TSTP Solution File: SYN683-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYN683-1 : TPTP v8.1.2. Released v2.5.0.
% 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 : n007.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 03:35:42 EDT 2023
% Result : Unsatisfiable 1.18s 0.72s
% Output : Proof 1.28s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.19 % Problem : SYN683-1 : TPTP v8.1.2. Released v2.5.0.
% 0.09/0.20 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.10/0.42 % Computer : n007.cluster.edu
% 0.10/0.42 % Model : x86_64 x86_64
% 0.10/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.42 % Memory : 8042.1875MB
% 0.10/0.42 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.42 % CPULimit : 300
% 0.10/0.42 % WCLimit : 300
% 0.10/0.42 % DateTime : Sat Aug 26 18:17:57 EDT 2023
% 0.10/0.42 % CPUTime :
% 1.18/0.72 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 1.18/0.72
% 1.18/0.72 % SZS status Unsatisfiable
% 1.18/0.72
% 1.18/0.72 % SZS output start Proof
% 1.18/0.73 Take the following subset of the input axioms:
% 1.18/0.73 fof(not_p2_19, negated_conjecture, ![X96]: ~p2(X96, f18(X96, f9(f17(c31))))).
% 1.18/0.73 fof(p25_12, negated_conjecture, p25(c36, c33)).
% 1.18/0.73 fof(p25_13, negated_conjecture, p25(c32, c36)).
% 1.18/0.73 fof(p2_31, negated_conjecture, ![X28, X29, X30]: (p2(X29, X30) | (~p2(X28, X29) | ~p2(X28, X30)))).
% 1.18/0.73 fof(p2_40, negated_conjecture, p2(f11(f4(c32), c34), f18(f11(f4(c36), c34), f9(f17(c31))))).
% 1.18/0.73 fof(p2_50, negated_conjecture, ![X35]: (p2(f11(f4(X35), c34), f11(f4(c32), c34)) | (~p25(X35, c33) | ~p25(c32, X35)))).
% 1.18/0.73 fof(p2_7, negated_conjecture, ![X28_2]: p2(X28_2, X28_2)).
% 1.18/0.73
% 1.18/0.73 Now clausify the problem and encode Horn clauses using encoding 3 of
% 1.18/0.73 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 1.18/0.73 We repeatedly replace C & s=t => u=v by the two clauses:
% 1.18/0.73 fresh(y, y, x1...xn) = u
% 1.18/0.73 C => fresh(s, t, x1...xn) = v
% 1.18/0.73 where fresh is a fresh function symbol and x1..xn are the free
% 1.18/0.73 variables of u and v.
% 1.18/0.73 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 1.18/0.73 input problem has no model of domain size 1).
% 1.18/0.73
% 1.18/0.73 The encoding turns the above axioms into the following unit equations and goals:
% 1.18/0.73
% 1.18/0.73 Axiom 1 (p2_7): p2(X, X) = true2.
% 1.18/0.73 Axiom 2 (p25_13): p25(c32, c36) = true2.
% 1.18/0.73 Axiom 3 (p25_12): p25(c36, c33) = true2.
% 1.18/0.73 Axiom 4 (p2_50): fresh51(X, X, Y) = true2.
% 1.18/0.73 Axiom 5 (p2_50): fresh50(X, X, Y) = fresh51(p25(Y, c33), true2, Y).
% 1.18/0.73 Axiom 6 (p2_31): fresh15(X, X, Y, Z) = true2.
% 1.18/0.73 Axiom 7 (p2_31): fresh16(X, X, Y, Z, W) = p2(Y, Z).
% 1.18/0.73 Axiom 8 (p2_50): fresh50(p25(c32, X), true2, X) = p2(f11(f4(X), c34), f11(f4(c32), c34)).
% 1.18/0.73 Axiom 9 (p2_31): fresh16(p2(X, Y), true2, Z, Y, X) = fresh15(p2(X, Z), true2, Z, Y).
% 1.18/0.73 Axiom 10 (p2_40): p2(f11(f4(c32), c34), f18(f11(f4(c36), c34), f9(f17(c31)))) = true2.
% 1.18/0.73
% 1.18/0.73 Goal 1 (not_p2_19): p2(X, f18(X, f9(f17(c31)))) = true2.
% 1.18/0.73 The goal is true when:
% 1.18/0.73 X = f11(f4(c36), c34)
% 1.18/0.73
% 1.18/0.73 Proof:
% 1.18/0.73 p2(f11(f4(c36), c34), f18(f11(f4(c36), c34), f9(f17(c31))))
% 1.18/0.73 = { by axiom 7 (p2_31) R->L }
% 1.18/0.73 fresh16(true2, true2, f11(f4(c36), c34), f18(f11(f4(c36), c34), f9(f17(c31))), f11(f4(c32), c34))
% 1.18/0.73 = { by axiom 10 (p2_40) R->L }
% 1.18/0.73 fresh16(p2(f11(f4(c32), c34), f18(f11(f4(c36), c34), f9(f17(c31)))), true2, f11(f4(c36), c34), f18(f11(f4(c36), c34), f9(f17(c31))), f11(f4(c32), c34))
% 1.18/0.73 = { by axiom 9 (p2_31) }
% 1.18/0.73 fresh15(p2(f11(f4(c32), c34), f11(f4(c36), c34)), true2, f11(f4(c36), c34), f18(f11(f4(c36), c34), f9(f17(c31))))
% 1.18/0.73 = { by axiom 7 (p2_31) R->L }
% 1.18/0.73 fresh15(fresh16(true2, true2, f11(f4(c32), c34), f11(f4(c36), c34), f11(f4(c36), c34)), true2, f11(f4(c36), c34), f18(f11(f4(c36), c34), f9(f17(c31))))
% 1.18/0.73 = { by axiom 1 (p2_7) R->L }
% 1.18/0.73 fresh15(fresh16(p2(f11(f4(c36), c34), f11(f4(c36), c34)), true2, f11(f4(c32), c34), f11(f4(c36), c34), f11(f4(c36), c34)), true2, f11(f4(c36), c34), f18(f11(f4(c36), c34), f9(f17(c31))))
% 1.18/0.73 = { by axiom 9 (p2_31) }
% 1.18/0.73 fresh15(fresh15(p2(f11(f4(c36), c34), f11(f4(c32), c34)), true2, f11(f4(c32), c34), f11(f4(c36), c34)), true2, f11(f4(c36), c34), f18(f11(f4(c36), c34), f9(f17(c31))))
% 1.18/0.73 = { by axiom 8 (p2_50) R->L }
% 1.18/0.73 fresh15(fresh15(fresh50(p25(c32, c36), true2, c36), true2, f11(f4(c32), c34), f11(f4(c36), c34)), true2, f11(f4(c36), c34), f18(f11(f4(c36), c34), f9(f17(c31))))
% 1.28/0.73 = { by axiom 2 (p25_13) }
% 1.28/0.73 fresh15(fresh15(fresh50(true2, true2, c36), true2, f11(f4(c32), c34), f11(f4(c36), c34)), true2, f11(f4(c36), c34), f18(f11(f4(c36), c34), f9(f17(c31))))
% 1.28/0.73 = { by axiom 5 (p2_50) }
% 1.28/0.73 fresh15(fresh15(fresh51(p25(c36, c33), true2, c36), true2, f11(f4(c32), c34), f11(f4(c36), c34)), true2, f11(f4(c36), c34), f18(f11(f4(c36), c34), f9(f17(c31))))
% 1.28/0.73 = { by axiom 3 (p25_12) }
% 1.28/0.73 fresh15(fresh15(fresh51(true2, true2, c36), true2, f11(f4(c32), c34), f11(f4(c36), c34)), true2, f11(f4(c36), c34), f18(f11(f4(c36), c34), f9(f17(c31))))
% 1.28/0.73 = { by axiom 4 (p2_50) }
% 1.28/0.73 fresh15(fresh15(true2, true2, f11(f4(c32), c34), f11(f4(c36), c34)), true2, f11(f4(c36), c34), f18(f11(f4(c36), c34), f9(f17(c31))))
% 1.28/0.73 = { by axiom 6 (p2_31) }
% 1.28/0.73 fresh15(true2, true2, f11(f4(c36), c34), f18(f11(f4(c36), c34), f9(f17(c31))))
% 1.28/0.73 = { by axiom 6 (p2_31) }
% 1.28/0.73 true2
% 1.28/0.73 % SZS output end Proof
% 1.28/0.73
% 1.28/0.73 RESULT: Unsatisfiable (the axioms are contradictory).
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