TSTP Solution File: ITP103^1 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP103^1 : 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 : n023.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 00:29:07 EDT 2022
% Result : Theorem 10.08s 10.34s
% Output : Proof 10.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : ITP103^1 : TPTP v8.1.0. Released v7.5.0.
% 0.12/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n023.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sat Jun 4 02:28:55 EDT 2022
% 0.12/0.34 % CPUTime :
% 10.08/10.34 % SZS status Theorem
% 10.08/10.34 % Mode: mode507:USE_SINE=true:SINE_TOLERANCE=3.0:SINE_GENERALITY_THRESHOLD=0:SINE_RANK_LIMIT=1.:SINE_DEPTH=1
% 10.08/10.34 % Inferences: 24
% 10.08/10.34 % SZS output start Proof
% 10.08/10.34 thf(conj_2,conjecture,((ord_less_nat @ ((times_times_nat @ n) @ k)) @ (size_size_list_a @ xs))).
% 10.08/10.34 thf(h0,negated_conjecture,(~(((ord_less_nat @ ((times_times_nat @ n) @ k)) @ (size_size_list_a @ xs)))),inference(assume_negation,[status(cth)],[conj_2])).
% 10.08/10.34 thf(ax257, axiom, (~(p123)|p129), file('<stdin>', ax257)).
% 10.08/10.34 thf(pax26, axiom, (p26=>![X14:nat]:~(ford_less_nat @ X14 @ X14)), file('<stdin>', pax26)).
% 10.08/10.34 thf(pax46, axiom, (p46=>![X11:nat, X9:nat]:(ford_less_nat @ X11 @ X9=>ford_less_nat @ X11 @ (fsuc @ X9))), file('<stdin>', pax46)).
% 10.08/10.34 thf(ax3, axiom, (~(p100)|~(p379)), file('<stdin>', ax3)).
% 10.08/10.34 thf(ax256, axiom, (~(p129)|p130), file('<stdin>', ax256)).
% 10.08/10.34 thf(ax264, axiom, p123, file('<stdin>', ax264)).
% 10.08/10.34 thf(pax39, axiom, (p39=>![X11:nat, X9:nat]:(ford_less_nat @ (fsuc @ X11) @ (fsuc @ X9)=>ford_less_nat @ X11 @ X9)), file('<stdin>', pax39)).
% 10.08/10.34 thf(pax59, axiom, (p59=>![X8:nat]:(ford_less_nat @ fzero_zero_nat @ X8=>~(![X9:nat]:~((X8)=(fsuc @ X9))))), file('<stdin>', pax59)).
% 10.08/10.34 thf(pax96, axiom, (p96=>![X8:nat, X9:nat]:(ford_less_nat @ X8 @ X9=>ford_less_nat @ fzero_zero_nat @ X9)), file('<stdin>', pax96)).
% 10.08/10.34 thf(ax360, axiom, p26, file('<stdin>', ax360)).
% 10.08/10.34 thf(ax340, axiom, p46, file('<stdin>', ax340)).
% 10.08/10.34 thf(nax379, axiom, (p379<=![X1:list_a]:~((fsize_size_list_a @ X1)=(fdivide_divide_nat @ (fsize_size_list_a @ fxs) @ fk))), file('<stdin>', nax379)).
% 10.08/10.34 thf(ax286, axiom, p100, file('<stdin>', ax286)).
% 10.08/10.34 thf(ax255, axiom, (~(p130)|~(p119)|p128), file('<stdin>', ax255)).
% 10.08/10.34 thf(pax16, axiom, (p16=>![X14:nat]:ford_less_nat @ X14 @ (fsuc @ X14)), file('<stdin>', pax16)).
% 10.08/10.34 thf(ax347, axiom, p39, file('<stdin>', ax347)).
% 10.08/10.34 thf(ax327, axiom, p59, file('<stdin>', ax327)).
% 10.08/10.34 thf(ax290, axiom, p96, file('<stdin>', ax290)).
% 10.08/10.34 thf(pax68, axiom, (p68=>![X8:nat, X9:nat, X4:nat]:(ford_less_nat @ X8 @ (ftimes_times_nat @ X9 @ X4)=>ford_less_nat @ (fdivide_divide_nat @ X8 @ X4) @ X9)), file('<stdin>', pax68)).
% 10.08/10.34 thf(pax128, axiom, (p128=>(fsuc @ fn)=(fdivide_divide_nat @ (fsize_size_list_a @ fxs) @ fk)), file('<stdin>', pax128)).
% 10.08/10.34 thf(ax267, axiom, p119, file('<stdin>', ax267)).
% 10.08/10.34 thf(pax40, axiom, (p40=>![X11:nat, X9:nat]:(~(ford_less_nat @ X11 @ X9)=>(ford_less_nat @ X11 @ (fsuc @ X9)=>(X9)=(X11)))), file('<stdin>', pax40)).
% 10.08/10.34 thf(ax370, axiom, p16, file('<stdin>', ax370)).
% 10.08/10.34 thf(pax11, axiom, (p11=>![X14:nat]:ford_less_nat @ fzero_zero_nat @ (fsuc @ X14)), file('<stdin>', pax11)).
% 10.08/10.34 thf(pax15, axiom, (p15=>![X14:nat, X15:nat]:(ford_less_nat @ X14 @ X15=>ford_less_nat @ (fsuc @ X14) @ (fsuc @ X15))), file('<stdin>', pax15)).
% 10.08/10.34 thf(ax318, axiom, p68, file('<stdin>', ax318)).
% 10.08/10.34 thf(ax346, axiom, p40, file('<stdin>', ax346)).
% 10.08/10.34 thf(ax375, axiom, p11, file('<stdin>', ax375)).
% 10.08/10.34 thf(ax371, axiom, p15, file('<stdin>', ax371)).
% 10.08/10.34 thf(pax23, axiom, (p23=>![X14:nat, X15:nat]:(~((X14)=(X15))=>(~(ford_less_nat @ X14 @ X15)=>ford_less_nat @ X15 @ X14))), file('<stdin>', pax23)).
% 10.08/10.34 thf(nax121, axiom, (p121<=ford_less_nat @ (ftimes_times_nat @ fn @ fk) @ (fsize_size_list_a @ fxs)), file('<stdin>', nax121)).
% 10.08/10.34 thf(ax265, axiom, ~(p121), file('<stdin>', ax265)).
% 10.08/10.34 thf(pax66, axiom, (p66=>![X8:nat, X9:nat, X4:nat]:(ford_less_nat @ X8 @ X9=>(ford_less_nat @ fzero_zero_nat @ X4=>ford_less_nat @ (ftimes_times_nat @ X8 @ X4) @ (ftimes_times_nat @ X9 @ X4)))), file('<stdin>', pax66)).
% 10.08/10.34 thf(ax363, axiom, p23, file('<stdin>', ax363)).
% 10.08/10.34 thf(ax320, axiom, p66, file('<stdin>', ax320)).
% 10.08/10.34 thf(pax34, axiom, (p34=>![X11:nat]:(~((X11)=(fzero_zero_nat))=>ford_less_nat @ fzero_zero_nat @ X11)), file('<stdin>', pax34)).
% 10.08/10.34 thf(nax120, axiom, (p120<=(fk)=(fzero_zero_nat)), file('<stdin>', nax120)).
% 10.08/10.34 thf(ax266, axiom, ~(p120), file('<stdin>', ax266)).
% 10.08/10.34 thf(ax352, axiom, p34, file('<stdin>', ax352)).
% 10.08/10.34 thf(c_0_39, plain, (~p123|p129), inference(fof_simplification,[status(thm)],[ax257])).
% 10.08/10.34 thf(c_0_40, plain, ![X558:nat]:(~p26|~ford_less_nat @ X558 @ X558), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax26])])])])).
% 10.08/10.34 thf(c_0_41, plain, ![X522:nat, X523:nat]:(~p46|(~ford_less_nat @ X522 @ X523|ford_less_nat @ X522 @ (fsuc @ X523))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax46])])])).
% 10.08/10.34 thf(c_0_42, plain, (~p100|~p379), inference(fof_simplification,[status(thm)],[ax3])).
% 10.08/10.34 thf(c_0_43, plain, (~p129|p130), inference(fof_simplification,[status(thm)],[ax256])).
% 10.08/10.34 thf(c_0_44, plain, (p129|~p123), inference(split_conjunct,[status(thm)],[c_0_39])).
% 10.08/10.34 thf(c_0_45, plain, p123, inference(split_conjunct,[status(thm)],[ax264])).
% 10.08/10.34 thf(c_0_46, plain, ![X530:nat, X531:nat]:(~p39|(~ford_less_nat @ (fsuc @ X530) @ (fsuc @ X531)|ford_less_nat @ X530 @ X531)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax39])])])).
% 10.08/10.34 thf(c_0_47, plain, ![X478:nat]:(~p59|(~ford_less_nat @ fzero_zero_nat @ X478|(X478)=(fsuc @ (esk232_1 @ X478)))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax59])])])])])).
% 10.08/10.34 thf(c_0_48, plain, ![X372:nat, X373:nat]:(~p96|(~ford_less_nat @ X372 @ X373|ford_less_nat @ fzero_zero_nat @ X373)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax96])])])).
% 10.08/10.34 thf(c_0_49, plain, ![X2:nat]:(~p26|~ford_less_nat @ X2 @ X2), inference(split_conjunct,[status(thm)],[c_0_40])).
% 10.08/10.34 thf(c_0_50, plain, p26, inference(split_conjunct,[status(thm)],[ax360])).
% 10.08/10.34 thf(c_0_51, plain, ![X2:nat, X3:nat]:(ford_less_nat @ X2 @ (fsuc @ X3)|~p46|~ford_less_nat @ X2 @ X3), inference(split_conjunct,[status(thm)],[c_0_41])).
% 10.08/10.34 thf(c_0_52, plain, p46, inference(split_conjunct,[status(thm)],[ax340])).
% 10.08/10.34 thf(c_0_53, plain, ((fsize_size_list_a @ esk5_0)=(fdivide_divide_nat @ (fsize_size_list_a @ fxs) @ fk)|p379), inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax379])])])])).
% 10.08/10.34 thf(c_0_54, plain, (~p100|~p379), inference(split_conjunct,[status(thm)],[c_0_42])).
% 10.08/10.34 thf(c_0_55, plain, p100, inference(split_conjunct,[status(thm)],[ax286])).
% 10.08/10.34 thf(c_0_56, plain, (~p130|~p119|p128), inference(fof_simplification,[status(thm)],[ax255])).
% 10.08/10.34 thf(c_0_57, plain, (p130|~p129), inference(split_conjunct,[status(thm)],[c_0_43])).
% 10.08/10.34 thf(c_0_58, plain, p129, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_44, c_0_45])])).
% 10.08/10.34 thf(c_0_59, plain, ![X578:nat]:(~p16|ford_less_nat @ X578 @ (fsuc @ X578)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax16])])])).
% 10.08/10.34 thf(c_0_60, plain, ![X2:nat, X3:nat]:(ford_less_nat @ X2 @ X3|~p39|~ford_less_nat @ (fsuc @ X2) @ (fsuc @ X3)), inference(split_conjunct,[status(thm)],[c_0_46])).
% 10.08/10.34 thf(c_0_61, plain, p39, inference(split_conjunct,[status(thm)],[ax347])).
% 10.08/10.34 thf(c_0_62, plain, ![X2:nat]:((X2)=(fsuc @ (esk232_1 @ X2))|~p59|~ford_less_nat @ fzero_zero_nat @ X2), inference(split_conjunct,[status(thm)],[c_0_47])).
% 10.08/10.34 thf(c_0_63, plain, p59, inference(split_conjunct,[status(thm)],[ax327])).
% 10.08/10.34 thf(c_0_64, plain, ![X2:nat, X3:nat]:(ford_less_nat @ fzero_zero_nat @ X3|~p96|~ford_less_nat @ X2 @ X3), inference(split_conjunct,[status(thm)],[c_0_48])).
% 10.08/10.34 thf(c_0_65, plain, p96, inference(split_conjunct,[status(thm)],[ax290])).
% 10.08/10.34 thf(c_0_66, plain, ![X2:nat]:~ford_less_nat @ X2 @ X2, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_49, c_0_50])])).
% 10.08/10.34 thf(c_0_67, plain, ![X2:nat, X3:nat]:(ford_less_nat @ X2 @ (fsuc @ X3)|~ford_less_nat @ X2 @ X3), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_51, c_0_52])])).
% 10.08/10.34 thf(c_0_68, plain, ![X460:nat, X461:nat, X462:nat]:(~p68|(~ford_less_nat @ X460 @ (ftimes_times_nat @ X461 @ X462)|ford_less_nat @ (fdivide_divide_nat @ X460 @ X462) @ X461)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax68])])])).
% 10.08/10.34 thf(c_0_69, plain, (~p128|(fsuc @ fn)=(fdivide_divide_nat @ (fsize_size_list_a @ fxs) @ fk)), inference(fof_nnf,[status(thm)],[pax128])).
% 10.08/10.34 thf(c_0_70, plain, ((fsize_size_list_a @ esk5_0)=(fdivide_divide_nat @ (fsize_size_list_a @ fxs) @ fk)|p379), inference(split_conjunct,[status(thm)],[c_0_53])).
% 10.08/10.34 thf(c_0_71, plain, ~p379, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_54, c_0_55])])).
% 10.08/10.34 thf(c_0_72, plain, (p128|~p130|~p119), inference(split_conjunct,[status(thm)],[c_0_56])).
% 10.08/10.34 thf(c_0_73, plain, p119, inference(split_conjunct,[status(thm)],[ax267])).
% 10.08/10.34 thf(c_0_74, plain, p130, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_57, c_0_58])])).
% 10.08/10.34 thf(c_0_75, plain, ![X526:nat, X527:nat]:(~p40|(ford_less_nat @ X526 @ X527|(~ford_less_nat @ X526 @ (fsuc @ X527)|(X527)=(X526)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax40])])])])).
% 10.08/10.34 thf(c_0_76, plain, ![X2:nat]:(ford_less_nat @ X2 @ (fsuc @ X2)|~p16), inference(split_conjunct,[status(thm)],[c_0_59])).
% 10.08/10.34 thf(c_0_77, plain, p16, inference(split_conjunct,[status(thm)],[ax370])).
% 10.08/10.34 thf(c_0_78, plain, ![X586:nat]:(~p11|ford_less_nat @ fzero_zero_nat @ (fsuc @ X586)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax11])])])).
% 10.08/10.34 thf(c_0_79, plain, ![X2:nat, X3:nat]:(ford_less_nat @ X2 @ X3|~ford_less_nat @ (fsuc @ X2) @ (fsuc @ X3)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_60, c_0_61])])).
% 10.08/10.34 thf(c_0_80, plain, ![X2:nat]:((fsuc @ (esk232_1 @ X2))=(X2)|~ford_less_nat @ fzero_zero_nat @ X2), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_62, c_0_63])])).
% 10.08/10.34 thf(c_0_81, plain, ![X3:nat, X2:nat]:(ford_less_nat @ fzero_zero_nat @ X2|~ford_less_nat @ X3 @ X2), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_64, c_0_65])])).
% 10.08/10.34 thf(c_0_82, plain, ![X580:nat, X581:nat]:(~p15|(~ford_less_nat @ X580 @ X581|ford_less_nat @ (fsuc @ X580) @ (fsuc @ X581))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax15])])])).
% 10.08/10.34 thf(c_0_83, plain, ![X2:nat]:~ford_less_nat @ (fsuc @ X2) @ X2, inference(spm,[status(thm)],[c_0_66, c_0_67])).
% 10.08/10.34 thf(c_0_84, plain, ![X2:nat, X3:nat, X4:nat]:(ford_less_nat @ (fdivide_divide_nat @ X2 @ X4) @ X3|~p68|~ford_less_nat @ X2 @ (ftimes_times_nat @ X3 @ X4)), inference(split_conjunct,[status(thm)],[c_0_68])).
% 10.08/10.34 thf(c_0_85, plain, p68, inference(split_conjunct,[status(thm)],[ax318])).
% 10.08/10.34 thf(c_0_86, plain, ((fsuc @ fn)=(fdivide_divide_nat @ (fsize_size_list_a @ fxs) @ fk)|~p128), inference(split_conjunct,[status(thm)],[c_0_69])).
% 10.08/10.34 thf(c_0_87, plain, (fdivide_divide_nat @ (fsize_size_list_a @ fxs) @ fk)=(fsize_size_list_a @ esk5_0), inference(sr,[status(thm)],[c_0_70, c_0_71])).
% 10.08/10.34 thf(c_0_88, plain, p128, inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_72, c_0_73]), c_0_74])])).
% 10.08/10.34 thf(c_0_89, plain, ![X2:nat, X3:nat]:(ford_less_nat @ X2 @ X3|(X3)=(X2)|~p40|~ford_less_nat @ X2 @ (fsuc @ X3)), inference(split_conjunct,[status(thm)],[c_0_75])).
% 10.08/10.34 thf(c_0_90, plain, p40, inference(split_conjunct,[status(thm)],[ax346])).
% 10.08/10.34 thf(c_0_91, plain, ![X2:nat]:ford_less_nat @ X2 @ (fsuc @ X2), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_76, c_0_77])])).
% 10.08/10.34 thf(c_0_92, plain, ![X2:nat]:(ford_less_nat @ fzero_zero_nat @ (fsuc @ X2)|~p11), inference(split_conjunct,[status(thm)],[c_0_78])).
% 10.08/10.34 thf(c_0_93, plain, p11, inference(split_conjunct,[status(thm)],[ax375])).
% 10.08/10.34 thf(c_0_94, plain, ![X2:nat, X3:nat]:(ford_less_nat @ X2 @ (esk232_1 @ X3)|~ford_less_nat @ (fsuc @ X2) @ X3), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_79, c_0_80]), c_0_81])).
% 10.08/10.34 thf(c_0_95, plain, ![X2:nat, X3:nat]:(ford_less_nat @ (fsuc @ X2) @ (fsuc @ X3)|~p15|~ford_less_nat @ X2 @ X3), inference(split_conjunct,[status(thm)],[c_0_82])).
% 10.08/10.34 thf(c_0_96, plain, p15, inference(split_conjunct,[status(thm)],[ax371])).
% 10.08/10.34 thf(c_0_97, plain, ![X2:nat]:(~ford_less_nat @ X2 @ (esk232_1 @ X2)|~ford_less_nat @ fzero_zero_nat @ X2), inference(spm,[status(thm)],[c_0_83, c_0_80])).
% 10.08/10.34 thf(c_0_98, plain, ![X2:nat, X4:nat, X3:nat]:(ford_less_nat @ (fdivide_divide_nat @ X2 @ X3) @ X4|~ford_less_nat @ X2 @ (ftimes_times_nat @ X4 @ X3)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_84, c_0_85])])).
% 10.08/10.34 thf(c_0_99, plain, (fsize_size_list_a @ esk5_0)=(fsuc @ fn), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_86, c_0_87]), c_0_88])])).
% 10.08/10.34 thf(c_0_100, plain, ![X2:nat, X3:nat]:((X2)=(X3)|ford_less_nat @ X2 @ X3|~ford_less_nat @ X2 @ (fsuc @ X3)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_89, c_0_90])])).
% 10.08/10.34 thf(c_0_101, plain, ![X2:nat]:(ford_less_nat @ (esk232_1 @ X2) @ X2|~ford_less_nat @ fzero_zero_nat @ X2), inference(spm,[status(thm)],[c_0_91, c_0_80])).
% 10.08/10.34 thf(c_0_102, plain, ![X2:nat]:ford_less_nat @ fzero_zero_nat @ (fsuc @ X2), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_92, c_0_93])])).
% 10.08/10.34 thf(c_0_103, plain, ![X2:nat]:~ford_less_nat @ (fsuc @ (esk232_1 @ X2)) @ X2, inference(spm,[status(thm)],[c_0_66, c_0_94])).
% 10.08/10.34 thf(c_0_104, plain, ![X2:nat, X3:nat]:(ford_less_nat @ (fsuc @ X2) @ (fsuc @ X3)|~ford_less_nat @ X2 @ X3), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_95, c_0_96])])).
% 10.08/10.34 thf(c_0_105, plain, ![X2:nat, X3:nat]:(~ford_less_nat @ X2 @ (ftimes_times_nat @ (esk232_1 @ (fdivide_divide_nat @ X2 @ X3)) @ X3)|~ford_less_nat @ fzero_zero_nat @ (fdivide_divide_nat @ X2 @ X3)), inference(spm,[status(thm)],[c_0_97, c_0_98])).
% 10.08/10.34 thf(c_0_106, plain, (fdivide_divide_nat @ (fsize_size_list_a @ fxs) @ fk)=(fsuc @ fn), inference(rw,[status(thm)],[c_0_87, c_0_99])).
% 10.08/10.34 thf(c_0_107, plain, ![X2:nat]:((esk232_1 @ (fsuc @ X2))=(X2)|ford_less_nat @ (esk232_1 @ (fsuc @ X2)) @ X2), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100, c_0_101]), c_0_102])])).
% 10.08/10.34 thf(c_0_108, plain, ![X2:nat]:~ford_less_nat @ (esk232_1 @ (fsuc @ X2)) @ X2, inference(spm,[status(thm)],[c_0_103, c_0_104])).
% 10.08/10.34 thf(c_0_109, plain, ![X560:nat, X561:nat]:(~p23|((X560)=(X561)|(ford_less_nat @ X560 @ X561|ford_less_nat @ X561 @ X560))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax23])])])])).
% 10.08/10.34 thf(c_0_110, plain, (~ford_less_nat @ (ftimes_times_nat @ fn @ fk) @ (fsize_size_list_a @ fxs)|p121), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax121])])).
% 10.08/10.34 thf(c_0_111, plain, ~p121, inference(fof_simplification,[status(thm)],[ax265])).
% 10.08/10.34 thf(c_0_112, plain, ![X466:nat, X467:nat, X468:nat]:(~p66|(~ford_less_nat @ X466 @ X467|(~ford_less_nat @ fzero_zero_nat @ X468|ford_less_nat @ (ftimes_times_nat @ X466 @ X468) @ (ftimes_times_nat @ X467 @ X468)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax66])])])).
% 10.08/10.34 thf(c_0_113, plain, ~ford_less_nat @ (fsize_size_list_a @ fxs) @ (ftimes_times_nat @ (esk232_1 @ (fsuc @ fn)) @ fk), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105, c_0_106]), c_0_102])])).
% 10.08/10.34 thf(c_0_114, plain, ![X2:nat]:(esk232_1 @ (fsuc @ X2))=(X2), inference(sr,[status(thm)],[c_0_107, c_0_108])).
% 10.08/10.34 thf(c_0_115, plain, ![X3:nat, X2:nat]:((X2)=(X3)|ford_less_nat @ X2 @ X3|ford_less_nat @ X3 @ X2|~p23), inference(split_conjunct,[status(thm)],[c_0_109])).
% 10.08/10.34 thf(c_0_116, plain, p23, inference(split_conjunct,[status(thm)],[ax363])).
% 10.08/10.34 thf(c_0_117, plain, (p121|~ford_less_nat @ (ftimes_times_nat @ fn @ fk) @ (fsize_size_list_a @ fxs)), inference(split_conjunct,[status(thm)],[c_0_110])).
% 10.08/10.34 thf(c_0_118, plain, ~p121, inference(split_conjunct,[status(thm)],[c_0_111])).
% 10.08/10.34 thf(c_0_119, plain, ![X2:nat, X3:nat, X4:nat]:(ford_less_nat @ (ftimes_times_nat @ X2 @ X4) @ (ftimes_times_nat @ X3 @ X4)|~p66|~ford_less_nat @ X2 @ X3|~ford_less_nat @ fzero_zero_nat @ X4), inference(split_conjunct,[status(thm)],[c_0_112])).
% 10.08/10.34 thf(c_0_120, plain, p66, inference(split_conjunct,[status(thm)],[ax320])).
% 10.08/10.34 thf(c_0_121, plain, ~ford_less_nat @ (fsize_size_list_a @ fxs) @ (ftimes_times_nat @ fn @ fk), inference(rw,[status(thm)],[c_0_113, c_0_114])).
% 10.08/10.34 thf(c_0_122, plain, ![X3:nat, X2:nat]:((X2)=(X3)|ford_less_nat @ X2 @ X3|ford_less_nat @ X3 @ X2), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_115, c_0_116])])).
% 10.08/10.34 thf(c_0_123, plain, ~ford_less_nat @ (ftimes_times_nat @ fn @ fk) @ (fsize_size_list_a @ fxs), inference(sr,[status(thm)],[c_0_117, c_0_118])).
% 10.08/10.34 thf(c_0_124, plain, ![X2:nat, X3:nat]:~ford_less_nat @ X2 @ (ftimes_times_nat @ (fdivide_divide_nat @ X2 @ X3) @ X3), inference(spm,[status(thm)],[c_0_66, c_0_98])).
% 10.08/10.34 thf(c_0_125, plain, ![X2:nat, X3:nat, X4:nat]:(ford_less_nat @ (ftimes_times_nat @ X2 @ X3) @ (ftimes_times_nat @ X4 @ X3)|~ford_less_nat @ fzero_zero_nat @ X3|~ford_less_nat @ X2 @ X4), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_119, c_0_120])])).
% 10.08/10.34 thf(c_0_126, plain, (fsize_size_list_a @ fxs)=(ftimes_times_nat @ fn @ fk), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_121, c_0_122]), c_0_123])).
% 10.08/10.34 thf(c_0_127, plain, ![X540:nat]:(~p34|((X540)=(fzero_zero_nat)|ford_less_nat @ fzero_zero_nat @ X540)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax34])])])])).
% 10.08/10.34 thf(c_0_128, plain, ((fk)!=(fzero_zero_nat)|p120), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax120])])).
% 10.08/10.34 thf(c_0_129, plain, ~p120, inference(fof_simplification,[status(thm)],[ax266])).
% 10.08/10.34 thf(c_0_130, plain, ![X2:nat, X3:nat]:(~ford_less_nat @ X2 @ (fdivide_divide_nat @ (ftimes_times_nat @ X2 @ X3) @ X3)|~ford_less_nat @ fzero_zero_nat @ X3), inference(spm,[status(thm)],[c_0_124, c_0_125])).
% 10.08/10.34 thf(c_0_131, plain, (fdivide_divide_nat @ (ftimes_times_nat @ fn @ fk) @ fk)=(fsuc @ fn), inference(rw,[status(thm)],[c_0_106, c_0_126])).
% 10.08/10.34 thf(c_0_132, plain, ![X2:nat]:((X2)=(fzero_zero_nat)|ford_less_nat @ fzero_zero_nat @ X2|~p34), inference(split_conjunct,[status(thm)],[c_0_127])).
% 10.08/10.34 thf(c_0_133, plain, p34, inference(split_conjunct,[status(thm)],[ax352])).
% 10.08/10.34 thf(c_0_134, plain, (p120|(fk)!=(fzero_zero_nat)), inference(split_conjunct,[status(thm)],[c_0_128])).
% 10.08/10.34 thf(c_0_135, plain, ~p120, inference(split_conjunct,[status(thm)],[c_0_129])).
% 10.08/10.34 thf(c_0_136, plain, ~ford_less_nat @ fzero_zero_nat @ fk, inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130, c_0_131]), c_0_91])])).
% 10.08/10.34 thf(c_0_137, plain, ![X2:nat]:((X2)=(fzero_zero_nat)|ford_less_nat @ fzero_zero_nat @ X2), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_132, c_0_133])])).
% 10.08/10.34 thf(c_0_138, plain, (fk)!=(fzero_zero_nat), inference(sr,[status(thm)],[c_0_134, c_0_135])).
% 10.08/10.34 thf(c_0_139, plain, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_136, c_0_137]), c_0_138]), ['proof']).
% 10.08/10.34 thf(1,plain,$false,inference(eprover,[status(thm),assumptions([h0])],[])).
% 10.08/10.34 thf(0,theorem,((ord_less_nat @ ((times_times_nat @ n) @ k)) @ (size_size_list_a @ xs)),inference(contra,[status(thm),contra(discharge,[h0])],[1,h0])).
% 10.08/10.34 % SZS output end Proof
%------------------------------------------------------------------------------