TSTP Solution File: SEU323-10 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : SEU323-10 : TPTP v8.1.2. Released v7.3.0.
% 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 : n022.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 : Thu Aug 31 17:52:13 EDT 2023
% Result : Unsatisfiable 0.19s 0.41s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU323-10 : TPTP v8.1.2. Released v7.3.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.34 % Computer : n022.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Aug 23 18:01:56 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.41 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.19/0.41
% 0.19/0.41 % SZS status Unsatisfiable
% 0.19/0.41
% 0.19/0.42 % SZS output start Proof
% 0.19/0.42 Axiom 1 (t51_tops_1): top_str(sK2_t51_tops_1_A) = true.
% 0.19/0.42 Axiom 2 (t51_tops_1_1): topological_space(sK2_t51_tops_1_A) = true.
% 0.19/0.42 Axiom 3 (ifeq_axiom_001): ifeq(X, X, Y, Z) = Y.
% 0.19/0.42 Axiom 4 (t51_tops_1_2): element(sK1_t51_tops_1_B, powerset(the_carrier(sK2_t51_tops_1_A))) = true.
% 0.19/0.42 Axiom 5 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 0.19/0.42 Axiom 6 (dt_k3_subset_1): ifeq(element(X, powerset(Y)), true, element(subset_complement(Y, X), powerset(Y)), true) = true.
% 0.19/0.42 Axiom 7 (dt_k6_pre_topc): ifeq(element(X, powerset(the_carrier(Y))), true, ifeq(top_str(Y), true, element(topstr_closure(Y, X), powerset(the_carrier(Y))), true), true) = true.
% 0.19/0.42 Axiom 8 (fc2_tops_1): ifeq(element(X, powerset(the_carrier(Y))), true, ifeq(topological_space(Y), true, ifeq(top_str(Y), true, closed_subset(topstr_closure(Y, X), Y), true), true), true) = true.
% 0.19/0.42 Axiom 9 (d1_tops_1): ifeq2(element(X, powerset(the_carrier(Y))), true, ifeq2(top_str(Y), true, subset_complement(the_carrier(Y), topstr_closure(Y, subset_complement(the_carrier(Y), X))), interior(Y, X)), interior(Y, X)) = interior(Y, X).
% 0.19/0.42 Axiom 10 (fc3_tops_1): ifeq(element(X, powerset(the_carrier(Y))), true, ifeq(closed_subset(X, Y), true, ifeq(topological_space(Y), true, ifeq(top_str(Y), true, open_subset(subset_complement(the_carrier(Y), X), Y), true), true), true), true) = true.
% 0.19/0.42
% 0.19/0.42 Lemma 11: element(subset_complement(the_carrier(sK2_t51_tops_1_A), sK1_t51_tops_1_B), powerset(the_carrier(sK2_t51_tops_1_A))) = true.
% 0.19/0.42 Proof:
% 0.19/0.42 element(subset_complement(the_carrier(sK2_t51_tops_1_A), sK1_t51_tops_1_B), powerset(the_carrier(sK2_t51_tops_1_A)))
% 0.19/0.42 = { by axiom 3 (ifeq_axiom_001) R->L }
% 0.19/0.42 ifeq(true, true, element(subset_complement(the_carrier(sK2_t51_tops_1_A), sK1_t51_tops_1_B), powerset(the_carrier(sK2_t51_tops_1_A))), true)
% 0.19/0.42 = { by axiom 4 (t51_tops_1_2) R->L }
% 0.19/0.42 ifeq(element(sK1_t51_tops_1_B, powerset(the_carrier(sK2_t51_tops_1_A))), true, element(subset_complement(the_carrier(sK2_t51_tops_1_A), sK1_t51_tops_1_B), powerset(the_carrier(sK2_t51_tops_1_A))), true)
% 0.19/0.42 = { by axiom 6 (dt_k3_subset_1) }
% 0.19/0.42 true
% 0.19/0.42
% 0.19/0.42 Goal 1 (t51_tops_1_3): open_subset(interior(sK2_t51_tops_1_A, sK1_t51_tops_1_B), sK2_t51_tops_1_A) = true.
% 0.19/0.42 Proof:
% 0.19/0.42 open_subset(interior(sK2_t51_tops_1_A, sK1_t51_tops_1_B), sK2_t51_tops_1_A)
% 0.19/0.42 = { by axiom 9 (d1_tops_1) R->L }
% 0.19/0.42 open_subset(ifeq2(element(sK1_t51_tops_1_B, powerset(the_carrier(sK2_t51_tops_1_A))), true, ifeq2(top_str(sK2_t51_tops_1_A), true, subset_complement(the_carrier(sK2_t51_tops_1_A), topstr_closure(sK2_t51_tops_1_A, subset_complement(the_carrier(sK2_t51_tops_1_A), sK1_t51_tops_1_B))), interior(sK2_t51_tops_1_A, sK1_t51_tops_1_B)), interior(sK2_t51_tops_1_A, sK1_t51_tops_1_B)), sK2_t51_tops_1_A)
% 0.19/0.42 = { by axiom 4 (t51_tops_1_2) }
% 0.19/0.42 open_subset(ifeq2(true, true, ifeq2(top_str(sK2_t51_tops_1_A), true, subset_complement(the_carrier(sK2_t51_tops_1_A), topstr_closure(sK2_t51_tops_1_A, subset_complement(the_carrier(sK2_t51_tops_1_A), sK1_t51_tops_1_B))), interior(sK2_t51_tops_1_A, sK1_t51_tops_1_B)), interior(sK2_t51_tops_1_A, sK1_t51_tops_1_B)), sK2_t51_tops_1_A)
% 0.19/0.42 = { by axiom 5 (ifeq_axiom) }
% 0.19/0.42 open_subset(ifeq2(top_str(sK2_t51_tops_1_A), true, subset_complement(the_carrier(sK2_t51_tops_1_A), topstr_closure(sK2_t51_tops_1_A, subset_complement(the_carrier(sK2_t51_tops_1_A), sK1_t51_tops_1_B))), interior(sK2_t51_tops_1_A, sK1_t51_tops_1_B)), sK2_t51_tops_1_A)
% 0.19/0.42 = { by axiom 1 (t51_tops_1) }
% 0.19/0.42 open_subset(ifeq2(true, true, subset_complement(the_carrier(sK2_t51_tops_1_A), topstr_closure(sK2_t51_tops_1_A, subset_complement(the_carrier(sK2_t51_tops_1_A), sK1_t51_tops_1_B))), interior(sK2_t51_tops_1_A, sK1_t51_tops_1_B)), sK2_t51_tops_1_A)
% 0.19/0.42 = { by axiom 5 (ifeq_axiom) }
% 0.19/0.42 open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A), topstr_closure(sK2_t51_tops_1_A, subset_complement(the_carrier(sK2_t51_tops_1_A), sK1_t51_tops_1_B))), sK2_t51_tops_1_A)
% 0.19/0.42 = { by axiom 3 (ifeq_axiom_001) R->L }
% 0.19/0.42 ifeq(true, true, open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A), topstr_closure(sK2_t51_tops_1_A, subset_complement(the_carrier(sK2_t51_tops_1_A), sK1_t51_tops_1_B))), sK2_t51_tops_1_A), true)
% 0.19/0.42 = { by axiom 1 (t51_tops_1) R->L }
% 0.19/0.42 ifeq(top_str(sK2_t51_tops_1_A), true, open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A), topstr_closure(sK2_t51_tops_1_A, subset_complement(the_carrier(sK2_t51_tops_1_A), sK1_t51_tops_1_B))), sK2_t51_tops_1_A), true)
% 0.19/0.42 = { by axiom 3 (ifeq_axiom_001) R->L }
% 0.19/0.42 ifeq(true, true, ifeq(top_str(sK2_t51_tops_1_A), true, open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A), topstr_closure(sK2_t51_tops_1_A, subset_complement(the_carrier(sK2_t51_tops_1_A), sK1_t51_tops_1_B))), sK2_t51_tops_1_A), true), true)
% 0.19/0.42 = { by axiom 2 (t51_tops_1_1) R->L }
% 0.19/0.42 ifeq(topological_space(sK2_t51_tops_1_A), true, ifeq(top_str(sK2_t51_tops_1_A), true, open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A), topstr_closure(sK2_t51_tops_1_A, subset_complement(the_carrier(sK2_t51_tops_1_A), sK1_t51_tops_1_B))), sK2_t51_tops_1_A), true), true)
% 0.19/0.42 = { by axiom 3 (ifeq_axiom_001) R->L }
% 0.19/0.42 ifeq(true, true, ifeq(topological_space(sK2_t51_tops_1_A), true, ifeq(top_str(sK2_t51_tops_1_A), true, open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A), topstr_closure(sK2_t51_tops_1_A, subset_complement(the_carrier(sK2_t51_tops_1_A), sK1_t51_tops_1_B))), sK2_t51_tops_1_A), true), true), true)
% 0.19/0.42 = { by axiom 8 (fc2_tops_1) R->L }
% 0.19/0.42 ifeq(ifeq(element(subset_complement(the_carrier(sK2_t51_tops_1_A), sK1_t51_tops_1_B), powerset(the_carrier(sK2_t51_tops_1_A))), true, ifeq(topological_space(sK2_t51_tops_1_A), true, ifeq(top_str(sK2_t51_tops_1_A), true, closed_subset(topstr_closure(sK2_t51_tops_1_A, subset_complement(the_carrier(sK2_t51_tops_1_A), sK1_t51_tops_1_B)), sK2_t51_tops_1_A), true), true), true), true, ifeq(topological_space(sK2_t51_tops_1_A), true, ifeq(top_str(sK2_t51_tops_1_A), true, open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A), topstr_closure(sK2_t51_tops_1_A, subset_complement(the_carrier(sK2_t51_tops_1_A), sK1_t51_tops_1_B))), sK2_t51_tops_1_A), true), true), true)
% 0.19/0.42 = { by lemma 11 }
% 0.19/0.42 ifeq(ifeq(true, true, ifeq(topological_space(sK2_t51_tops_1_A), true, ifeq(top_str(sK2_t51_tops_1_A), true, closed_subset(topstr_closure(sK2_t51_tops_1_A, subset_complement(the_carrier(sK2_t51_tops_1_A), sK1_t51_tops_1_B)), sK2_t51_tops_1_A), true), true), true), true, ifeq(topological_space(sK2_t51_tops_1_A), true, ifeq(top_str(sK2_t51_tops_1_A), true, open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A), topstr_closure(sK2_t51_tops_1_A, subset_complement(the_carrier(sK2_t51_tops_1_A), sK1_t51_tops_1_B))), sK2_t51_tops_1_A), true), true), true)
% 0.19/0.42 = { by axiom 3 (ifeq_axiom_001) }
% 0.19/0.42 ifeq(ifeq(topological_space(sK2_t51_tops_1_A), true, ifeq(top_str(sK2_t51_tops_1_A), true, closed_subset(topstr_closure(sK2_t51_tops_1_A, subset_complement(the_carrier(sK2_t51_tops_1_A), sK1_t51_tops_1_B)), sK2_t51_tops_1_A), true), true), true, ifeq(topological_space(sK2_t51_tops_1_A), true, ifeq(top_str(sK2_t51_tops_1_A), true, open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A), topstr_closure(sK2_t51_tops_1_A, subset_complement(the_carrier(sK2_t51_tops_1_A), sK1_t51_tops_1_B))), sK2_t51_tops_1_A), true), true), true)
% 0.19/0.42 = { by axiom 2 (t51_tops_1_1) }
% 0.19/0.42 ifeq(ifeq(true, true, ifeq(top_str(sK2_t51_tops_1_A), true, closed_subset(topstr_closure(sK2_t51_tops_1_A, subset_complement(the_carrier(sK2_t51_tops_1_A), sK1_t51_tops_1_B)), sK2_t51_tops_1_A), true), true), true, ifeq(topological_space(sK2_t51_tops_1_A), true, ifeq(top_str(sK2_t51_tops_1_A), true, open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A), topstr_closure(sK2_t51_tops_1_A, subset_complement(the_carrier(sK2_t51_tops_1_A), sK1_t51_tops_1_B))), sK2_t51_tops_1_A), true), true), true)
% 0.19/0.42 = { by axiom 3 (ifeq_axiom_001) }
% 0.19/0.42 ifeq(ifeq(top_str(sK2_t51_tops_1_A), true, closed_subset(topstr_closure(sK2_t51_tops_1_A, subset_complement(the_carrier(sK2_t51_tops_1_A), sK1_t51_tops_1_B)), sK2_t51_tops_1_A), true), true, ifeq(topological_space(sK2_t51_tops_1_A), true, ifeq(top_str(sK2_t51_tops_1_A), true, open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A), topstr_closure(sK2_t51_tops_1_A, subset_complement(the_carrier(sK2_t51_tops_1_A), sK1_t51_tops_1_B))), sK2_t51_tops_1_A), true), true), true)
% 0.19/0.42 = { by axiom 1 (t51_tops_1) }
% 0.19/0.42 ifeq(ifeq(true, true, closed_subset(topstr_closure(sK2_t51_tops_1_A, subset_complement(the_carrier(sK2_t51_tops_1_A), sK1_t51_tops_1_B)), sK2_t51_tops_1_A), true), true, ifeq(topological_space(sK2_t51_tops_1_A), true, ifeq(top_str(sK2_t51_tops_1_A), true, open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A), topstr_closure(sK2_t51_tops_1_A, subset_complement(the_carrier(sK2_t51_tops_1_A), sK1_t51_tops_1_B))), sK2_t51_tops_1_A), true), true), true)
% 0.19/0.42 = { by axiom 3 (ifeq_axiom_001) }
% 0.19/0.42 ifeq(closed_subset(topstr_closure(sK2_t51_tops_1_A, subset_complement(the_carrier(sK2_t51_tops_1_A), sK1_t51_tops_1_B)), sK2_t51_tops_1_A), true, ifeq(topological_space(sK2_t51_tops_1_A), true, ifeq(top_str(sK2_t51_tops_1_A), true, open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A), topstr_closure(sK2_t51_tops_1_A, subset_complement(the_carrier(sK2_t51_tops_1_A), sK1_t51_tops_1_B))), sK2_t51_tops_1_A), true), true), true)
% 0.19/0.42 = { by axiom 3 (ifeq_axiom_001) R->L }
% 0.19/0.42 ifeq(true, true, ifeq(closed_subset(topstr_closure(sK2_t51_tops_1_A, subset_complement(the_carrier(sK2_t51_tops_1_A), sK1_t51_tops_1_B)), sK2_t51_tops_1_A), true, ifeq(topological_space(sK2_t51_tops_1_A), true, ifeq(top_str(sK2_t51_tops_1_A), true, open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A), topstr_closure(sK2_t51_tops_1_A, subset_complement(the_carrier(sK2_t51_tops_1_A), sK1_t51_tops_1_B))), sK2_t51_tops_1_A), true), true), true), true)
% 0.19/0.42 = { by axiom 7 (dt_k6_pre_topc) R->L }
% 0.19/0.42 ifeq(ifeq(element(subset_complement(the_carrier(sK2_t51_tops_1_A), sK1_t51_tops_1_B), powerset(the_carrier(sK2_t51_tops_1_A))), true, ifeq(top_str(sK2_t51_tops_1_A), true, element(topstr_closure(sK2_t51_tops_1_A, subset_complement(the_carrier(sK2_t51_tops_1_A), sK1_t51_tops_1_B)), powerset(the_carrier(sK2_t51_tops_1_A))), true), true), true, ifeq(closed_subset(topstr_closure(sK2_t51_tops_1_A, subset_complement(the_carrier(sK2_t51_tops_1_A), sK1_t51_tops_1_B)), sK2_t51_tops_1_A), true, ifeq(topological_space(sK2_t51_tops_1_A), true, ifeq(top_str(sK2_t51_tops_1_A), true, open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A), topstr_closure(sK2_t51_tops_1_A, subset_complement(the_carrier(sK2_t51_tops_1_A), sK1_t51_tops_1_B))), sK2_t51_tops_1_A), true), true), true), true)
% 0.19/0.42 = { by lemma 11 }
% 0.19/0.42 ifeq(ifeq(true, true, ifeq(top_str(sK2_t51_tops_1_A), true, element(topstr_closure(sK2_t51_tops_1_A, subset_complement(the_carrier(sK2_t51_tops_1_A), sK1_t51_tops_1_B)), powerset(the_carrier(sK2_t51_tops_1_A))), true), true), true, ifeq(closed_subset(topstr_closure(sK2_t51_tops_1_A, subset_complement(the_carrier(sK2_t51_tops_1_A), sK1_t51_tops_1_B)), sK2_t51_tops_1_A), true, ifeq(topological_space(sK2_t51_tops_1_A), true, ifeq(top_str(sK2_t51_tops_1_A), true, open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A), topstr_closure(sK2_t51_tops_1_A, subset_complement(the_carrier(sK2_t51_tops_1_A), sK1_t51_tops_1_B))), sK2_t51_tops_1_A), true), true), true), true)
% 0.19/0.42 = { by axiom 3 (ifeq_axiom_001) }
% 0.19/0.42 ifeq(ifeq(top_str(sK2_t51_tops_1_A), true, element(topstr_closure(sK2_t51_tops_1_A, subset_complement(the_carrier(sK2_t51_tops_1_A), sK1_t51_tops_1_B)), powerset(the_carrier(sK2_t51_tops_1_A))), true), true, ifeq(closed_subset(topstr_closure(sK2_t51_tops_1_A, subset_complement(the_carrier(sK2_t51_tops_1_A), sK1_t51_tops_1_B)), sK2_t51_tops_1_A), true, ifeq(topological_space(sK2_t51_tops_1_A), true, ifeq(top_str(sK2_t51_tops_1_A), true, open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A), topstr_closure(sK2_t51_tops_1_A, subset_complement(the_carrier(sK2_t51_tops_1_A), sK1_t51_tops_1_B))), sK2_t51_tops_1_A), true), true), true), true)
% 0.19/0.42 = { by axiom 1 (t51_tops_1) }
% 0.19/0.42 ifeq(ifeq(true, true, element(topstr_closure(sK2_t51_tops_1_A, subset_complement(the_carrier(sK2_t51_tops_1_A), sK1_t51_tops_1_B)), powerset(the_carrier(sK2_t51_tops_1_A))), true), true, ifeq(closed_subset(topstr_closure(sK2_t51_tops_1_A, subset_complement(the_carrier(sK2_t51_tops_1_A), sK1_t51_tops_1_B)), sK2_t51_tops_1_A), true, ifeq(topological_space(sK2_t51_tops_1_A), true, ifeq(top_str(sK2_t51_tops_1_A), true, open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A), topstr_closure(sK2_t51_tops_1_A, subset_complement(the_carrier(sK2_t51_tops_1_A), sK1_t51_tops_1_B))), sK2_t51_tops_1_A), true), true), true), true)
% 0.19/0.42 = { by axiom 3 (ifeq_axiom_001) }
% 0.19/0.42 ifeq(element(topstr_closure(sK2_t51_tops_1_A, subset_complement(the_carrier(sK2_t51_tops_1_A), sK1_t51_tops_1_B)), powerset(the_carrier(sK2_t51_tops_1_A))), true, ifeq(closed_subset(topstr_closure(sK2_t51_tops_1_A, subset_complement(the_carrier(sK2_t51_tops_1_A), sK1_t51_tops_1_B)), sK2_t51_tops_1_A), true, ifeq(topological_space(sK2_t51_tops_1_A), true, ifeq(top_str(sK2_t51_tops_1_A), true, open_subset(subset_complement(the_carrier(sK2_t51_tops_1_A), topstr_closure(sK2_t51_tops_1_A, subset_complement(the_carrier(sK2_t51_tops_1_A), sK1_t51_tops_1_B))), sK2_t51_tops_1_A), true), true), true), true)
% 0.19/0.42 = { by axiom 10 (fc3_tops_1) }
% 0.19/0.42 true
% 0.19/0.42 % SZS output end Proof
% 0.19/0.42
% 0.19/0.42 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------