0.10/0.12	% Problem    : SLH0177^1 : TPTP v8.2.0. Released v8.2.0.
0.10/0.13	% Command    : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
0.14/0.33	Computer   : n014.cluster.edu
0.14/0.33	Model      : x86_64 x86_64
0.14/0.33	CPUModel   : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.14/0.33	RAMPerCPU  : 8042.1875MB
0.14/0.33	OS         : Linux 3.10.0-693.el7.x86_64
0.14/0.33	% CPULimit   : 30
0.14/0.34	% DateTime   : Mon Jul  3 03:42:24 EDT 2023
0.14/0.34	% CPUTime    : 
5.92/6.14	% SZS status Theorem
5.92/6.14	% Mode: mode507:USE_SINE=true:SINE_TOLERANCE=3.0:SINE_GENERALITY_THRESHOLD=0:SINE_RANK_LIMIT=1.:SINE_DEPTH=1
5.92/6.14	% Inferences: 403
5.92/6.14	% SZS output start Proof
5.92/6.14	thf(ty_a, type, a : $tType).
5.92/6.14	thf(ty_real, type, real : $tType).
5.92/6.14	thf(ty_zero_zero_real, type, zero_zero_real : real).
5.92/6.14	thf(ty_plus_plus_real, type, plus_plus_real : (real>real>real)).
5.92/6.14	thf(ty_eigen__0, type, eigen__0 : a).
5.92/6.14	thf(ty_f2, type, f2 : (a>real)).
5.92/6.14	thf(sP1,plain,sP1 <=> (((plus_plus_real @ (f2 @ eigen__0)) @ zero_zero_real) = (f2 @ eigen__0)),introduced(definition,[new_symbols(definition,[sP1])])).
5.92/6.14	thf(sP2,plain,sP2 <=> (![X1:real]:((((plus_plus_real @ (f2 @ eigen__0)) @ zero_zero_real) = X1) => (X1 = ((plus_plus_real @ (f2 @ eigen__0)) @ zero_zero_real)))),introduced(definition,[new_symbols(definition,[sP2])])).
5.92/6.14	thf(sP3,plain,sP3 <=> ((f2 @ eigen__0) = ((plus_plus_real @ (f2 @ eigen__0)) @ zero_zero_real)),introduced(definition,[new_symbols(definition,[sP3])])).
5.92/6.14	thf(sP4,plain,sP4 <=> (![X1:real]:(![X2:real]:((X1 = X2) => (X2 = X1)))),introduced(definition,[new_symbols(definition,[sP4])])).
5.92/6.14	thf(sP5,plain,sP5 <=> (sP1 => sP3),introduced(definition,[new_symbols(definition,[sP5])])).
5.92/6.14	thf(sP6,plain,sP6 <=> (![X1:real]:(((plus_plus_real @ X1) @ zero_zero_real) = X1)),introduced(definition,[new_symbols(definition,[sP6])])).
5.92/6.14	thf(conj_0,conjecture,(f2 = (^[X1:a]:((plus_plus_real @ (f2 @ X1)) @ zero_zero_real)))).
5.92/6.14	thf(h0,negated_conjecture,(~((f2 = (^[X1:a]:((plus_plus_real @ (f2 @ X1)) @ zero_zero_real))))),inference(assume_negation,[status(cth)],[conj_0])).
5.92/6.14	thf(h1,assumption,(~((![X1:a]:((f2 @ X1) = ((plus_plus_real @ (f2 @ X1)) @ zero_zero_real))))),introduced(assumption,[])).
5.92/6.14	thf(h2,assumption,(~(sP3)),introduced(assumption,[])).
5.92/6.14	thf(1,plain,(~(sP6) | sP1),inference(all_rule,[status(thm)],[])).
5.92/6.14	thf(2,plain,((~(sP5) | ~(sP1)) | sP3),inference(prop_rule,[status(thm)],[])).
5.92/6.14	thf(3,plain,(~(sP2) | sP5),inference(all_rule,[status(thm)],[])).
5.92/6.14	thf(4,plain,(~(sP4) | sP2),inference(all_rule,[status(thm)],[])).
5.92/6.14	thf(5,plain,sP4,inference(@eq_sym,[status(thm)],[])).
5.92/6.14	thf(fact_0_add_Oright__neutral,axiom,sP6).
5.92/6.14	thf(6,plain,$false,inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,4,5,h2,fact_0_add_Oright__neutral])).
5.92/6.14	thf(7,plain,$false,inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,6,h2])).
5.92/6.14	thf(8,plain,$false,inference(tab_fe,[status(thm),assumptions([h0]),tab_fe(discharge,[h1])],[h0,7,h1])).
5.92/6.14	thf(0,theorem,(f2 = (^[X1:a]:((plus_plus_real @ (f2 @ X1)) @ zero_zero_real))),inference(contra,[status(thm),contra(discharge,[h0])],[8,h0])).
5.92/6.14	% SZS output end Proof
5.92/6.15	EOF