TSTP Solution File: SYN668-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYN668-1 : 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 : n018.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 03:35:38 EDT 2023
% Result : Unsatisfiable 0.20s 0.50s
% 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 : SYN668-1 : TPTP v8.1.2. Released v2.5.0.
% 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 : n018.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
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Aug 26 20:20:45 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.50 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 0.20/0.50
% 0.20/0.50 % SZS status Unsatisfiable
% 0.20/0.50
% 0.20/0.51 % SZS output start Proof
% 0.20/0.51 Take the following subset of the input axioms:
% 0.20/0.51 fof(not_p2_18, negated_conjecture, ![X96]: ~p2(X96, f18(X96, f9(f17(c31))))).
% 0.20/0.51 fof(p25_12, negated_conjecture, p25(c33, c36)).
% 0.20/0.51 fof(p25_14, negated_conjecture, p25(c32, c33)).
% 0.20/0.51 fof(p2_30, negated_conjecture, ![X28, X29, X30]: (p2(X29, X30) | (~p2(X28, X29) | ~p2(X28, X30)))).
% 0.20/0.51 fof(p2_38, negated_conjecture, p2(f11(f4(c32), c34), f18(f11(f4(c33), c34), f9(f17(c31))))).
% 0.20/0.51 fof(p2_50, negated_conjecture, ![X36]: (p2(f11(f4(X36), c34), f11(f4(c32), c34)) | (~p25(X36, c36) | ~p25(c32, X36)))).
% 0.20/0.51 fof(p2_7, negated_conjecture, ![X28_2]: p2(X28_2, X28_2)).
% 0.20/0.51
% 0.20/0.51 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.51 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.51 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.51 fresh(y, y, x1...xn) = u
% 0.20/0.51 C => fresh(s, t, x1...xn) = v
% 0.20/0.51 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.51 variables of u and v.
% 0.20/0.51 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.51 input problem has no model of domain size 1).
% 0.20/0.51
% 0.20/0.51 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.51
% 0.20/0.51 Axiom 1 (p2_7): p2(X, X) = true2.
% 0.20/0.51 Axiom 2 (p25_14): p25(c32, c33) = true2.
% 0.20/0.51 Axiom 3 (p25_12): p25(c33, c36) = true2.
% 0.20/0.51 Axiom 4 (p2_50): fresh49(X, X, Y) = true2.
% 0.20/0.51 Axiom 5 (p2_50): fresh48(X, X, Y) = fresh49(p25(Y, c36), true2, Y).
% 0.20/0.51 Axiom 6 (p2_30): fresh15(X, X, Y, Z) = true2.
% 0.20/0.51 Axiom 7 (p2_30): fresh16(X, X, Y, Z, W) = p2(Y, Z).
% 0.20/0.51 Axiom 8 (p2_50): fresh48(p25(c32, X), true2, X) = p2(f11(f4(X), c34), f11(f4(c32), c34)).
% 0.20/0.51 Axiom 9 (p2_30): fresh16(p2(X, Y), true2, Z, Y, X) = fresh15(p2(X, Z), true2, Z, Y).
% 0.20/0.51 Axiom 10 (p2_38): p2(f11(f4(c32), c34), f18(f11(f4(c33), c34), f9(f17(c31)))) = true2.
% 0.20/0.51
% 0.20/0.51 Goal 1 (not_p2_18): p2(X, f18(X, f9(f17(c31)))) = true2.
% 0.20/0.51 The goal is true when:
% 0.20/0.51 X = f11(f4(c33), c34)
% 0.20/0.51
% 0.20/0.51 Proof:
% 0.20/0.51 p2(f11(f4(c33), c34), f18(f11(f4(c33), c34), f9(f17(c31))))
% 0.20/0.51 = { by axiom 7 (p2_30) R->L }
% 0.20/0.51 fresh16(true2, true2, f11(f4(c33), c34), f18(f11(f4(c33), c34), f9(f17(c31))), f11(f4(c32), c34))
% 0.20/0.51 = { by axiom 10 (p2_38) R->L }
% 0.20/0.51 fresh16(p2(f11(f4(c32), c34), f18(f11(f4(c33), c34), f9(f17(c31)))), true2, f11(f4(c33), c34), f18(f11(f4(c33), c34), f9(f17(c31))), f11(f4(c32), c34))
% 0.20/0.51 = { by axiom 9 (p2_30) }
% 0.20/0.51 fresh15(p2(f11(f4(c32), c34), f11(f4(c33), c34)), true2, f11(f4(c33), c34), f18(f11(f4(c33), c34), f9(f17(c31))))
% 0.20/0.51 = { by axiom 7 (p2_30) R->L }
% 0.20/0.51 fresh15(fresh16(true2, true2, f11(f4(c32), c34), f11(f4(c33), c34), f11(f4(c33), c34)), true2, f11(f4(c33), c34), f18(f11(f4(c33), c34), f9(f17(c31))))
% 0.20/0.51 = { by axiom 1 (p2_7) R->L }
% 0.20/0.51 fresh15(fresh16(p2(f11(f4(c33), c34), f11(f4(c33), c34)), true2, f11(f4(c32), c34), f11(f4(c33), c34), f11(f4(c33), c34)), true2, f11(f4(c33), c34), f18(f11(f4(c33), c34), f9(f17(c31))))
% 0.20/0.51 = { by axiom 9 (p2_30) }
% 0.20/0.51 fresh15(fresh15(p2(f11(f4(c33), c34), f11(f4(c32), c34)), true2, f11(f4(c32), c34), f11(f4(c33), c34)), true2, f11(f4(c33), c34), f18(f11(f4(c33), c34), f9(f17(c31))))
% 0.20/0.51 = { by axiom 8 (p2_50) R->L }
% 0.20/0.51 fresh15(fresh15(fresh48(p25(c32, c33), true2, c33), true2, f11(f4(c32), c34), f11(f4(c33), c34)), true2, f11(f4(c33), c34), f18(f11(f4(c33), c34), f9(f17(c31))))
% 0.20/0.51 = { by axiom 2 (p25_14) }
% 0.20/0.51 fresh15(fresh15(fresh48(true2, true2, c33), true2, f11(f4(c32), c34), f11(f4(c33), c34)), true2, f11(f4(c33), c34), f18(f11(f4(c33), c34), f9(f17(c31))))
% 0.20/0.51 = { by axiom 5 (p2_50) }
% 0.20/0.51 fresh15(fresh15(fresh49(p25(c33, c36), true2, c33), true2, f11(f4(c32), c34), f11(f4(c33), c34)), true2, f11(f4(c33), c34), f18(f11(f4(c33), c34), f9(f17(c31))))
% 0.20/0.51 = { by axiom 3 (p25_12) }
% 0.20/0.51 fresh15(fresh15(fresh49(true2, true2, c33), true2, f11(f4(c32), c34), f11(f4(c33), c34)), true2, f11(f4(c33), c34), f18(f11(f4(c33), c34), f9(f17(c31))))
% 0.20/0.51 = { by axiom 4 (p2_50) }
% 0.20/0.51 fresh15(fresh15(true2, true2, f11(f4(c32), c34), f11(f4(c33), c34)), true2, f11(f4(c33), c34), f18(f11(f4(c33), c34), f9(f17(c31))))
% 0.20/0.51 = { by axiom 6 (p2_30) }
% 0.20/0.51 fresh15(true2, true2, f11(f4(c33), c34), f18(f11(f4(c33), c34), f9(f17(c31))))
% 0.20/0.51 = { by axiom 6 (p2_30) }
% 0.20/0.51 true2
% 0.20/0.51 % SZS output end Proof
% 0.20/0.51
% 0.20/0.51 RESULT: Unsatisfiable (the axioms are contradictory).
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