TSTP Solution File: SYN570-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYN570-1 : 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 : n025.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 03:35:17 EDT 2023
% Result : Unsatisfiable 0.19s 0.43s
% 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 : SYN570-1 : 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 : n025.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 : Sat Aug 26 21:02:53 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.43 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.19/0.43
% 0.19/0.43 % SZS status Unsatisfiable
% 0.19/0.43
% 0.19/0.44 % SZS output start Proof
% 0.19/0.44 Take the following subset of the input axioms:
% 0.19/0.44 fof(not_p9_10, negated_conjecture, ~p9(f4(c12), f8(c13))).
% 0.19/0.44 fof(p2_18, negated_conjecture, ![X7, X8, X9]: (p2(X8, X9) | (~p2(X7, X8) | ~p2(X7, X9)))).
% 0.19/0.44 fof(p2_5, negated_conjecture, ![X7_2]: p2(X7_2, X7_2)).
% 0.19/0.44 fof(p2_8, negated_conjecture, p2(c12, f5(c15))).
% 0.19/0.44 fof(p3_13, negated_conjecture, ![X15, X16]: (p3(f4(X15), f4(X16)) | ~p2(X15, X16))).
% 0.19/0.44 fof(p3_17, negated_conjecture, ![X12, X13, X14]: (p3(X13, X14) | (~p3(X12, X13) | ~p3(X12, X14)))).
% 0.19/0.44 fof(p3_4, negated_conjecture, ![X12_2]: p3(X12_2, X12_2)).
% 0.19/0.44 fof(p3_9, negated_conjecture, ![X17]: p3(f4(f5(X17)), X17)).
% 0.19/0.44 fof(p7_2, negated_conjecture, ![X21]: p7(X21, X21)).
% 0.19/0.44 fof(p9_19, negated_conjecture, ![X26, X27, X29, X28]: (p9(X26, X27) | (~p7(X29, X27) | (~p9(X28, X29) | ~p3(X28, X26))))).
% 0.19/0.44 fof(p9_7, negated_conjecture, p9(c15, f8(c13))).
% 0.19/0.44
% 0.19/0.44 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.44 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.44 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.44 fresh(y, y, x1...xn) = u
% 0.19/0.44 C => fresh(s, t, x1...xn) = v
% 0.19/0.44 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.44 variables of u and v.
% 0.19/0.44 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.44 input problem has no model of domain size 1).
% 0.19/0.44
% 0.19/0.44 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.44
% 0.19/0.44 Axiom 1 (p3_4): p3(X, X) = true.
% 0.19/0.44 Axiom 2 (p2_5): p2(X, X) = true.
% 0.19/0.44 Axiom 3 (p7_2): p7(X, X) = true.
% 0.19/0.44 Axiom 4 (p2_8): p2(c12, f5(c15)) = true.
% 0.19/0.44 Axiom 5 (p9_7): p9(c15, f8(c13)) = true.
% 0.19/0.44 Axiom 6 (p3_9): p3(f4(f5(X)), X) = true.
% 0.19/0.44 Axiom 7 (p9_19): fresh19(X, X, Y, Z) = true.
% 0.19/0.44 Axiom 8 (p2_18): fresh10(X, X, Y, Z) = true.
% 0.19/0.44 Axiom 9 (p3_13): fresh9(X, X, Y, Z) = true.
% 0.19/0.44 Axiom 10 (p3_17): fresh7(X, X, Y, Z) = true.
% 0.19/0.44 Axiom 11 (p9_19): fresh(X, X, Y, Z, W) = p9(Y, Z).
% 0.19/0.44 Axiom 12 (p2_18): fresh11(X, X, Y, Z, W) = p2(Y, Z).
% 0.19/0.44 Axiom 13 (p3_17): fresh8(X, X, Y, Z, W) = p3(Y, Z).
% 0.19/0.44 Axiom 14 (p9_19): fresh18(X, X, Y, Z, W, V) = fresh19(p7(W, Z), true, Y, Z).
% 0.19/0.44 Axiom 15 (p3_13): fresh9(p2(X, Y), true, X, Y) = p3(f4(X), f4(Y)).
% 0.19/0.44 Axiom 16 (p2_18): fresh11(p2(X, Y), true, Z, Y, X) = fresh10(p2(X, Z), true, Z, Y).
% 0.19/0.44 Axiom 17 (p3_17): fresh8(p3(X, Y), true, Z, Y, X) = fresh7(p3(X, Z), true, Z, Y).
% 0.19/0.44 Axiom 18 (p9_19): fresh18(p9(X, Y), true, Z, W, Y, X) = fresh(p3(X, Z), true, Z, W, Y).
% 0.19/0.44
% 0.19/0.44 Goal 1 (not_p9_10): p9(f4(c12), f8(c13)) = true.
% 0.19/0.44 Proof:
% 0.19/0.45 p9(f4(c12), f8(c13))
% 0.19/0.45 = { by axiom 11 (p9_19) R->L }
% 0.19/0.45 fresh(true, true, f4(c12), f8(c13), f8(c13))
% 0.19/0.45 = { by axiom 10 (p3_17) R->L }
% 0.19/0.45 fresh(fresh7(true, true, c15, f4(c12)), true, f4(c12), f8(c13), f8(c13))
% 0.19/0.45 = { by axiom 10 (p3_17) R->L }
% 0.19/0.45 fresh(fresh7(fresh7(true, true, f4(c12), c15), true, c15, f4(c12)), true, f4(c12), f8(c13), f8(c13))
% 0.19/0.45 = { by axiom 9 (p3_13) R->L }
% 0.19/0.45 fresh(fresh7(fresh7(fresh9(true, true, f5(c15), c12), true, f4(c12), c15), true, c15, f4(c12)), true, f4(c12), f8(c13), f8(c13))
% 0.19/0.45 = { by axiom 8 (p2_18) R->L }
% 0.19/0.45 fresh(fresh7(fresh7(fresh9(fresh10(true, true, f5(c15), c12), true, f5(c15), c12), true, f4(c12), c15), true, c15, f4(c12)), true, f4(c12), f8(c13), f8(c13))
% 0.19/0.45 = { by axiom 4 (p2_8) R->L }
% 0.19/0.45 fresh(fresh7(fresh7(fresh9(fresh10(p2(c12, f5(c15)), true, f5(c15), c12), true, f5(c15), c12), true, f4(c12), c15), true, c15, f4(c12)), true, f4(c12), f8(c13), f8(c13))
% 0.19/0.45 = { by axiom 16 (p2_18) R->L }
% 0.19/0.45 fresh(fresh7(fresh7(fresh9(fresh11(p2(c12, c12), true, f5(c15), c12, c12), true, f5(c15), c12), true, f4(c12), c15), true, c15, f4(c12)), true, f4(c12), f8(c13), f8(c13))
% 0.19/0.45 = { by axiom 2 (p2_5) }
% 0.19/0.45 fresh(fresh7(fresh7(fresh9(fresh11(true, true, f5(c15), c12, c12), true, f5(c15), c12), true, f4(c12), c15), true, c15, f4(c12)), true, f4(c12), f8(c13), f8(c13))
% 0.19/0.45 = { by axiom 12 (p2_18) }
% 0.19/0.45 fresh(fresh7(fresh7(fresh9(p2(f5(c15), c12), true, f5(c15), c12), true, f4(c12), c15), true, c15, f4(c12)), true, f4(c12), f8(c13), f8(c13))
% 0.19/0.45 = { by axiom 15 (p3_13) }
% 0.19/0.45 fresh(fresh7(fresh7(p3(f4(f5(c15)), f4(c12)), true, f4(c12), c15), true, c15, f4(c12)), true, f4(c12), f8(c13), f8(c13))
% 0.19/0.45 = { by axiom 17 (p3_17) R->L }
% 0.19/0.45 fresh(fresh7(fresh8(p3(f4(f5(c15)), c15), true, f4(c12), c15, f4(f5(c15))), true, c15, f4(c12)), true, f4(c12), f8(c13), f8(c13))
% 0.19/0.45 = { by axiom 6 (p3_9) }
% 0.19/0.45 fresh(fresh7(fresh8(true, true, f4(c12), c15, f4(f5(c15))), true, c15, f4(c12)), true, f4(c12), f8(c13), f8(c13))
% 0.19/0.45 = { by axiom 13 (p3_17) }
% 0.19/0.45 fresh(fresh7(p3(f4(c12), c15), true, c15, f4(c12)), true, f4(c12), f8(c13), f8(c13))
% 0.19/0.45 = { by axiom 17 (p3_17) R->L }
% 0.19/0.45 fresh(fresh8(p3(f4(c12), f4(c12)), true, c15, f4(c12), f4(c12)), true, f4(c12), f8(c13), f8(c13))
% 0.19/0.45 = { by axiom 1 (p3_4) }
% 0.19/0.45 fresh(fresh8(true, true, c15, f4(c12), f4(c12)), true, f4(c12), f8(c13), f8(c13))
% 0.19/0.45 = { by axiom 13 (p3_17) }
% 0.19/0.45 fresh(p3(c15, f4(c12)), true, f4(c12), f8(c13), f8(c13))
% 0.19/0.45 = { by axiom 18 (p9_19) R->L }
% 0.19/0.45 fresh18(p9(c15, f8(c13)), true, f4(c12), f8(c13), f8(c13), c15)
% 0.19/0.45 = { by axiom 5 (p9_7) }
% 0.19/0.45 fresh18(true, true, f4(c12), f8(c13), f8(c13), c15)
% 0.19/0.45 = { by axiom 14 (p9_19) }
% 0.19/0.45 fresh19(p7(f8(c13), f8(c13)), true, f4(c12), f8(c13))
% 0.19/0.45 = { by axiom 3 (p7_2) }
% 0.19/0.45 fresh19(true, true, f4(c12), f8(c13))
% 0.19/0.45 = { by axiom 7 (p9_19) }
% 0.19/0.45 true
% 0.19/0.45 % SZS output end Proof
% 0.19/0.45
% 0.19/0.45 RESULT: Unsatisfiable (the axioms are contradictory).
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