TSTP Solution File: NUN073+1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : NUN073+1 : TPTP v8.1.2. Released v7.3.0.
% 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 : n005.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 12:51:51 EDT 2023
% Result : Theorem 0.20s 0.56s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUN073+1 : TPTP v8.1.2. Released v7.3.0.
% 0.07/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n005.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Aug 27 09:31:53 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.56 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.20/0.56
% 0.20/0.56 % SZS status Theorem
% 0.20/0.56
% 0.20/0.56 % SZS output start Proof
% 0.20/0.56 Take the following subset of the input axioms:
% 0.20/0.56 fof(axiom_3a, axiom, ![X3, X10]: (![Y12]: (![Y13]: (~id(Y13, Y12) | ~r2(X3, Y13)) | ~r2(X10, Y12)) | id(X3, X10))).
% 0.20/0.56 fof(axiom_7a, axiom, ![X7, Y10]: (![Y20]: (~id(Y20, Y10) | ~r1(Y20)) | ~r2(X7, Y10))).
% 0.20/0.56 fof(oneunidtwo, conjecture, ![Y1]: (![Y2]: (![Y4]: (~r1(Y4) | ~r2(Y4, Y2)) | ~id(Y2, Y1)) | ![Y3]: (![Y5]: (~r1(Y5) | ~r2(Y5, Y3)) | ~r2(Y3, Y1)))).
% 0.20/0.56
% 0.20/0.56 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.56 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.56 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.56 fresh(y, y, x1...xn) = u
% 0.20/0.56 C => fresh(s, t, x1...xn) = v
% 0.20/0.56 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.56 variables of u and v.
% 0.20/0.56 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.56 input problem has no model of domain size 1).
% 0.20/0.56
% 0.20/0.56 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.56
% 0.20/0.56 Axiom 1 (oneunidtwo_1): r1(y4) = true2.
% 0.20/0.56 Axiom 2 (oneunidtwo): id(y2, y1) = true2.
% 0.20/0.56 Axiom 3 (oneunidtwo_3): r2(y4, y2) = true2.
% 0.20/0.56 Axiom 4 (oneunidtwo_4): r2(y3, y1) = true2.
% 0.20/0.56 Axiom 5 (oneunidtwo_5): r2(y5, y3) = true2.
% 0.20/0.56 Axiom 6 (axiom_3a): fresh20(X, X, Y, Z) = true2.
% 0.20/0.56 Axiom 7 (axiom_3a): fresh19(X, X, Y, Z, W, V) = fresh20(id(V, W), true2, Y, Z).
% 0.20/0.56 Axiom 8 (axiom_3a): fresh12(X, X, Y, Z, W, V) = id(Y, Z).
% 0.20/0.56 Axiom 9 (axiom_3a): fresh19(r2(X, Y), true2, Z, X, Y, W) = fresh12(r2(Z, W), true2, Z, X, Y, W).
% 0.20/0.56
% 0.20/0.56 Goal 1 (axiom_7a): tuple(id(X, Y), r1(X), r2(Z, Y)) = tuple(true2, true2, true2).
% 0.20/0.56 The goal is true when:
% 0.20/0.56 X = y4
% 0.20/0.56 Y = y3
% 0.20/0.56 Z = y5
% 0.20/0.56
% 0.20/0.56 Proof:
% 0.20/0.56 tuple(id(y4, y3), r1(y4), r2(y5, y3))
% 0.20/0.56 = { by axiom 5 (oneunidtwo_5) }
% 0.20/0.56 tuple(id(y4, y3), r1(y4), true2)
% 0.20/0.56 = { by axiom 8 (axiom_3a) R->L }
% 0.20/0.56 tuple(fresh12(true2, true2, y4, y3, y1, y2), r1(y4), true2)
% 0.20/0.56 = { by axiom 3 (oneunidtwo_3) R->L }
% 0.20/0.56 tuple(fresh12(r2(y4, y2), true2, y4, y3, y1, y2), r1(y4), true2)
% 0.20/0.56 = { by axiom 9 (axiom_3a) R->L }
% 0.20/0.56 tuple(fresh19(r2(y3, y1), true2, y4, y3, y1, y2), r1(y4), true2)
% 0.20/0.56 = { by axiom 4 (oneunidtwo_4) }
% 0.20/0.56 tuple(fresh19(true2, true2, y4, y3, y1, y2), r1(y4), true2)
% 0.20/0.56 = { by axiom 7 (axiom_3a) }
% 0.20/0.56 tuple(fresh20(id(y2, y1), true2, y4, y3), r1(y4), true2)
% 0.20/0.56 = { by axiom 2 (oneunidtwo) }
% 0.20/0.56 tuple(fresh20(true2, true2, y4, y3), r1(y4), true2)
% 0.20/0.56 = { by axiom 6 (axiom_3a) }
% 0.20/0.56 tuple(true2, r1(y4), true2)
% 0.20/0.56 = { by axiom 1 (oneunidtwo_1) }
% 0.20/0.56 tuple(true2, true2, true2)
% 0.20/0.56 % SZS output end Proof
% 0.20/0.56
% 0.20/0.56 RESULT: Theorem (the conjecture is true).
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