TSTP Solution File: SYN311-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SYN311-1 : 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 : n004.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 15.53s 2.35s
% Output : Proof 15.53s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SYN311-1 : TPTP v8.1.2. Released v1.2.0.
% 0.14/0.14 % 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 : n004.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 17:31:07 EDT 2023
% 0.14/0.35 % CPUTime :
% 15.53/2.35 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 15.53/2.35
% 15.53/2.35 % SZS status Unsatisfiable
% 15.53/2.35
% 15.53/2.36 % SZS output start Proof
% 15.53/2.36 Take the following subset of the input axioms:
% 15.53/2.36 fof(clause1, negated_conjecture, ![X3, X, X1, X2]: (p(X3, X, X1, X2) | ~p(X, X1, X2, X3))).
% 15.53/2.37 fof(clause2, negated_conjecture, ![X3_2, X4, X1_2, X2_2]: (p(X3_2, X2_2, X1_2, X4) | ~p(X4, X1_2, X2_2, X3_2))).
% 15.53/2.37 fof(clause3, negated_conjecture, ![X3_2, X4, X1_2, X2_2]: (p(X4, X1_2, X2_2, g(X3_2)) | ~p(X4, X1_2, X2_2, X3_2))).
% 15.53/2.37 fof(clause4, negated_conjecture, ![X3_2, X4, X1_2, X2_2]: (p(f(X4), X1_2, X2_2, X3_2) | ~p(X4, X1_2, X2_2, X3_2))).
% 15.53/2.37 fof(clause5, negated_conjecture, p(a, b, c, d)).
% 15.53/2.37 fof(clause6, negated_conjecture, ~p(f(g(d)), f(g(c)), f(g(b)), f(g(a)))).
% 15.53/2.37
% 15.53/2.37 Now clausify the problem and encode Horn clauses using encoding 3 of
% 15.53/2.37 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 15.53/2.37 We repeatedly replace C & s=t => u=v by the two clauses:
% 15.53/2.37 fresh(y, y, x1...xn) = u
% 15.53/2.37 C => fresh(s, t, x1...xn) = v
% 15.53/2.37 where fresh is a fresh function symbol and x1..xn are the free
% 15.53/2.37 variables of u and v.
% 15.53/2.37 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 15.53/2.37 input problem has no model of domain size 1).
% 15.53/2.37
% 15.53/2.37 The encoding turns the above axioms into the following unit equations and goals:
% 15.53/2.37
% 15.53/2.37 Axiom 1 (clause5): p(a, b, c, d) = true.
% 15.53/2.37 Axiom 2 (clause4): fresh(X, X, Y, Z, W, V) = true.
% 15.53/2.37 Axiom 3 (clause2): fresh4(X, X, Y, Z, W, V) = true.
% 15.53/2.37 Axiom 4 (clause1): fresh3(X, X, Y, Z, W, V) = true.
% 15.53/2.37 Axiom 5 (clause3): fresh2(X, X, Y, Z, W, V) = true.
% 15.53/2.37 Axiom 6 (clause4): fresh(p(X, Y, Z, W), true, X, Y, Z, W) = p(f(X), Y, Z, W).
% 15.53/2.37 Axiom 7 (clause2): fresh4(p(X, Y, Z, W), true, W, Z, Y, X) = p(W, Z, Y, X).
% 15.53/2.37 Axiom 8 (clause1): fresh3(p(X, Y, Z, W), true, W, X, Y, Z) = p(W, X, Y, Z).
% 15.53/2.37 Axiom 9 (clause3): fresh2(p(X, Y, Z, W), true, X, Y, Z, W) = p(X, Y, Z, g(W)).
% 15.53/2.37
% 15.53/2.37 Goal 1 (clause6): p(f(g(d)), f(g(c)), f(g(b)), f(g(a))) = true.
% 15.53/2.37 Proof:
% 15.53/2.37 p(f(g(d)), f(g(c)), f(g(b)), f(g(a)))
% 15.53/2.37 = { by axiom 6 (clause4) R->L }
% 15.53/2.37 fresh(p(g(d), f(g(c)), f(g(b)), f(g(a))), true, g(d), f(g(c)), f(g(b)), f(g(a)))
% 15.53/2.37 = { by axiom 8 (clause1) R->L }
% 15.53/2.37 fresh(fresh3(p(f(g(c)), f(g(b)), f(g(a)), g(d)), true, g(d), f(g(c)), f(g(b)), f(g(a))), true, g(d), f(g(c)), f(g(b)), f(g(a)))
% 15.53/2.37 = { by axiom 9 (clause3) R->L }
% 15.53/2.37 fresh(fresh3(fresh2(p(f(g(c)), f(g(b)), f(g(a)), d), true, f(g(c)), f(g(b)), f(g(a)), d), true, g(d), f(g(c)), f(g(b)), f(g(a))), true, g(d), f(g(c)), f(g(b)), f(g(a)))
% 15.53/2.37 = { by axiom 6 (clause4) R->L }
% 15.53/2.37 fresh(fresh3(fresh2(fresh(p(g(c), f(g(b)), f(g(a)), d), true, g(c), f(g(b)), f(g(a)), d), true, f(g(c)), f(g(b)), f(g(a)), d), true, g(d), f(g(c)), f(g(b)), f(g(a))), true, g(d), f(g(c)), f(g(b)), f(g(a)))
% 15.53/2.37 = { by axiom 8 (clause1) R->L }
% 15.53/2.37 fresh(fresh3(fresh2(fresh(fresh3(p(f(g(b)), f(g(a)), d, g(c)), true, g(c), f(g(b)), f(g(a)), d), true, g(c), f(g(b)), f(g(a)), d), true, f(g(c)), f(g(b)), f(g(a)), d), true, g(d), f(g(c)), f(g(b)), f(g(a))), true, g(d), f(g(c)), f(g(b)), f(g(a)))
% 15.53/2.37 = { by axiom 9 (clause3) R->L }
% 15.53/2.37 fresh(fresh3(fresh2(fresh(fresh3(fresh2(p(f(g(b)), f(g(a)), d, c), true, f(g(b)), f(g(a)), d, c), true, g(c), f(g(b)), f(g(a)), d), true, g(c), f(g(b)), f(g(a)), d), true, f(g(c)), f(g(b)), f(g(a)), d), true, g(d), f(g(c)), f(g(b)), f(g(a))), true, g(d), f(g(c)), f(g(b)), f(g(a)))
% 15.53/2.37 = { by axiom 6 (clause4) R->L }
% 15.53/2.37 fresh(fresh3(fresh2(fresh(fresh3(fresh2(fresh(p(g(b), f(g(a)), d, c), true, g(b), f(g(a)), d, c), true, f(g(b)), f(g(a)), d, c), true, g(c), f(g(b)), f(g(a)), d), true, g(c), f(g(b)), f(g(a)), d), true, f(g(c)), f(g(b)), f(g(a)), d), true, g(d), f(g(c)), f(g(b)), f(g(a))), true, g(d), f(g(c)), f(g(b)), f(g(a)))
% 15.53/2.37 = { by axiom 8 (clause1) R->L }
% 15.53/2.37 fresh(fresh3(fresh2(fresh(fresh3(fresh2(fresh(fresh3(p(f(g(a)), d, c, g(b)), true, g(b), f(g(a)), d, c), true, g(b), f(g(a)), d, c), true, f(g(b)), f(g(a)), d, c), true, g(c), f(g(b)), f(g(a)), d), true, g(c), f(g(b)), f(g(a)), d), true, f(g(c)), f(g(b)), f(g(a)), d), true, g(d), f(g(c)), f(g(b)), f(g(a))), true, g(d), f(g(c)), f(g(b)), f(g(a)))
% 15.53/2.37 = { by axiom 9 (clause3) R->L }
% 15.53/2.37 fresh(fresh3(fresh2(fresh(fresh3(fresh2(fresh(fresh3(fresh2(p(f(g(a)), d, c, b), true, f(g(a)), d, c, b), true, g(b), f(g(a)), d, c), true, g(b), f(g(a)), d, c), true, f(g(b)), f(g(a)), d, c), true, g(c), f(g(b)), f(g(a)), d), true, g(c), f(g(b)), f(g(a)), d), true, f(g(c)), f(g(b)), f(g(a)), d), true, g(d), f(g(c)), f(g(b)), f(g(a))), true, g(d), f(g(c)), f(g(b)), f(g(a)))
% 15.53/2.37 = { by axiom 6 (clause4) R->L }
% 15.53/2.37 fresh(fresh3(fresh2(fresh(fresh3(fresh2(fresh(fresh3(fresh2(fresh(p(g(a), d, c, b), true, g(a), d, c, b), true, f(g(a)), d, c, b), true, g(b), f(g(a)), d, c), true, g(b), f(g(a)), d, c), true, f(g(b)), f(g(a)), d, c), true, g(c), f(g(b)), f(g(a)), d), true, g(c), f(g(b)), f(g(a)), d), true, f(g(c)), f(g(b)), f(g(a)), d), true, g(d), f(g(c)), f(g(b)), f(g(a))), true, g(d), f(g(c)), f(g(b)), f(g(a)))
% 15.53/2.37 = { by axiom 8 (clause1) R->L }
% 15.53/2.37 fresh(fresh3(fresh2(fresh(fresh3(fresh2(fresh(fresh3(fresh2(fresh(fresh3(p(d, c, b, g(a)), true, g(a), d, c, b), true, g(a), d, c, b), true, f(g(a)), d, c, b), true, g(b), f(g(a)), d, c), true, g(b), f(g(a)), d, c), true, f(g(b)), f(g(a)), d, c), true, g(c), f(g(b)), f(g(a)), d), true, g(c), f(g(b)), f(g(a)), d), true, f(g(c)), f(g(b)), f(g(a)), d), true, g(d), f(g(c)), f(g(b)), f(g(a))), true, g(d), f(g(c)), f(g(b)), f(g(a)))
% 15.53/2.37 = { by axiom 9 (clause3) R->L }
% 15.53/2.37 fresh(fresh3(fresh2(fresh(fresh3(fresh2(fresh(fresh3(fresh2(fresh(fresh3(fresh2(p(d, c, b, a), true, d, c, b, a), true, g(a), d, c, b), true, g(a), d, c, b), true, f(g(a)), d, c, b), true, g(b), f(g(a)), d, c), true, g(b), f(g(a)), d, c), true, f(g(b)), f(g(a)), d, c), true, g(c), f(g(b)), f(g(a)), d), true, g(c), f(g(b)), f(g(a)), d), true, f(g(c)), f(g(b)), f(g(a)), d), true, g(d), f(g(c)), f(g(b)), f(g(a))), true, g(d), f(g(c)), f(g(b)), f(g(a)))
% 15.53/2.37 = { by axiom 7 (clause2) R->L }
% 15.53/2.37 fresh(fresh3(fresh2(fresh(fresh3(fresh2(fresh(fresh3(fresh2(fresh(fresh3(fresh2(fresh4(p(a, b, c, d), true, d, c, b, a), true, d, c, b, a), true, g(a), d, c, b), true, g(a), d, c, b), true, f(g(a)), d, c, b), true, g(b), f(g(a)), d, c), true, g(b), f(g(a)), d, c), true, f(g(b)), f(g(a)), d, c), true, g(c), f(g(b)), f(g(a)), d), true, g(c), f(g(b)), f(g(a)), d), true, f(g(c)), f(g(b)), f(g(a)), d), true, g(d), f(g(c)), f(g(b)), f(g(a))), true, g(d), f(g(c)), f(g(b)), f(g(a)))
% 15.53/2.37 = { by axiom 1 (clause5) }
% 15.53/2.37 fresh(fresh3(fresh2(fresh(fresh3(fresh2(fresh(fresh3(fresh2(fresh(fresh3(fresh2(fresh4(true, true, d, c, b, a), true, d, c, b, a), true, g(a), d, c, b), true, g(a), d, c, b), true, f(g(a)), d, c, b), true, g(b), f(g(a)), d, c), true, g(b), f(g(a)), d, c), true, f(g(b)), f(g(a)), d, c), true, g(c), f(g(b)), f(g(a)), d), true, g(c), f(g(b)), f(g(a)), d), true, f(g(c)), f(g(b)), f(g(a)), d), true, g(d), f(g(c)), f(g(b)), f(g(a))), true, g(d), f(g(c)), f(g(b)), f(g(a)))
% 15.53/2.37 = { by axiom 3 (clause2) }
% 15.53/2.37 fresh(fresh3(fresh2(fresh(fresh3(fresh2(fresh(fresh3(fresh2(fresh(fresh3(fresh2(true, true, d, c, b, a), true, g(a), d, c, b), true, g(a), d, c, b), true, f(g(a)), d, c, b), true, g(b), f(g(a)), d, c), true, g(b), f(g(a)), d, c), true, f(g(b)), f(g(a)), d, c), true, g(c), f(g(b)), f(g(a)), d), true, g(c), f(g(b)), f(g(a)), d), true, f(g(c)), f(g(b)), f(g(a)), d), true, g(d), f(g(c)), f(g(b)), f(g(a))), true, g(d), f(g(c)), f(g(b)), f(g(a)))
% 15.53/2.37 = { by axiom 5 (clause3) }
% 15.53/2.37 fresh(fresh3(fresh2(fresh(fresh3(fresh2(fresh(fresh3(fresh2(fresh(fresh3(true, true, g(a), d, c, b), true, g(a), d, c, b), true, f(g(a)), d, c, b), true, g(b), f(g(a)), d, c), true, g(b), f(g(a)), d, c), true, f(g(b)), f(g(a)), d, c), true, g(c), f(g(b)), f(g(a)), d), true, g(c), f(g(b)), f(g(a)), d), true, f(g(c)), f(g(b)), f(g(a)), d), true, g(d), f(g(c)), f(g(b)), f(g(a))), true, g(d), f(g(c)), f(g(b)), f(g(a)))
% 15.53/2.37 = { by axiom 4 (clause1) }
% 15.53/2.37 fresh(fresh3(fresh2(fresh(fresh3(fresh2(fresh(fresh3(fresh2(fresh(true, true, g(a), d, c, b), true, f(g(a)), d, c, b), true, g(b), f(g(a)), d, c), true, g(b), f(g(a)), d, c), true, f(g(b)), f(g(a)), d, c), true, g(c), f(g(b)), f(g(a)), d), true, g(c), f(g(b)), f(g(a)), d), true, f(g(c)), f(g(b)), f(g(a)), d), true, g(d), f(g(c)), f(g(b)), f(g(a))), true, g(d), f(g(c)), f(g(b)), f(g(a)))
% 15.53/2.37 = { by axiom 2 (clause4) }
% 15.53/2.37 fresh(fresh3(fresh2(fresh(fresh3(fresh2(fresh(fresh3(fresh2(true, true, f(g(a)), d, c, b), true, g(b), f(g(a)), d, c), true, g(b), f(g(a)), d, c), true, f(g(b)), f(g(a)), d, c), true, g(c), f(g(b)), f(g(a)), d), true, g(c), f(g(b)), f(g(a)), d), true, f(g(c)), f(g(b)), f(g(a)), d), true, g(d), f(g(c)), f(g(b)), f(g(a))), true, g(d), f(g(c)), f(g(b)), f(g(a)))
% 15.53/2.37 = { by axiom 5 (clause3) }
% 15.53/2.37 fresh(fresh3(fresh2(fresh(fresh3(fresh2(fresh(fresh3(true, true, g(b), f(g(a)), d, c), true, g(b), f(g(a)), d, c), true, f(g(b)), f(g(a)), d, c), true, g(c), f(g(b)), f(g(a)), d), true, g(c), f(g(b)), f(g(a)), d), true, f(g(c)), f(g(b)), f(g(a)), d), true, g(d), f(g(c)), f(g(b)), f(g(a))), true, g(d), f(g(c)), f(g(b)), f(g(a)))
% 15.53/2.37 = { by axiom 4 (clause1) }
% 15.53/2.37 fresh(fresh3(fresh2(fresh(fresh3(fresh2(fresh(true, true, g(b), f(g(a)), d, c), true, f(g(b)), f(g(a)), d, c), true, g(c), f(g(b)), f(g(a)), d), true, g(c), f(g(b)), f(g(a)), d), true, f(g(c)), f(g(b)), f(g(a)), d), true, g(d), f(g(c)), f(g(b)), f(g(a))), true, g(d), f(g(c)), f(g(b)), f(g(a)))
% 15.53/2.38 = { by axiom 2 (clause4) }
% 15.53/2.38 fresh(fresh3(fresh2(fresh(fresh3(fresh2(true, true, f(g(b)), f(g(a)), d, c), true, g(c), f(g(b)), f(g(a)), d), true, g(c), f(g(b)), f(g(a)), d), true, f(g(c)), f(g(b)), f(g(a)), d), true, g(d), f(g(c)), f(g(b)), f(g(a))), true, g(d), f(g(c)), f(g(b)), f(g(a)))
% 15.53/2.38 = { by axiom 5 (clause3) }
% 15.53/2.38 fresh(fresh3(fresh2(fresh(fresh3(true, true, g(c), f(g(b)), f(g(a)), d), true, g(c), f(g(b)), f(g(a)), d), true, f(g(c)), f(g(b)), f(g(a)), d), true, g(d), f(g(c)), f(g(b)), f(g(a))), true, g(d), f(g(c)), f(g(b)), f(g(a)))
% 15.53/2.38 = { by axiom 4 (clause1) }
% 15.53/2.38 fresh(fresh3(fresh2(fresh(true, true, g(c), f(g(b)), f(g(a)), d), true, f(g(c)), f(g(b)), f(g(a)), d), true, g(d), f(g(c)), f(g(b)), f(g(a))), true, g(d), f(g(c)), f(g(b)), f(g(a)))
% 15.53/2.38 = { by axiom 2 (clause4) }
% 15.53/2.38 fresh(fresh3(fresh2(true, true, f(g(c)), f(g(b)), f(g(a)), d), true, g(d), f(g(c)), f(g(b)), f(g(a))), true, g(d), f(g(c)), f(g(b)), f(g(a)))
% 15.53/2.38 = { by axiom 5 (clause3) }
% 15.53/2.38 fresh(fresh3(true, true, g(d), f(g(c)), f(g(b)), f(g(a))), true, g(d), f(g(c)), f(g(b)), f(g(a)))
% 15.53/2.38 = { by axiom 4 (clause1) }
% 15.53/2.38 fresh(true, true, g(d), f(g(c)), f(g(b)), f(g(a)))
% 15.53/2.38 = { by axiom 2 (clause4) }
% 15.53/2.38 true
% 15.53/2.38 % SZS output end Proof
% 15.53/2.38
% 15.53/2.38 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------