TSTP Solution File: PUZ075+1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : PUZ075+1 : TPTP v8.1.2. Released v3.5.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n020.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 13:24:12 EDT 2023
% Result : Theorem 6.80s 1.30s
% Output : Proof 6.80s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : PUZ075+1 : TPTP v8.1.2. Released v3.5.0.
% 0.00/0.15 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.16/0.37 % Computer : n020.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Sat Aug 26 21:59:29 EDT 2023
% 0.16/0.37 % CPUTime :
% 6.80/1.30 Command-line arguments: --ground-connectedness --complete-subsets
% 6.80/1.30
% 6.80/1.30 % SZS status Theorem
% 6.80/1.30
% 6.80/1.30 % SZS output start Proof
% 6.80/1.30 Take the following subset of the input axioms:
% 6.80/1.32 fof(tlhfof24987, axiom, ![TLH24985, TLH24986]: (edge(TLH24986, TLH24985) <=> ((TLH24986=cell1 & TLH24985=cell2) | ((TLH24986=cell2 & TLH24985=cell3) | ((TLH24986=cell3 & TLH24985=cell4) | ((TLH24986=cell4 & TLH24985=cell5) | ((TLH24986=cell5 & TLH24985=cell6) | ((TLH24986=cell6 & TLH24985=cell7) | ((TLH24986=cell7 & TLH24985=cell8) | ((TLH24986=cell8 & TLH24985=cell9) | ((TLH24986=cell9 & TLH24985=cell10) | ((TLH24986=cell11 & TLH24985=cell12) | ((TLH24986=cell12 & TLH24985=cell13) | ((TLH24986=cell13 & TLH24985=cell14) | ((TLH24986=cell14 & TLH24985=cell15) | ((TLH24986=cell15 & TLH24985=cell16) | ((TLH24986=cell16 & TLH24985=cell17) | ((TLH24986=cell17 & TLH24985=cell18) | ((TLH24986=cell18 & TLH24985=cell19) | ((TLH24986=cell19 & TLH24985=cell20) | ((TLH24986=cell21 & TLH24985=cell22) | ((TLH24986=cell22 & TLH24985=cell23) | ((TLH24986=cell23 & TLH24985=cell24) | ((TLH24986=cell24 & TLH24985=cell25) | ((TLH24986=cell25 & TLH24985=cell26) | ((TLH24986=cell26 & TLH24985=cell27) | ((TLH24986=cell27 & TLH24985=cell28) | ((TLH24986=cell28 & TLH24985=cell29) | ((TLH24986=cell29 & TLH24985=cell30) | ((TLH24986=cell31 & TLH24985=cell32) | ((TLH24986=cell32 & TLH24985=cell33) | ((TLH24986=cell33 & TLH24985=cell34) | ((TLH24986=cell34 & TLH24985=cell35) | ((TLH24986=cell35 & TLH24985=cell36) | ((TLH24986=cell36 & TLH24985=cell37) | ((TLH24986=cell37 & TLH24985=cell38) | ((TLH24986=cell38 & TLH24985=cell39) | ((TLH24986=cell39 & TLH24985=cell40) | ((TLH24986=cell41 & TLH24985=cell42) | ((TLH24986=cell42 & TLH24985=cell43) | ((TLH24986=cell43 & TLH24985=cell44) | ((TLH24986=cell44 & TLH24985=cell45) | ((TLH24986=cell45 & TLH24985=cell46) | ((TLH24986=cell46 & TLH24985=cell47) | ((TLH24986=cell47 & TLH24985=cell48) | ((TLH24986=cell48 & TLH24985=cell49) | ((TLH24986=cell49 & TLH24985=cell50) | ((TLH24986=cell51 & TLH24985=cell52) | ((TLH24986=cell52 & TLH24985=cell53) | ((TLH24986=cell53 & TLH24985=cell54) | ((TLH24986=cell54 & TLH24985=cell55) | ((TLH24986=cell55 & TLH24985=cell56) | ((TLH24986=cell56 & TLH24985=cell57) | ((TLH24986=cell57 & TLH24985=cell58) | ((TLH24986=cell58 & TLH24985=cell59) | ((TLH24986=cell59 & TLH24985=cell60) | ((TLH24986=cell61 & TLH24985=cell62) | ((TLH24986=cell62 & TLH24985=cell63) | ((TLH24986=cell63 & TLH24985=cell64) | ((TLH24986=cell64 & TLH24985=cell65) | ((TLH24986=cell65 & TLH24985=cell66) | ((TLH24986=cell66 & TLH24985=cell67) | ((TLH24986=cell67 & TLH24985=cell68) | ((TLH24986=cell68 & TLH24985=cell69) | ((TLH24986=cell69 & TLH24985=cell70) | ((TLH24986=cell71 & TLH24985=cell72) | ((TLH24986=cell72 & TLH24985=cell73) | ((TLH24986=cell73 & TLH24985=cell74) | ((TLH24986=cell74 & TLH24985=cell75) | ((TLH24986=cell75 & TLH24985=cell76) | ((TLH24986=cell76 & TLH24985=cell77) | ((TLH24986=cell77 & TLH24985=cell78) | ((TLH24986=cell78 & TLH24985=cell79) | ((TLH24986=cell79 & TLH24985=cell80) | ((TLH24986=cell81 & TLH24985=cell82) | ((TLH24986=cell82 & TLH24985=cell83) | ((TLH24986=cell83 & TLH24985=cell84) | ((TLH24986=cell84 & TLH24985=cell85) | ((TLH24986=cell85 & TLH24985=cell86) | ((TLH24986=cell86 & TLH24985=cell87) | ((TLH24986=cell87 & TLH24985=cell88) | ((TLH24986=cell88 & TLH24985=cell89) | ((TLH24986=cell89 & TLH24985=cell90) | ((TLH24986=cell91 & TLH24985=cell92) | ((TLH24986=cell92 & TLH24985=cell93) | ((TLH24986=cell93 & TLH24985=cell94) | ((TLH24986=cell94 & TLH24985=cell95) | ((TLH24986=cell95 & TLH24985=cell96) | ((TLH24986=cell96 & TLH24985=cell97) | ((TLH24986=cell97 & TLH24985=cell98) | ((TLH24986=cell98 & TLH24985=cell99) | ((TLH24986=cell99 & TLH24985=cell100) | ((TLH24986=cell1 & TLH24985=cell11) | ((TLH24986=cell2 & TLH24985=cell12) | ((TLH24986=cell3 & TLH24985=cell13) | ((TLH24986=cell4 & TLH24985=cell14) | ((TLH24986=cell5 & TLH24985=cell15) | ((TLH24986=cell6 & TLH24985=cell16) | ((TLH24986=cell7 & TLH24985=cell17) | ((TLH24986=cell8 & TLH24985=cell18) | ((TLH24986=cell9 & TLH24985=cell19) | ((TLH24986=cell10 & TLH24985=cell20) | ((TLH24986=cell11 & TLH24985=cell21) | ((TLH24986=cell12 & TLH24985=cell22) | ((TLH24986=cell13 & TLH24985=cell23) | ((TLH24986=cell14 & TLH24985=cell24) | ((TLH24986=cell15 & TLH24985=cell25) | ((TLH24986=cell16 & TLH24985=cell26) | ((TLH24986=cell17 & TLH24985=cell27) | ((TLH24986=cell18 & TLH24985=cell28) | ((TLH24986=cell19 & TLH24985=cell29) | ((TLH24986=cell20 & TLH24985=cell30) | ((TLH24986=cell21 & TLH24985=cell31) | ((TLH24986=cell22 & TLH24985=cell32) | ((TLH24986=cell23 & TLH24985=cell33) | ((TLH24986=cell24 & TLH24985=cell34) | ((TLH24986=cell25 & TLH24985=cell35) | ((TLH24986=cell26 & TLH24985=cell36) | ((TLH24986=cell27 & TLH24985=cell37) | ((TLH24986=cell28 & TLH24985=cell38) | ((TLH24986=cell29 & TLH24985=cell39) | ((TLH24986=cell30 & TLH24985=cell40) | ((TLH24986=cell31 & TLH24985=cell41) | ((TLH24986=cell32 & TLH24985=cell42) | ((TLH24986=cell33 & TLH24985=cell43) | ((TLH24986=cell34 & TLH24985=cell44) | ((TLH24986=cell35 & TLH24985=cell45) | ((TLH24986=cell36 & TLH24985=cell46) | ((TLH24986=cell37 & TLH24985=cell47) | ((TLH24986=cell38 & TLH24985=cell48) | ((TLH24986=cell39 & TLH24985=cell49) | ((TLH24986=cell40 & TLH24985=cell50) | ((TLH24986=cell41 & TLH24985=cell51) | ((TLH24986=cell42 & TLH24985=cell52) | ((TLH24986=cell43 & TLH24985=cell53) | ((TLH24986=cell44 & TLH24985=cell54) | ((TLH24986=cell45 & TLH24985=cell55) | ((TLH24986=cell46 & TLH24985=cell56) | ((TLH24986=cell47 & TLH24985=cell57) | ((TLH24986=cell48 & TLH24985=cell58) | ((TLH24986=cell49 & TLH24985=cell59) | ((TLH24986=cell50 & TLH24985=cell60) | ((TLH24986=cell51 & TLH24985=cell61) | ((TLH24986=cell52 & TLH24985=cell62) | ((TLH24986=cell53 & TLH24985=cell63) | ((TLH24986=cell54 & TLH24985=cell64) | ((TLH24986=cell55 & TLH24985=cell65) | ((TLH24986=cell56 & TLH24985=cell66) | ((TLH24986=cell57 & TLH24985=cell67) | ((TLH24986=cell58 & TLH24985=cell68) | ((TLH24986=cell59 & TLH24985=cell69) | ((TLH24986=cell60 & TLH24985=cell70) | ((TLH24986=cell61 & TLH24985=cell71) | ((TLH24986=cell62 & TLH24985=cell72) | ((TLH24986=cell63 & TLH24985=cell73) | ((TLH24986=cell64 & TLH24985=cell74) | ((TLH24986=cell65 & TLH24985=cell75) | ((TLH24986=cell66 & TLH24985=cell76) | ((TLH24986=cell67 & TLH24985=cell77) | ((TLH24986=cell68 & TLH24985=cell78) | ((TLH24986=cell69 & TLH24985=cell79) | ((TLH24986=cell70 & TLH24985=cell80) | ((TLH24986=cell71 & TLH24985=cell81) | ((TLH24986=cell72 & TLH24985=cell82) | ((TLH24986=cell73 & TLH24985=cell83) | ((TLH24986=cell74 & TLH24985=cell84) | ((TLH24986=cell75 & TLH24985=cell85) | ((TLH24986=cell76 & TLH24985=cell86) | ((TLH24986=cell77 & TLH24985=cell87) | ((TLH24986=cell78 & TLH24985=cell88) | ((TLH24986=cell79 & TLH24985=cell89) | ((TLH24986=cell80 & TLH24985=cell90) | ((TLH24986=cell81 & TLH24985=cell91) | ((TLH24986=cell82 & TLH24985=cell92) | ((TLH24986=cell83 & TLH24985=cell93) | ((TLH24986=cell84 & TLH24985=cell94) | ((TLH24986=cell85 & TLH24985=cell95) | ((TLH24986=cell86 & TLH24985=cell96) | ((TLH24986=cell87 & TLH24985=cell97) | ((TLH24986=cell88 & TLH24985=cell98) | ((TLH24986=cell89 & TLH24985=cell99) | (TLH24986=cell90 & TLH24985=cell100)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))).
% 6.80/1.32 fof(tlhfof24988, axiom, ![Y, X]: (adj(X, Y) <=> (edge(X, Y) | edge(Y, X)))).
% 6.80/1.32 fof(tlhfof24989, conjecture, adj(cell12, cell13)).
% 6.80/1.32
% 6.80/1.32 Now clausify the problem and encode Horn clauses using encoding 3 of
% 6.80/1.32 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 6.80/1.32 We repeatedly replace C & s=t => u=v by the two clauses:
% 6.80/1.32 fresh(y, y, x1...xn) = u
% 6.80/1.32 C => fresh(s, t, x1...xn) = v
% 6.80/1.32 where fresh is a fresh function symbol and x1..xn are the free
% 6.80/1.32 variables of u and v.
% 6.80/1.32 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 6.80/1.32 input problem has no model of domain size 1).
% 6.80/1.32
% 6.80/1.32 The encoding turns the above axioms into the following unit equations and goals:
% 6.80/1.33
% 6.80/1.33 Axiom 1 (tlhfof24988_1): fresh(X, X, Y, Z) = true.
% 6.80/1.33 Axiom 2 (tlhfof24987_13): fresh292(X, X, Y, Z) = edge(Z, Y).
% 6.80/1.33 Axiom 3 (tlhfof24987_13): fresh291(X, X, Y, Z) = true.
% 6.80/1.33 Axiom 4 (tlhfof24987_13): fresh292(X, cell12, Y, X) = fresh291(Y, cell13, Y, X).
% 6.80/1.33 Axiom 5 (tlhfof24988_1): fresh(edge(X, Y), true, Y, X) = adj(X, Y).
% 6.80/1.33
% 6.80/1.33 Goal 1 (tlhfof24989): adj(cell12, cell13) = true.
% 6.80/1.33 Proof:
% 6.80/1.33 adj(cell12, cell13)
% 6.80/1.33 = { by axiom 5 (tlhfof24988_1) R->L }
% 6.80/1.33 fresh(edge(cell12, cell13), true, cell13, cell12)
% 6.80/1.33 = { by axiom 2 (tlhfof24987_13) R->L }
% 6.80/1.33 fresh(fresh292(cell12, cell12, cell13, cell12), true, cell13, cell12)
% 6.80/1.33 = { by axiom 4 (tlhfof24987_13) }
% 6.80/1.33 fresh(fresh291(cell13, cell13, cell13, cell12), true, cell13, cell12)
% 6.80/1.33 = { by axiom 3 (tlhfof24987_13) }
% 6.80/1.33 fresh(true, true, cell13, cell12)
% 6.80/1.33 = { by axiom 1 (tlhfof24988_1) }
% 6.80/1.33 true
% 6.80/1.33 % SZS output end Proof
% 6.80/1.33
% 6.80/1.33 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------