TSTP Solution File: SYN652-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYN652-1 : 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 : n009.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 03:35:34 EDT 2023
% Result : Unsatisfiable 0.18s 0.49s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SYN652-1 : TPTP v8.1.2. Released v2.5.0.
% 0.03/0.12 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.11/0.32 % Computer : n009.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Sat Aug 26 19:31:35 EDT 2023
% 0.11/0.33 % CPUTime :
% 0.18/0.49 Command-line arguments: --ground-connectedness --complete-subsets
% 0.18/0.49
% 0.18/0.49 % SZS status Unsatisfiable
% 0.18/0.49
% 0.18/0.50 % SZS output start Proof
% 0.18/0.50 Take the following subset of the input axioms:
% 0.18/0.50 fof(not_p4_18, negated_conjecture, ~p4(f5(c31, c33), f15(f17(c36, c31), c34))).
% 0.18/0.50 fof(p14_14, negated_conjecture, ![X6]: p14(X6, X6)).
% 0.18/0.50 fof(p27_17, negated_conjecture, p27(f8(f10(c28, f13(c29, c30)), c32), c33)).
% 0.18/0.50 fof(p4_16, negated_conjecture, p4(c34, f5(c35, c32))).
% 0.18/0.50 fof(p4_23, negated_conjecture, ![X53, X54, X55]: (p4(X54, X55) | (~p4(X53, X54) | ~p4(X53, X55)))).
% 0.18/0.50 fof(p4_34, negated_conjecture, ![X60, X61]: p4(f15(f17(c36, X60), f5(c35, X61)), f5(X60, X61))).
% 0.18/0.50 fof(p4_41, negated_conjecture, ![X56, X57, X58, X59]: (p4(f15(X56, X57), f15(X58, X59)) | (~p14(X56, X58) | ~p4(X57, X59)))).
% 0.18/0.50 fof(p4_46, negated_conjecture, ![X73, X74]: (p4(f5(c31, X73), f5(c31, X74)) | ~p27(f8(f10(c28, f13(c29, c30)), X73), X74))).
% 0.18/0.50 fof(p4_5, negated_conjecture, ![X53_2]: p4(X53_2, X53_2)).
% 0.18/0.50
% 0.18/0.50 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.18/0.50 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.18/0.50 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.18/0.50 fresh(y, y, x1...xn) = u
% 0.18/0.50 C => fresh(s, t, x1...xn) = v
% 0.18/0.50 where fresh is a fresh function symbol and x1..xn are the free
% 0.18/0.50 variables of u and v.
% 0.18/0.50 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.18/0.50 input problem has no model of domain size 1).
% 0.18/0.50
% 0.18/0.50 The encoding turns the above axioms into the following unit equations and goals:
% 0.18/0.50
% 0.18/0.50 Axiom 1 (p14_14): p14(X, X) = true.
% 0.18/0.50 Axiom 2 (p4_5): p4(X, X) = true.
% 0.18/0.50 Axiom 3 (p4_23): fresh20(X, X, Y, Z) = true.
% 0.18/0.50 Axiom 4 (p4_46): fresh13(X, X, Y, Z) = true.
% 0.18/0.50 Axiom 5 (p4_16): p4(c34, f5(c35, c32)) = true.
% 0.18/0.50 Axiom 6 (p4_23): fresh21(X, X, Y, Z, W) = p4(Y, Z).
% 0.18/0.50 Axiom 7 (p4_41): fresh18(X, X, Y, Z, W, V) = true.
% 0.18/0.50 Axiom 8 (p4_41): fresh19(X, X, Y, Z, W, V) = p4(f15(Y, Z), f15(W, V)).
% 0.18/0.50 Axiom 9 (p4_23): fresh21(p4(X, Y), true, Z, Y, X) = fresh20(p4(X, Z), true, Z, Y).
% 0.18/0.50 Axiom 10 (p4_41): fresh19(p14(X, Y), true, X, Z, Y, W) = fresh18(p4(Z, W), true, X, Z, Y, W).
% 0.18/0.50 Axiom 11 (p27_17): p27(f8(f10(c28, f13(c29, c30)), c32), c33) = true.
% 0.18/0.50 Axiom 12 (p4_34): p4(f15(f17(c36, X), f5(c35, Y)), f5(X, Y)) = true.
% 0.18/0.50 Axiom 13 (p4_46): fresh13(p27(f8(f10(c28, f13(c29, c30)), X), Y), true, X, Y) = p4(f5(c31, X), f5(c31, Y)).
% 0.18/0.50
% 0.18/0.50 Lemma 14: fresh20(p4(X, Y), true, Y, X) = p4(Y, X).
% 0.18/0.50 Proof:
% 0.18/0.50 fresh20(p4(X, Y), true, Y, X)
% 0.18/0.50 = { by axiom 9 (p4_23) R->L }
% 0.18/0.50 fresh21(p4(X, X), true, Y, X, X)
% 0.18/0.50 = { by axiom 2 (p4_5) }
% 0.18/0.50 fresh21(true, true, Y, X, X)
% 0.18/0.50 = { by axiom 6 (p4_23) }
% 0.18/0.50 p4(Y, X)
% 0.18/0.50
% 0.18/0.50 Goal 1 (not_p4_18): p4(f5(c31, c33), f15(f17(c36, c31), c34)) = true.
% 0.18/0.50 Proof:
% 0.18/0.50 p4(f5(c31, c33), f15(f17(c36, c31), c34))
% 0.18/0.50 = { by axiom 6 (p4_23) R->L }
% 0.18/0.50 fresh21(true, true, f5(c31, c33), f15(f17(c36, c31), c34), f15(f17(c36, c31), f5(c35, c32)))
% 0.18/0.50 = { by axiom 3 (p4_23) R->L }
% 0.18/0.50 fresh21(fresh20(true, true, f15(f17(c36, c31), f5(c35, c32)), f15(f17(c36, c31), c34)), true, f5(c31, c33), f15(f17(c36, c31), c34), f15(f17(c36, c31), f5(c35, c32)))
% 0.18/0.50 = { by axiom 7 (p4_41) R->L }
% 0.18/0.50 fresh21(fresh20(fresh18(true, true, f17(c36, c31), c34, f17(c36, c31), f5(c35, c32)), true, f15(f17(c36, c31), f5(c35, c32)), f15(f17(c36, c31), c34)), true, f5(c31, c33), f15(f17(c36, c31), c34), f15(f17(c36, c31), f5(c35, c32)))
% 0.18/0.50 = { by axiom 5 (p4_16) R->L }
% 0.18/0.50 fresh21(fresh20(fresh18(p4(c34, f5(c35, c32)), true, f17(c36, c31), c34, f17(c36, c31), f5(c35, c32)), true, f15(f17(c36, c31), f5(c35, c32)), f15(f17(c36, c31), c34)), true, f5(c31, c33), f15(f17(c36, c31), c34), f15(f17(c36, c31), f5(c35, c32)))
% 0.18/0.50 = { by axiom 10 (p4_41) R->L }
% 0.18/0.50 fresh21(fresh20(fresh19(p14(f17(c36, c31), f17(c36, c31)), true, f17(c36, c31), c34, f17(c36, c31), f5(c35, c32)), true, f15(f17(c36, c31), f5(c35, c32)), f15(f17(c36, c31), c34)), true, f5(c31, c33), f15(f17(c36, c31), c34), f15(f17(c36, c31), f5(c35, c32)))
% 0.18/0.50 = { by axiom 1 (p14_14) }
% 0.18/0.50 fresh21(fresh20(fresh19(true, true, f17(c36, c31), c34, f17(c36, c31), f5(c35, c32)), true, f15(f17(c36, c31), f5(c35, c32)), f15(f17(c36, c31), c34)), true, f5(c31, c33), f15(f17(c36, c31), c34), f15(f17(c36, c31), f5(c35, c32)))
% 0.18/0.50 = { by axiom 8 (p4_41) }
% 0.18/0.50 fresh21(fresh20(p4(f15(f17(c36, c31), c34), f15(f17(c36, c31), f5(c35, c32))), true, f15(f17(c36, c31), f5(c35, c32)), f15(f17(c36, c31), c34)), true, f5(c31, c33), f15(f17(c36, c31), c34), f15(f17(c36, c31), f5(c35, c32)))
% 0.18/0.50 = { by lemma 14 }
% 0.18/0.50 fresh21(p4(f15(f17(c36, c31), f5(c35, c32)), f15(f17(c36, c31), c34)), true, f5(c31, c33), f15(f17(c36, c31), c34), f15(f17(c36, c31), f5(c35, c32)))
% 0.18/0.50 = { by axiom 9 (p4_23) }
% 0.18/0.50 fresh20(p4(f15(f17(c36, c31), f5(c35, c32)), f5(c31, c33)), true, f5(c31, c33), f15(f17(c36, c31), c34))
% 0.18/0.50 = { by axiom 6 (p4_23) R->L }
% 0.18/0.50 fresh20(fresh21(true, true, f15(f17(c36, c31), f5(c35, c32)), f5(c31, c33), f5(c31, c32)), true, f5(c31, c33), f15(f17(c36, c31), c34))
% 0.18/0.50 = { by axiom 4 (p4_46) R->L }
% 0.18/0.50 fresh20(fresh21(fresh13(true, true, c32, c33), true, f15(f17(c36, c31), f5(c35, c32)), f5(c31, c33), f5(c31, c32)), true, f5(c31, c33), f15(f17(c36, c31), c34))
% 0.18/0.50 = { by axiom 11 (p27_17) R->L }
% 0.18/0.50 fresh20(fresh21(fresh13(p27(f8(f10(c28, f13(c29, c30)), c32), c33), true, c32, c33), true, f15(f17(c36, c31), f5(c35, c32)), f5(c31, c33), f5(c31, c32)), true, f5(c31, c33), f15(f17(c36, c31), c34))
% 0.18/0.50 = { by axiom 13 (p4_46) }
% 0.18/0.50 fresh20(fresh21(p4(f5(c31, c32), f5(c31, c33)), true, f15(f17(c36, c31), f5(c35, c32)), f5(c31, c33), f5(c31, c32)), true, f5(c31, c33), f15(f17(c36, c31), c34))
% 0.18/0.50 = { by axiom 9 (p4_23) }
% 0.18/0.51 fresh20(fresh20(p4(f5(c31, c32), f15(f17(c36, c31), f5(c35, c32))), true, f15(f17(c36, c31), f5(c35, c32)), f5(c31, c33)), true, f5(c31, c33), f15(f17(c36, c31), c34))
% 0.18/0.51 = { by lemma 14 R->L }
% 0.18/0.51 fresh20(fresh20(fresh20(p4(f15(f17(c36, c31), f5(c35, c32)), f5(c31, c32)), true, f5(c31, c32), f15(f17(c36, c31), f5(c35, c32))), true, f15(f17(c36, c31), f5(c35, c32)), f5(c31, c33)), true, f5(c31, c33), f15(f17(c36, c31), c34))
% 0.18/0.51 = { by axiom 12 (p4_34) }
% 0.18/0.51 fresh20(fresh20(fresh20(true, true, f5(c31, c32), f15(f17(c36, c31), f5(c35, c32))), true, f15(f17(c36, c31), f5(c35, c32)), f5(c31, c33)), true, f5(c31, c33), f15(f17(c36, c31), c34))
% 0.18/0.51 = { by axiom 3 (p4_23) }
% 0.18/0.51 fresh20(fresh20(true, true, f15(f17(c36, c31), f5(c35, c32)), f5(c31, c33)), true, f5(c31, c33), f15(f17(c36, c31), c34))
% 0.18/0.51 = { by axiom 3 (p4_23) }
% 0.18/0.51 fresh20(true, true, f5(c31, c33), f15(f17(c36, c31), c34))
% 0.18/0.51 = { by axiom 3 (p4_23) }
% 0.18/0.51 true
% 0.18/0.51 % SZS output end Proof
% 0.18/0.51
% 0.18/0.51 RESULT: Unsatisfiable (the axioms are contradictory).
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