TSTP Solution File: SYN058+1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SYN058+1 : TPTP v8.1.2. Released v2.0.0.
% 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 : n026.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 : Fri Sep 1 03:32:56 EDT 2023
% Result : Theorem 0.19s 0.37s
% Output : Proof 0.19s
% 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 : SYN058+1 : TPTP v8.1.2. Released v2.0.0.
% 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 : n026.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 : Sat Aug 26 21:16:48 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.37 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.19/0.37
% 0.19/0.37 % SZS status Theorem
% 0.19/0.37
% 0.19/0.37 % SZS output start Proof
% 0.19/0.37 Take the following subset of the input axioms:
% 0.19/0.37 fof(pel28, conjecture, ![X]: ((big_p(X) & big_f(X)) => big_g(X))).
% 0.19/0.37 fof(pel28_1, axiom, ![X2]: (big_p(X2) => ![Z]: big_q(Z))).
% 0.19/0.37 fof(pel28_2, axiom, ![X2]: (big_q(X2) | big_r(X2)) => ?[X1]: (big_q(X1) & big_s(X1))).
% 0.19/0.37 fof(pel28_3, axiom, ?[X2]: big_s(X2) => ![X1_2]: (big_f(X1_2) => big_g(X1_2))).
% 0.19/0.37
% 0.19/0.37 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.37 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.37 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.37 fresh(y, y, x1...xn) = u
% 0.19/0.37 C => fresh(s, t, x1...xn) = v
% 0.19/0.37 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.37 variables of u and v.
% 0.19/0.37 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.37 input problem has no model of domain size 1).
% 0.19/0.37
% 0.19/0.37 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.37
% 0.19/0.37 Axiom 1 (pel28): big_p(x) = true.
% 0.19/0.37 Axiom 2 (pel28_1): big_f(x) = true.
% 0.19/0.37 Axiom 3 (pel28_2_1): fresh5(X, X) = true.
% 0.19/0.37 Axiom 4 (pel28_3): fresh(X, X, Y) = true.
% 0.19/0.37 Axiom 5 (pel28_1): fresh6(X, X, Y) = true.
% 0.19/0.37 Axiom 6 (pel28_2_1): fresh5(big_q(x2), true) = big_s(x1).
% 0.19/0.37 Axiom 7 (pel28_1): fresh6(big_p(X), true, Y) = big_q(Y).
% 0.19/0.37 Axiom 8 (pel28_3): fresh2(X, X, Y, Z) = big_g(Z).
% 0.19/0.37 Axiom 9 (pel28_3): fresh2(big_f(X), true, Y, X) = fresh(big_s(Y), true, X).
% 0.19/0.37
% 0.19/0.37 Goal 1 (pel28_2): big_g(x) = true.
% 0.19/0.37 Proof:
% 0.19/0.37 big_g(x)
% 0.19/0.37 = { by axiom 8 (pel28_3) R->L }
% 0.19/0.37 fresh2(true, true, x1, x)
% 0.19/0.37 = { by axiom 2 (pel28_1) R->L }
% 0.19/0.37 fresh2(big_f(x), true, x1, x)
% 0.19/0.37 = { by axiom 9 (pel28_3) }
% 0.19/0.37 fresh(big_s(x1), true, x)
% 0.19/0.37 = { by axiom 6 (pel28_2_1) R->L }
% 0.19/0.37 fresh(fresh5(big_q(x2), true), true, x)
% 0.19/0.37 = { by axiom 7 (pel28_1) R->L }
% 0.19/0.37 fresh(fresh5(fresh6(big_p(x), true, x2), true), true, x)
% 0.19/0.37 = { by axiom 1 (pel28) }
% 0.19/0.37 fresh(fresh5(fresh6(true, true, x2), true), true, x)
% 0.19/0.37 = { by axiom 5 (pel28_1) }
% 0.19/0.37 fresh(fresh5(true, true), true, x)
% 0.19/0.37 = { by axiom 3 (pel28_2_1) }
% 0.19/0.37 fresh(true, true, x)
% 0.19/0.37 = { by axiom 4 (pel28_3) }
% 0.19/0.37 true
% 0.19/0.37 % SZS output end Proof
% 0.19/0.37
% 0.19/0.38 RESULT: Theorem (the conjecture is true).
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