TSTP Solution File: PRO029^16 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : PRO029^16 : TPTP v8.1.2. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n010.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 : 300s
% DateTime : Thu Aug 31 13:08:31 EDT 2023
% Result : Theorem 0.19s 0.43s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : PRO029^16 : TPTP v8.1.2. Released v8.1.0.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n010.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Aug 28 18:59:34 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.43 % SZS status Theorem
% 0.19/0.43 % Mode: cade22grackle2xfee4
% 0.19/0.43 % Steps: 127
% 0.19/0.43 % SZS output start Proof
% 0.19/0.43 thf(ty_mindex, type, mindex : $tType).
% 0.19/0.43 thf(ty_mworld, type, mworld : $tType).
% 0.19/0.43 thf(ty_'#u', type, '#u' : mindex).
% 0.19/0.43 thf(ty_mactual, type, mactual : mworld).
% 0.19/0.43 thf(ty_paid, type, paid : (mworld>$o)).
% 0.19/0.43 thf(ty_called, type, called : (mworld>$o)).
% 0.19/0.43 thf(ty_mrel, type, mrel : (mindex>mworld>mworld>$o)).
% 0.19/0.43 thf(ty_charge, type, charge : (mworld>$o)).
% 0.19/0.43 thf(ty_'#c', type, '#c' : mindex).
% 0.19/0.43 thf(ty_eigen__0, type, eigen__0 : mworld).
% 0.19/0.43 thf(sP1,plain,sP1 <=> (paid @ eigen__0),introduced(definition,[new_symbols(definition,[sP1])])).
% 0.19/0.43 thf(sP2,plain,sP2 <=> ((((mrel @ '#c') @ mactual) @ mactual) => ((paid @ mactual) => (![X1:mworld]:((((mrel @ '#u') @ mactual) @ X1) => (paid @ X1))))),introduced(definition,[new_symbols(definition,[sP2])])).
% 0.19/0.43 thf(sP3,plain,sP3 <=> (![X1:mworld]:((((mrel @ '#u') @ mactual) @ X1) => ((called @ X1) => (![X2:mworld]:((((mrel @ '#c') @ X1) @ X2) => (called @ X2)))))),introduced(definition,[new_symbols(definition,[sP3])])).
% 0.19/0.43 thf(sP4,plain,sP4 <=> ((called @ eigen__0) => (![X1:mworld]:((((mrel @ '#c') @ eigen__0) @ X1) => (called @ X1)))),introduced(definition,[new_symbols(definition,[sP4])])).
% 0.19/0.43 thf(sP5,plain,sP5 <=> ((paid @ mactual) => (![X1:mworld]:((((mrel @ '#u') @ mactual) @ X1) => (paid @ X1)))),introduced(definition,[new_symbols(definition,[sP5])])).
% 0.19/0.43 thf(sP6,plain,sP6 <=> ((((mrel @ '#u') @ mactual) @ eigen__0) => sP4),introduced(definition,[new_symbols(definition,[sP6])])).
% 0.19/0.43 thf(sP7,plain,sP7 <=> (![X1:mworld]:((((mrel @ '#c') @ mactual) @ X1) => (called @ X1))),introduced(definition,[new_symbols(definition,[sP7])])).
% 0.19/0.43 thf(sP8,plain,sP8 <=> ((((mrel @ '#c') @ mactual) @ mactual) => (called @ mactual)),introduced(definition,[new_symbols(definition,[sP8])])).
% 0.19/0.43 thf(sP9,plain,sP9 <=> ((charge @ mactual) => (~(((![X1:mworld]:((((mrel @ '#u') @ mactual) @ X1) => (charge @ X1))) => (~((![X1:mworld]:((((mrel @ '#c') @ mactual) @ X1) => (charge @ X1))))))))),introduced(definition,[new_symbols(definition,[sP9])])).
% 0.19/0.43 thf(sP10,plain,sP10 <=> ((((mrel @ '#u') @ mactual) @ eigen__0) => (~((![X1:mworld]:((((mrel @ '#c') @ eigen__0) @ X1) => (called @ X1)))))),introduced(definition,[new_symbols(definition,[sP10])])).
% 0.19/0.43 thf(sP11,plain,sP11 <=> (((mrel @ '#c') @ mactual) @ mactual),introduced(definition,[new_symbols(definition,[sP11])])).
% 0.19/0.43 thf(sP12,plain,sP12 <=> (charge @ eigen__0),introduced(definition,[new_symbols(definition,[sP12])])).
% 0.19/0.43 thf(sP13,plain,sP13 <=> (called @ eigen__0),introduced(definition,[new_symbols(definition,[sP13])])).
% 0.19/0.43 thf(sP14,plain,sP14 <=> ((called @ mactual) => (paid @ mactual)),introduced(definition,[new_symbols(definition,[sP14])])).
% 0.19/0.43 thf(sP15,plain,sP15 <=> ((~(sP7)) => (![X1:mworld]:((((mrel @ '#u') @ mactual) @ X1) => (~((![X2:mworld]:((((mrel @ '#c') @ X1) @ X2) => (called @ X2)))))))),introduced(definition,[new_symbols(definition,[sP15])])).
% 0.19/0.43 thf(sP16,plain,sP16 <=> (sP12 => (~((sP13 => sP1)))),introduced(definition,[new_symbols(definition,[sP16])])).
% 0.19/0.43 thf(sP17,plain,sP17 <=> (![X1:mworld]:((((mrel @ '#u') @ mactual) @ X1) => (charge @ X1))),introduced(definition,[new_symbols(definition,[sP17])])).
% 0.19/0.43 thf(sP18,plain,sP18 <=> (sP17 => (~((![X1:mworld]:((((mrel @ '#c') @ mactual) @ X1) => (charge @ X1)))))),introduced(definition,[new_symbols(definition,[sP18])])).
% 0.19/0.43 thf(sP19,plain,sP19 <=> (called @ mactual),introduced(definition,[new_symbols(definition,[sP19])])).
% 0.19/0.43 thf(sP20,plain,sP20 <=> (![X1:mworld]:((((mrel @ '#u') @ mactual) @ X1) => (paid @ X1))),introduced(definition,[new_symbols(definition,[sP20])])).
% 0.19/0.43 thf(sP21,plain,sP21 <=> ((((mrel @ '#u') @ mactual) @ eigen__0) => sP1),introduced(definition,[new_symbols(definition,[sP21])])).
% 0.19/0.43 thf(sP22,plain,sP22 <=> (![X1:mworld]:((((mrel @ '#u') @ mactual) @ X1) => (~((![X2:mworld]:((((mrel @ '#c') @ X1) @ X2) => (called @ X2))))))),introduced(definition,[new_symbols(definition,[sP22])])).
% 0.19/0.43 thf(sP23,plain,sP23 <=> (![X1:mworld]:(((mrel @ '#c') @ X1) @ X1)),introduced(definition,[new_symbols(definition,[sP23])])).
% 0.19/0.43 thf(sP24,plain,sP24 <=> (![X1:mworld]:((((mrel @ '#c') @ mactual) @ X1) => ((paid @ X1) => (![X2:mworld]:((((mrel @ '#u') @ X1) @ X2) => (paid @ X2)))))),introduced(definition,[new_symbols(definition,[sP24])])).
% 0.19/0.43 thf(sP25,plain,sP25 <=> ((((mrel @ '#u') @ mactual) @ eigen__0) => sP12),introduced(definition,[new_symbols(definition,[sP25])])).
% 0.19/0.43 thf(sP26,plain,sP26 <=> (((mrel @ '#u') @ mactual) @ eigen__0),introduced(definition,[new_symbols(definition,[sP26])])).
% 0.19/0.43 thf(sP27,plain,sP27 <=> (![X1:mworld]:((((mrel @ '#c') @ eigen__0) @ X1) => (called @ X1))),introduced(definition,[new_symbols(definition,[sP27])])).
% 0.19/0.43 thf(sP28,plain,sP28 <=> (paid @ mactual),introduced(definition,[new_symbols(definition,[sP28])])).
% 0.19/0.43 thf(sP29,plain,sP29 <=> (charge @ mactual),introduced(definition,[new_symbols(definition,[sP29])])).
% 0.19/0.43 thf(sP30,plain,sP30 <=> (sP13 => sP1),introduced(definition,[new_symbols(definition,[sP30])])).
% 0.19/0.43 thf(def_mlocal,definition,(mlocal = (^[X1:mworld>$o]:(X1 @ mactual)))).
% 0.19/0.43 thf(def_mnot,definition,(mnot = (^[X1:mworld>$o]:(^[X2:mworld]:((~) @ (X1 @ X2)))))).
% 0.19/0.43 thf(def_mand,definition,(mand = (^[X1:mworld>$o]:(^[X2:mworld>$o]:(^[X3:mworld]:((X1 @ X3) & (X2 @ X3))))))).
% 0.19/0.43 thf(def_mor,definition,(mor = (^[X1:mworld>$o]:(^[X2:mworld>$o]:(^[X3:mworld]:((X1 @ X3) | (X2 @ X3))))))).
% 0.19/0.43 thf(def_mimplies,definition,(mimplies = (^[X1:mworld>$o]:(^[X2:mworld>$o]:(^[X3:mworld]:(((^[X4:$o]:(^[X5:$o]:(X4 => X5))) @ (X1 @ X3)) @ (X2 @ X3))))))).
% 0.19/0.43 thf(def_mequiv,definition,(mequiv = (^[X1:mworld>$o]:(^[X2:mworld>$o]:(^[X3:mworld]:((X1 @ X3) <=> (X2 @ X3))))))).
% 0.19/0.43 thf(def_mbox,definition,(mbox = (^[X1:mindex]:(^[X2:mworld>$o]:(^[X3:mworld]:(![X4:mworld]:(((^[X5:$o]:(^[X6:$o]:(X5 => X6))) @ (((mrel @ X1) @ X3) @ X4)) @ (X2 @ X4)))))))).
% 0.19/0.43 thf(def_mdia,definition,(mdia = (^[X1:mindex]:(^[X2:mworld>$o]:(^[X3:mworld]:(?[X4:mworld]:((((mrel @ X1) @ X3) @ X4) & (X2 @ X4)))))))).
% 0.19/0.43 thf(requirement_1,conjecture,((~((sP29 => (~(sP14))))) => (![X1:mworld]:((((mrel @ '#u') @ mactual) @ X1) => (~(((charge @ X1) => (~(((called @ X1) => (paid @ X1))))))))))).
% 0.19/0.43 thf(h0,negated_conjecture,(~(((~((sP29 => (~(sP14))))) => (![X1:mworld]:((((mrel @ '#u') @ mactual) @ X1) => (~(((charge @ X1) => (~(((called @ X1) => (paid @ X1)))))))))))),inference(assume_negation,[status(cth)],[requirement_1])).
% 0.19/0.43 thf(h1,assumption,(~((sP29 => (~(sP14))))),introduced(assumption,[])).
% 0.19/0.43 thf(h2,assumption,(~((![X1:mworld]:((((mrel @ '#u') @ mactual) @ X1) => (~(((charge @ X1) => (~(((called @ X1) => (paid @ X1))))))))))),introduced(assumption,[])).
% 0.19/0.43 thf(h3,assumption,sP29,introduced(assumption,[])).
% 0.19/0.43 thf(h4,assumption,sP14,introduced(assumption,[])).
% 0.19/0.43 thf(h5,assumption,(~((sP26 => (~(sP16))))),introduced(assumption,[])).
% 0.19/0.43 thf(h6,assumption,sP26,introduced(assumption,[])).
% 0.19/0.43 thf(h7,assumption,sP16,introduced(assumption,[])).
% 0.19/0.43 thf(1,plain,((~(sP4) | ~(sP13)) | sP27),inference(prop_rule,[status(thm)],[])).
% 0.19/0.43 thf(2,plain,((~(sP6) | ~(sP26)) | sP4),inference(prop_rule,[status(thm)],[])).
% 0.19/0.43 thf(3,plain,((~(sP10) | ~(sP26)) | ~(sP27)),inference(prop_rule,[status(thm)],[])).
% 0.19/0.43 thf(4,plain,((~(sP21) | ~(sP26)) | sP1),inference(prop_rule,[status(thm)],[])).
% 0.19/0.43 thf(5,plain,((~(sP25) | ~(sP26)) | sP12),inference(prop_rule,[status(thm)],[])).
% 0.19/0.43 thf(6,plain,(~(sP3) | sP6),inference(all_rule,[status(thm)],[])).
% 0.19/0.43 thf(7,plain,(~(sP20) | sP21),inference(all_rule,[status(thm)],[])).
% 0.19/0.43 thf(8,plain,(~(sP17) | sP25),inference(all_rule,[status(thm)],[])).
% 0.19/0.43 thf(9,plain,(~(sP22) | sP10),inference(all_rule,[status(thm)],[])).
% 0.19/0.43 thf(10,plain,((~(sP5) | ~(sP28)) | sP20),inference(prop_rule,[status(thm)],[])).
% 0.19/0.43 thf(11,plain,((~(sP2) | ~(sP11)) | sP5),inference(prop_rule,[status(thm)],[])).
% 0.19/0.43 thf(12,plain,((~(sP8) | ~(sP11)) | sP19),inference(prop_rule,[status(thm)],[])).
% 0.19/0.43 thf(13,plain,(~(sP23) | sP11),inference(all_rule,[status(thm)],[])).
% 0.19/0.43 thf(14,plain,(~(sP24) | sP2),inference(all_rule,[status(thm)],[])).
% 0.19/0.43 thf(15,plain,(~(sP7) | sP8),inference(all_rule,[status(thm)],[])).
% 0.19/0.43 thf(16,plain,(sP18 | sP17),inference(prop_rule,[status(thm)],[])).
% 0.19/0.43 thf(17,plain,((~(sP15) | sP7) | sP22),inference(prop_rule,[status(thm)],[])).
% 0.19/0.43 thf(18,plain,((~(sP9) | ~(sP29)) | ~(sP18)),inference(prop_rule,[status(thm)],[])).
% 0.19/0.43 thf(19,plain,(sP30 | ~(sP1)),inference(prop_rule,[status(thm)],[])).
% 0.19/0.43 thf(20,plain,(sP30 | sP13),inference(prop_rule,[status(thm)],[])).
% 0.19/0.43 thf(21,plain,((~(sP14) | ~(sP19)) | sP28),inference(prop_rule,[status(thm)],[])).
% 0.19/0.43 thf(22,plain,((~(sP16) | ~(sP12)) | ~(sP30)),inference(prop_rule,[status(thm)],[])).
% 0.19/0.43 thf(axiom_3,axiom,sP15).
% 0.19/0.43 thf(axiom_2,axiom,sP24).
% 0.19/0.43 thf(axiom_1,axiom,sP3).
% 0.19/0.43 thf(axiom_charge_u,axiom,sP9).
% 0.19/0.43 thf('mrel_#c_reflexive',axiom,sP23).
% 0.19/0.43 thf(23,plain,$false,inference(prop_unsat,[status(thm),assumptions([h6,h7,h5,h3,h4,h1,h2,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,h3,h4,h6,h7,axiom_3,axiom_2,axiom_1,axiom_charge_u,'mrel_#c_reflexive'])).
% 0.19/0.43 thf(24,plain,$false,inference(tab_negimp,[status(thm),assumptions([h5,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h6,h7])],[h5,23,h6,h7])).
% 0.19/0.43 thf(25,plain,$false,inference(tab_negall,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__0)],[h2,24,h5])).
% 0.19/0.43 thf(26,plain,$false,inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h1,25,h3,h4])).
% 0.19/0.43 thf(27,plain,$false,inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,26,h1,h2])).
% 0.19/0.43 thf(0,theorem,((~((sP29 => (~(sP14))))) => (![X1:mworld]:((((mrel @ '#u') @ mactual) @ X1) => (~(((charge @ X1) => (~(((called @ X1) => (paid @ X1)))))))))),inference(contra,[status(thm),contra(discharge,[h0])],[27,h0])).
% 0.19/0.43 % SZS output end Proof
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