TSTP Solution File: SYN310-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYN310-1 : TPTP v8.1.2. Released v1.2.0.
% 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 : n027.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 0.22s 0.41s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SYN310-1 : TPTP v8.1.2. Released v1.2.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.19/0.36 % Computer : n027.cluster.edu
% 0.19/0.36 % Model : x86_64 x86_64
% 0.19/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.36 % Memory : 8042.1875MB
% 0.19/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.19/0.36 % CPULimit : 300
% 0.19/0.36 % WCLimit : 300
% 0.19/0.36 % DateTime : Sat Aug 26 20:50:20 EDT 2023
% 0.19/0.36 % CPUTime :
% 0.22/0.41 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.22/0.41
% 0.22/0.41 % SZS status Unsatisfiable
% 0.22/0.41
% 0.22/0.43 % SZS output start Proof
% 0.22/0.43 Take the following subset of the input axioms:
% 0.22/0.43 fof(clause1, negated_conjecture, ![X2, X1, X]: (~p(X2, X1, X) | p(X, X1, X2))).
% 0.22/0.43 fof(clause2, negated_conjecture, ![X2_2, X1_2, X3]: (~p(X1_2, X3, X2_2) | p(X3, X1_2, X2_2))).
% 0.22/0.43 fof(clause3, negated_conjecture, ![X2_2, X1_2, X3]: (~p(X3, X1_2, g(X2_2)) | p(X3, X1_2, X2_2))).
% 0.22/0.43 fof(clause4, negated_conjecture, ![X2_2, X1_2, X3]: (~p(f(X3), X1_2, X2_2) | p(X3, X1_2, X2_2))).
% 0.22/0.43 fof(clause5, negated_conjecture, ~p(a, b, c)).
% 0.22/0.43 fof(clause6, negated_conjecture, p(f(g(a)), f(g(b)), f(g(c)))).
% 0.22/0.43
% 0.22/0.43 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.22/0.43 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.22/0.43 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.22/0.43 fresh(y, y, x1...xn) = u
% 0.22/0.43 C => fresh(s, t, x1...xn) = v
% 0.22/0.43 where fresh is a fresh function symbol and x1..xn are the free
% 0.22/0.43 variables of u and v.
% 0.22/0.43 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.22/0.43 input problem has no model of domain size 1).
% 0.22/0.43
% 0.22/0.43 The encoding turns the above axioms into the following unit equations and goals:
% 0.22/0.43
% 0.22/0.43 Axiom 1 (clause4): fresh(X, X, Y, Z, W) = true.
% 0.22/0.43 Axiom 2 (clause2): fresh4(X, X, Y, Z, W) = true.
% 0.22/0.43 Axiom 3 (clause1): fresh3(X, X, Y, Z, W) = true.
% 0.22/0.43 Axiom 4 (clause3): fresh2(X, X, Y, Z, W) = true.
% 0.22/0.43 Axiom 5 (clause2): fresh4(p(X, Y, Z), true, X, Y, Z) = p(Y, X, Z).
% 0.22/0.43 Axiom 6 (clause1): fresh3(p(X, Y, Z), true, X, Y, Z) = p(Z, Y, X).
% 0.22/0.43 Axiom 7 (clause6): p(f(g(a)), f(g(b)), f(g(c))) = true.
% 0.22/0.43 Axiom 8 (clause4): fresh(p(f(X), Y, Z), true, X, Y, Z) = p(X, Y, Z).
% 0.22/0.43 Axiom 9 (clause3): fresh2(p(X, Y, g(Z)), true, X, Y, Z) = p(X, Y, Z).
% 0.22/0.43
% 0.22/0.43 Goal 1 (clause5): p(a, b, c) = true.
% 0.22/0.43 Proof:
% 0.22/0.43 p(a, b, c)
% 0.22/0.43 = { by axiom 6 (clause1) R->L }
% 0.22/0.43 fresh3(p(c, b, a), true, c, b, a)
% 0.22/0.43 = { by axiom 9 (clause3) R->L }
% 0.22/0.43 fresh3(fresh2(p(c, b, g(a)), true, c, b, a), true, c, b, a)
% 0.22/0.43 = { by axiom 6 (clause1) R->L }
% 0.22/0.43 fresh3(fresh2(fresh3(p(g(a), b, c), true, g(a), b, c), true, c, b, a), true, c, b, a)
% 0.22/0.43 = { by axiom 5 (clause2) R->L }
% 0.22/0.43 fresh3(fresh2(fresh3(fresh4(p(b, g(a), c), true, b, g(a), c), true, g(a), b, c), true, c, b, a), true, c, b, a)
% 0.22/0.43 = { by axiom 9 (clause3) R->L }
% 0.22/0.43 fresh3(fresh2(fresh3(fresh4(fresh2(p(b, g(a), g(c)), true, b, g(a), c), true, b, g(a), c), true, g(a), b, c), true, c, b, a), true, c, b, a)
% 0.22/0.43 = { by axiom 6 (clause1) R->L }
% 0.22/0.43 fresh3(fresh2(fresh3(fresh4(fresh2(fresh3(p(g(c), g(a), b), true, g(c), g(a), b), true, b, g(a), c), true, b, g(a), c), true, g(a), b, c), true, c, b, a), true, c, b, a)
% 0.22/0.43 = { by axiom 9 (clause3) R->L }
% 0.22/0.43 fresh3(fresh2(fresh3(fresh4(fresh2(fresh3(fresh2(p(g(c), g(a), g(b)), true, g(c), g(a), b), true, g(c), g(a), b), true, b, g(a), c), true, b, g(a), c), true, g(a), b, c), true, c, b, a), true, c, b, a)
% 0.22/0.43 = { by axiom 8 (clause4) R->L }
% 0.22/0.43 fresh3(fresh2(fresh3(fresh4(fresh2(fresh3(fresh2(fresh(p(f(g(c)), g(a), g(b)), true, g(c), g(a), g(b)), true, g(c), g(a), b), true, g(c), g(a), b), true, b, g(a), c), true, b, g(a), c), true, g(a), b, c), true, c, b, a), true, c, b, a)
% 0.22/0.43 = { by axiom 6 (clause1) R->L }
% 0.22/0.44 fresh3(fresh2(fresh3(fresh4(fresh2(fresh3(fresh2(fresh(fresh3(p(g(b), g(a), f(g(c))), true, g(b), g(a), f(g(c))), true, g(c), g(a), g(b)), true, g(c), g(a), b), true, g(c), g(a), b), true, b, g(a), c), true, b, g(a), c), true, g(a), b, c), true, c, b, a), true, c, b, a)
% 0.22/0.44 = { by axiom 8 (clause4) R->L }
% 0.22/0.44 fresh3(fresh2(fresh3(fresh4(fresh2(fresh3(fresh2(fresh(fresh3(fresh(p(f(g(b)), g(a), f(g(c))), true, g(b), g(a), f(g(c))), true, g(b), g(a), f(g(c))), true, g(c), g(a), g(b)), true, g(c), g(a), b), true, g(c), g(a), b), true, b, g(a), c), true, b, g(a), c), true, g(a), b, c), true, c, b, a), true, c, b, a)
% 0.22/0.44 = { by axiom 5 (clause2) R->L }
% 0.22/0.44 fresh3(fresh2(fresh3(fresh4(fresh2(fresh3(fresh2(fresh(fresh3(fresh(fresh4(p(g(a), f(g(b)), f(g(c))), true, g(a), f(g(b)), f(g(c))), true, g(b), g(a), f(g(c))), true, g(b), g(a), f(g(c))), true, g(c), g(a), g(b)), true, g(c), g(a), b), true, g(c), g(a), b), true, b, g(a), c), true, b, g(a), c), true, g(a), b, c), true, c, b, a), true, c, b, a)
% 0.22/0.44 = { by axiom 8 (clause4) R->L }
% 0.22/0.44 fresh3(fresh2(fresh3(fresh4(fresh2(fresh3(fresh2(fresh(fresh3(fresh(fresh4(fresh(p(f(g(a)), f(g(b)), f(g(c))), true, g(a), f(g(b)), f(g(c))), true, g(a), f(g(b)), f(g(c))), true, g(b), g(a), f(g(c))), true, g(b), g(a), f(g(c))), true, g(c), g(a), g(b)), true, g(c), g(a), b), true, g(c), g(a), b), true, b, g(a), c), true, b, g(a), c), true, g(a), b, c), true, c, b, a), true, c, b, a)
% 0.22/0.44 = { by axiom 7 (clause6) }
% 0.22/0.44 fresh3(fresh2(fresh3(fresh4(fresh2(fresh3(fresh2(fresh(fresh3(fresh(fresh4(fresh(true, true, g(a), f(g(b)), f(g(c))), true, g(a), f(g(b)), f(g(c))), true, g(b), g(a), f(g(c))), true, g(b), g(a), f(g(c))), true, g(c), g(a), g(b)), true, g(c), g(a), b), true, g(c), g(a), b), true, b, g(a), c), true, b, g(a), c), true, g(a), b, c), true, c, b, a), true, c, b, a)
% 0.22/0.44 = { by axiom 1 (clause4) }
% 0.22/0.44 fresh3(fresh2(fresh3(fresh4(fresh2(fresh3(fresh2(fresh(fresh3(fresh(fresh4(true, true, g(a), f(g(b)), f(g(c))), true, g(b), g(a), f(g(c))), true, g(b), g(a), f(g(c))), true, g(c), g(a), g(b)), true, g(c), g(a), b), true, g(c), g(a), b), true, b, g(a), c), true, b, g(a), c), true, g(a), b, c), true, c, b, a), true, c, b, a)
% 0.22/0.44 = { by axiom 2 (clause2) }
% 0.22/0.44 fresh3(fresh2(fresh3(fresh4(fresh2(fresh3(fresh2(fresh(fresh3(fresh(true, true, g(b), g(a), f(g(c))), true, g(b), g(a), f(g(c))), true, g(c), g(a), g(b)), true, g(c), g(a), b), true, g(c), g(a), b), true, b, g(a), c), true, b, g(a), c), true, g(a), b, c), true, c, b, a), true, c, b, a)
% 0.22/0.44 = { by axiom 1 (clause4) }
% 0.22/0.44 fresh3(fresh2(fresh3(fresh4(fresh2(fresh3(fresh2(fresh(fresh3(true, true, g(b), g(a), f(g(c))), true, g(c), g(a), g(b)), true, g(c), g(a), b), true, g(c), g(a), b), true, b, g(a), c), true, b, g(a), c), true, g(a), b, c), true, c, b, a), true, c, b, a)
% 0.22/0.44 = { by axiom 3 (clause1) }
% 0.22/0.44 fresh3(fresh2(fresh3(fresh4(fresh2(fresh3(fresh2(fresh(true, true, g(c), g(a), g(b)), true, g(c), g(a), b), true, g(c), g(a), b), true, b, g(a), c), true, b, g(a), c), true, g(a), b, c), true, c, b, a), true, c, b, a)
% 0.22/0.44 = { by axiom 1 (clause4) }
% 0.22/0.44 fresh3(fresh2(fresh3(fresh4(fresh2(fresh3(fresh2(true, true, g(c), g(a), b), true, g(c), g(a), b), true, b, g(a), c), true, b, g(a), c), true, g(a), b, c), true, c, b, a), true, c, b, a)
% 0.22/0.44 = { by axiom 4 (clause3) }
% 0.22/0.44 fresh3(fresh2(fresh3(fresh4(fresh2(fresh3(true, true, g(c), g(a), b), true, b, g(a), c), true, b, g(a), c), true, g(a), b, c), true, c, b, a), true, c, b, a)
% 0.22/0.44 = { by axiom 3 (clause1) }
% 0.22/0.44 fresh3(fresh2(fresh3(fresh4(fresh2(true, true, b, g(a), c), true, b, g(a), c), true, g(a), b, c), true, c, b, a), true, c, b, a)
% 0.22/0.44 = { by axiom 4 (clause3) }
% 0.22/0.44 fresh3(fresh2(fresh3(fresh4(true, true, b, g(a), c), true, g(a), b, c), true, c, b, a), true, c, b, a)
% 0.22/0.44 = { by axiom 2 (clause2) }
% 0.22/0.44 fresh3(fresh2(fresh3(true, true, g(a), b, c), true, c, b, a), true, c, b, a)
% 0.22/0.44 = { by axiom 3 (clause1) }
% 0.22/0.44 fresh3(fresh2(true, true, c, b, a), true, c, b, a)
% 0.22/0.44 = { by axiom 4 (clause3) }
% 0.22/0.44 fresh3(true, true, c, b, a)
% 0.22/0.44 = { by axiom 3 (clause1) }
% 0.22/0.44 true
% 0.22/0.44 % SZS output end Proof
% 0.22/0.44
% 0.22/0.44 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------