TSTP Solution File: RNG123+1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : RNG123+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 : n027.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 13:59:25 EDT 2023
% Result : Theorem 3.02s 0.83s
% Output : Proof 3.02s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG123+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.34 % Computer : n027.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.19/0.34 % WCLimit : 300
% 0.19/0.34 % DateTime : Sun Aug 27 02:41:35 EDT 2023
% 0.19/0.34 % CPUTime :
% 3.02/0.83 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 3.02/0.83
% 3.02/0.83 % SZS status Theorem
% 3.02/0.83
% 3.02/0.83 % SZS output start Proof
% 3.02/0.83 Take the following subset of the input axioms:
% 3.02/0.83 fof(mDefIdeal, definition, ![W0]: (aIdeal0(W0) <=> (aSet0(W0) & ![W1]: (aElementOf0(W1, W0) => (![W2]: (aElementOf0(W2, W0) => aElementOf0(sdtpldt0(W1, W2), W0)) & ![W2_2]: (aElement0(W2_2) => aElementOf0(sdtasdt0(W2_2, W1), W0))))))).
% 3.02/0.83 fof(m__, conjecture, aElementOf0(xr, xI)).
% 3.02/0.83 fof(m__2174, hypothesis, aIdeal0(xI) & xI=sdtpldt1(slsdtgt0(xa), slsdtgt0(xb))).
% 3.02/0.83 fof(m__2690, hypothesis, aElementOf0(smndt0(sdtasdt0(xq, xu)), xI)).
% 3.02/0.83 fof(m__2699, hypothesis, aElementOf0(xb, xI)).
% 3.02/0.83 fof(m__2718, hypothesis, xr=sdtpldt0(smndt0(sdtasdt0(xq, xu)), xb)).
% 3.02/0.83
% 3.02/0.83 Now clausify the problem and encode Horn clauses using encoding 3 of
% 3.02/0.83 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 3.02/0.83 We repeatedly replace C & s=t => u=v by the two clauses:
% 3.02/0.83 fresh(y, y, x1...xn) = u
% 3.02/0.83 C => fresh(s, t, x1...xn) = v
% 3.02/0.84 where fresh is a fresh function symbol and x1..xn are the free
% 3.02/0.84 variables of u and v.
% 3.02/0.84 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 3.02/0.84 input problem has no model of domain size 1).
% 3.02/0.84
% 3.02/0.84 The encoding turns the above axioms into the following unit equations and goals:
% 3.02/0.84
% 3.02/0.84 Axiom 1 (m__2174_1): aIdeal0(xI) = true.
% 3.02/0.84 Axiom 2 (m__2699): aElementOf0(xb, xI) = true.
% 3.02/0.84 Axiom 3 (m__2690): aElementOf0(smndt0(sdtasdt0(xq, xu)), xI) = true.
% 3.02/0.84 Axiom 4 (m__2718): xr = sdtpldt0(smndt0(sdtasdt0(xq, xu)), xb).
% 3.02/0.84 Axiom 5 (mDefIdeal_6): fresh130(X, X, Y, Z, W) = true.
% 3.02/0.84 Axiom 6 (mDefIdeal_6): fresh47(X, X, Y, Z, W) = aElementOf0(sdtpldt0(Z, W), Y).
% 3.02/0.84 Axiom 7 (mDefIdeal_6): fresh129(X, X, Y, Z, W) = fresh130(aElementOf0(Z, Y), true, Y, Z, W).
% 3.02/0.84 Axiom 8 (mDefIdeal_6): fresh129(aIdeal0(X), true, X, Y, Z) = fresh47(aElementOf0(Z, X), true, X, Y, Z).
% 3.02/0.84
% 3.02/0.84 Goal 1 (m__): aElementOf0(xr, xI) = true.
% 3.02/0.84 Proof:
% 3.02/0.84 aElementOf0(xr, xI)
% 3.02/0.84 = { by axiom 4 (m__2718) }
% 3.02/0.84 aElementOf0(sdtpldt0(smndt0(sdtasdt0(xq, xu)), xb), xI)
% 3.02/0.84 = { by axiom 6 (mDefIdeal_6) R->L }
% 3.02/0.84 fresh47(true, true, xI, smndt0(sdtasdt0(xq, xu)), xb)
% 3.02/0.84 = { by axiom 2 (m__2699) R->L }
% 3.02/0.84 fresh47(aElementOf0(xb, xI), true, xI, smndt0(sdtasdt0(xq, xu)), xb)
% 3.02/0.84 = { by axiom 8 (mDefIdeal_6) R->L }
% 3.02/0.84 fresh129(aIdeal0(xI), true, xI, smndt0(sdtasdt0(xq, xu)), xb)
% 3.02/0.84 = { by axiom 1 (m__2174_1) }
% 3.02/0.84 fresh129(true, true, xI, smndt0(sdtasdt0(xq, xu)), xb)
% 3.02/0.84 = { by axiom 7 (mDefIdeal_6) }
% 3.02/0.84 fresh130(aElementOf0(smndt0(sdtasdt0(xq, xu)), xI), true, xI, smndt0(sdtasdt0(xq, xu)), xb)
% 3.02/0.84 = { by axiom 3 (m__2690) }
% 3.02/0.84 fresh130(true, true, xI, smndt0(sdtasdt0(xq, xu)), xb)
% 3.02/0.84 = { by axiom 5 (mDefIdeal_6) }
% 3.02/0.84 true
% 3.02/0.84 % SZS output end Proof
% 3.02/0.84
% 3.02/0.84 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------