TSTP Solution File: COM147+1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : COM147+1 : TPTP v8.1.2. Released v6.4.0.
% 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 : n008.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 : Wed Aug 30 18:45:40 EDT 2023
% Result : Theorem 0.21s 0.62s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : COM147+1 : TPTP v8.1.2. Released v6.4.0.
% 0.00/0.15 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.15/0.36 % Computer : n008.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Tue Aug 29 13:23:32 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.21/0.62 Command-line arguments: --ground-connectedness --complete-subsets
% 0.21/0.62
% 0.21/0.62 % SZS status Theorem
% 0.21/0.62
% 0.21/0.62 % SZS output start Proof
% 0.21/0.62 Take the following subset of the input axioms:
% 0.21/0.62 fof('T-Progress-T-abs', conjecture, ![Vx, VS, VTin]: ((vtcheck(vempty, vabs(Vx, VS, ve1), VTin) & ~visValue(vabs(Vx, VS, ve1))) => ?[Veout]: vreduce(vabs(Vx, VS, ve1))=vsomeExp(Veout))).
% 0.21/0.62 fof(isValue0, axiom, ![VExp0, Ve, Vx2, VS2]: (VExp0=vabs(Vx2, VS2, Ve) => visValue(VExp0))).
% 0.21/0.62
% 0.21/0.62 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.62 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.62 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.62 fresh(y, y, x1...xn) = u
% 0.21/0.62 C => fresh(s, t, x1...xn) = v
% 0.21/0.62 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.62 variables of u and v.
% 0.21/0.62 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.62 input problem has no model of domain size 1).
% 0.21/0.62
% 0.21/0.62 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.62
% 0.21/0.62 Axiom 1 (isValue0): fresh62(X, X, Y) = true2.
% 0.21/0.62 Axiom 2 (isValue0): fresh62(X, vabs(Y, Z, W), X) = visValue(X).
% 0.21/0.62
% 0.21/0.62 Goal 1 (T-Progress-T-abs_2): visValue(vabs(vx, vs, ve1)) = true2.
% 0.21/0.62 Proof:
% 0.21/0.62 visValue(vabs(vx, vs, ve1))
% 0.21/0.62 = { by axiom 2 (isValue0) R->L }
% 0.21/0.62 fresh62(vabs(vx, vs, ve1), vabs(vx, vs, ve1), vabs(vx, vs, ve1))
% 0.21/0.62 = { by axiom 1 (isValue0) }
% 0.21/0.62 true2
% 0.21/0.62 % SZS output end Proof
% 0.21/0.62
% 0.21/0.62 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------