TSTP Solution File: CSR066+1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : CSR066+1 : TPTP v8.1.2. Released v3.4.0.
% 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 : Wed Aug 30 21:41:38 EDT 2023
% Result : Theorem 0.20s 0.49s
% 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
% 0.00/0.12 % Problem : CSR066+1 : TPTP v8.1.2. Released v3.4.0.
% 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 : Mon Aug 28 08:03:24 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.49 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.20/0.49
% 0.20/0.49 % SZS status Theorem
% 0.20/0.49
% 0.20/0.50 % SZS output start Proof
% 0.20/0.50 Take the following subset of the input axioms:
% 0.20/0.50 fof(just10, axiom, relationexistsall(c_tptp_8_271, c_tptpcol_16_25972, c_shavingrazor_manual)).
% 0.20/0.50 fof(just11, axiom, shavingrazor_manual(c_theprototypicalshavingrazor_manual)).
% 0.20/0.50 fof(just12, axiom, ![OBJ, COL1, COL2]: ~(isa(OBJ, COL1) & (isa(OBJ, COL2) & disjointwith(COL1, COL2)))).
% 0.20/0.50 fof(just31, axiom, ![X]: (shavingrazor_manual(X) => isa(X, c_shavingrazor_manual))).
% 0.20/0.50 fof(just32, axiom, ![X2]: (isa(X2, c_tptpcol_16_25972) => tptpcol_16_25972(X2))).
% 0.20/0.50 fof(just4, axiom, ![TERM, INDEPCOL, PRED, DEPCOL]: ((isa(TERM, INDEPCOL) & relationexistsall(PRED, DEPCOL, INDEPCOL)) => isa(f_relationexistsallfn(TERM, PRED, DEPCOL, INDEPCOL), DEPCOL))).
% 0.20/0.50 fof(just9, axiom, ![TERM2]: (shavingrazor_manual(TERM2) => tptp_8_271(f_relationexistsallfn(TERM2, c_tptp_8_271, c_tptpcol_16_25972, c_shavingrazor_manual), TERM2))).
% 0.20/0.50 fof(query66, conjecture, ?[X2]: (mtvisible(f_contentmtofcdafromeventfn(f_urlreferentfn(f_urlfn(s_http_webnjiteducjohnsontreebiochhtm)), c_translation_21)) => (tptp_8_271(X2, c_theprototypicalshavingrazor_manual) & tptpcol_16_25972(X2)))).
% 0.20/0.50
% 0.20/0.50 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.50 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.50 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.50 fresh(y, y, x1...xn) = u
% 0.20/0.50 C => fresh(s, t, x1...xn) = v
% 0.20/0.50 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.50 variables of u and v.
% 0.20/0.50 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.50 input problem has no model of domain size 1).
% 0.20/0.50
% 0.20/0.50 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.50
% 0.20/0.50 Axiom 1 (just11): shavingrazor_manual(c_theprototypicalshavingrazor_manual) = true2.
% 0.20/0.50 Axiom 2 (just10): relationexistsall(c_tptp_8_271, c_tptpcol_16_25972, c_shavingrazor_manual) = true2.
% 0.20/0.50 Axiom 3 (just9): fresh(X, X, Y) = true2.
% 0.20/0.50 Axiom 4 (just31): fresh31(X, X, Y) = true2.
% 0.20/0.50 Axiom 5 (just32): fresh30(X, X, Y) = true2.
% 0.20/0.50 Axiom 6 (just31): fresh31(shavingrazor_manual(X), true2, X) = isa(X, c_shavingrazor_manual).
% 0.20/0.50 Axiom 7 (just32): fresh30(isa(X, c_tptpcol_16_25972), true2, X) = tptpcol_16_25972(X).
% 0.20/0.50 Axiom 8 (just9): fresh(shavingrazor_manual(X), true2, X) = tptp_8_271(f_relationexistsallfn(X, c_tptp_8_271, c_tptpcol_16_25972, c_shavingrazor_manual), X).
% 0.20/0.50 Axiom 9 (just4): fresh22(X, X, Y, Z, W, V) = isa(f_relationexistsallfn(Y, W, V, Z), V).
% 0.20/0.50 Axiom 10 (just4): fresh21(X, X, Y, Z, W, V) = true2.
% 0.20/0.50 Axiom 11 (just4): fresh22(relationexistsall(X, Y, Z), true2, W, Z, X, Y) = fresh21(isa(W, Z), true2, W, Z, X, Y).
% 0.20/0.50
% 0.20/0.50 Goal 1 (query66_1): tuple2(tptp_8_271(X, c_theprototypicalshavingrazor_manual), tptpcol_16_25972(X)) = tuple2(true2, true2).
% 0.20/0.50 The goal is true when:
% 0.20/0.50 X = f_relationexistsallfn(c_theprototypicalshavingrazor_manual, c_tptp_8_271, c_tptpcol_16_25972, c_shavingrazor_manual)
% 0.20/0.50
% 0.20/0.50 Proof:
% 0.20/0.50 tuple2(tptp_8_271(f_relationexistsallfn(c_theprototypicalshavingrazor_manual, c_tptp_8_271, c_tptpcol_16_25972, c_shavingrazor_manual), c_theprototypicalshavingrazor_manual), tptpcol_16_25972(f_relationexistsallfn(c_theprototypicalshavingrazor_manual, c_tptp_8_271, c_tptpcol_16_25972, c_shavingrazor_manual)))
% 0.20/0.50 = { by axiom 7 (just32) R->L }
% 0.20/0.50 tuple2(tptp_8_271(f_relationexistsallfn(c_theprototypicalshavingrazor_manual, c_tptp_8_271, c_tptpcol_16_25972, c_shavingrazor_manual), c_theprototypicalshavingrazor_manual), fresh30(isa(f_relationexistsallfn(c_theprototypicalshavingrazor_manual, c_tptp_8_271, c_tptpcol_16_25972, c_shavingrazor_manual), c_tptpcol_16_25972), true2, f_relationexistsallfn(c_theprototypicalshavingrazor_manual, c_tptp_8_271, c_tptpcol_16_25972, c_shavingrazor_manual)))
% 0.20/0.50 = { by axiom 9 (just4) R->L }
% 0.20/0.50 tuple2(tptp_8_271(f_relationexistsallfn(c_theprototypicalshavingrazor_manual, c_tptp_8_271, c_tptpcol_16_25972, c_shavingrazor_manual), c_theprototypicalshavingrazor_manual), fresh30(fresh22(true2, true2, c_theprototypicalshavingrazor_manual, c_shavingrazor_manual, c_tptp_8_271, c_tptpcol_16_25972), true2, f_relationexistsallfn(c_theprototypicalshavingrazor_manual, c_tptp_8_271, c_tptpcol_16_25972, c_shavingrazor_manual)))
% 0.20/0.50 = { by axiom 2 (just10) R->L }
% 0.20/0.50 tuple2(tptp_8_271(f_relationexistsallfn(c_theprototypicalshavingrazor_manual, c_tptp_8_271, c_tptpcol_16_25972, c_shavingrazor_manual), c_theprototypicalshavingrazor_manual), fresh30(fresh22(relationexistsall(c_tptp_8_271, c_tptpcol_16_25972, c_shavingrazor_manual), true2, c_theprototypicalshavingrazor_manual, c_shavingrazor_manual, c_tptp_8_271, c_tptpcol_16_25972), true2, f_relationexistsallfn(c_theprototypicalshavingrazor_manual, c_tptp_8_271, c_tptpcol_16_25972, c_shavingrazor_manual)))
% 0.20/0.50 = { by axiom 11 (just4) }
% 0.20/0.50 tuple2(tptp_8_271(f_relationexistsallfn(c_theprototypicalshavingrazor_manual, c_tptp_8_271, c_tptpcol_16_25972, c_shavingrazor_manual), c_theprototypicalshavingrazor_manual), fresh30(fresh21(isa(c_theprototypicalshavingrazor_manual, c_shavingrazor_manual), true2, c_theprototypicalshavingrazor_manual, c_shavingrazor_manual, c_tptp_8_271, c_tptpcol_16_25972), true2, f_relationexistsallfn(c_theprototypicalshavingrazor_manual, c_tptp_8_271, c_tptpcol_16_25972, c_shavingrazor_manual)))
% 0.20/0.50 = { by axiom 6 (just31) R->L }
% 0.20/0.50 tuple2(tptp_8_271(f_relationexistsallfn(c_theprototypicalshavingrazor_manual, c_tptp_8_271, c_tptpcol_16_25972, c_shavingrazor_manual), c_theprototypicalshavingrazor_manual), fresh30(fresh21(fresh31(shavingrazor_manual(c_theprototypicalshavingrazor_manual), true2, c_theprototypicalshavingrazor_manual), true2, c_theprototypicalshavingrazor_manual, c_shavingrazor_manual, c_tptp_8_271, c_tptpcol_16_25972), true2, f_relationexistsallfn(c_theprototypicalshavingrazor_manual, c_tptp_8_271, c_tptpcol_16_25972, c_shavingrazor_manual)))
% 0.20/0.50 = { by axiom 1 (just11) }
% 0.20/0.50 tuple2(tptp_8_271(f_relationexistsallfn(c_theprototypicalshavingrazor_manual, c_tptp_8_271, c_tptpcol_16_25972, c_shavingrazor_manual), c_theprototypicalshavingrazor_manual), fresh30(fresh21(fresh31(true2, true2, c_theprototypicalshavingrazor_manual), true2, c_theprototypicalshavingrazor_manual, c_shavingrazor_manual, c_tptp_8_271, c_tptpcol_16_25972), true2, f_relationexistsallfn(c_theprototypicalshavingrazor_manual, c_tptp_8_271, c_tptpcol_16_25972, c_shavingrazor_manual)))
% 0.20/0.50 = { by axiom 4 (just31) }
% 0.20/0.50 tuple2(tptp_8_271(f_relationexistsallfn(c_theprototypicalshavingrazor_manual, c_tptp_8_271, c_tptpcol_16_25972, c_shavingrazor_manual), c_theprototypicalshavingrazor_manual), fresh30(fresh21(true2, true2, c_theprototypicalshavingrazor_manual, c_shavingrazor_manual, c_tptp_8_271, c_tptpcol_16_25972), true2, f_relationexistsallfn(c_theprototypicalshavingrazor_manual, c_tptp_8_271, c_tptpcol_16_25972, c_shavingrazor_manual)))
% 0.20/0.50 = { by axiom 10 (just4) }
% 0.20/0.50 tuple2(tptp_8_271(f_relationexistsallfn(c_theprototypicalshavingrazor_manual, c_tptp_8_271, c_tptpcol_16_25972, c_shavingrazor_manual), c_theprototypicalshavingrazor_manual), fresh30(true2, true2, f_relationexistsallfn(c_theprototypicalshavingrazor_manual, c_tptp_8_271, c_tptpcol_16_25972, c_shavingrazor_manual)))
% 0.20/0.50 = { by axiom 5 (just32) }
% 0.20/0.50 tuple2(tptp_8_271(f_relationexistsallfn(c_theprototypicalshavingrazor_manual, c_tptp_8_271, c_tptpcol_16_25972, c_shavingrazor_manual), c_theprototypicalshavingrazor_manual), true2)
% 0.20/0.50 = { by axiom 8 (just9) R->L }
% 0.20/0.50 tuple2(fresh(shavingrazor_manual(c_theprototypicalshavingrazor_manual), true2, c_theprototypicalshavingrazor_manual), true2)
% 0.20/0.50 = { by axiom 1 (just11) }
% 0.20/0.50 tuple2(fresh(true2, true2, c_theprototypicalshavingrazor_manual), true2)
% 0.20/0.50 = { by axiom 3 (just9) }
% 0.20/0.50 tuple2(true2, true2)
% 0.20/0.50 % SZS output end Proof
% 0.20/0.50
% 0.20/0.50 RESULT: Theorem (the conjecture is true).
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