TSTP Solution File: SYN631-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYN631-1 : 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 : n024.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 03:35:31 EDT 2023
% Result : Unsatisfiable 11.96s 1.97s
% Output : Proof 12.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN631-1 : 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
% 0.14/0.34 % Computer : n024.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sat Aug 26 18:06:39 EDT 2023
% 0.14/0.35 % CPUTime :
% 11.96/1.97 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 11.96/1.97
% 11.96/1.97 % SZS status Unsatisfiable
% 11.96/1.97
% 12.59/1.97 % SZS output start Proof
% 12.59/1.97 Take the following subset of the input axioms:
% 12.59/1.97 fof(not_p23_13, negated_conjecture, ~p23(f13(f16(c27), f14(c28)), f11(c24))).
% 12.59/1.97 fof(p10_1, negated_conjecture, ![X0]: p10(X0, X0)).
% 12.59/1.97 fof(p12_32, negated_conjecture, ![X8, X9, X10, X11]: (p12(f13(X8, X9), f13(X10, X11)) | (~p5(X8, X10) | ~p5(X9, X11)))).
% 12.59/1.97 fof(p23_12, negated_conjecture, p23(f13(c27, f14(c28)), f11(f15(c24)))).
% 12.59/1.97 fof(p23_29, negated_conjecture, ![X25, X26, X28, X27]: (p23(X25, X26) | (~p12(X28, X25) | (~p23(X28, X27) | ~p10(X27, X26))))).
% 12.59/1.97 fof(p23_35, negated_conjecture, ![X30, X29, X31]: (p23(f13(f19(X29, X30, X31), X31), f11(X29)) | ~p23(f13(X30, X31), f11(f15(X29))))).
% 12.59/1.97 fof(p5_11, negated_conjecture, ![X44, X45]: p5(f16(f18(X44, X45)), X45)).
% 12.59/1.97 fof(p5_18, negated_conjecture, ![X42, X43]: (p5(f16(X42), f16(X43)) | ~p5(X42, X43))).
% 12.59/1.97 fof(p5_25, negated_conjecture, ![X37, X38, X39]: (p5(X38, X39) | (~p5(X37, X38) | ~p5(X37, X39)))).
% 12.59/1.97 fof(p5_34, negated_conjecture, ![X30_2, X29_2, X31_2]: (p5(X30_2, f18(f20(c29), f19(X29_2, X30_2, X31_2))) | ~p23(f13(X30_2, X31_2), f11(f15(X29_2))))).
% 12.59/1.97 fof(p5_5, negated_conjecture, ![X37_2]: p5(X37_2, X37_2)).
% 12.59/1.97
% 12.59/1.97 Now clausify the problem and encode Horn clauses using encoding 3 of
% 12.59/1.97 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 12.59/1.97 We repeatedly replace C & s=t => u=v by the two clauses:
% 12.59/1.97 fresh(y, y, x1...xn) = u
% 12.59/1.97 C => fresh(s, t, x1...xn) = v
% 12.59/1.97 where fresh is a fresh function symbol and x1..xn are the free
% 12.59/1.97 variables of u and v.
% 12.59/1.97 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 12.59/1.97 input problem has no model of domain size 1).
% 12.59/1.97
% 12.59/1.97 The encoding turns the above axioms into the following unit equations and goals:
% 12.59/1.97
% 12.59/1.98 Axiom 1 (p5_5): p5(X, X) = true.
% 12.59/1.98 Axiom 2 (p10_1): p10(X, X) = true.
% 12.59/1.98 Axiom 3 (p5_11): p5(f16(f18(X, Y)), Y) = true.
% 12.59/1.98 Axiom 4 (p23_29): fresh46(X, X, Y, Z) = true.
% 12.59/1.98 Axiom 5 (p5_18): fresh17(X, X, Y, Z) = true.
% 12.59/1.98 Axiom 6 (p5_25): fresh13(X, X, Y, Z) = true.
% 12.59/1.98 Axiom 7 (p23_29): fresh25(X, X, Y, Z, W) = p23(Y, Z).
% 12.59/1.98 Axiom 8 (p23_35): fresh24(X, X, Y, Z, W) = true.
% 12.59/1.98 Axiom 9 (p5_18): fresh17(p5(X, Y), true, X, Y) = p5(f16(X), f16(Y)).
% 12.59/1.98 Axiom 10 (p5_25): fresh14(X, X, Y, Z, W) = p5(Y, Z).
% 12.59/1.98 Axiom 11 (p5_34): fresh10(X, X, Y, Z, W) = true.
% 12.59/1.98 Axiom 12 (p23_12): p23(f13(c27, f14(c28)), f11(f15(c24))) = true.
% 12.59/1.98 Axiom 13 (p23_29): fresh45(X, X, Y, Z, W, V) = fresh46(p10(V, Z), true, Y, Z).
% 12.59/1.98 Axiom 14 (p12_32): fresh31(X, X, Y, Z, W, V) = p12(f13(Y, Z), f13(W, V)).
% 12.59/1.98 Axiom 15 (p12_32): fresh30(X, X, Y, Z, W, V) = true.
% 12.59/1.98 Axiom 16 (p5_25): fresh14(p5(X, Y), true, Z, Y, X) = fresh13(p5(X, Z), true, Z, Y).
% 12.59/1.98 Axiom 17 (p23_29): fresh45(p23(X, Y), true, Z, W, X, Y) = fresh25(p12(X, Z), true, Z, W, Y).
% 12.59/1.98 Axiom 18 (p12_32): fresh31(p5(X, Y), true, Z, X, W, Y) = fresh30(p5(Z, W), true, Z, X, W, Y).
% 12.59/1.98 Axiom 19 (p23_35): fresh24(p23(f13(X, Y), f11(f15(Z))), true, Z, X, Y) = p23(f13(f19(Z, X, Y), Y), f11(Z)).
% 12.59/1.98 Axiom 20 (p5_34): fresh10(p23(f13(X, Y), f11(f15(Z))), true, X, Z, Y) = p5(X, f18(f20(c29), f19(Z, X, Y))).
% 12.59/1.98
% 12.59/1.98 Lemma 21: fresh13(p5(X, Y), true, Y, X) = p5(Y, X).
% 12.59/1.98 Proof:
% 12.59/1.98 fresh13(p5(X, Y), true, Y, X)
% 12.59/1.98 = { by axiom 16 (p5_25) R->L }
% 12.59/1.98 fresh14(p5(X, X), true, Y, X, X)
% 12.59/1.98 = { by axiom 1 (p5_5) }
% 12.59/1.98 fresh14(true, true, Y, X, X)
% 12.59/1.98 = { by axiom 10 (p5_25) }
% 12.59/1.98 p5(Y, X)
% 12.59/1.98
% 12.59/1.98 Goal 1 (not_p23_13): p23(f13(f16(c27), f14(c28)), f11(c24)) = true.
% 12.59/1.98 Proof:
% 12.59/1.98 p23(f13(f16(c27), f14(c28)), f11(c24))
% 12.59/1.98 = { by axiom 7 (p23_29) R->L }
% 12.59/1.98 fresh25(true, true, f13(f16(c27), f14(c28)), f11(c24), f11(c24))
% 12.59/1.98 = { by axiom 15 (p12_32) R->L }
% 12.59/1.98 fresh25(fresh30(true, true, f19(c24, c27, f14(c28)), f14(c28), f16(c27), f14(c28)), true, f13(f16(c27), f14(c28)), f11(c24), f11(c24))
% 12.59/1.98 = { by axiom 6 (p5_25) R->L }
% 12.59/1.98 fresh25(fresh30(fresh13(true, true, f19(c24, c27, f14(c28)), f16(c27)), true, f19(c24, c27, f14(c28)), f14(c28), f16(c27), f14(c28)), true, f13(f16(c27), f14(c28)), f11(c24), f11(c24))
% 12.59/1.98 = { by axiom 6 (p5_25) R->L }
% 12.59/1.98 fresh25(fresh30(fresh13(fresh13(true, true, f16(c27), f19(c24, c27, f14(c28))), true, f19(c24, c27, f14(c28)), f16(c27)), true, f19(c24, c27, f14(c28)), f14(c28), f16(c27), f14(c28)), true, f13(f16(c27), f14(c28)), f11(c24), f11(c24))
% 12.59/1.98 = { by axiom 5 (p5_18) R->L }
% 12.59/1.98 fresh25(fresh30(fresh13(fresh13(fresh17(true, true, f18(f20(c29), f19(c24, c27, f14(c28))), c27), true, f16(c27), f19(c24, c27, f14(c28))), true, f19(c24, c27, f14(c28)), f16(c27)), true, f19(c24, c27, f14(c28)), f14(c28), f16(c27), f14(c28)), true, f13(f16(c27), f14(c28)), f11(c24), f11(c24))
% 12.59/1.98 = { by axiom 6 (p5_25) R->L }
% 12.59/1.98 fresh25(fresh30(fresh13(fresh13(fresh17(fresh13(true, true, f18(f20(c29), f19(c24, c27, f14(c28))), c27), true, f18(f20(c29), f19(c24, c27, f14(c28))), c27), true, f16(c27), f19(c24, c27, f14(c28))), true, f19(c24, c27, f14(c28)), f16(c27)), true, f19(c24, c27, f14(c28)), f14(c28), f16(c27), f14(c28)), true, f13(f16(c27), f14(c28)), f11(c24), f11(c24))
% 12.59/1.98 = { by axiom 11 (p5_34) R->L }
% 12.59/1.98 fresh25(fresh30(fresh13(fresh13(fresh17(fresh13(fresh10(true, true, c27, c24, f14(c28)), true, f18(f20(c29), f19(c24, c27, f14(c28))), c27), true, f18(f20(c29), f19(c24, c27, f14(c28))), c27), true, f16(c27), f19(c24, c27, f14(c28))), true, f19(c24, c27, f14(c28)), f16(c27)), true, f19(c24, c27, f14(c28)), f14(c28), f16(c27), f14(c28)), true, f13(f16(c27), f14(c28)), f11(c24), f11(c24))
% 12.59/1.98 = { by axiom 12 (p23_12) R->L }
% 12.59/1.98 fresh25(fresh30(fresh13(fresh13(fresh17(fresh13(fresh10(p23(f13(c27, f14(c28)), f11(f15(c24))), true, c27, c24, f14(c28)), true, f18(f20(c29), f19(c24, c27, f14(c28))), c27), true, f18(f20(c29), f19(c24, c27, f14(c28))), c27), true, f16(c27), f19(c24, c27, f14(c28))), true, f19(c24, c27, f14(c28)), f16(c27)), true, f19(c24, c27, f14(c28)), f14(c28), f16(c27), f14(c28)), true, f13(f16(c27), f14(c28)), f11(c24), f11(c24))
% 12.59/1.98 = { by axiom 20 (p5_34) }
% 12.59/1.98 fresh25(fresh30(fresh13(fresh13(fresh17(fresh13(p5(c27, f18(f20(c29), f19(c24, c27, f14(c28)))), true, f18(f20(c29), f19(c24, c27, f14(c28))), c27), true, f18(f20(c29), f19(c24, c27, f14(c28))), c27), true, f16(c27), f19(c24, c27, f14(c28))), true, f19(c24, c27, f14(c28)), f16(c27)), true, f19(c24, c27, f14(c28)), f14(c28), f16(c27), f14(c28)), true, f13(f16(c27), f14(c28)), f11(c24), f11(c24))
% 12.59/1.98 = { by lemma 21 }
% 12.59/1.98 fresh25(fresh30(fresh13(fresh13(fresh17(p5(f18(f20(c29), f19(c24, c27, f14(c28))), c27), true, f18(f20(c29), f19(c24, c27, f14(c28))), c27), true, f16(c27), f19(c24, c27, f14(c28))), true, f19(c24, c27, f14(c28)), f16(c27)), true, f19(c24, c27, f14(c28)), f14(c28), f16(c27), f14(c28)), true, f13(f16(c27), f14(c28)), f11(c24), f11(c24))
% 12.59/1.98 = { by axiom 9 (p5_18) }
% 12.59/1.98 fresh25(fresh30(fresh13(fresh13(p5(f16(f18(f20(c29), f19(c24, c27, f14(c28)))), f16(c27)), true, f16(c27), f19(c24, c27, f14(c28))), true, f19(c24, c27, f14(c28)), f16(c27)), true, f19(c24, c27, f14(c28)), f14(c28), f16(c27), f14(c28)), true, f13(f16(c27), f14(c28)), f11(c24), f11(c24))
% 12.59/1.98 = { by axiom 16 (p5_25) R->L }
% 12.59/1.98 fresh25(fresh30(fresh13(fresh14(p5(f16(f18(f20(c29), f19(c24, c27, f14(c28)))), f19(c24, c27, f14(c28))), true, f16(c27), f19(c24, c27, f14(c28)), f16(f18(f20(c29), f19(c24, c27, f14(c28))))), true, f19(c24, c27, f14(c28)), f16(c27)), true, f19(c24, c27, f14(c28)), f14(c28), f16(c27), f14(c28)), true, f13(f16(c27), f14(c28)), f11(c24), f11(c24))
% 12.59/1.98 = { by axiom 3 (p5_11) }
% 12.59/1.98 fresh25(fresh30(fresh13(fresh14(true, true, f16(c27), f19(c24, c27, f14(c28)), f16(f18(f20(c29), f19(c24, c27, f14(c28))))), true, f19(c24, c27, f14(c28)), f16(c27)), true, f19(c24, c27, f14(c28)), f14(c28), f16(c27), f14(c28)), true, f13(f16(c27), f14(c28)), f11(c24), f11(c24))
% 12.59/1.98 = { by axiom 10 (p5_25) }
% 12.59/1.98 fresh25(fresh30(fresh13(p5(f16(c27), f19(c24, c27, f14(c28))), true, f19(c24, c27, f14(c28)), f16(c27)), true, f19(c24, c27, f14(c28)), f14(c28), f16(c27), f14(c28)), true, f13(f16(c27), f14(c28)), f11(c24), f11(c24))
% 12.59/1.98 = { by lemma 21 }
% 12.59/1.98 fresh25(fresh30(p5(f19(c24, c27, f14(c28)), f16(c27)), true, f19(c24, c27, f14(c28)), f14(c28), f16(c27), f14(c28)), true, f13(f16(c27), f14(c28)), f11(c24), f11(c24))
% 12.59/1.98 = { by axiom 18 (p12_32) R->L }
% 12.59/1.98 fresh25(fresh31(p5(f14(c28), f14(c28)), true, f19(c24, c27, f14(c28)), f14(c28), f16(c27), f14(c28)), true, f13(f16(c27), f14(c28)), f11(c24), f11(c24))
% 12.59/1.98 = { by axiom 1 (p5_5) }
% 12.59/1.98 fresh25(fresh31(true, true, f19(c24, c27, f14(c28)), f14(c28), f16(c27), f14(c28)), true, f13(f16(c27), f14(c28)), f11(c24), f11(c24))
% 12.59/1.98 = { by axiom 14 (p12_32) }
% 12.59/1.98 fresh25(p12(f13(f19(c24, c27, f14(c28)), f14(c28)), f13(f16(c27), f14(c28))), true, f13(f16(c27), f14(c28)), f11(c24), f11(c24))
% 12.59/1.98 = { by axiom 17 (p23_29) R->L }
% 12.59/1.98 fresh45(p23(f13(f19(c24, c27, f14(c28)), f14(c28)), f11(c24)), true, f13(f16(c27), f14(c28)), f11(c24), f13(f19(c24, c27, f14(c28)), f14(c28)), f11(c24))
% 12.59/1.98 = { by axiom 19 (p23_35) R->L }
% 12.59/1.99 fresh45(fresh24(p23(f13(c27, f14(c28)), f11(f15(c24))), true, c24, c27, f14(c28)), true, f13(f16(c27), f14(c28)), f11(c24), f13(f19(c24, c27, f14(c28)), f14(c28)), f11(c24))
% 12.59/1.99 = { by axiom 12 (p23_12) }
% 12.59/1.99 fresh45(fresh24(true, true, c24, c27, f14(c28)), true, f13(f16(c27), f14(c28)), f11(c24), f13(f19(c24, c27, f14(c28)), f14(c28)), f11(c24))
% 12.59/1.99 = { by axiom 8 (p23_35) }
% 12.59/1.99 fresh45(true, true, f13(f16(c27), f14(c28)), f11(c24), f13(f19(c24, c27, f14(c28)), f14(c28)), f11(c24))
% 12.59/1.99 = { by axiom 13 (p23_29) }
% 12.72/1.99 fresh46(p10(f11(c24), f11(c24)), true, f13(f16(c27), f14(c28)), f11(c24))
% 12.72/1.99 = { by axiom 2 (p10_1) }
% 12.72/1.99 fresh46(true, true, f13(f16(c27), f14(c28)), f11(c24))
% 12.72/1.99 = { by axiom 4 (p23_29) }
% 12.72/1.99 true
% 12.72/1.99 % SZS output end Proof
% 12.72/1.99
% 12.72/1.99 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------