TSTP Solution File: SYN571-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYN571-1 : 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 : n001.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 0.20s 0.43s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN571-1 : 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 : n001.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 20:12:16 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.43 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.20/0.43
% 0.20/0.43 % SZS status Unsatisfiable
% 0.20/0.43
% 0.20/0.44 % SZS output start Proof
% 0.20/0.44 Take the following subset of the input axioms:
% 0.20/0.44 fof(not_p11_4, negated_conjecture, ![X40]: ~p11(c13, f5(X40))).
% 0.20/0.44 fof(not_p11_6, negated_conjecture, ![X39]: ~p11(X39, f3(X39, f5(f6(f7(c12)))))).
% 0.20/0.44 fof(p11_15, negated_conjecture, ![X6, X7, X8]: (p11(X6, f3(X7, X8)) | ~p11(f9(X6, X8), X7))).
% 0.20/0.44 fof(p11_17, negated_conjecture, ![X0, X1, X2, X3]: (p11(X0, X1) | (~p2(X2, X0) | (~p2(X3, X1) | ~p11(X2, X3))))).
% 0.20/0.44 fof(p11_3, negated_conjecture, ![X10]: p11(f5(X10), c14)).
% 0.20/0.44 fof(p11_7, negated_conjecture, ![X9]: (p11(c14, X9) | ~p11(f5(f10(X9)), X9))).
% 0.20/0.44 fof(p2_12, negated_conjecture, ![X11, X12, X13]: (p2(X12, X13) | (~p2(X11, X12) | ~p2(X11, X13)))).
% 0.20/0.44 fof(p2_14, negated_conjecture, ![X24, X25]: p2(f9(f5(X24), f5(X25)), f5(f8(X24, X25)))).
% 0.20/0.44 fof(p2_2, negated_conjecture, ![X11_2]: p2(X11_2, X11_2)).
% 0.20/0.44
% 0.20/0.44 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.44 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.44 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.44 fresh(y, y, x1...xn) = u
% 0.20/0.44 C => fresh(s, t, x1...xn) = v
% 0.20/0.44 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.44 variables of u and v.
% 0.20/0.44 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.44 input problem has no model of domain size 1).
% 0.20/0.44
% 0.20/0.44 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.44
% 0.20/0.44 Axiom 1 (p2_2): p2(X, X) = true2.
% 0.20/0.44 Axiom 2 (p11_3): p11(f5(X), c14) = true2.
% 0.20/0.44 Axiom 3 (p11_7): fresh15(X, X, Y) = true2.
% 0.20/0.44 Axiom 4 (p11_17): fresh20(X, X, Y, Z) = true2.
% 0.20/0.44 Axiom 5 (p2_12): fresh13(X, X, Y, Z) = true2.
% 0.20/0.44 Axiom 6 (p11_15): fresh17(X, X, Y, Z, W) = true2.
% 0.20/0.44 Axiom 7 (p11_17): fresh16(X, X, Y, Z, W) = p11(Y, Z).
% 0.20/0.44 Axiom 8 (p2_12): fresh14(X, X, Y, Z, W) = p2(Y, Z).
% 0.20/0.44 Axiom 9 (p11_17): fresh19(X, X, Y, Z, W, V) = fresh20(p2(W, Y), true2, Y, Z).
% 0.20/0.44 Axiom 10 (p11_7): fresh15(p11(f5(f10(X)), X), true2, X) = p11(c14, X).
% 0.20/0.44 Axiom 11 (p2_12): fresh14(p2(X, Y), true2, Z, Y, X) = fresh13(p2(X, Z), true2, Z, Y).
% 0.20/0.44 Axiom 12 (p11_17): fresh19(p11(X, Y), true2, Z, W, X, Y) = fresh16(p2(Y, W), true2, Z, W, X).
% 0.20/0.44 Axiom 13 (p2_14): p2(f9(f5(X), f5(Y)), f5(f8(X, Y))) = true2.
% 0.20/0.44 Axiom 14 (p11_15): fresh17(p11(f9(X, Y), Z), true2, X, Z, Y) = p11(X, f3(Z, Y)).
% 0.20/0.44
% 0.20/0.44 Goal 1 (not_p11_6): p11(X, f3(X, f5(f6(f7(c12))))) = true2.
% 0.20/0.44 The goal is true when:
% 0.20/0.44 X = c14
% 0.20/0.44
% 0.20/0.44 Proof:
% 0.20/0.44 p11(c14, f3(c14, f5(f6(f7(c12)))))
% 0.20/0.44 = { by axiom 10 (p11_7) R->L }
% 0.20/0.44 fresh15(p11(f5(f10(f3(c14, f5(f6(f7(c12)))))), f3(c14, f5(f6(f7(c12))))), true2, f3(c14, f5(f6(f7(c12)))))
% 0.20/0.44 = { by axiom 14 (p11_15) R->L }
% 0.20/0.44 fresh15(fresh17(p11(f9(f5(f10(f3(c14, f5(f6(f7(c12)))))), f5(f6(f7(c12)))), c14), true2, f5(f10(f3(c14, f5(f6(f7(c12)))))), c14, f5(f6(f7(c12)))), true2, f3(c14, f5(f6(f7(c12)))))
% 0.20/0.44 = { by axiom 7 (p11_17) R->L }
% 0.20/0.44 fresh15(fresh17(fresh16(true2, true2, f9(f5(f10(f3(c14, f5(f6(f7(c12)))))), f5(f6(f7(c12)))), c14, f5(f8(f10(f3(c14, f5(f6(f7(c12))))), f6(f7(c12))))), true2, f5(f10(f3(c14, f5(f6(f7(c12)))))), c14, f5(f6(f7(c12)))), true2, f3(c14, f5(f6(f7(c12)))))
% 0.20/0.44 = { by axiom 1 (p2_2) R->L }
% 0.20/0.44 fresh15(fresh17(fresh16(p2(c14, c14), true2, f9(f5(f10(f3(c14, f5(f6(f7(c12)))))), f5(f6(f7(c12)))), c14, f5(f8(f10(f3(c14, f5(f6(f7(c12))))), f6(f7(c12))))), true2, f5(f10(f3(c14, f5(f6(f7(c12)))))), c14, f5(f6(f7(c12)))), true2, f3(c14, f5(f6(f7(c12)))))
% 0.20/0.44 = { by axiom 12 (p11_17) R->L }
% 0.20/0.44 fresh15(fresh17(fresh19(p11(f5(f8(f10(f3(c14, f5(f6(f7(c12))))), f6(f7(c12)))), c14), true2, f9(f5(f10(f3(c14, f5(f6(f7(c12)))))), f5(f6(f7(c12)))), c14, f5(f8(f10(f3(c14, f5(f6(f7(c12))))), f6(f7(c12)))), c14), true2, f5(f10(f3(c14, f5(f6(f7(c12)))))), c14, f5(f6(f7(c12)))), true2, f3(c14, f5(f6(f7(c12)))))
% 0.20/0.44 = { by axiom 2 (p11_3) }
% 0.20/0.45 fresh15(fresh17(fresh19(true2, true2, f9(f5(f10(f3(c14, f5(f6(f7(c12)))))), f5(f6(f7(c12)))), c14, f5(f8(f10(f3(c14, f5(f6(f7(c12))))), f6(f7(c12)))), c14), true2, f5(f10(f3(c14, f5(f6(f7(c12)))))), c14, f5(f6(f7(c12)))), true2, f3(c14, f5(f6(f7(c12)))))
% 0.20/0.45 = { by axiom 9 (p11_17) }
% 0.20/0.45 fresh15(fresh17(fresh20(p2(f5(f8(f10(f3(c14, f5(f6(f7(c12))))), f6(f7(c12)))), f9(f5(f10(f3(c14, f5(f6(f7(c12)))))), f5(f6(f7(c12))))), true2, f9(f5(f10(f3(c14, f5(f6(f7(c12)))))), f5(f6(f7(c12)))), c14), true2, f5(f10(f3(c14, f5(f6(f7(c12)))))), c14, f5(f6(f7(c12)))), true2, f3(c14, f5(f6(f7(c12)))))
% 0.20/0.45 = { by axiom 8 (p2_12) R->L }
% 0.20/0.45 fresh15(fresh17(fresh20(fresh14(true2, true2, f5(f8(f10(f3(c14, f5(f6(f7(c12))))), f6(f7(c12)))), f9(f5(f10(f3(c14, f5(f6(f7(c12)))))), f5(f6(f7(c12)))), f9(f5(f10(f3(c14, f5(f6(f7(c12)))))), f5(f6(f7(c12))))), true2, f9(f5(f10(f3(c14, f5(f6(f7(c12)))))), f5(f6(f7(c12)))), c14), true2, f5(f10(f3(c14, f5(f6(f7(c12)))))), c14, f5(f6(f7(c12)))), true2, f3(c14, f5(f6(f7(c12)))))
% 0.20/0.45 = { by axiom 1 (p2_2) R->L }
% 0.20/0.45 fresh15(fresh17(fresh20(fresh14(p2(f9(f5(f10(f3(c14, f5(f6(f7(c12)))))), f5(f6(f7(c12)))), f9(f5(f10(f3(c14, f5(f6(f7(c12)))))), f5(f6(f7(c12))))), true2, f5(f8(f10(f3(c14, f5(f6(f7(c12))))), f6(f7(c12)))), f9(f5(f10(f3(c14, f5(f6(f7(c12)))))), f5(f6(f7(c12)))), f9(f5(f10(f3(c14, f5(f6(f7(c12)))))), f5(f6(f7(c12))))), true2, f9(f5(f10(f3(c14, f5(f6(f7(c12)))))), f5(f6(f7(c12)))), c14), true2, f5(f10(f3(c14, f5(f6(f7(c12)))))), c14, f5(f6(f7(c12)))), true2, f3(c14, f5(f6(f7(c12)))))
% 0.20/0.45 = { by axiom 11 (p2_12) }
% 0.20/0.45 fresh15(fresh17(fresh20(fresh13(p2(f9(f5(f10(f3(c14, f5(f6(f7(c12)))))), f5(f6(f7(c12)))), f5(f8(f10(f3(c14, f5(f6(f7(c12))))), f6(f7(c12))))), true2, f5(f8(f10(f3(c14, f5(f6(f7(c12))))), f6(f7(c12)))), f9(f5(f10(f3(c14, f5(f6(f7(c12)))))), f5(f6(f7(c12))))), true2, f9(f5(f10(f3(c14, f5(f6(f7(c12)))))), f5(f6(f7(c12)))), c14), true2, f5(f10(f3(c14, f5(f6(f7(c12)))))), c14, f5(f6(f7(c12)))), true2, f3(c14, f5(f6(f7(c12)))))
% 0.20/0.45 = { by axiom 13 (p2_14) }
% 0.20/0.45 fresh15(fresh17(fresh20(fresh13(true2, true2, f5(f8(f10(f3(c14, f5(f6(f7(c12))))), f6(f7(c12)))), f9(f5(f10(f3(c14, f5(f6(f7(c12)))))), f5(f6(f7(c12))))), true2, f9(f5(f10(f3(c14, f5(f6(f7(c12)))))), f5(f6(f7(c12)))), c14), true2, f5(f10(f3(c14, f5(f6(f7(c12)))))), c14, f5(f6(f7(c12)))), true2, f3(c14, f5(f6(f7(c12)))))
% 0.20/0.45 = { by axiom 5 (p2_12) }
% 0.20/0.45 fresh15(fresh17(fresh20(true2, true2, f9(f5(f10(f3(c14, f5(f6(f7(c12)))))), f5(f6(f7(c12)))), c14), true2, f5(f10(f3(c14, f5(f6(f7(c12)))))), c14, f5(f6(f7(c12)))), true2, f3(c14, f5(f6(f7(c12)))))
% 0.20/0.45 = { by axiom 4 (p11_17) }
% 0.20/0.45 fresh15(fresh17(true2, true2, f5(f10(f3(c14, f5(f6(f7(c12)))))), c14, f5(f6(f7(c12)))), true2, f3(c14, f5(f6(f7(c12)))))
% 0.20/0.45 = { by axiom 6 (p11_15) }
% 0.20/0.45 fresh15(true2, true2, f3(c14, f5(f6(f7(c12)))))
% 0.20/0.45 = { by axiom 3 (p11_7) }
% 0.20/0.45 true2
% 0.20/0.45 % SZS output end Proof
% 0.20/0.45
% 0.20/0.45 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------