0.07/0.13	% Problem  : SLH0107^1 : TPTP v8.2.0. Released v8.2.0.
0.07/0.14	% Command  : lash -P picomus -M modes -p tstp -t %d %s
0.14/0.36	% Computer : n002.cluster.edu
0.14/0.36	% Model    : x86_64 x86_64
0.14/0.36	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.14/0.36	% Memory   : 8042.1875MB
0.14/0.36	% OS       : Linux 3.10.0-693.el7.x86_64
0.14/0.36	% CPULimit : 30
0.14/0.36	% WCLimit  : 30
0.14/0.36	% DateTime : Mon Jul  3 03:48:07 EDT 2023
0.14/0.36	% CPUTime  : 
0.21/0.54	% SZS status Theorem
0.21/0.54	% Mode: cade22sinegrackle2x6978
0.21/0.54	% Steps: 958
0.21/0.54	% SZS output start Proof
0.21/0.54	thf(ty_real, type, real : $tType).
0.21/0.54	thf(ty_nat, type, nat : $tType).
0.21/0.54	thf(ty_d_nom, type, d_nom : (real>nat>real)).
0.21/0.54	thf(ty_zero_zero_real, type, zero_zero_real : real).
0.21/0.54	thf(ty_zero_zero_nat, type, zero_zero_nat : nat).
0.21/0.54	thf(ty_i, type, i : real).
0.21/0.54	thf(ty_m, type, m : nat).
0.21/0.54	thf(ty_i_nom, type, i_nom : (real>nat>real)).
0.21/0.54	thf(sP1,plain,sP1 <=> (![X1:nat]:((~((X1 = zero_zero_nat))) => ((((i_nom @ i) @ X1) = zero_zero_real) = (i = zero_zero_real)))),introduced(definition,[new_symbols(definition,[sP1])])).
0.21/0.54	thf(sP2,plain,sP2 <=> (((d_nom @ i) @ m) = zero_zero_real),introduced(definition,[new_symbols(definition,[sP2])])).
0.21/0.54	thf(sP3,plain,sP3 <=> (i = zero_zero_real),introduced(definition,[new_symbols(definition,[sP3])])).
0.21/0.54	thf(sP4,plain,sP4 <=> ((((i_nom @ i) @ m) = zero_zero_real) = sP3),introduced(definition,[new_symbols(definition,[sP4])])).
0.21/0.54	thf(sP5,plain,sP5 <=> (m = zero_zero_nat),introduced(definition,[new_symbols(definition,[sP5])])).
0.21/0.54	thf(sP6,plain,sP6 <=> ((~(sP5)) => sP4),introduced(definition,[new_symbols(definition,[sP6])])).
0.21/0.54	thf(sP7,plain,sP7 <=> (((i_nom @ i) @ m) = zero_zero_real),introduced(definition,[new_symbols(definition,[sP7])])).
0.21/0.54	thf(conj_0,conjecture,(sP2 = sP3)).
0.21/0.54	thf(h0,negated_conjecture,(~((sP2 = sP3))),inference(assume_negation,[status(cth)],[conj_0])).
0.21/0.54	thf(h1,assumption,sP2,introduced(assumption,[])).
0.21/0.54	thf(h2,assumption,sP3,introduced(assumption,[])).
0.21/0.54	thf(h3,assumption,(~(sP2)),introduced(assumption,[])).
0.21/0.54	thf(h4,assumption,(~(sP3)),introduced(assumption,[])).
0.21/0.54	thf(h5,assumption,sP7,introduced(assumption,[])).
0.21/0.54	thf(h6,assumption,(~(sP7)),introduced(assumption,[])).
0.21/0.54	thf(1,plain,((~(sP4) | ~(sP7)) | sP3),inference(prop_rule,[status(thm)],[])).
0.21/0.54	thf(2,plain,((~(sP6) | sP5) | sP4),inference(prop_rule,[status(thm)],[])).
0.21/0.54	thf(3,plain,(~(sP1) | sP6),inference(all_rule,[status(thm)],[])).
0.21/0.54	thf(fact_1_i__nom__0__iff__i__0,axiom,sP1).
0.21/0.54	thf(fact_0_that,axiom,(~(sP5))).
0.21/0.54	thf(4,plain,$false,inference(prop_unsat,[status(thm),assumptions([h1,h5,h1,h2,h0])],[1,2,3,h2,h5,fact_1_i__nom__0__iff__i__0,fact_0_that])).
0.21/0.54	thf(5,plain,$false,inference(tab_conflict,[status(thm),assumptions([h3,h6,h1,h2,h0])],[h1,h3])).
0.21/0.54	thf(fact_3__092_060open_062_I_Ed_094_123m_125_A_061_A0_J_A_061_A_I_Ei_094_123m_125_A_061_A0_J_092_060close_062,axiom,(sP2 = sP7)).
0.21/0.54	thf(6,plain,$false,inference(tab_bq,[status(thm),assumptions([h1,h2,h0]),tab_bq(discharge,[h1,h5]),tab_bq(discharge,[h3,h6])],[fact_3__092_060open_062_I_Ed_094_123m_125_A_061_A0_J_A_061_A_I_Ei_094_123m_125_A_061_A0_J_092_060close_062,4,5,h1,h5,h3,h6])).
0.21/0.54	thf(7,plain,$false,inference(tab_conflict,[status(thm),assumptions([h1,h5,h3,h4,h0])],[h1,h3])).
0.21/0.54	thf(8,plain,((~(sP4) | sP7) | ~(sP3)),inference(prop_rule,[status(thm)],[])).
0.21/0.54	thf(9,plain,((~(sP6) | sP5) | sP4),inference(prop_rule,[status(thm)],[])).
0.21/0.54	thf(10,plain,(~(sP1) | sP6),inference(all_rule,[status(thm)],[])).
0.21/0.54	thf(11,plain,$false,inference(prop_unsat,[status(thm),assumptions([h3,h6,h3,h4,h0])],[8,9,10,h4,h6,fact_1_i__nom__0__iff__i__0,fact_0_that])).
0.21/0.54	thf(12,plain,$false,inference(tab_bq,[status(thm),assumptions([h3,h4,h0]),tab_bq(discharge,[h1,h5]),tab_bq(discharge,[h3,h6])],[fact_3__092_060open_062_I_Ed_094_123m_125_A_061_A0_J_A_061_A_I_Ei_094_123m_125_A_061_A0_J_092_060close_062,7,11,h1,h5,h3,h6])).
0.21/0.54	thf(13,plain,$false,inference(tab_be,[status(thm),assumptions([h0]),tab_be(discharge,[h1,h2]),tab_be(discharge,[h3,h4])],[h0,6,12,h1,h2,h3,h4])).
0.21/0.54	thf(0,theorem,(sP2 = sP3),inference(contra,[status(thm),contra(discharge,[h0])],[13,h0])).
0.21/0.54	% SZS output end Proof
0.21/0.55	EOF