TSTP Solution File: SYN312-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYN312-1 : TPTP v8.1.2. Bugfixed v2.0.0.
% 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 : n006.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 03:34:01 EDT 2023
% Result : Unsatisfiable 38.56s 5.38s
% Output : Proof 39.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SYN312-1 : TPTP v8.1.2. Bugfixed v2.0.0.
% 0.12/0.14 % 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 : n006.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 17:07:07 EDT 2023
% 0.14/0.35 % CPUTime :
% 38.56/5.38 Command-line arguments: --ground-connectedness --complete-subsets
% 38.56/5.38
% 38.56/5.38 % SZS status Unsatisfiable
% 38.56/5.38
% 39.08/5.40 % SZS output start Proof
% 39.08/5.40 Take the following subset of the input axioms:
% 39.08/5.40 fof(clause1, negated_conjecture, ![X, X3, X2, X1]: (p(X, X3, X2) | (~p(X, X1, X2) | ~p(X1, X3, X2)))).
% 39.08/5.40 fof(clause2, negated_conjecture, ![X4, X2_2, X1_2]: (p(X2_2, X1_2, X4) | ~p(X4, X1_2, X2_2))).
% 39.08/5.40 fof(clause3, negated_conjecture, ![X4, X2_2, X1_2]: (p(X1_2, X4, X2_2) | ~p(X4, X1_2, X2_2))).
% 39.08/5.40 fof(clause4, negated_conjecture, ![X4, X2_2, X1_2]: (p(X4, X1_2, f(X2_2)) | ~p(X4, X1_2, X2_2))).
% 39.08/5.40 fof(clause5, negated_conjecture, ![X4, X2_2, X1_2]: (p(g(X4), X1_2, X2_2) | ~p(X4, X1_2, X2_2))).
% 39.08/5.40 fof(clause6, negated_conjecture, p(a, f(b), c)).
% 39.08/5.40 fof(clause7, negated_conjecture, p(f(b), d, c)).
% 39.08/5.40 fof(clause8, negated_conjecture, ~p(f(g(a)), f(g(d)), f(g(c)))).
% 39.08/5.40
% 39.08/5.40 Now clausify the problem and encode Horn clauses using encoding 3 of
% 39.08/5.40 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 39.08/5.40 We repeatedly replace C & s=t => u=v by the two clauses:
% 39.08/5.40 fresh(y, y, x1...xn) = u
% 39.08/5.40 C => fresh(s, t, x1...xn) = v
% 39.08/5.40 where fresh is a fresh function symbol and x1..xn are the free
% 39.08/5.40 variables of u and v.
% 39.08/5.40 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 39.08/5.40 input problem has no model of domain size 1).
% 39.08/5.40
% 39.08/5.40 The encoding turns the above axioms into the following unit equations and goals:
% 39.08/5.40
% 39.08/5.40 Axiom 1 (clause6): p(a, f(b), c) = true.
% 39.08/5.40 Axiom 2 (clause7): p(f(b), d, c) = true.
% 39.08/5.40 Axiom 3 (clause5): fresh(X, X, Y, Z, W) = true.
% 39.08/5.40 Axiom 4 (clause1): fresh6(X, X, Y, Z, W) = true.
% 39.08/5.40 Axiom 5 (clause2): fresh4(X, X, Y, Z, W) = true.
% 39.08/5.40 Axiom 6 (clause3): fresh3(X, X, Y, Z, W) = true.
% 39.08/5.40 Axiom 7 (clause4): fresh2(X, X, Y, Z, W) = true.
% 39.08/5.40 Axiom 8 (clause1): fresh5(X, X, Y, Z, W, V) = p(Y, Z, W).
% 39.08/5.40 Axiom 9 (clause5): fresh(p(X, Y, Z), true, X, Y, Z) = p(g(X), Y, Z).
% 39.08/5.40 Axiom 10 (clause2): fresh4(p(X, Y, Z), true, Z, Y, X) = p(Z, Y, X).
% 39.08/5.40 Axiom 11 (clause3): fresh3(p(X, Y, Z), true, Y, X, Z) = p(Y, X, Z).
% 39.08/5.40 Axiom 12 (clause4): fresh2(p(X, Y, Z), true, X, Y, Z) = p(X, Y, f(Z)).
% 39.08/5.40 Axiom 13 (clause1): fresh5(p(X, Y, Z), true, W, Y, Z, X) = fresh6(p(W, X, Z), true, W, Y, Z).
% 39.08/5.40
% 39.08/5.40 Goal 1 (clause8): p(f(g(a)), f(g(d)), f(g(c))) = true.
% 39.08/5.40 Proof:
% 39.08/5.40 p(f(g(a)), f(g(d)), f(g(c)))
% 39.08/5.40 = { by axiom 12 (clause4) R->L }
% 39.08/5.40 fresh2(p(f(g(a)), f(g(d)), g(c)), true, f(g(a)), f(g(d)), g(c))
% 39.08/5.40 = { by axiom 11 (clause3) R->L }
% 39.08/5.40 fresh2(fresh3(p(f(g(d)), f(g(a)), g(c)), true, f(g(a)), f(g(d)), g(c)), true, f(g(a)), f(g(d)), g(c))
% 39.08/5.40 = { by axiom 10 (clause2) R->L }
% 39.08/5.40 fresh2(fresh3(fresh4(p(g(c), f(g(a)), f(g(d))), true, f(g(d)), f(g(a)), g(c)), true, f(g(a)), f(g(d)), g(c)), true, f(g(a)), f(g(d)), g(c))
% 39.08/5.40 = { by axiom 12 (clause4) R->L }
% 39.08/5.40 fresh2(fresh3(fresh4(fresh2(p(g(c), f(g(a)), g(d)), true, g(c), f(g(a)), g(d)), true, f(g(d)), f(g(a)), g(c)), true, f(g(a)), f(g(d)), g(c)), true, f(g(a)), f(g(d)), g(c))
% 39.08/5.40 = { by axiom 9 (clause5) R->L }
% 39.08/5.40 fresh2(fresh3(fresh4(fresh2(fresh(p(c, f(g(a)), g(d)), true, c, f(g(a)), g(d)), true, g(c), f(g(a)), g(d)), true, f(g(d)), f(g(a)), g(c)), true, f(g(a)), f(g(d)), g(c)), true, f(g(a)), f(g(d)), g(c))
% 39.08/5.40 = { by axiom 10 (clause2) R->L }
% 39.08/5.40 fresh2(fresh3(fresh4(fresh2(fresh(fresh4(p(g(d), f(g(a)), c), true, c, f(g(a)), g(d)), true, c, f(g(a)), g(d)), true, g(c), f(g(a)), g(d)), true, f(g(d)), f(g(a)), g(c)), true, f(g(a)), f(g(d)), g(c)), true, f(g(a)), f(g(d)), g(c))
% 39.08/5.40 = { by axiom 9 (clause5) R->L }
% 39.08/5.40 fresh2(fresh3(fresh4(fresh2(fresh(fresh4(fresh(p(d, f(g(a)), c), true, d, f(g(a)), c), true, c, f(g(a)), g(d)), true, c, f(g(a)), g(d)), true, g(c), f(g(a)), g(d)), true, f(g(d)), f(g(a)), g(c)), true, f(g(a)), f(g(d)), g(c)), true, f(g(a)), f(g(d)), g(c))
% 39.08/5.40 = { by axiom 11 (clause3) R->L }
% 39.08/5.40 fresh2(fresh3(fresh4(fresh2(fresh(fresh4(fresh(fresh3(p(f(g(a)), d, c), true, d, f(g(a)), c), true, d, f(g(a)), c), true, c, f(g(a)), g(d)), true, c, f(g(a)), g(d)), true, g(c), f(g(a)), g(d)), true, f(g(d)), f(g(a)), g(c)), true, f(g(a)), f(g(d)), g(c)), true, f(g(a)), f(g(d)), g(c))
% 39.08/5.40 = { by axiom 8 (clause1) R->L }
% 39.08/5.40 fresh2(fresh3(fresh4(fresh2(fresh(fresh4(fresh(fresh3(fresh5(true, true, f(g(a)), d, c, f(b)), true, d, f(g(a)), c), true, d, f(g(a)), c), true, c, f(g(a)), g(d)), true, c, f(g(a)), g(d)), true, g(c), f(g(a)), g(d)), true, f(g(d)), f(g(a)), g(c)), true, f(g(a)), f(g(d)), g(c)), true, f(g(a)), f(g(d)), g(c))
% 39.08/5.40 = { by axiom 2 (clause7) R->L }
% 39.08/5.40 fresh2(fresh3(fresh4(fresh2(fresh(fresh4(fresh(fresh3(fresh5(p(f(b), d, c), true, f(g(a)), d, c, f(b)), true, d, f(g(a)), c), true, d, f(g(a)), c), true, c, f(g(a)), g(d)), true, c, f(g(a)), g(d)), true, g(c), f(g(a)), g(d)), true, f(g(d)), f(g(a)), g(c)), true, f(g(a)), f(g(d)), g(c)), true, f(g(a)), f(g(d)), g(c))
% 39.08/5.41 = { by axiom 13 (clause1) }
% 39.08/5.41 fresh2(fresh3(fresh4(fresh2(fresh(fresh4(fresh(fresh3(fresh6(p(f(g(a)), f(b), c), true, f(g(a)), d, c), true, d, f(g(a)), c), true, d, f(g(a)), c), true, c, f(g(a)), g(d)), true, c, f(g(a)), g(d)), true, g(c), f(g(a)), g(d)), true, f(g(d)), f(g(a)), g(c)), true, f(g(a)), f(g(d)), g(c)), true, f(g(a)), f(g(d)), g(c))
% 39.08/5.41 = { by axiom 10 (clause2) R->L }
% 39.08/5.41 fresh2(fresh3(fresh4(fresh2(fresh(fresh4(fresh(fresh3(fresh6(fresh4(p(c, f(b), f(g(a))), true, f(g(a)), f(b), c), true, f(g(a)), d, c), true, d, f(g(a)), c), true, d, f(g(a)), c), true, c, f(g(a)), g(d)), true, c, f(g(a)), g(d)), true, g(c), f(g(a)), g(d)), true, f(g(d)), f(g(a)), g(c)), true, f(g(a)), f(g(d)), g(c)), true, f(g(a)), f(g(d)), g(c))
% 39.08/5.41 = { by axiom 12 (clause4) R->L }
% 39.08/5.41 fresh2(fresh3(fresh4(fresh2(fresh(fresh4(fresh(fresh3(fresh6(fresh4(fresh2(p(c, f(b), g(a)), true, c, f(b), g(a)), true, f(g(a)), f(b), c), true, f(g(a)), d, c), true, d, f(g(a)), c), true, d, f(g(a)), c), true, c, f(g(a)), g(d)), true, c, f(g(a)), g(d)), true, g(c), f(g(a)), g(d)), true, f(g(d)), f(g(a)), g(c)), true, f(g(a)), f(g(d)), g(c)), true, f(g(a)), f(g(d)), g(c))
% 39.08/5.41 = { by axiom 10 (clause2) R->L }
% 39.08/5.41 fresh2(fresh3(fresh4(fresh2(fresh(fresh4(fresh(fresh3(fresh6(fresh4(fresh2(fresh4(p(g(a), f(b), c), true, c, f(b), g(a)), true, c, f(b), g(a)), true, f(g(a)), f(b), c), true, f(g(a)), d, c), true, d, f(g(a)), c), true, d, f(g(a)), c), true, c, f(g(a)), g(d)), true, c, f(g(a)), g(d)), true, g(c), f(g(a)), g(d)), true, f(g(d)), f(g(a)), g(c)), true, f(g(a)), f(g(d)), g(c)), true, f(g(a)), f(g(d)), g(c))
% 39.08/5.41 = { by axiom 9 (clause5) R->L }
% 39.08/5.41 fresh2(fresh3(fresh4(fresh2(fresh(fresh4(fresh(fresh3(fresh6(fresh4(fresh2(fresh4(fresh(p(a, f(b), c), true, a, f(b), c), true, c, f(b), g(a)), true, c, f(b), g(a)), true, f(g(a)), f(b), c), true, f(g(a)), d, c), true, d, f(g(a)), c), true, d, f(g(a)), c), true, c, f(g(a)), g(d)), true, c, f(g(a)), g(d)), true, g(c), f(g(a)), g(d)), true, f(g(d)), f(g(a)), g(c)), true, f(g(a)), f(g(d)), g(c)), true, f(g(a)), f(g(d)), g(c))
% 39.08/5.41 = { by axiom 1 (clause6) }
% 39.08/5.41 fresh2(fresh3(fresh4(fresh2(fresh(fresh4(fresh(fresh3(fresh6(fresh4(fresh2(fresh4(fresh(true, true, a, f(b), c), true, c, f(b), g(a)), true, c, f(b), g(a)), true, f(g(a)), f(b), c), true, f(g(a)), d, c), true, d, f(g(a)), c), true, d, f(g(a)), c), true, c, f(g(a)), g(d)), true, c, f(g(a)), g(d)), true, g(c), f(g(a)), g(d)), true, f(g(d)), f(g(a)), g(c)), true, f(g(a)), f(g(d)), g(c)), true, f(g(a)), f(g(d)), g(c))
% 39.08/5.41 = { by axiom 3 (clause5) }
% 39.08/5.41 fresh2(fresh3(fresh4(fresh2(fresh(fresh4(fresh(fresh3(fresh6(fresh4(fresh2(fresh4(true, true, c, f(b), g(a)), true, c, f(b), g(a)), true, f(g(a)), f(b), c), true, f(g(a)), d, c), true, d, f(g(a)), c), true, d, f(g(a)), c), true, c, f(g(a)), g(d)), true, c, f(g(a)), g(d)), true, g(c), f(g(a)), g(d)), true, f(g(d)), f(g(a)), g(c)), true, f(g(a)), f(g(d)), g(c)), true, f(g(a)), f(g(d)), g(c))
% 39.08/5.41 = { by axiom 5 (clause2) }
% 39.08/5.41 fresh2(fresh3(fresh4(fresh2(fresh(fresh4(fresh(fresh3(fresh6(fresh4(fresh2(true, true, c, f(b), g(a)), true, f(g(a)), f(b), c), true, f(g(a)), d, c), true, d, f(g(a)), c), true, d, f(g(a)), c), true, c, f(g(a)), g(d)), true, c, f(g(a)), g(d)), true, g(c), f(g(a)), g(d)), true, f(g(d)), f(g(a)), g(c)), true, f(g(a)), f(g(d)), g(c)), true, f(g(a)), f(g(d)), g(c))
% 39.08/5.41 = { by axiom 7 (clause4) }
% 39.08/5.41 fresh2(fresh3(fresh4(fresh2(fresh(fresh4(fresh(fresh3(fresh6(fresh4(true, true, f(g(a)), f(b), c), true, f(g(a)), d, c), true, d, f(g(a)), c), true, d, f(g(a)), c), true, c, f(g(a)), g(d)), true, c, f(g(a)), g(d)), true, g(c), f(g(a)), g(d)), true, f(g(d)), f(g(a)), g(c)), true, f(g(a)), f(g(d)), g(c)), true, f(g(a)), f(g(d)), g(c))
% 39.08/5.41 = { by axiom 5 (clause2) }
% 39.08/5.41 fresh2(fresh3(fresh4(fresh2(fresh(fresh4(fresh(fresh3(fresh6(true, true, f(g(a)), d, c), true, d, f(g(a)), c), true, d, f(g(a)), c), true, c, f(g(a)), g(d)), true, c, f(g(a)), g(d)), true, g(c), f(g(a)), g(d)), true, f(g(d)), f(g(a)), g(c)), true, f(g(a)), f(g(d)), g(c)), true, f(g(a)), f(g(d)), g(c))
% 39.08/5.41 = { by axiom 4 (clause1) }
% 39.08/5.41 fresh2(fresh3(fresh4(fresh2(fresh(fresh4(fresh(fresh3(true, true, d, f(g(a)), c), true, d, f(g(a)), c), true, c, f(g(a)), g(d)), true, c, f(g(a)), g(d)), true, g(c), f(g(a)), g(d)), true, f(g(d)), f(g(a)), g(c)), true, f(g(a)), f(g(d)), g(c)), true, f(g(a)), f(g(d)), g(c))
% 39.08/5.41 = { by axiom 6 (clause3) }
% 39.08/5.41 fresh2(fresh3(fresh4(fresh2(fresh(fresh4(fresh(true, true, d, f(g(a)), c), true, c, f(g(a)), g(d)), true, c, f(g(a)), g(d)), true, g(c), f(g(a)), g(d)), true, f(g(d)), f(g(a)), g(c)), true, f(g(a)), f(g(d)), g(c)), true, f(g(a)), f(g(d)), g(c))
% 39.08/5.41 = { by axiom 3 (clause5) }
% 39.08/5.41 fresh2(fresh3(fresh4(fresh2(fresh(fresh4(true, true, c, f(g(a)), g(d)), true, c, f(g(a)), g(d)), true, g(c), f(g(a)), g(d)), true, f(g(d)), f(g(a)), g(c)), true, f(g(a)), f(g(d)), g(c)), true, f(g(a)), f(g(d)), g(c))
% 39.08/5.41 = { by axiom 5 (clause2) }
% 39.08/5.41 fresh2(fresh3(fresh4(fresh2(fresh(true, true, c, f(g(a)), g(d)), true, g(c), f(g(a)), g(d)), true, f(g(d)), f(g(a)), g(c)), true, f(g(a)), f(g(d)), g(c)), true, f(g(a)), f(g(d)), g(c))
% 39.08/5.41 = { by axiom 3 (clause5) }
% 39.08/5.41 fresh2(fresh3(fresh4(fresh2(true, true, g(c), f(g(a)), g(d)), true, f(g(d)), f(g(a)), g(c)), true, f(g(a)), f(g(d)), g(c)), true, f(g(a)), f(g(d)), g(c))
% 39.08/5.41 = { by axiom 7 (clause4) }
% 39.08/5.41 fresh2(fresh3(fresh4(true, true, f(g(d)), f(g(a)), g(c)), true, f(g(a)), f(g(d)), g(c)), true, f(g(a)), f(g(d)), g(c))
% 39.08/5.41 = { by axiom 5 (clause2) }
% 39.08/5.41 fresh2(fresh3(true, true, f(g(a)), f(g(d)), g(c)), true, f(g(a)), f(g(d)), g(c))
% 39.08/5.41 = { by axiom 6 (clause3) }
% 39.08/5.41 fresh2(true, true, f(g(a)), f(g(d)), g(c))
% 39.08/5.41 = { by axiom 7 (clause4) }
% 39.08/5.41 true
% 39.08/5.41 % SZS output end Proof
% 39.08/5.41
% 39.08/5.41 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------