TSTP Solution File: ITP018^2 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP018^2 : TPTP v8.1.0. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n025.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 00:28:37 EDT 2022
% Result : Theorem 77.70s 77.71s
% Output : Proof 77.70s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : ITP018^2 : TPTP v8.1.0. Bugfixed v7.5.0.
% 0.10/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.14/0.33 % Computer : n025.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 600
% 0.14/0.33 % DateTime : Thu Jun 2 21:21:45 EDT 2022
% 0.14/0.33 % CPUTime :
% 77.70/77.71 % SZS status Theorem
% 77.70/77.71 % Mode: mode484
% 77.70/77.71 % Inferences: 148
% 77.70/77.71 % SZS output start Proof
% 77.70/77.71 thf(ty_del, type, del : $tType).
% 77.70/77.71 thf(ty_tp__ty_2Erealax_2Ereal, type, tp__ty_2Erealax_2Ereal : $tType).
% 77.70/77.71 thf(ty_c_2Ebinary__ieee_2Efloat__to__real, type, c_2Ebinary__ieee_2Efloat__to__real : (del>del>$i)).
% 77.70/77.71 thf(ty_eigen__1, type, eigen__1 : del).
% 77.70/77.71 thf(ty_c_2Ebinary__ieee_2Eulp, type, c_2Ebinary__ieee_2Eulp : (del>del>$i)).
% 77.70/77.71 thf(ty_c_2Ebinary__ieee_2Efloat__negate, type, c_2Ebinary__ieee_2Efloat__negate : (del>del>$i)).
% 77.70/77.71 thf(ty_eigen__0, type, eigen__0 : del).
% 77.70/77.71 thf(ty_surj__ty_2Erealax_2Ereal, type, surj__ty_2Erealax_2Ereal : ($i>tp__ty_2Erealax_2Ereal)).
% 77.70/77.71 thf(ty_c_2Ebinary__ieee_2Efloat__plus__min, type, c_2Ebinary__ieee_2Efloat__plus__min : (del>del>$i)).
% 77.70/77.71 thf(ty_ap, type, ap : ($i>$i>$i)).
% 77.70/77.71 thf(ty_ty_2Epair_2Eprod, type, ty_2Epair_2Eprod : (del>del>del)).
% 77.70/77.71 thf(ty_c_2Ebool_2Ethe__value, type, c_2Ebool_2Ethe__value : (del>$i)).
% 77.70/77.71 thf(ty_c_2Erealax_2Ereal__neg, type, c_2Erealax_2Ereal__neg : $i).
% 77.70/77.71 thf(conj_thm_2Ebinary__ieee_2Eneg__ulp,conjecture,(![X1:del]:(![X2:del]:((surj__ty_2Erealax_2Ereal @ ((ap @ c_2Erealax_2Ereal__neg) @ ((ap @ ((c_2Ebinary__ieee_2Eulp @ X1) @ X2)) @ (c_2Ebool_2Ethe__value @ ((ty_2Epair_2Eprod @ X1) @ X2))))) = (surj__ty_2Erealax_2Ereal @ ((ap @ ((c_2Ebinary__ieee_2Efloat__to__real @ X1) @ X2)) @ ((ap @ ((c_2Ebinary__ieee_2Efloat__negate @ X1) @ X2)) @ ((ap @ ((c_2Ebinary__ieee_2Efloat__plus__min @ X1) @ X2)) @ (c_2Ebool_2Ethe__value @ ((ty_2Epair_2Eprod @ X1) @ X2)))))))))).
% 77.70/77.71 thf(h0,negated_conjecture,(~((![X1:del]:(![X2:del]:((surj__ty_2Erealax_2Ereal @ ((ap @ c_2Erealax_2Ereal__neg) @ ((ap @ ((c_2Ebinary__ieee_2Eulp @ X1) @ X2)) @ (c_2Ebool_2Ethe__value @ ((ty_2Epair_2Eprod @ X1) @ X2))))) = (surj__ty_2Erealax_2Ereal @ ((ap @ ((c_2Ebinary__ieee_2Efloat__to__real @ X1) @ X2)) @ ((ap @ ((c_2Ebinary__ieee_2Efloat__negate @ X1) @ X2)) @ ((ap @ ((c_2Ebinary__ieee_2Efloat__plus__min @ X1) @ X2)) @ (c_2Ebool_2Ethe__value @ ((ty_2Epair_2Eprod @ X1) @ X2))))))))))),inference(assume_negation,[status(cth)],[conj_thm_2Ebinary__ieee_2Eneg__ulp])).
% 77.70/77.71 thf(h1,assumption,(~((![X1:del]:((surj__ty_2Erealax_2Ereal @ ((ap @ c_2Erealax_2Ereal__neg) @ ((ap @ ((c_2Ebinary__ieee_2Eulp @ eigen__0) @ X1)) @ (c_2Ebool_2Ethe__value @ ((ty_2Epair_2Eprod @ eigen__0) @ X1))))) = (surj__ty_2Erealax_2Ereal @ ((ap @ ((c_2Ebinary__ieee_2Efloat__to__real @ eigen__0) @ X1)) @ ((ap @ ((c_2Ebinary__ieee_2Efloat__negate @ eigen__0) @ X1)) @ ((ap @ ((c_2Ebinary__ieee_2Efloat__plus__min @ eigen__0) @ X1)) @ (c_2Ebool_2Ethe__value @ ((ty_2Epair_2Eprod @ eigen__0) @ X1)))))))))),introduced(assumption,[])).
% 77.70/77.71 thf(h2,assumption,(~(((surj__ty_2Erealax_2Ereal @ ((ap @ c_2Erealax_2Ereal__neg) @ ((ap @ ((c_2Ebinary__ieee_2Eulp @ eigen__0) @ eigen__1)) @ (c_2Ebool_2Ethe__value @ ((ty_2Epair_2Eprod @ eigen__0) @ eigen__1))))) = (surj__ty_2Erealax_2Ereal @ ((ap @ ((c_2Ebinary__ieee_2Efloat__to__real @ eigen__0) @ eigen__1)) @ ((ap @ ((c_2Ebinary__ieee_2Efloat__negate @ eigen__0) @ eigen__1)) @ ((ap @ ((c_2Ebinary__ieee_2Efloat__plus__min @ eigen__0) @ eigen__1)) @ (c_2Ebool_2Ethe__value @ ((ty_2Epair_2Eprod @ eigen__0) @ eigen__1))))))))),introduced(assumption,[])).
% 77.70/77.71 thf(pax20, axiom, (p20=>![X100:tp__ty_2Erealax_2Ereal]:(fsurj__ty_2Erealax_2Ereal @ (finj__ty_2Erealax_2Ereal @ X100))=(X100)), file('<stdin>', pax20)).
% 77.70/77.71 thf(pax16, axiom, (p16=>![X102:tp__ty_2Erealax_2Ereal]:(finj__ty_2Erealax_2Ereal @ (ffo__c_2Erealax_2Ereal__neg @ X102))=(fap @ fc_2Erealax_2Ereal__neg @ (finj__ty_2Erealax_2Ereal @ X102))), file('<stdin>', pax16)).
% 77.70/77.71 thf(ax1492, axiom, p20, file('<stdin>', ax1492)).
% 77.70/77.71 thf(ax1496, axiom, p16, file('<stdin>', ax1496)).
% 77.70/77.71 thf(pax18, axiom, (p18=>![X101:$i]:(fmem @ X101 @ fty_2Erealax_2Ereal=>(X101)=(finj__ty_2Erealax_2Ereal @ (fsurj__ty_2Erealax_2Ereal @ X101)))), file('<stdin>', pax18)).
% 77.70/77.71 thf(nax1, axiom, (p1<=(fsurj__ty_2Erealax_2Ereal @ (fap @ fc_2Erealax_2Ereal__neg @ (fap @ (fc_2Ebinary__ieee_2Eulp @ f__0 @ f__1) @ (fc_2Ebool_2Ethe__value @ (fty_2Epair_2Eprod @ f__0 @ f__1)))))=(fsurj__ty_2Erealax_2Ereal @ (fap @ (fc_2Ebinary__ieee_2Efloat__to__real @ f__0 @ f__1) @ (fap @ (fc_2Ebinary__ieee_2Efloat__negate @ f__0 @ f__1) @ (fap @ (fc_2Ebinary__ieee_2Efloat__plus__min @ f__0 @ f__1) @ (fc_2Ebool_2Ethe__value @ (fty_2Epair_2Eprod @ f__0 @ f__1))))))), file('<stdin>', nax1)).
% 77.70/77.71 thf(ax1511, axiom, ~(p1), file('<stdin>', ax1511)).
% 77.70/77.71 thf(pax4, axiom, (p4=>![X103:del, X104:del, X97:$i]:(fmem @ X97 @ (fty_2Ebinary__ieee_2Efloat @ X103 @ X104)=>(fsurj__ty_2Erealax_2Ereal @ (fap @ (fc_2Ebinary__ieee_2Efloat__to__real @ X103 @ X104) @ (fap @ (fc_2Ebinary__ieee_2Efloat__negate @ X103 @ X104) @ X97)))=(fsurj__ty_2Erealax_2Ereal @ (fap @ fc_2Erealax_2Ereal__neg @ (fap @ (fc_2Ebinary__ieee_2Efloat__to__real @ X103 @ X104) @ X97))))), file('<stdin>', pax4)).
% 77.70/77.71 thf(ax1494, axiom, p18, file('<stdin>', ax1494)).
% 77.70/77.71 thf(pax3, axiom, (p3=>![X103:del, X104:del]:(fsurj__ty_2Erealax_2Ereal @ (fap @ (fc_2Ebinary__ieee_2Eulp @ X103 @ X104) @ (fc_2Ebool_2Ethe__value @ (fty_2Epair_2Eprod @ X103 @ X104))))=(fsurj__ty_2Erealax_2Ereal @ (fap @ (fc_2Ebinary__ieee_2Efloat__to__real @ X103 @ X104) @ (fap @ (fc_2Ebinary__ieee_2Efloat__plus__min @ X103 @ X104) @ (fc_2Ebool_2Ethe__value @ (fty_2Epair_2Eprod @ X103 @ X104)))))), file('<stdin>', pax3)).
% 77.70/77.71 thf(pax24, axiom, (p24=>![X94:del, X95:del, X5:$i]:(fmem @ X5 @ (farr @ X94 @ X95)=>![X6:$i]:(fmem @ X6 @ X94=>fmem @ (fap @ X5 @ X6) @ X95))), file('<stdin>', pax24)).
% 77.70/77.71 thf(pax13, axiom, (p13=>![X103:del, X104:del]:fmem @ (fc_2Ebinary__ieee_2Efloat__to__real @ X103 @ X104) @ (farr @ (fty_2Ebinary__ieee_2Efloat @ X103 @ X104) @ fty_2Erealax_2Ereal)), file('<stdin>', pax13)).
% 77.70/77.71 thf(ax1508, axiom, p4, file('<stdin>', ax1508)).
% 77.70/77.71 thf(ax1509, axiom, p3, file('<stdin>', ax1509)).
% 77.70/77.71 thf(ax1488, axiom, p24, file('<stdin>', ax1488)).
% 77.70/77.71 thf(ax1499, axiom, p13, file('<stdin>', ax1499)).
% 77.70/77.71 thf(pax14, axiom, (p14=>![X103:del, X104:del]:fmem @ (fc_2Ebinary__ieee_2Efloat__plus__min @ X103 @ X104) @ (farr @ (fty_2Ebool_2Eitself @ (fty_2Epair_2Eprod @ X103 @ X104)) @ (fty_2Ebinary__ieee_2Efloat @ X103 @ X104))), file('<stdin>', pax14)).
% 77.70/77.71 thf(ax1498, axiom, p14, file('<stdin>', ax1498)).
% 77.70/77.71 thf(pax12, axiom, (p12=>![X103:del]:fmem @ (fc_2Ebool_2Ethe__value @ X103) @ (fty_2Ebool_2Eitself @ X103)), file('<stdin>', pax12)).
% 77.70/77.71 thf(pax11, axiom, (p11=>![X103:del, X104:del]:fmem @ (fc_2Ebinary__ieee_2Eulp @ X103 @ X104) @ (farr @ (fty_2Ebool_2Eitself @ (fty_2Epair_2Eprod @ X103 @ X104)) @ fty_2Erealax_2Ereal)), file('<stdin>', pax11)).
% 77.70/77.71 thf(ax1500, axiom, p12, file('<stdin>', ax1500)).
% 77.70/77.71 thf(ax1501, axiom, p11, file('<stdin>', ax1501)).
% 77.70/77.71 thf(c_0_22, plain, ![X1017:tp__ty_2Erealax_2Ereal]:(~p20|(fsurj__ty_2Erealax_2Ereal @ (finj__ty_2Erealax_2Ereal @ X1017))=(X1017)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax20])])])).
% 77.70/77.71 thf(c_0_23, plain, ![X1023:tp__ty_2Erealax_2Ereal]:(~p16|(finj__ty_2Erealax_2Ereal @ (ffo__c_2Erealax_2Ereal__neg @ X1023))=(fap @ fc_2Erealax_2Ereal__neg @ (finj__ty_2Erealax_2Ereal @ X1023))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax16])])])).
% 77.70/77.71 thf(c_0_24, plain, ![X92:tp__ty_2Erealax_2Ereal]:((fsurj__ty_2Erealax_2Ereal @ (finj__ty_2Erealax_2Ereal @ X92))=(X92)|~p20), inference(split_conjunct,[status(thm)],[c_0_22])).
% 77.70/77.71 thf(c_0_25, plain, p20, inference(split_conjunct,[status(thm)],[ax1492])).
% 77.70/77.71 thf(c_0_26, plain, ![X92:tp__ty_2Erealax_2Ereal]:((finj__ty_2Erealax_2Ereal @ (ffo__c_2Erealax_2Ereal__neg @ X92))=(fap @ fc_2Erealax_2Ereal__neg @ (finj__ty_2Erealax_2Ereal @ X92))|~p16), inference(split_conjunct,[status(thm)],[c_0_23])).
% 77.70/77.71 thf(c_0_27, plain, p16, inference(split_conjunct,[status(thm)],[ax1496])).
% 77.70/77.71 thf(c_0_28, plain, ![X1021:$i]:(~p18|(~fmem @ X1021 @ fty_2Erealax_2Ereal|(X1021)=(finj__ty_2Erealax_2Ereal @ (fsurj__ty_2Erealax_2Ereal @ X1021)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax18])])])).
% 77.70/77.71 thf(c_0_29, plain, ((fsurj__ty_2Erealax_2Ereal @ (fap @ fc_2Erealax_2Ereal__neg @ (fap @ (fc_2Ebinary__ieee_2Eulp @ f__0 @ f__1) @ (fc_2Ebool_2Ethe__value @ (fty_2Epair_2Eprod @ f__0 @ f__1)))))!=(fsurj__ty_2Erealax_2Ereal @ (fap @ (fc_2Ebinary__ieee_2Efloat__to__real @ f__0 @ f__1) @ (fap @ (fc_2Ebinary__ieee_2Efloat__negate @ f__0 @ f__1) @ (fap @ (fc_2Ebinary__ieee_2Efloat__plus__min @ f__0 @ f__1) @ (fc_2Ebool_2Ethe__value @ (fty_2Epair_2Eprod @ f__0 @ f__1))))))|p1), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax1])])).
% 77.70/77.71 thf(c_0_30, plain, ~p1, inference(fof_simplification,[status(thm)],[ax1511])).
% 77.70/77.71 thf(c_0_31, plain, ![X1047:del, X1048:del, X1049:$i]:(~p4|(~fmem @ X1049 @ (fty_2Ebinary__ieee_2Efloat @ X1047 @ X1048)|(fsurj__ty_2Erealax_2Ereal @ (fap @ (fc_2Ebinary__ieee_2Efloat__to__real @ X1047 @ X1048) @ (fap @ (fc_2Ebinary__ieee_2Efloat__negate @ X1047 @ X1048) @ X1049)))=(fsurj__ty_2Erealax_2Ereal @ (fap @ fc_2Erealax_2Ereal__neg @ (fap @ (fc_2Ebinary__ieee_2Efloat__to__real @ X1047 @ X1048) @ X1049))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax4])])])).
% 77.70/77.71 thf(c_0_32, plain, ![X92:tp__ty_2Erealax_2Ereal]:(fsurj__ty_2Erealax_2Ereal @ (finj__ty_2Erealax_2Ereal @ X92))=(X92), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_24, c_0_25])])).
% 77.70/77.71 thf(c_0_33, plain, ![X92:tp__ty_2Erealax_2Ereal]:(finj__ty_2Erealax_2Ereal @ (ffo__c_2Erealax_2Ereal__neg @ X92))=(fap @ fc_2Erealax_2Ereal__neg @ (finj__ty_2Erealax_2Ereal @ X92)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_26, c_0_27])])).
% 77.70/77.71 thf(c_0_34, plain, ![X3:$i]:((X3)=(finj__ty_2Erealax_2Ereal @ (fsurj__ty_2Erealax_2Ereal @ X3))|~p18|~fmem @ X3 @ fty_2Erealax_2Ereal), inference(split_conjunct,[status(thm)],[c_0_28])).
% 77.70/77.71 thf(c_0_35, plain, p18, inference(split_conjunct,[status(thm)],[ax1494])).
% 77.70/77.71 thf(c_0_36, plain, ![X1053:del, X1054:del]:(~p3|(fsurj__ty_2Erealax_2Ereal @ (fap @ (fc_2Ebinary__ieee_2Eulp @ X1053 @ X1054) @ (fc_2Ebool_2Ethe__value @ (fty_2Epair_2Eprod @ X1053 @ X1054))))=(fsurj__ty_2Erealax_2Ereal @ (fap @ (fc_2Ebinary__ieee_2Efloat__to__real @ X1053 @ X1054) @ (fap @ (fc_2Ebinary__ieee_2Efloat__plus__min @ X1053 @ X1054) @ (fc_2Ebool_2Ethe__value @ (fty_2Epair_2Eprod @ X1053 @ X1054)))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax3])])])).
% 77.70/77.71 thf(c_0_37, plain, ![X985:del, X986:del, X987:$i, X988:$i]:(~p24|(~fmem @ X987 @ (farr @ X985 @ X986)|(~fmem @ X988 @ X985|fmem @ (fap @ X987 @ X988) @ X986))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax24])])])).
% 77.70/77.71 thf(c_0_38, plain, ![X1033:del, X1034:del]:(~p13|fmem @ (fc_2Ebinary__ieee_2Efloat__to__real @ X1033 @ X1034) @ (farr @ (fty_2Ebinary__ieee_2Efloat @ X1033 @ X1034) @ fty_2Erealax_2Ereal)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax13])])])).
% 77.70/77.71 thf(c_0_39, plain, (p1|(fsurj__ty_2Erealax_2Ereal @ (fap @ fc_2Erealax_2Ereal__neg @ (fap @ (fc_2Ebinary__ieee_2Eulp @ f__0 @ f__1) @ (fc_2Ebool_2Ethe__value @ (fty_2Epair_2Eprod @ f__0 @ f__1)))))!=(fsurj__ty_2Erealax_2Ereal @ (fap @ (fc_2Ebinary__ieee_2Efloat__to__real @ f__0 @ f__1) @ (fap @ (fc_2Ebinary__ieee_2Efloat__negate @ f__0 @ f__1) @ (fap @ (fc_2Ebinary__ieee_2Efloat__plus__min @ f__0 @ f__1) @ (fc_2Ebool_2Ethe__value @ (fty_2Epair_2Eprod @ f__0 @ f__1))))))), inference(split_conjunct,[status(thm)],[c_0_29])).
% 77.70/77.71 thf(c_0_40, plain, ~p1, inference(split_conjunct,[status(thm)],[c_0_30])).
% 77.70/77.71 thf(c_0_41, plain, ![X1:del, X3:$i, X4:del]:((fsurj__ty_2Erealax_2Ereal @ (fap @ (fc_2Ebinary__ieee_2Efloat__to__real @ X1 @ X4) @ (fap @ (fc_2Ebinary__ieee_2Efloat__negate @ X1 @ X4) @ X3)))=(fsurj__ty_2Erealax_2Ereal @ (fap @ fc_2Erealax_2Ereal__neg @ (fap @ (fc_2Ebinary__ieee_2Efloat__to__real @ X1 @ X4) @ X3)))|~p4|~fmem @ X3 @ (fty_2Ebinary__ieee_2Efloat @ X1 @ X4)), inference(split_conjunct,[status(thm)],[c_0_31])).
% 77.70/77.71 thf(c_0_42, plain, p4, inference(split_conjunct,[status(thm)],[ax1508])).
% 77.70/77.71 thf(c_0_43, plain, ![X92:tp__ty_2Erealax_2Ereal]:(fsurj__ty_2Erealax_2Ereal @ (fap @ fc_2Erealax_2Ereal__neg @ (finj__ty_2Erealax_2Ereal @ X92)))=(ffo__c_2Erealax_2Ereal__neg @ X92), inference(spm,[status(thm)],[c_0_32, c_0_33])).
% 77.70/77.71 thf(c_0_44, plain, ![X3:$i]:((finj__ty_2Erealax_2Ereal @ (fsurj__ty_2Erealax_2Ereal @ X3))=(X3)|~fmem @ X3 @ fty_2Erealax_2Ereal), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_34, c_0_35])])).
% 77.70/77.71 thf(c_0_45, plain, ![X1:del, X4:del]:((fsurj__ty_2Erealax_2Ereal @ (fap @ (fc_2Ebinary__ieee_2Eulp @ X1 @ X4) @ (fc_2Ebool_2Ethe__value @ (fty_2Epair_2Eprod @ X1 @ X4))))=(fsurj__ty_2Erealax_2Ereal @ (fap @ (fc_2Ebinary__ieee_2Efloat__to__real @ X1 @ X4) @ (fap @ (fc_2Ebinary__ieee_2Efloat__plus__min @ X1 @ X4) @ (fc_2Ebool_2Ethe__value @ (fty_2Epair_2Eprod @ X1 @ X4)))))|~p3), inference(split_conjunct,[status(thm)],[c_0_36])).
% 77.70/77.71 thf(c_0_46, plain, p3, inference(split_conjunct,[status(thm)],[ax1509])).
% 77.70/77.71 thf(c_0_47, plain, ![X3:$i, X5:$i, X4:del, X1:del]:(fmem @ (fap @ X3 @ X5) @ X4|~p24|~fmem @ X3 @ (farr @ X1 @ X4)|~fmem @ X5 @ X1), inference(split_conjunct,[status(thm)],[c_0_37])).
% 77.70/77.71 thf(c_0_48, plain, p24, inference(split_conjunct,[status(thm)],[ax1488])).
% 77.70/77.71 thf(c_0_49, plain, ![X1:del, X4:del]:(fmem @ (fc_2Ebinary__ieee_2Efloat__to__real @ X1 @ X4) @ (farr @ (fty_2Ebinary__ieee_2Efloat @ X1 @ X4) @ fty_2Erealax_2Ereal)|~p13), inference(split_conjunct,[status(thm)],[c_0_38])).
% 77.70/77.71 thf(c_0_50, plain, p13, inference(split_conjunct,[status(thm)],[ax1499])).
% 77.70/77.71 thf(c_0_51, plain, (fsurj__ty_2Erealax_2Ereal @ (fap @ (fc_2Ebinary__ieee_2Efloat__to__real @ f__0 @ f__1) @ (fap @ (fc_2Ebinary__ieee_2Efloat__negate @ f__0 @ f__1) @ (fap @ (fc_2Ebinary__ieee_2Efloat__plus__min @ f__0 @ f__1) @ (fc_2Ebool_2Ethe__value @ (fty_2Epair_2Eprod @ f__0 @ f__1))))))!=(fsurj__ty_2Erealax_2Ereal @ (fap @ fc_2Erealax_2Ereal__neg @ (fap @ (fc_2Ebinary__ieee_2Eulp @ f__0 @ f__1) @ (fc_2Ebool_2Ethe__value @ (fty_2Epair_2Eprod @ f__0 @ f__1))))), inference(sr,[status(thm)],[c_0_39, c_0_40])).
% 77.70/77.71 thf(c_0_52, plain, ![X1:del, X3:$i, X4:del]:((fsurj__ty_2Erealax_2Ereal @ (fap @ (fc_2Ebinary__ieee_2Efloat__to__real @ X1 @ X4) @ (fap @ (fc_2Ebinary__ieee_2Efloat__negate @ X1 @ X4) @ X3)))=(fsurj__ty_2Erealax_2Ereal @ (fap @ fc_2Erealax_2Ereal__neg @ (fap @ (fc_2Ebinary__ieee_2Efloat__to__real @ X1 @ X4) @ X3)))|~fmem @ X3 @ (fty_2Ebinary__ieee_2Efloat @ X1 @ X4)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_41, c_0_42])])).
% 77.70/77.71 thf(c_0_53, plain, ![X3:$i]:((ffo__c_2Erealax_2Ereal__neg @ (fsurj__ty_2Erealax_2Ereal @ X3))=(fsurj__ty_2Erealax_2Ereal @ (fap @ fc_2Erealax_2Ereal__neg @ X3))|~fmem @ X3 @ fty_2Erealax_2Ereal), inference(spm,[status(thm)],[c_0_43, c_0_44])).
% 77.70/77.71 thf(c_0_54, plain, ![X1:del, X4:del]:(fsurj__ty_2Erealax_2Ereal @ (fap @ (fc_2Ebinary__ieee_2Efloat__to__real @ X1 @ X4) @ (fap @ (fc_2Ebinary__ieee_2Efloat__plus__min @ X1 @ X4) @ (fc_2Ebool_2Ethe__value @ (fty_2Epair_2Eprod @ X1 @ X4)))))=(fsurj__ty_2Erealax_2Ereal @ (fap @ (fc_2Ebinary__ieee_2Eulp @ X1 @ X4) @ (fc_2Ebool_2Ethe__value @ (fty_2Epair_2Eprod @ X1 @ X4)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_45, c_0_46])])).
% 77.70/77.71 thf(c_0_55, plain, ![X1:del, X3:$i, X5:$i, X4:del]:(fmem @ (fap @ X3 @ X5) @ X1|~fmem @ X3 @ (farr @ X4 @ X1)|~fmem @ X5 @ X4), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_47, c_0_48])])).
% 77.70/77.71 thf(c_0_56, plain, ![X1:del, X4:del]:fmem @ (fc_2Ebinary__ieee_2Efloat__to__real @ X1 @ X4) @ (farr @ (fty_2Ebinary__ieee_2Efloat @ X1 @ X4) @ fty_2Erealax_2Ereal), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_49, c_0_50])])).
% 77.70/77.71 thf(c_0_57, plain, ![X1029:del, X1030:del]:(~p14|fmem @ (fc_2Ebinary__ieee_2Efloat__plus__min @ X1029 @ X1030) @ (farr @ (fty_2Ebool_2Eitself @ (fty_2Epair_2Eprod @ X1029 @ X1030)) @ (fty_2Ebinary__ieee_2Efloat @ X1029 @ X1030))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax14])])])).
% 77.70/77.71 thf(c_0_58, plain, ((fsurj__ty_2Erealax_2Ereal @ (fap @ fc_2Erealax_2Ereal__neg @ (fap @ (fc_2Ebinary__ieee_2Efloat__to__real @ f__0 @ f__1) @ (fap @ (fc_2Ebinary__ieee_2Efloat__plus__min @ f__0 @ f__1) @ (fc_2Ebool_2Ethe__value @ (fty_2Epair_2Eprod @ f__0 @ f__1))))))!=(fsurj__ty_2Erealax_2Ereal @ (fap @ fc_2Erealax_2Ereal__neg @ (fap @ (fc_2Ebinary__ieee_2Eulp @ f__0 @ f__1) @ (fc_2Ebool_2Ethe__value @ (fty_2Epair_2Eprod @ f__0 @ f__1)))))|~fmem @ (fap @ (fc_2Ebinary__ieee_2Efloat__plus__min @ f__0 @ f__1) @ (fc_2Ebool_2Ethe__value @ (fty_2Epair_2Eprod @ f__0 @ f__1))) @ (fty_2Ebinary__ieee_2Efloat @ f__0 @ f__1)), inference(spm,[status(thm)],[c_0_51, c_0_52])).
% 77.70/77.71 thf(c_0_59, plain, ![X1:del, X4:del]:((fsurj__ty_2Erealax_2Ereal @ (fap @ fc_2Erealax_2Ereal__neg @ (fap @ (fc_2Ebinary__ieee_2Efloat__to__real @ X1 @ X4) @ (fap @ (fc_2Ebinary__ieee_2Efloat__plus__min @ X1 @ X4) @ (fc_2Ebool_2Ethe__value @ (fty_2Epair_2Eprod @ X1 @ X4))))))=(ffo__c_2Erealax_2Ereal__neg @ (fsurj__ty_2Erealax_2Ereal @ (fap @ (fc_2Ebinary__ieee_2Eulp @ X1 @ X4) @ (fc_2Ebool_2Ethe__value @ (fty_2Epair_2Eprod @ X1 @ X4)))))|~fmem @ (fap @ (fc_2Ebinary__ieee_2Efloat__to__real @ X1 @ X4) @ (fap @ (fc_2Ebinary__ieee_2Efloat__plus__min @ X1 @ X4) @ (fc_2Ebool_2Ethe__value @ (fty_2Epair_2Eprod @ X1 @ X4)))) @ fty_2Erealax_2Ereal), inference(spm,[status(thm)],[c_0_53, c_0_54])).
% 77.70/77.71 thf(c_0_60, plain, ![X1:del, X3:$i, X4:del]:(fmem @ (fap @ (fc_2Ebinary__ieee_2Efloat__to__real @ X1 @ X4) @ X3) @ fty_2Erealax_2Ereal|~fmem @ X3 @ (fty_2Ebinary__ieee_2Efloat @ X1 @ X4)), inference(spm,[status(thm)],[c_0_55, c_0_56])).
% 77.70/77.71 thf(c_0_61, plain, ![X1:del, X4:del]:(fmem @ (fc_2Ebinary__ieee_2Efloat__plus__min @ X1 @ X4) @ (farr @ (fty_2Ebool_2Eitself @ (fty_2Epair_2Eprod @ X1 @ X4)) @ (fty_2Ebinary__ieee_2Efloat @ X1 @ X4))|~p14), inference(split_conjunct,[status(thm)],[c_0_57])).
% 77.70/77.71 thf(c_0_62, plain, p14, inference(split_conjunct,[status(thm)],[ax1498])).
% 77.70/77.71 thf(c_0_63, plain, ![X1037:del]:(~p12|fmem @ (fc_2Ebool_2Ethe__value @ X1037) @ (fty_2Ebool_2Eitself @ X1037)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax12])])])).
% 77.70/77.71 thf(c_0_64, plain, ![X1039:del, X1040:del]:(~p11|fmem @ (fc_2Ebinary__ieee_2Eulp @ X1039 @ X1040) @ (farr @ (fty_2Ebool_2Eitself @ (fty_2Epair_2Eprod @ X1039 @ X1040)) @ fty_2Erealax_2Ereal)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax11])])])).
% 77.70/77.71 thf(c_0_65, plain, ((ffo__c_2Erealax_2Ereal__neg @ (fsurj__ty_2Erealax_2Ereal @ (fap @ (fc_2Ebinary__ieee_2Eulp @ f__0 @ f__1) @ (fc_2Ebool_2Ethe__value @ (fty_2Epair_2Eprod @ f__0 @ f__1)))))!=(fsurj__ty_2Erealax_2Ereal @ (fap @ fc_2Erealax_2Ereal__neg @ (fap @ (fc_2Ebinary__ieee_2Eulp @ f__0 @ f__1) @ (fc_2Ebool_2Ethe__value @ (fty_2Epair_2Eprod @ f__0 @ f__1)))))|~fmem @ (fap @ (fc_2Ebinary__ieee_2Efloat__plus__min @ f__0 @ f__1) @ (fc_2Ebool_2Ethe__value @ (fty_2Epair_2Eprod @ f__0 @ f__1))) @ (fty_2Ebinary__ieee_2Efloat @ f__0 @ f__1)), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_58, c_0_59]), c_0_60])).
% 77.70/77.71 thf(c_0_66, plain, ![X1:del, X4:del]:fmem @ (fc_2Ebinary__ieee_2Efloat__plus__min @ X1 @ X4) @ (farr @ (fty_2Ebool_2Eitself @ (fty_2Epair_2Eprod @ X1 @ X4)) @ (fty_2Ebinary__ieee_2Efloat @ X1 @ X4)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_61, c_0_62])])).
% 77.70/77.71 thf(c_0_67, plain, ![X1:del]:(fmem @ (fc_2Ebool_2Ethe__value @ X1) @ (fty_2Ebool_2Eitself @ X1)|~p12), inference(split_conjunct,[status(thm)],[c_0_63])).
% 77.70/77.71 thf(c_0_68, plain, p12, inference(split_conjunct,[status(thm)],[ax1500])).
% 77.70/77.71 thf(c_0_69, plain, ![X1:del, X4:del]:(fmem @ (fc_2Ebinary__ieee_2Eulp @ X1 @ X4) @ (farr @ (fty_2Ebool_2Eitself @ (fty_2Epair_2Eprod @ X1 @ X4)) @ fty_2Erealax_2Ereal)|~p11), inference(split_conjunct,[status(thm)],[c_0_64])).
% 77.70/77.71 thf(c_0_70, plain, p11, inference(split_conjunct,[status(thm)],[ax1501])).
% 77.70/77.71 thf(c_0_71, plain, (~fmem @ (fap @ (fc_2Ebinary__ieee_2Efloat__plus__min @ f__0 @ f__1) @ (fc_2Ebool_2Ethe__value @ (fty_2Epair_2Eprod @ f__0 @ f__1))) @ (fty_2Ebinary__ieee_2Efloat @ f__0 @ f__1)|~fmem @ (fap @ (fc_2Ebinary__ieee_2Eulp @ f__0 @ f__1) @ (fc_2Ebool_2Ethe__value @ (fty_2Epair_2Eprod @ f__0 @ f__1))) @ fty_2Erealax_2Ereal), inference(spm,[status(thm)],[c_0_65, c_0_53])).
% 77.70/77.71 thf(c_0_72, plain, ![X1:del, X3:$i, X4:del]:(fmem @ (fap @ (fc_2Ebinary__ieee_2Efloat__plus__min @ X1 @ X4) @ X3) @ (fty_2Ebinary__ieee_2Efloat @ X1 @ X4)|~fmem @ X3 @ (fty_2Ebool_2Eitself @ (fty_2Epair_2Eprod @ X1 @ X4))), inference(spm,[status(thm)],[c_0_55, c_0_66])).
% 77.70/77.71 thf(c_0_73, plain, ![X1:del]:fmem @ (fc_2Ebool_2Ethe__value @ X1) @ (fty_2Ebool_2Eitself @ X1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_67, c_0_68])])).
% 77.70/77.71 thf(c_0_74, plain, ![X1:del, X4:del]:fmem @ (fc_2Ebinary__ieee_2Eulp @ X1 @ X4) @ (farr @ (fty_2Ebool_2Eitself @ (fty_2Epair_2Eprod @ X1 @ X4)) @ fty_2Erealax_2Ereal), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_69, c_0_70])])).
% 77.70/77.71 thf(c_0_75, plain, ~fmem @ (fap @ (fc_2Ebinary__ieee_2Eulp @ f__0 @ f__1) @ (fc_2Ebool_2Ethe__value @ (fty_2Epair_2Eprod @ f__0 @ f__1))) @ fty_2Erealax_2Ereal, inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71, c_0_72]), c_0_73])])).
% 77.70/77.71 thf(c_0_76, plain, ![X1:del, X3:$i, X4:del]:(fmem @ (fap @ (fc_2Ebinary__ieee_2Eulp @ X1 @ X4) @ X3) @ fty_2Erealax_2Ereal|~fmem @ X3 @ (fty_2Ebool_2Eitself @ (fty_2Epair_2Eprod @ X1 @ X4))), inference(spm,[status(thm)],[c_0_55, c_0_74])).
% 77.70/77.71 thf(c_0_77, plain, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75, c_0_76]), c_0_73])]), ['proof']).
% 77.70/77.71 thf(1,plain,$false,inference(eprover,[status(thm),assumptions([h2,h1,h0])],[])).
% 77.70/77.71 thf(2,plain,$false,inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,1,h2])).
% 77.70/77.71 thf(3,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,2,h1])).
% 77.70/77.71 thf(0,theorem,(![X1:del]:(![X2:del]:((surj__ty_2Erealax_2Ereal @ ((ap @ c_2Erealax_2Ereal__neg) @ ((ap @ ((c_2Ebinary__ieee_2Eulp @ X1) @ X2)) @ (c_2Ebool_2Ethe__value @ ((ty_2Epair_2Eprod @ X1) @ X2))))) = (surj__ty_2Erealax_2Ereal @ ((ap @ ((c_2Ebinary__ieee_2Efloat__to__real @ X1) @ X2)) @ ((ap @ ((c_2Ebinary__ieee_2Efloat__negate @ X1) @ X2)) @ ((ap @ ((c_2Ebinary__ieee_2Efloat__plus__min @ X1) @ X2)) @ (c_2Ebool_2Ethe__value @ ((ty_2Epair_2Eprod @ X1) @ X2))))))))),inference(contra,[status(thm),contra(discharge,[h0])],[3,h0])).
% 77.70/77.71 % SZS output end Proof
%------------------------------------------------------------------------------