%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : SET865-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 0.14s 10.49s
% Output : Proof 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET865-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/10.39 % Computer : n016.cluster.edu
% 0.10/10.39 % Model : x86_64 x86_64
% 0.10/10.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.39 % Memory : 8046.5625MB
% 0.10/10.39 % OS : Linux 6.8.0-71-generic
% 0.10/10.39 % CPULimit : 300
% 0.10/10.39 % WCLimit : 300
% 0.10/10.39 % DateTime : Mon Sep 28 03:09:46 UTC 2026
% 0.10/10.39 % CPUTime :
% 0.10/10.39 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/10.49 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-every 2
% 0.14/10.49
% 0.14/10.49 % SZS status Unsatisfiable
% 0.14/10.49
% 0.14/10.51 % SZS output start Proof
% 0.14/10.51 Axiom 1 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.14/10.51 Axiom 2 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 0.14/10.51 Axiom 3 (cls_Zorn_OHausdorff_0): c_in(c_Zorn_OHausdorff__1(X, Y), c_Zorn_Omaxchain(X, Y), tc_set(tc_set(Y))) = true.
% 0.14/10.51 Axiom 4 (cls_Zorn_Omaxchain__subset__chain_0): c_lessequals(c_Zorn_Omaxchain(X, Y), c_Zorn_Ochain(X, Y), tc_set(tc_set(tc_set(Y)))) = true.
% 0.14/10.51 Axiom 5 (cls_conjecture_1): ifeq(c_in(X, v_S, tc_set(t_a)), true, c_in(v_x(X), v_S, tc_set(t_a)), true) = true.
% 0.14/10.51 Axiom 6 (cls_conjecture_2): ifeq(c_in(X, v_S, tc_set(t_a)), true, c_lessequals(X, v_x(X), tc_set(t_a)), true) = true.
% 0.14/10.51 Axiom 7 (cls_conjecture_0): ifeq(c_in(X, c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(t_a))), true, c_in(c_Union(X, t_a), v_S, tc_set(t_a)), true) = true.
% 0.14/10.51 Axiom 8 (cls_Set_OsubsetD_0): ifeq(c_lessequals(X, Y, tc_set(Z)), true, ifeq(c_in(W, X, Z), true, c_in(W, Y, Z), true), true) = true.
% 0.14/10.51 Axiom 9 (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.
% 0.14/10.51
% 0.14/10.51 Goal 1 (cls_conjecture_3): tuple(X, c_in(X, v_S, tc_set(t_a))) = tuple(v_x(X), true).
% 0.14/10.51 The goal is true when:
% 0.14/10.51 X = c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)
% 0.14/10.51
% 0.14/10.51 Proof:
% 0.14/10.51 tuple(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), c_in(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_S, tc_set(t_a)))
% 0.14/10.51 = { by axiom 1 (ifeq_axiom) R->L }
% 0.14/10.51 tuple(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), ifeq(true, true, c_in(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_S, tc_set(t_a)), true))
% 0.14/10.51 = { by axiom 8 (cls_Set_OsubsetD_0) R->L }
% 0.14/10.51 tuple(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), ifeq(ifeq(c_lessequals(c_Zorn_Omaxchain(v_S, t_a), c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(tc_set(t_a)))), true, ifeq(c_in(c_Zorn_OHausdorff__1(v_S, t_a), c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a))), true, c_in(c_Zorn_OHausdorff__1(v_S, t_a), c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(t_a))), true), true), true, c_in(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_S, tc_set(t_a)), true))
% 0.14/10.51 = { by axiom 4 (cls_Zorn_Omaxchain__subset__chain_0) }
% 0.14/10.51 tuple(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), ifeq(ifeq(true, true, ifeq(c_in(c_Zorn_OHausdorff__1(v_S, t_a), c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a))), true, c_in(c_Zorn_OHausdorff__1(v_S, t_a), c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(t_a))), true), true), true, c_in(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_S, tc_set(t_a)), true))
% 0.14/10.51 = { by axiom 1 (ifeq_axiom) }
% 0.14/10.51 tuple(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), ifeq(ifeq(c_in(c_Zorn_OHausdorff__1(v_S, t_a), c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a))), true, c_in(c_Zorn_OHausdorff__1(v_S, t_a), c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(t_a))), true), true, c_in(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_S, tc_set(t_a)), true))
% 0.14/10.51 = { by axiom 3 (cls_Zorn_OHausdorff_0) }
% 0.14/10.51 tuple(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), ifeq(ifeq(true, true, c_in(c_Zorn_OHausdorff__1(v_S, t_a), c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(t_a))), true), true, c_in(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_S, tc_set(t_a)), true))
% 0.14/10.51 = { by axiom 1 (ifeq_axiom) }
% 0.14/10.51 tuple(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), ifeq(c_in(c_Zorn_OHausdorff__1(v_S, t_a), c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(t_a))), true, c_in(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_S, tc_set(t_a)), true))
% 0.14/10.51 = { by axiom 7 (cls_conjecture_0) }
% 0.14/10.51 tuple(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), true)
% 0.14/10.51 = { by axiom 2 (ifeq_axiom) R->L }
% 0.14/10.51 tuple(ifeq2(true, true, c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a))), true)
% 0.14/10.51 = { by axiom 2 (ifeq_axiom) R->L }
% 0.14/10.51 tuple(ifeq2(true, true, ifeq2(true, true, c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a))), v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a))), true)
% 0.14/10.51 = { by axiom 6 (cls_conjecture_2) R->L }
% 0.14/10.51 tuple(ifeq2(ifeq(c_in(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_S, tc_set(t_a)), true, c_lessequals(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)), tc_set(t_a)), true), true, ifeq2(true, true, c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a))), v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a))), true)
% 0.14/10.51 = { by axiom 1 (ifeq_axiom) R->L }
% 0.14/10.51 tuple(ifeq2(ifeq(ifeq(true, true, c_in(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_S, tc_set(t_a)), true), true, c_lessequals(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)), tc_set(t_a)), true), true, ifeq2(true, true, c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a))), v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a))), true)
% 0.14/10.51 = { by axiom 8 (cls_Set_OsubsetD_0) R->L }
% 0.14/10.51 tuple(ifeq2(ifeq(ifeq(ifeq(c_lessequals(c_Zorn_Omaxchain(v_S, t_a), c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(tc_set(t_a)))), true, ifeq(c_in(c_Zorn_OHausdorff__1(v_S, t_a), c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a))), true, c_in(c_Zorn_OHausdorff__1(v_S, t_a), c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(t_a))), true), true), true, c_in(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_S, tc_set(t_a)), true), true, c_lessequals(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)), tc_set(t_a)), true), true, ifeq2(true, true, c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a))), v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a))), true)
% 0.14/10.51 = { by axiom 4 (cls_Zorn_Omaxchain__subset__chain_0) }
% 0.14/10.51 tuple(ifeq2(ifeq(ifeq(ifeq(true, true, ifeq(c_in(c_Zorn_OHausdorff__1(v_S, t_a), c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a))), true, c_in(c_Zorn_OHausdorff__1(v_S, t_a), c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(t_a))), true), true), true, c_in(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_S, tc_set(t_a)), true), true, c_lessequals(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)), tc_set(t_a)), true), true, ifeq2(true, true, c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a))), v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a))), true)
% 0.14/10.51 = { by axiom 1 (ifeq_axiom) }
% 0.14/10.51 tuple(ifeq2(ifeq(ifeq(ifeq(c_in(c_Zorn_OHausdorff__1(v_S, t_a), c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a))), true, c_in(c_Zorn_OHausdorff__1(v_S, t_a), c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(t_a))), true), true, c_in(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_S, tc_set(t_a)), true), true, c_lessequals(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)), tc_set(t_a)), true), true, ifeq2(true, true, c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a))), v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a))), true)
% 0.14/10.51 = { by axiom 3 (cls_Zorn_OHausdorff_0) }
% 0.14/10.51 tuple(ifeq2(ifeq(ifeq(ifeq(true, true, c_in(c_Zorn_OHausdorff__1(v_S, t_a), c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(t_a))), true), true, c_in(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_S, tc_set(t_a)), true), true, c_lessequals(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)), tc_set(t_a)), true), true, ifeq2(true, true, c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a))), v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a))), true)
% 0.14/10.51 = { by axiom 1 (ifeq_axiom) }
% 0.14/10.51 tuple(ifeq2(ifeq(ifeq(c_in(c_Zorn_OHausdorff__1(v_S, t_a), c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(t_a))), true, c_in(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_S, tc_set(t_a)), true), true, c_lessequals(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)), tc_set(t_a)), true), true, ifeq2(true, true, c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a))), v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a))), true)
% 0.14/10.51 = { by axiom 7 (cls_conjecture_0) }
% 0.14/10.51 tuple(ifeq2(ifeq(true, true, c_lessequals(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)), tc_set(t_a)), true), true, ifeq2(true, true, c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a))), v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a))), true)
% 0.14/10.51 = { by axiom 1 (ifeq_axiom) }
% 0.14/10.51 tuple(ifeq2(c_lessequals(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)), tc_set(t_a)), true, ifeq2(true, true, c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a))), v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a))), true)
% 0.14/10.51 = { by axiom 5 (cls_conjecture_1) R->L }
% 0.14/10.51 tuple(ifeq2(c_lessequals(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)), tc_set(t_a)), true, ifeq2(ifeq(c_in(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_S, tc_set(t_a)), true, c_in(v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)), v_S, tc_set(t_a)), true), true, c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a))), v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a))), true)
% 0.14/10.51 = { by axiom 1 (ifeq_axiom) R->L }
% 0.14/10.51 tuple(ifeq2(c_lessequals(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)), tc_set(t_a)), true, ifeq2(ifeq(ifeq(true, true, c_in(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_S, tc_set(t_a)), true), true, c_in(v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)), v_S, tc_set(t_a)), true), true, c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a))), v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a))), true)
% 0.14/10.51 = { by axiom 8 (cls_Set_OsubsetD_0) R->L }
% 0.14/10.52 tuple(ifeq2(c_lessequals(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)), tc_set(t_a)), true, ifeq2(ifeq(ifeq(ifeq(c_lessequals(c_Zorn_Omaxchain(v_S, t_a), c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(tc_set(t_a)))), true, ifeq(c_in(c_Zorn_OHausdorff__1(v_S, t_a), c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a))), true, c_in(c_Zorn_OHausdorff__1(v_S, t_a), c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(t_a))), true), true), true, c_in(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_S, tc_set(t_a)), true), true, c_in(v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)), v_S, tc_set(t_a)), true), true, c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a))), v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a))), true)
% 0.14/10.52 = { by axiom 4 (cls_Zorn_Omaxchain__subset__chain_0) }
% 0.14/10.52 tuple(ifeq2(c_lessequals(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)), tc_set(t_a)), true, ifeq2(ifeq(ifeq(ifeq(true, true, ifeq(c_in(c_Zorn_OHausdorff__1(v_S, t_a), c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a))), true, c_in(c_Zorn_OHausdorff__1(v_S, t_a), c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(t_a))), true), true), true, c_in(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_S, tc_set(t_a)), true), true, c_in(v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)), v_S, tc_set(t_a)), true), true, c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a))), v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a))), true)
% 0.14/10.52 = { by axiom 1 (ifeq_axiom) }
% 0.14/10.52 tuple(ifeq2(c_lessequals(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)), tc_set(t_a)), true, ifeq2(ifeq(ifeq(ifeq(c_in(c_Zorn_OHausdorff__1(v_S, t_a), c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a))), true, c_in(c_Zorn_OHausdorff__1(v_S, t_a), c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(t_a))), true), true, c_in(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_S, tc_set(t_a)), true), true, c_in(v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)), v_S, tc_set(t_a)), true), true, c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a))), v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a))), true)
% 0.14/10.52 = { by axiom 3 (cls_Zorn_OHausdorff_0) }
% 0.14/10.52 tuple(ifeq2(c_lessequals(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)), tc_set(t_a)), true, ifeq2(ifeq(ifeq(ifeq(true, true, c_in(c_Zorn_OHausdorff__1(v_S, t_a), c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(t_a))), true), true, c_in(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_S, tc_set(t_a)), true), true, c_in(v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)), v_S, tc_set(t_a)), true), true, c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a))), v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a))), true)
% 0.14/10.52 = { by axiom 1 (ifeq_axiom) }
% 0.14/10.52 tuple(ifeq2(c_lessequals(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)), tc_set(t_a)), true, ifeq2(ifeq(ifeq(c_in(c_Zorn_OHausdorff__1(v_S, t_a), c_Zorn_Ochain(v_S, t_a), tc_set(tc_set(t_a))), true, c_in(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_S, tc_set(t_a)), true), true, c_in(v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)), v_S, tc_set(t_a)), true), true, c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a))), v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a))), true)
% 0.14/10.52 = { by axiom 7 (cls_conjecture_0) }
% 0.14/10.52 tuple(ifeq2(c_lessequals(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)), tc_set(t_a)), true, ifeq2(ifeq(true, true, c_in(v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)), v_S, tc_set(t_a)), true), true, c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a))), v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a))), true)
% 0.14/10.52 = { by axiom 1 (ifeq_axiom) }
% 0.14/10.52 tuple(ifeq2(c_lessequals(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)), tc_set(t_a)), true, ifeq2(c_in(v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)), v_S, tc_set(t_a)), true, c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a))), v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a))), true)
% 0.14/10.52 = { by axiom 2 (ifeq_axiom) R->L }
% 0.14/10.52 tuple(ifeq2(c_lessequals(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)), tc_set(t_a)), true, ifeq2(true, true, ifeq2(c_in(v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)), v_S, tc_set(t_a)), true, c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a))), v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a))), v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a))), true)
% 0.14/10.52 = { by axiom 3 (cls_Zorn_OHausdorff_0) R->L }
% 0.14/10.52 tuple(ifeq2(c_lessequals(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)), tc_set(t_a)), true, ifeq2(c_in(c_Zorn_OHausdorff__1(v_S, t_a), c_Zorn_Omaxchain(v_S, t_a), tc_set(tc_set(t_a))), true, ifeq2(c_in(v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)), v_S, tc_set(t_a)), true, c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a), v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a))), v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a))), v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a))), true)
% 0.14/10.52 = { by axiom 9 (cls_Zorn_Omaxchain__Zorn_0) }
% 0.14/10.52 tuple(v_x(c_Union(c_Zorn_OHausdorff__1(v_S, t_a), t_a)), true)
% 0.14/10.52 % SZS output end Proof
% 0.14/10.52
% 0.14/10.52 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------