TSTP Solution File: SYN637-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYN637-1 : 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 : n023.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 03:35:32 EDT 2023
% Result : Unsatisfiable 0.17s 0.51s
% Output : Proof 0.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : SYN637-1 : TPTP v8.1.2. Released v2.5.0.
% 0.02/0.11 % 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 : n023.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 19:15:11 EDT 2023
% 0.11/0.32 % CPUTime :
% 0.17/0.51 Command-line arguments: --flatten
% 0.17/0.51
% 0.17/0.51 % SZS status Unsatisfiable
% 0.17/0.51
% 0.17/0.53 % SZS output start Proof
% 0.17/0.53 Take the following subset of the input axioms:
% 0.17/0.53 fof(not_p22_41, negated_conjecture, ~p22(f16(f17(c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c29))), f16(f17(c27, f5(c25, c26, c27))))).
% 0.17/0.53 fof(p20_7, negated_conjecture, p20(f12(c25), c28)).
% 0.17/0.53 fof(p22_28, negated_conjecture, ![X20, X21, X22, X23]: (p22(X20, X21) | (~p4(X22, X20) | (~p4(X23, X21) | ~p22(X22, X23))))).
% 0.17/0.53 fof(p22_40, negated_conjecture, p22(f16(f17(c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c27))), f16(f17(c27, f5(c25, c26, c27))))).
% 0.17/0.53 fof(p4_12, negated_conjecture, ![X39, X40]: (p4(f16(X39), f16(X40)) | ~p4(X39, X40))).
% 0.17/0.53 fof(p4_32, negated_conjecture, ![X41, X42, X43, X44]: (p4(f17(X41, X42), f17(X43, X44)) | (~p4(X41, X43) | ~p4(X42, X44)))).
% 0.17/0.53 fof(p4_39, negated_conjecture, ![X51]: p4(f5(f8(f11(c25), f9(f10(c25), c28)), X51, c27), f5(f8(f11(c25), f9(f10(c25), c28)), X51, c29))).
% 0.17/0.53 fof(p4_4, negated_conjecture, ![X36]: p4(X36, X36)).
% 0.17/0.53
% 0.17/0.53 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.17/0.53 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.17/0.53 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.17/0.53 fresh(y, y, x1...xn) = u
% 0.17/0.53 C => fresh(s, t, x1...xn) = v
% 0.17/0.53 where fresh is a fresh function symbol and x1..xn are the free
% 0.17/0.53 variables of u and v.
% 0.17/0.53 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.17/0.53 input problem has no model of domain size 1).
% 0.17/0.53
% 0.17/0.53 The encoding turns the above axioms into the following unit equations and goals:
% 0.17/0.53
% 0.17/0.53 Axiom 1 (p4_4): p4(X, X) = true.
% 0.17/0.53 Axiom 2 (p20_7): p20(f12(c25), c28) = true.
% 0.17/0.53 Axiom 3 (p22_28): fresh46(X, X, Y, Z) = true.
% 0.17/0.53 Axiom 4 (p4_12): fresh18(X, X, Y, Z) = true.
% 0.17/0.53 Axiom 5 (p22_28): fresh35(X, X, Y, Z, W) = p22(Y, Z).
% 0.17/0.53 Axiom 6 (p22_28): fresh45(X, X, Y, Z, W, V) = fresh46(p4(W, Y), true, Y, Z).
% 0.17/0.53 Axiom 7 (p4_12): fresh18(p4(X, Y), true, X, Y) = p4(f16(X), f16(Y)).
% 0.17/0.53 Axiom 8 (p4_32): fresh14(X, X, Y, Z, W, V) = true.
% 0.17/0.53 Axiom 9 (p4_32): fresh15(X, X, Y, Z, W, V) = p4(f17(Y, Z), f17(W, V)).
% 0.17/0.53 Axiom 10 (p22_28): fresh45(p22(X, Y), true, Z, W, X, Y) = fresh35(p4(Y, W), true, Z, W, X).
% 0.17/0.53 Axiom 11 (p4_32): fresh15(p4(X, Y), true, Z, X, W, Y) = fresh14(p4(Z, W), true, Z, X, W, Y).
% 0.17/0.53 Axiom 12 (p22_40): p22(f16(f17(c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c27))), f16(f17(c27, f5(c25, c26, c27)))) = true.
% 0.17/0.53 Axiom 13 (p4_39): p4(f5(f8(f11(c25), f9(f10(c25), c28)), X, c27), f5(f8(f11(c25), f9(f10(c25), c28)), X, c29)) = true.
% 0.17/0.53
% 0.17/0.53 Goal 1 (not_p22_41): p22(f16(f17(c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c29))), f16(f17(c27, f5(c25, c26, c27)))) = true.
% 0.17/0.53 Proof:
% 0.17/0.53 p22(f16(f17(c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c29))), f16(f17(c27, f5(c25, c26, c27))))
% 0.17/0.53 = { by axiom 5 (p22_28) R->L }
% 0.17/0.53 fresh35(p20(f12(c25), c28), p20(f12(c25), c28), f16(f17(c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c29))), f16(f17(c27, f5(c25, c26, c27))), f16(f17(c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c27))))
% 0.17/0.53 = { by axiom 2 (p20_7) }
% 0.17/0.53 fresh35(true, p20(f12(c25), c28), f16(f17(c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c29))), f16(f17(c27, f5(c25, c26, c27))), f16(f17(c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c27))))
% 0.17/0.53 = { by axiom 1 (p4_4) R->L }
% 0.17/0.53 fresh35(p4(f16(f17(c27, f5(c25, c26, c27))), f16(f17(c27, f5(c25, c26, c27)))), p20(f12(c25), c28), f16(f17(c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c29))), f16(f17(c27, f5(c25, c26, c27))), f16(f17(c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c27))))
% 0.17/0.53 = { by axiom 2 (p20_7) }
% 0.17/0.53 fresh35(p4(f16(f17(c27, f5(c25, c26, c27))), f16(f17(c27, f5(c25, c26, c27)))), true, f16(f17(c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c29))), f16(f17(c27, f5(c25, c26, c27))), f16(f17(c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c27))))
% 0.17/0.53 = { by axiom 10 (p22_28) R->L }
% 0.17/0.53 fresh45(p22(f16(f17(c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c27))), f16(f17(c27, f5(c25, c26, c27)))), true, f16(f17(c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c29))), f16(f17(c27, f5(c25, c26, c27))), f16(f17(c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c27))), f16(f17(c27, f5(c25, c26, c27))))
% 0.17/0.53 = { by axiom 2 (p20_7) R->L }
% 0.17/0.53 fresh45(p22(f16(f17(c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c27))), f16(f17(c27, f5(c25, c26, c27)))), p20(f12(c25), c28), f16(f17(c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c29))), f16(f17(c27, f5(c25, c26, c27))), f16(f17(c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c27))), f16(f17(c27, f5(c25, c26, c27))))
% 0.17/0.53 = { by axiom 12 (p22_40) }
% 0.17/0.53 fresh45(true, p20(f12(c25), c28), f16(f17(c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c29))), f16(f17(c27, f5(c25, c26, c27))), f16(f17(c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c27))), f16(f17(c27, f5(c25, c26, c27))))
% 0.17/0.53 = { by axiom 2 (p20_7) R->L }
% 0.17/0.53 fresh45(p20(f12(c25), c28), p20(f12(c25), c28), f16(f17(c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c29))), f16(f17(c27, f5(c25, c26, c27))), f16(f17(c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c27))), f16(f17(c27, f5(c25, c26, c27))))
% 0.17/0.54 = { by axiom 6 (p22_28) }
% 0.17/0.54 fresh46(p4(f16(f17(c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c27))), f16(f17(c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c29)))), true, f16(f17(c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c29))), f16(f17(c27, f5(c25, c26, c27))))
% 0.17/0.54 = { by axiom 2 (p20_7) R->L }
% 0.17/0.54 fresh46(p4(f16(f17(c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c27))), f16(f17(c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c29)))), p20(f12(c25), c28), f16(f17(c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c29))), f16(f17(c27, f5(c25, c26, c27))))
% 0.17/0.54 = { by axiom 7 (p4_12) R->L }
% 0.17/0.54 fresh46(fresh18(p4(f17(c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c27)), f17(c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c29))), true, f17(c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c27)), f17(c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c29))), p20(f12(c25), c28), f16(f17(c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c29))), f16(f17(c27, f5(c25, c26, c27))))
% 0.17/0.54 = { by axiom 2 (p20_7) R->L }
% 0.17/0.54 fresh46(fresh18(p4(f17(c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c27)), f17(c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c29))), p20(f12(c25), c28), f17(c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c27)), f17(c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c29))), p20(f12(c25), c28), f16(f17(c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c29))), f16(f17(c27, f5(c25, c26, c27))))
% 0.17/0.54 = { by axiom 9 (p4_32) R->L }
% 0.17/0.54 fresh46(fresh18(fresh15(p20(f12(c25), c28), p20(f12(c25), c28), c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c27), c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c29)), p20(f12(c25), c28), f17(c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c27)), f17(c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c29))), p20(f12(c25), c28), f16(f17(c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c29))), f16(f17(c27, f5(c25, c26, c27))))
% 0.17/0.54 = { by axiom 2 (p20_7) }
% 0.17/0.54 fresh46(fresh18(fresh15(true, p20(f12(c25), c28), c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c27), c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c29)), p20(f12(c25), c28), f17(c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c27)), f17(c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c29))), p20(f12(c25), c28), f16(f17(c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c29))), f16(f17(c27, f5(c25, c26, c27))))
% 0.17/0.54 = { by axiom 13 (p4_39) R->L }
% 0.17/0.54 fresh46(fresh18(fresh15(p4(f5(f8(f11(c25), f9(f10(c25), c28)), c26, c27), f5(f8(f11(c25), f9(f10(c25), c28)), c26, c29)), p20(f12(c25), c28), c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c27), c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c29)), p20(f12(c25), c28), f17(c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c27)), f17(c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c29))), p20(f12(c25), c28), f16(f17(c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c29))), f16(f17(c27, f5(c25, c26, c27))))
% 0.17/0.54 = { by axiom 2 (p20_7) }
% 0.17/0.54 fresh46(fresh18(fresh15(p4(f5(f8(f11(c25), f9(f10(c25), c28)), c26, c27), f5(f8(f11(c25), f9(f10(c25), c28)), c26, c29)), true, c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c27), c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c29)), p20(f12(c25), c28), f17(c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c27)), f17(c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c29))), p20(f12(c25), c28), f16(f17(c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c29))), f16(f17(c27, f5(c25, c26, c27))))
% 0.17/0.54 = { by axiom 11 (p4_32) }
% 0.17/0.54 fresh46(fresh18(fresh14(p4(c27, c27), true, c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c27), c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c29)), p20(f12(c25), c28), f17(c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c27)), f17(c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c29))), p20(f12(c25), c28), f16(f17(c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c29))), f16(f17(c27, f5(c25, c26, c27))))
% 0.17/0.54 = { by axiom 2 (p20_7) R->L }
% 0.17/0.54 fresh46(fresh18(fresh14(p4(c27, c27), p20(f12(c25), c28), c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c27), c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c29)), p20(f12(c25), c28), f17(c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c27)), f17(c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c29))), p20(f12(c25), c28), f16(f17(c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c29))), f16(f17(c27, f5(c25, c26, c27))))
% 0.17/0.54 = { by axiom 1 (p4_4) }
% 0.17/0.54 fresh46(fresh18(fresh14(true, p20(f12(c25), c28), c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c27), c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c29)), p20(f12(c25), c28), f17(c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c27)), f17(c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c29))), p20(f12(c25), c28), f16(f17(c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c29))), f16(f17(c27, f5(c25, c26, c27))))
% 0.17/0.54 = { by axiom 2 (p20_7) R->L }
% 0.17/0.54 fresh46(fresh18(fresh14(p20(f12(c25), c28), p20(f12(c25), c28), c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c27), c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c29)), p20(f12(c25), c28), f17(c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c27)), f17(c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c29))), p20(f12(c25), c28), f16(f17(c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c29))), f16(f17(c27, f5(c25, c26, c27))))
% 0.17/0.54 = { by axiom 8 (p4_32) }
% 0.17/0.54 fresh46(fresh18(true, p20(f12(c25), c28), f17(c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c27)), f17(c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c29))), p20(f12(c25), c28), f16(f17(c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c29))), f16(f17(c27, f5(c25, c26, c27))))
% 0.17/0.54 = { by axiom 2 (p20_7) R->L }
% 0.17/0.54 fresh46(fresh18(p20(f12(c25), c28), p20(f12(c25), c28), f17(c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c27)), f17(c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c29))), p20(f12(c25), c28), f16(f17(c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c29))), f16(f17(c27, f5(c25, c26, c27))))
% 0.17/0.54 = { by axiom 4 (p4_12) }
% 0.17/0.54 fresh46(true, p20(f12(c25), c28), f16(f17(c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c29))), f16(f17(c27, f5(c25, c26, c27))))
% 0.17/0.54 = { by axiom 2 (p20_7) R->L }
% 0.17/0.54 fresh46(p20(f12(c25), c28), p20(f12(c25), c28), f16(f17(c27, f5(f8(f11(c25), f9(f10(c25), c28)), c26, c29))), f16(f17(c27, f5(c25, c26, c27))))
% 0.17/0.54 = { by axiom 3 (p22_28) }
% 0.17/0.54 true
% 0.17/0.54 % SZS output end Proof
% 0.17/0.54
% 0.17/0.54 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------