TSTP Solution File: SYO691-1.000 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYO691-1.000 : TPTP v8.1.2. Released v7.3.0.
% 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 : n028.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 04:58:54 EDT 2023
% Result : Unsatisfiable 0.21s 0.53s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO691-1.000 : TPTP v8.1.2. Released v7.3.0.
% 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 : n028.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 01:18:36 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.21/0.53 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.21/0.53
% 0.21/0.53 % SZS status Unsatisfiable
% 0.21/0.53
% 0.21/0.54 % SZS output start Proof
% 0.21/0.54 Take the following subset of the input axioms:
% 0.21/0.54 fof(prove, negated_conjecture, ![X]: ~seq(succ(succ(succ(zero))), X, X)).
% 0.21/0.54 fof(rewrite_left, axiom, ![Z, Y, X2]: (~step(X2, Y) | step(f(X2, Z), f(Y, Z)))).
% 0.21/0.54 fof(rewrite_sequence_succ, axiom, ![N, Z2, Y2, X2]: (~seq(N, X2, Y2) | (~step(Y2, Z2) | seq(succ(N), X2, Z2)))).
% 0.21/0.54 fof(rewrite_sequence_zero, axiom, ![X2]: seq(zero, X2, X2)).
% 0.21/0.54 fof(rewrite_top, axiom, ![Y2, X2]: (~top(X2, Y2) | step(X2, Y2))).
% 0.21/0.54 fof(rule_1, axiom, ![Z2, Y2, X2]: top(f(f(Z2, Y2), f(X2, a)), f(f(X2, f(Y2, a)), Z2))).
% 0.21/0.54
% 0.21/0.54 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.54 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.54 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.54 fresh(y, y, x1...xn) = u
% 0.21/0.54 C => fresh(s, t, x1...xn) = v
% 0.21/0.54 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.54 variables of u and v.
% 0.21/0.54 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.54 input problem has no model of domain size 1).
% 0.21/0.54
% 0.21/0.54 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.54
% 0.21/0.54 Axiom 1 (rewrite_sequence_zero): seq(zero, X, X) = true2.
% 0.21/0.54 Axiom 2 (rewrite_top): fresh(X, X, Y, Z) = true2.
% 0.21/0.54 Axiom 3 (rewrite_left): fresh4(X, X, Y, Z, W) = true2.
% 0.21/0.54 Axiom 4 (rewrite_sequence_succ): fresh2(X, X, Y, Z, W) = true2.
% 0.21/0.54 Axiom 5 (rewrite_top): fresh(top(X, Y), true2, X, Y) = step(X, Y).
% 0.21/0.54 Axiom 6 (rewrite_sequence_succ): fresh3(X, X, Y, Z, W, V) = seq(succ(Y), Z, V).
% 0.21/0.54 Axiom 7 (rewrite_left): fresh4(step(X, Y), true2, X, Y, Z) = step(f(X, Z), f(Y, Z)).
% 0.21/0.54 Axiom 8 (rewrite_sequence_succ): fresh3(step(X, Y), true2, Z, W, X, Y) = fresh2(seq(Z, W, X), true2, Z, W, Y).
% 0.21/0.54 Axiom 9 (rule_1): top(f(f(X, Y), f(Z, a)), f(f(Z, f(Y, a)), X)) = true2.
% 0.21/0.54
% 0.21/0.54 Lemma 10: step(f(f(X, Y), f(Z, a)), f(f(Z, f(Y, a)), X)) = true2.
% 0.21/0.54 Proof:
% 0.21/0.54 step(f(f(X, Y), f(Z, a)), f(f(Z, f(Y, a)), X))
% 0.21/0.54 = { by axiom 5 (rewrite_top) R->L }
% 0.21/0.54 fresh(top(f(f(X, Y), f(Z, a)), f(f(Z, f(Y, a)), X)), true2, f(f(X, Y), f(Z, a)), f(f(Z, f(Y, a)), X))
% 0.21/0.54 = { by axiom 9 (rule_1) }
% 0.21/0.54 fresh(true2, true2, f(f(X, Y), f(Z, a)), f(f(Z, f(Y, a)), X))
% 0.21/0.54 = { by axiom 2 (rewrite_top) }
% 0.21/0.54 true2
% 0.21/0.54
% 0.21/0.54 Goal 1 (prove): seq(succ(succ(succ(zero))), X, X) = true2.
% 0.21/0.54 The goal is true when:
% 0.21/0.54 X = f(f(f(f(f(a, a), f(a, a)), a), f(a, a)), f(f(f(a, a), f(a, a)), a))
% 0.21/0.54
% 0.21/0.54 Proof:
% 0.21/0.54 seq(succ(succ(succ(zero))), f(f(f(f(f(a, a), f(a, a)), a), f(a, a)), f(f(f(a, a), f(a, a)), a)), f(f(f(f(f(a, a), f(a, a)), a), f(a, a)), f(f(f(a, a), f(a, a)), a)))
% 0.21/0.54 = { by axiom 6 (rewrite_sequence_succ) R->L }
% 0.21/0.54 fresh3(true2, true2, succ(succ(zero)), f(f(f(f(f(a, a), f(a, a)), a), f(a, a)), f(f(f(a, a), f(a, a)), a)), f(f(f(f(a, a), f(f(a, a), a)), f(a, a)), f(f(f(a, a), f(a, a)), a)), f(f(f(f(f(a, a), f(a, a)), a), f(a, a)), f(f(f(a, a), f(a, a)), a)))
% 0.21/0.54 = { by axiom 3 (rewrite_left) R->L }
% 0.21/0.55 fresh3(fresh4(true2, true2, f(f(f(a, a), f(f(a, a), a)), f(a, a)), f(f(f(f(a, a), f(a, a)), a), f(a, a)), f(f(f(a, a), f(a, a)), a)), true2, succ(succ(zero)), f(f(f(f(f(a, a), f(a, a)), a), f(a, a)), f(f(f(a, a), f(a, a)), a)), f(f(f(f(a, a), f(f(a, a), a)), f(a, a)), f(f(f(a, a), f(a, a)), a)), f(f(f(f(f(a, a), f(a, a)), a), f(a, a)), f(f(f(a, a), f(a, a)), a)))
% 0.21/0.55 = { by axiom 3 (rewrite_left) R->L }
% 0.21/0.55 fresh3(fresh4(fresh4(true2, true2, f(f(a, a), f(f(a, a), a)), f(f(f(a, a), f(a, a)), a), f(a, a)), true2, f(f(f(a, a), f(f(a, a), a)), f(a, a)), f(f(f(f(a, a), f(a, a)), a), f(a, a)), f(f(f(a, a), f(a, a)), a)), true2, succ(succ(zero)), f(f(f(f(f(a, a), f(a, a)), a), f(a, a)), f(f(f(a, a), f(a, a)), a)), f(f(f(f(a, a), f(f(a, a), a)), f(a, a)), f(f(f(a, a), f(a, a)), a)), f(f(f(f(f(a, a), f(a, a)), a), f(a, a)), f(f(f(a, a), f(a, a)), a)))
% 0.21/0.55 = { by lemma 10 R->L }
% 0.21/0.55 fresh3(fresh4(fresh4(step(f(f(a, a), f(f(a, a), a)), f(f(f(a, a), f(a, a)), a)), true2, f(f(a, a), f(f(a, a), a)), f(f(f(a, a), f(a, a)), a), f(a, a)), true2, f(f(f(a, a), f(f(a, a), a)), f(a, a)), f(f(f(f(a, a), f(a, a)), a), f(a, a)), f(f(f(a, a), f(a, a)), a)), true2, succ(succ(zero)), f(f(f(f(f(a, a), f(a, a)), a), f(a, a)), f(f(f(a, a), f(a, a)), a)), f(f(f(f(a, a), f(f(a, a), a)), f(a, a)), f(f(f(a, a), f(a, a)), a)), f(f(f(f(f(a, a), f(a, a)), a), f(a, a)), f(f(f(a, a), f(a, a)), a)))
% 0.21/0.55 = { by axiom 7 (rewrite_left) }
% 0.21/0.55 fresh3(fresh4(step(f(f(f(a, a), f(f(a, a), a)), f(a, a)), f(f(f(f(a, a), f(a, a)), a), f(a, a))), true2, f(f(f(a, a), f(f(a, a), a)), f(a, a)), f(f(f(f(a, a), f(a, a)), a), f(a, a)), f(f(f(a, a), f(a, a)), a)), true2, succ(succ(zero)), f(f(f(f(f(a, a), f(a, a)), a), f(a, a)), f(f(f(a, a), f(a, a)), a)), f(f(f(f(a, a), f(f(a, a), a)), f(a, a)), f(f(f(a, a), f(a, a)), a)), f(f(f(f(f(a, a), f(a, a)), a), f(a, a)), f(f(f(a, a), f(a, a)), a)))
% 0.21/0.55 = { by axiom 7 (rewrite_left) }
% 0.21/0.55 fresh3(step(f(f(f(f(a, a), f(f(a, a), a)), f(a, a)), f(f(f(a, a), f(a, a)), a)), f(f(f(f(f(a, a), f(a, a)), a), f(a, a)), f(f(f(a, a), f(a, a)), a))), true2, succ(succ(zero)), f(f(f(f(f(a, a), f(a, a)), a), f(a, a)), f(f(f(a, a), f(a, a)), a)), f(f(f(f(a, a), f(f(a, a), a)), f(a, a)), f(f(f(a, a), f(a, a)), a)), f(f(f(f(f(a, a), f(a, a)), a), f(a, a)), f(f(f(a, a), f(a, a)), a)))
% 0.21/0.55 = { by axiom 8 (rewrite_sequence_succ) }
% 0.21/0.55 fresh2(seq(succ(succ(zero)), f(f(f(f(f(a, a), f(a, a)), a), f(a, a)), f(f(f(a, a), f(a, a)), a)), f(f(f(f(a, a), f(f(a, a), a)), f(a, a)), f(f(f(a, a), f(a, a)), a))), true2, succ(succ(zero)), f(f(f(f(f(a, a), f(a, a)), a), f(a, a)), f(f(f(a, a), f(a, a)), a)), f(f(f(f(f(a, a), f(a, a)), a), f(a, a)), f(f(f(a, a), f(a, a)), a)))
% 0.21/0.55 = { by axiom 6 (rewrite_sequence_succ) R->L }
% 0.21/0.55 fresh2(fresh3(true2, true2, succ(zero), f(f(f(f(f(a, a), f(a, a)), a), f(a, a)), f(f(f(a, a), f(a, a)), a)), f(f(f(f(a, a), f(a, a)), f(f(a, a), a)), f(f(f(a, a), f(a, a)), a)), f(f(f(f(a, a), f(f(a, a), a)), f(a, a)), f(f(f(a, a), f(a, a)), a))), true2, succ(succ(zero)), f(f(f(f(f(a, a), f(a, a)), a), f(a, a)), f(f(f(a, a), f(a, a)), a)), f(f(f(f(f(a, a), f(a, a)), a), f(a, a)), f(f(f(a, a), f(a, a)), a)))
% 0.21/0.55 = { by axiom 3 (rewrite_left) R->L }
% 0.21/0.55 fresh2(fresh3(fresh4(true2, true2, f(f(f(a, a), f(a, a)), f(f(a, a), a)), f(f(f(a, a), f(f(a, a), a)), f(a, a)), f(f(f(a, a), f(a, a)), a)), true2, succ(zero), f(f(f(f(f(a, a), f(a, a)), a), f(a, a)), f(f(f(a, a), f(a, a)), a)), f(f(f(f(a, a), f(a, a)), f(f(a, a), a)), f(f(f(a, a), f(a, a)), a)), f(f(f(f(a, a), f(f(a, a), a)), f(a, a)), f(f(f(a, a), f(a, a)), a))), true2, succ(succ(zero)), f(f(f(f(f(a, a), f(a, a)), a), f(a, a)), f(f(f(a, a), f(a, a)), a)), f(f(f(f(f(a, a), f(a, a)), a), f(a, a)), f(f(f(a, a), f(a, a)), a)))
% 0.21/0.55 = { by lemma 10 R->L }
% 0.21/0.55 fresh2(fresh3(fresh4(step(f(f(f(a, a), f(a, a)), f(f(a, a), a)), f(f(f(a, a), f(f(a, a), a)), f(a, a))), true2, f(f(f(a, a), f(a, a)), f(f(a, a), a)), f(f(f(a, a), f(f(a, a), a)), f(a, a)), f(f(f(a, a), f(a, a)), a)), true2, succ(zero), f(f(f(f(f(a, a), f(a, a)), a), f(a, a)), f(f(f(a, a), f(a, a)), a)), f(f(f(f(a, a), f(a, a)), f(f(a, a), a)), f(f(f(a, a), f(a, a)), a)), f(f(f(f(a, a), f(f(a, a), a)), f(a, a)), f(f(f(a, a), f(a, a)), a))), true2, succ(succ(zero)), f(f(f(f(f(a, a), f(a, a)), a), f(a, a)), f(f(f(a, a), f(a, a)), a)), f(f(f(f(f(a, a), f(a, a)), a), f(a, a)), f(f(f(a, a), f(a, a)), a)))
% 0.21/0.55 = { by axiom 7 (rewrite_left) }
% 0.21/0.55 fresh2(fresh3(step(f(f(f(f(a, a), f(a, a)), f(f(a, a), a)), f(f(f(a, a), f(a, a)), a)), f(f(f(f(a, a), f(f(a, a), a)), f(a, a)), f(f(f(a, a), f(a, a)), a))), true2, succ(zero), f(f(f(f(f(a, a), f(a, a)), a), f(a, a)), f(f(f(a, a), f(a, a)), a)), f(f(f(f(a, a), f(a, a)), f(f(a, a), a)), f(f(f(a, a), f(a, a)), a)), f(f(f(f(a, a), f(f(a, a), a)), f(a, a)), f(f(f(a, a), f(a, a)), a))), true2, succ(succ(zero)), f(f(f(f(f(a, a), f(a, a)), a), f(a, a)), f(f(f(a, a), f(a, a)), a)), f(f(f(f(f(a, a), f(a, a)), a), f(a, a)), f(f(f(a, a), f(a, a)), a)))
% 0.21/0.55 = { by axiom 8 (rewrite_sequence_succ) }
% 0.21/0.55 fresh2(fresh2(seq(succ(zero), f(f(f(f(f(a, a), f(a, a)), a), f(a, a)), f(f(f(a, a), f(a, a)), a)), f(f(f(f(a, a), f(a, a)), f(f(a, a), a)), f(f(f(a, a), f(a, a)), a))), true2, succ(zero), f(f(f(f(f(a, a), f(a, a)), a), f(a, a)), f(f(f(a, a), f(a, a)), a)), f(f(f(f(a, a), f(f(a, a), a)), f(a, a)), f(f(f(a, a), f(a, a)), a))), true2, succ(succ(zero)), f(f(f(f(f(a, a), f(a, a)), a), f(a, a)), f(f(f(a, a), f(a, a)), a)), f(f(f(f(f(a, a), f(a, a)), a), f(a, a)), f(f(f(a, a), f(a, a)), a)))
% 0.21/0.55 = { by axiom 6 (rewrite_sequence_succ) R->L }
% 0.21/0.55 fresh2(fresh2(fresh3(true2, true2, zero, f(f(f(f(f(a, a), f(a, a)), a), f(a, a)), f(f(f(a, a), f(a, a)), a)), f(f(f(f(f(a, a), f(a, a)), a), f(a, a)), f(f(f(a, a), f(a, a)), a)), f(f(f(f(a, a), f(a, a)), f(f(a, a), a)), f(f(f(a, a), f(a, a)), a))), true2, succ(zero), f(f(f(f(f(a, a), f(a, a)), a), f(a, a)), f(f(f(a, a), f(a, a)), a)), f(f(f(f(a, a), f(f(a, a), a)), f(a, a)), f(f(f(a, a), f(a, a)), a))), true2, succ(succ(zero)), f(f(f(f(f(a, a), f(a, a)), a), f(a, a)), f(f(f(a, a), f(a, a)), a)), f(f(f(f(f(a, a), f(a, a)), a), f(a, a)), f(f(f(a, a), f(a, a)), a)))
% 0.21/0.55 = { by lemma 10 R->L }
% 0.21/0.55 fresh2(fresh2(fresh3(step(f(f(f(f(f(a, a), f(a, a)), a), f(a, a)), f(f(f(a, a), f(a, a)), a)), f(f(f(f(a, a), f(a, a)), f(f(a, a), a)), f(f(f(a, a), f(a, a)), a))), true2, zero, f(f(f(f(f(a, a), f(a, a)), a), f(a, a)), f(f(f(a, a), f(a, a)), a)), f(f(f(f(f(a, a), f(a, a)), a), f(a, a)), f(f(f(a, a), f(a, a)), a)), f(f(f(f(a, a), f(a, a)), f(f(a, a), a)), f(f(f(a, a), f(a, a)), a))), true2, succ(zero), f(f(f(f(f(a, a), f(a, a)), a), f(a, a)), f(f(f(a, a), f(a, a)), a)), f(f(f(f(a, a), f(f(a, a), a)), f(a, a)), f(f(f(a, a), f(a, a)), a))), true2, succ(succ(zero)), f(f(f(f(f(a, a), f(a, a)), a), f(a, a)), f(f(f(a, a), f(a, a)), a)), f(f(f(f(f(a, a), f(a, a)), a), f(a, a)), f(f(f(a, a), f(a, a)), a)))
% 0.21/0.55 = { by axiom 8 (rewrite_sequence_succ) }
% 0.21/0.55 fresh2(fresh2(fresh2(seq(zero, f(f(f(f(f(a, a), f(a, a)), a), f(a, a)), f(f(f(a, a), f(a, a)), a)), f(f(f(f(f(a, a), f(a, a)), a), f(a, a)), f(f(f(a, a), f(a, a)), a))), true2, zero, f(f(f(f(f(a, a), f(a, a)), a), f(a, a)), f(f(f(a, a), f(a, a)), a)), f(f(f(f(a, a), f(a, a)), f(f(a, a), a)), f(f(f(a, a), f(a, a)), a))), true2, succ(zero), f(f(f(f(f(a, a), f(a, a)), a), f(a, a)), f(f(f(a, a), f(a, a)), a)), f(f(f(f(a, a), f(f(a, a), a)), f(a, a)), f(f(f(a, a), f(a, a)), a))), true2, succ(succ(zero)), f(f(f(f(f(a, a), f(a, a)), a), f(a, a)), f(f(f(a, a), f(a, a)), a)), f(f(f(f(f(a, a), f(a, a)), a), f(a, a)), f(f(f(a, a), f(a, a)), a)))
% 0.21/0.55 = { by axiom 1 (rewrite_sequence_zero) }
% 0.21/0.55 fresh2(fresh2(fresh2(true2, true2, zero, f(f(f(f(f(a, a), f(a, a)), a), f(a, a)), f(f(f(a, a), f(a, a)), a)), f(f(f(f(a, a), f(a, a)), f(f(a, a), a)), f(f(f(a, a), f(a, a)), a))), true2, succ(zero), f(f(f(f(f(a, a), f(a, a)), a), f(a, a)), f(f(f(a, a), f(a, a)), a)), f(f(f(f(a, a), f(f(a, a), a)), f(a, a)), f(f(f(a, a), f(a, a)), a))), true2, succ(succ(zero)), f(f(f(f(f(a, a), f(a, a)), a), f(a, a)), f(f(f(a, a), f(a, a)), a)), f(f(f(f(f(a, a), f(a, a)), a), f(a, a)), f(f(f(a, a), f(a, a)), a)))
% 0.21/0.55 = { by axiom 4 (rewrite_sequence_succ) }
% 0.21/0.55 fresh2(fresh2(true2, true2, succ(zero), f(f(f(f(f(a, a), f(a, a)), a), f(a, a)), f(f(f(a, a), f(a, a)), a)), f(f(f(f(a, a), f(f(a, a), a)), f(a, a)), f(f(f(a, a), f(a, a)), a))), true2, succ(succ(zero)), f(f(f(f(f(a, a), f(a, a)), a), f(a, a)), f(f(f(a, a), f(a, a)), a)), f(f(f(f(f(a, a), f(a, a)), a), f(a, a)), f(f(f(a, a), f(a, a)), a)))
% 0.21/0.55 = { by axiom 4 (rewrite_sequence_succ) }
% 0.21/0.55 fresh2(true2, true2, succ(succ(zero)), f(f(f(f(f(a, a), f(a, a)), a), f(a, a)), f(f(f(a, a), f(a, a)), a)), f(f(f(f(f(a, a), f(a, a)), a), f(a, a)), f(f(f(a, a), f(a, a)), a)))
% 0.21/0.55 = { by axiom 4 (rewrite_sequence_succ) }
% 0.21/0.55 true2
% 0.21/0.55 % SZS output end Proof
% 0.21/0.55
% 0.21/0.55 RESULT: Unsatisfiable (the axioms are contradictory).
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