TSTP Solution File: SYN613-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYN613-1 : 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 : n015.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 03:35:27 EDT 2023
% Result : Unsatisfiable 0.21s 0.49s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SYN613-1 : TPTP v8.1.2. Released v2.5.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35 % Computer : n015.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Aug 26 21:33:38 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.49 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 0.21/0.49
% 0.21/0.49 % SZS status Unsatisfiable
% 0.21/0.49
% 0.21/0.49 % SZS output start Proof
% 0.21/0.49 Take the following subset of the input axioms:
% 0.21/0.49 fof(not_p17_22, negated_conjecture, ~p17(c19, f4(f7(f10(c20), f8(f9(c21), c22))), c23)).
% 0.21/0.49 fof(p11_1, negated_conjecture, ![X0]: p11(X0, X0)).
% 0.21/0.49 fof(p11_15, negated_conjecture, ![X1, X2, X0_2]: (p11(X1, X2) | (~p11(X0_2, X1) | ~p11(X0_2, X2)))).
% 0.21/0.49 fof(p11_7, negated_conjecture, p11(c23, f12(f9(c21)))).
% 0.21/0.49 fof(p11_8, negated_conjecture, p11(c24, f12(f9(c21)))).
% 0.21/0.49 fof(p16_6, negated_conjecture, ![X14]: p16(X14, X14)).
% 0.21/0.49 fof(p17_21, negated_conjecture, p17(c19, f4(f7(f10(c20), f8(f9(c21), c22))), c24)).
% 0.21/0.49 fof(p17_29, negated_conjecture, ![X17, X18, X19, X22, X21, X20]: (p17(X17, X18, X19) | (~p3(X22, X18) | (~p16(X21, X17) | (~p11(X20, X19) | ~p17(X21, X22, X20)))))).
% 0.21/0.49 fof(p3_4, negated_conjecture, ![X36]: p3(X36, X36)).
% 0.21/0.49
% 0.21/0.49 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.49 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.49 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.49 fresh(y, y, x1...xn) = u
% 0.21/0.49 C => fresh(s, t, x1...xn) = v
% 0.21/0.49 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.49 variables of u and v.
% 0.21/0.49 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.49 input problem has no model of domain size 1).
% 0.21/0.49
% 0.21/0.49 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.49
% 0.21/0.49 Axiom 1 (p11_1): p11(X, X) = true.
% 0.21/0.49 Axiom 2 (p3_4): p3(X, X) = true.
% 0.21/0.49 Axiom 3 (p16_6): p16(X, X) = true.
% 0.21/0.49 Axiom 4 (p11_7): p11(c23, f12(f9(c21))) = true.
% 0.21/0.49 Axiom 5 (p11_8): p11(c24, f12(f9(c21))) = true.
% 0.21/0.49 Axiom 6 (p11_15): fresh24(X, X, Y, Z) = true.
% 0.21/0.49 Axiom 7 (p17_29): fresh34(X, X, Y, Z, W) = true.
% 0.21/0.49 Axiom 8 (p11_15): fresh25(X, X, Y, Z, W) = p11(Y, Z).
% 0.21/0.49 Axiom 9 (p17_29): fresh32(X, X, Y, Z, W, V) = p17(Y, Z, W).
% 0.21/0.49 Axiom 10 (p11_15): fresh25(p11(X, Y), true, Z, Y, X) = fresh24(p11(X, Z), true, Z, Y).
% 0.21/0.49 Axiom 11 (p17_29): fresh33(X, X, Y, Z, W, V, U) = fresh34(p11(U, W), true, Y, Z, W).
% 0.21/0.49 Axiom 12 (p17_21): p17(c19, f4(f7(f10(c20), f8(f9(c21), c22))), c24) = true.
% 0.21/0.49 Axiom 13 (p17_29): fresh31(X, X, Y, Z, W, V, U, T) = fresh32(p3(V, Z), true, Y, Z, W, T).
% 0.21/0.49 Axiom 14 (p17_29): fresh31(p17(X, Y, Z), true, W, V, U, Y, X, Z) = fresh33(p16(X, W), true, W, V, U, Y, Z).
% 0.21/0.49
% 0.21/0.49 Lemma 15: fresh24(p11(X, Y), true, Y, X) = p11(Y, X).
% 0.21/0.49 Proof:
% 0.21/0.49 fresh24(p11(X, Y), true, Y, X)
% 0.21/0.49 = { by axiom 10 (p11_15) R->L }
% 0.21/0.49 fresh25(p11(X, X), true, Y, X, X)
% 0.21/0.49 = { by axiom 1 (p11_1) }
% 0.21/0.49 fresh25(true, true, Y, X, X)
% 0.21/0.49 = { by axiom 8 (p11_15) }
% 0.21/0.50 p11(Y, X)
% 0.21/0.50
% 0.21/0.50 Goal 1 (not_p17_22): p17(c19, f4(f7(f10(c20), f8(f9(c21), c22))), c23) = true.
% 0.21/0.50 Proof:
% 0.21/0.50 p17(c19, f4(f7(f10(c20), f8(f9(c21), c22))), c23)
% 0.21/0.50 = { by axiom 9 (p17_29) R->L }
% 0.21/0.50 fresh32(true, true, c19, f4(f7(f10(c20), f8(f9(c21), c22))), c23, c24)
% 0.21/0.50 = { by axiom 2 (p3_4) R->L }
% 0.21/0.50 fresh32(p3(f4(f7(f10(c20), f8(f9(c21), c22))), f4(f7(f10(c20), f8(f9(c21), c22)))), true, c19, f4(f7(f10(c20), f8(f9(c21), c22))), c23, c24)
% 0.21/0.50 = { by axiom 13 (p17_29) R->L }
% 0.21/0.50 fresh31(true, true, c19, f4(f7(f10(c20), f8(f9(c21), c22))), c23, f4(f7(f10(c20), f8(f9(c21), c22))), c19, c24)
% 0.21/0.50 = { by axiom 12 (p17_21) R->L }
% 0.21/0.50 fresh31(p17(c19, f4(f7(f10(c20), f8(f9(c21), c22))), c24), true, c19, f4(f7(f10(c20), f8(f9(c21), c22))), c23, f4(f7(f10(c20), f8(f9(c21), c22))), c19, c24)
% 0.21/0.50 = { by axiom 14 (p17_29) }
% 0.21/0.50 fresh33(p16(c19, c19), true, c19, f4(f7(f10(c20), f8(f9(c21), c22))), c23, f4(f7(f10(c20), f8(f9(c21), c22))), c24)
% 0.21/0.50 = { by axiom 3 (p16_6) }
% 0.21/0.50 fresh33(true, true, c19, f4(f7(f10(c20), f8(f9(c21), c22))), c23, f4(f7(f10(c20), f8(f9(c21), c22))), c24)
% 0.21/0.50 = { by axiom 11 (p17_29) }
% 0.21/0.50 fresh34(p11(c24, c23), true, c19, f4(f7(f10(c20), f8(f9(c21), c22))), c23)
% 0.21/0.50 = { by axiom 8 (p11_15) R->L }
% 0.21/0.50 fresh34(fresh25(true, true, c24, c23, f12(f9(c21))), true, c19, f4(f7(f10(c20), f8(f9(c21), c22))), c23)
% 0.21/0.50 = { by axiom 6 (p11_15) R->L }
% 0.21/0.50 fresh34(fresh25(fresh24(true, true, f12(f9(c21)), c23), true, c24, c23, f12(f9(c21))), true, c19, f4(f7(f10(c20), f8(f9(c21), c22))), c23)
% 0.21/0.50 = { by axiom 4 (p11_7) R->L }
% 0.21/0.50 fresh34(fresh25(fresh24(p11(c23, f12(f9(c21))), true, f12(f9(c21)), c23), true, c24, c23, f12(f9(c21))), true, c19, f4(f7(f10(c20), f8(f9(c21), c22))), c23)
% 0.21/0.50 = { by lemma 15 }
% 0.21/0.50 fresh34(fresh25(p11(f12(f9(c21)), c23), true, c24, c23, f12(f9(c21))), true, c19, f4(f7(f10(c20), f8(f9(c21), c22))), c23)
% 0.21/0.50 = { by axiom 10 (p11_15) }
% 0.21/0.50 fresh34(fresh24(p11(f12(f9(c21)), c24), true, c24, c23), true, c19, f4(f7(f10(c20), f8(f9(c21), c22))), c23)
% 0.21/0.50 = { by lemma 15 R->L }
% 0.21/0.50 fresh34(fresh24(fresh24(p11(c24, f12(f9(c21))), true, f12(f9(c21)), c24), true, c24, c23), true, c19, f4(f7(f10(c20), f8(f9(c21), c22))), c23)
% 0.21/0.50 = { by axiom 5 (p11_8) }
% 0.21/0.50 fresh34(fresh24(fresh24(true, true, f12(f9(c21)), c24), true, c24, c23), true, c19, f4(f7(f10(c20), f8(f9(c21), c22))), c23)
% 0.21/0.50 = { by axiom 6 (p11_15) }
% 0.21/0.50 fresh34(fresh24(true, true, c24, c23), true, c19, f4(f7(f10(c20), f8(f9(c21), c22))), c23)
% 0.21/0.50 = { by axiom 6 (p11_15) }
% 0.21/0.50 fresh34(true, true, c19, f4(f7(f10(c20), f8(f9(c21), c22))), c23)
% 0.21/0.50 = { by axiom 7 (p17_29) }
% 0.21/0.50 true
% 0.21/0.50 % SZS output end Proof
% 0.21/0.50
% 0.21/0.50 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------