom,
! [X1] :
( bot(X1)
=> ti(X1,bot_bot(X1)) = bot_bot(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Orderings_Obot__class_Obot_res) ).
fof(arity_HOL_Obool___Orderings_Obot,axiom,
bot(bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Obot) ).
fof(fact_23_empty__def,axiom,
! [X1] : bot_bot(fun(X1,bool)) = hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(bool,fun(X1,bool),combk(bool,X1),fFalse)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_empty__def) ).
fof(help_COMBK_1_1_U,axiom,
! [X1,X3,X65,X66] : hAPP(X1,X3,hAPP(X3,fun(X1,X3),combk(X3,X1),X65),X66) = ti(X3,X65),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_U) ).
fof(tsy_c_fFalse_res,hypothesis,
ti(bool,fFalse) = fFalse,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_fFalse_res) ).
fof(c_0_20,plain,
! [X594] :
( ti(bool,X594) = fFalse
| ti(bool,X594) = fTrue ),
inference(variable_rename,[status(thm)],[help_fFalse_1_1_T]) ).
fof(c_0_21,plain,
! [X333,X334] : hAPP(fun(X333,bool),X333,the(X333),hAPP(X333,fun(X333,bool),fequal(X333),X334)) = ti(X333,X334),
inference(variable_rename,[status(thm)],[fact_54_the__sym__eq__trivial]) ).
fof(c_0_22,plain,
! [X109,X110,X111,X112] : ti(X109,hAPP(X110,X109,X111,X112)) = hAPP(X110,X109,X111,X112),
inference(variable_rename,[status(thm)],[tsy_c_hAPP_res]) ).
cnf(c_0_23,plain,
( ti(bool,X1) = fFalse
| ti(bool,X1) = fTrue ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_24,plain,
hAPP(fun(X1,bool),X1,the(X1),hAPP(X1,fun(X1,bool),fequal(X1),X2)) = ti(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_25,plain,
ti(X1,hAPP(X2,X1,X3,X4)) = hAPP(X2,X1,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_26,plain,
~ hBOOL(fFalse),
inference(fof_simplification,[status(thm)],[help_fFalse_1_1_U]) ).
fof(c_0_27,plain,
! [X559] :
( hBOOL(hAPP(bool,bool,fNot,X559))
| hBOOL(X559) ),
inference(variable_rename,[status(thm)],[help_fNot_2_1_U]) ).
cnf(c_0_28,plain,
( hAPP(fun(bool,bool),bool,the(bool),hAPP(bool,fun(bool,bool),fequal(bool),X1)) = fTrue
| hAPP(fun(bool,bool),bool,the(bool),hAPP(bool,fun(bool,bool),fequal(bool),X1)) = fFalse ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_24]),c_0_24]) ).
cnf(c_0_29,plain,
hAPP(fun(X1,bool),X1,the(X1),hAPP(X1,fun(X1,bool),fequal(X1),hAPP(X2,X1,X3,X4))) = hAPP(X2,X1,X3,X4),
inference(rw,[status(thm)],[c_0_25,c_0_24]) ).
fof(c_0_30,plain,
~ hBOOL(fFalse),
inference(fof_nnf,[status(thm)],[c_0_26]) ).
fof(c_0_31,plain,
! [X105,X106,X107,X108] : hAPP(X105,X106,X107,ti(X105,X108)) = hAPP(X105,X106,X107,X108),
inference(variable_rename,[status(thm)],[tsy_c_hAPP_arg2]) ).
cnf(c_0_32,plain,
( hBOOL(hAPP(bool,bool,fNot,X1))
| hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_33,plain,
( hAPP(X1,bool,X2,X3) = fFalse
| hAPP(X1,bool,X2,X3) = fTrue ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_34,plain,
~ hBOOL(fFalse),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
fof(c_0_35,plain,
! [X1,X26] : ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),bot_bot(fun(X1,bool)))),
inference(fof_simplification,[status(thm)],[fact_11_emptyE]) ).
fof(c_0_36,plain,
! [X425,X426] : hAPP(fun(X425,bool),fun(X425,bool),collect(X425),X426) = ti(fun(X425,bool),X426),
inference(variable_rename,[status(thm)],[fact_77_Collect__def]) ).
fof(c_0_37,hypothesis,
! [X113] :
( ( hBOOL(ti(bool,X113))
| ~ hBOOL(X113) )
& ( hBOOL(X113)
| ~ hBOOL(ti(bool,X113)) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_hBOOL_arg1])])]) ).
cnf(c_0_38,plain,
hAPP(X1,X2,X3,ti(X1,X4)) = hAPP(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_39,plain,
( hBOOL(X1)
| hAPP(bool,bool,fNot,X1) = fTrue ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]) ).
fof(c_0_40,plain,
! [X388,X389] :
( ( hBOOL(hAPP(X388,bool,bot_bot(fun(X388,bool)),X389))
| ~ hBOOL(hAPP(fun(X388,bool),bool,hAPP(X388,fun(fun(X388,bool),bool),member(X388),X389),bot_bot(fun(X388,bool)))) )
& ( hBOOL(hAPP(fun(X388,bool),bool,hAPP(X388,fun(fun(X388,bool),bool),member(X388),X389),bot_bot(fun(X388,bool))))
| ~ hBOOL(hAPP(X388,bool,bot_bot(fun(X388,bool)),X389)) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_66_bot__empty__eq])])]) ).
fof(c_0_41,plain,
! [X180,X181] : ~ hBOOL(hAPP(fun(X180,bool),bool,hAPP(X180,fun(fun(X180,bool),bool),member(X180),X181),bot_bot(fun(X180,bool)))),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_35])]) ).
fof(c_0_42,plain,
! [X294,X295,X296] :
( hAPP(X294,X295,bot_bot(fun(X294,X295)),X296) = bot_bot(X295)
| ~ bot(X295) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_43_bot__apply])])])]) ).
fof(c_0_43,negated_conjecture,
~ hBOOL(hAPP(fun(hoare_509422987triple(x_a),bool),bool,hAPP(fun(hoare_509422987triple(x_a),bool),fun(fun(hoare_509422987triple(x_a),bool),bool),hoare_122391849derivs(x_a),g),hAPP(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool),hAPP(hoare_509422987triple(x_a),fun(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool)),insert(hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse))),c),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)))),bot_bot(fun(hoare_509422987triple(x_a),bool))))),
inference(assume_negation,[status(cth)],[conj_0]) ).
cnf(c_0_44,plain,
hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2) = ti(fun(X1,bool),X2),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
fof(c_0_45,plain,
! [X138,X139,X140,X141,X142] :
( ( hBOOL(hAPP(fun(hoare_509422987triple(X138),bool),bool,hAPP(fun(hoare_509422987triple(X138),bool),fun(fun(hoare_509422987triple(X138),bool),bool),hoare_122391849derivs(X138),X139),hAPP(fun(hoare_509422987triple(X138),bool),fun(hoare_509422987triple(X138),bool),hAPP(hoare_509422987triple(X138),fun(fun(hoare_509422987triple(X138),bool),fun(hoare_509422987triple(X138),bool)),insert(hoare_509422987triple(X138)),hAPP(fun(X138,fun(state,bool)),hoare_509422987triple(X138),hAPP(com,fun(fun(X138,fun(state,bool)),hoare_509422987triple(X138)),hAPP(fun(X138,fun(state,bool)),fun(com,fun(fun(X138,fun(state,bool)),hoare_509422987triple(X138))),hoare_1008221573triple(X138),X142),X140),X141)),bot_bot(fun(hoare_509422987triple(X138),bool)))))
| ~ hBOOL(hAPP(fun(hoare_509422987triple(X138),bool),bool,hAPP(fun(hoare_509422987triple(X138),bool),fun(fun(hoare_509422987triple(X138),bool),bool),hoare_122391849derivs(X138),X139),hAPP(fun(hoare_509422987triple(X138),bool),fun(hoare_509422987triple(X138),bool),hAPP(hoare_509422987triple(X138),fun(fun(hoare_509422987triple(X138),bool),fun(hoare_509422987triple(X138),bool)),insert(hoare_509422987triple(X138)),hAPP(fun(X138,fun(state,bool)),hoare_509422987triple(X138),hAPP(com,fun(fun(X138,fun(state,bool)),hoare_509422987triple(X138)),hAPP(fun(X138,fun(state,bool)),fun(com,fun(fun(X138,fun(state,bool)),hoare_509422987triple(X138))),hoare_1008221573triple(X138),hAPP(fun(state,bool),fun(X138,fun(state,bool)),combk(fun(state,bool),X138),hAPP(state,fun(state,bool),hAPP(fun(state,fun(state,bool)),fun(state,fun(state,bool)),combc(state,state,bool),fequal(state)),esk2_5(X138,X139,X140,X141,X142)))),X140),hAPP(fun(state,bool),fun(X138,fun(state,bool)),combk(fun(state,bool),X138),hAPP(X138,fun(state,bool),X141,esk1_5(X138,X139,X140,X141,X142))))),bot_bot(fun(hoare_509422987triple(X138),bool))))) )
& ( hBOOL(hAPP(fun(hoare_509422987triple(X138),bool),bool,hAPP(fun(hoare_509422987triple(X138),bool),fun(fun(hoare_509422987triple(X138),bool),bool),hoare_122391849derivs(X138),X139),hAPP(fun(hoare_509422987triple(X138),bool),fun(hoare_509422987triple(X138),bool),hAPP(hoare_509422987triple(X138),fun(fun(hoare_509422987triple(X138),bool),fun(hoare_509422987triple(X138),bool)),insert(hoare_509422987triple(X138)),hAPP(fun(X138,fun(state,bool)),hoare_509422987triple(X138),hAPP(com,fun(fun(X138,fun(state,bool)),hoare_509422987triple(X138)),hAPP(fun(X138,fun(state,bool)),fun(com,fun(fun(X138,fun(state,bool)),hoare_509422987triple(X138))),hoare_1008221573triple(X138),X142),X140),X141)),bot_bot(fun(hoare_509422987triple(X138),bool)))))
| hBOOL(hAPP(state,bool,hAPP(X138,fun(state,bool),X142,esk1_5(X138,X139,X140,X141,X142)),esk2_5(X138,X139,X140,X141,X142))) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_5_escape])])])])]) ).
fof(c_0_46,plain,
! [X182,X183] : hAPP(fun(X182,bool),fun(X182,bool),collect(X182),hAPP(X182,fun(X182,bool),fequal(X182),X183)) = hAPP(fun(X182,bool),fun(X182,bool),hAPP(X182,fun(fun(X182,bool),fun(X182,bool)),insert(X182),X183),bot_bot(fun(X182,bool))),
inference(variable_rename,[status(thm)],[fact_12_singleton__conv2]) ).
fof(c_0_47,plain,
! [X101,X102,X103,X104] : hAPP(X101,X102,ti(fun(X101,X102),X103),X104) = hAPP(X101,X102,X103,X104),
inference(variable_rename,[status(thm)],[tsy_c_hAPP_arg1]) ).
fof(c_0_48,plain,
! [X96] :
( ti(X96,bot_bot(X96)) = bot_bot(X96)
| ~ bot(X96) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[tsy_c_Orderings_Obot__class_Obot_res])])]) ).
cnf(c_0_49,hypothesis,
( ~ hBOOL(ti(bool,X1))
| hBOOL(X1) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_50,plain,
hAPP(X1,X2,X3,hAPP(fun(X1,bool),X1,the(X1),hAPP(X1,fun(X1,bool),fequal(X1),X4))) = hAPP(X1,X2,X3,X4),
inference(rw,[status(thm)],[c_0_38,c_0_24]) ).
cnf(c_0_51,plain,
hAPP(bool,bool,fNot,fFalse) = fTrue,
inference(spm,[status(thm)],[c_0_34,c_0_39]) ).
cnf(c_0_52,plain,
( ~ hBOOL(hAPP(X1,bool,bot_bot(fun(X1,bool)),X2))
| hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),bot_bot(fun(X1,bool)))) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_53,plain,
~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),bot_bot(fun(X1,bool)))),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_54,plain,
( ~ bot(X1)
| hAPP(X2,X1,bot_bot(fun(X2,X1)),X3) = bot_bot(X1) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_55,plain,
bot(bool),
inference(split_conjunct,[status(thm)],[arity_HOL_Obool___Orderings_Obot]) ).
fof(c_0_56,negated_conjecture,
~ hBOOL(hAPP(fun(hoare_509422987triple(x_a),bool),bool,hAPP(fun(hoare_509422987triple(x_a),bool),fun(fun(hoare_509422987triple(x_a),bool),bool),hoare_122391849derivs(x_a),g),hAPP(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool),hAPP(hoare_509422987triple(x_a),fun(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool)),insert(hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse))),c),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)))),bot_bot(fun(hoare_509422987triple(x_a),bool))))),
inference(fof_simplification,[status(thm)],[c_0_43]) ).
cnf(c_0_57,plain,
hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2) = hAPP(fun(fun(X1,bool),bool),fun(X1,bool),the(fun(X1,bool)),hAPP(fun(X1,bool),fun(fun(X1,bool),bool),fequal(fun(X1,bool)),X2)),
inference(rw,[status(thm)],[c_0_44,c_0_24]) ).
fof(c_0_58,plain,
! [X227] : bot_bot(fun(X227,bool)) = hAPP(fun(X227,bool),fun(X227,bool),collect(X227),hAPP(bool,fun(X227,bool),combk(bool,X227),fFalse)),
inference(variable_rename,[status(thm)],[fact_23_empty__def]) ).
cnf(c_0_59,plain,
( hBOOL(hAPP(fun(hoare_509422987triple(X1),bool),bool,hAPP(fun(hoare_509422987triple(X1),bool),fun(fun(hoare_509422987triple(X1),bool),bool),hoare_122391849derivs(X1),X3),hAPP(fun(hoare_509422987triple(X1),bool),fun(hoare_509422987triple(X1),bool),hAPP(hoare_509422987triple(X1),fun(fun(hoare_509422987triple(X1),bool),fun(hoare_509422987triple(X1),bool)),insert(hoare_509422987triple(X1)),hAPP(fun(X1,fun(state,bool)),hoare_509422987triple(X1),hAPP(com,fun(fun(X1,fun(state,bool)),hoare_509422987triple(X1)),hAPP(fun(X1,fun(state,bool)),fun(com,fun(fun(X1,fun(state,bool)),hoare_509422987triple(X1))),hoare_1008221573triple(X1),X2),X4),X5)),bot_bot(fun(hoare_509422987triple(X1),bool)))))
| hBOOL(hAPP(state,bool,hAPP(X1,fun(state,bool),X2,esk1_5(X1,X3,X4,X5,X2)),esk2_5(X1,X3,X4,X5,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_60,plain,
hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(X1,fun(X1,bool),fequal(X1),X2)) = hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),bot_bot(fun(X1,bool))),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
fof(c_0_61,plain,
! [X572,X573,X574,X575] : hAPP(X572,X573,hAPP(X573,fun(X572,X573),combk(X573,X572),X574),X575) = ti(X573,X574),
inference(variable_rename,[status(thm)],[help_COMBK_1_1_U]) ).
cnf(c_0_62,plain,
hAPP(X1,X2,ti(fun(X1,X2),X3),X4) = hAPP(X1,X2,X3,X4),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_63,plain,
( ~ bot(X1)
| ti(X1,bot_bot(X1)) = bot_bot(X1) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_64,hypothesis,
( ~ hBOOL(hAPP(fun(bool,bool),bool,the(bool),hAPP(bool,fun(bool,bool),fequal(bool),X1)))
| hBOOL(X1) ),
inference(rw,[status(thm)],[c_0_49,c_0_24]) ).
cnf(c_0_65,plain,
( hAPP(bool,X2,X3,fFalse) = hAPP(bool,X2,X3,X1)
| hAPP(fun(bool,bool),bool,the(bool),hAPP(bool,fun(bool,bool),fequal(bool),X1)) = fTrue ),
inference(spm,[status(thm)],[c_0_50,c_0_33]) ).
cnf(c_0_66,plain,
hBOOL(fTrue),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_51]),c_0_34]) ).
cnf(c_0_67,hypothesis,
ti(bool,fFalse) = fFalse,
inference(split_conjunct,[status(thm)],[tsy_c_fFalse_res]) ).
cnf(c_0_68,plain,
~ hBOOL(hAPP(X1,bool,bot_bot(fun(X1,bool)),X2)),
inference(sr,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_69,plain,
hAPP(X1,bool,bot_bot(fun(X1,bool)),X2) = bot_bot(bool),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
fof(c_0_70,negated_conjecture,
~ hBOOL(hAPP(fun(hoare_509422987triple(x_a),bool),bool,hAPP(fun(hoare_509422987triple(x_a),bool),fun(fun(hoare_509422987triple(x_a),bool),bool),hoare_122391849derivs(x_a),g),hAPP(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool),hAPP(hoare_509422987triple(x_a),fun(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool)),insert(hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse))),c),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)))),bot_bot(fun(hoare_509422987triple(x_a),bool))))),
inference(fof_nnf,[status(thm)],[c_0_56]) ).
cnf(c_0_71,plain,
hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(X2,fun(X1,bool),X3,X4)) = hAPP(X2,fun(X1,bool),X3,X4),
inference(spm,[status(thm)],[c_0_29,c_0_57]) ).
cnf(c_0_72,plain,
bot_bot(fun(X1,bool)) = hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(bool,fun(X1,bool),combk(bool,X1),fFalse)),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_73,plain,
( hBOOL(hAPP(state,bool,hAPP(X1,fun(state,bool),X3,esk1_5(X1,X2,X4,X5,X3)),esk2_5(X1,X2,X4,X5,X3)))
| hBOOL(hAPP(fun(hoare_509422987triple(X1),bool),bool,hAPP(fun(hoare_509422987triple(X1),bool),fun(fun(hoare_509422987triple(X1),bool),bool),hoare_122391849derivs(X1),X2),hAPP(fun(hoare_509422987triple(X1),bool),fun(hoare_509422987triple(X1),bool),collect(hoare_509422987triple(X1)),hAPP(hoare_509422987triple(X1),fun(hoare_509422987triple(X1),bool),fequal(hoare_509422987triple(X1)),hAPP(fun(X1,fun(state,bool)),hoare_509422987triple(X1),hAPP(com,fun(fun(X1,fun(state,bool)),hoare_509422987triple(X1)),hAPP(fun(X1,fun(state,bool)),fun(com,fun(fun(X1,fun(state,bool)),hoare_509422987triple(X1))),hoare_1008221573triple(X1),X3),X4),X5))))) ),
inference(rw,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_74,plain,
hAPP(X1,X2,hAPP(X2,fun(X1,X2),combk(X2,X1),X3),X4) = ti(X2,X3),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_75,plain,
hAPP(X1,X2,hAPP(fun(fun(X1,X2),bool),fun(X1,X2),the(fun(X1,X2)),hAPP(fun(X1,X2),fun(fun(X1,X2),bool),fequal(fun(X1,X2)),X3)),X4) = hAPP(X1,X2,X3,X4),
inference(rw,[status(thm)],[c_0_62,c_0_24]) ).
cnf(c_0_76,plain,
( ~ bot(X1)
| hAPP(fun(X1,bool),X1,the(X1),hAPP(X1,fun(X1,bool),fequal(X1),bot_bot(X1))) = bot_bot(X1) ),
inference(rw,[status(thm)],[c_0_63,c_0_24]) ).
cnf(c_0_77,hypothesis,
( hBOOL(X3)
| hAPP(bool,X1,X2,fFalse) = hAPP(bool,X1,X2,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_66])]) ).
cnf(c_0_78,hypothesis,
hAPP(fun(bool,bool),bool,the(bool),hAPP(bool,fun(bool,bool),fequal(bool),fFalse)) = fFalse,
inference(rw,[status(thm)],[c_0_67,c_0_24]) ).
cnf(c_0_79,plain,
~ hBOOL(bot_bot(bool)),
inference(rw,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_80,negated_conjecture,
~ hBOOL(hAPP(fun(hoare_509422987triple(x_a),bool),bool,hAPP(fun(hoare_509422987triple(x_a),bool),fun(fun(hoare_509422987triple(x_a),bool),bool),hoare_122391849derivs(x_a),g),hAPP(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool),hAPP(hoare_509422987triple(x_a),fun(fun(hoare_509422987triple(x_a),bool),fun(hoare_509422987triple(x_a),bool)),insert(hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),hAPP(bool,fun(state,bool),combk(bool,state),fFalse))),c),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)))),bot_bot(fun(hoare_509422987triple(x_a),bool))))),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_81,plain,
hAPP(fun(X1,bool),fun(X1,bool),hAPP(X1,fun(fun(X1,bool),fun(X1,bool)),insert(X1),X2),bot_bot(fun(X1,bool))) = hAPP(X1,fun(X1,bool),fequal(X1),X2),
inference(rw,[status(thm)],[c_0_60,c_0_71]) ).
cnf(c_0_82,plain,
hAPP(bool,fun(X1,bool),combk(bool,X1),fFalse) = bot_bot(fun(X1,bool)),
inference(rw,[status(thm)],[c_0_72,c_0_71]) ).
cnf(c_0_83,plain,
( hBOOL(hAPP(state,bool,hAPP(X1,fun(state,bool),X3,esk1_5(X1,X2,X4,X5,X3)),esk2_5(X1,X2,X4,X5,X3)))
| hBOOL(hAPP(fun(hoare_509422987triple(X1),bool),bool,hAPP(fun(hoare_509422987triple(X1),bool),fun(fun(hoare_509422987triple(X1),bool),bool),hoare_122391849derivs(X1),X2),hAPP(hoare_509422987triple(X1),fun(hoare_509422987triple(X1),bool),fequal(hoare_509422987triple(X1)),hAPP(fun(X1,fun(state,bool)),hoare_509422987triple(X1),hAPP(com,fun(fun(X1,fun(state,bool)),hoare_509422987triple(X1)),hAPP(fun(X1,fun(state,bool)),fun(com,fun(fun(X1,fun(state,bool)),hoare_509422987triple(X1))),hoare_1008221573triple(X1),X3),X4),X5)))) ),
inference(rw,[status(thm)],[c_0_73,c_0_71]) ).
cnf(c_0_84,plain,
hAPP(X1,X2,hAPP(X2,fun(X1,X2),combk(X2,X1),X3),X4) = hAPP(fun(X2,bool),X2,the(X2),hAPP(X2,fun(X2,bool),fequal(X2),X3)),
inference(rw,[status(thm)],[c_0_74,c_0_24]) ).
cnf(c_0_85,plain,
hAPP(X1,bool,hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2),X3) = hAPP(X1,bool,X2,X3),
inference(spm,[status(thm)],[c_0_75,c_0_57]) ).
cnf(c_0_86,hypothesis,
bot_bot(bool) = fFalse,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_78]),c_0_55])]),c_0_79]) ).
cnf(c_0_87,negated_conjecture,
~ hBOOL(hAPP(fun(hoare_509422987triple(x_a),bool),bool,hAPP(fun(hoare_509422987triple(x_a),bool),fun(fun(hoare_509422987triple(x_a),bool),bool),hoare_122391849derivs(x_a),g),hAPP(hoare_509422987triple(x_a),fun(hoare_509422987triple(x_a),bool),fequal(hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a),hAPP(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a)),hAPP(fun(x_a,fun(state,bool)),fun(com,fun(fun(x_a,fun(state,bool)),hoare_509422987triple(x_a))),hoare_1008221573triple(x_a),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),combk(fun(state,bool),x_a),bot_bot(fun(state,bool)))),c),hAPP(fun(state,bool),fun(x_a,fun(state,bool)),hAPP(fun(x_a,fun(fun(state,bool),fun(state,bool))),fun(fun(state,bool),fun(x_a,fun(state,bool))),combc(x_a,fun(state,bool),fun(state,bool)),hAPP(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool))),hAPP(fun(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool))),fun(fun(x_a,fun(state,fun(bool,bool))),fun(x_a,fun(fun(state,bool),fun(state,bool)))),combb(fun(state,fun(bool,bool)),fun(fun(state,bool),fun(state,bool)),x_a),combs(state,bool,bool)),hAPP(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool))),hAPP(fun(fun(state,bool),fun(state,fun(bool,bool))),fun(fun(x_a,fun(state,bool)),fun(x_a,fun(state,fun(bool,bool)))),combb(fun(state,bool),fun(state,fun(bool,bool)),x_a),hAPP(fun(bool,fun(bool,bool)),fun(fun(state,bool),fun(state,fun(bool,bool))),combb(bool,fun(bool,bool),state),fconj)),p))),hAPP(fun(state,bool),fun(state,bool),hAPP(fun(bool,bool),fun(fun(state,bool),fun(state,bool)),combb(bool,bool,state),fNot),b)))))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_82]) ).
cnf(c_0_88,plain,
( hBOOL(hAPP(state,bool,X3,esk2_5(X1,X2,X4,X5,hAPP(fun(state,bool),fun(X1,fun(state,bool)),combk(fun(state,bool),X1),X3))))
| hBOOL(hAPP(fun(hoare_509422987triple(X1),bool),bool,hAPP(fun(hoare_509422987triple(X1),bool),fun(fun(hoare_509422987triple(X1),bool),bool),hoare_122391849derivs(X1),X2),hAPP(hoare_509422987triple(X1),fun(hoare_509422987triple(X1),bool),fequal(hoare_509422987triple(X1)),hAPP(fun(X1,fun(state,bool)),hoare_509422987triple(X1),hAPP(com,fun(fun(X1,fun(state,bool)),hoare_509422987triple(X1)),hAPP(fun(X1,fun(state,bool)),fun(com,fun(fun(X1,fun(state,bool)),hoare_509422987triple(X1))),hoare_1008221573triple(X1),hAPP(fun(state,bool),fun(X1,fun(state,bool)),combk(fun(state,bool),X1),X3)),X4),X5)))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_57]),c_0_85]) ).
cnf(c_0_89,plain,
hAPP(X1,bool,bot_bot(fun(X1,bool)),X2) = fFalse,
inference(rw,[status(thm)],[c_0_69,c_0_86]) ).
cnf(c_0_90,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_89]),c_0_34]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW470+5 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.38 % Computer : n017.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Mon Sep 21 09:51:26 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.43 Running first-order theorem proving
% 0.13/0.43 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
% 87.56/13.16 % Version: 3.5.1
% 87.56/13.16 % Preprocessing class: FSLSSMSMSSSNFFN.
% 87.56/13.16 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 87.56/13.16 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 87.56/13.16 % Starting new_bool_3 with 300s (1) cores
% 87.56/13.16 % Starting new_bool_1 with 300s (1) cores
% 87.56/13.16 % Starting sh5l with 300s (1) cores
% 87.56/13.16 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 2033064 completed with status 0
% 87.56/13.16 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 87.56/13.16 % Preprocessing class: FSLSSMSMSSSNFFN.
% 87.56/13.16 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 87.56/13.16 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 87.56/13.16 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 87.56/13.16 % No SInE strategy applied
% 87.56/13.16 % Search class: FGHSM-FSLM33-DFFFFFNN
% 87.56/13.16 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 87.56/13.16 % Starting SubtermCWHack with 136s (1) cores
% 87.56/13.16 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 87.56/13.16 % Starting U----_206b_01_C11_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 87.56/13.16 % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S04BN with 136s (1) cores
% 87.56/13.16 % Starting G-E--_208_C09_12_F1_SE_CS_SP_PS_S070I with 136s (1) cores
% 87.56/13.16 % U----_206b_01_C11_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with pid 2033083 completed with status 0
% 87.56/13.16 % Result found by U----_206b_01_C11_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN
% 87.56/13.16 % Preprocessing class: FSLSSMSMSSSNFFN.
% 87.56/13.16 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 87.56/13.16 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 87.56/13.16 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 87.56/13.16 % No SInE strategy applied
% 87.56/13.16 % Search class: FGHSM-FSLM33-DFFFFFNN
% 87.56/13.16 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 87.56/13.16 % Starting SubtermCWHack with 136s (1) cores
% 87.56/13.16 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 87.56/13.16 % Starting U----_206b_01_C11_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 87.56/13.16 % Preprocessing time : 0.005 s
% 87.56/13.16 % Presaturation interreduction done
% 87.56/13.16
% 87.56/13.16 % Proof found!
% 87.56/13.16 % SZS status Theorem
% 87.56/13.16 % SZS output start CNFRefutation
% See solution above
% 87.56/13.16 % Parsed axioms : 163
% 87.56/13.16 % Removed by relevancy pruning/SinE : 0
% 87.56/13.16 % Initial clauses : 236
% 87.56/13.16 % Removed in clause preprocessing : 3
% 87.56/13.16 % Initial clauses in saturation : 233
% 87.56/13.16 % Processed clauses : 35651
% 87.56/13.16 % ...of these trivial : 411
% 87.56/13.16 % ...subsumed : 31585
% 87.56/13.16 % ...remaining for further processing : 3655
% 87.56/13.16 % Other redundant clauses eliminated : 179
% 87.56/13.16 % Clauses deleted for lack of memory : 0
% 87.56/13.16 % Backward-subsumed : 148
% 87.56/13.16 % Backward-rewritten : 178
% 87.56/13.16 % Generated clauses : 595476
% 87.56/13.16 % ...of the previous two non-redundant : 526096
% 87.56/13.16 % ...aggressively subsumed : 0
% 87.56/13.16 % Contextual simplify-reflections : 40
% 87.56/13.16 % Paramodulations : 595152
% 87.56/13.16 % Factorizations : 35
% 87.56/13.16 % NegExts : 0
% 87.56/13.16 % Equation resolutions : 286
% 87.56/13.16 % Disequality decompositions : 0
% 87.56/13.16 % Total rewrite steps : 427697
% 87.56/13.16 % ...of those cached : 406205
% 87.56/13.16 % Propositional unsat checks : 0
% 87.56/13.16 % Propositional check models : 0
% 87.56/13.16 % Propositional check unsatisfiable : 0
% 87.56/13.16 % Propositional clauses : 0
% 87.56/13.16 % Propositional clauses after purity: 0
% 87.56/13.16 % Propositional unsat core size : 0
% 87.56/13.16 % Propositional preprocessing time : 0.000
% 87.56/13.16 % Propositional encoding time : 0.000
% 87.56/13.16 % Propositional solver time : 0.000
% 87.56/13.16 % Success case prop preproc time : 0.000
% 87.56/13.16 % Success case prop encoding time : 0.000
% 87.56/13.16 % Success case prop solver time : 0.000
% 87.56/13.16 % Current number of processed clauses : 3112
% 87.56/13.16 % Positive orientable unit clauses : 265
% 87.56/13.16 % Positive unorientable unit clauses: 52
% 87.56/13.16 % Negative unit clauses : 199
% 87.56/13.16 % Non-unit-clauses : 2596
% 87.56/13.16 % Current number of unprocessed clauses: 488638
% 87.56/13.16 % ...number of literals in the above : 1496714
% 87.56/13.16 % Current number of archived formulas : 0
% 87.56/13.16 % Current number of archived clauses : 543
% 87.56/13.16 % Clause-clause subsumption calls (NU) : 1616205
% 87.56/13.16 % Rec. Clause-clause subsumption calls : 868642
% 87.56/13.16 % Non-unit clause-clause subsumptions : 14142
% 87.56/13.16 % Unit Clause-clause subsumption calls : 48330
% 87.56/13.16 % Rewrite failures with RHS unbound : 0
% 87.56/13.16 % BW rewrite match attempts : 142799
% 87.56/13.16 % BW rewrite match successes : 296
% 87.56/13.16 % Condensation attempts : 0
% 87.56/13.16 % Condensation successes : 0
% 87.56/13.16 % Termbank termtop insertions : 45087240
% 87.56/13.16 % Search garbage collected termcells : 3268
% 87.56/13.16
% 87.56/13.16 % -------------------------------------------------
% 87.56/13.16 % User time : 12.141 s
% 87.56/13.16 % System time : 0.312 s
% 87.56/13.16 % Total time : 12.453 s
% 87.56/13.16 % Maximum resident set size: 4948 pages
% 87.56/13.16
% 87.56/13.16 % -------------------------------------------------
% 87.56/13.16 % User time : 60.761 s
% 87.56/13.16 % System time : 1.340 s
% 87.56/13.16 % Total time : 62.102 s
% 87.56/13.16 % Maximum resident set size: 5120 pages
% 87.56/13.16 % E exiting
%------------------------------------------------------------------------------