TSTP Solution File: NUM587+1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : NUM587+1 : TPTP v8.1.2. Released v4.0.0.
% 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 : n021.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 11:57:07 EDT 2023
% Result : Theorem 21.10s 3.06s
% Output : Proof 21.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : NUM587+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.11 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.31 % Computer : n021.cluster.edu
% 0.13/0.31 % Model : x86_64 x86_64
% 0.13/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.31 % Memory : 8042.1875MB
% 0.13/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.31 % CPULimit : 300
% 0.13/0.31 % WCLimit : 300
% 0.13/0.31 % DateTime : Fri Aug 25 14:45:41 EDT 2023
% 0.13/0.31 % CPUTime :
% 21.10/3.06 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 21.10/3.06
% 21.10/3.06 % SZS status Theorem
% 21.10/3.06
% 21.10/3.07 % SZS output start Proof
% 21.10/3.07 Take the following subset of the input axioms:
% 21.10/3.07 fof(mDefSub, definition, ![W0]: (aSet0(W0) => ![W1]: (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2]: (aElementOf0(W2, W1) => aElementOf0(W2, W0)))))).
% 21.10/3.07 fof(m__, conjecture, aElementOf0(xx, xT)).
% 21.10/3.07 fof(m__3291, hypothesis, aSet0(xT) & isFinite0(xT)).
% 21.10/3.07 fof(m__3453, hypothesis, aFunction0(xc) & (szDzozmdt0(xc)=slbdtsldtrb0(xS, xK) & aSubsetOf0(sdtlcdtrc0(xc, szDzozmdt0(xc)), xT))).
% 21.10/3.07 fof(m__4263, hypothesis, xx=sdtlpdtrp0(xc, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))) & aElementOf0(sdtlpdtrp0(xc, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))), sdtlcdtrc0(xc, szDzozmdt0(xc)))).
% 21.10/3.07
% 21.10/3.07 Now clausify the problem and encode Horn clauses using encoding 3 of
% 21.10/3.07 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 21.10/3.07 We repeatedly replace C & s=t => u=v by the two clauses:
% 21.10/3.07 fresh(y, y, x1...xn) = u
% 21.10/3.07 C => fresh(s, t, x1...xn) = v
% 21.10/3.07 where fresh is a fresh function symbol and x1..xn are the free
% 21.10/3.07 variables of u and v.
% 21.10/3.07 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 21.10/3.07 input problem has no model of domain size 1).
% 21.10/3.07
% 21.10/3.07 The encoding turns the above axioms into the following unit equations and goals:
% 21.10/3.07
% 21.10/3.07 Axiom 1 (m__3291): aSet0(xT) = true2.
% 21.10/3.07 Axiom 2 (mDefSub_2): fresh315(X, X, Y, Z) = true2.
% 21.10/3.07 Axiom 3 (mDefSub_2): fresh52(X, X, Y, Z) = aElementOf0(Z, Y).
% 21.10/3.07 Axiom 4 (m__3453_1): aSubsetOf0(sdtlcdtrc0(xc, szDzozmdt0(xc)), xT) = true2.
% 21.10/3.07 Axiom 5 (mDefSub_2): fresh314(X, X, Y, Z, W) = fresh315(aSet0(Y), true2, Y, W).
% 21.10/3.07 Axiom 6 (m__4263): xx = sdtlpdtrp0(xc, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))).
% 21.10/3.07 Axiom 7 (mDefSub_2): fresh314(aSubsetOf0(X, Y), true2, Y, X, Z) = fresh52(aElementOf0(Z, X), true2, Y, Z).
% 21.10/3.07 Axiom 8 (m__4263_1): aElementOf0(sdtlpdtrp0(xc, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))), sdtlcdtrc0(xc, szDzozmdt0(xc))) = true2.
% 21.10/3.07
% 21.10/3.07 Goal 1 (m__): aElementOf0(xx, xT) = true2.
% 21.10/3.07 Proof:
% 21.10/3.07 aElementOf0(xx, xT)
% 21.10/3.07 = { by axiom 3 (mDefSub_2) R->L }
% 21.10/3.07 fresh52(true2, true2, xT, xx)
% 21.10/3.07 = { by axiom 8 (m__4263_1) R->L }
% 21.10/3.07 fresh52(aElementOf0(sdtlpdtrp0(xc, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))), sdtlcdtrc0(xc, szDzozmdt0(xc))), true2, xT, xx)
% 21.10/3.07 = { by axiom 6 (m__4263) R->L }
% 21.10/3.07 fresh52(aElementOf0(xx, sdtlcdtrc0(xc, szDzozmdt0(xc))), true2, xT, xx)
% 21.10/3.07 = { by axiom 7 (mDefSub_2) R->L }
% 21.10/3.07 fresh314(aSubsetOf0(sdtlcdtrc0(xc, szDzozmdt0(xc)), xT), true2, xT, sdtlcdtrc0(xc, szDzozmdt0(xc)), xx)
% 21.10/3.07 = { by axiom 4 (m__3453_1) }
% 21.10/3.07 fresh314(true2, true2, xT, sdtlcdtrc0(xc, szDzozmdt0(xc)), xx)
% 21.10/3.07 = { by axiom 5 (mDefSub_2) }
% 21.10/3.07 fresh315(aSet0(xT), true2, xT, xx)
% 21.10/3.07 = { by axiom 1 (m__3291) }
% 21.10/3.07 fresh315(true2, true2, xT, xx)
% 21.10/3.07 = { by axiom 2 (mDefSub_2) }
% 21.10/3.07 true2
% 21.10/3.07 % SZS output end Proof
% 21.10/3.07
% 21.10/3.07 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------