TSTP Solution File: SYN563-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYN563-1 : 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 03:35:16 EDT 2023
% Result : Unsatisfiable 0.20s 0.55s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN563-1 : TPTP v8.1.2. Released v2.5.0.
% 0.07/0.13 % 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 : n007.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 18:07:11 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.55 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 0.20/0.55
% 0.20/0.55 % SZS status Unsatisfiable
% 0.20/0.55
% 0.20/0.55 % SZS output start Proof
% 0.20/0.55 Take the following subset of the input axioms:
% 0.20/0.56 fof(not_p6_5, negated_conjecture, ~p6(f4(c7), f3(f4(c8)))).
% 0.20/0.56 fof(p2_1, negated_conjecture, ![X0]: p2(X0, X0)).
% 0.20/0.56 fof(p2_11, negated_conjecture, ![X3, X4]: (p2(f3(X3), f3(X4)) | ~p2(X3, X4))).
% 0.20/0.56 fof(p2_4, negated_conjecture, p2(f4(c7), f4(c8))).
% 0.20/0.56 fof(p5_15, negated_conjecture, ![X7, X8, X9]: (p5(X7, X8) | (~p5(X9, X8) | ~p6(X7, X9)))).
% 0.20/0.56 fof(p5_7, negated_conjecture, ![X16]: p5(f3(f3(X16)), f3(f4(X16)))).
% 0.20/0.56 fof(p6_10, negated_conjecture, ![X10, X11]: (p6(f4(X10), X11) | ~p5(X10, X11))).
% 0.20/0.56 fof(p6_14, negated_conjecture, ![X17, X18, X19]: (p6(X17, X18) | (~p6(X17, X19) | ~p6(X19, X18)))).
% 0.20/0.56 fof(p6_16, negated_conjecture, ![X23, X24, X26, X25]: (p6(X23, X24) | (~p2(X26, X23) | (~p6(X26, X25) | ~p2(X25, X24))))).
% 0.20/0.56 fof(p6_2, negated_conjecture, ![X22]: p6(X22, X22)).
% 0.20/0.56 fof(p6_9, negated_conjecture, ![X27]: (p6(c7, f3(X27)) | ~p6(c7, X27))).
% 0.20/0.56
% 0.20/0.56 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.56 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.56 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.56 fresh(y, y, x1...xn) = u
% 0.20/0.56 C => fresh(s, t, x1...xn) = v
% 0.20/0.56 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.56 variables of u and v.
% 0.20/0.56 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.56 input problem has no model of domain size 1).
% 0.20/0.56
% 0.20/0.56 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.56
% 0.20/0.56 Axiom 1 (p6_2): p6(X, X) = true.
% 0.20/0.56 Axiom 2 (p2_1): p2(X, X) = true.
% 0.20/0.56 Axiom 3 (p6_9): fresh(X, X, Y) = true.
% 0.20/0.56 Axiom 4 (p2_4): p2(f4(c7), f4(c8)) = true.
% 0.20/0.56 Axiom 5 (p6_16): fresh18(X, X, Y, Z) = true.
% 0.20/0.56 Axiom 6 (p2_11): fresh13(X, X, Y, Z) = true.
% 0.20/0.56 Axiom 7 (p5_15): fresh9(X, X, Y, Z) = true.
% 0.20/0.56 Axiom 8 (p6_10): fresh6(X, X, Y, Z) = true.
% 0.20/0.56 Axiom 9 (p6_14): fresh4(X, X, Y, Z) = true.
% 0.20/0.56 Axiom 10 (p6_9): fresh(p6(c7, X), true, X) = p6(c7, f3(X)).
% 0.20/0.56 Axiom 11 (p5_15): fresh10(X, X, Y, Z, W) = p5(Y, Z).
% 0.20/0.56 Axiom 12 (p6_14): fresh5(X, X, Y, Z, W) = p6(Y, Z).
% 0.20/0.56 Axiom 13 (p6_16): fresh3(X, X, Y, Z, W) = p6(Y, Z).
% 0.20/0.56 Axiom 14 (p5_7): p5(f3(f3(X)), f3(f4(X))) = true.
% 0.20/0.56 Axiom 15 (p6_16): fresh17(X, X, Y, Z, W, V) = fresh18(p2(W, Y), true, Y, Z).
% 0.20/0.56 Axiom 16 (p2_11): fresh13(p2(X, Y), true, X, Y) = p2(f3(X), f3(Y)).
% 0.20/0.56 Axiom 17 (p6_10): fresh6(p5(X, Y), true, X, Y) = p6(f4(X), Y).
% 0.20/0.56 Axiom 18 (p5_15): fresh10(p5(X, Y), true, Z, Y, X) = fresh9(p6(Z, X), true, Z, Y).
% 0.20/0.56 Axiom 19 (p6_14): fresh5(p6(X, Y), true, Z, Y, X) = fresh4(p6(Z, X), true, Z, Y).
% 0.20/0.56 Axiom 20 (p6_16): fresh17(p6(X, Y), true, Z, W, X, Y) = fresh3(p2(Y, W), true, Z, W, X).
% 0.20/0.56
% 0.20/0.56 Goal 1 (not_p6_5): p6(f4(c7), f3(f4(c8))) = true.
% 0.20/0.56 Proof:
% 0.20/0.56 p6(f4(c7), f3(f4(c8)))
% 0.20/0.56 = { by axiom 12 (p6_14) R->L }
% 0.20/0.56 fresh5(true, true, f4(c7), f3(f4(c8)), f3(f4(c7)))
% 0.20/0.56 = { by axiom 5 (p6_16) R->L }
% 0.20/0.56 fresh5(fresh18(true, true, f3(f4(c7)), f3(f4(c8))), true, f4(c7), f3(f4(c8)), f3(f4(c7)))
% 0.20/0.56 = { by axiom 2 (p2_1) R->L }
% 0.20/0.56 fresh5(fresh18(p2(f3(f4(c7)), f3(f4(c7))), true, f3(f4(c7)), f3(f4(c8))), true, f4(c7), f3(f4(c8)), f3(f4(c7)))
% 0.20/0.56 = { by axiom 15 (p6_16) R->L }
% 0.20/0.56 fresh5(fresh17(true, true, f3(f4(c7)), f3(f4(c8)), f3(f4(c7)), f3(f4(c7))), true, f4(c7), f3(f4(c8)), f3(f4(c7)))
% 0.20/0.56 = { by axiom 1 (p6_2) R->L }
% 0.20/0.56 fresh5(fresh17(p6(f3(f4(c7)), f3(f4(c7))), true, f3(f4(c7)), f3(f4(c8)), f3(f4(c7)), f3(f4(c7))), true, f4(c7), f3(f4(c8)), f3(f4(c7)))
% 0.20/0.56 = { by axiom 20 (p6_16) }
% 0.20/0.56 fresh5(fresh3(p2(f3(f4(c7)), f3(f4(c8))), true, f3(f4(c7)), f3(f4(c8)), f3(f4(c7))), true, f4(c7), f3(f4(c8)), f3(f4(c7)))
% 0.20/0.56 = { by axiom 16 (p2_11) R->L }
% 0.20/0.56 fresh5(fresh3(fresh13(p2(f4(c7), f4(c8)), true, f4(c7), f4(c8)), true, f3(f4(c7)), f3(f4(c8)), f3(f4(c7))), true, f4(c7), f3(f4(c8)), f3(f4(c7)))
% 0.20/0.56 = { by axiom 4 (p2_4) }
% 0.20/0.56 fresh5(fresh3(fresh13(true, true, f4(c7), f4(c8)), true, f3(f4(c7)), f3(f4(c8)), f3(f4(c7))), true, f4(c7), f3(f4(c8)), f3(f4(c7)))
% 0.20/0.56 = { by axiom 6 (p2_11) }
% 0.20/0.56 fresh5(fresh3(true, true, f3(f4(c7)), f3(f4(c8)), f3(f4(c7))), true, f4(c7), f3(f4(c8)), f3(f4(c7)))
% 0.20/0.56 = { by axiom 13 (p6_16) }
% 0.20/0.56 fresh5(p6(f3(f4(c7)), f3(f4(c8))), true, f4(c7), f3(f4(c8)), f3(f4(c7)))
% 0.20/0.56 = { by axiom 19 (p6_14) }
% 0.20/0.56 fresh4(p6(f4(c7), f3(f4(c7))), true, f4(c7), f3(f4(c8)))
% 0.20/0.56 = { by axiom 17 (p6_10) R->L }
% 0.20/0.56 fresh4(fresh6(p5(c7, f3(f4(c7))), true, c7, f3(f4(c7))), true, f4(c7), f3(f4(c8)))
% 0.20/0.56 = { by axiom 11 (p5_15) R->L }
% 0.20/0.56 fresh4(fresh6(fresh10(true, true, c7, f3(f4(c7)), f3(f3(c7))), true, c7, f3(f4(c7))), true, f4(c7), f3(f4(c8)))
% 0.20/0.56 = { by axiom 14 (p5_7) R->L }
% 0.20/0.56 fresh4(fresh6(fresh10(p5(f3(f3(c7)), f3(f4(c7))), true, c7, f3(f4(c7)), f3(f3(c7))), true, c7, f3(f4(c7))), true, f4(c7), f3(f4(c8)))
% 0.20/0.56 = { by axiom 18 (p5_15) }
% 0.20/0.56 fresh4(fresh6(fresh9(p6(c7, f3(f3(c7))), true, c7, f3(f4(c7))), true, c7, f3(f4(c7))), true, f4(c7), f3(f4(c8)))
% 0.20/0.56 = { by axiom 10 (p6_9) R->L }
% 0.20/0.56 fresh4(fresh6(fresh9(fresh(p6(c7, f3(c7)), true, f3(c7)), true, c7, f3(f4(c7))), true, c7, f3(f4(c7))), true, f4(c7), f3(f4(c8)))
% 0.20/0.56 = { by axiom 10 (p6_9) R->L }
% 0.20/0.56 fresh4(fresh6(fresh9(fresh(fresh(p6(c7, c7), true, c7), true, f3(c7)), true, c7, f3(f4(c7))), true, c7, f3(f4(c7))), true, f4(c7), f3(f4(c8)))
% 0.20/0.56 = { by axiom 1 (p6_2) }
% 0.20/0.56 fresh4(fresh6(fresh9(fresh(fresh(true, true, c7), true, f3(c7)), true, c7, f3(f4(c7))), true, c7, f3(f4(c7))), true, f4(c7), f3(f4(c8)))
% 0.20/0.56 = { by axiom 3 (p6_9) }
% 0.20/0.56 fresh4(fresh6(fresh9(fresh(true, true, f3(c7)), true, c7, f3(f4(c7))), true, c7, f3(f4(c7))), true, f4(c7), f3(f4(c8)))
% 0.20/0.56 = { by axiom 3 (p6_9) }
% 0.20/0.56 fresh4(fresh6(fresh9(true, true, c7, f3(f4(c7))), true, c7, f3(f4(c7))), true, f4(c7), f3(f4(c8)))
% 0.20/0.56 = { by axiom 7 (p5_15) }
% 0.20/0.56 fresh4(fresh6(true, true, c7, f3(f4(c7))), true, f4(c7), f3(f4(c8)))
% 0.20/0.56 = { by axiom 8 (p6_10) }
% 0.20/0.56 fresh4(true, true, f4(c7), f3(f4(c8)))
% 0.20/0.56 = { by axiom 9 (p6_14) }
% 0.20/0.56 true
% 0.20/0.56 % SZS output end Proof
% 0.20/0.56
% 0.20/0.56 RESULT: Unsatisfiable (the axioms are contradictory).
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