TSTP Solution File: PUZ150^18 by Lash---1.13
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : PUZ150^18 : 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 : n012.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 13:22:08 EDT 2023
% Result : Theorem 0.21s 0.42s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : PUZ150^18 : TPTP v8.1.2. Released v8.1.0.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.35 % Computer : n012.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Aug 26 21:58:25 EDT 2023
% 0.21/0.35 % CPUTime :
% 0.21/0.42 % SZS status Theorem
% 0.21/0.42 % Mode: cade22grackle2xfee4
% 0.21/0.42 % Steps: 152
% 0.21/0.42 % SZS output start Proof
% 0.21/0.42 thf(ty_mindex, type, mindex : $tType).
% 0.21/0.42 thf(ty_mworld, type, mworld : $tType).
% 0.21/0.42 thf(ty_mactual, type, mactual : mworld).
% 0.21/0.42 thf(ty_'#b', type, '#b' : mindex).
% 0.21/0.42 thf(ty_eigen__2, type, eigen__2 : mworld).
% 0.21/0.42 thf(ty_eigen__1, type, eigen__1 : mworld).
% 0.21/0.42 thf(ty_'#a', type, '#a' : mindex).
% 0.21/0.42 thf(ty_eigen__0, type, eigen__0 : mworld).
% 0.21/0.42 thf(ty_a0, type, a0 : (mworld>$o)).
% 0.21/0.42 thf(ty_mrel, type, mrel : (mindex>mworld>mworld>$o)).
% 0.21/0.42 thf(ty_'#c', type, '#c' : mindex).
% 0.21/0.42 thf(sP1,plain,sP1 <=> (a0 @ mactual),introduced(definition,[new_symbols(definition,[sP1])])).
% 0.21/0.42 thf(sP2,plain,sP2 <=> (![X1:mworld]:((((mrel @ '#c') @ eigen__2) @ X1) => (~((a0 @ X1))))),introduced(definition,[new_symbols(definition,[sP2])])).
% 0.21/0.42 thf(sP3,plain,sP3 <=> ((((mrel @ '#c') @ eigen__2) @ mactual) => (~(sP1))),introduced(definition,[new_symbols(definition,[sP3])])).
% 0.21/0.42 thf(sP4,plain,sP4 <=> (![X1:mworld]:(![X2:mworld]:(((mrel @ '#c') @ X1) @ X2))),introduced(definition,[new_symbols(definition,[sP4])])).
% 0.21/0.42 thf(sP5,plain,sP5 <=> (![X1:mworld]:(((mrel @ '#c') @ eigen__2) @ X1)),introduced(definition,[new_symbols(definition,[sP5])])).
% 0.21/0.42 thf(sP6,plain,sP6 <=> (((mrel @ '#c') @ eigen__2) @ mactual),introduced(definition,[new_symbols(definition,[sP6])])).
% 0.21/0.42 thf(def_mlocal,definition,(mlocal = (^[X1:mworld>$o]:(X1 @ mactual)))).
% 0.21/0.42 thf(def_mnot,definition,(mnot = (^[X1:mworld>$o]:(^[X2:mworld]:((~) @ (X1 @ X2)))))).
% 0.21/0.42 thf(def_mand,definition,(mand = (^[X1:mworld>$o]:(^[X2:mworld>$o]:(^[X3:mworld]:((X1 @ X3) & (X2 @ X3))))))).
% 0.21/0.42 thf(def_mor,definition,(mor = (^[X1:mworld>$o]:(^[X2:mworld>$o]:(^[X3:mworld]:((X1 @ X3) | (X2 @ X3))))))).
% 0.21/0.42 thf(def_mimplies,definition,(mimplies = (^[X1:mworld>$o]:(^[X2:mworld>$o]:(^[X3:mworld]:(((^[X4:$o]:(^[X5:$o]:(X4 => X5))) @ (X1 @ X3)) @ (X2 @ X3))))))).
% 0.21/0.42 thf(def_mequiv,definition,(mequiv = (^[X1:mworld>$o]:(^[X2:mworld>$o]:(^[X3:mworld]:((X1 @ X3) <=> (X2 @ X3))))))).
% 0.21/0.42 thf(def_mbox,definition,(mbox = (^[X1:mindex]:(^[X2:mworld>$o]:(^[X3:mworld]:(![X4:mworld]:(((^[X5:$o]:(^[X6:$o]:(X5 => X6))) @ (((mrel @ X1) @ X3) @ X4)) @ (X2 @ X4)))))))).
% 0.21/0.42 thf(def_mdia,definition,(mdia = (^[X1:mindex]:(^[X2:mworld>$o]:(^[X3:mworld]:(?[X4:mworld]:((((mrel @ X1) @ X3) @ X4) & (X2 @ X4)))))))).
% 0.21/0.42 thf(con,conjecture,(![X1:mworld]:((((mrel @ '#b') @ mactual) @ X1) => (![X2:mworld]:((((mrel @ '#a') @ X1) @ X2) => (![X3:mworld]:((((mrel @ '#b') @ X2) @ X3) => (~((![X4:mworld]:((((mrel @ '#c') @ X3) @ X4) => (~((a0 @ X4)))))))))))))).
% 0.21/0.42 thf(h0,negated_conjecture,(~((![X1:mworld]:((((mrel @ '#b') @ mactual) @ X1) => (![X2:mworld]:((((mrel @ '#a') @ X1) @ X2) => (![X3:mworld]:((((mrel @ '#b') @ X2) @ X3) => (~((![X4:mworld]:((((mrel @ '#c') @ X3) @ X4) => (~((a0 @ X4))))))))))))))),inference(assume_negation,[status(cth)],[con])).
% 0.21/0.42 thf(h1,assumption,(~(((((mrel @ '#b') @ mactual) @ eigen__0) => (![X1:mworld]:((((mrel @ '#a') @ eigen__0) @ X1) => (![X2:mworld]:((((mrel @ '#b') @ X1) @ X2) => (~((![X3:mworld]:((((mrel @ '#c') @ X2) @ X3) => (~((a0 @ X3)))))))))))))),introduced(assumption,[])).
% 0.21/0.42 thf(h2,assumption,(((mrel @ '#b') @ mactual) @ eigen__0),introduced(assumption,[])).
% 0.21/0.42 thf(h3,assumption,(~((![X1:mworld]:((((mrel @ '#a') @ eigen__0) @ X1) => (![X2:mworld]:((((mrel @ '#b') @ X1) @ X2) => (~((![X3:mworld]:((((mrel @ '#c') @ X2) @ X3) => (~((a0 @ X3))))))))))))),introduced(assumption,[])).
% 0.21/0.42 thf(h4,assumption,(~(((((mrel @ '#a') @ eigen__0) @ eigen__1) => (![X1:mworld]:((((mrel @ '#b') @ eigen__1) @ X1) => (~((![X2:mworld]:((((mrel @ '#c') @ X1) @ X2) => (~((a0 @ X2)))))))))))),introduced(assumption,[])).
% 0.21/0.42 thf(h5,assumption,(((mrel @ '#a') @ eigen__0) @ eigen__1),introduced(assumption,[])).
% 0.21/0.42 thf(h6,assumption,(~((![X1:mworld]:((((mrel @ '#b') @ eigen__1) @ X1) => (~((![X2:mworld]:((((mrel @ '#c') @ X1) @ X2) => (~((a0 @ X2))))))))))),introduced(assumption,[])).
% 0.21/0.42 thf(h7,assumption,(~(((((mrel @ '#b') @ eigen__1) @ eigen__2) => (~(sP2))))),introduced(assumption,[])).
% 0.21/0.42 thf(h8,assumption,(((mrel @ '#b') @ eigen__1) @ eigen__2),introduced(assumption,[])).
% 0.21/0.42 thf(h9,assumption,sP2,introduced(assumption,[])).
% 0.21/0.42 thf(1,plain,(~(sP5) | sP6),inference(all_rule,[status(thm)],[])).
% 0.21/0.42 thf(2,plain,(~(sP4) | sP5),inference(all_rule,[status(thm)],[])).
% 0.21/0.42 thf(3,plain,((~(sP3) | ~(sP6)) | ~(sP1)),inference(prop_rule,[status(thm)],[])).
% 0.21/0.42 thf(4,plain,(~(sP2) | sP3),inference(all_rule,[status(thm)],[])).
% 0.21/0.42 thf(axiom_a0,axiom,sP1).
% 0.21/0.42 thf('mrel_#c_universal',axiom,sP4).
% 0.21/0.42 thf(5,plain,$false,inference(prop_unsat,[status(thm),assumptions([h8,h9,h7,h5,h6,h4,h2,h3,h1,h0])],[1,2,3,4,h9,axiom_a0,'mrel_#c_universal'])).
% 0.21/0.42 thf(6,plain,$false,inference(tab_negimp,[status(thm),assumptions([h7,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h8,h9])],[h7,5,h8,h9])).
% 0.21/0.42 thf(7,plain,$false,inference(tab_negall,[status(thm),assumptions([h5,h6,h4,h2,h3,h1,h0]),tab_negall(discharge,[h7]),tab_negall(eigenvar,eigen__2)],[h6,6,h7])).
% 0.21/0.42 thf(8,plain,$false,inference(tab_negimp,[status(thm),assumptions([h4,h2,h3,h1,h0]),tab_negimp(discharge,[h5,h6])],[h4,7,h5,h6])).
% 0.21/0.42 thf(9,plain,$false,inference(tab_negall,[status(thm),assumptions([h2,h3,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,8,h4])).
% 0.21/0.42 thf(10,plain,$false,inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,9,h2,h3])).
% 0.21/0.42 thf(11,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,10,h1])).
% 0.21/0.42 thf(0,theorem,(![X1:mworld]:((((mrel @ '#b') @ mactual) @ X1) => (![X2:mworld]:((((mrel @ '#a') @ X1) @ X2) => (![X3:mworld]:((((mrel @ '#b') @ X2) @ X3) => (~((![X4:mworld]:((((mrel @ '#c') @ X3) @ X4) => (~((a0 @ X4))))))))))))),inference(contra,[status(thm),contra(discharge,[h0])],[11,h0])).
% 0.21/0.42 % SZS output end Proof
%------------------------------------------------------------------------------