TSTP Solution File: RNG105+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : RNG105+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 : n001.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 13:59:19 EDT 2023
% Result : Theorem 106.33s 14.09s
% Output : Proof 106.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG105+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
% 0.13/0.34 % Computer : n001.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 03:00:17 EDT 2023
% 0.13/0.34 % CPUTime :
% 106.33/14.09 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 106.33/14.09
% 106.33/14.09 % SZS status Theorem
% 106.33/14.09
% 106.33/14.09 % SZS output start Proof
% 106.33/14.09 Take the following subset of the input axioms:
% 106.55/14.09 fof(mDefPrIdeal, definition, ![W0]: (aElement0(W0) => ![W1]: (W1=slsdtgt0(W0) <=> (aSet0(W1) & ![W2]: (aElementOf0(W2, W1) <=> ?[W3]: (aElement0(W3) & sdtasdt0(W0, W3)=W2)))))).
% 106.55/14.09 fof(mSortsB, axiom, ![W0_2, W1_2]: ((aElement0(W0_2) & aElement0(W1_2)) => aElement0(sdtpldt0(W0_2, W1_2)))).
% 106.55/14.09 fof(mSortsB_02, axiom, ![W0_2, W1_2]: ((aElement0(W0_2) & aElement0(W1_2)) => aElement0(sdtasdt0(W0_2, W1_2)))).
% 106.55/14.09 fof(m__, conjecture, aElementOf0(sdtpldt0(xx, xy), slsdtgt0(xc)) & aElementOf0(sdtasdt0(xz, xx), slsdtgt0(xc))).
% 106.55/14.09 fof(m__1905, hypothesis, aElement0(xc)).
% 106.55/14.09 fof(m__1933, hypothesis, aElementOf0(xx, slsdtgt0(xc)) & (aElementOf0(xy, slsdtgt0(xc)) & aElement0(xz))).
% 106.55/14.09 fof(m__1956, hypothesis, aElement0(xu) & sdtasdt0(xc, xu)=xx).
% 106.55/14.09 fof(m__1979, hypothesis, aElement0(xv) & sdtasdt0(xc, xv)=xy).
% 106.55/14.09 fof(m__2010, hypothesis, sdtpldt0(xx, xy)=sdtasdt0(xc, sdtpldt0(xu, xv))).
% 106.55/14.09 fof(m__2043, hypothesis, sdtasdt0(xz, xx)=sdtasdt0(xc, sdtasdt0(xu, xz))).
% 106.55/14.10
% 106.55/14.10 Now clausify the problem and encode Horn clauses using encoding 3 of
% 106.55/14.10 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 106.55/14.10 We repeatedly replace C & s=t => u=v by the two clauses:
% 106.55/14.10 fresh(y, y, x1...xn) = u
% 106.55/14.10 C => fresh(s, t, x1...xn) = v
% 106.55/14.10 where fresh is a fresh function symbol and x1..xn are the free
% 106.55/14.10 variables of u and v.
% 106.55/14.10 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 106.55/14.10 input problem has no model of domain size 1).
% 106.55/14.10
% 106.55/14.10 The encoding turns the above axioms into the following unit equations and goals:
% 106.55/14.10
% 106.55/14.10 Axiom 1 (m__1905): aElement0(xc) = true.
% 106.55/14.10 Axiom 2 (m__1933): aElement0(xz) = true.
% 106.55/14.10 Axiom 3 (m__1956_1): aElement0(xu) = true.
% 106.55/14.10 Axiom 4 (m__1979_1): aElement0(xv) = true.
% 106.55/14.10 Axiom 5 (m__2043): sdtasdt0(xz, xx) = sdtasdt0(xc, sdtasdt0(xu, xz)).
% 106.55/14.10 Axiom 6 (m__2010): sdtpldt0(xx, xy) = sdtasdt0(xc, sdtpldt0(xu, xv)).
% 106.55/14.10 Axiom 7 (mDefPrIdeal_2): fresh66(X, X, Y, Z) = true.
% 106.55/14.10 Axiom 8 (mDefPrIdeal_3): fresh37(X, X, Y, Z) = true.
% 106.55/14.10 Axiom 9 (mSortsB): fresh11(X, X, Y, Z) = aElement0(sdtpldt0(Y, Z)).
% 106.55/14.10 Axiom 10 (mSortsB): fresh10(X, X, Y, Z) = true.
% 106.55/14.10 Axiom 11 (mSortsB_02): fresh9(X, X, Y, Z) = aElement0(sdtasdt0(Y, Z)).
% 106.55/14.10 Axiom 12 (mSortsB_02): fresh8(X, X, Y, Z) = true.
% 106.55/14.10 Axiom 13 (mDefPrIdeal_2): fresh65(X, X, Y, Z, W) = fresh66(Z, slsdtgt0(Y), Z, W).
% 106.55/14.10 Axiom 14 (mDefPrIdeal_2): fresh39(X, X, Y, Z, W) = aElementOf0(W, Z).
% 106.55/14.10 Axiom 15 (mDefPrIdeal_3): fresh38(X, X, Y, Z, W) = equiv(Y, Z).
% 106.55/14.10 Axiom 16 (mSortsB): fresh11(aElement0(X), true, Y, X) = fresh10(aElement0(Y), true, Y, X).
% 106.55/14.10 Axiom 17 (mSortsB_02): fresh9(aElement0(X), true, Y, X) = fresh8(aElement0(Y), true, Y, X).
% 106.55/14.10 Axiom 18 (mDefPrIdeal_3): fresh38(aElement0(X), true, Y, Z, X) = fresh37(sdtasdt0(Y, X), Z, Y, Z).
% 106.55/14.10 Axiom 19 (mDefPrIdeal_2): fresh65(equiv(X, Y), true, X, Z, Y) = fresh39(aElement0(X), true, X, Z, Y).
% 106.55/14.10
% 106.55/14.10 Lemma 20: fresh65(X, X, Y, slsdtgt0(Y), Z) = true.
% 106.55/14.10 Proof:
% 106.55/14.10 fresh65(X, X, Y, slsdtgt0(Y), Z)
% 106.55/14.10 = { by axiom 13 (mDefPrIdeal_2) }
% 106.55/14.10 fresh66(slsdtgt0(Y), slsdtgt0(Y), slsdtgt0(Y), Z)
% 106.55/14.10 = { by axiom 7 (mDefPrIdeal_2) }
% 106.55/14.10 true
% 106.55/14.10
% 106.55/14.10 Lemma 21: fresh38(aElement0(X), true, Y, sdtasdt0(Y, X), X) = true.
% 106.55/14.10 Proof:
% 106.55/14.10 fresh38(aElement0(X), true, Y, sdtasdt0(Y, X), X)
% 106.55/14.10 = { by axiom 18 (mDefPrIdeal_3) }
% 106.55/14.10 fresh37(sdtasdt0(Y, X), sdtasdt0(Y, X), Y, sdtasdt0(Y, X))
% 106.55/14.10 = { by axiom 8 (mDefPrIdeal_3) }
% 106.55/14.10 true
% 106.55/14.10
% 106.55/14.10 Goal 1 (m__): tuple(aElementOf0(sdtpldt0(xx, xy), slsdtgt0(xc)), aElementOf0(sdtasdt0(xz, xx), slsdtgt0(xc))) = tuple(true, true).
% 106.55/14.10 Proof:
% 106.55/14.10 tuple(aElementOf0(sdtpldt0(xx, xy), slsdtgt0(xc)), aElementOf0(sdtasdt0(xz, xx), slsdtgt0(xc)))
% 106.55/14.10 = { by axiom 14 (mDefPrIdeal_2) R->L }
% 106.55/14.10 tuple(fresh39(true, true, xc, slsdtgt0(xc), sdtpldt0(xx, xy)), aElementOf0(sdtasdt0(xz, xx), slsdtgt0(xc)))
% 106.55/14.10 = { by axiom 1 (m__1905) R->L }
% 106.55/14.10 tuple(fresh39(aElement0(xc), true, xc, slsdtgt0(xc), sdtpldt0(xx, xy)), aElementOf0(sdtasdt0(xz, xx), slsdtgt0(xc)))
% 106.55/14.10 = { by axiom 19 (mDefPrIdeal_2) R->L }
% 106.55/14.10 tuple(fresh65(equiv(xc, sdtpldt0(xx, xy)), true, xc, slsdtgt0(xc), sdtpldt0(xx, xy)), aElementOf0(sdtasdt0(xz, xx), slsdtgt0(xc)))
% 106.55/14.10 = { by axiom 15 (mDefPrIdeal_3) R->L }
% 106.55/14.10 tuple(fresh65(fresh38(true, true, xc, sdtpldt0(xx, xy), sdtpldt0(xu, xv)), true, xc, slsdtgt0(xc), sdtpldt0(xx, xy)), aElementOf0(sdtasdt0(xz, xx), slsdtgt0(xc)))
% 106.55/14.10 = { by axiom 10 (mSortsB) R->L }
% 106.55/14.10 tuple(fresh65(fresh38(fresh10(true, true, xu, xv), true, xc, sdtpldt0(xx, xy), sdtpldt0(xu, xv)), true, xc, slsdtgt0(xc), sdtpldt0(xx, xy)), aElementOf0(sdtasdt0(xz, xx), slsdtgt0(xc)))
% 106.55/14.10 = { by axiom 3 (m__1956_1) R->L }
% 106.55/14.10 tuple(fresh65(fresh38(fresh10(aElement0(xu), true, xu, xv), true, xc, sdtpldt0(xx, xy), sdtpldt0(xu, xv)), true, xc, slsdtgt0(xc), sdtpldt0(xx, xy)), aElementOf0(sdtasdt0(xz, xx), slsdtgt0(xc)))
% 106.55/14.10 = { by axiom 16 (mSortsB) R->L }
% 106.55/14.10 tuple(fresh65(fresh38(fresh11(aElement0(xv), true, xu, xv), true, xc, sdtpldt0(xx, xy), sdtpldt0(xu, xv)), true, xc, slsdtgt0(xc), sdtpldt0(xx, xy)), aElementOf0(sdtasdt0(xz, xx), slsdtgt0(xc)))
% 106.55/14.10 = { by axiom 4 (m__1979_1) }
% 106.55/14.10 tuple(fresh65(fresh38(fresh11(true, true, xu, xv), true, xc, sdtpldt0(xx, xy), sdtpldt0(xu, xv)), true, xc, slsdtgt0(xc), sdtpldt0(xx, xy)), aElementOf0(sdtasdt0(xz, xx), slsdtgt0(xc)))
% 106.55/14.10 = { by axiom 9 (mSortsB) }
% 106.55/14.10 tuple(fresh65(fresh38(aElement0(sdtpldt0(xu, xv)), true, xc, sdtpldt0(xx, xy), sdtpldt0(xu, xv)), true, xc, slsdtgt0(xc), sdtpldt0(xx, xy)), aElementOf0(sdtasdt0(xz, xx), slsdtgt0(xc)))
% 106.55/14.10 = { by axiom 6 (m__2010) }
% 106.55/14.10 tuple(fresh65(fresh38(aElement0(sdtpldt0(xu, xv)), true, xc, sdtasdt0(xc, sdtpldt0(xu, xv)), sdtpldt0(xu, xv)), true, xc, slsdtgt0(xc), sdtpldt0(xx, xy)), aElementOf0(sdtasdt0(xz, xx), slsdtgt0(xc)))
% 106.55/14.10 = { by lemma 21 }
% 106.55/14.10 tuple(fresh65(true, true, xc, slsdtgt0(xc), sdtpldt0(xx, xy)), aElementOf0(sdtasdt0(xz, xx), slsdtgt0(xc)))
% 106.55/14.10 = { by lemma 20 }
% 106.55/14.10 tuple(true, aElementOf0(sdtasdt0(xz, xx), slsdtgt0(xc)))
% 106.55/14.10 = { by axiom 14 (mDefPrIdeal_2) R->L }
% 106.55/14.10 tuple(true, fresh39(true, true, xc, slsdtgt0(xc), sdtasdt0(xz, xx)))
% 106.55/14.10 = { by axiom 1 (m__1905) R->L }
% 106.55/14.10 tuple(true, fresh39(aElement0(xc), true, xc, slsdtgt0(xc), sdtasdt0(xz, xx)))
% 106.55/14.10 = { by axiom 19 (mDefPrIdeal_2) R->L }
% 106.55/14.10 tuple(true, fresh65(equiv(xc, sdtasdt0(xz, xx)), true, xc, slsdtgt0(xc), sdtasdt0(xz, xx)))
% 106.55/14.10 = { by axiom 15 (mDefPrIdeal_3) R->L }
% 106.55/14.10 tuple(true, fresh65(fresh38(true, true, xc, sdtasdt0(xz, xx), sdtasdt0(xu, xz)), true, xc, slsdtgt0(xc), sdtasdt0(xz, xx)))
% 106.55/14.10 = { by axiom 12 (mSortsB_02) R->L }
% 106.55/14.10 tuple(true, fresh65(fresh38(fresh8(true, true, xu, xz), true, xc, sdtasdt0(xz, xx), sdtasdt0(xu, xz)), true, xc, slsdtgt0(xc), sdtasdt0(xz, xx)))
% 106.55/14.10 = { by axiom 3 (m__1956_1) R->L }
% 106.55/14.10 tuple(true, fresh65(fresh38(fresh8(aElement0(xu), true, xu, xz), true, xc, sdtasdt0(xz, xx), sdtasdt0(xu, xz)), true, xc, slsdtgt0(xc), sdtasdt0(xz, xx)))
% 106.55/14.10 = { by axiom 17 (mSortsB_02) R->L }
% 106.55/14.10 tuple(true, fresh65(fresh38(fresh9(aElement0(xz), true, xu, xz), true, xc, sdtasdt0(xz, xx), sdtasdt0(xu, xz)), true, xc, slsdtgt0(xc), sdtasdt0(xz, xx)))
% 106.55/14.10 = { by axiom 2 (m__1933) }
% 106.55/14.10 tuple(true, fresh65(fresh38(fresh9(true, true, xu, xz), true, xc, sdtasdt0(xz, xx), sdtasdt0(xu, xz)), true, xc, slsdtgt0(xc), sdtasdt0(xz, xx)))
% 106.55/14.10 = { by axiom 11 (mSortsB_02) }
% 106.55/14.10 tuple(true, fresh65(fresh38(aElement0(sdtasdt0(xu, xz)), true, xc, sdtasdt0(xz, xx), sdtasdt0(xu, xz)), true, xc, slsdtgt0(xc), sdtasdt0(xz, xx)))
% 106.55/14.10 = { by axiom 5 (m__2043) }
% 106.55/14.10 tuple(true, fresh65(fresh38(aElement0(sdtasdt0(xu, xz)), true, xc, sdtasdt0(xc, sdtasdt0(xu, xz)), sdtasdt0(xu, xz)), true, xc, slsdtgt0(xc), sdtasdt0(xz, xx)))
% 106.55/14.10 = { by lemma 21 }
% 106.55/14.10 tuple(true, fresh65(true, true, xc, slsdtgt0(xc), sdtasdt0(xz, xx)))
% 106.55/14.10 = { by lemma 20 }
% 106.55/14.10 tuple(true, true)
% 106.55/14.10 % SZS output end Proof
% 106.55/14.10
% 106.55/14.10 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------