TSTP Solution File: SWW321+1 by ET---2.0
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%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SWW321+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n025.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 : 600s
% DateTime : Thu Jul 21 00:10:33 EDT 2022
% Result : Theorem 0.96s 2.15s
% Output : CNFRefutation 0.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 16
% Syntax : Number of formulae : 72 ( 27 unt; 0 def)
% Number of atoms : 136 ( 20 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 113 ( 49 ~; 47 |; 4 &)
% ( 2 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 15 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 25 ( 25 usr; 13 con; 0-3 aty)
% Number of variables : 161 ( 14 sgn 83 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_derivs__insertD,axiom,
! [X13,X15,X4,X5] :
( c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X5)),X15),X13))
=> ( c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X5)),X15),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_HOL_Obool))))
& c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,X13) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_derivs__insertD) ).
fof(fact_asm,axiom,
! [X4,X13,X5] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_HOL_Obool)),X13),X4))
=> c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,X13) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_asm) ).
fof(fact_subset__insertI,axiom,
! [X6,X22,X5] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X22),hAPP(hAPP(c_Set_Oinsert(X5),X6),X22))),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_subset__insertI) ).
fof(fact_insert__absorb2,axiom,
! [X19,X20,X5] : hAPP(hAPP(c_Set_Oinsert(X5),X20),hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)) = hAPP(hAPP(c_Set_Oinsert(X5),X20),X19),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_insert__absorb2) ).
fof(fact_insert__absorb,axiom,
! [X19,X6,X5] :
( hBOOL(hAPP(hAPP(c_member(X5),X6),X19))
=> hAPP(hAPP(c_Set_Oinsert(X5),X6),X19) = X19 ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_insert__absorb) ).
fof(fact_ex__in__conv,axiom,
! [X19,X5] :
( ? [X3] : hBOOL(hAPP(hAPP(c_member(X5),X3),X19))
<=> X19 != c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_ex__in__conv) ).
fof(fact_weaken,axiom,
! [X13,X66,X4,X5] :
( c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,X66)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_HOL_Obool)),X13),X66))
=> c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,X13) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_weaken) ).
fof(fact_subset__empty,axiom,
! [X19,X5] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),X19),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))
<=> X19 = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_subset__empty) ).
fof(fact_empty,axiom,
! [X4,X5] : c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_HOL_Obool))),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_empty) ).
fof(fact_cut,axiom,
! [X4,X13,X14,X5] :
( c_Hoare__Mirabelle_Ohoare__derivs(X5,X14,X13)
=> ( c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,X14)
=> c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,X13) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_cut) ).
fof(conj_0,hypothesis,
! [X304] :
( c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P_H,X304)),hAPP(v_c0,X304)),hAPP(v_Q_H,X304))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_HOL_Obool))))
=> c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P,X304)),hAPP(v_c0,X304)),hAPP(v_Q,X304))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_HOL_Obool)))) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',conj_0) ).
fof(conj_4,hypothesis,
c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P_H,v_x)),hAPP(v_c0,v_x)),hAPP(v_Q_H,v_x))),hAPP(c_Set_Oimage(t_a,tc_Hoare__Mirabelle_Otriple(t_b),hAPP(hAPP(c_COMBS(t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(c_COMBS(t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),hAPP(hAPP(c_COMBB(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),c_Hoare__Mirabelle_Otriple_Otriple(t_b)),v_P_H)),v_c0)),v_Q_H)),v_F))),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',conj_4) ).
fof(fact_hoare__derivs_Oinsert,axiom,
! [X13,X15,X4,X5] :
( c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X5)),X15),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X5),tc_HOL_Obool))))
=> ( c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,X13)
=> c_Hoare__Mirabelle_Ohoare__derivs(X5,X4,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X5)),X15),X13)) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_hoare__derivs_Oinsert) ).
fof(fact_insert__commute,axiom,
! [X19,X24,X20,X5] : hAPP(hAPP(c_Set_Oinsert(X5),X20),hAPP(hAPP(c_Set_Oinsert(X5),X24),X19)) = hAPP(hAPP(c_Set_Oinsert(X5),X24),hAPP(hAPP(c_Set_Oinsert(X5),X20),X19)),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',fact_insert__commute) ).
fof(conj_5,conjecture,
c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P,v_x)),hAPP(v_c0,v_x)),hAPP(v_Q,v_x))),hAPP(c_Set_Oimage(t_a,tc_Hoare__Mirabelle_Otriple(t_b),hAPP(hAPP(c_COMBS(t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(c_COMBS(t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),hAPP(hAPP(c_COMBB(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),c_Hoare__Mirabelle_Otriple_Otriple(t_b)),v_P)),v_c0)),v_Q)),v_F))),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',conj_5) ).
fof(conj_3,hypothesis,
( c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(c_Set_Oimage(t_a,tc_Hoare__Mirabelle_Otriple(t_b),hAPP(hAPP(c_COMBS(t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(c_COMBS(t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),hAPP(hAPP(c_COMBB(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),c_Hoare__Mirabelle_Otriple_Otriple(t_b)),v_P_H)),v_c0)),v_Q_H)),v_F))
=> c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(c_Set_Oimage(t_a,tc_Hoare__Mirabelle_Otriple(t_b),hAPP(hAPP(c_COMBS(t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(c_COMBS(t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),hAPP(hAPP(c_COMBB(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),c_Hoare__Mirabelle_Otriple_Otriple(t_b)),v_P)),v_c0)),v_Q)),v_F)) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',conj_3) ).
fof(c_0_16,plain,
! [X16,X17,X18,X19] :
( ( c_Hoare__Mirabelle_Ohoare__derivs(X19,X18,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X19)),X17),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X19),tc_HOL_Obool))))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X19,X18,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X19)),X17),X16)) )
& ( c_Hoare__Mirabelle_Ohoare__derivs(X19,X18,X16)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X19,X18,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X19)),X17),X16)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_derivs__insertD])])]) ).
fof(c_0_17,plain,
! [X14,X15,X16] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(X16),tc_HOL_Obool)),X15),X14))
| c_Hoare__Mirabelle_Ohoare__derivs(X16,X14,X15) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_asm])]) ).
fof(c_0_18,plain,
! [X23,X24,X25] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25,tc_HOL_Obool)),X24),hAPP(hAPP(c_Set_Oinsert(X25),X23),X24))),
inference(variable_rename,[status(thm)],[fact_subset__insertI]) ).
fof(c_0_19,plain,
! [X21,X22,X23] : hAPP(hAPP(c_Set_Oinsert(X23),X22),hAPP(hAPP(c_Set_Oinsert(X23),X22),X21)) = hAPP(hAPP(c_Set_Oinsert(X23),X22),X21),
inference(variable_rename,[status(thm)],[fact_insert__absorb2]) ).
cnf(c_0_20,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X4)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_21,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool)),X3),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_22,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2))),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_23,plain,
hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)) = hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_24,plain,
! [X20,X21,X22] :
( ~ hBOOL(hAPP(hAPP(c_member(X22),X21),X20))
| hAPP(hAPP(c_Set_Oinsert(X22),X21),X20) = X20 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__absorb])]) ).
fof(c_0_25,plain,
! [X20,X21,X22,X20,X21] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X21),X22),X20))
| X20 != c_Orderings_Obot__class_Obot(tc_fun(X21,tc_HOL_Obool)) )
& ( X20 = c_Orderings_Obot__class_Obot(tc_fun(X21,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(X21),esk6_2(X20,X21)),X20)) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ex__in__conv])])])])])]) ).
fof(c_0_26,plain,
! [X67,X68,X69,X70] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X70,X69,X68)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(X70),tc_HOL_Obool)),X67),X68))
| c_Hoare__Mirabelle_Ohoare__derivs(X70,X69,X67) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_weaken])]) ).
fof(c_0_27,plain,
! [X20,X21,X20,X21] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X21,tc_HOL_Obool)),X20),c_Orderings_Obot__class_Obot(tc_fun(X21,tc_HOL_Obool))))
| X20 = c_Orderings_Obot__class_Obot(tc_fun(X21,tc_HOL_Obool)) )
& ( X20 != c_Orderings_Obot__class_Obot(tc_fun(X21,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X21,tc_HOL_Obool)),X20),c_Orderings_Obot__class_Obot(tc_fun(X21,tc_HOL_Obool)))) ) ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__empty])])])]) ).
fof(c_0_28,plain,
! [X6,X7] : c_Hoare__Mirabelle_Ohoare__derivs(X7,X6,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X7),tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[fact_empty]) ).
fof(c_0_29,plain,
! [X15,X16,X17,X18] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X18,X17,X16)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X18,X15,X17)
| c_Hoare__Mirabelle_Ohoare__derivs(X18,X15,X16) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_cut])]) ).
fof(c_0_30,hypothesis,
! [X305] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P_H,X305)),hAPP(v_c0,X305)),hAPP(v_Q_H,X305))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_HOL_Obool))))
| c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P,X305)),hAPP(v_c0,X305)),hAPP(v_Q,X305))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_HOL_Obool)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_0])]) ).
cnf(c_0_31,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),X3),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool))))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_32,hypothesis,
c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P_H,v_x)),hAPP(v_c0,v_x)),hAPP(v_Q_H,v_x))),hAPP(c_Set_Oimage(t_a,tc_Hoare__Mirabelle_Otriple(t_b),hAPP(hAPP(c_COMBS(t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(c_COMBS(t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),hAPP(hAPP(c_COMBB(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),c_Hoare__Mirabelle_Otriple_Otriple(t_b)),v_P_H)),v_c0)),v_Q_H)),v_F))),
inference(split_conjunct,[status(thm)],[conj_4]) ).
cnf(c_0_33,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),X4),X3)),X2)) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_34,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_35,plain,
( hAPP(hAPP(c_Set_Oinsert(X1),X2),X3) = X3
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_36,plain,
( hBOOL(hAPP(hAPP(c_member(X1),esk6_2(X2,X1)),X2))
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_37,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool)),X3),X4))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_38,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))
| X2 != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_39,plain,
c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool))),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
fof(c_0_40,plain,
! [X16,X17,X18,X19] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(X19,X18,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X19)),X17),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X19),tc_HOL_Obool))))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X19,X18,X16)
| c_Hoare__Mirabelle_Ohoare__derivs(X19,X18,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X19)),X17),X16)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hoare__derivs_Oinsert])]) ).
cnf(c_0_41,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X4)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_42,hypothesis,
( c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P,X1)),hAPP(v_c0,X1)),hAPP(v_Q,X1))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_HOL_Obool))))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P_H,X1)),hAPP(v_c0,X1)),hAPP(v_Q_H,X1))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_HOL_Obool)))) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_43,hypothesis,
c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P_H,v_x)),hAPP(v_c0,v_x)),hAPP(v_Q_H,v_x))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_HOL_Obool)))),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_44,plain,
c_Hoare__Mirabelle_Ohoare__derivs(X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),X2),X3),X3),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_45,plain,
( hAPP(hAPP(c_Set_Oinsert(X1),esk6_2(X2,X1)),X2) = X2
| X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_46,plain,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)
| X3 != c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool)) ),
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,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),X3),X4))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X4)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X1)),X3),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool)))) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
fof(c_0_48,plain,
! [X25,X26,X27,X28] : hAPP(hAPP(c_Set_Oinsert(X28),X27),hAPP(hAPP(c_Set_Oinsert(X28),X26),X25)) = hAPP(hAPP(c_Set_Oinsert(X28),X26),hAPP(hAPP(c_Set_Oinsert(X28),X27),X25)),
inference(variable_rename,[status(thm)],[fact_insert__commute]) ).
cnf(c_0_49,hypothesis,
( c_Hoare__Mirabelle_Ohoare__derivs(t_b,X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P,X2)),hAPP(v_c0,X2)),hAPP(v_Q,X2))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_HOL_Obool))))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P_H,X2)),hAPP(v_c0,X2)),hAPP(v_Q_H,X2))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_HOL_Obool))))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(t_b,X1,v_G) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_50,hypothesis,
( c_Hoare__Mirabelle_Ohoare__derivs(t_b,X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P_H,v_x)),hAPP(v_c0,v_x)),hAPP(v_Q_H,v_x))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_HOL_Obool))))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(t_b,X1,v_G) ),
inference(spm,[status(thm)],[c_0_41,c_0_43]) ).
cnf(c_0_51,plain,
c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X2),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46]) ).
cnf(c_0_52,hypothesis,
( c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P_H,v_x)),hAPP(v_c0,v_x)),hAPP(v_Q_H,v_x))),X1))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,X1) ),
inference(spm,[status(thm)],[c_0_47,c_0_43]) ).
cnf(c_0_53,plain,
hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4)) = hAPP(hAPP(c_Set_Oinsert(X1),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_54,hypothesis,
( c_Hoare__Mirabelle_Ohoare__derivs(t_b,X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P,v_x)),hAPP(v_c0,v_x)),hAPP(v_Q,v_x))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_HOL_Obool))))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(t_b,X1,v_G) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51])]) ).
cnf(c_0_55,hypothesis,
( c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)),X1),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P_H,v_x)),hAPP(v_c0,v_x)),hAPP(v_Q_H,v_x))),X2)))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)),X1),X2)) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_56,hypothesis,
( c_Hoare__Mirabelle_Ohoare__derivs(t_b,X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P_H,v_x)),hAPP(v_c0,v_x)),hAPP(v_Q_H,v_x))),X2))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(t_b,X1,v_G)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,X2) ),
inference(spm,[status(thm)],[c_0_41,c_0_52]) ).
cnf(c_0_57,hypothesis,
( c_Hoare__Mirabelle_Ohoare__derivs(t_b,X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P,v_x)),hAPP(v_c0,v_x)),hAPP(v_Q,v_x))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_HOL_Obool))))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(t_b,X2,v_G)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(t_b,X1,X2) ),
inference(spm,[status(thm)],[c_0_41,c_0_54]) ).
cnf(c_0_58,hypothesis,
( c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P_H,v_x)),hAPP(v_c0,v_x)),hAPP(v_Q_H,v_x))),X1))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)),X2),X1)) ),
inference(spm,[status(thm)],[c_0_20,c_0_55]) ).
cnf(c_0_59,hypothesis,
( c_Hoare__Mirabelle_Ohoare__derivs(t_b,X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P_H,v_x)),hAPP(v_c0,v_x)),hAPP(v_Q_H,v_x))),v_G))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(t_b,X1,v_G) ),
inference(spm,[status(thm)],[c_0_56,c_0_51]) ).
fof(c_0_60,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P,v_x)),hAPP(v_c0,v_x)),hAPP(v_Q,v_x))),hAPP(c_Set_Oimage(t_a,tc_Hoare__Mirabelle_Otriple(t_b),hAPP(hAPP(c_COMBS(t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(c_COMBS(t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),hAPP(hAPP(c_COMBB(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),c_Hoare__Mirabelle_Otriple_Otriple(t_b)),v_P)),v_c0)),v_Q)),v_F))),
inference(assume_negation,[status(cth)],[conj_5]) ).
cnf(c_0_61,hypothesis,
( c_Hoare__Mirabelle_Ohoare__derivs(t_b,X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P,v_x)),hAPP(v_c0,v_x)),hAPP(v_Q,v_x))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_HOL_Obool))))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(t_b,X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)),X2),v_G)) ),
inference(spm,[status(thm)],[c_0_57,c_0_44]) ).
cnf(c_0_62,hypothesis,
c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P_H,v_x)),hAPP(v_c0,v_x)),hAPP(v_Q_H,v_x))),v_G)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_51])]) ).
fof(c_0_63,hypothesis,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(c_Set_Oimage(t_a,tc_Hoare__Mirabelle_Otriple(t_b),hAPP(hAPP(c_COMBS(t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(c_COMBS(t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),hAPP(hAPP(c_COMBB(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),c_Hoare__Mirabelle_Otriple_Otriple(t_b)),v_P_H)),v_c0)),v_Q_H)),v_F))
| c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(c_Set_Oimage(t_a,tc_Hoare__Mirabelle_Otriple(t_b),hAPP(hAPP(c_COMBS(t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(c_COMBS(t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),hAPP(hAPP(c_COMBB(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),c_Hoare__Mirabelle_Otriple_Otriple(t_b)),v_P)),v_c0)),v_Q)),v_F)) ),
inference(fof_nnf,[status(thm)],[conj_3]) ).
fof(c_0_64,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P,v_x)),hAPP(v_c0,v_x)),hAPP(v_Q,v_x))),hAPP(c_Set_Oimage(t_a,tc_Hoare__Mirabelle_Otriple(t_b),hAPP(hAPP(c_COMBS(t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(c_COMBS(t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),hAPP(hAPP(c_COMBB(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),c_Hoare__Mirabelle_Otriple_Otriple(t_b)),v_P)),v_c0)),v_Q)),v_F))),
inference(fof_simplification,[status(thm)],[c_0_60]) ).
cnf(c_0_65,hypothesis,
c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P,v_x)),hAPP(v_c0,v_x)),hAPP(v_Q,v_x))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_HOL_Obool)))),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_66,hypothesis,
( c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(c_Set_Oimage(t_a,tc_Hoare__Mirabelle_Otriple(t_b),hAPP(hAPP(c_COMBS(t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(c_COMBS(t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),hAPP(hAPP(c_COMBB(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),c_Hoare__Mirabelle_Otriple_Otriple(t_b)),v_P)),v_c0)),v_Q)),v_F))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(c_Set_Oimage(t_a,tc_Hoare__Mirabelle_Otriple(t_b),hAPP(hAPP(c_COMBS(t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(c_COMBS(t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),hAPP(hAPP(c_COMBB(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),c_Hoare__Mirabelle_Otriple_Otriple(t_b)),v_P_H)),v_c0)),v_Q_H)),v_F)) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_67,hypothesis,
c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(c_Set_Oimage(t_a,tc_Hoare__Mirabelle_Otriple(t_b),hAPP(hAPP(c_COMBS(t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(c_COMBS(t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),hAPP(hAPP(c_COMBB(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),c_Hoare__Mirabelle_Otriple_Otriple(t_b)),v_P_H)),v_c0)),v_Q_H)),v_F)),
inference(spm,[status(thm)],[c_0_20,c_0_32]) ).
cnf(c_0_68,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P,v_x)),hAPP(v_c0,v_x)),hAPP(v_Q,v_x))),hAPP(c_Set_Oimage(t_a,tc_Hoare__Mirabelle_Otriple(t_b),hAPP(hAPP(c_COMBS(t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(c_COMBS(t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),hAPP(hAPP(c_COMBB(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),c_Hoare__Mirabelle_Otriple_Otriple(t_b)),v_P)),v_c0)),v_Q)),v_F))),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_69,hypothesis,
( c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P,v_x)),hAPP(v_c0,v_x)),hAPP(v_Q,v_x))),X1))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,X1) ),
inference(spm,[status(thm)],[c_0_47,c_0_65]) ).
cnf(c_0_70,hypothesis,
c_Hoare__Mirabelle_Ohoare__derivs(t_b,v_G,hAPP(c_Set_Oimage(t_a,tc_Hoare__Mirabelle_Otriple(t_b),hAPP(hAPP(c_COMBS(t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(hAPP(c_COMBS(t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),hAPP(hAPP(c_COMBB(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),c_Hoare__Mirabelle_Otriple_Otriple(t_b)),v_P)),v_c0)),v_Q)),v_F)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_66,c_0_67])]) ).
cnf(c_0_71,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_70])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWW321+1 : TPTP v8.1.0. Released v5.2.0.
% 0.07/0.14 % Command : run_ET %s %d
% 0.14/0.36 % Computer : n025.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Sat Jun 4 20:47:01 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.96/2.15 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.96/2.15 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.96/2.15 # Preprocessing time : 0.246 s
% 0.96/2.15
% 0.96/2.15 # Proof found!
% 0.96/2.15 # SZS status Theorem
% 0.96/2.15 # SZS output start CNFRefutation
% See solution above
% 0.96/2.15 # Proof object total steps : 72
% 0.96/2.15 # Proof object clause steps : 40
% 0.96/2.15 # Proof object formula steps : 32
% 0.96/2.15 # Proof object conjectures : 5
% 0.96/2.15 # Proof object clause conjectures : 2
% 0.96/2.15 # Proof object formula conjectures : 3
% 0.96/2.15 # Proof object initial clauses used : 17
% 0.96/2.15 # Proof object initial formulas used : 16
% 0.96/2.15 # Proof object generating inferences : 22
% 0.96/2.15 # Proof object simplifying inferences : 11
% 0.96/2.15 # Training examples: 0 positive, 0 negative
% 0.96/2.15 # Parsed axioms : 5233
% 0.96/2.15 # Removed by relevancy pruning/SinE : 5132
% 0.96/2.15 # Initial clauses : 170
% 0.96/2.15 # Removed in clause preprocessing : 16
% 0.96/2.15 # Initial clauses in saturation : 154
% 0.96/2.15 # Processed clauses : 657
% 0.96/2.15 # ...of these trivial : 13
% 0.96/2.15 # ...subsumed : 331
% 0.96/2.15 # ...remaining for further processing : 313
% 0.96/2.15 # Other redundant clauses eliminated : 6
% 0.96/2.15 # Clauses deleted for lack of memory : 0
% 0.96/2.15 # Backward-subsumed : 15
% 0.96/2.15 # Backward-rewritten : 11
% 0.96/2.15 # Generated clauses : 3876
% 0.96/2.15 # ...of the previous two non-trivial : 3223
% 0.96/2.15 # Contextual simplify-reflections : 47
% 0.96/2.15 # Paramodulations : 3858
% 0.96/2.15 # Factorizations : 0
% 0.96/2.15 # Equation resolutions : 19
% 0.96/2.15 # Current number of processed clauses : 282
% 0.96/2.15 # Positive orientable unit clauses : 54
% 0.96/2.15 # Positive unorientable unit clauses: 5
% 0.96/2.15 # Negative unit clauses : 18
% 0.96/2.15 # Non-unit-clauses : 205
% 0.96/2.15 # Current number of unprocessed clauses: 2612
% 0.96/2.15 # ...number of literals in the above : 6437
% 0.96/2.15 # Current number of archived formulas : 0
% 0.96/2.15 # Current number of archived clauses : 26
% 0.96/2.15 # Clause-clause subsumption calls (NU) : 12096
% 0.96/2.15 # Rec. Clause-clause subsumption calls : 7824
% 0.96/2.15 # Non-unit clause-clause subsumptions : 322
% 0.96/2.15 # Unit Clause-clause subsumption calls : 1314
% 0.96/2.15 # Rewrite failures with RHS unbound : 36
% 0.96/2.15 # BW rewrite match attempts : 611
% 0.96/2.15 # BW rewrite match successes : 39
% 0.96/2.15 # Condensation attempts : 0
% 0.96/2.15 # Condensation successes : 0
% 0.96/2.15 # Termbank termtop insertions : 266277
% 0.96/2.15
% 0.96/2.15 # -------------------------------------------------
% 0.96/2.15 # User time : 0.377 s
% 0.96/2.15 # System time : 0.012 s
% 0.96/2.15 # Total time : 0.389 s
% 0.96/2.15 # Maximum resident set size: 15916 pages
% 0.96/24.14 eprover: CPU time limit exceeded, terminating
% 0.96/24.15 eprover: CPU time limit exceeded, terminating
% 0.96/24.16 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.96/24.16 eprover: No such file or directory
% 0.96/24.17 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.96/24.17 eprover: No such file or directory
% 0.96/24.17 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.96/24.17 eprover: No such file or directory
% 0.96/24.17 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.96/24.17 eprover: No such file or directory
% 0.96/24.17 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.96/24.17 eprover: No such file or directory
% 0.96/24.18 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.96/24.18 eprover: No such file or directory
% 0.96/24.18 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.96/24.18 eprover: No such file or directory
% 0.96/24.18 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.96/24.18 eprover: No such file or directory
% 0.96/24.18 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.96/24.18 eprover: No such file or directory
% 0.96/24.19 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.96/24.19 eprover: No such file or directory
% 0.96/24.19 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.96/24.19 eprover: No such file or directory
% 0.96/24.19 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.96/24.19 eprover: No such file or directory
% 0.96/24.20 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.96/24.20 eprover: No such file or directory
% 0.96/24.20 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.96/24.20 eprover: No such file or directory
% 0.96/24.20 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.96/24.20 eprover: No such file or directory
% 0.96/24.20 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.96/24.20 eprover: No such file or directory
% 0.96/24.20 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.96/24.20 eprover: No such file or directory
% 0.96/24.21 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.96/24.21 eprover: No such file or directory
% 0.96/24.21 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.96/24.21 eprover: No such file or directory
% 0.96/24.21 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.96/24.21 eprover: No such file or directory
% 0.96/24.21 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.96/24.21 eprover: No such file or directory
% 0.96/24.22 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.96/24.22 eprover: No such file or directory
%------------------------------------------------------------------------------