TSTP Solution File: RNG125+4 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : RNG125+4 : 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 : n012.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 13:59:26 EDT 2023
% Result : Theorem 0.19s 0.76s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG125+4 : 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 : n012.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
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sun Aug 27 02:21:10 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.76 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.19/0.76
% 0.19/0.76 % SZS status Theorem
% 0.19/0.76
% 0.19/0.76 % SZS output start Proof
% 0.19/0.76 Take the following subset of the input axioms:
% 0.19/0.76 fof(m__2129, hypothesis, aElement0(xc) & (?[W0]: (aElement0(W0) & sdtasdt0(xc, W0)=xa) & (doDivides0(xc, xa) & (aDivisorOf0(xc, xa) & (aElement0(xc) & (?[W0_2]: (aElement0(W0_2) & sdtasdt0(xc, W0_2)=xb) & (doDivides0(xc, xb) & (aDivisorOf0(xc, xb) & (![W0_2]: ((((aElement0(W0_2) & (?[W1]: (aElement0(W1) & sdtasdt0(W0_2, W1)=xa) | doDivides0(W0_2, xa))) | aDivisorOf0(W0_2, xa)) & (?[W1_2]: (aElement0(W1_2) & sdtasdt0(W0_2, W1_2)=xb) | (doDivides0(W0_2, xb) | aDivisorOf0(W0_2, xb)))) => (?[W1_2]: (aElement0(W1_2) & sdtasdt0(W0_2, W1_2)=xc) & doDivides0(W0_2, xc))) & aGcdOfAnd0(xc, xa, xb)))))))))).
% 0.19/0.76 fof(m__2383, hypothesis, ~((?[W0_2]: (aElement0(W0_2) & sdtasdt0(xu, W0_2)=xa) | (doDivides0(xu, xa) | aDivisorOf0(xu, xa))) & (?[W0_2]: (aElement0(W0_2) & sdtasdt0(xu, W0_2)=xb) | (doDivides0(xu, xb) | aDivisorOf0(xu, xb))))).
% 0.19/0.76 fof(m__2479, hypothesis, ~~(?[W0_2]: (aElement0(W0_2) & sdtasdt0(xu, W0_2)=xa) & doDivides0(xu, xa))).
% 0.19/0.76 fof(m__2612, hypothesis, ~~(?[W0_2]: (aElement0(W0_2) & sdtasdt0(xu, W0_2)=xb) & doDivides0(xu, xb))).
% 0.19/0.76
% 0.19/0.76 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.76 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.76 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.76 fresh(y, y, x1...xn) = u
% 0.19/0.76 C => fresh(s, t, x1...xn) = v
% 0.19/0.76 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.76 variables of u and v.
% 0.19/0.76 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.76 input problem has no model of domain size 1).
% 0.19/0.76
% 0.19/0.76 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.76
% 0.19/0.76 Axiom 1 (m__2612_1): aElement0(w0) = true2.
% 0.19/0.76 Axiom 2 (m__2612): sdtasdt0(xu, w0) = xb.
% 0.19/0.76 Axiom 3 (m__2479_2): doDivides0(xu, xa) = true2.
% 0.19/0.76 Axiom 4 (m__2383_2): fresh14(X, X) = true2.
% 0.19/0.76 Axiom 5 (m__2383_2): fresh14(doDivides0(xu, xa), true2) = or.
% 0.19/0.76
% 0.19/0.76 Goal 1 (m__2383_1): tuple4(sdtasdt0(xu, X), aElement0(X), or) = tuple4(xb, true2, true2).
% 0.19/0.76 The goal is true when:
% 0.19/0.76 X = w0
% 0.19/0.76
% 0.19/0.76 Proof:
% 0.19/0.76 tuple4(sdtasdt0(xu, w0), aElement0(w0), or)
% 0.19/0.76 = { by axiom 5 (m__2383_2) R->L }
% 0.19/0.76 tuple4(sdtasdt0(xu, w0), aElement0(w0), fresh14(doDivides0(xu, xa), true2))
% 0.19/0.76 = { by axiom 3 (m__2479_2) }
% 0.19/0.76 tuple4(sdtasdt0(xu, w0), aElement0(w0), fresh14(true2, true2))
% 0.19/0.76 = { by axiom 4 (m__2383_2) }
% 0.19/0.76 tuple4(sdtasdt0(xu, w0), aElement0(w0), true2)
% 0.19/0.76 = { by axiom 1 (m__2612_1) }
% 0.19/0.76 tuple4(sdtasdt0(xu, w0), true2, true2)
% 0.19/0.76 = { by axiom 2 (m__2612) }
% 0.19/0.76 tuple4(xb, true2, true2)
% 0.19/0.76 % SZS output end Proof
% 0.19/0.76
% 0.19/0.76 RESULT: Theorem (the conjecture is true).
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