TSTP Solution File: NUM630+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : NUM630+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 : 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 11:57:23 EDT 2023
% Result : Theorem 12.53s 1.98s
% Output : Proof 12.53s
% 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 : NUM630+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 : n022.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 : Fri Aug 25 12:10:55 EDT 2023
% 0.13/0.34 % CPUTime :
% 12.53/1.98 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 12.53/1.98
% 12.53/1.98 % SZS status Theorem
% 12.53/1.98
% 12.53/1.98 % SZS output start Proof
% 12.53/1.98 Take the following subset of the input axioms:
% 12.53/1.98 fof(m__, conjecture, sdtlpdtrp0(xc, sdtpldt0(xP, szmzizndt0(sdtlpdtrp0(xN, xn))))=sdtlpdtrp0(sdtlpdtrp0(xC, xn), xP)).
% 12.53/1.98 fof(m__4151, hypothesis, aFunction0(xC) & (szDzozmdt0(xC)=szNzAzT0 & ![W0]: (aElementOf0(W0, szNzAzT0) => (aFunction0(sdtlpdtrp0(xC, W0)) & (szDzozmdt0(sdtlpdtrp0(xC, W0))=slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk) & ![W1]: ((aSet0(W1) & aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) => sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1)=sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))))))).
% 12.53/1.98 fof(m__5164, hypothesis, aSet0(xP) & xP=sdtmndt0(xQ, szmzizndt0(xQ))).
% 12.53/1.98 fof(m__5309, hypothesis, aElementOf0(xn, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (aElementOf0(xn, szNzAzT0) & sdtlpdtrp0(xe, xn)=xp)).
% 12.53/1.98 fof(m__5585, hypothesis, xD=sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn)))).
% 12.53/1.98 fof(m__5599, hypothesis, aElementOf0(xP, slbdtsldtrb0(xD, xk))).
% 12.53/1.98
% 12.53/1.98 Now clausify the problem and encode Horn clauses using encoding 3 of
% 12.53/1.98 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 12.53/1.98 We repeatedly replace C & s=t => u=v by the two clauses:
% 12.53/1.98 fresh(y, y, x1...xn) = u
% 12.53/1.98 C => fresh(s, t, x1...xn) = v
% 12.53/1.98 where fresh is a fresh function symbol and x1..xn are the free
% 12.53/1.98 variables of u and v.
% 12.53/1.98 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 12.53/1.98 input problem has no model of domain size 1).
% 12.53/1.98
% 12.53/1.98 The encoding turns the above axioms into the following unit equations and goals:
% 12.53/1.98
% 12.53/1.98 Axiom 1 (m__5164_1): aSet0(xP) = true2.
% 12.53/1.98 Axiom 2 (m__5309_1): aElementOf0(xn, szNzAzT0) = true2.
% 12.53/1.98 Axiom 3 (m__5599): aElementOf0(xP, slbdtsldtrb0(xD, xk)) = true2.
% 12.53/1.98 Axiom 4 (m__4151_2): fresh128(X, X, Y, Z) = sdtlpdtrp0(sdtlpdtrp0(xC, Y), Z).
% 12.53/1.98 Axiom 5 (m__4151_2): fresh127(X, X, Y, Z) = fresh128(aSet0(Z), true2, Y, Z).
% 12.53/1.98 Axiom 6 (m__4151_2): fresh126(X, X, Y, Z) = fresh127(aElementOf0(Y, szNzAzT0), true2, Y, Z).
% 12.53/1.98 Axiom 7 (m__5585): xD = sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))).
% 12.53/1.98 Axiom 8 (m__4151_2): fresh126(aElementOf0(X, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, Y), szmzizndt0(sdtlpdtrp0(xN, Y))), xk)), true2, Y, X) = sdtlpdtrp0(xc, sdtpldt0(X, szmzizndt0(sdtlpdtrp0(xN, Y)))).
% 12.53/1.98
% 12.53/1.98 Goal 1 (m__): sdtlpdtrp0(xc, sdtpldt0(xP, szmzizndt0(sdtlpdtrp0(xN, xn)))) = sdtlpdtrp0(sdtlpdtrp0(xC, xn), xP).
% 12.53/1.98 Proof:
% 12.53/1.98 sdtlpdtrp0(xc, sdtpldt0(xP, szmzizndt0(sdtlpdtrp0(xN, xn))))
% 12.53/1.98 = { by axiom 8 (m__4151_2) R->L }
% 12.53/1.98 fresh126(aElementOf0(xP, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, xn), szmzizndt0(sdtlpdtrp0(xN, xn))), xk)), true2, xn, xP)
% 12.53/1.98 = { by axiom 7 (m__5585) R->L }
% 12.53/1.98 fresh126(aElementOf0(xP, slbdtsldtrb0(xD, xk)), true2, xn, xP)
% 12.53/1.98 = { by axiom 3 (m__5599) }
% 12.53/1.98 fresh126(true2, true2, xn, xP)
% 12.53/1.98 = { by axiom 6 (m__4151_2) }
% 12.53/1.98 fresh127(aElementOf0(xn, szNzAzT0), true2, xn, xP)
% 12.53/1.98 = { by axiom 2 (m__5309_1) }
% 12.53/1.98 fresh127(true2, true2, xn, xP)
% 12.53/1.98 = { by axiom 5 (m__4151_2) }
% 12.53/1.98 fresh128(aSet0(xP), true2, xn, xP)
% 12.53/1.98 = { by axiom 1 (m__5164_1) }
% 12.53/1.98 fresh128(true2, true2, xn, xP)
% 12.53/1.98 = { by axiom 4 (m__4151_2) }
% 12.53/1.98 sdtlpdtrp0(sdtlpdtrp0(xC, xn), xP)
% 12.53/1.98 % SZS output end Proof
% 12.53/1.98
% 12.53/1.98 RESULT: Theorem (the conjecture is true).
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