%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : SET864-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:39:17 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.43s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET864-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n013.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 28 03:03:36 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.43 Command-line arguments: --flatten --complete-subsets
% 0.12/0.43
% 0.12/0.43 % SZS status Unsatisfiable
% 0.12/0.43
% 0.12/0.44 % SZS output start Proof
% 0.12/0.44 Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.12/0.44 Axiom 2 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 0.12/0.44 Axiom 3 (cls_conjecture_0): c_in(v_c, c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a))) = true.
% 0.12/0.44 Axiom 4 (cls_conjecture_2): c_in(c_Union(v_c, t_a), v_S, tc_set(t_a)) = true.
% 0.12/0.44 Axiom 5 (cls_conjecture_4): ifeq(c_in(X, v_S, tc_set(t_a)), true, c_lessequals(X, v_x(X), tc_set(t_a)), true) = true.
% 0.12/0.44 Axiom 6 (cls_conjecture_3): ifeq(c_in(X, v_S, tc_set(t_a)), true, c_in(v_x(X), v_S, tc_set(t_a)), true) = true.
% 0.12/0.44 Axiom 7 (cls_Zorn_Omaxchain__Zorn_0): ifeq2(c_lessequals(c_Union(X, Y), Z, tc_set(Y)), true, ifeq2(c_in(X, c_Zorn_Omaxchain(W, Y), tc_set(tc_set(Y))), true, ifeq2(c_in(Z, W, tc_set(Y)), true, c_Union(X, Y), Z), Z), Z) = Z.
% 0.12/0.44
% 0.12/0.44 Lemma 8: c_in(c_Union(v_c, t_a), v_S, tc_set(t_a)) = c_in(v_c, c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a))).
% 0.12/0.44 Proof:
% 0.12/0.44 c_in(c_Union(v_c, t_a), v_S, tc_set(t_a))
% 0.12/0.44 = { by axiom 4 (cls_conjecture_2) }
% 0.12/0.44 true
% 0.12/0.44 = { by axiom 3 (cls_conjecture_0) R->L }
% 0.12/0.44 c_in(v_c, c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a)))
% 0.12/0.44
% 0.12/0.44 Goal 1 (cls_conjecture_5): tuple(X, c_in(X, v_S, tc_set(t_a))) = tuple(v_x(X), true).
% 0.12/0.44 The goal is true when:
% 0.12/0.44 X = c_Union(v_c, t_a)
% 0.12/0.45
% 0.12/0.45 Proof:
% 0.12/0.45 tuple(c_Union(v_c, t_a), c_in(c_Union(v_c, t_a), v_S, tc_set(t_a)))
% 0.12/0.45 = { by axiom 2 (ifeq_axiom) R->L }
% 0.12/0.45 tuple(ifeq2(c_in(c_Union(v_c, t_a), v_S, tc_set(t_a)), c_in(c_Union(v_c, t_a), v_S, tc_set(t_a)), c_Union(v_c, t_a), v_x(c_Union(v_c, t_a))), c_in(c_Union(v_c, t_a), v_S, tc_set(t_a)))
% 0.12/0.45 = { by lemma 8 }
% 0.12/0.45 tuple(ifeq2(c_in(v_c, c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a))), c_in(c_Union(v_c, t_a), v_S, tc_set(t_a)), c_Union(v_c, t_a), v_x(c_Union(v_c, t_a))), c_in(c_Union(v_c, t_a), v_S, tc_set(t_a)))
% 0.12/0.45 = { by axiom 3 (cls_conjecture_0) }
% 0.12/0.45 tuple(ifeq2(true, c_in(c_Union(v_c, t_a), v_S, tc_set(t_a)), c_Union(v_c, t_a), v_x(c_Union(v_c, t_a))), c_in(c_Union(v_c, t_a), v_S, tc_set(t_a)))
% 0.12/0.45 = { by axiom 6 (cls_conjecture_3) R->L }
% 0.12/0.45 tuple(ifeq2(ifeq(c_in(c_Union(v_c, t_a), v_S, tc_set(t_a)), true, c_in(v_x(c_Union(v_c, t_a)), v_S, tc_set(t_a)), true), c_in(c_Union(v_c, t_a), v_S, tc_set(t_a)), c_Union(v_c, t_a), v_x(c_Union(v_c, t_a))), c_in(c_Union(v_c, t_a), v_S, tc_set(t_a)))
% 0.12/0.45 = { by axiom 3 (cls_conjecture_0) R->L }
% 0.12/0.45 tuple(ifeq2(ifeq(c_in(c_Union(v_c, t_a), v_S, tc_set(t_a)), true, c_in(v_x(c_Union(v_c, t_a)), v_S, tc_set(t_a)), c_in(v_c, c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a)))), c_in(c_Union(v_c, t_a), v_S, tc_set(t_a)), c_Union(v_c, t_a), v_x(c_Union(v_c, t_a))), c_in(c_Union(v_c, t_a), v_S, tc_set(t_a)))
% 0.12/0.45 = { by axiom 3 (cls_conjecture_0) R->L }
% 0.12/0.45 tuple(ifeq2(ifeq(c_in(c_Union(v_c, t_a), v_S, tc_set(t_a)), c_in(v_c, c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a))), c_in(v_x(c_Union(v_c, t_a)), v_S, tc_set(t_a)), c_in(v_c, c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a)))), c_in(c_Union(v_c, t_a), v_S, tc_set(t_a)), c_Union(v_c, t_a), v_x(c_Union(v_c, t_a))), c_in(c_Union(v_c, t_a), v_S, tc_set(t_a)))
% 0.12/0.45 = { by lemma 8 R->L }
% 0.12/0.45 tuple(ifeq2(ifeq(c_in(c_Union(v_c, t_a), v_S, tc_set(t_a)), c_in(v_c, c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a))), c_in(v_x(c_Union(v_c, t_a)), v_S, tc_set(t_a)), c_in(c_Union(v_c, t_a), v_S, tc_set(t_a))), c_in(c_Union(v_c, t_a), v_S, tc_set(t_a)), c_Union(v_c, t_a), v_x(c_Union(v_c, t_a))), c_in(c_Union(v_c, t_a), v_S, tc_set(t_a)))
% 0.12/0.45 = { by lemma 8 R->L }
% 0.12/0.45 tuple(ifeq2(ifeq(c_in(c_Union(v_c, t_a), v_S, tc_set(t_a)), c_in(c_Union(v_c, t_a), v_S, tc_set(t_a)), c_in(v_x(c_Union(v_c, t_a)), v_S, tc_set(t_a)), c_in(c_Union(v_c, t_a), v_S, tc_set(t_a))), c_in(c_Union(v_c, t_a), v_S, tc_set(t_a)), c_Union(v_c, t_a), v_x(c_Union(v_c, t_a))), c_in(c_Union(v_c, t_a), v_S, tc_set(t_a)))
% 0.12/0.45 = { by axiom 1 (ifeq_axiom) }
% 0.12/0.45 tuple(ifeq2(c_in(v_x(c_Union(v_c, t_a)), v_S, tc_set(t_a)), c_in(c_Union(v_c, t_a), v_S, tc_set(t_a)), c_Union(v_c, t_a), v_x(c_Union(v_c, t_a))), c_in(c_Union(v_c, t_a), v_S, tc_set(t_a)))
% 0.12/0.45 = { by axiom 2 (ifeq_axiom) R->L }
% 0.12/0.45 tuple(ifeq2(c_in(c_Union(v_c, t_a), v_S, tc_set(t_a)), c_in(c_Union(v_c, t_a), v_S, tc_set(t_a)), ifeq2(c_in(v_x(c_Union(v_c, t_a)), v_S, tc_set(t_a)), c_in(c_Union(v_c, t_a), v_S, tc_set(t_a)), c_Union(v_c, t_a), v_x(c_Union(v_c, t_a))), v_x(c_Union(v_c, t_a))), c_in(c_Union(v_c, t_a), v_S, tc_set(t_a)))
% 0.12/0.45 = { by lemma 8 }
% 0.12/0.45 tuple(ifeq2(c_in(v_c, c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a))), c_in(c_Union(v_c, t_a), v_S, tc_set(t_a)), ifeq2(c_in(v_x(c_Union(v_c, t_a)), v_S, tc_set(t_a)), c_in(c_Union(v_c, t_a), v_S, tc_set(t_a)), c_Union(v_c, t_a), v_x(c_Union(v_c, t_a))), v_x(c_Union(v_c, t_a))), c_in(c_Union(v_c, t_a), v_S, tc_set(t_a)))
% 0.12/0.45 = { by axiom 3 (cls_conjecture_0) }
% 0.12/0.45 tuple(ifeq2(true, c_in(c_Union(v_c, t_a), v_S, tc_set(t_a)), ifeq2(c_in(v_x(c_Union(v_c, t_a)), v_S, tc_set(t_a)), c_in(c_Union(v_c, t_a), v_S, tc_set(t_a)), c_Union(v_c, t_a), v_x(c_Union(v_c, t_a))), v_x(c_Union(v_c, t_a))), c_in(c_Union(v_c, t_a), v_S, tc_set(t_a)))
% 0.12/0.45 = { by axiom 5 (cls_conjecture_4) R->L }
% 0.12/0.45 tuple(ifeq2(ifeq(c_in(c_Union(v_c, t_a), v_S, tc_set(t_a)), true, c_lessequals(c_Union(v_c, t_a), v_x(c_Union(v_c, t_a)), tc_set(t_a)), true), c_in(c_Union(v_c, t_a), v_S, tc_set(t_a)), ifeq2(c_in(v_x(c_Union(v_c, t_a)), v_S, tc_set(t_a)), c_in(c_Union(v_c, t_a), v_S, tc_set(t_a)), c_Union(v_c, t_a), v_x(c_Union(v_c, t_a))), v_x(c_Union(v_c, t_a))), c_in(c_Union(v_c, t_a), v_S, tc_set(t_a)))
% 0.12/0.45 = { by axiom 3 (cls_conjecture_0) R->L }
% 0.12/0.45 tuple(ifeq2(ifeq(c_in(c_Union(v_c, t_a), v_S, tc_set(t_a)), true, c_lessequals(c_Union(v_c, t_a), v_x(c_Union(v_c, t_a)), tc_set(t_a)), c_in(v_c, c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a)))), c_in(c_Union(v_c, t_a), v_S, tc_set(t_a)), ifeq2(c_in(v_x(c_Union(v_c, t_a)), v_S, tc_set(t_a)), c_in(c_Union(v_c, t_a), v_S, tc_set(t_a)), c_Union(v_c, t_a), v_x(c_Union(v_c, t_a))), v_x(c_Union(v_c, t_a))), c_in(c_Union(v_c, t_a), v_S, tc_set(t_a)))
% 0.12/0.45 = { by axiom 3 (cls_conjecture_0) R->L }
% 0.12/0.45 tuple(ifeq2(ifeq(c_in(c_Union(v_c, t_a), v_S, tc_set(t_a)), c_in(v_c, c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a))), c_lessequals(c_Union(v_c, t_a), v_x(c_Union(v_c, t_a)), tc_set(t_a)), c_in(v_c, c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a)))), c_in(c_Union(v_c, t_a), v_S, tc_set(t_a)), ifeq2(c_in(v_x(c_Union(v_c, t_a)), v_S, tc_set(t_a)), c_in(c_Union(v_c, t_a), v_S, tc_set(t_a)), c_Union(v_c, t_a), v_x(c_Union(v_c, t_a))), v_x(c_Union(v_c, t_a))), c_in(c_Union(v_c, t_a), v_S, tc_set(t_a)))
% 0.12/0.45 = { by lemma 8 R->L }
% 0.12/0.45 tuple(ifeq2(ifeq(c_in(c_Union(v_c, t_a), v_S, tc_set(t_a)), c_in(v_c, c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a))), c_lessequals(c_Union(v_c, t_a), v_x(c_Union(v_c, t_a)), tc_set(t_a)), c_in(c_Union(v_c, t_a), v_S, tc_set(t_a))), c_in(c_Union(v_c, t_a), v_S, tc_set(t_a)), ifeq2(c_in(v_x(c_Union(v_c, t_a)), v_S, tc_set(t_a)), c_in(c_Union(v_c, t_a), v_S, tc_set(t_a)), c_Union(v_c, t_a), v_x(c_Union(v_c, t_a))), v_x(c_Union(v_c, t_a))), c_in(c_Union(v_c, t_a), v_S, tc_set(t_a)))
% 0.12/0.45 = { by lemma 8 R->L }
% 0.12/0.45 tuple(ifeq2(ifeq(c_in(c_Union(v_c, t_a), v_S, tc_set(t_a)), c_in(c_Union(v_c, t_a), v_S, tc_set(t_a)), c_lessequals(c_Union(v_c, t_a), v_x(c_Union(v_c, t_a)), tc_set(t_a)), c_in(c_Union(v_c, t_a), v_S, tc_set(t_a))), c_in(c_Union(v_c, t_a), v_S, tc_set(t_a)), ifeq2(c_in(v_x(c_Union(v_c, t_a)), v_S, tc_set(t_a)), c_in(c_Union(v_c, t_a), v_S, tc_set(t_a)), c_Union(v_c, t_a), v_x(c_Union(v_c, t_a))), v_x(c_Union(v_c, t_a))), c_in(c_Union(v_c, t_a), v_S, tc_set(t_a)))
% 0.12/0.45 = { by axiom 1 (ifeq_axiom) }
% 0.12/0.45 tuple(ifeq2(c_lessequals(c_Union(v_c, t_a), v_x(c_Union(v_c, t_a)), tc_set(t_a)), c_in(c_Union(v_c, t_a), v_S, tc_set(t_a)), ifeq2(c_in(v_x(c_Union(v_c, t_a)), v_S, tc_set(t_a)), c_in(c_Union(v_c, t_a), v_S, tc_set(t_a)), c_Union(v_c, t_a), v_x(c_Union(v_c, t_a))), v_x(c_Union(v_c, t_a))), c_in(c_Union(v_c, t_a), v_S, tc_set(t_a)))
% 0.12/0.45 = { by axiom 2 (ifeq_axiom) R->L }
% 0.12/0.45 tuple(ifeq2(c_lessequals(c_Union(v_c, t_a), v_x(c_Union(v_c, t_a)), tc_set(t_a)), c_in(c_Union(v_c, t_a), v_S, tc_set(t_a)), ifeq2(c_in(c_Union(v_c, t_a), v_S, tc_set(t_a)), c_in(c_Union(v_c, t_a), v_S, tc_set(t_a)), ifeq2(c_in(v_x(c_Union(v_c, t_a)), v_S, tc_set(t_a)), c_in(c_Union(v_c, t_a), v_S, tc_set(t_a)), c_Union(v_c, t_a), v_x(c_Union(v_c, t_a))), v_x(c_Union(v_c, t_a))), v_x(c_Union(v_c, t_a))), c_in(c_Union(v_c, t_a), v_S, tc_set(t_a)))
% 0.12/0.45 = { by lemma 8 }
% 0.12/0.45 tuple(ifeq2(c_lessequals(c_Union(v_c, t_a), v_x(c_Union(v_c, t_a)), tc_set(t_a)), c_in(c_Union(v_c, t_a), v_S, tc_set(t_a)), ifeq2(c_in(v_c, c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a))), c_in(c_Union(v_c, t_a), v_S, tc_set(t_a)), ifeq2(c_in(v_x(c_Union(v_c, t_a)), v_S, tc_set(t_a)), c_in(c_Union(v_c, t_a), v_S, tc_set(t_a)), c_Union(v_c, t_a), v_x(c_Union(v_c, t_a))), v_x(c_Union(v_c, t_a))), v_x(c_Union(v_c, t_a))), c_in(c_Union(v_c, t_a), v_S, tc_set(t_a)))
% 0.12/0.45 = { by lemma 8 }
% 0.12/0.45 tuple(ifeq2(c_lessequals(c_Union(v_c, t_a), v_x(c_Union(v_c, t_a)), tc_set(t_a)), c_in(v_c, c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a))), ifeq2(c_in(v_c, c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a))), c_in(c_Union(v_c, t_a), v_S, tc_set(t_a)), ifeq2(c_in(v_x(c_Union(v_c, t_a)), v_S, tc_set(t_a)), c_in(c_Union(v_c, t_a), v_S, tc_set(t_a)), c_Union(v_c, t_a), v_x(c_Union(v_c, t_a))), v_x(c_Union(v_c, t_a))), v_x(c_Union(v_c, t_a))), c_in(c_Union(v_c, t_a), v_S, tc_set(t_a)))
% 0.12/0.45 = { by lemma 8 }
% 0.12/0.45 tuple(ifeq2(c_lessequals(c_Union(v_c, t_a), v_x(c_Union(v_c, t_a)), tc_set(t_a)), c_in(v_c, c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a))), ifeq2(c_in(v_c, c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a))), c_in(v_c, c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a))), ifeq2(c_in(v_x(c_Union(v_c, t_a)), v_S, tc_set(t_a)), c_in(c_Union(v_c, t_a), v_S, tc_set(t_a)), c_Union(v_c, t_a), v_x(c_Union(v_c, t_a))), v_x(c_Union(v_c, t_a))), v_x(c_Union(v_c, t_a))), c_in(c_Union(v_c, t_a), v_S, tc_set(t_a)))
% 0.12/0.45 = { by lemma 8 }
% 0.12/0.45 tuple(ifeq2(c_lessequals(c_Union(v_c, t_a), v_x(c_Union(v_c, t_a)), tc_set(t_a)), c_in(v_c, c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a))), ifeq2(c_in(v_c, c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a))), c_in(v_c, c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a))), ifeq2(c_in(v_x(c_Union(v_c, t_a)), v_S, tc_set(t_a)), c_in(v_c, c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a))), c_Union(v_c, t_a), v_x(c_Union(v_c, t_a))), v_x(c_Union(v_c, t_a))), v_x(c_Union(v_c, t_a))), c_in(c_Union(v_c, t_a), v_S, tc_set(t_a)))
% 0.12/0.45 = { by axiom 3 (cls_conjecture_0) }
% 0.12/0.45 tuple(ifeq2(c_lessequals(c_Union(v_c, t_a), v_x(c_Union(v_c, t_a)), tc_set(t_a)), true, ifeq2(c_in(v_c, c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a))), c_in(v_c, c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a))), ifeq2(c_in(v_x(c_Union(v_c, t_a)), v_S, tc_set(t_a)), c_in(v_c, c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a))), c_Union(v_c, t_a), v_x(c_Union(v_c, t_a))), v_x(c_Union(v_c, t_a))), v_x(c_Union(v_c, t_a))), c_in(c_Union(v_c, t_a), v_S, tc_set(t_a)))
% 0.12/0.45 = { by axiom 3 (cls_conjecture_0) }
% 0.12/0.45 tuple(ifeq2(c_lessequals(c_Union(v_c, t_a), v_x(c_Union(v_c, t_a)), tc_set(t_a)), true, ifeq2(c_in(v_c, c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a))), true, ifeq2(c_in(v_x(c_Union(v_c, t_a)), v_S, tc_set(t_a)), c_in(v_c, c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a))), c_Union(v_c, t_a), v_x(c_Union(v_c, t_a))), v_x(c_Union(v_c, t_a))), v_x(c_Union(v_c, t_a))), c_in(c_Union(v_c, t_a), v_S, tc_set(t_a)))
% 0.12/0.45 = { by axiom 3 (cls_conjecture_0) }
% 0.12/0.45 tuple(ifeq2(c_lessequals(c_Union(v_c, t_a), v_x(c_Union(v_c, t_a)), tc_set(t_a)), true, ifeq2(c_in(v_c, c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a))), true, ifeq2(c_in(v_x(c_Union(v_c, t_a)), v_S, tc_set(t_a)), true, c_Union(v_c, t_a), v_x(c_Union(v_c, t_a))), v_x(c_Union(v_c, t_a))), v_x(c_Union(v_c, t_a))), c_in(c_Union(v_c, t_a), v_S, tc_set(t_a)))
% 0.12/0.45 = { by axiom 7 (cls_Zorn_Omaxchain__Zorn_0) }
% 0.12/0.45 tuple(v_x(c_Union(v_c, t_a)), c_in(c_Union(v_c, t_a), v_S, tc_set(t_a)))
% 0.12/0.45 = { by lemma 8 }
% 0.12/0.45 tuple(v_x(c_Union(v_c, t_a)), c_in(v_c, c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a))))
% 0.12/0.45 = { by axiom 3 (cls_conjecture_0) }
% 0.12/0.45 tuple(v_x(c_Union(v_c, t_a)), true)
% 0.12/0.45 % SZS output end Proof
% 0.12/0.45
% 0.12/0.45 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------