%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP247^3 : TPTP v9.2.1. Bugfixed v9.2.1.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Oct 14 12:39:52 PM UTC 2025
% Result : Theorem 24.65s 24.73s
% Output : Proof 24.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ITP247^3 : TPTP v9.2.1. Bugfixed v9.2.1.
% 0.11/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n003.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Oct 10 14:39:38 EDT 2025
% 0.13/0.34 % CPUTime :
% 24.65/24.73 % SZS status Theorem
% 24.65/24.73 % Mode: mode485:USE_SINE=true:SINE_TOLERANCE=1.2:SINE_GENERALITY_THRESHOLD=4:SINE_RANK_LIMIT=4.:SINE_DEPTH=0
% 24.65/24.73 % Inferences: 0
% 24.65/24.73 % SZS output start Proof
% 24.65/24.73 thf(conj_0,conjecture,((ord_less_eq_nat @ ((plus_plus_nat @ one_one_nat) @ (vEBT_VEBT_height @ ((nth_VEBT_VEBT @ treeList) @ ((vEBT_VEBT_high @ xa) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ (vEBT_VEBT_height @ ((((vEBT_Node @ (some_P7363390416028606310at_nat @ ((product_Pair_nat_nat @ mi) @ ma))) @ deg) @ treeList) @ summary)))).
% 24.65/24.73 thf(h0,negated_conjecture,(~(((ord_less_eq_nat @ ((plus_plus_nat @ one_one_nat) @ (vEBT_VEBT_height @ ((nth_VEBT_VEBT @ treeList) @ ((vEBT_VEBT_high @ xa) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ (vEBT_VEBT_height @ ((((vEBT_Node @ (some_P7363390416028606310at_nat @ ((product_Pair_nat_nat @ mi) @ ma))) @ deg) @ treeList) @ summary))))),inference(assume_negation,[status(cth)],[conj_0])).
% 24.65/24.73 thf(pax196, axiom, (p196=>(fm)=(fna)), file('<stdin>', pax196)).
% 24.65/24.73 thf(pax15, axiom, (p15=>![X1754:nat]:(fdivide_divide_nat @ (fplus_plus_nat @ X1754 @ X1754) @ (fnumeral_numeral_nat @ (fbit0 @ fone)))=(X1754)), file('<stdin>', pax15)).
% 24.65/24.73 thf(pax211, axiom, (p211=>(fdeg)=(fplus_plus_nat @ fna @ fm)), file('<stdin>', pax211)).
% 24.65/24.73 thf(ax1135, axiom, p196, file('<stdin>', ax1135)).
% 24.65/24.73 thf(nax1, axiom, (p1<=ford_less_eq_nat @ (fplus_plus_nat @ fone_one_nat @ (fvEBT_VEBT_height @ (fnth_VEBT_VEBT @ ftreeList @ (fvEBT_VEBT_high @ fxa @ (fdivide_divide_nat @ fdeg @ (fnumeral_numeral_nat @ (fbit0 @ fone))))))) @ (fvEBT_VEBT_height @ (fvEBT_Node @ (fsome_P7363390416028606310at_nat @ (fproduct_Pair_nat_nat @ fmi @ fma)) @ fdeg @ ftreeList @ fsummary))), file('<stdin>', nax1)).
% 24.65/24.73 thf(ax1330, axiom, ~(p1), file('<stdin>', ax1330)).
% 24.65/24.73 thf(ax1316, axiom, p15, file('<stdin>', ax1316)).
% 24.65/24.73 thf(ax1120, axiom, p211, file('<stdin>', ax1120)).
% 24.65/24.73 thf(nax333, axiom, (p333<=(fvEBT_invar_vebt @ (fnth_VEBT_VEBT @ ftreeList @ (fvEBT_VEBT_high @ fxa @ (fdivide_divide_nat @ fdeg @ (fnumeral_numeral_nat @ (fbit0 @ fone))))) @ fna=>~(fmember_VEBT_VEBT @ (fnth_VEBT_VEBT @ ftreeList @ (fvEBT_VEBT_high @ fxa @ (fdivide_divide_nat @ fdeg @ (fnumeral_numeral_nat @ (fbit0 @ fone))))) @ (fset_VEBT_VEBT2 @ ftreeList)))), file('<stdin>', nax333)).
% 24.65/24.73 thf(ax998, axiom, ~(p333), file('<stdin>', ax998)).
% 24.65/24.73 thf(pax10, axiom, (p10=>![X1756:vEBT_VEBT, X1757:list_VEBT_VEBT, X1758:option4927543243414619207at_nat, X1717:nat, X1759:vEBT_VEBT]:(fmember_VEBT_VEBT @ X1756 @ (fset_VEBT_VEBT2 @ X1757)=>ford_less_eq_nat @ (fplus_plus_nat @ fone_one_nat @ (fvEBT_VEBT_height @ X1756)) @ (fvEBT_VEBT_height @ (fvEBT_Node @ X1758 @ X1717 @ X1757 @ X1759)))), file('<stdin>', pax10)).
% 24.65/24.73 thf(ax1321, axiom, p10, file('<stdin>', ax1321)).
% 24.65/24.73 thf(c_0_12, plain, (~p196|(fm)=(fna)), inference(fof_nnf,[status(thm)],[pax196])).
% 24.65/24.73 thf(c_0_13, plain, ![X6731:nat]:(~p15|(fdivide_divide_nat @ (fplus_plus_nat @ X6731 @ X6731) @ (fnumeral_numeral_nat @ (fbit0 @ fone)))=(X6731)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax15])])])).
% 24.65/24.73 thf(c_0_14, plain, (~p211|(fdeg)=(fplus_plus_nat @ fna @ fm)), inference(fof_nnf,[status(thm)],[pax211])).
% 24.65/24.73 thf(c_0_15, plain, ((fm)=(fna)|~p196), inference(split_conjunct,[status(thm)],[c_0_12])).
% 24.65/24.73 thf(c_0_16, plain, p196, inference(split_conjunct,[status(thm)],[ax1135])).
% 24.65/24.73 thf(c_0_17, plain, (~ford_less_eq_nat @ (fplus_plus_nat @ fone_one_nat @ (fvEBT_VEBT_height @ (fnth_VEBT_VEBT @ ftreeList @ (fvEBT_VEBT_high @ fxa @ (fdivide_divide_nat @ fdeg @ (fnumeral_numeral_nat @ (fbit0 @ fone))))))) @ (fvEBT_VEBT_height @ (fvEBT_Node @ (fsome_P7363390416028606310at_nat @ (fproduct_Pair_nat_nat @ fmi @ fma)) @ fdeg @ ftreeList @ fsummary))|p1), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax1])])).
% 24.65/24.73 thf(c_0_18, plain, ~p1, inference(fof_simplification,[status(thm)],[ax1330])).
% 24.65/24.73 thf(c_0_19, plain, ![X3:nat]:((fdivide_divide_nat @ (fplus_plus_nat @ X3 @ X3) @ (fnumeral_numeral_nat @ (fbit0 @ fone)))=(X3)|~p15), inference(split_conjunct,[status(thm)],[c_0_13])).
% 24.65/24.73 thf(c_0_20, plain, p15, inference(split_conjunct,[status(thm)],[ax1316])).
% 24.65/24.73 thf(c_0_21, plain, ((fdeg)=(fplus_plus_nat @ fna @ fm)|~p211), inference(split_conjunct,[status(thm)],[c_0_14])).
% 24.65/24.73 thf(c_0_22, plain, (fm)=(fna), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_15, c_0_16])])).
% 24.65/24.73 thf(c_0_23, plain, p211, inference(split_conjunct,[status(thm)],[ax1120])).
% 24.65/24.73 thf(c_0_24, plain, ((fvEBT_invar_vebt @ (fnth_VEBT_VEBT @ ftreeList @ (fvEBT_VEBT_high @ fxa @ (fdivide_divide_nat @ fdeg @ (fnumeral_numeral_nat @ (fbit0 @ fone))))) @ fna|p333)&(fmember_VEBT_VEBT @ (fnth_VEBT_VEBT @ ftreeList @ (fvEBT_VEBT_high @ fxa @ (fdivide_divide_nat @ fdeg @ (fnumeral_numeral_nat @ (fbit0 @ fone))))) @ (fset_VEBT_VEBT2 @ ftreeList)|p333)), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax333])])])).
% 24.65/24.73 thf(c_0_25, plain, ~p333, inference(fof_simplification,[status(thm)],[ax998])).
% 24.65/24.73 thf(c_0_26, plain, (p1|~ford_less_eq_nat @ (fplus_plus_nat @ fone_one_nat @ (fvEBT_VEBT_height @ (fnth_VEBT_VEBT @ ftreeList @ (fvEBT_VEBT_high @ fxa @ (fdivide_divide_nat @ fdeg @ (fnumeral_numeral_nat @ (fbit0 @ fone))))))) @ (fvEBT_VEBT_height @ (fvEBT_Node @ (fsome_P7363390416028606310at_nat @ (fproduct_Pair_nat_nat @ fmi @ fma)) @ fdeg @ ftreeList @ fsummary))), inference(split_conjunct,[status(thm)],[c_0_17])).
% 24.65/24.73 thf(c_0_27, plain, ~p1, inference(split_conjunct,[status(thm)],[c_0_18])).
% 24.65/24.73 thf(c_0_28, plain, ![X3:nat]:(fdivide_divide_nat @ (fplus_plus_nat @ X3 @ X3) @ (fnumeral_numeral_nat @ (fbit0 @ fone)))=(X3), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_19, c_0_20])])).
% 24.65/24.73 thf(c_0_29, plain, (fplus_plus_nat @ fna @ fna)=(fdeg), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_21, c_0_22]), c_0_23])])).
% 24.65/24.73 thf(c_0_30, plain, ![X6747:vEBT_VEBT, X6748:list_VEBT_VEBT, X6749:option4927543243414619207at_nat, X6750:nat, X6751:vEBT_VEBT]:(~p10|(~fmember_VEBT_VEBT @ X6747 @ (fset_VEBT_VEBT2 @ X6748)|ford_less_eq_nat @ (fplus_plus_nat @ fone_one_nat @ (fvEBT_VEBT_height @ X6747)) @ (fvEBT_VEBT_height @ (fvEBT_Node @ X6749 @ X6750 @ X6748 @ X6751)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax10])])])).
% 24.65/24.73 thf(c_0_31, plain, (fmember_VEBT_VEBT @ (fnth_VEBT_VEBT @ ftreeList @ (fvEBT_VEBT_high @ fxa @ (fdivide_divide_nat @ fdeg @ (fnumeral_numeral_nat @ (fbit0 @ fone))))) @ (fset_VEBT_VEBT2 @ ftreeList)|p333), inference(split_conjunct,[status(thm)],[c_0_24])).
% 24.65/24.73 thf(c_0_32, plain, ~p333, inference(split_conjunct,[status(thm)],[c_0_25])).
% 24.65/24.73 thf(c_0_33, plain, ~ford_less_eq_nat @ (fplus_plus_nat @ fone_one_nat @ (fvEBT_VEBT_height @ (fnth_VEBT_VEBT @ ftreeList @ (fvEBT_VEBT_high @ fxa @ (fdivide_divide_nat @ fdeg @ (fnumeral_numeral_nat @ (fbit0 @ fone))))))) @ (fvEBT_VEBT_height @ (fvEBT_Node @ (fsome_P7363390416028606310at_nat @ (fproduct_Pair_nat_nat @ fmi @ fma)) @ fdeg @ ftreeList @ fsummary)), inference(sr,[status(thm)],[c_0_26, c_0_27])).
% 24.65/24.73 thf(c_0_34, plain, (fdivide_divide_nat @ fdeg @ (fnumeral_numeral_nat @ (fbit0 @ fone)))=(fna), inference(spm,[status(thm)],[c_0_28, c_0_29])).
% 24.65/24.73 thf(c_0_35, plain, ![X3:nat, X1419:option4927543243414619207at_nat, X66:vEBT_VEBT, X25:vEBT_VEBT, X24:list_VEBT_VEBT]:(ford_less_eq_nat @ (fplus_plus_nat @ fone_one_nat @ (fvEBT_VEBT_height @ X25)) @ (fvEBT_VEBT_height @ (fvEBT_Node @ X1419 @ X3 @ X24 @ X66))|~p10|~fmember_VEBT_VEBT @ X25 @ (fset_VEBT_VEBT2 @ X24)), inference(split_conjunct,[status(thm)],[c_0_30])).
% 24.65/24.73 thf(c_0_36, plain, p10, inference(split_conjunct,[status(thm)],[ax1321])).
% 24.65/24.73 thf(c_0_37, plain, fmember_VEBT_VEBT @ (fnth_VEBT_VEBT @ ftreeList @ (fvEBT_VEBT_high @ fxa @ (fdivide_divide_nat @ fdeg @ (fnumeral_numeral_nat @ (fbit0 @ fone))))) @ (fset_VEBT_VEBT2 @ ftreeList), inference(sr,[status(thm)],[c_0_31, c_0_32])).
% 24.65/24.73 thf(c_0_38, plain, ~ford_less_eq_nat @ (fplus_plus_nat @ fone_one_nat @ (fvEBT_VEBT_height @ (fnth_VEBT_VEBT @ ftreeList @ (fvEBT_VEBT_high @ fxa @ fna)))) @ (fvEBT_VEBT_height @ (fvEBT_Node @ (fsome_P7363390416028606310at_nat @ (fproduct_Pair_nat_nat @ fmi @ fma)) @ fdeg @ ftreeList @ fsummary)), inference(rw,[status(thm)],[c_0_33, c_0_34])).
% 24.65/24.73 thf(c_0_39, plain, ![X3:nat, X1419:option4927543243414619207at_nat, X66:vEBT_VEBT, X25:vEBT_VEBT, X24:list_VEBT_VEBT]:(ford_less_eq_nat @ (fplus_plus_nat @ fone_one_nat @ (fvEBT_VEBT_height @ X25)) @ (fvEBT_VEBT_height @ (fvEBT_Node @ X1419 @ X3 @ X24 @ X66))|~fmember_VEBT_VEBT @ X25 @ (fset_VEBT_VEBT2 @ X24)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_35, c_0_36])])).
% 24.65/24.73 thf(c_0_40, plain, fmember_VEBT_VEBT @ (fnth_VEBT_VEBT @ ftreeList @ (fvEBT_VEBT_high @ fxa @ fna)) @ (fset_VEBT_VEBT2 @ ftreeList), inference(rw,[status(thm)],[c_0_37, c_0_34])).
% 24.65/24.73 thf(c_0_41, plain, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38, c_0_39]), c_0_40])]), ['proof']).
% 24.65/24.73 thf(1,plain,$false,inference(eprover,[status(thm),assumptions([h0])],[])).
% 24.65/24.73 thf(0,theorem,((ord_less_eq_nat @ ((plus_plus_nat @ one_one_nat) @ (vEBT_VEBT_height @ ((nth_VEBT_VEBT @ treeList) @ ((vEBT_VEBT_high @ xa) @ ((divide_divide_nat @ deg) @ (numeral_numeral_nat @ (bit0 @ one)))))))) @ (vEBT_VEBT_height @ ((((vEBT_Node @ (some_P7363390416028606310at_nat @ ((product_Pair_nat_nat @ mi) @ ma))) @ deg) @ treeList) @ summary))),inference(contra,[status(thm),contra(discharge,[h0])],[1,h0])).
% 24.65/24.73 % SZS output end Proof
%------------------------------------------------------------------------------