0.08/0.13	% Problem    : SLH0373^1 : TPTP v8.2.0. Released v8.2.0.
0.08/0.14	% Command    : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
0.15/0.36	Computer   : n023.cluster.edu
0.15/0.36	Model      : x86_64 x86_64
0.15/0.36	CPUModel   : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.15/0.36	RAMPerCPU  : 8042.1875MB
0.15/0.36	OS         : Linux 3.10.0-693.el7.x86_64
0.15/0.36	% CPULimit   : 30
0.15/0.36	% DateTime   : Mon Jul  3 05:17:36 EDT 2023
0.15/0.36	% CPUTime    : 
5.28/5.53	% SZS status Theorem
5.28/5.53	% Mode: mode507:USE_SINE=true:SINE_TOLERANCE=3.0:SINE_GENERALITY_THRESHOLD=0:SINE_RANK_LIMIT=1.:SINE_DEPTH=1
5.28/5.53	% Inferences: 131
5.28/5.53	% SZS output start Proof
5.28/5.53	thf(ty_n, type, n : $tType).
5.28/5.53	thf(ty_set_n, type, set_n : $tType).
5.28/5.53	thf(ty_real, type, real : $tType).
5.28/5.53	thf(ty_a, type, a : n).
5.28/5.53	thf(ty_minus_minus_real, type, minus_minus_real : (real>real>real)).
5.28/5.53	thf(ty_b, type, b : n).
5.28/5.53	thf(ty_topolo4938530945907275839cbox_n, type, topolo4938530945907275839cbox_n : (n>n>set_n)).
5.28/5.53	thf(ty_hensto8291394388724566237n_real, type, hensto8291394388724566237n_real : ((n>real)>set_n>$o)).
5.28/5.53	thf(ty_topolo8397586749496365753n_real, type, topolo8397586749496365753n_real : (set_n>(n>real)>$o)).
5.28/5.53	thf(ty_g, type, g : (n>real)).
5.28/5.53	thf(ty_f, type, f : (n>real)).
5.28/5.53	thf(sP1,plain,sP1 <=> (![X1:n>real]:(((topolo8397586749496365753n_real @ ((topolo4938530945907275839cbox_n @ a) @ b)) @ g) => (((topolo8397586749496365753n_real @ ((topolo4938530945907275839cbox_n @ a) @ b)) @ X1) => ((topolo8397586749496365753n_real @ ((topolo4938530945907275839cbox_n @ a) @ b)) @ (^[X2:n]:((minus_minus_real @ (g @ X2)) @ (X1 @ X2))))))),introduced(definition,[new_symbols(definition,[sP1])])).
5.28/5.53	thf(sP2,plain,sP2 <=> (((topolo8397586749496365753n_real @ ((topolo4938530945907275839cbox_n @ a) @ b)) @ f) => ((topolo8397586749496365753n_real @ ((topolo4938530945907275839cbox_n @ a) @ b)) @ (^[X1:n]:((minus_minus_real @ (g @ X1)) @ (f @ X1))))),introduced(definition,[new_symbols(definition,[sP2])])).
5.28/5.53	thf(sP3,plain,sP3 <=> (![X1:n>real]:(![X2:n>real]:(((topolo8397586749496365753n_real @ ((topolo4938530945907275839cbox_n @ a) @ b)) @ X1) => (((topolo8397586749496365753n_real @ ((topolo4938530945907275839cbox_n @ a) @ b)) @ X2) => ((topolo8397586749496365753n_real @ ((topolo4938530945907275839cbox_n @ a) @ b)) @ (^[X3:n]:((minus_minus_real @ (X1 @ X3)) @ (X2 @ X3)))))))),introduced(definition,[new_symbols(definition,[sP3])])).
5.28/5.53	thf(sP4,plain,sP4 <=> ((topolo8397586749496365753n_real @ ((topolo4938530945907275839cbox_n @ a) @ b)) @ (^[X1:n]:((minus_minus_real @ (g @ X1)) @ (f @ X1)))),introduced(definition,[new_symbols(definition,[sP4])])).
5.28/5.53	thf(sP5,plain,sP5 <=> ((topolo8397586749496365753n_real @ ((topolo4938530945907275839cbox_n @ a) @ b)) @ g),introduced(definition,[new_symbols(definition,[sP5])])).
5.28/5.53	thf(sP6,plain,sP6 <=> (![X1:set_n]:(![X2:n>real]:(![X3:n>real]:(((topolo8397586749496365753n_real @ X1) @ X2) => (((topolo8397586749496365753n_real @ X1) @ X3) => ((topolo8397586749496365753n_real @ X1) @ (^[X4:n]:((minus_minus_real @ (X2 @ X4)) @ (X3 @ X4))))))))),introduced(definition,[new_symbols(definition,[sP6])])).
5.28/5.53	thf(sP7,plain,sP7 <=> (sP5 => sP2),introduced(definition,[new_symbols(definition,[sP7])])).
5.28/5.53	thf(sP8,plain,sP8 <=> ((topolo8397586749496365753n_real @ ((topolo4938530945907275839cbox_n @ a) @ b)) @ f),introduced(definition,[new_symbols(definition,[sP8])])).
5.28/5.53	thf(conj_0,conjecture,sP4).
5.28/5.53	thf(h0,negated_conjecture,(~(sP4)),inference(assume_negation,[status(cth)],[conj_0])).
5.28/5.53	thf(h1,assumption,((hensto8291394388724566237n_real @ f) @ ((topolo4938530945907275839cbox_n @ a) @ b)),introduced(assumption,[])).
5.28/5.53	thf(h2,assumption,((hensto8291394388724566237n_real @ g) @ ((topolo4938530945907275839cbox_n @ a) @ b)),introduced(assumption,[])).
5.28/5.53	thf(1,plain,(~(sP6) | sP3),inference(all_rule,[status(thm)],[])).
5.28/5.53	thf(2,plain,(~(sP3) | sP1),inference(all_rule,[status(thm)],[])).
5.28/5.53	thf(3,plain,(~(sP1) | sP7),inference(all_rule,[status(thm)],[])).
5.28/5.53	thf(4,plain,((~(sP7) | ~(sP5)) | sP2),inference(prop_rule,[status(thm)],[])).
5.28/5.53	thf(5,plain,((~(sP2) | ~(sP8)) | sP4),inference(prop_rule,[status(thm)],[])).
5.28/5.53	thf(fact_3_cont_I1_J,axiom,sP8).
5.28/5.53	thf(fact_2_cont_I2_J,axiom,sP5).
5.28/5.53	thf(fact_0_continuous__on__diff,axiom,sP6).
5.28/5.53	thf(6,plain,$false,inference(prop_unsat,[status(thm),assumptions([h1,h2,h0])],[1,2,3,4,5,h0,fact_3_cont_I1_J,fact_2_cont_I2_J,fact_0_continuous__on__diff])).
5.28/5.53	thf(fact_7__092_060open_062_092_060And_062thesis_O_A_I_092_060lbrakk_062f_Aintegrable__on_Acbox_Aa_Ab_059_Ag_Aintegrable__on_Acbox_Aa_Ab_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,(~((((hensto8291394388724566237n_real @ f) @ ((topolo4938530945907275839cbox_n @ a) @ b)) => (~(((hensto8291394388724566237n_real @ g) @ ((topolo4938530945907275839cbox_n @ a) @ b)))))))).
5.28/5.53	thf(7,plain,$false,inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[fact_7__092_060open_062_092_060And_062thesis_O_A_I_092_060lbrakk_062f_Aintegrable__on_Acbox_Aa_Ab_059_Ag_Aintegrable__on_Acbox_Aa_Ab_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,6,h1,h2])).
5.28/5.53	thf(0,theorem,sP4,inference(contra,[status(thm),contra(discharge,[h0])],[7,h0])).
5.28/5.53	% SZS output end Proof
5.28/5.53	EOF