TSTP Solution File: RNG103+2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : RNG103+2 : 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 : n026.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 13:59:18 EDT 2023
% Result : Theorem 23.77s 4.51s
% Output : Proof 23.77s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : RNG103+2 : 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
% 0.09/0.31 % Computer : n026.cluster.edu
% 0.09/0.31 % Model : x86_64 x86_64
% 0.09/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.31 % Memory : 8042.1875MB
% 0.09/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.31 % CPULimit : 300
% 0.09/0.31 % WCLimit : 300
% 0.09/0.31 % DateTime : Sun Aug 27 02:28:49 EDT 2023
% 0.09/0.31 % CPUTime :
% 23.77/4.51 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 23.77/4.51
% 23.77/4.51 % SZS status Theorem
% 23.77/4.53
% 23.77/4.53 % SZS output start Proof
% 23.77/4.53 Take the following subset of the input axioms:
% 23.77/4.53 fof(mAMDistr, axiom, ![W0, W1, W2]: ((aElement0(W0) & (aElement0(W1) & aElement0(W2))) => (sdtasdt0(W0, sdtpldt0(W1, W2))=sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2)) & sdtasdt0(sdtpldt0(W1, W2), W0)=sdtpldt0(sdtasdt0(W1, W0), sdtasdt0(W2, W0))))).
% 23.77/4.53 fof(m__, conjecture, sdtpldt0(xx, xy)=sdtasdt0(xc, sdtpldt0(xu, xv))).
% 23.77/4.53 fof(m__1905, hypothesis, aElement0(xc)).
% 23.77/4.53 fof(m__1956, hypothesis, aElement0(xu) & sdtasdt0(xc, xu)=xx).
% 23.77/4.53 fof(m__1979, hypothesis, aElement0(xv) & sdtasdt0(xc, xv)=xy).
% 23.77/4.53
% 23.77/4.53 Now clausify the problem and encode Horn clauses using encoding 3 of
% 23.77/4.53 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 23.77/4.53 We repeatedly replace C & s=t => u=v by the two clauses:
% 23.77/4.53 fresh(y, y, x1...xn) = u
% 23.77/4.53 C => fresh(s, t, x1...xn) = v
% 23.77/4.53 where fresh is a fresh function symbol and x1..xn are the free
% 23.77/4.53 variables of u and v.
% 23.77/4.53 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 23.77/4.53 input problem has no model of domain size 1).
% 23.77/4.53
% 23.77/4.53 The encoding turns the above axioms into the following unit equations and goals:
% 23.77/4.53
% 23.77/4.53 Axiom 1 (m__1905): aElement0(xc) = true.
% 23.77/4.53 Axiom 2 (m__1956_1): aElement0(xu) = true.
% 23.77/4.53 Axiom 3 (m__1979_1): aElement0(xv) = true.
% 23.77/4.53 Axiom 4 (m__1956): sdtasdt0(xc, xu) = xx.
% 23.77/4.53 Axiom 5 (m__1979): sdtasdt0(xc, xv) = xy.
% 23.77/4.53 Axiom 6 (mAMDistr): fresh165(X, X, Y, Z, W) = sdtasdt0(Y, sdtpldt0(Z, W)).
% 23.77/4.53 Axiom 7 (mAMDistr): fresh62(X, X, Y, Z, W) = sdtpldt0(sdtasdt0(Y, Z), sdtasdt0(Y, W)).
% 23.77/4.53 Axiom 8 (mAMDistr): fresh164(X, X, Y, Z, W) = fresh165(aElement0(Y), true, Y, Z, W).
% 23.77/4.53 Axiom 9 (mAMDistr): fresh164(aElement0(X), true, Y, Z, X) = fresh62(aElement0(Z), true, Y, Z, X).
% 23.77/4.53
% 23.77/4.53 Goal 1 (m__): sdtpldt0(xx, xy) = sdtasdt0(xc, sdtpldt0(xu, xv)).
% 23.77/4.53 Proof:
% 23.77/4.53 sdtpldt0(xx, xy)
% 23.77/4.53 = { by axiom 5 (m__1979) R->L }
% 23.77/4.53 sdtpldt0(xx, sdtasdt0(xc, xv))
% 23.77/4.53 = { by axiom 4 (m__1956) R->L }
% 23.77/4.53 sdtpldt0(sdtasdt0(xc, xu), sdtasdt0(xc, xv))
% 23.77/4.53 = { by axiom 7 (mAMDistr) R->L }
% 23.77/4.53 fresh62(true, true, xc, xu, xv)
% 23.77/4.53 = { by axiom 2 (m__1956_1) R->L }
% 23.77/4.53 fresh62(aElement0(xu), true, xc, xu, xv)
% 23.77/4.53 = { by axiom 9 (mAMDistr) R->L }
% 23.77/4.53 fresh164(aElement0(xv), true, xc, xu, xv)
% 23.77/4.53 = { by axiom 3 (m__1979_1) }
% 23.77/4.53 fresh164(true, true, xc, xu, xv)
% 23.77/4.53 = { by axiom 8 (mAMDistr) }
% 23.77/4.53 fresh165(aElement0(xc), true, xc, xu, xv)
% 23.77/4.53 = { by axiom 1 (m__1905) }
% 23.77/4.53 fresh165(true, true, xc, xu, xv)
% 23.77/4.53 = { by axiom 6 (mAMDistr) }
% 23.77/4.53 sdtasdt0(xc, sdtpldt0(xu, xv))
% 23.77/4.53 % SZS output end Proof
% 23.77/4.53
% 23.77/4.53 RESULT: Theorem (the conjecture is true).
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