TSTP Solution File: SEU324+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SEU324+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n025.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 : 600s
% DateTime : Tue Jul 19 13:30:58 EDT 2022
% Result : Theorem 0.92s 1.19s
% Output : Refutation 0.92s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SEU324+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n025.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun Jun 19 06:36:28 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.43/1.01 ============================== Prover9 ===============================
% 0.43/1.01 Prover9 (32) version 2009-11A, November 2009.
% 0.43/1.01 Process 6591 was started by sandbox on n025.cluster.edu,
% 0.43/1.01 Sun Jun 19 06:36:29 2022
% 0.43/1.01 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_6436_n025.cluster.edu".
% 0.43/1.01 ============================== end of head ===========================
% 0.43/1.01
% 0.43/1.01 ============================== INPUT =================================
% 0.43/1.01
% 0.43/1.01 % Reading from file /tmp/Prover9_6436_n025.cluster.edu
% 0.43/1.01
% 0.43/1.01 set(prolog_style_variables).
% 0.43/1.01 set(auto2).
% 0.43/1.01 % set(auto2) -> set(auto).
% 0.43/1.01 % set(auto) -> set(auto_inference).
% 0.43/1.01 % set(auto) -> set(auto_setup).
% 0.43/1.01 % set(auto_setup) -> set(predicate_elim).
% 0.43/1.01 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.43/1.01 % set(auto) -> set(auto_limits).
% 0.43/1.01 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.43/1.01 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.43/1.01 % set(auto) -> set(auto_denials).
% 0.43/1.01 % set(auto) -> set(auto_process).
% 0.43/1.01 % set(auto2) -> assign(new_constants, 1).
% 0.43/1.01 % set(auto2) -> assign(fold_denial_max, 3).
% 0.43/1.01 % set(auto2) -> assign(max_weight, "200.000").
% 0.43/1.01 % set(auto2) -> assign(max_hours, 1).
% 0.43/1.01 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.43/1.01 % set(auto2) -> assign(max_seconds, 0).
% 0.43/1.01 % set(auto2) -> assign(max_minutes, 5).
% 0.43/1.01 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.43/1.01 % set(auto2) -> set(sort_initial_sos).
% 0.43/1.01 % set(auto2) -> assign(sos_limit, -1).
% 0.43/1.01 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.43/1.01 % set(auto2) -> assign(max_megs, 400).
% 0.43/1.01 % set(auto2) -> assign(stats, some).
% 0.43/1.01 % set(auto2) -> clear(echo_input).
% 0.43/1.01 % set(auto2) -> set(quiet).
% 0.43/1.01 % set(auto2) -> clear(print_initial_clauses).
% 0.43/1.01 % set(auto2) -> clear(print_given).
% 0.43/1.01 assign(lrs_ticks,-1).
% 0.43/1.01 assign(sos_limit,10000).
% 0.43/1.01 assign(order,kbo).
% 0.43/1.01 set(lex_order_vars).
% 0.43/1.01 clear(print_given).
% 0.43/1.01
% 0.43/1.01 % formulas(sos). % not echoed (25 formulas)
% 0.43/1.01
% 0.43/1.01 ============================== end of input ==========================
% 0.43/1.01
% 0.43/1.01 % From the command line: assign(max_seconds, 300).
% 0.43/1.01
% 0.43/1.01 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.43/1.01
% 0.43/1.01 % Formulas that are not ordinary clauses:
% 0.43/1.01 1 (all A (top_str(A) -> (all B (element(B,powerset(the_carrier(A))) -> interior(A,B) = subset_complement(the_carrier(A),topstr_closure(A,subset_complement(the_carrier(A),B))))))) # label(d1_tops_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 2 (all A all B (top_str(A) & element(B,powerset(the_carrier(A))) -> element(interior(A,B),powerset(the_carrier(A))))) # label(dt_k1_tops_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 3 $T # label(dt_k1_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 4 (all A all B (element(B,powerset(A)) -> element(subset_complement(A,B),powerset(A)))) # label(dt_k3_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 5 (all A all B (top_str(A) & element(B,powerset(the_carrier(A))) -> element(topstr_closure(A,B),powerset(the_carrier(A))))) # label(dt_k6_pre_topc) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 6 (all A (top_str(A) -> one_sorted_str(A))) # label(dt_l1_pre_topc) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 7 $T # label(dt_l1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 8 $T # label(dt_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 9 $T # label(dt_u1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 10 (exists A top_str(A)) # label(existence_l1_pre_topc) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 11 (exists A one_sorted_str(A)) # label(existence_l1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 12 (all A exists B element(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 13 (all A all B (topological_space(A) & top_str(A) & element(B,powerset(the_carrier(A))) -> closed_subset(topstr_closure(A,B),A))) # label(fc2_tops_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 14 (all A all B (topological_space(A) & top_str(A) & closed_subset(B,A) & element(B,powerset(the_carrier(A))) -> open_subset(subset_complement(the_carrier(A),B),A))) # label(fc3_tops_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 15 (all A all B (topological_space(A) & top_str(A) & open_subset(B,A) & element(B,powerset(the_carrier(A))) -> closed_subset(subset_complement(the_carrier(A),B),A))) # label(fc4_tops_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 16 (all A all B (topological_space(A) & top_str(A) & element(B,powerset(the_carrier(A))) -> open_subset(interior(A,B),A))) # label(fc6_tops_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 17 (all A all B (element(B,powerset(A)) -> subset_complement(A,subset_complement(A,B)) = B)) # label(involutiveness_k3_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 18 (all A (topological_space(A) & top_str(A) -> (exists B (element(B,powerset(the_carrier(A))) & open_subset(B,A))))) # label(rc1_tops_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 19 (all A (topological_space(A) & top_str(A) -> (exists B (element(B,powerset(the_carrier(A))) & open_subset(B,A) & closed_subset(B,A))))) # label(rc2_tops_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 20 (all A (topological_space(A) & top_str(A) -> (exists B (element(B,powerset(the_carrier(A))) & closed_subset(B,A))))) # label(rc6_pre_topc) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 21 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 22 (all A (top_str(A) -> (all B (element(B,powerset(the_carrier(A))) -> (open_subset(B,A) <-> closed_subset(subset_complement(the_carrier(A),B),A)))))) # label(t30_tops_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 23 (all A all B (element(A,powerset(B)) <-> subset(A,B))) # label(t3_subset) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 24 (all A (top_str(A) -> (all B (element(B,powerset(the_carrier(A))) -> (closed_subset(B,A) -> topstr_closure(A,B) = B) & (topological_space(A) & topstr_closure(A,B) = B -> closed_subset(B,A)))))) # label(t52_pre_topc) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.01 25 -(all A (topological_space(A) & top_str(A) -> (all B (top_str(B) -> (all C (element(C,powerset(the_carrier(A))) -> (all D (element(D,powerset(the_carrier(B))) -> (open_subset(D,B) -> interior(B,D) = D) & (interior(A,C) = C -> open_subset(C,A)))))))))) # label(t55_tops_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.43/1.01
% 0.43/1.01 ============================== end of process non-clausal formulas ===
% 0.43/1.01
% 0.43/1.01 ============================== PROCESS INITIAL CLAUSES ===============
% 0.43/1.01
% 0.43/1.01 ============================== PREDICATE ELIMINATION =================
% 0.43/1.01 26 -top_str(A) | one_sorted_str(A) # label(dt_l1_pre_topc) # label(axiom). [clausify(6)].
% 0.43/1.01 27 top_str(c1) # label(existence_l1_pre_topc) # label(axiom). [clausify(10)].
% 0.43/1.01 28 top_str(c3) # label(t55_tops_1) # label(negated_conjecture). [clausify(25)].
% 0.43/1.01 29 top_str(c4) # label(t55_tops_1) # label(negated_conjecture). [clausify(25)].
% 0.43/1.01 Derived: one_sorted_str(c1). [resolve(26,a,27,a)].
% 0.43/1.01 Derived: one_sorted_str(c3). [resolve(26,a,28,a)].
% 0.43/1.01 Derived: one_sorted_str(c4). [resolve(26,a,29,a)].
% 0.43/1.01 30 -topological_space(A) | -top_str(A) | open_subset(f2(A),A) # label(rc1_tops_1) # label(axiom). [clausify(18)].
% 0.43/1.01 Derived: -topological_space(c1) | open_subset(f2(c1),c1). [resolve(30,b,27,a)].
% 0.43/1.01 Derived: -topological_space(c3) | open_subset(f2(c3),c3). [resolve(30,b,28,a)].
% 0.43/1.01 Derived: -topological_space(c4) | open_subset(f2(c4),c4). [resolve(30,b,29,a)].
% 0.43/1.01 31 -topological_space(A) | -top_str(A) | open_subset(f3(A),A) # label(rc2_tops_1) # label(axiom). [clausify(19)].
% 0.43/1.01 Derived: -topological_space(c1) | open_subset(f3(c1),c1). [resolve(31,b,27,a)].
% 0.43/1.01 Derived: -topological_space(c3) | open_subset(f3(c3),c3). [resolve(31,b,28,a)].
% 0.43/1.01 Derived: -topological_space(c4) | open_subset(f3(c4),c4). [resolve(31,b,29,a)].
% 0.43/1.01 32 -topological_space(A) | -top_str(A) | closed_subset(f3(A),A) # label(rc2_tops_1) # label(axiom). [clausify(19)].
% 0.43/1.01 Derived: -topological_space(c1) | closed_subset(f3(c1),c1). [resolve(32,b,27,a)].
% 0.43/1.01 Derived: -topological_space(c3) | closed_subset(f3(c3),c3). [resolve(32,b,28,a)].
% 0.43/1.01 Derived: -topological_space(c4) | closed_subset(f3(c4),c4). [resolve(32,b,29,a)].
% 0.43/1.01 33 -topological_space(A) | -top_str(A) | closed_subset(f4(A),A) # label(rc6_pre_topc) # label(axiom). [clausify(20)].
% 0.43/1.01 Derived: -topological_space(c1) | closed_subset(f4(c1),c1). [resolve(33,b,27,a)].
% 0.43/1.01 Derived: -topological_space(c3) | closed_subset(f4(c3),c3). [resolve(33,b,28,a)].
% 0.43/1.01 Derived: -topological_space(c4) | closed_subset(f4(c4),c4). [resolve(33,b,29,a)].
% 0.43/1.01 34 -topological_space(A) | -top_str(A) | element(f2(A),powerset(the_carrier(A))) # label(rc1_tops_1) # label(axiom). [clausify(18)].
% 0.43/1.01 Derived: -topological_space(c1) | element(f2(c1),powerset(the_carrier(c1))). [resolve(34,b,27,a)].
% 0.43/1.01 Derived: -topological_space(c3) | element(f2(c3),powerset(the_carrier(c3))). [resolve(34,b,28,a)].
% 0.43/1.01 Derived: -topological_space(c4) | element(f2(c4),powerset(the_carrier(c4))). [resolve(34,b,29,a)].
% 0.43/1.01 35 -topological_space(A) | -top_str(A) | element(f3(A),powerset(the_carrier(A))) # label(rc2_tops_1) # label(axiom). [clausify(19)].
% 0.43/1.01 Derived: -topological_space(c1) | element(f3(c1),powerset(the_carrier(c1))). [resolve(35,b,27,a)].
% 0.43/1.01 Derived: -topological_space(c3) | element(f3(c3),powerset(the_carrier(c3))). [resolve(35,b,28,a)].
% 0.43/1.01 Derived: -topological_space(c4) | element(f3(c4),powerset(the_carrier(c4))). [resolve(35,b,29,a)].
% 0.43/1.01 36 -topological_space(A) | -top_str(A) | element(f4(A),powerset(the_carrier(A))) # label(rc6_pre_topc) # label(axiom). [clausify(20)].
% 0.43/1.01 Derived: -topological_space(c1) | element(f4(c1),powerset(the_carrier(c1))). [resolve(36,b,27,a)].
% 0.43/1.01 Derived: -topological_space(c3) | element(f4(c3),powerset(the_carrier(c3))). [resolve(36,b,28,a)].
% 0.43/1.01 Derived: -topological_space(c4) | element(f4(c4),powerset(the_carrier(c4))). [resolve(36,b,29,a)].
% 0.43/1.01 37 -top_str(A) | -element(B,powerset(the_carrier(A))) | element(interior(A,B),powerset(the_carrier(A))) # label(dt_k1_tops_1) # label(axiom). [clausify(2)].
% 0.43/1.01 Derived: -element(A,powerset(the_carrier(c1))) | element(interior(c1,A),powerset(the_carrier(c1))). [resolve(37,a,27,a)].
% 0.43/1.01 Derived: -element(A,powerset(the_carrier(c3))) | element(interior(c3,A),powerset(the_carrier(c3))). [resolve(37,a,28,a)].
% 0.43/1.01 Derived: -element(A,powerset(the_carrier(c4))) | element(interior(c4,A),powerset(the_carrier(c4))). [resolve(37,a,29,a)].
% 0.43/1.01 38 -top_str(A) | -element(B,powerset(the_carrier(A))) | element(topstr_closure(A,B),powerset(the_carrier(A))) # label(dt_k6_pre_topc) # label(axiom). [clausify(5)].
% 0.43/1.01 Derived: -element(A,powerset(the_carrier(c1))) | element(topstr_closure(c1,A),powerset(the_carrier(c1))). [resolve(38,a,27,a)].
% 0.43/1.01 Derived: -element(A,powerset(the_carrier(c3))) | element(topstr_closure(c3,A),powerset(the_carrier(c3))). [resolve(38,a,28,a)].
% 0.43/1.01 Derived: -element(A,powerset(the_carrier(c4))) | element(topstr_closure(c4,A),powerset(the_carrier(c4))). [resolve(38,a,29,a)].
% 0.43/1.01 39 -topological_space(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | closed_subset(topstr_closure(A,B),A) # label(fc2_tops_1) # label(axiom). [clausify(13)].
% 0.43/1.01 Derived: -topological_space(c1) | -element(A,powerset(the_carrier(c1))) | closed_subset(topstr_closure(c1,A),c1). [resolve(39,b,27,a)].
% 0.43/1.01 Derived: -topological_space(c3) | -element(A,powerset(the_carrier(c3))) | closed_subset(topstr_closure(c3,A),c3). [resolve(39,b,28,a)].
% 0.43/1.01 Derived: -topological_space(c4) | -element(A,powerset(the_carrier(c4))) | closed_subset(topstr_closure(c4,A),c4). [resolve(39,b,29,a)].
% 0.43/1.01 40 -topological_space(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | open_subset(interior(A,B),A) # label(fc6_tops_1) # label(axiom). [clausify(16)].
% 0.43/1.01 Derived: -topological_space(c1) | -element(A,powerset(the_carrier(c1))) | open_subset(interior(c1,A),c1). [resolve(40,b,27,a)].
% 0.43/1.01 Derived: -topological_space(c3) | -element(A,powerset(the_carrier(c3))) | open_subset(interior(c3,A),c3). [resolve(40,b,28,a)].
% 0.43/1.01 Derived: -topological_space(c4) | -element(A,powerset(the_carrier(c4))) | open_subset(interior(c4,A),c4). [resolve(40,b,29,a)].
% 0.43/1.01 41 -top_str(A) | -element(B,powerset(the_carrier(A))) | -closed_subset(B,A) | topstr_closure(A,B) = B # label(t52_pre_topc) # label(axiom). [clausify(24)].
% 0.43/1.01 Derived: -element(A,powerset(the_carrier(c1))) | -closed_subset(A,c1) | topstr_closure(c1,A) = A. [resolve(41,a,27,a)].
% 0.43/1.01 Derived: -element(A,powerset(the_carrier(c3))) | -closed_subset(A,c3) | topstr_closure(c3,A) = A. [resolve(41,a,28,a)].
% 0.43/1.01 Derived: -element(A,powerset(the_carrier(c4))) | -closed_subset(A,c4) | topstr_closure(c4,A) = A. [resolve(41,a,29,a)].
% 0.43/1.01 42 -top_str(A) | -element(B,powerset(the_carrier(A))) | -open_subset(B,A) | closed_subset(subset_complement(the_carrier(A),B),A) # label(t30_tops_1) # label(axiom). [clausify(22)].
% 0.43/1.01 Derived: -element(A,powerset(the_carrier(c1))) | -open_subset(A,c1) | closed_subset(subset_complement(the_carrier(c1),A),c1). [resolve(42,a,27,a)].
% 0.43/1.01 Derived: -element(A,powerset(the_carrier(c3))) | -open_subset(A,c3) | closed_subset(subset_complement(the_carrier(c3),A),c3). [resolve(42,a,28,a)].
% 0.43/1.01 Derived: -element(A,powerset(the_carrier(c4))) | -open_subset(A,c4) | closed_subset(subset_complement(the_carrier(c4),A),c4). [resolve(42,a,29,a)].
% 0.43/1.01 43 -top_str(A) | -element(B,powerset(the_carrier(A))) | open_subset(B,A) | -closed_subset(subset_complement(the_carrier(A),B),A) # label(t30_tops_1) # label(axiom). [clausify(22)].
% 0.43/1.01 Derived: -element(A,powerset(the_carrier(c1))) | open_subset(A,c1) | -closed_subset(subset_complement(the_carrier(c1),A),c1). [resolve(43,a,27,a)].
% 0.43/1.01 Derived: -element(A,powerset(the_carrier(c3))) | open_subset(A,c3) | -closed_subset(subset_complement(the_carrier(c3),A),c3). [resolve(43,a,28,a)].
% 0.43/1.01 Derived: -element(A,powerset(the_carrier(c4))) | open_subset(A,c4) | -closed_subset(subset_complement(the_carrier(c4),A),c4). [resolve(43,a,29,a)].
% 0.43/1.01 44 -top_str(A) | -element(B,powerset(the_carrier(A))) | -topological_space(A) | topstr_closure(A,B) != B | closed_subset(B,A) # label(t52_pre_topc) # label(axiom). [clausify(24)].
% 0.43/1.01 Derived: -element(A,powerset(the_carrier(c1))) | -topological_space(c1) | topstr_closure(c1,A) != A | closed_subset(A,c1). [resolve(44,a,27,a)].
% 0.43/1.01 Derived: -element(A,powerset(the_carrier(c3))) | -topological_space(c3) | topstr_closure(c3,A) != A | closed_subset(A,c3). [resolve(44,a,28,a)].
% 0.43/1.01 Derived: -element(A,powerset(the_carrier(c4))) | -topological_space(c4) | topstr_closure(c4,A) != A | closed_subset(A,c4). [resolve(44,a,29,a)].
% 0.43/1.01 45 -topological_space(A) | -top_str(A) | -closed_subset(B,A) | -element(B,powerset(the_carrier(A))) | open_subset(subset_complement(the_carrier(A),B),A) # label(fc3_tops_1) # label(axiom). [clausify(14)].
% 0.43/1.01 Derived: -topological_space(c1) | -closed_subset(A,c1) | -element(A,powerset(the_carrier(c1))) | open_subset(subset_complement(the_carrier(c1),A),c1). [resolve(45,b,27,a)].
% 0.43/1.01 Derived: -topological_space(c3) | -closed_subset(A,c3) | -element(A,powerset(the_carrier(c3))) | open_subset(subset_complement(the_carrier(c3),A),c3). [resolve(45,b,28,a)].
% 0.43/1.01 Derived: -topological_space(c4) | -closed_subset(A,c4) | -element(A,powerset(the_carrier(c4))) | open_subset(subset_complement(the_carrier(c4),A),c4). [resolve(45,b,29,a)].
% 0.43/1.01 46 -topological_space(A) | -top_str(A) | -open_subset(B,A) | -element(B,powerset(the_carrier(A))) | closed_subset(subset_complement(the_carrier(A),B),A) # label(fc4_tops_1) # label(axiom). [clausify(15)].
% 0.43/1.01 47 -top_str(A) | -element(B,powerset(the_carrier(A))) | interior(A,B) = subset_complement(the_carrier(A),topstr_closure(A,subset_complement(the_carrier(A),B))) # label(d1_tops_1) # label(axiom). [clausify(1)].
% 0.43/1.01 Derived: -element(A,powerset(the_carrier(c1))) | interior(c1,A) = subset_complement(the_carrier(c1),topstr_closure(c1,subset_complement(the_carrier(c1),A))). [resolve(47,a,27,a)].
% 0.43/1.01 Derived: -element(A,powerset(the_carrier(c3))) | interior(c3,A) = subset_complement(the_carrier(c3),topstr_closure(c3,subset_complement(the_carrier(c3),A))). [resolve(47,a,28,a)].
% 0.43/1.01 Derived: -element(A,powerset(the_carrier(c4))) | interior(c4,A) = subset_complement(the_carrier(c4),topstr_closure(c4,subset_complement(the_carrier(c4),A))). [resolve(47,a,29,a)].
% 0.43/1.01 48 element(A,powerset(B)) | -subset(A,B) # label(t3_subset) # label(axiom). [clausify(23)].
% 0.43/1.01 49 subset(A,A) # label(reflexivity_r1_tarski) # label(axiom). [clausify(21)].
% 0.43/1.01 50 -element(A,powerset(B)) | subset(A,B) # label(t3_subset) # label(axiom). [clausify(23)].
% 0.92/1.19 Derived: element(A,powerset(A)). [resolve(48,b,49,a)].
% 0.92/1.19
% 0.92/1.19 ============================== end predicate elimination =============
% 0.92/1.19
% 0.92/1.19 Auto_denials: (non-Horn, no changes).
% 0.92/1.19
% 0.92/1.19 Term ordering decisions:
% 0.92/1.19 Function symbol KB weights: c1=1. c3=1. c4=1. c5=1. c6=1. subset_complement=1. topstr_closure=1. interior=1. the_carrier=1. powerset=1. f1=1. f2=1. f3=1. f4=1.
% 0.92/1.19
% 0.92/1.19 ============================== end of process initial clauses ========
% 0.92/1.19
% 0.92/1.19 ============================== CLAUSES FOR SEARCH ====================
% 0.92/1.19
% 0.92/1.19 ============================== end of clauses for search =============
% 0.92/1.19
% 0.92/1.19 ============================== SEARCH ================================
% 0.92/1.19
% 0.92/1.19 % Starting search at 0.02 seconds.
% 0.92/1.19
% 0.92/1.19 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 208 (0.00 of 0.15 sec).
% 0.92/1.19
% 0.92/1.19 ============================== PROOF =================================
% 0.92/1.19 % SZS status Theorem
% 0.92/1.19 % SZS output start Refutation
% 0.92/1.19
% 0.92/1.19 % Proof 1 at 0.19 (+ 0.00) seconds.
% 0.92/1.19 % Length of proof is 52.
% 0.92/1.19 % Level of proof is 13.
% 0.92/1.19 % Maximum clause weight is 18.000.
% 0.92/1.19 % Given clauses 636.
% 0.92/1.19
% 0.92/1.19 1 (all A (top_str(A) -> (all B (element(B,powerset(the_carrier(A))) -> interior(A,B) = subset_complement(the_carrier(A),topstr_closure(A,subset_complement(the_carrier(A),B))))))) # label(d1_tops_1) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.19 2 (all A all B (top_str(A) & element(B,powerset(the_carrier(A))) -> element(interior(A,B),powerset(the_carrier(A))))) # label(dt_k1_tops_1) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.19 4 (all A all B (element(B,powerset(A)) -> element(subset_complement(A,B),powerset(A)))) # label(dt_k3_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.19 5 (all A all B (top_str(A) & element(B,powerset(the_carrier(A))) -> element(topstr_closure(A,B),powerset(the_carrier(A))))) # label(dt_k6_pre_topc) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.19 16 (all A all B (topological_space(A) & top_str(A) & element(B,powerset(the_carrier(A))) -> open_subset(interior(A,B),A))) # label(fc6_tops_1) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.19 17 (all A all B (element(B,powerset(A)) -> subset_complement(A,subset_complement(A,B)) = B)) # label(involutiveness_k3_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.19 22 (all A (top_str(A) -> (all B (element(B,powerset(the_carrier(A))) -> (open_subset(B,A) <-> closed_subset(subset_complement(the_carrier(A),B),A)))))) # label(t30_tops_1) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.19 24 (all A (top_str(A) -> (all B (element(B,powerset(the_carrier(A))) -> (closed_subset(B,A) -> topstr_closure(A,B) = B) & (topological_space(A) & topstr_closure(A,B) = B -> closed_subset(B,A)))))) # label(t52_pre_topc) # label(axiom) # label(non_clause). [assumption].
% 0.92/1.19 25 -(all A (topological_space(A) & top_str(A) -> (all B (top_str(B) -> (all C (element(C,powerset(the_carrier(A))) -> (all D (element(D,powerset(the_carrier(B))) -> (open_subset(D,B) -> interior(B,D) = D) & (interior(A,C) = C -> open_subset(C,A)))))))))) # label(t55_tops_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.92/1.19 28 top_str(c3) # label(t55_tops_1) # label(negated_conjecture). [clausify(25)].
% 0.92/1.19 29 top_str(c4) # label(t55_tops_1) # label(negated_conjecture). [clausify(25)].
% 0.92/1.19 37 -top_str(A) | -element(B,powerset(the_carrier(A))) | element(interior(A,B),powerset(the_carrier(A))) # label(dt_k1_tops_1) # label(axiom). [clausify(2)].
% 0.92/1.19 38 -top_str(A) | -element(B,powerset(the_carrier(A))) | element(topstr_closure(A,B),powerset(the_carrier(A))) # label(dt_k6_pre_topc) # label(axiom). [clausify(5)].
% 0.92/1.19 40 -topological_space(A) | -top_str(A) | -element(B,powerset(the_carrier(A))) | open_subset(interior(A,B),A) # label(fc6_tops_1) # label(axiom). [clausify(16)].
% 0.92/1.19 41 -top_str(A) | -element(B,powerset(the_carrier(A))) | -closed_subset(B,A) | topstr_closure(A,B) = B # label(t52_pre_topc) # label(axiom). [clausify(24)].
% 0.92/1.19 42 -top_str(A) | -element(B,powerset(the_carrier(A))) | -open_subset(B,A) | closed_subset(subset_complement(the_carrier(A),B),A) # label(t30_tops_1) # label(axiom). [clausify(22)].
% 0.92/1.19 47 -top_str(A) | -element(B,powerset(the_carrier(A))) | interior(A,B) = subset_complement(the_carrier(A),topstr_closure(A,subset_complement(the_carrier(A),B))) # label(d1_tops_1) # label(axiom). [clausify(1)].
% 0.92/1.19 51 topological_space(c3) # label(t55_tops_1) # label(negated_conjecture). [clausify(25)].
% 0.92/1.19 53 element(c5,powerset(the_carrier(c3))) # label(t55_tops_1) # label(negated_conjecture). [clausify(25)].
% 0.92/1.19 54 element(c6,powerset(the_carrier(c4))) # label(t55_tops_1) # label(negated_conjecture). [clausify(25)].
% 0.92/1.19 55 open_subset(c6,c4) | interior(c3,c5) = c5 # label(t55_tops_1) # label(negated_conjecture). [clausify(25)].
% 0.92/1.19 56 interior(c4,c6) != c6 | -open_subset(c5,c3) # label(t55_tops_1) # label(negated_conjecture). [clausify(25)].
% 0.92/1.19 57 open_subset(c6,c4) | -open_subset(c5,c3) # label(t55_tops_1) # label(negated_conjecture). [clausify(25)].
% 0.92/1.19 58 -element(A,powerset(B)) | element(subset_complement(B,A),powerset(B)) # label(dt_k3_subset_1) # label(axiom). [clausify(4)].
% 0.92/1.19 59 interior(c4,c6) != c6 | interior(c3,c5) = c5 # label(t55_tops_1) # label(negated_conjecture). [clausify(25)].
% 0.92/1.19 60 -element(A,powerset(B)) | subset_complement(B,subset_complement(B,A)) = A # label(involutiveness_k3_subset_1) # label(axiom). [clausify(17)].
% 0.92/1.19 91 -element(A,powerset(the_carrier(c4))) | element(interior(c4,A),powerset(the_carrier(c4))). [resolve(37,a,29,a)].
% 0.92/1.19 94 -element(A,powerset(the_carrier(c4))) | element(topstr_closure(c4,A),powerset(the_carrier(c4))). [resolve(38,a,29,a)].
% 0.92/1.19 100 -topological_space(c3) | -element(A,powerset(the_carrier(c3))) | open_subset(interior(c3,A),c3). [resolve(40,b,28,a)].
% 0.92/1.19 101 -element(A,powerset(the_carrier(c3))) | open_subset(interior(c3,A),c3). [copy(100),unit_del(a,51)].
% 0.92/1.19 105 -element(A,powerset(the_carrier(c4))) | -closed_subset(A,c4) | topstr_closure(c4,A) = A. [resolve(41,a,29,a)].
% 0.92/1.19 108 -element(A,powerset(the_carrier(c4))) | -open_subset(A,c4) | closed_subset(subset_complement(the_carrier(c4),A),c4). [resolve(42,a,29,a)].
% 0.92/1.19 124 -element(A,powerset(the_carrier(c4))) | interior(c4,A) = subset_complement(the_carrier(c4),topstr_closure(c4,subset_complement(the_carrier(c4),A))). [resolve(47,a,29,a)].
% 0.92/1.19 125 -element(A,powerset(the_carrier(c4))) | subset_complement(the_carrier(c4),topstr_closure(c4,subset_complement(the_carrier(c4),A))) = interior(c4,A). [copy(124),flip(b)].
% 0.92/1.19 127 element(subset_complement(the_carrier(c4),c6),powerset(the_carrier(c4))). [resolve(58,a,54,a)].
% 0.92/1.19 130 subset_complement(the_carrier(c4),subset_complement(the_carrier(c4),c6)) = c6. [resolve(60,a,54,a)].
% 0.92/1.19 145 element(interior(c4,c6),powerset(the_carrier(c4))). [resolve(91,a,54,a)].
% 0.92/1.19 167 open_subset(interior(c3,c5),c3). [resolve(101,a,53,a)].
% 0.92/1.19 175 closed_subset(subset_complement(the_carrier(c4),c6),c4) | interior(c3,c5) = c5. [resolve(108,b,55,a),unit_del(a,54)].
% 0.92/1.19 190 subset_complement(the_carrier(c4),topstr_closure(c4,subset_complement(the_carrier(c4),c6))) = interior(c4,c6). [resolve(125,a,54,a)].
% 0.92/1.19 216 element(topstr_closure(c4,subset_complement(the_carrier(c4),c6)),powerset(the_carrier(c4))). [resolve(127,a,94,a)].
% 0.92/1.19 283 subset_complement(the_carrier(c4),subset_complement(the_carrier(c4),interior(c4,c6))) = interior(c4,c6). [resolve(145,a,60,a)].
% 0.92/1.19 481 topstr_closure(c4,subset_complement(the_carrier(c4),c6)) = subset_complement(the_carrier(c4),interior(c4,c6)). [resolve(216,a,60,a),rewrite([190(11)]),flip(a)].
% 0.92/1.19 487 interior(c3,c5) = c5 | subset_complement(the_carrier(c4),interior(c4,c6)) = subset_complement(the_carrier(c4),c6). [resolve(175,a,105,b),rewrite([481(19)]),unit_del(b,127)].
% 0.92/1.19 1703 interior(c3,c5) = c5 | interior(c4,c6) = c6. [para(487(b,1),283(a,1,2)),rewrite([130(12)]),flip(b)].
% 0.92/1.19 1705 interior(c3,c5) = c5. [resolve(1703,b,59,a),merge(b)].
% 0.92/1.19 1708 open_subset(c5,c3). [back_rewrite(167),rewrite([1705(3)])].
% 0.92/1.19 1709 open_subset(c6,c4). [back_unit_del(57),unit_del(b,1708)].
% 0.92/1.19 1710 interior(c4,c6) != c6. [back_unit_del(56),unit_del(b,1708)].
% 0.92/1.19 1711 closed_subset(subset_complement(the_carrier(c4),c6),c4). [resolve(1709,a,108,b),unit_del(a,54)].
% 0.92/1.19 1712 subset_complement(the_carrier(c4),interior(c4,c6)) = subset_complement(the_carrier(c4),c6). [resolve(1711,a,105,b),rewrite([481(14)]),unit_del(a,127)].
% 0.92/1.19 1717 $F. [back_rewrite(283),rewrite([1712(8),130(7)]),flip(a),unit_del(a,1710)].
% 0.92/1.19
% 0.92/1.19 % SZS output end Refutation
% 0.92/1.19 ============================== end of proof ==========================
% 0.92/1.19
% 0.92/1.19 ============================== STATISTICS ============================
% 0.92/1.19
% 0.92/1.19 Given=636. Generated=2483. Kept=1652. proofs=1.
% 0.92/1.19 Usable=529. Sos=838. Demods=372. Limbo=5, Disabled=371. Hints=0.
% 0.92/1.19 Megabytes=2.16.
% 0.92/1.19 User_CPU=0.19, System_CPU=0.00, Wall_clock=0.
% 0.92/1.19
% 0.92/1.19 ============================== end of statistics =====================
% 0.92/1.19
% 0.92/1.19 ============================== end of search =========================
% 0.92/1.19
% 0.92/1.19 THEOREM PROVED
% 0.92/1.19 % SZS status Theorem
% 0.92/1.19
% 0.92/1.19 Exiting with 1 proof.
% 0.92/1.19
% 0.92/1.19 Process 6591 exit (max_proofs) Sun Jun 19 06:36:29 2022
% 0.92/1.19 Prover9 interrupted
%------------------------------------------------------------------------------