TSTP Solution File: SET171^3 by Lash---1.13
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SET171^3 : TPTP v8.1.2. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n013.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 15:16:17 EDT 2023
% Result : Theorem 0.18s 0.40s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET171^3 : TPTP v8.1.2. Released v3.6.0.
% 0.00/0.14 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.15/0.33 % Computer : n013.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Sat Aug 26 15:14:17 EDT 2023
% 0.15/0.33 % CPUTime :
% 0.18/0.40 % SZS status Theorem
% 0.18/0.40 % Mode: cade22grackle2xfee4
% 0.18/0.40 % Steps: 28
% 0.18/0.40 % SZS output start Proof
% 0.18/0.40 thf(ty_eigen__2, type, eigen__2 : ($i>$o)).
% 0.18/0.40 thf(ty_eigen__1, type, eigen__1 : ($i>$o)).
% 0.18/0.40 thf(ty_eigen__0, type, eigen__0 : ($i>$o)).
% 0.18/0.40 thf(ty_eigen__3, type, eigen__3 : $i).
% 0.18/0.40 thf(sP1,plain,sP1 <=> ((~((eigen__0 @ eigen__3))) => (eigen__1 @ eigen__3)),introduced(definition,[new_symbols(definition,[sP1])])).
% 0.18/0.40 thf(sP2,plain,sP2 <=> (eigen__1 @ eigen__3),introduced(definition,[new_symbols(definition,[sP2])])).
% 0.18/0.40 thf(sP3,plain,sP3 <=> (eigen__2 @ eigen__3),introduced(definition,[new_symbols(definition,[sP3])])).
% 0.18/0.40 thf(sP4,plain,sP4 <=> (eigen__0 @ eigen__3),introduced(definition,[new_symbols(definition,[sP4])])).
% 0.18/0.40 thf(sP5,plain,sP5 <=> ((~(sP4)) => sP3),introduced(definition,[new_symbols(definition,[sP5])])).
% 0.18/0.40 thf(sP6,plain,sP6 <=> (sP2 => (~(sP3))),introduced(definition,[new_symbols(definition,[sP6])])).
% 0.18/0.40 thf(def_in,definition,(in = (^[X1:$i]:(^[X2:$i>$o]:(X2 @ X1))))).
% 0.18/0.40 thf(def_is_a,definition,(is_a = (^[X1:$i]:(^[X2:$i>$o]:(X2 @ X1))))).
% 0.18/0.40 thf(def_emptyset,definition,(emptyset = (^[X1:$i]:$false))).
% 0.18/0.40 thf(def_unord_pair,definition,(unord_pair = (^[X1:$i]:(^[X2:$i]:(^[X3:$i]:((X3 = X1) | (X3 = X2))))))).
% 0.18/0.40 thf(def_singleton,definition,(singleton = (^[X1:$i]:(^[X2:$i]:(X2 = X1))))).
% 0.18/0.40 thf(def_union,definition,(union = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X1 @ X3) | (X2 @ X3))))))).
% 0.18/0.40 thf(def_excl_union,definition,(excl_union = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(((X1 @ X3) & ((~) @ (X2 @ X3))) | (((~) @ (X1 @ X3)) & (X2 @ X3)))))))).
% 0.18/0.40 thf(def_intersection,definition,(intersection = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X1 @ X3) & (X2 @ X3))))))).
% 0.18/0.40 thf(def_setminus,definition,(setminus = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X1 @ X3) & ((~) @ (X2 @ X3)))))))).
% 0.18/0.40 thf(def_complement,definition,(complement = (^[X1:$i>$o]:(^[X2:$i]:((~) @ (X1 @ X2)))))).
% 0.18/0.40 thf(def_disjoint,definition,(disjoint = (^[X1:$i>$o]:(^[X2:$i>$o]:(((intersection @ X1) @ X2) = emptyset))))).
% 0.18/0.40 thf(def_subset,definition,(subset = (^[X1:$i>$o]:(^[X2:$i>$o]:(![X3:$i]:(((^[X4:$o]:(^[X5:$o]:(X4 => X5))) @ (X1 @ X3)) @ (X2 @ X3))))))).
% 0.18/0.40 thf(def_meets,definition,(meets = (^[X1:$i>$o]:(^[X2:$i>$o]:(?[X3:$i]:((X1 @ X3) & (X2 @ X3))))))).
% 0.18/0.40 thf(def_misses,definition,(misses = (^[X1:$i>$o]:(^[X2:$i>$o]:((~) @ (?[X3:$i]:((X1 @ X3) & (X2 @ X3)))))))).
% 0.18/0.40 thf(union_distributes_over_intersection,conjecture,(![X1:$i>$o]:(![X2:$i>$o]:(![X3:$i>$o]:((^[X4:$i]:((~((X1 @ X4))) => (~(((X2 @ X4) => (~((X3 @ X4)))))))) = (^[X4:$i]:(~((((~((X1 @ X4))) => (X2 @ X4)) => (~(((~((X1 @ X4))) => (X3 @ X4))))))))))))).
% 0.18/0.40 thf(h0,negated_conjecture,(~((![X1:$i>$o]:(![X2:$i>$o]:(![X3:$i>$o]:((^[X4:$i]:((~((X1 @ X4))) => (~(((X2 @ X4) => (~((X3 @ X4)))))))) = (^[X4:$i]:(~((((~((X1 @ X4))) => (X2 @ X4)) => (~(((~((X1 @ X4))) => (X3 @ X4)))))))))))))),inference(assume_negation,[status(cth)],[union_distributes_over_intersection])).
% 0.18/0.40 thf(h1,assumption,(~((![X1:$i>$o]:(![X2:$i>$o]:((^[X3:$i]:((~((eigen__0 @ X3))) => (~(((X1 @ X3) => (~((X2 @ X3)))))))) = (^[X3:$i]:(~((((~((eigen__0 @ X3))) => (X1 @ X3)) => (~(((~((eigen__0 @ X3))) => (X2 @ X3))))))))))))),introduced(assumption,[])).
% 0.18/0.40 thf(h2,assumption,(~((![X1:$i>$o]:((^[X2:$i]:((~((eigen__0 @ X2))) => (~(((eigen__1 @ X2) => (~((X1 @ X2)))))))) = (^[X2:$i]:(~((((~((eigen__0 @ X2))) => (eigen__1 @ X2)) => (~(((~((eigen__0 @ X2))) => (X1 @ X2)))))))))))),introduced(assumption,[])).
% 0.18/0.40 thf(h3,assumption,(~(((^[X1:$i]:((~((eigen__0 @ X1))) => (~(((eigen__1 @ X1) => (~((eigen__2 @ X1)))))))) = (^[X1:$i]:(~((((~((eigen__0 @ X1))) => (eigen__1 @ X1)) => (~(((~((eigen__0 @ X1))) => (eigen__2 @ X1))))))))))),introduced(assumption,[])).
% 0.18/0.40 thf(h4,assumption,(~((![X1:$i]:(((~((eigen__0 @ X1))) => (~(((eigen__1 @ X1) => (~((eigen__2 @ X1))))))) = (~((((~((eigen__0 @ X1))) => (eigen__1 @ X1)) => (~(((~((eigen__0 @ X1))) => (eigen__2 @ X1))))))))))),introduced(assumption,[])).
% 0.18/0.40 thf(h5,assumption,(~((((~(sP4)) => (~(sP6))) = (~((sP1 => (~(sP5)))))))),introduced(assumption,[])).
% 0.18/0.40 thf(h6,assumption,(~(sP4)),introduced(assumption,[])).
% 0.18/0.40 thf(h7,assumption,sP6,introduced(assumption,[])).
% 0.18/0.40 thf(h8,assumption,sP1,introduced(assumption,[])).
% 0.18/0.40 thf(h9,assumption,sP5,introduced(assumption,[])).
% 0.18/0.40 thf(1,plain,((~(sP6) | ~(sP2)) | ~(sP3)),inference(prop_rule,[status(thm)],[])).
% 0.18/0.40 thf(2,plain,((~(sP1) | sP4) | sP2),inference(prop_rule,[status(thm)],[])).
% 0.18/0.40 thf(3,plain,((~(sP5) | sP4) | sP3),inference(prop_rule,[status(thm)],[])).
% 0.18/0.40 thf(4,plain,$false,inference(prop_unsat,[status(thm),assumptions([h8,h9,h6,h7,h5,h4,h3,h2,h1,h0])],[1,2,3,h6,h7,h8,h9])).
% 0.18/0.40 7:429: Could not find hyp name
% 0.18/0.40 s = imp (imp (imp (imp (__0 __3) False) (__1 __3)) (imp (imp (imp (__0 __3) False) (__2 __3)) False)) False
% 0.18/0.40 hyp:
% 0.18/0.40 [418] h6: imp (__0 __3) False
% 0.18/0.40 [422] h7: imp (__1 __3) (imp (__2 __3) False)
% 0.18/0.40 [431] h5: imp (eq:$o (imp (imp (__0 __3) False) (imp (imp (__1 __3) (imp (__2 __3) False)) False)) (imp (imp (imp (imp (__0 __3) False) (__1 __3)) (imp (imp (imp (__0 __3) False) (__2 __3)) False)) False)) False
% 0.18/0.40 [415] h4: imp (Pi:$i (\_:$i.eq:$o (imp (imp (__0 ^0) False) (imp (imp (__1 ^0) (imp (__2 ^0) False)) False)) (imp (imp (imp (imp (__0 ^0) False) (__1 ^0)) (imp (imp (imp (__0 ^0) False) (__2 ^0)) False)) False))) False
% 0.18/0.40 [412] h3: imp (eq:$i>$o (\_:$i.imp (imp (__0 ^0) False) (imp (imp (__1 ^0) (imp (__2 ^0) False)) False)) (\_:$i.imp (imp (imp (imp (__0 ^0) False) (__1 ^0)) (imp (imp (imp (__0 ^0) False) (__2 ^0)) False)) False)) False
% 0.18/0.40 [398] h2: imp (Pi:$i>$o (\_:$i>$o.eq:$i>$o (\_:$i.imp (imp (__0 ^0) False) (imp (imp (__1 ^0) (imp (^1 ^0) False)) False)) (\_:$i.imp (imp (imp (imp (__0 ^0) False) (__1 ^0)) (imp (imp (imp (__0 ^0) False) (^1 ^0)) False)) False))) False
% 0.18/0.40 [385] h1: imp (Pi:$i>$o (\_:$i>$o.Pi:$i>$o (\_:$i>$o.eq:$i>$o (\_:$i.imp (imp (__0 ^0) False) (imp (imp (^2 ^0) (imp (^1 ^0) False)) False)) (\_:$i.imp (imp (imp (imp (__0 ^0) False) (^2 ^0)) (imp (imp (imp (__0 ^0) False) (^1 ^0)) False)) False)))) False
% 0.18/0.40 [370] h0: imp (Pi:$i>$o (\_:$i>$o.Pi:$i>$o (\_:$i>$o.Pi:$i>$o (\_:$i>$o.eq:$i>$o (\_:$i.imp (imp (^3 ^0) False) (imp (imp (^2 ^0) (imp (^1 ^0) False)) False)) (\_:$i.imp (imp (imp (imp (^3 ^0) False) (^2 ^0)) (imp (imp (imp (^3 ^0) False) (^1 ^0)) False)) False))))) False
% 0.18/0.40 % SZS status Error
% 0.18/0.40 Exception: Failure("Could not find hyp name")
% 0.18/0.44 % SZS status Theorem
% 0.18/0.44 % Mode: cade22grackle2x798d
% 0.18/0.44 % Steps: 52
%------------------------------------------------------------------------------