TSTP Solution File: LCL491+1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : LCL491+1 : TPTP v8.1.2. Released v3.3.0.
% 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 : n031.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 08:19:12 EDT 2023
% Result : Theorem 0.22s 0.51s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : LCL491+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.15 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.15/0.37 % Computer : n031.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Thu Aug 24 19:11:06 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.22/0.51 Command-line arguments: --no-flatten-goal
% 0.22/0.51
% 0.22/0.51 % SZS status Theorem
% 0.22/0.51
% 0.22/0.51 % SZS output start Proof
% 0.22/0.51 Take the following subset of the input axioms:
% 0.22/0.51 fof(hilbert_op_or, axiom, op_or).
% 0.22/0.51 fof(hilbert_or_2, conjecture, or_2).
% 0.22/0.51 fof(or_2, axiom, or_2 <=> ![X, Y]: is_a_theorem(implies(Y, or(X, Y)))).
% 0.22/0.51 fof(principia_r2, axiom, r2).
% 0.22/0.51 fof(r2, axiom, r2 <=> ![P, Q]: is_a_theorem(implies(Q, or(P, Q)))).
% 0.22/0.51
% 0.22/0.51 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.22/0.51 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.22/0.51 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.22/0.51 fresh(y, y, x1...xn) = u
% 0.22/0.51 C => fresh(s, t, x1...xn) = v
% 0.22/0.51 where fresh is a fresh function symbol and x1..xn are the free
% 0.22/0.51 variables of u and v.
% 0.22/0.51 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.22/0.51 input problem has no model of domain size 1).
% 0.22/0.51
% 0.22/0.51 The encoding turns the above axioms into the following unit equations and goals:
% 0.22/0.51
% 0.22/0.51 Axiom 1 (hilbert_op_or): op_or = true.
% 0.22/0.51 Axiom 2 (principia_r2): r2 = true.
% 0.22/0.51 Axiom 3 (or_2): fresh17(X, X) = true.
% 0.22/0.51 Axiom 4 (r2_1): fresh10(X, X, Y, Z) = true.
% 0.22/0.51 Axiom 5 (r2_1): fresh10(r2, true, X, Y) = is_a_theorem(implies(Y, or(X, Y))).
% 0.22/0.51 Axiom 6 (or_2): fresh17(is_a_theorem(implies(y5, or(x5, y5))), true) = or_2.
% 0.22/0.51
% 0.22/0.51 Goal 1 (hilbert_or_2): or_2 = true.
% 0.22/0.51 Proof:
% 0.22/0.51 or_2
% 0.22/0.51 = { by axiom 6 (or_2) R->L }
% 0.22/0.51 fresh17(is_a_theorem(implies(y5, or(x5, y5))), true)
% 0.22/0.52 = { by axiom 5 (r2_1) R->L }
% 0.22/0.52 fresh17(fresh10(r2, true, x5, y5), true)
% 0.22/0.52 = { by axiom 2 (principia_r2) }
% 0.22/0.52 fresh17(fresh10(true, true, x5, y5), true)
% 0.22/0.52 = { by axiom 1 (hilbert_op_or) R->L }
% 0.22/0.52 fresh17(fresh10(op_or, true, x5, y5), true)
% 0.22/0.52 = { by axiom 1 (hilbert_op_or) R->L }
% 0.22/0.52 fresh17(fresh10(op_or, op_or, x5, y5), true)
% 0.22/0.52 = { by axiom 4 (r2_1) }
% 0.22/0.52 fresh17(true, true)
% 0.22/0.52 = { by axiom 1 (hilbert_op_or) R->L }
% 0.22/0.52 fresh17(op_or, true)
% 0.22/0.52 = { by axiom 1 (hilbert_op_or) R->L }
% 0.22/0.52 fresh17(op_or, op_or)
% 0.22/0.52 = { by axiom 3 (or_2) }
% 0.22/0.52 true
% 0.22/0.52 % SZS output end Proof
% 0.22/0.52
% 0.22/0.52 RESULT: Theorem (the conjecture is true).
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