TSTP Solution File: SYN586-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYN586-1 : 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 : n017.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 03:35:21 EDT 2023
% Result : Unsatisfiable 0.19s 0.47s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.12 % Problem : SYN586-1 : TPTP v8.1.2. Released v2.5.0.
% 0.13/0.13 % 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 : n017.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 17:47:56 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.47 Command-line arguments: --flatten
% 0.19/0.47
% 0.19/0.47 % SZS status Unsatisfiable
% 0.19/0.47
% 0.19/0.48 % SZS output start Proof
% 0.19/0.48 Take the following subset of the input axioms:
% 0.19/0.48 fof(not_p15_23, negated_conjecture, ~p15(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c19)), c20)).
% 0.19/0.48 fof(p15_17, negated_conjecture, ![X9, X10, X11, X12]: (p15(X9, X10) | (~p2(X11, X9) | (~p2(X12, X10) | ~p15(X11, X12))))).
% 0.19/0.48 fof(p15_22, negated_conjecture, p15(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c21)), c20)).
% 0.19/0.48 fof(p2_20, negated_conjecture, ![X16, X17, X18, X19]: (p2(f4(X16, X17), f4(X18, X19)) | (~p2(X16, X18) | ~p3(X17, X19)))).
% 0.19/0.48 fof(p2_4, negated_conjecture, ![X13]: p2(X13, X13)).
% 0.19/0.48 fof(p3_12, negated_conjecture, ![X27, X28]: (p3(f11(X27), f11(X28)) | ~p3(X27, X28))).
% 0.19/0.48 fof(p3_5, negated_conjecture, p3(c21, c19)).
% 0.19/0.48
% 0.19/0.48 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.48 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.48 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.48 fresh(y, y, x1...xn) = u
% 0.19/0.48 C => fresh(s, t, x1...xn) = v
% 0.19/0.48 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.48 variables of u and v.
% 0.19/0.48 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.48 input problem has no model of domain size 1).
% 0.19/0.48
% 0.19/0.48 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.48
% 0.19/0.48 Axiom 1 (p2_4): p2(X, X) = true.
% 0.19/0.48 Axiom 2 (p3_5): p3(c21, c19) = true.
% 0.19/0.48 Axiom 3 (p15_17): fresh24(X, X, Y, Z) = true.
% 0.19/0.48 Axiom 4 (p3_12): fresh9(X, X, Y, Z) = true.
% 0.19/0.48 Axiom 5 (p15_17): fresh18(X, X, Y, Z, W) = p15(Y, Z).
% 0.19/0.49 Axiom 6 (p15_17): fresh23(X, X, Y, Z, W, V) = fresh24(p2(W, Y), true, Y, Z).
% 0.19/0.49 Axiom 7 (p2_20): fresh14(X, X, Y, Z, W, V) = true.
% 0.19/0.49 Axiom 8 (p3_12): fresh9(p3(X, Y), true, X, Y) = p3(f11(X), f11(Y)).
% 0.19/0.49 Axiom 9 (p2_20): fresh15(X, X, Y, Z, W, V) = p2(f4(Y, Z), f4(W, V)).
% 0.19/0.49 Axiom 10 (p15_17): fresh23(p15(X, Y), true, Z, W, X, Y) = fresh18(p2(Y, W), true, Z, W, X).
% 0.19/0.49 Axiom 11 (p2_20): fresh15(p2(X, Y), true, X, Z, Y, W) = fresh14(p3(Z, W), true, X, Z, Y, W).
% 0.19/0.49 Axiom 12 (p15_22): p15(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c21)), c20) = true.
% 0.19/0.49
% 0.19/0.49 Goal 1 (not_p15_23): p15(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c19)), c20) = true.
% 0.19/0.49 Proof:
% 0.19/0.49 p15(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c19)), c20)
% 0.19/0.49 = { by axiom 5 (p15_17) R->L }
% 0.19/0.49 fresh18(p3(c21, c19), p3(c21, c19), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c19)), c20, f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c21)))
% 0.19/0.49 = { by axiom 2 (p3_5) }
% 0.19/0.49 fresh18(true, p3(c21, c19), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c19)), c20, f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c21)))
% 0.19/0.49 = { by axiom 1 (p2_4) R->L }
% 0.19/0.49 fresh18(p2(c20, c20), p3(c21, c19), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c19)), c20, f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c21)))
% 0.19/0.49 = { by axiom 2 (p3_5) }
% 0.19/0.49 fresh18(p2(c20, c20), true, f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c19)), c20, f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c21)))
% 0.19/0.49 = { by axiom 10 (p15_17) R->L }
% 0.19/0.49 fresh23(p15(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c21)), c20), true, f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c19)), c20, f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c21)), c20)
% 0.19/0.49 = { by axiom 2 (p3_5) R->L }
% 0.19/0.49 fresh23(p15(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c21)), c20), p3(c21, c19), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c19)), c20, f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c21)), c20)
% 0.19/0.49 = { by axiom 12 (p15_22) }
% 0.19/0.49 fresh23(true, p3(c21, c19), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c19)), c20, f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c21)), c20)
% 0.19/0.49 = { by axiom 2 (p3_5) R->L }
% 0.19/0.49 fresh23(p3(c21, c19), p3(c21, c19), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c19)), c20, f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c21)), c20)
% 0.19/0.49 = { by axiom 6 (p15_17) }
% 0.19/0.49 fresh24(p2(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c21)), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c19))), true, f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c19)), c20)
% 0.19/0.49 = { by axiom 2 (p3_5) R->L }
% 0.19/0.49 fresh24(p2(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c21)), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c19))), p3(c21, c19), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c19)), c20)
% 0.19/0.49 = { by axiom 9 (p2_20) R->L }
% 0.19/0.49 fresh24(fresh15(p3(c21, c19), p3(c21, c19), f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c21), f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c19)), p3(c21, c19), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c19)), c20)
% 0.19/0.49 = { by axiom 2 (p3_5) }
% 0.19/0.49 fresh24(fresh15(true, p3(c21, c19), f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c21), f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c19)), p3(c21, c19), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c19)), c20)
% 0.19/0.49 = { by axiom 1 (p2_4) R->L }
% 0.19/0.49 fresh24(fresh15(p2(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f6(f10(c16), f6(f7(f8(f9(c17))), c18))), p3(c21, c19), f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c21), f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c19)), p3(c21, c19), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c19)), c20)
% 0.19/0.49 = { by axiom 2 (p3_5) }
% 0.19/0.49 fresh24(fresh15(p2(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f6(f10(c16), f6(f7(f8(f9(c17))), c18))), true, f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c21), f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c19)), p3(c21, c19), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c19)), c20)
% 0.19/0.49 = { by axiom 11 (p2_20) }
% 0.19/0.49 fresh24(fresh14(p3(f11(c21), f11(c19)), true, f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c21), f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c19)), p3(c21, c19), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c19)), c20)
% 0.19/0.49 = { by axiom 2 (p3_5) R->L }
% 0.19/0.49 fresh24(fresh14(p3(f11(c21), f11(c19)), p3(c21, c19), f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c21), f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c19)), p3(c21, c19), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c19)), c20)
% 0.19/0.49 = { by axiom 8 (p3_12) R->L }
% 0.19/0.49 fresh24(fresh14(fresh9(p3(c21, c19), true, c21, c19), p3(c21, c19), f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c21), f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c19)), p3(c21, c19), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c19)), c20)
% 0.19/0.49 = { by axiom 2 (p3_5) R->L }
% 0.19/0.49 fresh24(fresh14(fresh9(p3(c21, c19), p3(c21, c19), c21, c19), p3(c21, c19), f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c21), f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c19)), p3(c21, c19), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c19)), c20)
% 0.19/0.49 = { by axiom 4 (p3_12) }
% 0.19/0.49 fresh24(fresh14(true, p3(c21, c19), f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c21), f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c19)), p3(c21, c19), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c19)), c20)
% 0.19/0.49 = { by axiom 2 (p3_5) R->L }
% 0.19/0.49 fresh24(fresh14(p3(c21, c19), p3(c21, c19), f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c21), f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c19)), p3(c21, c19), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c19)), c20)
% 0.19/0.49 = { by axiom 7 (p2_20) }
% 0.19/0.49 fresh24(true, p3(c21, c19), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c19)), c20)
% 0.19/0.50 = { by axiom 2 (p3_5) R->L }
% 0.19/0.50 fresh24(p3(c21, c19), p3(c21, c19), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f11(c19)), c20)
% 0.19/0.50 = { by axiom 3 (p15_17) }
% 0.19/0.50 true
% 0.19/0.50 % SZS output end Proof
% 0.19/0.50
% 0.19/0.50 RESULT: Unsatisfiable (the axioms are contradictory).
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