TSTP Solution File: ITP110^1 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP110^1 : 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 : 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 : Sun Jul 17 00:29:08 EDT 2022
% Result : Theorem 0.19s 0.48s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : ITP110^1 : TPTP v8.1.0. Released v7.5.0.
% 0.07/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n026.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sat Jun 4 01:58:14 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.48 % SZS status Theorem
% 0.19/0.48 % Mode: mode507:USE_SINE=true:SINE_TOLERANCE=3.0:SINE_GENERALITY_THRESHOLD=0:SINE_RANK_LIMIT=1.:SINE_DEPTH=1
% 0.19/0.48 % Inferences: 27
% 0.19/0.48 % SZS output start Proof
% 0.19/0.48 thf(ty_a, type, a : $tType).
% 0.19/0.48 thf(ty_extended_ereal, type, extended_ereal : $tType).
% 0.19/0.48 thf(ty_set_a, type, set_a : $tType).
% 0.19/0.48 thf(ty_member_a, type, member_a : (a>set_a>$o)).
% 0.19/0.48 thf(ty_eigen__1, type, eigen__1 : a).
% 0.19/0.48 thf(ty_eigen__0, type, eigen__0 : a).
% 0.19/0.48 thf(ty_lower_1391529426main_a, type, lower_1391529426main_a : ((a>extended_ereal)>set_a)).
% 0.19/0.48 thf(ty_top_top_set_a, type, top_top_set_a : set_a).
% 0.19/0.48 thf(ty_lower_311861424x_on_a, type, lower_311861424x_on_a : (set_a>(a>extended_ereal)>$o)).
% 0.19/0.48 thf(ty_f, type, f : (a>extended_ereal)).
% 0.19/0.48 thf(ty_convex_a, type, convex_a : (set_a>$o)).
% 0.19/0.48 thf(sP1,plain,sP1 <=> ((lower_311861424x_on_a @ top_top_set_a) @ f),introduced(definition,[new_symbols(definition,[sP1])])).
% 0.19/0.48 thf(sP2,plain,sP2 <=> (convex_a @ (lower_1391529426main_a @ f)),introduced(definition,[new_symbols(definition,[sP2])])).
% 0.19/0.48 thf(conj_0,conjecture,(sP1 = sP2)).
% 0.19/0.48 thf(h0,negated_conjecture,(~((sP1 = sP2))),inference(assume_negation,[status(cth)],[conj_0])).
% 0.19/0.48 thf(h1,assumption,sP1,introduced(assumption,[])).
% 0.19/0.48 thf(h2,assumption,sP2,introduced(assumption,[])).
% 0.19/0.48 thf(h3,assumption,(~(sP1)),introduced(assumption,[])).
% 0.19/0.48 thf(h4,assumption,(~(sP2)),introduced(assumption,[])).
% 0.19/0.48 thf(h5,assumption,((member_a @ eigen__0) @ top_top_set_a),introduced(assumption,[])).
% 0.19/0.48 thf(nax1, axiom, (p1<=fconvex_a @ (flower_1391529426main_a @ ff)), file('<stdin>', nax1)).
% 0.19/0.48 thf(ax37, axiom, ~(p1), file('<stdin>', ax37)).
% 0.19/0.48 thf(pax2, axiom, (p2=>![X8:a > extended_ereal]:(flower_311861424x_on_a @ ftop_top_set_a @ X8=>fconvex_a @ (flower_1391529426main_a @ X8))), file('<stdin>', pax2)).
% 0.19/0.48 thf(pax19, axiom, (p19=>flower_311861424x_on_a @ ftop_top_set_a @ ff), file('<stdin>', pax19)).
% 0.19/0.48 thf(ax36, axiom, p2, file('<stdin>', ax36)).
% 0.19/0.48 thf(ax19, axiom, p19, file('<stdin>', ax19)).
% 0.19/0.48 thf(c_0_6, plain, (~fconvex_a @ (flower_1391529426main_a @ ff)|p1), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax1])])).
% 0.19/0.48 thf(c_0_7, plain, ~p1, inference(fof_simplification,[status(thm)],[ax37])).
% 0.19/0.48 thf(c_0_8, plain, ![X45:a > extended_ereal]:(~p2|(~flower_311861424x_on_a @ ftop_top_set_a @ X45|fconvex_a @ (flower_1391529426main_a @ X45))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax2])])])).
% 0.19/0.48 thf(c_0_9, plain, (~p19|flower_311861424x_on_a @ ftop_top_set_a @ ff), inference(fof_nnf,[status(thm)],[pax19])).
% 0.19/0.48 thf(c_0_10, plain, (p1|~fconvex_a @ (flower_1391529426main_a @ ff)), inference(split_conjunct,[status(thm)],[c_0_6])).
% 0.19/0.48 thf(c_0_11, plain, ~p1, inference(split_conjunct,[status(thm)],[c_0_7])).
% 0.19/0.48 thf(c_0_12, plain, ![X1:a > extended_ereal]:(fconvex_a @ (flower_1391529426main_a @ X1)|~p2|~flower_311861424x_on_a @ ftop_top_set_a @ X1), inference(split_conjunct,[status(thm)],[c_0_8])).
% 0.19/0.48 thf(c_0_13, plain, p2, inference(split_conjunct,[status(thm)],[ax36])).
% 0.19/0.48 thf(c_0_14, plain, (flower_311861424x_on_a @ ftop_top_set_a @ ff|~p19), inference(split_conjunct,[status(thm)],[c_0_9])).
% 0.19/0.48 thf(c_0_15, plain, p19, inference(split_conjunct,[status(thm)],[ax19])).
% 0.19/0.48 thf(c_0_16, plain, ~fconvex_a @ (flower_1391529426main_a @ ff), inference(sr,[status(thm)],[c_0_10, c_0_11])).
% 0.19/0.48 thf(c_0_17, plain, ![X1:a > extended_ereal]:(fconvex_a @ (flower_1391529426main_a @ X1)|~flower_311861424x_on_a @ ftop_top_set_a @ X1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_12, c_0_13])])).
% 0.19/0.48 thf(c_0_18, plain, flower_311861424x_on_a @ ftop_top_set_a @ ff, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_14, c_0_15])])).
% 0.19/0.48 thf(c_0_19, plain, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16, c_0_17]), c_0_18])]), ['proof']).
% 0.19/0.48 thf(1,plain,$false,inference(eprover,[status(thm),assumptions([h4,h5,h1,h2,h0])],[])).
% 0.19/0.48 thf(nax1, axiom, (p1<=fconvex_a @ (flower_1391529426main_a @ ff)), file('<stdin>', nax1)).
% 0.19/0.48 thf(ax35, axiom, ~(p1), file('<stdin>', ax35)).
% 0.19/0.48 thf(pax2, axiom, (p2=>![X9:a > extended_ereal]:(flower_311861424x_on_a @ ftop_top_set_a @ X9=>fconvex_a @ (flower_1391529426main_a @ X9))), file('<stdin>', pax2)).
% 0.19/0.48 thf(pax19, axiom, (p19=>flower_311861424x_on_a @ ftop_top_set_a @ ff), file('<stdin>', pax19)).
% 0.19/0.48 thf(ax52, axiom, p2, file('<stdin>', ax52)).
% 0.19/0.48 thf(ax53, axiom, p19, file('<stdin>', ax53)).
% 0.19/0.48 thf(c_0_6, plain, (~fconvex_a @ (flower_1391529426main_a @ ff)|p1), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax1])])).
% 0.19/0.48 thf(c_0_7, plain, ~p1, inference(fof_simplification,[status(thm)],[ax35])).
% 0.19/0.48 thf(c_0_8, plain, ![X54:a > extended_ereal]:(~p2|(~flower_311861424x_on_a @ ftop_top_set_a @ X54|fconvex_a @ (flower_1391529426main_a @ X54))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax2])])])).
% 0.19/0.48 thf(c_0_9, plain, (~p19|flower_311861424x_on_a @ ftop_top_set_a @ ff), inference(fof_nnf,[status(thm)],[pax19])).
% 0.19/0.48 thf(c_0_10, plain, (p1|~fconvex_a @ (flower_1391529426main_a @ ff)), inference(split_conjunct,[status(thm)],[c_0_6])).
% 0.19/0.48 thf(c_0_11, plain, ~p1, inference(split_conjunct,[status(thm)],[c_0_7])).
% 0.19/0.48 thf(c_0_12, plain, ![X2:a > extended_ereal]:(fconvex_a @ (flower_1391529426main_a @ X2)|~p2|~flower_311861424x_on_a @ ftop_top_set_a @ X2), inference(split_conjunct,[status(thm)],[c_0_8])).
% 0.19/0.48 thf(c_0_13, plain, p2, inference(split_conjunct,[status(thm)],[ax52])).
% 0.19/0.48 thf(c_0_14, plain, (flower_311861424x_on_a @ ftop_top_set_a @ ff|~p19), inference(split_conjunct,[status(thm)],[c_0_9])).
% 0.19/0.48 thf(c_0_15, plain, p19, inference(split_conjunct,[status(thm)],[ax53])).
% 0.19/0.48 thf(c_0_16, plain, ~fconvex_a @ (flower_1391529426main_a @ ff), inference(sr,[status(thm)],[c_0_10, c_0_11])).
% 0.19/0.48 thf(c_0_17, plain, ![X2:a > extended_ereal]:(fconvex_a @ (flower_1391529426main_a @ X2)|~flower_311861424x_on_a @ ftop_top_set_a @ X2), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_12, c_0_13])])).
% 0.19/0.48 thf(c_0_18, plain, flower_311861424x_on_a @ ftop_top_set_a @ ff, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_14, c_0_15])])).
% 0.19/0.48 thf(c_0_19, plain, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16, c_0_17]), c_0_18])]), ['proof']).
% 0.19/0.48 thf(2,plain,$false,inference(eprover,[status(thm),assumptions([h1,h5,h1,h2,h0])],[])).
% 0.19/0.48 thf(fact_0__092_060open_062convex_A_Idomain_Af_J_A_092_060Longrightarrow_062_ALower__Semicontinuous__Mirabelle__mxyexokbxt_Oconvex__on_AUNIV_Af_092_060close_062,axiom,(sP2 => sP1)).
% 0.19/0.48 thf(3,plain,$false,inference(tab_imp,[status(thm),assumptions([h5,h1,h2,h0]),tab_imp(discharge,[h4]),tab_imp(discharge,[h1])],[fact_0__092_060open_062convex_A_Idomain_Af_J_A_092_060Longrightarrow_062_ALower__Semicontinuous__Mirabelle__mxyexokbxt_Oconvex__on_AUNIV_Af_092_060close_062,1,2,h4,h1])).
% 0.19/0.48 thf(fact_29_UNIV__witness,axiom,(~((![X1:a]:(~(((member_a @ X1) @ top_top_set_a))))))).
% 0.19/0.48 thf(4,plain,$false,inference(tab_negall,[status(thm),assumptions([h1,h2,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__0)],[fact_29_UNIV__witness,3,h5])).
% 0.19/0.48 thf(h6,assumption,((member_a @ eigen__1) @ top_top_set_a),introduced(assumption,[])).
% 0.19/0.48 thf(5,plain,$false,inference(tab_conflict,[status(thm),assumptions([h4,h6,h3,h4,h0])],[h4,h4])).
% 0.19/0.48 thf(6,plain,$false,inference(tab_conflict,[status(thm),assumptions([h1,h6,h3,h4,h0])],[h1,h3])).
% 0.19/0.48 thf(7,plain,$false,inference(tab_imp,[status(thm),assumptions([h6,h3,h4,h0]),tab_imp(discharge,[h4]),tab_imp(discharge,[h1])],[fact_0__092_060open_062convex_A_Idomain_Af_J_A_092_060Longrightarrow_062_ALower__Semicontinuous__Mirabelle__mxyexokbxt_Oconvex__on_AUNIV_Af_092_060close_062,5,6,h4,h1])).
% 0.19/0.48 thf(8,plain,$false,inference(tab_negall,[status(thm),assumptions([h3,h4,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__1)],[fact_29_UNIV__witness,7,h6])).
% 0.19/0.48 thf(9,plain,$false,inference(tab_be,[status(thm),assumptions([h0]),tab_be(discharge,[h1,h2]),tab_be(discharge,[h3,h4])],[h0,4,8,h1,h2,h3,h4])).
% 0.19/0.48 thf(0,theorem,(sP1 = sP2),inference(contra,[status(thm),contra(discharge,[h0])],[9,h0])).
% 0.19/0.48 % SZS output end Proof
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