TSTP Solution File: NUM631+3 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : NUM631+3 : 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 : n022.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 11:57:24 EDT 2023
% Result : Theorem 35.57s 4.96s
% Output : Proof 36.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM631+3 : 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 : n022.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 : Fri Aug 25 16:20:10 EDT 2023
% 0.12/0.34 % CPUTime :
% 35.57/4.96 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 35.57/4.96
% 35.57/4.96 % SZS status Theorem
% 35.57/4.96
% 36.13/4.97 % SZS output start Proof
% 36.13/4.97 Take the following subset of the input axioms:
% 36.13/4.97 fof(mConsDiff, axiom, ![W0]: (aSet0(W0) => ![W1]: (aElementOf0(W1, W0) => sdtpldt0(sdtmndt0(W0, W1), W1)=W0))).
% 36.13/4.97 fof(m__, conjecture, sdtlpdtrp0(xc, xQ)=sdtlpdtrp0(xd, xn)).
% 36.13/4.97 fof(m__4660, hypothesis, aFunction0(xe) & (szDzozmdt0(xe)=szNzAzT0 & ![W0_2]: (aElementOf0(W0_2, szNzAzT0) => (aElementOf0(sdtlpdtrp0(xe, W0_2), sdtlpdtrp0(xN, W0_2)) & (![W1_2]: (aElementOf0(W1_2, sdtlpdtrp0(xN, W0_2)) => sdtlseqdt0(sdtlpdtrp0(xe, W0_2), W1_2)) & sdtlpdtrp0(xe, W0_2)=szmzizndt0(sdtlpdtrp0(xN, W0_2))))))).
% 36.13/4.97 fof(m__4730, hypothesis, aFunction0(xd) & (szDzozmdt0(xd)=szNzAzT0 & ![W0_2]: (aElementOf0(W0_2, szNzAzT0) => ![W1_2]: ((aSet0(W1_2) & (((![W2]: (aElementOf0(W2, W1_2) => aElementOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(W0_2)))) | aSubsetOf0(W1_2, sdtlpdtrp0(xN, szszuzczcdt0(W0_2)))) & sbrdtbr0(W1_2)=xk) | aElementOf0(W1_2, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0_2)), xk)))) => sdtlpdtrp0(xd, W0_2)=sdtlpdtrp0(sdtlpdtrp0(xC, W0_2), W1_2))))).
% 36.13/4.98 fof(m__5078, hypothesis, aSet0(xQ) & (![W0_2]: (aElementOf0(W0_2, xQ) => aElementOf0(W0_2, xO)) & (aSubsetOf0(xQ, xO) & (sbrdtbr0(xQ)=xK & aElementOf0(xQ, slbdtsldtrb0(xO, xK)))))).
% 36.13/4.98 fof(m__5147, hypothesis, aElementOf0(xp, xQ) & (![W0_2]: (aElementOf0(W0_2, xQ) => sdtlseqdt0(xp, W0_2)) & xp=szmzizndt0(xQ))).
% 36.13/4.98 fof(m__5164, hypothesis, aSet0(xP) & (![W0_2]: (aElementOf0(W0_2, xQ) => sdtlseqdt0(szmzizndt0(xQ), W0_2)) & (![W0_2]: (aElementOf0(W0_2, xP) <=> (aElement0(W0_2) & (aElementOf0(W0_2, xQ) & W0_2!=szmzizndt0(xQ)))) & xP=sdtmndt0(xQ, szmzizndt0(xQ))))).
% 36.13/4.98 fof(m__5217, hypothesis, sbrdtbr0(xP)=xk).
% 36.13/4.98 fof(m__5309, hypothesis, aElementOf0(xn, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, xn)=szDzizrdt0(xd) & (aElementOf0(xn, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (aElementOf0(xn, szNzAzT0) & sdtlpdtrp0(xe, xn)=xp)))).
% 36.13/4.98 fof(m__5334, hypothesis, ![W0_2]: (aElementOf0(W0_2, xP) => aElementOf0(W0_2, sdtlpdtrp0(xN, szszuzczcdt0(xn)))) & aSubsetOf0(xP, sdtlpdtrp0(xN, szszuzczcdt0(xn)))).
% 36.13/4.98 fof(m__5632, hypothesis, ![W0_2]: (aElementOf0(W0_2, sdtlpdtrp0(xN, xn)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, xn)), W0_2)) & (aSet0(sdtpldt0(xP, szmzizndt0(sdtlpdtrp0(xN, xn)))) & (![W0_2]: (aElementOf0(W0_2, sdtpldt0(xP, szmzizndt0(sdtlpdtrp0(xN, xn)))) <=> (aElement0(W0_2) & (aElementOf0(W0_2, xP) | W0_2=szmzizndt0(sdtlpdtrp0(xN, xn))))) & sdtlpdtrp0(xc, sdtpldt0(xP, szmzizndt0(sdtlpdtrp0(xN, xn))))=sdtlpdtrp0(sdtlpdtrp0(xC, xn), xP)))).
% 36.13/4.98
% 36.13/4.98 Now clausify the problem and encode Horn clauses using encoding 3 of
% 36.13/4.98 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 36.13/4.98 We repeatedly replace C & s=t => u=v by the two clauses:
% 36.13/4.98 fresh(y, y, x1...xn) = u
% 36.13/4.98 C => fresh(s, t, x1...xn) = v
% 36.13/4.98 where fresh is a fresh function symbol and x1..xn are the free
% 36.13/4.98 variables of u and v.
% 36.13/4.98 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 36.13/4.98 input problem has no model of domain size 1).
% 36.13/4.98
% 36.13/4.98 The encoding turns the above axioms into the following unit equations and goals:
% 36.13/4.98
% 36.13/4.98 Axiom 1 (m__5078_1): aSet0(xQ) = true2.
% 36.13/4.98 Axiom 2 (m__5164_1): aSet0(xP) = true2.
% 36.13/4.98 Axiom 3 (m__5147): xp = szmzizndt0(xQ).
% 36.13/4.98 Axiom 4 (m__5217): sbrdtbr0(xP) = xk.
% 36.13/4.98 Axiom 5 (m__5309_2): aElementOf0(xn, szNzAzT0) = true2.
% 36.13/4.98 Axiom 6 (m__5147_1): aElementOf0(xp, xQ) = true2.
% 36.13/4.98 Axiom 7 (m__5309): sdtlpdtrp0(xe, xn) = xp.
% 36.13/4.98 Axiom 8 (m__5164): xP = sdtmndt0(xQ, szmzizndt0(xQ)).
% 36.13/4.98 Axiom 9 (m__4660_2): fresh62(X, X, Y) = sdtlpdtrp0(xe, Y).
% 36.13/4.98 Axiom 10 (m__4730_4): fresh292(X, X, Y, Z) = sdtlpdtrp0(xd, Y).
% 36.13/4.98 Axiom 11 (m__4730_4): fresh290(X, X, Y, Z) = sdtlpdtrp0(sdtlpdtrp0(xC, Y), Z).
% 36.13/4.98 Axiom 12 (mConsDiff): fresh264(X, X, Y, Z) = sdtpldt0(sdtmndt0(Y, Z), Z).
% 36.13/4.98 Axiom 13 (mConsDiff): fresh15(X, X, Y, Z) = Y.
% 36.13/4.98 Axiom 14 (m__5334): aSubsetOf0(xP, sdtlpdtrp0(xN, szszuzczcdt0(xn))) = true2.
% 36.13/4.98 Axiom 15 (m__4730_4): fresh291(X, X, Y, Z) = fresh292(sbrdtbr0(Z), xk, Y, Z).
% 36.13/4.98 Axiom 16 (m__4730_4): fresh289(X, X, Y, Z) = fresh290(aSet0(Z), true2, Y, Z).
% 36.13/4.98 Axiom 17 (m__4660_2): fresh62(aElementOf0(X, szNzAzT0), true2, X) = szmzizndt0(sdtlpdtrp0(xN, X)).
% 36.13/4.98 Axiom 18 (mConsDiff): fresh264(aElementOf0(X, Y), true2, Y, X) = fresh15(aSet0(Y), true2, Y, X).
% 36.13/4.98 Axiom 19 (m__5632): sdtlpdtrp0(xc, sdtpldt0(xP, szmzizndt0(sdtlpdtrp0(xN, xn)))) = sdtlpdtrp0(sdtlpdtrp0(xC, xn), xP).
% 36.13/4.98 Axiom 20 (m__4730_4): fresh289(aSubsetOf0(X, sdtlpdtrp0(xN, szszuzczcdt0(Y))), true2, Y, X) = fresh291(aElementOf0(Y, szNzAzT0), true2, Y, X).
% 36.13/4.98
% 36.13/4.98 Goal 1 (m__): sdtlpdtrp0(xc, xQ) = sdtlpdtrp0(xd, xn).
% 36.13/4.98 Proof:
% 36.13/4.98 sdtlpdtrp0(xc, xQ)
% 36.13/4.98 = { by axiom 13 (mConsDiff) R->L }
% 36.13/4.98 sdtlpdtrp0(xc, fresh15(true2, true2, xQ, xp))
% 36.13/4.98 = { by axiom 1 (m__5078_1) R->L }
% 36.13/4.98 sdtlpdtrp0(xc, fresh15(aSet0(xQ), true2, xQ, xp))
% 36.13/4.98 = { by axiom 18 (mConsDiff) R->L }
% 36.13/4.98 sdtlpdtrp0(xc, fresh264(aElementOf0(xp, xQ), true2, xQ, xp))
% 36.13/4.98 = { by axiom 6 (m__5147_1) }
% 36.13/4.98 sdtlpdtrp0(xc, fresh264(true2, true2, xQ, xp))
% 36.13/4.98 = { by axiom 12 (mConsDiff) }
% 36.13/4.98 sdtlpdtrp0(xc, sdtpldt0(sdtmndt0(xQ, xp), xp))
% 36.13/4.98 = { by axiom 3 (m__5147) }
% 36.13/4.98 sdtlpdtrp0(xc, sdtpldt0(sdtmndt0(xQ, szmzizndt0(xQ)), xp))
% 36.13/4.98 = { by axiom 8 (m__5164) R->L }
% 36.13/4.98 sdtlpdtrp0(xc, sdtpldt0(xP, xp))
% 36.13/4.98 = { by axiom 7 (m__5309) R->L }
% 36.13/4.98 sdtlpdtrp0(xc, sdtpldt0(xP, sdtlpdtrp0(xe, xn)))
% 36.13/4.98 = { by axiom 9 (m__4660_2) R->L }
% 36.13/4.98 sdtlpdtrp0(xc, sdtpldt0(xP, fresh62(true2, true2, xn)))
% 36.13/4.98 = { by axiom 5 (m__5309_2) R->L }
% 36.13/4.98 sdtlpdtrp0(xc, sdtpldt0(xP, fresh62(aElementOf0(xn, szNzAzT0), true2, xn)))
% 36.13/4.98 = { by axiom 17 (m__4660_2) }
% 36.13/4.98 sdtlpdtrp0(xc, sdtpldt0(xP, szmzizndt0(sdtlpdtrp0(xN, xn))))
% 36.13/4.98 = { by axiom 19 (m__5632) }
% 36.13/4.98 sdtlpdtrp0(sdtlpdtrp0(xC, xn), xP)
% 36.13/4.98 = { by axiom 11 (m__4730_4) R->L }
% 36.13/4.98 fresh290(true2, true2, xn, xP)
% 36.13/4.98 = { by axiom 2 (m__5164_1) R->L }
% 36.13/4.98 fresh290(aSet0(xP), true2, xn, xP)
% 36.13/4.98 = { by axiom 16 (m__4730_4) R->L }
% 36.13/4.98 fresh289(true2, true2, xn, xP)
% 36.13/4.98 = { by axiom 14 (m__5334) R->L }
% 36.13/4.98 fresh289(aSubsetOf0(xP, sdtlpdtrp0(xN, szszuzczcdt0(xn))), true2, xn, xP)
% 36.13/4.98 = { by axiom 20 (m__4730_4) }
% 36.13/4.98 fresh291(aElementOf0(xn, szNzAzT0), true2, xn, xP)
% 36.13/4.98 = { by axiom 5 (m__5309_2) }
% 36.13/4.98 fresh291(true2, true2, xn, xP)
% 36.13/4.98 = { by axiom 15 (m__4730_4) }
% 36.13/4.98 fresh292(sbrdtbr0(xP), xk, xn, xP)
% 36.13/4.98 = { by axiom 4 (m__5217) }
% 36.13/4.98 fresh292(xk, xk, xn, xP)
% 36.13/4.98 = { by axiom 10 (m__4730_4) }
% 36.13/4.98 sdtlpdtrp0(xd, xn)
% 36.13/4.98 % SZS output end Proof
% 36.13/4.98
% 36.13/4.98 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------