TSTP Solution File: SWW336+1 by E---3.1.00
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%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SWW336+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat May 4 10:00:49 EDT 2024
% Result : Theorem 59.94s 10.04s
% Output : CNFRefutation 59.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 13
% Syntax : Number of formulae : 69 ( 26 unt; 0 def)
% Number of atoms : 154 ( 35 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 137 ( 52 ~; 62 |; 8 &)
% ( 3 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 20 ( 20 usr; 8 con; 0-3 aty)
% Number of variables : 143 ( 10 sgn 78 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(conj_4,conjecture,
! [X10] :
( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X3),v_G))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,X10,X3) )
=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X3),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),v_ts)))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,X10,X3) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Ih5eZGw8Zg/E---3.1_9995.p',conj_4) ).
fof(fact_Collect__mem__eq,axiom,
! [X12,X5] : hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBC(X5,tc_fun(X5,tc_HOL_Obool),tc_HOL_Obool),c_member(X5)),X12)) = X12,
file('/export/starexec/sandbox2/tmp/tmp.Ih5eZGw8Zg/E---3.1_9995.p',fact_Collect__mem__eq) ).
fof(fact_Collect__def,axiom,
! [X11,X5] : hAPP(c_Set_OCollect(X5),X11) = X11,
file('/export/starexec/sandbox2/tmp/tmp.Ih5eZGw8Zg/E---3.1_9995.p',fact_Collect__def) ).
fof(conj_3,hypothesis,
! [X10] :
( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X3),v_G))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,X10,X3) )
=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X3),v_ts))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,X10,X3) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Ih5eZGw8Zg/E---3.1_9995.p',conj_3) ).
fof(help_c__COMBC__1,axiom,
! [X137,X40,X11,X5,X138,X17] : hAPP(hAPP(hAPP(c_COMBC(X17,X138,X5),X11),X40),X137) = hAPP(hAPP(X11,X137),X40),
file('/export/starexec/sandbox2/tmp/tmp.Ih5eZGw8Zg/E---3.1_9995.p',help_c__COMBC__1) ).
fof(fact_mem__def,axiom,
! [X12,X16,X5] :
( hBOOL(hAPP(hAPP(c_member(X5),X16),X12))
<=> hBOOL(hAPP(X12,X16)) ),
file('/export/starexec/sandbox2/tmp/tmp.Ih5eZGw8Zg/E---3.1_9995.p',fact_mem__def) ).
fof(fact_insert__code,axiom,
! [X16,X12,X18,X5] :
( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X5),X18),X12),X16))
<=> ( X18 = X16
| hBOOL(hAPP(X12,X16)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Ih5eZGw8Zg/E---3.1_9995.p',fact_insert__code) ).
fof(help_c__fequal__2,axiom,
! [X18,X16] :
( X16 != X18
| hBOOL(hAPP(hAPP(c_fequal,X16),X18)) ),
file('/export/starexec/sandbox2/tmp/tmp.Ih5eZGw8Zg/E---3.1_9995.p',help_c__fequal__2) ).
fof(fact_singleton__conv2,axiom,
! [X6,X5] : hAPP(c_Set_OCollect(X5),hAPP(c_fequal,X6)) = hAPP(hAPP(c_Set_Oinsert(X5),X6),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))),
file('/export/starexec/sandbox2/tmp/tmp.Ih5eZGw8Zg/E---3.1_9995.p',fact_singleton__conv2) ).
fof(help_c__fequal__1,axiom,
! [X18,X16] :
( ~ hBOOL(hAPP(hAPP(c_fequal,X16),X18))
| X16 = X18 ),
file('/export/starexec/sandbox2/tmp/tmp.Ih5eZGw8Zg/E---3.1_9995.p',help_c__fequal__1) ).
fof(conj_1,hypothesis,
! [X10] :
( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X3),v_G))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,X10,X3) )
=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X3),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,X10,X3) ) ),
file('/export/starexec/sandbox2/tmp/tmp.Ih5eZGw8Zg/E---3.1_9995.p',conj_1) ).
fof(fact_some__eq__ex,axiom,
! [X5,X11] :
( hBOOL(hAPP(X11,c_Hilbert__Choice_OEps(X5,X11)))
<=> ? [X118] : hBOOL(hAPP(X11,X118)) ),
file('/export/starexec/sandbox2/tmp/tmp.Ih5eZGw8Zg/E---3.1_9995.p',fact_some__eq__ex) ).
fof(fact_some__sym__eq__trivial,axiom,
! [X16,X5] : c_Hilbert__Choice_OEps(X5,hAPP(c_fequal,X16)) = X16,
file('/export/starexec/sandbox2/tmp/tmp.Ih5eZGw8Zg/E---3.1_9995.p',fact_some__sym__eq__trivial) ).
fof(c_0_13,negated_conjecture,
~ ! [X10] :
( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X3),v_G))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,X10,X3) )
=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X3),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),v_ts)))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,X10,X3) ) ),
inference(assume_negation,[status(cth)],[conj_4]) ).
fof(c_0_14,plain,
! [X4672,X4673] : hAPP(c_Set_OCollect(X4673),hAPP(hAPP(c_COMBC(X4673,tc_fun(X4673,tc_HOL_Obool),tc_HOL_Obool),c_member(X4673)),X4672)) = X4672,
inference(variable_rename,[status(thm)],[fact_Collect__mem__eq]) ).
fof(c_0_15,plain,
! [X6021,X6022] : hAPP(c_Set_OCollect(X6022),X6021) = X6021,
inference(variable_rename,[status(thm)],[fact_Collect__def]) ).
fof(c_0_16,hypothesis,
! [X296,X298] :
( ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),esk5_1(X296)),v_G))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X298),v_ts))
| c_Hoare__Mirabelle_Otriple__valid(t_a,X296,X298) )
& ( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,X296,esk5_1(X296))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X298),v_ts))
| c_Hoare__Mirabelle_Otriple__valid(t_a,X296,X298) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_3])])])])])]) ).
fof(c_0_17,negated_conjecture,
! [X283] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X283),v_G))
| c_Hoare__Mirabelle_Otriple__valid(t_a,esk1_0,X283) )
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),esk2_0),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),v_ts)))
& ~ c_Hoare__Mirabelle_Otriple__valid(t_a,esk1_0,esk2_0) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])])])]) ).
fof(c_0_18,plain,
! [X4674,X4675,X4676,X4677,X4678,X4679] : hAPP(hAPP(hAPP(c_COMBC(X4679,X4678,X4677),X4676),X4675),X4674) = hAPP(hAPP(X4676,X4674),X4675),
inference(variable_rename,[status(thm)],[help_c__COMBC__1]) ).
cnf(c_0_19,plain,
hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,plain,
hAPP(c_Set_OCollect(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_21,plain,
! [X312,X313,X314] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X314),X313),X312))
| hBOOL(hAPP(X312,X313)) )
& ( ~ hBOOL(hAPP(X312,X313))
| hBOOL(hAPP(hAPP(c_member(X314),X313),X312)) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mem__def])])]) ).
cnf(c_0_22,hypothesis,
( c_Hoare__Mirabelle_Otriple__valid(t_a,X1,X2)
| ~ c_Hoare__Mirabelle_Otriple__valid(t_a,X1,esk5_1(X1))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X2),v_ts)) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,negated_conjecture,
( c_Hoare__Mirabelle_Otriple__valid(t_a,esk1_0,X1)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X1),v_G)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_24,plain,
hAPP(hAPP(hAPP(c_COMBC(X1,X2,X3),X4),X5),X6) = hAPP(hAPP(X4,X6),X5),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_25,plain,
hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2) = X2,
inference(rw,[status(thm)],[c_0_19,c_0_20]) ).
fof(c_0_26,plain,
! [X569,X570,X571,X572] :
( ( ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X572),X571),X570),X569))
| X571 = X569
| hBOOL(hAPP(X570,X569)) )
& ( X571 != X569
| hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X572),X571),X570),X569)) )
& ( ~ hBOOL(hAPP(X570,X569))
| hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X572),X571),X570),X569)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__code])])])]) ).
cnf(c_0_27,plain,
( hBOOL(hAPP(X3,X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_28,negated_conjecture,
hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),esk2_0),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),v_ts))),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_29,plain,
! [X18,X16] :
( X16 != X18
| hBOOL(hAPP(hAPP(c_fequal,X16),X18)) ),
inference(fof_simplification,[status(thm)],[help_c__fequal__2]) ).
cnf(c_0_30,negated_conjecture,
( c_Hoare__Mirabelle_Otriple__valid(t_a,esk1_0,X1)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),esk5_1(esk1_0)),v_G))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X1),v_ts)) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_31,plain,
( hBOOL(hAPP(hAPP(c_member(X3),X2),X1))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_32,hypothesis,
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),esk5_1(X1)),v_G))
| c_Hoare__Mirabelle_Otriple__valid(t_a,X1,X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X2),v_ts)) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_33,plain,
hAPP(hAPP(c_member(X1),X2),X3) = hAPP(X3,X2),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_34,plain,
( X2 = X4
| hBOOL(hAPP(X3,X4))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_35,negated_conjecture,
hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),v_ts),esk2_0)),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
fof(c_0_36,plain,
! [X923,X924] : hAPP(c_Set_OCollect(X924),hAPP(c_fequal,X923)) = hAPP(hAPP(c_Set_Oinsert(X924),X923),c_Orderings_Obot__class_Obot(tc_fun(X924,tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[fact_singleton__conv2]) ).
fof(c_0_37,plain,
! [X18,X16] :
( ~ hBOOL(hAPP(hAPP(c_fequal,X16),X18))
| X16 = X18 ),
inference(fof_simplification,[status(thm)],[help_c__fequal__1]) ).
fof(c_0_38,plain,
! [X5901,X5902] :
( X5902 != X5901
| hBOOL(hAPP(hAPP(c_fequal,X5902),X5901)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_29])]) ).
cnf(c_0_39,negated_conjecture,
( c_Hoare__Mirabelle_Otriple__valid(t_a,esk1_0,X1)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X1),v_ts))
| ~ hBOOL(hAPP(v_G,esk5_1(esk1_0))) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_40,hypothesis,
( c_Hoare__Mirabelle_Otriple__valid(t_a,X1,X2)
| hBOOL(hAPP(v_G,esk5_1(X1)))
| ~ hBOOL(hAPP(v_ts,X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_33]),c_0_33]) ).
cnf(c_0_41,negated_conjecture,
( esk2_0 = v_t
| hBOOL(hAPP(v_ts,esk2_0)) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
fof(c_0_42,hypothesis,
! [X293,X295] :
( ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),esk4_1(X293)),v_G))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X295),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))))
| c_Hoare__Mirabelle_Otriple__valid(t_a,X293,X295) )
& ( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,X293,esk4_1(X293))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X295),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))))
| c_Hoare__Mirabelle_Otriple__valid(t_a,X293,X295) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_1])])])])])]) ).
cnf(c_0_43,plain,
hAPP(c_Set_OCollect(X1),hAPP(c_fequal,X2)) = hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
fof(c_0_44,plain,
! [X5899,X5900] :
( ~ hBOOL(hAPP(hAPP(c_fequal,X5900),X5899))
| X5900 = X5899 ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_37])]) ).
fof(c_0_45,plain,
! [X14778,X14779,X14781,X14782,X14783] :
( ( ~ hBOOL(hAPP(X14779,c_Hilbert__Choice_OEps(X14778,X14779)))
| hBOOL(hAPP(X14779,esk500_2(X14778,X14779))) )
& ( ~ hBOOL(hAPP(X14782,X14783))
| hBOOL(hAPP(X14782,c_Hilbert__Choice_OEps(X14781,X14782))) ) ),
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_some__eq__ex])])])])])]) ).
fof(c_0_46,plain,
! [X14774,X14775] : c_Hilbert__Choice_OEps(X14775,hAPP(c_fequal,X14774)) = X14774,
inference(variable_rename,[status(thm)],[fact_some__sym__eq__trivial]) ).
cnf(c_0_47,plain,
( hBOOL(hAPP(hAPP(c_fequal,X1),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_48,negated_conjecture,
( c_Hoare__Mirabelle_Otriple__valid(t_a,esk1_0,X1)
| ~ hBOOL(hAPP(v_G,esk5_1(esk1_0)))
| ~ hBOOL(hAPP(v_ts,X1)) ),
inference(rw,[status(thm)],[c_0_39,c_0_33]) ).
cnf(c_0_49,hypothesis,
( esk2_0 = v_t
| c_Hoare__Mirabelle_Otriple__valid(t_a,X1,esk2_0)
| hBOOL(hAPP(v_G,esk5_1(X1))) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_50,negated_conjecture,
~ c_Hoare__Mirabelle_Otriple__valid(t_a,esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_51,hypothesis,
( c_Hoare__Mirabelle_Otriple__valid(t_a,X1,X2)
| ~ c_Hoare__Mirabelle_Otriple__valid(t_a,X1,esk4_1(X1))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X2),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool))))) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_52,plain,
hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = hAPP(c_fequal,X2),
inference(rw,[status(thm)],[c_0_43,c_0_20]) ).
cnf(c_0_53,hypothesis,
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),esk4_1(X1)),v_G))
| c_Hoare__Mirabelle_Otriple__valid(t_a,X1,X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X2),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool))))) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_54,plain,
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_fequal,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_55,plain,
( hBOOL(hAPP(X1,esk500_2(X2,X1)))
| ~ hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X2,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_56,plain,
c_Hilbert__Choice_OEps(X1,hAPP(c_fequal,X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_57,plain,
hBOOL(hAPP(hAPP(c_fequal,X1),X1)),
inference(er,[status(thm)],[c_0_47]) ).
cnf(c_0_58,negated_conjecture,
( esk2_0 = v_t
| c_Hoare__Mirabelle_Otriple__valid(t_a,esk1_0,X1)
| ~ hBOOL(hAPP(v_ts,X1)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50]) ).
cnf(c_0_59,hypothesis,
( c_Hoare__Mirabelle_Otriple__valid(t_a,X1,X2)
| ~ c_Hoare__Mirabelle_Otriple__valid(t_a,X1,esk4_1(X1))
| ~ hBOOL(hAPP(hAPP(c_fequal,v_t),X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_52]),c_0_33]) ).
cnf(c_0_60,negated_conjecture,
( c_Hoare__Mirabelle_Otriple__valid(t_a,esk1_0,X1)
| ~ hBOOL(hAPP(v_G,X1)) ),
inference(rw,[status(thm)],[c_0_23,c_0_33]) ).
cnf(c_0_61,hypothesis,
( c_Hoare__Mirabelle_Otriple__valid(t_a,X1,X2)
| hBOOL(hAPP(v_G,esk4_1(X1)))
| ~ hBOOL(hAPP(hAPP(c_fequal,v_t),X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_53,c_0_33]),c_0_52]),c_0_33]) ).
cnf(c_0_62,plain,
esk500_2(X1,hAPP(c_fequal,X2)) = X2,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_56]),c_0_57])]) ).
cnf(c_0_63,negated_conjecture,
esk2_0 = v_t,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_58]),c_0_41]) ).
cnf(c_0_64,negated_conjecture,
( c_Hoare__Mirabelle_Otriple__valid(t_a,esk1_0,X1)
| ~ hBOOL(hAPP(hAPP(c_fequal,v_t),X1))
| ~ hBOOL(hAPP(v_G,esk4_1(esk1_0))) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_65,hypothesis,
( c_Hoare__Mirabelle_Otriple__valid(t_a,X1,v_t)
| hBOOL(hAPP(v_G,esk4_1(X1))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_55]),c_0_62]),c_0_56]),c_0_57])]) ).
cnf(c_0_66,negated_conjecture,
~ c_Hoare__Mirabelle_Otriple__valid(t_a,esk1_0,v_t),
inference(rw,[status(thm)],[c_0_50,c_0_63]) ).
cnf(c_0_67,negated_conjecture,
( c_Hoare__Mirabelle_Otriple__valid(t_a,esk1_0,X1)
| ~ hBOOL(hAPP(hAPP(c_fequal,v_t),X1)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_66]) ).
cnf(c_0_68,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_57])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.80/0.84 % Problem : SWW336+1 : TPTP v8.1.2. Released v5.2.0.
% 0.80/0.85 % Command : run_E %s %d THM
% 0.85/1.06 % Computer : n012.cluster.edu
% 0.85/1.06 % Model : x86_64 x86_64
% 0.85/1.06 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.85/1.06 % Memory : 8042.1875MB
% 0.85/1.06 % OS : Linux 3.10.0-693.el7.x86_64
% 0.85/1.06 % CPULimit : 300
% 0.85/1.06 % WCLimit : 300
% 0.85/1.06 % DateTime : Fri May 3 12:52:41 EDT 2024
% 0.85/1.06 % CPUTime :
% 1.89/2.07 Running first-order theorem proving
% 1.89/2.07 Running: /export/starexec/sandbox2/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/sandbox2/tmp/tmp.Ih5eZGw8Zg/E---3.1_9995.p
% 59.94/10.04 # Version: 3.1.0
% 59.94/10.04 # Preprocessing class: FMLMSMSMSSSNFFN.
% 59.94/10.04 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 59.94/10.04 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 59.94/10.04 # Starting new_bool_3 with 300s (1) cores
% 59.94/10.04 # Starting new_bool_1 with 300s (1) cores
% 59.94/10.04 # Starting sh5l with 300s (1) cores
% 59.94/10.04 # sh5l with pid 10152 completed with status 0
% 59.94/10.04 # Result found by sh5l
% 59.94/10.04 # Preprocessing class: FMLMSMSMSSSNFFN.
% 59.94/10.04 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 59.94/10.04 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 59.94/10.04 # Starting new_bool_3 with 300s (1) cores
% 59.94/10.04 # Starting new_bool_1 with 300s (1) cores
% 59.94/10.04 # Starting sh5l with 300s (1) cores
% 59.94/10.04 # SinE strategy is gf500_gu_R04_F100_L20000
% 59.94/10.04 # Search class: FGHSM-SMLM33-DFFFFFNN
% 59.94/10.04 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 59.94/10.04 # Starting SAT001_MinMin_p005000_rr with 163s (1) cores
% 59.94/10.04 # SAT001_MinMin_p005000_rr with pid 10155 completed with status 0
% 59.94/10.04 # Result found by SAT001_MinMin_p005000_rr
% 59.94/10.04 # Preprocessing class: FMLMSMSMSSSNFFN.
% 59.94/10.04 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 59.94/10.04 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 59.94/10.04 # Starting new_bool_3 with 300s (1) cores
% 59.94/10.04 # Starting new_bool_1 with 300s (1) cores
% 59.94/10.04 # Starting sh5l with 300s (1) cores
% 59.94/10.04 # SinE strategy is gf500_gu_R04_F100_L20000
% 59.94/10.04 # Search class: FGHSM-SMLM33-DFFFFFNN
% 59.94/10.04 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 59.94/10.04 # Starting SAT001_MinMin_p005000_rr with 163s (1) cores
% 59.94/10.04 # Preprocessing time : 0.092 s
% 59.94/10.04 # Presaturation interreduction done
% 59.94/10.04
% 59.94/10.04 # Proof found!
% 59.94/10.04 # SZS status Theorem
% 59.94/10.04 # SZS output start CNFRefutation
% See solution above
% 59.94/10.04 # Parsed axioms : 5228
% 59.94/10.04 # Removed by relevancy pruning/SinE : 791
% 59.94/10.04 # Initial clauses : 6495
% 59.94/10.04 # Removed in clause preprocessing : 180
% 59.94/10.04 # Initial clauses in saturation : 6315
% 59.94/10.04 # Processed clauses : 22695
% 59.94/10.04 # ...of these trivial : 560
% 59.94/10.04 # ...subsumed : 8658
% 59.94/10.04 # ...remaining for further processing : 13477
% 59.94/10.04 # Other redundant clauses eliminated : 1197
% 59.94/10.04 # Clauses deleted for lack of memory : 0
% 59.94/10.04 # Backward-subsumed : 431
% 59.94/10.04 # Backward-rewritten : 541
% 59.94/10.04 # Generated clauses : 247295
% 59.94/10.04 # ...of the previous two non-redundant : 238292
% 59.94/10.04 # ...aggressively subsumed : 0
% 59.94/10.04 # Contextual simplify-reflections : 45
% 59.94/10.04 # Paramodulations : 246117
% 59.94/10.04 # Factorizations : 4
% 59.94/10.04 # NegExts : 0
% 59.94/10.04 # Equation resolutions : 1231
% 59.94/10.04 # Disequality decompositions : 0
% 59.94/10.04 # Total rewrite steps : 41760
% 59.94/10.04 # ...of those cached : 28997
% 59.94/10.04 # Propositional unsat checks : 3
% 59.94/10.04 # Propositional check models : 2
% 59.94/10.04 # Propositional check unsatisfiable : 0
% 59.94/10.04 # Propositional clauses : 0
% 59.94/10.04 # Propositional clauses after purity: 0
% 59.94/10.04 # Propositional unsat core size : 0
% 59.94/10.04 # Propositional preprocessing time : 0.000
% 59.94/10.04 # Propositional encoding time : 0.151
% 59.94/10.04 # Propositional solver time : 0.063
% 59.94/10.04 # Success case prop preproc time : 0.000
% 59.94/10.04 # Success case prop encoding time : 0.000
% 59.94/10.04 # Success case prop solver time : 0.000
% 59.94/10.04 # Current number of processed clauses : 7016
% 59.94/10.04 # Positive orientable unit clauses : 1480
% 59.94/10.04 # Positive unorientable unit clauses: 108
% 59.94/10.04 # Negative unit clauses : 884
% 59.94/10.04 # Non-unit-clauses : 4544
% 59.94/10.04 # Current number of unprocessed clauses: 195930
% 59.94/10.04 # ...number of literals in the above : 415343
% 59.94/10.04 # Current number of archived formulas : 0
% 59.94/10.04 # Current number of archived clauses : 6037
% 59.94/10.04 # Clause-clause subsumption calls (NU) : 5493523
% 59.94/10.04 # Rec. Clause-clause subsumption calls : 3201360
% 59.94/10.04 # Non-unit clause-clause subsumptions : 6324
% 59.94/10.04 # Unit Clause-clause subsumption calls : 207843
% 59.94/10.04 # Rewrite failures with RHS unbound : 269
% 59.94/10.04 # BW rewrite match attempts : 35953
% 59.94/10.04 # BW rewrite match successes : 1299
% 59.94/10.04 # Condensation attempts : 0
% 59.94/10.04 # Condensation successes : 0
% 59.94/10.04 # Termbank termtop insertions : 6572969
% 59.94/10.04 # Search garbage collected termcells : 95477
% 59.94/10.04
% 59.94/10.04 # -------------------------------------------------
% 59.94/10.04 # User time : 7.455 s
% 59.94/10.04 # System time : 0.220 s
% 59.94/10.04 # Total time : 7.675 s
% 59.94/10.04 # Maximum resident set size: 36228 pages
% 59.94/10.04
% 59.94/10.04 # -------------------------------------------------
% 59.94/10.04 # User time : 7.603 s
% 59.94/10.04 # System time : 0.229 s
% 59.94/10.04 # Total time : 7.832 s
% 59.94/10.04 # Maximum resident set size: 9480 pages
% 59.94/10.04 % E---3.1 exiting
% 59.94/10.04 % E exiting
%------------------------------------------------------------------------------