TSTP Solution File: RNG104+2 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : RNG104+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 : n023.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 37.30s 5.13s
% Output : Proof 37.30s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : RNG104+2 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35 % Computer : n023.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun Aug 27 01:47:56 EDT 2023
% 0.14/0.35 % CPUTime :
% 37.30/5.13 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 37.30/5.13
% 37.30/5.13 % SZS status Theorem
% 37.30/5.13
% 37.30/5.13 % SZS output start Proof
% 37.30/5.13 Take the following subset of the input axioms:
% 37.30/5.13 fof(mMulAsso, axiom, ![W0, W1, W2]: ((aElement0(W0) & (aElement0(W1) & aElement0(W2))) => sdtasdt0(sdtasdt0(W0, W1), W2)=sdtasdt0(W0, sdtasdt0(W1, W2)))).
% 37.30/5.13 fof(mMulComm, axiom, ![W0_2, W1_2]: ((aElement0(W0_2) & aElement0(W1_2)) => sdtasdt0(W0_2, W1_2)=sdtasdt0(W1_2, W0_2))).
% 37.30/5.13 fof(mSortsB_02, axiom, ![W0_2, W1_2]: ((aElement0(W0_2) & aElement0(W1_2)) => aElement0(sdtasdt0(W0_2, W1_2)))).
% 37.30/5.13 fof(m__, conjecture, sdtasdt0(xz, xx)=sdtasdt0(xc, sdtasdt0(xu, xz))).
% 37.30/5.13 fof(m__1905, hypothesis, aElement0(xc)).
% 37.30/5.14 fof(m__1933, hypothesis, ?[W0_2]: (aElement0(W0_2) & sdtasdt0(xc, W0_2)=xx) & (aElementOf0(xx, slsdtgt0(xc)) & (?[W0_2]: (aElement0(W0_2) & sdtasdt0(xc, W0_2)=xy) & (aElementOf0(xy, slsdtgt0(xc)) & aElement0(xz))))).
% 37.30/5.14 fof(m__1956, hypothesis, aElement0(xu) & sdtasdt0(xc, xu)=xx).
% 37.30/5.14
% 37.30/5.14 Now clausify the problem and encode Horn clauses using encoding 3 of
% 37.30/5.14 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 37.30/5.14 We repeatedly replace C & s=t => u=v by the two clauses:
% 37.30/5.14 fresh(y, y, x1...xn) = u
% 37.30/5.14 C => fresh(s, t, x1...xn) = v
% 37.30/5.14 where fresh is a fresh function symbol and x1..xn are the free
% 37.30/5.14 variables of u and v.
% 37.30/5.14 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 37.30/5.14 input problem has no model of domain size 1).
% 37.30/5.14
% 37.30/5.14 The encoding turns the above axioms into the following unit equations and goals:
% 37.30/5.14
% 37.30/5.14 Axiom 1 (m__1905): aElement0(xc) = true.
% 37.30/5.14 Axiom 2 (m__1933_2): aElement0(xz) = true.
% 37.30/5.14 Axiom 3 (m__1956_1): aElement0(xu) = true.
% 37.30/5.14 Axiom 4 (m__1956): sdtasdt0(xc, xu) = xx.
% 37.30/5.14 Axiom 5 (mMulComm): fresh17(X, X, Y, Z) = sdtasdt0(Y, Z).
% 37.30/5.14 Axiom 6 (mMulComm): fresh16(X, X, Y, Z) = sdtasdt0(Z, Y).
% 37.30/5.14 Axiom 7 (mSortsB_02): fresh9(X, X, Y, Z) = aElement0(sdtasdt0(Y, Z)).
% 37.30/5.14 Axiom 8 (mSortsB_02): fresh8(X, X, Y, Z) = true.
% 37.30/5.14 Axiom 9 (mMulAsso): fresh169(X, X, Y, Z, W) = sdtasdt0(Y, sdtasdt0(Z, W)).
% 37.30/5.14 Axiom 10 (mMulAsso): fresh18(X, X, Y, Z, W) = sdtasdt0(sdtasdt0(Y, Z), W).
% 37.30/5.14 Axiom 11 (mMulComm): fresh17(aElement0(X), true, Y, X) = fresh16(aElement0(Y), true, Y, X).
% 37.30/5.14 Axiom 12 (mSortsB_02): fresh9(aElement0(X), true, Y, X) = fresh8(aElement0(Y), true, Y, X).
% 37.30/5.14 Axiom 13 (mMulAsso): fresh168(X, X, Y, Z, W) = fresh169(aElement0(Y), true, Y, Z, W).
% 37.30/5.14 Axiom 14 (mMulAsso): fresh168(aElement0(X), true, Y, Z, X) = fresh18(aElement0(Z), true, Y, Z, X).
% 37.30/5.14
% 37.30/5.14 Lemma 15: fresh17(aElement0(X), true, xc, X) = sdtasdt0(X, xc).
% 37.30/5.14 Proof:
% 37.30/5.14 fresh17(aElement0(X), true, xc, X)
% 37.30/5.14 = { by axiom 11 (mMulComm) }
% 37.30/5.14 fresh16(aElement0(xc), true, xc, X)
% 37.30/5.14 = { by axiom 1 (m__1905) }
% 37.30/5.14 fresh16(true, true, xc, X)
% 37.30/5.14 = { by axiom 6 (mMulComm) }
% 37.30/5.14 sdtasdt0(X, xc)
% 37.30/5.14
% 37.30/5.14 Goal 1 (m__): sdtasdt0(xz, xx) = sdtasdt0(xc, sdtasdt0(xu, xz)).
% 37.30/5.14 Proof:
% 37.30/5.14 sdtasdt0(xz, xx)
% 37.30/5.14 = { by axiom 4 (m__1956) R->L }
% 37.30/5.14 sdtasdt0(xz, sdtasdt0(xc, xu))
% 37.30/5.14 = { by axiom 5 (mMulComm) R->L }
% 37.30/5.14 sdtasdt0(xz, fresh17(true, true, xc, xu))
% 37.30/5.14 = { by axiom 3 (m__1956_1) R->L }
% 37.30/5.14 sdtasdt0(xz, fresh17(aElement0(xu), true, xc, xu))
% 37.30/5.14 = { by lemma 15 }
% 37.30/5.14 sdtasdt0(xz, sdtasdt0(xu, xc))
% 37.30/5.14 = { by axiom 9 (mMulAsso) R->L }
% 37.30/5.14 fresh169(true, true, xz, xu, xc)
% 37.30/5.14 = { by axiom 2 (m__1933_2) R->L }
% 37.30/5.14 fresh169(aElement0(xz), true, xz, xu, xc)
% 37.30/5.14 = { by axiom 13 (mMulAsso) R->L }
% 37.30/5.14 fresh168(true, true, xz, xu, xc)
% 37.30/5.14 = { by axiom 1 (m__1905) R->L }
% 37.30/5.14 fresh168(aElement0(xc), true, xz, xu, xc)
% 37.30/5.14 = { by axiom 14 (mMulAsso) }
% 37.30/5.14 fresh18(aElement0(xu), true, xz, xu, xc)
% 37.30/5.14 = { by axiom 3 (m__1956_1) }
% 37.30/5.14 fresh18(true, true, xz, xu, xc)
% 37.30/5.14 = { by axiom 10 (mMulAsso) }
% 37.30/5.14 sdtasdt0(sdtasdt0(xz, xu), xc)
% 37.30/5.14 = { by axiom 5 (mMulComm) R->L }
% 37.30/5.14 sdtasdt0(fresh17(true, true, xz, xu), xc)
% 37.30/5.14 = { by axiom 3 (m__1956_1) R->L }
% 37.30/5.14 sdtasdt0(fresh17(aElement0(xu), true, xz, xu), xc)
% 37.30/5.14 = { by axiom 11 (mMulComm) }
% 37.30/5.14 sdtasdt0(fresh16(aElement0(xz), true, xz, xu), xc)
% 37.30/5.14 = { by axiom 2 (m__1933_2) }
% 37.30/5.14 sdtasdt0(fresh16(true, true, xz, xu), xc)
% 37.30/5.14 = { by axiom 6 (mMulComm) }
% 37.30/5.14 sdtasdt0(sdtasdt0(xu, xz), xc)
% 37.30/5.14 = { by lemma 15 R->L }
% 37.30/5.14 fresh17(aElement0(sdtasdt0(xu, xz)), true, xc, sdtasdt0(xu, xz))
% 37.30/5.14 = { by axiom 7 (mSortsB_02) R->L }
% 37.30/5.14 fresh17(fresh9(true, true, xu, xz), true, xc, sdtasdt0(xu, xz))
% 37.30/5.14 = { by axiom 2 (m__1933_2) R->L }
% 37.30/5.14 fresh17(fresh9(aElement0(xz), true, xu, xz), true, xc, sdtasdt0(xu, xz))
% 37.30/5.14 = { by axiom 12 (mSortsB_02) }
% 37.30/5.14 fresh17(fresh8(aElement0(xu), true, xu, xz), true, xc, sdtasdt0(xu, xz))
% 37.30/5.14 = { by axiom 3 (m__1956_1) }
% 37.30/5.14 fresh17(fresh8(true, true, xu, xz), true, xc, sdtasdt0(xu, xz))
% 37.30/5.14 = { by axiom 8 (mSortsB_02) }
% 37.30/5.14 fresh17(true, true, xc, sdtasdt0(xu, xz))
% 37.30/5.14 = { by axiom 5 (mMulComm) }
% 37.30/5.14 sdtasdt0(xc, sdtasdt0(xu, xz))
% 37.30/5.14 % SZS output end Proof
% 37.30/5.14
% 37.30/5.14 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------