TSTP Solution File: SYO059^4 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO059^4 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n006.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 : Thu Jul 21 19:29:56 EDT 2022
% Result : Theorem 1.93s 2.17s
% Output : Proof 1.93s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SYO059^4 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n006.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Fri Jul 8 19:32:21 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.93/2.17 % SZS status Theorem
% 1.93/2.17 % Mode: mode506
% 1.93/2.17 % Inferences: 18
% 1.93/2.17 % SZS output start Proof
% 1.93/2.17 thf(ty_a, type, a : ($i>$o)).
% 1.93/2.17 thf(ty_eigen__2, type, eigen__2 : $i).
% 1.93/2.17 thf(ty_eigen__0, type, eigen__0 : $i).
% 1.93/2.17 thf(ty_irel, type, irel : ($i>$i>$o)).
% 1.93/2.17 thf(h0, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])).
% 1.93/2.17 thf(eigendef_eigen__0, definition, eigen__0 = (eps__0 @ (^[X1:$i]:(~((~((![X2:$i]:(((irel @ X1) @ X2) => (~((![X3:$i]:(((irel @ X2) @ X3) => (a @ X3))))))))))))), introduced(definition,[new_symbols(definition,[eigen__0])])).
% 1.93/2.17 thf(eigendef_eigen__2, definition, eigen__2 = (eps__0 @ (^[X1:$i]:(~((((irel @ eigen__0) @ X1) => (a @ X1)))))), introduced(definition,[new_symbols(definition,[eigen__2])])).
% 1.93/2.17 thf(sP1,plain,sP1 <=> (![X1:$i]:((irel @ X1) @ X1)),introduced(definition,[new_symbols(definition,[sP1])])).
% 1.93/2.17 thf(sP2,plain,sP2 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (~((![X2:$i]:(((irel @ X1) @ X2) => (a @ X2))))))),introduced(definition,[new_symbols(definition,[sP2])])).
% 1.93/2.17 thf(sP3,plain,sP3 <=> (a @ eigen__2),introduced(definition,[new_symbols(definition,[sP3])])).
% 1.93/2.17 thf(sP4,plain,sP4 <=> ((irel @ eigen__0) @ eigen__0),introduced(definition,[new_symbols(definition,[sP4])])).
% 1.93/2.17 thf(sP5,plain,sP5 <=> (![X1:$i]:(~((![X2:$i]:(((irel @ X1) @ X2) => (~((![X3:$i]:(((irel @ X2) @ X3) => (a @ X3)))))))))),introduced(definition,[new_symbols(definition,[sP5])])).
% 1.93/2.17 thf(sP6,plain,sP6 <=> (sP4 => (~((![X1:$i]:(((irel @ eigen__0) @ X1) => (a @ X1)))))),introduced(definition,[new_symbols(definition,[sP6])])).
% 1.93/2.17 thf(sP7,plain,sP7 <=> (((irel @ eigen__0) @ eigen__2) => sP3),introduced(definition,[new_symbols(definition,[sP7])])).
% 1.93/2.17 thf(sP8,plain,sP8 <=> (![X1:$i]:(((irel @ eigen__0) @ X1) => (a @ X1))),introduced(definition,[new_symbols(definition,[sP8])])).
% 1.93/2.17 thf(sP9,plain,sP9 <=> ((!!) @ a),introduced(definition,[new_symbols(definition,[sP9])])).
% 1.93/2.17 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))).
% 1.93/2.17 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))).
% 1.93/2.17 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(~(((X1 @ X3) => (~((X2 @ X3))))))))))).
% 1.93/2.17 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(mor @ (mnot @ X1))))).
% 1.93/2.17 thf(def_mbox_s4,definition,(mbox_s4 = (^[X1:$i>$o]:(^[X2:$i]:(![X3:$i]:(((irel @ X2) @ X3) => (X1 @ X3))))))).
% 1.93/2.17 thf(def_iatom,definition,(iatom = (^[X1:$i>$o]:X1))).
% 1.93/2.17 thf(def_inot,definition,(inot = (^[X1:$i>$o]:(mnot @ (mbox_s4 @ X1))))).
% 1.93/2.17 thf(def_itrue,definition,(itrue = (^[X1:$i]:(~($false))))).
% 1.93/2.17 thf(def_ifalse,definition,(ifalse = (inot @ itrue))).
% 1.93/2.17 thf(def_iand,definition,(iand = mand)).
% 1.93/2.17 thf(def_ior,definition,(ior = (^[X1:$i>$o]:(^[X2:$i>$o]:((mor @ (mbox_s4 @ X1)) @ (mbox_s4 @ X2)))))).
% 1.93/2.17 thf(def_iimplies,definition,(iimplies = (^[X1:$i>$o]:(^[X2:$i>$o]:((mimplies @ (mbox_s4 @ X1)) @ (mbox_s4 @ X2)))))).
% 1.93/2.17 thf(def_iimplied,definition,(iimplied = (^[X1:$i>$o]:(^[X2:$i>$o]:((iimplies @ X2) @ X1))))).
% 1.93/2.17 thf(def_iequiv,definition,(iequiv = (^[X1:$i>$o]:(^[X2:$i>$o]:((iand @ ((iimplies @ X1) @ X2)) @ ((iimplies @ X2) @ X1)))))).
% 1.93/2.17 thf(def_ixor,definition,(ixor = (^[X1:$i>$o]:(^[X2:$i>$o]:(inot @ ((iequiv @ X1) @ X2)))))).
% 1.93/2.17 thf(def_ivalid,definition,(ivalid = (!!))).
% 1.93/2.17 thf(def_isatisfiable,definition,(isatisfiable = (^[X1:$i>$o]:(~((![X2:$i]:(~((X1 @ X2))))))))).
% 1.93/2.17 thf(def_icountersatisfiable,definition,(icountersatisfiable = (^[X1:$i>$o]:(~(((!!) @ X1)))))).
% 1.93/2.17 thf(def_iinvalid,definition,(iinvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))).
% 1.93/2.17 thf(con,conjecture,sP5).
% 1.93/2.17 thf(h1,negated_conjecture,(~(sP5)),inference(assume_negation,[status(cth)],[con])).
% 1.93/2.17 thf(1,plain,(~(sP9) | sP3),inference(all_rule,[status(thm)],[])).
% 1.93/2.17 thf(2,plain,(sP7 | ~(sP3)),inference(prop_rule,[status(thm)],[])).
% 1.93/2.17 thf(3,plain,(sP8 | ~(sP7)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2])).
% 1.93/2.17 thf(4,plain,((~(sP6) | ~(sP4)) | ~(sP8)),inference(prop_rule,[status(thm)],[])).
% 1.93/2.17 thf(5,plain,(~(sP1) | sP4),inference(all_rule,[status(thm)],[])).
% 1.93/2.17 thf(6,plain,(~(sP2) | sP6),inference(all_rule,[status(thm)],[])).
% 1.93/2.17 thf(7,plain,(sP5 | sP2),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0])).
% 1.93/2.17 thf(axiom1,axiom,(ivalid @ (iatom @ a))).
% 1.93/2.17 thf(8,plain,sP9,inference(preprocess,[status(thm)],[axiom1]).
% 1.93/2.17 thf(refl_axiom,axiom,sP1).
% 1.93/2.17 thf(9,plain,$false,inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,refl_axiom,h1])).
% 1.93/2.17 thf(10,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[9,h0])).
% 1.93/2.17 thf(0,theorem,sP5,inference(contra,[status(thm),contra(discharge,[h1])],[9,h1])).
% 1.93/2.17 % SZS output end Proof
%------------------------------------------------------------------------------