TSTP Solution File: SWW366+1 by ET---2.0
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%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SWW366+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n026.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 00:10:40 EDT 2022
% Result : Theorem 1.11s 29.30s
% Output : CNFRefutation 1.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 17
% Syntax : Number of formulae : 58 ( 33 unt; 0 def)
% Number of atoms : 102 ( 33 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 84 ( 40 ~; 30 |; 2 &)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 25 ( 25 usr; 11 con; 0-3 aty)
% Number of variables : 94 ( 1 sgn 56 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(conj_7,conjecture,
v_P(hAPP(hAPP(c_Set_Oinsert(t_a),hAPP(v_mgt__call,v_pn)),v_G),hAPP(hAPP(c_Set_Oinsert(t_a),v_mgt(c_Option_Othe(tc_Com_Ocom,c_Com_Obody(v_pn)))),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_HOL_Obool)))),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',conj_7) ).
fof(conj_1,hypothesis,
! [X281] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),X281),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)))
=> ( hAPP(c_Finite__Set_Ocard(t_a),X281) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))),v_n)
=> ! [X181] :
( v_wt(X181)
=> v_P(X281,hAPP(hAPP(c_Set_Oinsert(t_a),v_mgt(X181)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_HOL_Obool)))) ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',conj_1) ).
fof(fact_add__Suc__shift,axiom,
! [X25,X24] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X24)),X25) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24),hAPP(c_Nat_OSuc,X25)),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_add__Suc__shift) ).
fof(fact_add__Suc__right,axiom,
! [X25,X24] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24),hAPP(c_Nat_OSuc,X25)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24),X25)),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_add__Suc__right) ).
fof(fact_assms_I4_J,axiom,
! [X6] :
( hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),X6),v_U))
=> v_wt(c_Option_Othe(tc_Com_Ocom,c_Com_Obody(X6))) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_assms_I4_J) ).
fof(fact_le__add__diff__inverse,axiom,
! [X24,X25] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X25),X24))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24),X25)) = X24 ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_le__add__diff__inverse) ).
fof(conj_5,hypothesis,
hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),v_pn),v_U)),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',conj_5) ).
fof(conj_4,hypothesis,
hAPP(c_Finite__Set_Ocard(t_a),v_G) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))),hAPP(c_Nat_OSuc,v_n)),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',conj_4) ).
fof(conj_3,hypothesis,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,v_n)),hAPP(c_Finite__Set_Ocard(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)))),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',conj_3) ).
fof(fact_insert__mono,axiom,
! [X14,X22,X18,X11] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X11,tc_HOL_Obool)),X18),X22))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X11,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X11),X14),X18)),hAPP(hAPP(c_Set_Oinsert(X11),X14),X22))) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_insert__mono) ).
fof(fact_insert__image,axiom,
! [X2,X9,X13,X12,X11] :
( hBOOL(hAPP(hAPP(c_member(X11),X12),X13))
=> hAPP(hAPP(c_Set_Oinsert(X9),hAPP(X2,X12)),hAPP(c_Set_Oimage(X11,X9,X2),X13)) = hAPP(c_Set_Oimage(X11,X9,X2),X13) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_insert__image) ).
fof(fact_diff__add__inverse,axiom,
! [X24,X25] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25),X24)),X25) = X24,
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_diff__add__inverse) ).
fof(conj_2,hypothesis,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),v_G),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',conj_2) ).
fof(fact_finite__surj,axiom,
! [X2,X16,X9,X13,X11] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X11),X13))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X9,tc_HOL_Obool)),X16),hAPP(c_Set_Oimage(X11,X9,X2),X13)))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X9),X16)) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_finite__surj) ).
fof(fact_card__insert__if,axiom,
! [X12,X13,X11] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X11),X13))
=> ( ( hBOOL(hAPP(hAPP(c_member(X11),X12),X13))
=> hAPP(c_Finite__Set_Ocard(X11),hAPP(hAPP(c_Set_Oinsert(X11),X12),X13)) = hAPP(c_Finite__Set_Ocard(X11),X13) )
& ( ~ hBOOL(hAPP(hAPP(c_member(X11),X12),X13))
=> hAPP(c_Finite__Set_Ocard(X11),hAPP(hAPP(c_Set_Oinsert(X11),X12),X13)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X11),X13)) ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_card__insert__if) ).
fof(conj_0,hypothesis,
hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname),v_U)),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',conj_0) ).
fof(conj_6,hypothesis,
~ hBOOL(hAPP(hAPP(c_member(t_a),hAPP(v_mgt__call,v_pn)),v_G)),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',conj_6) ).
fof(c_0_17,negated_conjecture,
~ v_P(hAPP(hAPP(c_Set_Oinsert(t_a),hAPP(v_mgt__call,v_pn)),v_G),hAPP(hAPP(c_Set_Oinsert(t_a),v_mgt(c_Option_Othe(tc_Com_Ocom,c_Com_Obody(v_pn)))),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_HOL_Obool)))),
inference(assume_negation,[status(cth)],[conj_7]) ).
fof(c_0_18,negated_conjecture,
~ v_P(hAPP(hAPP(c_Set_Oinsert(t_a),hAPP(v_mgt__call,v_pn)),v_G),hAPP(hAPP(c_Set_Oinsert(t_a),v_mgt(c_Option_Othe(tc_Com_Ocom,c_Com_Obody(v_pn)))),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_HOL_Obool)))),
inference(fof_simplification,[status(thm)],[c_0_17]) ).
fof(c_0_19,hypothesis,
! [X282,X283] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),X282),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)))
| hAPP(c_Finite__Set_Ocard(t_a),X282) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))),v_n)
| ~ v_wt(X283)
| v_P(X282,hAPP(hAPP(c_Set_Oinsert(t_a),v_mgt(X283)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_HOL_Obool)))) ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_1])])])])]) ).
fof(c_0_20,plain,
! [X26,X27] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X27)),X26) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X27),hAPP(c_Nat_OSuc,X26)),
inference(variable_rename,[status(thm)],[fact_add__Suc__shift]) ).
fof(c_0_21,plain,
! [X26,X27] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X27),hAPP(c_Nat_OSuc,X26)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X27),X26)),
inference(variable_rename,[status(thm)],[fact_add__Suc__right]) ).
cnf(c_0_22,negated_conjecture,
~ v_P(hAPP(hAPP(c_Set_Oinsert(t_a),hAPP(v_mgt__call,v_pn)),v_G),hAPP(hAPP(c_Set_Oinsert(t_a),v_mgt(c_Option_Othe(tc_Com_Ocom,c_Com_Obody(v_pn)))),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_HOL_Obool)))),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_23,hypothesis,
( v_P(X1,hAPP(hAPP(c_Set_Oinsert(t_a),v_mgt(X2)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_HOL_Obool))))
| ~ v_wt(X2)
| hAPP(c_Finite__Set_Ocard(t_a),X1) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))),v_n)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),X1),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_24,plain,
! [X7] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),X7),v_U))
| v_wt(c_Option_Othe(tc_Com_Ocom,c_Com_Obody(X7))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_assms_I4_J])]) ).
fof(c_0_25,plain,
! [X26,X27] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X27),X26))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X27),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X26),X27)) = X26 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__add__diff__inverse])]) ).
cnf(c_0_26,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_27,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_28,negated_conjecture,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))),v_n) != hAPP(c_Finite__Set_Ocard(t_a),hAPP(hAPP(c_Set_Oinsert(t_a),hAPP(v_mgt__call,v_pn)),v_G))
| ~ v_wt(c_Option_Othe(tc_Com_Ocom,c_Com_Obody(v_pn)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(t_a),hAPP(v_mgt__call,v_pn)),v_G)),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_29,plain,
( v_wt(c_Option_Othe(tc_Com_Ocom,c_Com_Obody(X1)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),X1),v_U)) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_30,hypothesis,
hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),v_pn),v_U)),
inference(split_conjunct,[status(thm)],[conj_5]) ).
cnf(c_0_31,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1)) = X2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_32,hypothesis,
hAPP(c_Finite__Set_Ocard(t_a),v_G) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))),hAPP(c_Nat_OSuc,v_n)),
inference(split_conjunct,[status(thm)],[conj_4]) ).
cnf(c_0_33,hypothesis,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,v_n)),hAPP(c_Finite__Set_Ocard(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)))),
inference(split_conjunct,[status(thm)],[conj_3]) ).
cnf(c_0_34,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X1)),X2) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),
inference(rw,[status(thm)],[c_0_26,c_0_27]) ).
fof(c_0_35,plain,
! [X23,X24,X25,X26] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26,tc_HOL_Obool)),X25),X24))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X26),X23),X25)),hAPP(hAPP(c_Set_Oinsert(X26),X23),X24))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__mono])]) ).
fof(c_0_36,plain,
! [X14,X15,X16,X17,X18] :
( ~ hBOOL(hAPP(hAPP(c_member(X18),X17),X16))
| hAPP(hAPP(c_Set_Oinsert(X15),hAPP(X14,X17)),hAPP(c_Set_Oimage(X18,X15,X14),X16)) = hAPP(c_Set_Oimage(X18,X15,X14),X16) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__image])]) ).
cnf(c_0_37,negated_conjecture,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))),v_n) != hAPP(c_Finite__Set_Ocard(t_a),hAPP(hAPP(c_Set_Oinsert(t_a),hAPP(v_mgt__call,v_pn)),v_G))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(t_a),hAPP(v_mgt__call,v_pn)),v_G)),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30])]) ).
cnf(c_0_38,hypothesis,
hAPP(c_Finite__Set_Ocard(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n),hAPP(c_Finite__Set_Ocard(t_a),v_G))),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33])]),c_0_34]) ).
cnf(c_0_39,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),X4)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_40,plain,
( hAPP(hAPP(c_Set_Oinsert(X1),hAPP(X2,X3)),hAPP(c_Set_Oimage(X4,X1,X2),X5)) = hAPP(c_Set_Oimage(X4,X1,X2),X5)
| ~ hBOOL(hAPP(hAPP(c_member(X4),X3),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
fof(c_0_41,plain,
! [X26,X27] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X27),X26)),X27) = X26,
inference(variable_rename,[status(thm)],[fact_diff__add__inverse]) ).
cnf(c_0_42,negated_conjecture,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n),hAPP(c_Finite__Set_Ocard(t_a),v_G)))),v_n) != hAPP(c_Finite__Set_Ocard(t_a),hAPP(hAPP(c_Set_Oinsert(t_a),hAPP(v_mgt__call,v_pn)),v_G))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(t_a),hAPP(v_mgt__call,v_pn)),v_G)),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))) ),
inference(rw,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_43,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),hAPP(X2,X3)),X4)),hAPP(c_Set_Oimage(X5,X1,X2),X6)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),hAPP(c_Set_Oimage(X5,X1,X2),X6)))
| ~ hBOOL(hAPP(hAPP(c_member(X5),X3),X6)) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_44,hypothesis,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),v_G),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))),
inference(split_conjunct,[status(thm)],[conj_2]) ).
cnf(c_0_45,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X1) = X2,
inference(split_conjunct,[status(thm)],[c_0_41]) ).
fof(c_0_46,plain,
! [X17,X18,X19,X20,X21] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21),X20))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19,tc_HOL_Obool)),X18),hAPP(c_Set_Oimage(X21,X19,X17),X20)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X19),X18)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__surj])]) ).
cnf(c_0_47,negated_conjecture,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),v_n),hAPP(c_Finite__Set_Ocard(t_a),v_G)))),v_n) != hAPP(c_Finite__Set_Ocard(t_a),hAPP(hAPP(c_Set_Oinsert(t_a),hAPP(v_mgt__call,v_pn)),v_G)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44]),c_0_30])]) ).
cnf(c_0_48,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))),X1) = hAPP(c_Nat_OSuc,X2),
inference(spm,[status(thm)],[c_0_45,c_0_27]) ).
fof(c_0_49,plain,
! [X14,X15,X16] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X16),X14),X15))
| hAPP(c_Finite__Set_Ocard(X16),hAPP(hAPP(c_Set_Oinsert(X16),X14),X15)) = hAPP(c_Finite__Set_Ocard(X16),X15)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X16),X15)) )
& ( hBOOL(hAPP(hAPP(c_member(X16),X14),X15))
| hAPP(c_Finite__Set_Ocard(X16),hAPP(hAPP(c_Set_Oinsert(X16),X14),X15)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X16),X15))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X16),X15)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_card__insert__if])])])]) ).
cnf(c_0_50,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Set_Oimage(X3,X1,X4),X5)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X5)) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_51,hypothesis,
hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname),v_U)),
inference(split_conjunct,[status(thm)],[conj_0]) ).
fof(c_0_52,hypothesis,
~ hBOOL(hAPP(hAPP(c_member(t_a),hAPP(v_mgt__call,v_pn)),v_G)),
inference(fof_simplification,[status(thm)],[conj_6]) ).
cnf(c_0_53,negated_conjecture,
hAPP(c_Finite__Set_Ocard(t_a),hAPP(hAPP(c_Set_Oinsert(t_a),hAPP(v_mgt__call,v_pn)),v_G)) != hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(t_a),v_G)),
inference(rw,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_54,plain,
( hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X1),X2))
| hBOOL(hAPP(hAPP(c_member(X1),X3),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_55,hypothesis,
hBOOL(hAPP(c_Finite__Set_Ofinite(t_a),v_G)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_44]),c_0_51])]) ).
cnf(c_0_56,hypothesis,
~ hBOOL(hAPP(hAPP(c_member(t_a),hAPP(v_mgt__call,v_pn)),v_G)),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_57,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_55])]),c_0_56]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW366+1 : TPTP v8.1.0. Released v5.2.0.
% 0.07/0.13 % Command : run_ET %s %d
% 0.13/0.35 % Computer : n026.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sat Jun 4 19:16:59 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.08/24.10 eprover: CPU time limit exceeded, terminating
% 1.08/24.10 eprover: CPU time limit exceeded, terminating
% 1.08/24.11 eprover: CPU time limit exceeded, terminating
% 1.08/24.11 eprover: CPU time limit exceeded, terminating
% 1.11/29.30 # Running protocol protocol_eprover_2d86bd69119e7e9cc4417c0ee581499eaf828bb2 for 23 seconds:
% 1.11/29.30
% 1.11/29.30 # Failure: Resource limit exceeded (time)
% 1.11/29.30 # OLD status Res
% 1.11/29.30 # SinE strategy is GSinE(CountFormulas,,1.1,,02,500,1.0)
% 1.11/29.30 # Preprocessing time : 0.257 s
% 1.11/29.30 # Running protocol protocol_eprover_230b6c199cce1dcf6700db59e75a93feb83d1bd9 for 23 seconds:
% 1.11/29.30 # SinE strategy is GSinE(CountFormulas,hypos,1.1,,01,20000,1.0)
% 1.11/29.30 # Preprocessing time : 0.163 s
% 1.11/29.30
% 1.11/29.30 # Proof found!
% 1.11/29.30 # SZS status Theorem
% 1.11/29.30 # SZS output start CNFRefutation
% See solution above
% 1.11/29.30 # Proof object total steps : 58
% 1.11/29.30 # Proof object clause steps : 28
% 1.11/29.30 # Proof object formula steps : 30
% 1.11/29.30 # Proof object conjectures : 10
% 1.11/29.30 # Proof object clause conjectures : 7
% 1.11/29.30 # Proof object formula conjectures : 3
% 1.11/29.30 # Proof object initial clauses used : 17
% 1.11/29.30 # Proof object initial formulas used : 17
% 1.11/29.30 # Proof object generating inferences : 8
% 1.11/29.30 # Proof object simplifying inferences : 16
% 1.11/29.30 # Training examples: 0 positive, 0 negative
% 1.11/29.30 # Parsed axioms : 5231
% 1.11/29.30 # Removed by relevancy pruning/SinE : 4914
% 1.11/29.30 # Initial clauses : 474
% 1.11/29.30 # Removed in clause preprocessing : 18
% 1.11/29.30 # Initial clauses in saturation : 456
% 1.11/29.30 # Processed clauses : 9338
% 1.11/29.30 # ...of these trivial : 55
% 1.11/29.30 # ...subsumed : 7286
% 1.11/29.30 # ...remaining for further processing : 1997
% 1.11/29.30 # Other redundant clauses eliminated : 193
% 1.11/29.30 # Clauses deleted for lack of memory : 53138
% 1.11/29.30 # Backward-subsumed : 70
% 1.11/29.30 # Backward-rewritten : 60
% 1.11/29.30 # Generated clauses : 170247
% 1.11/29.30 # ...of the previous two non-trivial : 164050
% 1.11/29.30 # Contextual simplify-reflections : 198
% 1.11/29.30 # Paramodulations : 169991
% 1.11/29.30 # Factorizations : 4
% 1.11/29.30 # Equation resolutions : 253
% 1.11/29.30 # Current number of processed clauses : 1852
% 1.11/29.30 # Positive orientable unit clauses : 162
% 1.11/29.30 # Positive unorientable unit clauses: 62
% 1.11/29.30 # Negative unit clauses : 516
% 1.11/29.30 # Non-unit-clauses : 1112
% 1.11/29.30 # Current number of unprocessed clauses: 98652
% 1.11/29.30 # ...number of literals in the above : 244578
% 1.11/29.30 # Current number of archived formulas : 0
% 1.11/29.30 # Current number of archived clauses : 130
% 1.11/29.30 # Clause-clause subsumption calls (NU) : 137548
% 1.11/29.30 # Rec. Clause-clause subsumption calls : 74387
% 1.11/29.30 # Non-unit clause-clause subsumptions : 734
% 1.11/29.30 # Unit Clause-clause subsumption calls : 25102
% 1.11/29.30 # Rewrite failures with RHS unbound : 212
% 1.11/29.30 # BW rewrite match attempts : 19706
% 1.11/29.30 # BW rewrite match successes : 125
% 1.11/29.30 # Condensation attempts : 0
% 1.11/29.30 # Condensation successes : 0
% 1.11/29.30 # Termbank termtop insertions : 7332768
% 1.11/29.30
% 1.11/29.30 # -------------------------------------------------
% 1.11/29.30 # User time : 4.254 s
% 1.11/29.30 # System time : 0.101 s
% 1.11/29.30 # Total time : 4.355 s
% 1.11/29.30 # Maximum resident set size: 137900 pages
%------------------------------------------------------------------------------