TSTP Solution File: ITP179^1 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP179^1 : TPTP v8.1.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n032.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 : Sun Jul 17 00:29:24 EDT 2022
% Result : Theorem 4.39s 4.63s
% Output : Proof 4.39s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : ITP179^1 : TPTP v8.1.0. Released v7.5.0.
% 0.05/0.10 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.10/0.29 % Computer : n032.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 600
% 0.10/0.30 % DateTime : Fri Jun 3 15:19:46 EDT 2022
% 0.10/0.30 % CPUTime :
% 4.39/4.63 % SZS status Theorem
% 4.39/4.63 % Mode: mode507:USE_SINE=true:SINE_TOLERANCE=3.0:SINE_GENERALITY_THRESHOLD=0:SINE_RANK_LIMIT=1.:SINE_DEPTH=1
% 4.39/4.63 % Inferences: 39
% 4.39/4.63 % SZS output start Proof
% 4.39/4.63 thf(ty_set_Pr1174980151um_a_b, type, set_Pr1174980151um_a_b : $tType).
% 4.39/4.63 thf(ty_product_prod_nat_nat, type, product_prod_nat_nat : $tType).
% 4.39/4.63 thf(ty_produc1124793815um_a_b, type, produc1124793815um_a_b : $tType).
% 4.39/4.63 thf(ty_labele431970251um_a_b, type, labele431970251um_a_b : $tType).
% 4.39/4.63 thf(ty_set_nat, type, set_nat : $tType).
% 4.39/4.63 thf(ty_standard_Constant_a, type, standard_Constant_a : $tType).
% 4.39/4.63 thf(ty_labele935650037_a_nat, type, labele935650037_a_nat : $tType).
% 4.39/4.63 thf(ty_produc1032616263at_nat, type, produc1032616263at_nat : $tType).
% 4.39/4.63 thf(ty_sum_sum_a_b, type, sum_sum_a_b : $tType).
% 4.39/4.63 thf(ty_set_Pr409224873um_a_b, type, set_Pr409224873um_a_b : $tType).
% 4.39/4.63 thf(ty_nat, type, nat : $tType).
% 4.39/4.63 thf(ty_set_Sum_sum_a_b, type, set_Sum_sum_a_b : $tType).
% 4.39/4.63 thf(ty_set_Pr1647387645at_nat, type, set_Pr1647387645at_nat : $tType).
% 4.39/4.63 thf(ty_bot_bo575978147um_a_b, type, bot_bo575978147um_a_b : set_Pr1174980151um_a_b).
% 4.39/4.63 thf(ty_bot_bot_set_nat, type, bot_bot_set_nat : set_nat).
% 4.39/4.63 thf(ty_eigen__2, type, eigen__2 : sum_sum_a_b).
% 4.39/4.63 thf(ty_domain1368163076um_a_b, type, domain1368163076um_a_b : (set_Pr1174980151um_a_b>set_nat)).
% 4.39/4.63 thf(ty_labele195203296_a_nat, type, labele195203296_a_nat : (labele935650037_a_nat>set_Pr1647387645at_nat)).
% 4.39/4.63 thf(ty_labele577278695um_a_b, type, labele577278695um_a_b : (labele431970251um_a_b>set_Sum_sum_a_b)).
% 4.39/4.63 thf(ty_unival2092813468um_a_b, type, unival2092813468um_a_b : (set_Pr1174980151um_a_b>$o)).
% 4.39/4.63 thf(ty_labele1810595089_a_nat, type, labele1810595089_a_nat : (labele935650037_a_nat>set_nat)).
% 4.39/4.63 thf(ty_edge_p1382426714tant_a, type, edge_p1382426714tant_a : (set_Pr1174980151um_a_b>set_Pr1647387645at_nat>set_Pr409224873um_a_b>$o)).
% 4.39/4.63 thf(ty_v, type, v : sum_sum_a_b).
% 4.39/4.63 thf(ty_labele16114835_a_nat, type, labele16114835_a_nat : (set_Pr1647387645at_nat>set_nat>labele935650037_a_nat)).
% 4.39/4.63 thf(ty_eigen__1, type, eigen__1 : sum_sum_a_b).
% 4.39/4.63 thf(ty_eigen__0, type, eigen__0 : sum_sum_a_b).
% 4.39/4.63 thf(ty_labele1939049654um_a_b, type, labele1939049654um_a_b : (labele431970251um_a_b>set_Pr409224873um_a_b)).
% 4.39/4.63 thf(ty_eigen__4, type, eigen__4 : sum_sum_a_b).
% 4.39/4.63 thf(ty_restri572569417_a_nat, type, restri572569417_a_nat : (labele935650037_a_nat>labele935650037_a_nat)).
% 4.39/4.63 thf(ty_eigen__5, type, eigen__5 : sum_sum_a_b).
% 4.39/4.63 thf(ty_image_256773707um_a_b, type, image_256773707um_a_b : (set_Pr1174980151um_a_b>set_nat>set_Sum_sum_a_b)).
% 4.39/4.63 thf(ty_ord_le192794300um_a_b, type, ord_le192794300um_a_b : (set_Sum_sum_a_b>set_Sum_sum_a_b>$o)).
% 4.39/4.63 thf(ty_eigen__3, type, eigen__3 : sum_sum_a_b).
% 4.39/4.63 thf(ty_bot_bo810816657at_nat, type, bot_bo810816657at_nat : set_Pr1647387645at_nat).
% 4.39/4.63 thf(ty_zero_zero_nat, type, zero_zero_nat : nat).
% 4.39/4.63 thf(ty_restri1162247455um_a_b, type, restri1162247455um_a_b : (labele431970251um_a_b>labele431970251um_a_b)).
% 4.39/4.63 thf(ty_standard_S_Idt_a, type, standard_S_Idt_a : standard_Constant_a).
% 4.39/4.63 thf(ty_produc1808556047um_a_b, type, produc1808556047um_a_b : (nat>sum_sum_a_b>produc1124793815um_a_b)).
% 4.39/4.63 thf(ty_insert983991207um_a_b, type, insert983991207um_a_b : (produc1124793815um_a_b>set_Pr1174980151um_a_b>set_Pr1174980151um_a_b)).
% 4.39/4.63 thf(ty_produc407553657at_nat, type, produc407553657at_nat : (standard_Constant_a>product_prod_nat_nat>produc1032616263at_nat)).
% 4.39/4.63 thf(ty_member1294585472um_a_b, type, member1294585472um_a_b : (produc1124793815um_a_b>set_Pr1174980151um_a_b>$o)).
% 4.39/4.63 thf(ty_insert_nat, type, insert_nat : (nat>set_nat>set_nat)).
% 4.39/4.63 thf(ty_g, type, g : labele431970251um_a_b).
% 4.39/4.63 thf(ty_f, type, f : set_Pr1174980151um_a_b).
% 4.39/4.63 thf(ty_product_Pair_nat_nat, type, product_Pair_nat_nat : (nat>nat>product_prod_nat_nat)).
% 4.39/4.63 thf(ty_insert1625259895at_nat, type, insert1625259895at_nat : (produc1032616263at_nat>set_Pr1647387645at_nat>set_Pr1647387645at_nat)).
% 4.39/4.63 thf(sP1,plain,sP1 <=> (g = (restri1162247455um_a_b @ g)),introduced(definition,[new_symbols(definition,[sP1])])).
% 4.39/4.63 thf(conj_0,conjecture,(~(((~(((~(((~(((~((((labele1810595089_a_nat @ ((labele16114835_a_nat @ ((insert1625259895at_nat @ ((produc407553657at_nat @ standard_S_Idt_a) @ ((product_Pair_nat_nat @ zero_zero_nat) @ zero_zero_nat))) @ bot_bo810816657at_nat)) @ ((insert_nat @ zero_zero_nat) @ bot_bot_set_nat))) = (domain1368163076um_a_b @ ((insert983991207um_a_b @ ((produc1808556047um_a_b @ zero_zero_nat) @ v)) @ bot_bo575978147um_a_b))) => (~((((labele16114835_a_nat @ ((insert1625259895at_nat @ ((produc407553657at_nat @ standard_S_Idt_a) @ ((product_Pair_nat_nat @ zero_zero_nat) @ zero_zero_nat))) @ bot_bo810816657at_nat)) @ ((insert_nat @ zero_zero_nat) @ bot_bot_set_nat)) = (restri572569417_a_nat @ ((labele16114835_a_nat @ ((insert1625259895at_nat @ ((produc407553657at_nat @ standard_S_Idt_a) @ ((product_Pair_nat_nat @ zero_zero_nat) @ zero_zero_nat))) @ bot_bo810816657at_nat)) @ ((insert_nat @ zero_zero_nat) @ bot_bot_set_nat))))))))) => (~(sP1))))) => (~(((ord_le192794300um_a_b @ ((image_256773707um_a_b @ ((insert983991207um_a_b @ ((produc1808556047um_a_b @ zero_zero_nat) @ v)) @ bot_bo575978147um_a_b)) @ (labele1810595089_a_nat @ ((labele16114835_a_nat @ ((insert1625259895at_nat @ ((produc407553657at_nat @ standard_S_Idt_a) @ ((product_Pair_nat_nat @ zero_zero_nat) @ zero_zero_nat))) @ bot_bo810816657at_nat)) @ ((insert_nat @ zero_zero_nat) @ bot_bot_set_nat))))) @ (labele577278695um_a_b @ g))))))) => (~((unival2092813468um_a_b @ ((insert983991207um_a_b @ ((produc1808556047um_a_b @ zero_zero_nat) @ v)) @ bot_bo575978147um_a_b))))))) => (~((((edge_p1382426714tant_a @ ((insert983991207um_a_b @ ((produc1808556047um_a_b @ zero_zero_nat) @ v)) @ bot_bo575978147um_a_b)) @ (labele195203296_a_nat @ ((labele16114835_a_nat @ ((insert1625259895at_nat @ ((produc407553657at_nat @ standard_S_Idt_a) @ ((product_Pair_nat_nat @ zero_zero_nat) @ zero_zero_nat))) @ bot_bo810816657at_nat)) @ ((insert_nat @ zero_zero_nat) @ bot_bot_set_nat)))) @ (labele1939049654um_a_b @ g)))))))).
% 4.39/4.63 thf(h0,negated_conjecture,((~(((~(((~(((~((((labele1810595089_a_nat @ ((labele16114835_a_nat @ ((insert1625259895at_nat @ ((produc407553657at_nat @ standard_S_Idt_a) @ ((product_Pair_nat_nat @ zero_zero_nat) @ zero_zero_nat))) @ bot_bo810816657at_nat)) @ ((insert_nat @ zero_zero_nat) @ bot_bot_set_nat))) = (domain1368163076um_a_b @ ((insert983991207um_a_b @ ((produc1808556047um_a_b @ zero_zero_nat) @ v)) @ bot_bo575978147um_a_b))) => (~((((labele16114835_a_nat @ ((insert1625259895at_nat @ ((produc407553657at_nat @ standard_S_Idt_a) @ ((product_Pair_nat_nat @ zero_zero_nat) @ zero_zero_nat))) @ bot_bo810816657at_nat)) @ ((insert_nat @ zero_zero_nat) @ bot_bot_set_nat)) = (restri572569417_a_nat @ ((labele16114835_a_nat @ ((insert1625259895at_nat @ ((produc407553657at_nat @ standard_S_Idt_a) @ ((product_Pair_nat_nat @ zero_zero_nat) @ zero_zero_nat))) @ bot_bo810816657at_nat)) @ ((insert_nat @ zero_zero_nat) @ bot_bot_set_nat))))))))) => (~(sP1))))) => (~(((ord_le192794300um_a_b @ ((image_256773707um_a_b @ ((insert983991207um_a_b @ ((produc1808556047um_a_b @ zero_zero_nat) @ v)) @ bot_bo575978147um_a_b)) @ (labele1810595089_a_nat @ ((labele16114835_a_nat @ ((insert1625259895at_nat @ ((produc407553657at_nat @ standard_S_Idt_a) @ ((product_Pair_nat_nat @ zero_zero_nat) @ zero_zero_nat))) @ bot_bo810816657at_nat)) @ ((insert_nat @ zero_zero_nat) @ bot_bot_set_nat))))) @ (labele577278695um_a_b @ g))))))) => (~((unival2092813468um_a_b @ ((insert983991207um_a_b @ ((produc1808556047um_a_b @ zero_zero_nat) @ v)) @ bot_bo575978147um_a_b))))))) => (~((((edge_p1382426714tant_a @ ((insert983991207um_a_b @ ((produc1808556047um_a_b @ zero_zero_nat) @ v)) @ bot_bo575978147um_a_b)) @ (labele195203296_a_nat @ ((labele16114835_a_nat @ ((insert1625259895at_nat @ ((produc407553657at_nat @ standard_S_Idt_a) @ ((product_Pair_nat_nat @ zero_zero_nat) @ zero_zero_nat))) @ bot_bo810816657at_nat)) @ ((insert_nat @ zero_zero_nat) @ bot_bot_set_nat)))) @ (labele1939049654um_a_b @ g))))),inference(assume_negation,[status(cth)],[conj_0])).
% 4.39/4.63 thf(h1,assumption,((~(((~(((~((((labele1810595089_a_nat @ ((labele16114835_a_nat @ ((insert1625259895at_nat @ ((produc407553657at_nat @ standard_S_Idt_a) @ ((product_Pair_nat_nat @ zero_zero_nat) @ zero_zero_nat))) @ bot_bo810816657at_nat)) @ ((insert_nat @ zero_zero_nat) @ bot_bot_set_nat))) = (domain1368163076um_a_b @ ((insert983991207um_a_b @ ((produc1808556047um_a_b @ zero_zero_nat) @ v)) @ bot_bo575978147um_a_b))) => (~((((labele16114835_a_nat @ ((insert1625259895at_nat @ ((produc407553657at_nat @ standard_S_Idt_a) @ ((product_Pair_nat_nat @ zero_zero_nat) @ zero_zero_nat))) @ bot_bo810816657at_nat)) @ ((insert_nat @ zero_zero_nat) @ bot_bot_set_nat)) = (restri572569417_a_nat @ ((labele16114835_a_nat @ ((insert1625259895at_nat @ ((produc407553657at_nat @ standard_S_Idt_a) @ ((product_Pair_nat_nat @ zero_zero_nat) @ zero_zero_nat))) @ bot_bo810816657at_nat)) @ ((insert_nat @ zero_zero_nat) @ bot_bot_set_nat))))))))) => (~(sP1))))) => (~(((ord_le192794300um_a_b @ ((image_256773707um_a_b @ ((insert983991207um_a_b @ ((produc1808556047um_a_b @ zero_zero_nat) @ v)) @ bot_bo575978147um_a_b)) @ (labele1810595089_a_nat @ ((labele16114835_a_nat @ ((insert1625259895at_nat @ ((produc407553657at_nat @ standard_S_Idt_a) @ ((product_Pair_nat_nat @ zero_zero_nat) @ zero_zero_nat))) @ bot_bo810816657at_nat)) @ ((insert_nat @ zero_zero_nat) @ bot_bot_set_nat))))) @ (labele577278695um_a_b @ g))))))) => (~((unival2092813468um_a_b @ ((insert983991207um_a_b @ ((produc1808556047um_a_b @ zero_zero_nat) @ v)) @ bot_bo575978147um_a_b))))),introduced(assumption,[])).
% 4.39/4.63 thf(h2,assumption,(~((((edge_p1382426714tant_a @ ((insert983991207um_a_b @ ((produc1808556047um_a_b @ zero_zero_nat) @ v)) @ bot_bo575978147um_a_b)) @ (labele195203296_a_nat @ ((labele16114835_a_nat @ ((insert1625259895at_nat @ ((produc407553657at_nat @ standard_S_Idt_a) @ ((product_Pair_nat_nat @ zero_zero_nat) @ zero_zero_nat))) @ bot_bo810816657at_nat)) @ ((insert_nat @ zero_zero_nat) @ bot_bot_set_nat)))) @ (labele1939049654um_a_b @ g)))),introduced(assumption,[])).
% 4.39/4.63 thf(h3,assumption,((~(((~((((labele1810595089_a_nat @ ((labele16114835_a_nat @ ((insert1625259895at_nat @ ((produc407553657at_nat @ standard_S_Idt_a) @ ((product_Pair_nat_nat @ zero_zero_nat) @ zero_zero_nat))) @ bot_bo810816657at_nat)) @ ((insert_nat @ zero_zero_nat) @ bot_bot_set_nat))) = (domain1368163076um_a_b @ ((insert983991207um_a_b @ ((produc1808556047um_a_b @ zero_zero_nat) @ v)) @ bot_bo575978147um_a_b))) => (~((((labele16114835_a_nat @ ((insert1625259895at_nat @ ((produc407553657at_nat @ standard_S_Idt_a) @ ((product_Pair_nat_nat @ zero_zero_nat) @ zero_zero_nat))) @ bot_bo810816657at_nat)) @ ((insert_nat @ zero_zero_nat) @ bot_bot_set_nat)) = (restri572569417_a_nat @ ((labele16114835_a_nat @ ((insert1625259895at_nat @ ((produc407553657at_nat @ standard_S_Idt_a) @ ((product_Pair_nat_nat @ zero_zero_nat) @ zero_zero_nat))) @ bot_bo810816657at_nat)) @ ((insert_nat @ zero_zero_nat) @ bot_bot_set_nat))))))))) => (~(sP1))))) => (~(((ord_le192794300um_a_b @ ((image_256773707um_a_b @ ((insert983991207um_a_b @ ((produc1808556047um_a_b @ zero_zero_nat) @ v)) @ bot_bo575978147um_a_b)) @ (labele1810595089_a_nat @ ((labele16114835_a_nat @ ((insert1625259895at_nat @ ((produc407553657at_nat @ standard_S_Idt_a) @ ((product_Pair_nat_nat @ zero_zero_nat) @ zero_zero_nat))) @ bot_bo810816657at_nat)) @ ((insert_nat @ zero_zero_nat) @ bot_bot_set_nat))))) @ (labele577278695um_a_b @ g))))),introduced(assumption,[])).
% 4.39/4.63 thf(h4,assumption,(~((unival2092813468um_a_b @ ((insert983991207um_a_b @ ((produc1808556047um_a_b @ zero_zero_nat) @ v)) @ bot_bo575978147um_a_b)))),introduced(assumption,[])).
% 4.39/4.63 thf(h5,assumption,((~((((labele1810595089_a_nat @ ((labele16114835_a_nat @ ((insert1625259895at_nat @ ((produc407553657at_nat @ standard_S_Idt_a) @ ((product_Pair_nat_nat @ zero_zero_nat) @ zero_zero_nat))) @ bot_bo810816657at_nat)) @ ((insert_nat @ zero_zero_nat) @ bot_bot_set_nat))) = (domain1368163076um_a_b @ ((insert983991207um_a_b @ ((produc1808556047um_a_b @ zero_zero_nat) @ v)) @ bot_bo575978147um_a_b))) => (~((((labele16114835_a_nat @ ((insert1625259895at_nat @ ((produc407553657at_nat @ standard_S_Idt_a) @ ((product_Pair_nat_nat @ zero_zero_nat) @ zero_zero_nat))) @ bot_bo810816657at_nat)) @ ((insert_nat @ zero_zero_nat) @ bot_bot_set_nat)) = (restri572569417_a_nat @ ((labele16114835_a_nat @ ((insert1625259895at_nat @ ((produc407553657at_nat @ standard_S_Idt_a) @ ((product_Pair_nat_nat @ zero_zero_nat) @ zero_zero_nat))) @ bot_bo810816657at_nat)) @ ((insert_nat @ zero_zero_nat) @ bot_bot_set_nat))))))))) => (~(sP1))),introduced(assumption,[])).
% 4.39/4.63 thf(h6,assumption,(~(((ord_le192794300um_a_b @ ((image_256773707um_a_b @ ((insert983991207um_a_b @ ((produc1808556047um_a_b @ zero_zero_nat) @ v)) @ bot_bo575978147um_a_b)) @ (labele1810595089_a_nat @ ((labele16114835_a_nat @ ((insert1625259895at_nat @ ((produc407553657at_nat @ standard_S_Idt_a) @ ((product_Pair_nat_nat @ zero_zero_nat) @ zero_zero_nat))) @ bot_bo810816657at_nat)) @ ((insert_nat @ zero_zero_nat) @ bot_bot_set_nat))))) @ (labele577278695um_a_b @ g)))),introduced(assumption,[])).
% 4.39/4.63 thf(h7,assumption,(((labele1810595089_a_nat @ ((labele16114835_a_nat @ ((insert1625259895at_nat @ ((produc407553657at_nat @ standard_S_Idt_a) @ ((product_Pair_nat_nat @ zero_zero_nat) @ zero_zero_nat))) @ bot_bo810816657at_nat)) @ ((insert_nat @ zero_zero_nat) @ bot_bot_set_nat))) = (domain1368163076um_a_b @ ((insert983991207um_a_b @ ((produc1808556047um_a_b @ zero_zero_nat) @ v)) @ bot_bo575978147um_a_b))) => (~((((labele16114835_a_nat @ ((insert1625259895at_nat @ ((produc407553657at_nat @ standard_S_Idt_a) @ ((product_Pair_nat_nat @ zero_zero_nat) @ zero_zero_nat))) @ bot_bo810816657at_nat)) @ ((insert_nat @ zero_zero_nat) @ bot_bot_set_nat)) = (restri572569417_a_nat @ ((labele16114835_a_nat @ ((insert1625259895at_nat @ ((produc407553657at_nat @ standard_S_Idt_a) @ ((product_Pair_nat_nat @ zero_zero_nat) @ zero_zero_nat))) @ bot_bo810816657at_nat)) @ ((insert_nat @ zero_zero_nat) @ bot_bot_set_nat))))))),introduced(assumption,[])).
% 4.39/4.63 thf(h8,assumption,(~(sP1)),introduced(assumption,[])).
% 4.39/4.63 thf(h9,assumption,(~(((labele1810595089_a_nat @ ((labele16114835_a_nat @ ((insert1625259895at_nat @ ((produc407553657at_nat @ standard_S_Idt_a) @ ((product_Pair_nat_nat @ zero_zero_nat) @ zero_zero_nat))) @ bot_bo810816657at_nat)) @ ((insert_nat @ zero_zero_nat) @ bot_bot_set_nat))) = (domain1368163076um_a_b @ ((insert983991207um_a_b @ ((produc1808556047um_a_b @ zero_zero_nat) @ v)) @ bot_bo575978147um_a_b))))),introduced(assumption,[])).
% 4.39/4.63 thf(h10,assumption,(~((((labele16114835_a_nat @ ((insert1625259895at_nat @ ((produc407553657at_nat @ standard_S_Idt_a) @ ((product_Pair_nat_nat @ zero_zero_nat) @ zero_zero_nat))) @ bot_bo810816657at_nat)) @ ((insert_nat @ zero_zero_nat) @ bot_bot_set_nat)) = (restri572569417_a_nat @ ((labele16114835_a_nat @ ((insert1625259895at_nat @ ((produc407553657at_nat @ standard_S_Idt_a) @ ((product_Pair_nat_nat @ zero_zero_nat) @ zero_zero_nat))) @ bot_bo810816657at_nat)) @ ((insert_nat @ zero_zero_nat) @ bot_bot_set_nat)))))),introduced(assumption,[])).
% 4.39/4.63 thf(h11,assumption,((member1294585472um_a_b @ ((produc1808556047um_a_b @ zero_zero_nat) @ eigen__0)) @ f),introduced(assumption,[])).
% 4.39/4.63 thf(pax68, axiom, (p68=>![X87:set_Pr1647387645at_nat, X88:set_nat]:(flabele1810595089_a_nat @ (flabele16114835_a_nat @ X87 @ X88))=(X88)), file('<stdin>', pax68)).
% 4.39/4.63 thf(pax5, axiom, (p5=>(ff)=(finsert983991207um_a_b @ (fproduc1808556047um_a_b @ fzero_zero_nat @ fv) @ fbot_bo575978147um_a_b)), file('<stdin>', pax5)).
% 4.39/4.63 thf(pax6, axiom, (p6=>(fdomain1368163076um_a_b @ ff)=(finsert_nat @ fzero_zero_nat @ fbot_bot_set_nat)), file('<stdin>', pax6)).
% 4.39/4.63 thf(nax151, axiom, (p151<=(flabele1810595089_a_nat @ (flabele16114835_a_nat @ (finsert1625259895at_nat @ (fproduc407553657at_nat @ fstandard_S_Idt_a @ (fproduct_Pair_nat_nat @ fzero_zero_nat @ fzero_zero_nat)) @ fbot_bo810816657at_nat) @ (finsert_nat @ fzero_zero_nat @ fbot_bot_set_nat)))=(fdomain1368163076um_a_b @ (finsert983991207um_a_b @ (fproduc1808556047um_a_b @ fzero_zero_nat @ fv) @ fbot_bo575978147um_a_b))), file('<stdin>', nax151)).
% 4.39/4.63 thf(ax83, axiom, p68, file('<stdin>', ax83)).
% 4.39/4.63 thf(ax146, axiom, p5, file('<stdin>', ax146)).
% 4.39/4.63 thf(ax145, axiom, p6, file('<stdin>', ax145)).
% 4.39/4.63 thf(ax0, axiom, ~(p151), file('<stdin>', ax0)).
% 4.39/4.63 thf(c_0_8, plain, ![X377:set_Pr1647387645at_nat, X378:set_nat]:(~p68|(flabele1810595089_a_nat @ (flabele16114835_a_nat @ X377 @ X378))=(X378)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax68])])])).
% 4.39/4.63 thf(c_0_9, plain, (~p5|(ff)=(finsert983991207um_a_b @ (fproduc1808556047um_a_b @ fzero_zero_nat @ fv) @ fbot_bo575978147um_a_b)), inference(fof_nnf,[status(thm)],[pax5])).
% 4.39/4.63 thf(c_0_10, plain, (~p6|(fdomain1368163076um_a_b @ ff)=(finsert_nat @ fzero_zero_nat @ fbot_bot_set_nat)), inference(fof_nnf,[status(thm)],[pax6])).
% 4.39/4.63 thf(c_0_11, plain, ((flabele1810595089_a_nat @ (flabele16114835_a_nat @ (finsert1625259895at_nat @ (fproduc407553657at_nat @ fstandard_S_Idt_a @ (fproduct_Pair_nat_nat @ fzero_zero_nat @ fzero_zero_nat)) @ fbot_bo810816657at_nat) @ (finsert_nat @ fzero_zero_nat @ fbot_bot_set_nat)))!=(fdomain1368163076um_a_b @ (finsert983991207um_a_b @ (fproduc1808556047um_a_b @ fzero_zero_nat @ fv) @ fbot_bo575978147um_a_b))|p151), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax151])])).
% 4.39/4.63 thf(c_0_12, plain, ![X13:set_Pr1647387645at_nat, X1:set_nat]:((flabele1810595089_a_nat @ (flabele16114835_a_nat @ X13 @ X1))=(X1)|~p68), inference(split_conjunct,[status(thm)],[c_0_8])).
% 4.39/4.63 thf(c_0_13, plain, p68, inference(split_conjunct,[status(thm)],[ax83])).
% 4.39/4.63 thf(c_0_14, plain, ((ff)=(finsert983991207um_a_b @ (fproduc1808556047um_a_b @ fzero_zero_nat @ fv) @ fbot_bo575978147um_a_b)|~p5), inference(split_conjunct,[status(thm)],[c_0_9])).
% 4.39/4.63 thf(c_0_15, plain, p5, inference(split_conjunct,[status(thm)],[ax146])).
% 4.39/4.63 thf(c_0_16, plain, ((fdomain1368163076um_a_b @ ff)=(finsert_nat @ fzero_zero_nat @ fbot_bot_set_nat)|~p6), inference(split_conjunct,[status(thm)],[c_0_10])).
% 4.39/4.63 thf(c_0_17, plain, p6, inference(split_conjunct,[status(thm)],[ax145])).
% 4.39/4.63 thf(c_0_18, plain, ~p151, inference(fof_simplification,[status(thm)],[ax0])).
% 4.39/4.63 thf(c_0_19, plain, (p151|(flabele1810595089_a_nat @ (flabele16114835_a_nat @ (finsert1625259895at_nat @ (fproduc407553657at_nat @ fstandard_S_Idt_a @ (fproduct_Pair_nat_nat @ fzero_zero_nat @ fzero_zero_nat)) @ fbot_bo810816657at_nat) @ (finsert_nat @ fzero_zero_nat @ fbot_bot_set_nat)))!=(fdomain1368163076um_a_b @ (finsert983991207um_a_b @ (fproduc1808556047um_a_b @ fzero_zero_nat @ fv) @ fbot_bo575978147um_a_b))), inference(split_conjunct,[status(thm)],[c_0_11])).
% 4.39/4.63 thf(c_0_20, plain, ![X13:set_Pr1647387645at_nat, X1:set_nat]:(flabele1810595089_a_nat @ (flabele16114835_a_nat @ X13 @ X1))=(X1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_12, c_0_13])])).
% 4.39/4.63 thf(c_0_21, plain, (finsert983991207um_a_b @ (fproduc1808556047um_a_b @ fzero_zero_nat @ fv) @ fbot_bo575978147um_a_b)=(ff), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_14, c_0_15])])).
% 4.39/4.63 thf(c_0_22, plain, (fdomain1368163076um_a_b @ ff)=(finsert_nat @ fzero_zero_nat @ fbot_bot_set_nat), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_16, c_0_17])])).
% 4.39/4.63 thf(c_0_23, plain, ~p151, inference(split_conjunct,[status(thm)],[c_0_18])).
% 4.39/4.63 thf(c_0_24, plain, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_19, c_0_20]), c_0_21]), c_0_22])]), c_0_23]), ['proof']).
% 4.39/4.63 thf(1,plain,$false,inference(eprover,[status(thm),assumptions([h11,h9,h7,h5,h3,h1,h0])],[])).
% 4.39/4.63 thf(fact_8__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062v_O_A_I0_M_Av_J_A_092_060in_062_Af_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,(~((![X1:sum_sum_a_b]:(~(((member1294585472um_a_b @ ((produc1808556047um_a_b @ zero_zero_nat) @ X1)) @ f))))))).
% 4.39/4.63 thf(2,plain,$false,inference(tab_negall,[status(thm),assumptions([h9,h7,h5,h3,h1,h0]),tab_negall(discharge,[h11]),tab_negall(eigenvar,eigen__0)],[fact_8__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062v_O_A_I0_M_Av_J_A_092_060in_062_Af_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,1,h11])).
% 4.39/4.63 thf(h12,assumption,((member1294585472um_a_b @ ((produc1808556047um_a_b @ zero_zero_nat) @ eigen__1)) @ f),introduced(assumption,[])).
% 4.39/4.63 thf(pax8, axiom, (p8=>![X170:standard_Constant_a, X173:nat, X174:nat]:(flabele16114835_a_nat @ (finsert1625259895at_nat @ (fproduc407553657at_nat @ X170 @ (fproduct_Pair_nat_nat @ X173 @ X174)) @ fbot_bo810816657at_nat) @ (finsert_nat @ X173 @ (finsert_nat @ X174 @ fbot_bot_set_nat)))=(frestri572569417_a_nat @ (flabele16114835_a_nat @ (finsert1625259895at_nat @ (fproduc407553657at_nat @ X170 @ (fproduct_Pair_nat_nat @ X173 @ X174)) @ fbot_bo810816657at_nat) @ (finsert_nat @ X173 @ (finsert_nat @ X174 @ fbot_bot_set_nat))))), file('<stdin>', pax8)).
% 4.39/4.63 thf(pax114, axiom, (p114=>![X51:nat, X52:set_nat]:(finsert_nat @ X51 @ (finsert_nat @ X51 @ X52))=(finsert_nat @ X51 @ X52)), file('<stdin>', pax114)).
% 4.39/4.63 thf(nax156, axiom, (p156<=(flabele16114835_a_nat @ (finsert1625259895at_nat @ (fproduc407553657at_nat @ fstandard_S_Idt_a @ (fproduct_Pair_nat_nat @ fzero_zero_nat @ fzero_zero_nat)) @ fbot_bo810816657at_nat) @ (finsert_nat @ fzero_zero_nat @ fbot_bot_set_nat))=(frestri572569417_a_nat @ (flabele16114835_a_nat @ (finsert1625259895at_nat @ (fproduc407553657at_nat @ fstandard_S_Idt_a @ (fproduct_Pair_nat_nat @ fzero_zero_nat @ fzero_zero_nat)) @ fbot_bo810816657at_nat) @ (finsert_nat @ fzero_zero_nat @ fbot_bot_set_nat)))), file('<stdin>', nax156)).
% 4.39/4.63 thf(ax9, axiom, ~(p156), file('<stdin>', ax9)).
% 4.39/4.63 thf(ax152, axiom, p8, file('<stdin>', ax152)).
% 4.39/4.63 thf(ax46, axiom, p114, file('<stdin>', ax46)).
% 4.39/4.63 thf(c_0_6, plain, ![X575:standard_Constant_a, X576:nat, X577:nat]:(~p8|(flabele16114835_a_nat @ (finsert1625259895at_nat @ (fproduc407553657at_nat @ X575 @ (fproduct_Pair_nat_nat @ X576 @ X577)) @ fbot_bo810816657at_nat) @ (finsert_nat @ X576 @ (finsert_nat @ X577 @ fbot_bot_set_nat)))=(frestri572569417_a_nat @ (flabele16114835_a_nat @ (finsert1625259895at_nat @ (fproduc407553657at_nat @ X575 @ (fproduct_Pair_nat_nat @ X576 @ X577)) @ fbot_bo810816657at_nat) @ (finsert_nat @ X576 @ (finsert_nat @ X577 @ fbot_bot_set_nat))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax8])])])).
% 4.39/4.63 thf(c_0_7, plain, ![X307:nat, X308:set_nat]:(~p114|(finsert_nat @ X307 @ (finsert_nat @ X307 @ X308))=(finsert_nat @ X307 @ X308)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax114])])])).
% 4.39/4.63 thf(c_0_8, plain, ((flabele16114835_a_nat @ (finsert1625259895at_nat @ (fproduc407553657at_nat @ fstandard_S_Idt_a @ (fproduct_Pair_nat_nat @ fzero_zero_nat @ fzero_zero_nat)) @ fbot_bo810816657at_nat) @ (finsert_nat @ fzero_zero_nat @ fbot_bot_set_nat))!=(frestri572569417_a_nat @ (flabele16114835_a_nat @ (finsert1625259895at_nat @ (fproduc407553657at_nat @ fstandard_S_Idt_a @ (fproduct_Pair_nat_nat @ fzero_zero_nat @ fzero_zero_nat)) @ fbot_bo810816657at_nat) @ (finsert_nat @ fzero_zero_nat @ fbot_bot_set_nat)))|p156), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax156])])).
% 4.39/4.63 thf(c_0_9, plain, ~p156, inference(fof_simplification,[status(thm)],[ax9])).
% 4.39/4.63 thf(c_0_10, plain, ![X5:nat, X43:standard_Constant_a, X10:nat]:((flabele16114835_a_nat @ (finsert1625259895at_nat @ (fproduc407553657at_nat @ X43 @ (fproduct_Pair_nat_nat @ X5 @ X10)) @ fbot_bo810816657at_nat) @ (finsert_nat @ X5 @ (finsert_nat @ X10 @ fbot_bot_set_nat)))=(frestri572569417_a_nat @ (flabele16114835_a_nat @ (finsert1625259895at_nat @ (fproduc407553657at_nat @ X43 @ (fproduct_Pair_nat_nat @ X5 @ X10)) @ fbot_bo810816657at_nat) @ (finsert_nat @ X5 @ (finsert_nat @ X10 @ fbot_bot_set_nat))))|~p8), inference(split_conjunct,[status(thm)],[c_0_6])).
% 4.39/4.63 thf(c_0_11, plain, p8, inference(split_conjunct,[status(thm)],[ax152])).
% 4.39/4.63 thf(c_0_12, plain, ![X5:nat, X3:set_nat]:((finsert_nat @ X5 @ (finsert_nat @ X5 @ X3))=(finsert_nat @ X5 @ X3)|~p114), inference(split_conjunct,[status(thm)],[c_0_7])).
% 4.39/4.63 thf(c_0_13, plain, p114, inference(split_conjunct,[status(thm)],[ax46])).
% 4.39/4.63 thf(c_0_14, plain, (p156|(flabele16114835_a_nat @ (finsert1625259895at_nat @ (fproduc407553657at_nat @ fstandard_S_Idt_a @ (fproduct_Pair_nat_nat @ fzero_zero_nat @ fzero_zero_nat)) @ fbot_bo810816657at_nat) @ (finsert_nat @ fzero_zero_nat @ fbot_bot_set_nat))!=(frestri572569417_a_nat @ (flabele16114835_a_nat @ (finsert1625259895at_nat @ (fproduc407553657at_nat @ fstandard_S_Idt_a @ (fproduct_Pair_nat_nat @ fzero_zero_nat @ fzero_zero_nat)) @ fbot_bo810816657at_nat) @ (finsert_nat @ fzero_zero_nat @ fbot_bot_set_nat)))), inference(split_conjunct,[status(thm)],[c_0_8])).
% 4.39/4.63 thf(c_0_15, plain, ~p156, inference(split_conjunct,[status(thm)],[c_0_9])).
% 4.39/4.63 thf(c_0_16, plain, ![X5:nat, X43:standard_Constant_a, X10:nat]:(frestri572569417_a_nat @ (flabele16114835_a_nat @ (finsert1625259895at_nat @ (fproduc407553657at_nat @ X43 @ (fproduct_Pair_nat_nat @ X5 @ X10)) @ fbot_bo810816657at_nat) @ (finsert_nat @ X5 @ (finsert_nat @ X10 @ fbot_bot_set_nat))))=(flabele16114835_a_nat @ (finsert1625259895at_nat @ (fproduc407553657at_nat @ X43 @ (fproduct_Pair_nat_nat @ X5 @ X10)) @ fbot_bo810816657at_nat) @ (finsert_nat @ X5 @ (finsert_nat @ X10 @ fbot_bot_set_nat))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_10, c_0_11])])).
% 4.39/4.63 thf(c_0_17, plain, ![X5:nat, X3:set_nat]:(finsert_nat @ X5 @ (finsert_nat @ X5 @ X3))=(finsert_nat @ X5 @ X3), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_12, c_0_13])])).
% 4.39/4.63 thf(c_0_18, plain, (frestri572569417_a_nat @ (flabele16114835_a_nat @ (finsert1625259895at_nat @ (fproduc407553657at_nat @ fstandard_S_Idt_a @ (fproduct_Pair_nat_nat @ fzero_zero_nat @ fzero_zero_nat)) @ fbot_bo810816657at_nat) @ (finsert_nat @ fzero_zero_nat @ fbot_bot_set_nat)))!=(flabele16114835_a_nat @ (finsert1625259895at_nat @ (fproduc407553657at_nat @ fstandard_S_Idt_a @ (fproduct_Pair_nat_nat @ fzero_zero_nat @ fzero_zero_nat)) @ fbot_bo810816657at_nat) @ (finsert_nat @ fzero_zero_nat @ fbot_bot_set_nat)), inference(sr,[status(thm)],[c_0_14, c_0_15])).
% 4.39/4.63 thf(c_0_19, plain, ![X43:standard_Constant_a, X5:nat]:(frestri572569417_a_nat @ (flabele16114835_a_nat @ (finsert1625259895at_nat @ (fproduc407553657at_nat @ X43 @ (fproduct_Pair_nat_nat @ X5 @ X5)) @ fbot_bo810816657at_nat) @ (finsert_nat @ X5 @ fbot_bot_set_nat)))=(flabele16114835_a_nat @ (finsert1625259895at_nat @ (fproduc407553657at_nat @ X43 @ (fproduct_Pair_nat_nat @ X5 @ X5)) @ fbot_bo810816657at_nat) @ (finsert_nat @ X5 @ fbot_bot_set_nat)), inference(spm,[status(thm)],[c_0_16, c_0_17])).
% 4.39/4.63 thf(c_0_20, plain, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_18, c_0_19])]), ['proof']).
% 4.39/4.63 thf(3,plain,$false,inference(eprover,[status(thm),assumptions([h12,h10,h7,h5,h3,h1,h0])],[])).
% 4.39/4.63 thf(4,plain,$false,inference(tab_negall,[status(thm),assumptions([h10,h7,h5,h3,h1,h0]),tab_negall(discharge,[h12]),tab_negall(eigenvar,eigen__1)],[fact_8__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062v_O_A_I0_M_Av_J_A_092_060in_062_Af_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,3,h12])).
% 4.39/4.63 thf(5,plain,$false,inference(tab_imp,[status(thm),assumptions([h7,h5,h3,h1,h0]),tab_imp(discharge,[h9]),tab_imp(discharge,[h10])],[h7,2,4,h9,h10])).
% 4.39/4.63 thf(h13,assumption,((member1294585472um_a_b @ ((produc1808556047um_a_b @ zero_zero_nat) @ eigen__2)) @ f),introduced(assumption,[])).
% 4.39/4.63 thf(fact_0_g,axiom,sP1).
% 4.39/4.63 thf(6,plain,$false,inference(tab_conflict,[status(thm),assumptions([h13,h8,h5,h3,h1,h0])],[fact_0_g,h8])).
% 4.39/4.63 thf(7,plain,$false,inference(tab_negall,[status(thm),assumptions([h8,h5,h3,h1,h0]),tab_negall(discharge,[h13]),tab_negall(eigenvar,eigen__2)],[fact_8__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062v_O_A_I0_M_Av_J_A_092_060in_062_Af_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,6,h13])).
% 4.39/4.63 thf(8,plain,$false,inference(tab_imp,[status(thm),assumptions([h5,h3,h1,h0]),tab_imp(discharge,[h7]),tab_imp(discharge,[h8])],[h5,5,7,h7,h8])).
% 4.39/4.63 thf(h14,assumption,((member1294585472um_a_b @ ((produc1808556047um_a_b @ zero_zero_nat) @ eigen__3)) @ f),introduced(assumption,[])).
% 4.39/4.63 thf(pax5, axiom, (p5=>(ff)=(finsert983991207um_a_b @ (fproduc1808556047um_a_b @ fzero_zero_nat @ fv) @ fbot_bo575978147um_a_b)), file('<stdin>', pax5)).
% 4.39/4.63 thf(pax68, axiom, (p68=>![X92:set_Pr1647387645at_nat, X93:set_nat]:(flabele1810595089_a_nat @ (flabele16114835_a_nat @ X92 @ X93))=(X93)), file('<stdin>', pax68)).
% 4.39/4.63 thf(pax4, axiom, (p4=>ford_le192794300um_a_b @ (fimage_256773707um_a_b @ ff @ (finsert_nat @ fzero_zero_nat @ fbot_bot_set_nat)) @ (flabele577278695um_a_b @ fg)), file('<stdin>', pax4)).
% 4.39/4.63 thf(nax168, axiom, (p168<=ford_le192794300um_a_b @ (fimage_256773707um_a_b @ (finsert983991207um_a_b @ (fproduc1808556047um_a_b @ fzero_zero_nat @ fv) @ fbot_bo575978147um_a_b) @ (flabele1810595089_a_nat @ (flabele16114835_a_nat @ (finsert1625259895at_nat @ (fproduc407553657at_nat @ fstandard_S_Idt_a @ (fproduct_Pair_nat_nat @ fzero_zero_nat @ fzero_zero_nat)) @ fbot_bo810816657at_nat) @ (finsert_nat @ fzero_zero_nat @ fbot_bot_set_nat)))) @ (flabele577278695um_a_b @ fg)), file('<stdin>', nax168)).
% 4.39/4.63 thf(ax156, axiom, p5, file('<stdin>', ax156)).
% 4.39/4.63 thf(ax93, axiom, p68, file('<stdin>', ax93)).
% 4.39/4.63 thf(ax157, axiom, p4, file('<stdin>', ax157)).
% 4.39/4.63 thf(ax10, axiom, ~(p168), file('<stdin>', ax10)).
% 4.39/4.63 thf(c_0_8, plain, (~p5|(ff)=(finsert983991207um_a_b @ (fproduc1808556047um_a_b @ fzero_zero_nat @ fv) @ fbot_bo575978147um_a_b)), inference(fof_nnf,[status(thm)],[pax5])).
% 4.39/4.63 thf(c_0_9, plain, ![X412:set_Pr1647387645at_nat, X413:set_nat]:(~p68|(flabele1810595089_a_nat @ (flabele16114835_a_nat @ X412 @ X413))=(X413)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax68])])])).
% 4.39/4.63 thf(c_0_10, plain, (~p4|ford_le192794300um_a_b @ (fimage_256773707um_a_b @ ff @ (finsert_nat @ fzero_zero_nat @ fbot_bot_set_nat)) @ (flabele577278695um_a_b @ fg)), inference(fof_nnf,[status(thm)],[pax4])).
% 4.39/4.63 thf(c_0_11, plain, (~ford_le192794300um_a_b @ (fimage_256773707um_a_b @ (finsert983991207um_a_b @ (fproduc1808556047um_a_b @ fzero_zero_nat @ fv) @ fbot_bo575978147um_a_b) @ (flabele1810595089_a_nat @ (flabele16114835_a_nat @ (finsert1625259895at_nat @ (fproduc407553657at_nat @ fstandard_S_Idt_a @ (fproduct_Pair_nat_nat @ fzero_zero_nat @ fzero_zero_nat)) @ fbot_bo810816657at_nat) @ (finsert_nat @ fzero_zero_nat @ fbot_bot_set_nat)))) @ (flabele577278695um_a_b @ fg)|p168), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax168])])).
% 4.39/4.63 thf(c_0_12, plain, ((ff)=(finsert983991207um_a_b @ (fproduc1808556047um_a_b @ fzero_zero_nat @ fv) @ fbot_bo575978147um_a_b)|~p5), inference(split_conjunct,[status(thm)],[c_0_8])).
% 4.39/4.63 thf(c_0_13, plain, p5, inference(split_conjunct,[status(thm)],[ax156])).
% 4.39/4.63 thf(c_0_14, plain, ![X18:set_Pr1647387645at_nat, X6:set_nat]:((flabele1810595089_a_nat @ (flabele16114835_a_nat @ X18 @ X6))=(X6)|~p68), inference(split_conjunct,[status(thm)],[c_0_9])).
% 4.39/4.63 thf(c_0_15, plain, p68, inference(split_conjunct,[status(thm)],[ax93])).
% 4.39/4.63 thf(c_0_16, plain, (ford_le192794300um_a_b @ (fimage_256773707um_a_b @ ff @ (finsert_nat @ fzero_zero_nat @ fbot_bot_set_nat)) @ (flabele577278695um_a_b @ fg)|~p4), inference(split_conjunct,[status(thm)],[c_0_10])).
% 4.39/4.63 thf(c_0_17, plain, p4, inference(split_conjunct,[status(thm)],[ax157])).
% 4.39/4.63 thf(c_0_18, plain, ~p168, inference(fof_simplification,[status(thm)],[ax10])).
% 4.39/4.63 thf(c_0_19, plain, (p168|~ford_le192794300um_a_b @ (fimage_256773707um_a_b @ (finsert983991207um_a_b @ (fproduc1808556047um_a_b @ fzero_zero_nat @ fv) @ fbot_bo575978147um_a_b) @ (flabele1810595089_a_nat @ (flabele16114835_a_nat @ (finsert1625259895at_nat @ (fproduc407553657at_nat @ fstandard_S_Idt_a @ (fproduct_Pair_nat_nat @ fzero_zero_nat @ fzero_zero_nat)) @ fbot_bo810816657at_nat) @ (finsert_nat @ fzero_zero_nat @ fbot_bot_set_nat)))) @ (flabele577278695um_a_b @ fg)), inference(split_conjunct,[status(thm)],[c_0_11])).
% 4.39/4.63 thf(c_0_20, plain, (finsert983991207um_a_b @ (fproduc1808556047um_a_b @ fzero_zero_nat @ fv) @ fbot_bo575978147um_a_b)=(ff), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_12, c_0_13])])).
% 4.39/4.63 thf(c_0_21, plain, ![X18:set_Pr1647387645at_nat, X6:set_nat]:(flabele1810595089_a_nat @ (flabele16114835_a_nat @ X18 @ X6))=(X6), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_14, c_0_15])])).
% 4.39/4.63 thf(c_0_22, plain, ford_le192794300um_a_b @ (fimage_256773707um_a_b @ ff @ (finsert_nat @ fzero_zero_nat @ fbot_bot_set_nat)) @ (flabele577278695um_a_b @ fg), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_16, c_0_17])])).
% 4.39/4.63 thf(c_0_23, plain, ~p168, inference(split_conjunct,[status(thm)],[c_0_18])).
% 4.39/4.63 thf(c_0_24, plain, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_19, c_0_20]), c_0_21]), c_0_22])]), c_0_23]), ['proof']).
% 4.39/4.63 thf(9,plain,$false,inference(eprover,[status(thm),assumptions([h14,h6,h3,h1,h0])],[])).
% 4.39/4.63 thf(10,plain,$false,inference(tab_negall,[status(thm),assumptions([h6,h3,h1,h0]),tab_negall(discharge,[h14]),tab_negall(eigenvar,eigen__3)],[fact_8__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062v_O_A_I0_M_Av_J_A_092_060in_062_Af_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,9,h14])).
% 4.39/4.63 thf(11,plain,$false,inference(tab_imp,[status(thm),assumptions([h3,h1,h0]),tab_imp(discharge,[h5]),tab_imp(discharge,[h6])],[h3,8,10,h5,h6])).
% 4.39/4.63 thf(h15,assumption,((member1294585472um_a_b @ ((produc1808556047um_a_b @ zero_zero_nat) @ eigen__4)) @ f),introduced(assumption,[])).
% 4.39/4.63 thf(pax5, axiom, (p5=>(ff)=(finsert983991207um_a_b @ (fproduc1808556047um_a_b @ fzero_zero_nat @ fv) @ fbot_bo575978147um_a_b)), file('<stdin>', pax5)).
% 4.39/4.63 thf(pax10, axiom, (p10=>funival2092813468um_a_b @ ff), file('<stdin>', pax10)).
% 4.39/4.63 thf(nax178, axiom, (p178<=funival2092813468um_a_b @ (finsert983991207um_a_b @ (fproduc1808556047um_a_b @ fzero_zero_nat @ fv) @ fbot_bo575978147um_a_b)), file('<stdin>', nax178)).
% 4.39/4.63 thf(ax180, axiom, p5, file('<stdin>', ax180)).
% 4.39/4.63 thf(ax175, axiom, p10, file('<stdin>', ax175)).
% 4.39/4.63 thf(ax34, axiom, ~(p178), file('<stdin>', ax34)).
% 4.39/4.63 thf(c_0_6, plain, (~p5|(ff)=(finsert983991207um_a_b @ (fproduc1808556047um_a_b @ fzero_zero_nat @ fv) @ fbot_bo575978147um_a_b)), inference(fof_nnf,[status(thm)],[pax5])).
% 4.39/4.63 thf(c_0_7, plain, (~p10|funival2092813468um_a_b @ ff), inference(fof_nnf,[status(thm)],[pax10])).
% 4.39/4.63 thf(c_0_8, plain, (~funival2092813468um_a_b @ (finsert983991207um_a_b @ (fproduc1808556047um_a_b @ fzero_zero_nat @ fv) @ fbot_bo575978147um_a_b)|p178), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax178])])).
% 4.39/4.63 thf(c_0_9, plain, ((ff)=(finsert983991207um_a_b @ (fproduc1808556047um_a_b @ fzero_zero_nat @ fv) @ fbot_bo575978147um_a_b)|~p5), inference(split_conjunct,[status(thm)],[c_0_6])).
% 4.39/4.63 thf(c_0_10, plain, p5, inference(split_conjunct,[status(thm)],[ax180])).
% 4.39/4.63 thf(c_0_11, plain, (funival2092813468um_a_b @ ff|~p10), inference(split_conjunct,[status(thm)],[c_0_7])).
% 4.39/4.63 thf(c_0_12, plain, p10, inference(split_conjunct,[status(thm)],[ax175])).
% 4.39/4.63 thf(c_0_13, plain, ~p178, inference(fof_simplification,[status(thm)],[ax34])).
% 4.39/4.63 thf(c_0_14, plain, (p178|~funival2092813468um_a_b @ (finsert983991207um_a_b @ (fproduc1808556047um_a_b @ fzero_zero_nat @ fv) @ fbot_bo575978147um_a_b)), inference(split_conjunct,[status(thm)],[c_0_8])).
% 4.39/4.63 thf(c_0_15, plain, (finsert983991207um_a_b @ (fproduc1808556047um_a_b @ fzero_zero_nat @ fv) @ fbot_bo575978147um_a_b)=(ff), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_9, c_0_10])])).
% 4.39/4.63 thf(c_0_16, plain, funival2092813468um_a_b @ ff, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_11, c_0_12])])).
% 4.39/4.63 thf(c_0_17, plain, ~p178, inference(split_conjunct,[status(thm)],[c_0_13])).
% 4.39/4.63 thf(c_0_18, plain, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_14, c_0_15]), c_0_16])]), c_0_17]), ['proof']).
% 4.39/4.63 thf(12,plain,$false,inference(eprover,[status(thm),assumptions([h15,h4,h1,h0])],[])).
% 4.39/4.63 thf(13,plain,$false,inference(tab_negall,[status(thm),assumptions([h4,h1,h0]),tab_negall(discharge,[h15]),tab_negall(eigenvar,eigen__4)],[fact_8__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062v_O_A_I0_M_Av_J_A_092_060in_062_Af_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,12,h15])).
% 4.39/4.63 thf(14,plain,$false,inference(tab_imp,[status(thm),assumptions([h1,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h4])],[h1,11,13,h3,h4])).
% 4.39/4.63 thf(h16,assumption,((member1294585472um_a_b @ ((produc1808556047um_a_b @ zero_zero_nat) @ eigen__5)) @ f),introduced(assumption,[])).
% 4.39/4.63 thf(pax5, axiom, (p5=>(ff)=(finsert983991207um_a_b @ (fproduc1808556047um_a_b @ fzero_zero_nat @ fv) @ fbot_bo575978147um_a_b)), file('<stdin>', pax5)).
% 4.39/4.63 thf(pax70, axiom, (p70=>![X106:set_Pr1647387645at_nat, X107:set_nat]:(flabele195203296_a_nat @ (flabele16114835_a_nat @ X106 @ X107))=(X106)), file('<stdin>', pax70)).
% 4.39/4.63 thf(pax3, axiom, (p3=>fedge_p1382426714tant_a @ (finsert983991207um_a_b @ (fproduc1808556047um_a_b @ fzero_zero_nat @ fv) @ fbot_bo575978147um_a_b) @ (finsert1625259895at_nat @ (fproduc407553657at_nat @ fstandard_S_Idt_a @ (fproduct_Pair_nat_nat @ fzero_zero_nat @ fzero_zero_nat)) @ fbot_bo810816657at_nat) @ (flabele1939049654um_a_b @ fg)), file('<stdin>', pax3)).
% 4.39/4.63 thf(ax153, axiom, p5, file('<stdin>', ax153)).
% 4.39/4.63 thf(nax203, axiom, (p203<=fedge_p1382426714tant_a @ (finsert983991207um_a_b @ (fproduc1808556047um_a_b @ fzero_zero_nat @ fv) @ fbot_bo575978147um_a_b) @ (flabele195203296_a_nat @ (flabele16114835_a_nat @ (finsert1625259895at_nat @ (fproduc407553657at_nat @ fstandard_S_Idt_a @ (fproduct_Pair_nat_nat @ fzero_zero_nat @ fzero_zero_nat)) @ fbot_bo810816657at_nat) @ (finsert_nat @ fzero_zero_nat @ fbot_bot_set_nat))) @ (flabele1939049654um_a_b @ fg)), file('<stdin>', nax203)).
% 4.39/4.63 thf(ax88, axiom, p70, file('<stdin>', ax88)).
% 4.39/4.63 thf(ax155, axiom, p3, file('<stdin>', ax155)).
% 4.39/4.63 thf(ax7, axiom, ~(p203), file('<stdin>', ax7)).
% 4.39/4.63 thf(c_0_8, plain, (~p5|(ff)=(finsert983991207um_a_b @ (fproduc1808556047um_a_b @ fzero_zero_nat @ fv) @ fbot_bo575978147um_a_b)), inference(fof_nnf,[status(thm)],[pax5])).
% 4.39/4.63 thf(c_0_9, plain, ![X512:set_Pr1647387645at_nat, X513:set_nat]:(~p70|(flabele195203296_a_nat @ (flabele16114835_a_nat @ X512 @ X513))=(X512)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax70])])])).
% 4.39/4.63 thf(c_0_10, plain, (~p3|fedge_p1382426714tant_a @ (finsert983991207um_a_b @ (fproduc1808556047um_a_b @ fzero_zero_nat @ fv) @ fbot_bo575978147um_a_b) @ (finsert1625259895at_nat @ (fproduc407553657at_nat @ fstandard_S_Idt_a @ (fproduct_Pair_nat_nat @ fzero_zero_nat @ fzero_zero_nat)) @ fbot_bo810816657at_nat) @ (flabele1939049654um_a_b @ fg)), inference(fof_nnf,[status(thm)],[pax3])).
% 4.39/4.63 thf(c_0_11, plain, ((ff)=(finsert983991207um_a_b @ (fproduc1808556047um_a_b @ fzero_zero_nat @ fv) @ fbot_bo575978147um_a_b)|~p5), inference(split_conjunct,[status(thm)],[c_0_8])).
% 4.39/4.63 thf(c_0_12, plain, p5, inference(split_conjunct,[status(thm)],[ax153])).
% 4.39/4.63 thf(c_0_13, plain, (~fedge_p1382426714tant_a @ (finsert983991207um_a_b @ (fproduc1808556047um_a_b @ fzero_zero_nat @ fv) @ fbot_bo575978147um_a_b) @ (flabele195203296_a_nat @ (flabele16114835_a_nat @ (finsert1625259895at_nat @ (fproduc407553657at_nat @ fstandard_S_Idt_a @ (fproduct_Pair_nat_nat @ fzero_zero_nat @ fzero_zero_nat)) @ fbot_bo810816657at_nat) @ (finsert_nat @ fzero_zero_nat @ fbot_bot_set_nat))) @ (flabele1939049654um_a_b @ fg)|p203), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax203])])).
% 4.39/4.63 thf(c_0_14, plain, ![X3:set_nat, X2:set_Pr1647387645at_nat]:((flabele195203296_a_nat @ (flabele16114835_a_nat @ X2 @ X3))=(X2)|~p70), inference(split_conjunct,[status(thm)],[c_0_9])).
% 4.39/4.63 thf(c_0_15, plain, p70, inference(split_conjunct,[status(thm)],[ax88])).
% 4.39/4.63 thf(c_0_16, plain, (fedge_p1382426714tant_a @ (finsert983991207um_a_b @ (fproduc1808556047um_a_b @ fzero_zero_nat @ fv) @ fbot_bo575978147um_a_b) @ (finsert1625259895at_nat @ (fproduc407553657at_nat @ fstandard_S_Idt_a @ (fproduct_Pair_nat_nat @ fzero_zero_nat @ fzero_zero_nat)) @ fbot_bo810816657at_nat) @ (flabele1939049654um_a_b @ fg)|~p3), inference(split_conjunct,[status(thm)],[c_0_10])).
% 4.39/4.63 thf(c_0_17, plain, (finsert983991207um_a_b @ (fproduc1808556047um_a_b @ fzero_zero_nat @ fv) @ fbot_bo575978147um_a_b)=(ff), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_11, c_0_12])])).
% 4.39/4.63 thf(c_0_18, plain, p3, inference(split_conjunct,[status(thm)],[ax155])).
% 4.39/4.63 thf(c_0_19, plain, ~p203, inference(fof_simplification,[status(thm)],[ax7])).
% 4.39/4.63 thf(c_0_20, plain, (p203|~fedge_p1382426714tant_a @ (finsert983991207um_a_b @ (fproduc1808556047um_a_b @ fzero_zero_nat @ fv) @ fbot_bo575978147um_a_b) @ (flabele195203296_a_nat @ (flabele16114835_a_nat @ (finsert1625259895at_nat @ (fproduc407553657at_nat @ fstandard_S_Idt_a @ (fproduct_Pair_nat_nat @ fzero_zero_nat @ fzero_zero_nat)) @ fbot_bo810816657at_nat) @ (finsert_nat @ fzero_zero_nat @ fbot_bot_set_nat))) @ (flabele1939049654um_a_b @ fg)), inference(split_conjunct,[status(thm)],[c_0_13])).
% 4.39/4.63 thf(c_0_21, plain, ![X3:set_nat, X2:set_Pr1647387645at_nat]:(flabele195203296_a_nat @ (flabele16114835_a_nat @ X2 @ X3))=(X2), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_14, c_0_15])])).
% 4.39/4.63 thf(c_0_22, plain, fedge_p1382426714tant_a @ ff @ (finsert1625259895at_nat @ (fproduc407553657at_nat @ fstandard_S_Idt_a @ (fproduct_Pair_nat_nat @ fzero_zero_nat @ fzero_zero_nat)) @ fbot_bo810816657at_nat) @ (flabele1939049654um_a_b @ fg), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_16, c_0_17]), c_0_18])])).
% 4.39/4.63 thf(c_0_23, plain, ~p203, inference(split_conjunct,[status(thm)],[c_0_19])).
% 4.39/4.63 thf(c_0_24, plain, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_20, c_0_17]), c_0_21]), c_0_22])]), c_0_23]), ['proof']).
% 4.39/4.63 thf(15,plain,$false,inference(eprover,[status(thm),assumptions([h16,h2,h0])],[])).
% 4.39/4.63 thf(16,plain,$false,inference(tab_negall,[status(thm),assumptions([h2,h0]),tab_negall(discharge,[h16]),tab_negall(eigenvar,eigen__5)],[fact_8__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062v_O_A_I0_M_Av_J_A_092_060in_062_Af_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,15,h16])).
% 4.39/4.63 thf(17,plain,$false,inference(tab_imp,[status(thm),assumptions([h0]),tab_imp(discharge,[h1]),tab_imp(discharge,[h2])],[h0,14,16,h1,h2])).
% 4.39/4.63 thf(0,theorem,(~(((~(((~(((~(((~((((labele1810595089_a_nat @ ((labele16114835_a_nat @ ((insert1625259895at_nat @ ((produc407553657at_nat @ standard_S_Idt_a) @ ((product_Pair_nat_nat @ zero_zero_nat) @ zero_zero_nat))) @ bot_bo810816657at_nat)) @ ((insert_nat @ zero_zero_nat) @ bot_bot_set_nat))) = (domain1368163076um_a_b @ ((insert983991207um_a_b @ ((produc1808556047um_a_b @ zero_zero_nat) @ v)) @ bot_bo575978147um_a_b))) => (~((((labele16114835_a_nat @ ((insert1625259895at_nat @ ((produc407553657at_nat @ standard_S_Idt_a) @ ((product_Pair_nat_nat @ zero_zero_nat) @ zero_zero_nat))) @ bot_bo810816657at_nat)) @ ((insert_nat @ zero_zero_nat) @ bot_bot_set_nat)) = (restri572569417_a_nat @ ((labele16114835_a_nat @ ((insert1625259895at_nat @ ((produc407553657at_nat @ standard_S_Idt_a) @ ((product_Pair_nat_nat @ zero_zero_nat) @ zero_zero_nat))) @ bot_bo810816657at_nat)) @ ((insert_nat @ zero_zero_nat) @ bot_bot_set_nat))))))))) => (~(sP1))))) => (~(((ord_le192794300um_a_b @ ((image_256773707um_a_b @ ((insert983991207um_a_b @ ((produc1808556047um_a_b @ zero_zero_nat) @ v)) @ bot_bo575978147um_a_b)) @ (labele1810595089_a_nat @ ((labele16114835_a_nat @ ((insert1625259895at_nat @ ((produc407553657at_nat @ standard_S_Idt_a) @ ((product_Pair_nat_nat @ zero_zero_nat) @ zero_zero_nat))) @ bot_bo810816657at_nat)) @ ((insert_nat @ zero_zero_nat) @ bot_bot_set_nat))))) @ (labele577278695um_a_b @ g))))))) => (~((unival2092813468um_a_b @ ((insert983991207um_a_b @ ((produc1808556047um_a_b @ zero_zero_nat) @ v)) @ bot_bo575978147um_a_b))))))) => (~((((edge_p1382426714tant_a @ ((insert983991207um_a_b @ ((produc1808556047um_a_b @ zero_zero_nat) @ v)) @ bot_bo575978147um_a_b)) @ (labele195203296_a_nat @ ((labele16114835_a_nat @ ((insert1625259895at_nat @ ((produc407553657at_nat @ standard_S_Idt_a) @ ((product_Pair_nat_nat @ zero_zero_nat) @ zero_zero_nat))) @ bot_bo810816657at_nat)) @ ((insert_nat @ zero_zero_nat) @ bot_bot_set_nat)))) @ (labele1939049654um_a_b @ g))))))),inference(contra,[status(thm),contra(discharge,[h0])],[17,h0])).
% 4.39/4.63 % SZS output end Proof
%------------------------------------------------------------------------------