TSTP Solution File: SEU323+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SEU323+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n026.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 0.73s 1.02s
% Output : Refutation 0.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SEU323+1 : TPTP v8.1.0. Released v3.3.0.
% 0.10/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n026.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 20 12:34:56 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.69/1.00 ============================== Prover9 ===============================
% 0.69/1.00 Prover9 (32) version 2009-11A, November 2009.
% 0.69/1.00 Process 21458 was started by sandbox2 on n026.cluster.edu,
% 0.69/1.00 Mon Jun 20 12:34:57 2022
% 0.69/1.00 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_21189_n026.cluster.edu".
% 0.69/1.00 ============================== end of head ===========================
% 0.69/1.00
% 0.69/1.00 ============================== INPUT =================================
% 0.69/1.00
% 0.69/1.00 % Reading from file /tmp/Prover9_21189_n026.cluster.edu
% 0.69/1.00
% 0.69/1.00 set(prolog_style_variables).
% 0.69/1.00 set(auto2).
% 0.69/1.00 % set(auto2) -> set(auto).
% 0.69/1.00 % set(auto) -> set(auto_inference).
% 0.69/1.00 % set(auto) -> set(auto_setup).
% 0.69/1.00 % set(auto_setup) -> set(predicate_elim).
% 0.69/1.00 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.69/1.00 % set(auto) -> set(auto_limits).
% 0.69/1.00 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.69/1.00 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.69/1.00 % set(auto) -> set(auto_denials).
% 0.69/1.00 % set(auto) -> set(auto_process).
% 0.69/1.00 % set(auto2) -> assign(new_constants, 1).
% 0.69/1.00 % set(auto2) -> assign(fold_denial_max, 3).
% 0.69/1.00 % set(auto2) -> assign(max_weight, "200.000").
% 0.69/1.00 % set(auto2) -> assign(max_hours, 1).
% 0.69/1.00 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.69/1.00 % set(auto2) -> assign(max_seconds, 0).
% 0.69/1.00 % set(auto2) -> assign(max_minutes, 5).
% 0.69/1.00 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.69/1.00 % set(auto2) -> set(sort_initial_sos).
% 0.69/1.00 % set(auto2) -> assign(sos_limit, -1).
% 0.69/1.00 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.69/1.00 % set(auto2) -> assign(max_megs, 400).
% 0.69/1.00 % set(auto2) -> assign(stats, some).
% 0.69/1.00 % set(auto2) -> clear(echo_input).
% 0.69/1.00 % set(auto2) -> set(quiet).
% 0.69/1.00 % set(auto2) -> clear(print_initial_clauses).
% 0.69/1.00 % set(auto2) -> clear(print_given).
% 0.69/1.00 assign(lrs_ticks,-1).
% 0.69/1.00 assign(sos_limit,10000).
% 0.69/1.00 assign(order,kbo).
% 0.69/1.00 set(lex_order_vars).
% 0.69/1.00 clear(print_given).
% 0.69/1.00
% 0.69/1.00 % formulas(sos). % not echoed (21 formulas)
% 0.69/1.00
% 0.69/1.00 ============================== end of input ==========================
% 0.69/1.00
% 0.69/1.00 % From the command line: assign(max_seconds, 300).
% 0.69/1.00
% 0.69/1.00 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.69/1.00
% 0.69/1.00 % Formulas that are not ordinary clauses:
% 0.69/1.00 1 (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].
% 0.69/1.00 2 (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].
% 0.69/1.00 3 (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].
% 0.69/1.00 4 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.69/1.00 5 (exists A one_sorted_str(A)) # label(existence_l1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.69/1.00 6 (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].
% 0.69/1.00 7 (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].
% 0.69/1.00 8 $T # label(dt_l1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.69/1.00 9 (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].
% 0.69/1.00 10 (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].
% 0.69/1.00 11 (exists A top_str(A)) # label(existence_l1_pre_topc) # label(axiom) # label(non_clause). [assumption].
% 0.69/1.00 12 (all A exists B element(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.69/1.00 13 (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].
% 0.69/1.00 14 $T # label(dt_k1_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.69/1.00 15 (all A (top_str(A) -> one_sorted_str(A))) # label(dt_l1_pre_topc) # label(axiom) # label(non_clause). [assumption].
% 0.69/1.00 16 $T # label(dt_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.69/1.00 17 $T # label(dt_u1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.69/1.00 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].
% 0.69/1.00 19 (all A all B (element(A,powerset(B)) <-> subset(A,B))) # label(t3_subset) # label(axiom) # label(non_clause). [assumption].
% 0.69/1.00 20 (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].
% 0.69/1.00 21 -(all A (topological_space(A) & top_str(A) -> (all B (element(B,powerset(the_carrier(A))) -> open_subset(interior(A,B),A))))) # label(t51_tops_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.69/1.00
% 0.69/1.00 ============================== end of process non-clausal formulas ===
% 0.69/1.00
% 0.69/1.00 ============================== PROCESS INITIAL CLAUSES ===============
% 0.69/1.00
% 0.69/1.00 ============================== PREDICATE ELIMINATION =================
% 0.69/1.00 22 -topological_space(A) | -top_str(A) | closed_subset(f1(A),A) # label(rc6_pre_topc) # label(axiom). [clausify(2)].
% 0.69/1.00 23 top_str(c2) # label(existence_l1_pre_topc) # label(axiom). [clausify(11)].
% 0.69/1.00 24 top_str(c3) # label(t51_tops_1) # label(negated_conjecture). [clausify(21)].
% 0.69/1.00 Derived: -topological_space(c2) | closed_subset(f1(c2),c2). [resolve(22,b,23,a)].
% 0.69/1.00 Derived: -topological_space(c3) | closed_subset(f1(c3),c3). [resolve(22,b,24,a)].
% 0.69/1.00 25 -topological_space(A) | -top_str(A) | open_subset(f3(A),A) # label(rc1_tops_1) # label(axiom). [clausify(18)].
% 0.69/1.00 Derived: -topological_space(c2) | open_subset(f3(c2),c2). [resolve(25,b,23,a)].
% 0.69/1.00 Derived: -topological_space(c3) | open_subset(f3(c3),c3). [resolve(25,b,24,a)].
% 0.69/1.00 26 -topological_space(A) | -top_str(A) | element(f1(A),powerset(the_carrier(A))) # label(rc6_pre_topc) # label(axiom). [clausify(2)].
% 0.69/1.00 Derived: -topological_space(c2) | element(f1(c2),powerset(the_carrier(c2))). [resolve(26,b,23,a)].
% 0.69/1.00 Derived: -topological_space(c3) | element(f1(c3),powerset(the_carrier(c3))). [resolve(26,b,24,a)].
% 0.69/1.00 27 -topological_space(A) | -top_str(A) | element(f3(A),powerset(the_carrier(A))) # label(rc1_tops_1) # label(axiom). [clausify(18)].
% 0.69/1.00 Derived: -topological_space(c2) | element(f3(c2),powerset(the_carrier(c2))). [resolve(27,b,23,a)].
% 0.69/1.00 Derived: -topological_space(c3) | element(f3(c3),powerset(the_carrier(c3))). [resolve(27,b,24,a)].
% 0.69/1.00 28 -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(7)].
% 0.69/1.00 Derived: -element(A,powerset(the_carrier(c2))) | element(topstr_closure(c2,A),powerset(the_carrier(c2))). [resolve(28,a,23,a)].
% 0.69/1.00 Derived: -element(A,powerset(the_carrier(c3))) | element(topstr_closure(c3,A),powerset(the_carrier(c3))). [resolve(28,a,24,a)].
% 0.69/1.00 29 -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(9)].
% 0.69/1.00 Derived: -topological_space(c2) | -element(A,powerset(the_carrier(c2))) | closed_subset(topstr_closure(c2,A),c2). [resolve(29,b,23,a)].
% 0.69/1.00 Derived: -topological_space(c3) | -element(A,powerset(the_carrier(c3))) | closed_subset(topstr_closure(c3,A),c3). [resolve(29,b,24,a)].
% 0.69/1.00 30 -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(13)].
% 0.69/1.00 Derived: -element(A,powerset(the_carrier(c2))) | element(interior(c2,A),powerset(the_carrier(c2))). [resolve(30,a,23,a)].
% 0.69/1.00 Derived: -element(A,powerset(the_carrier(c3))) | element(interior(c3,A),powerset(the_carrier(c3))). [resolve(30,a,24,a)].
% 0.73/1.02 31 -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(1)].
% 0.73/1.02 Derived: -topological_space(c2) | -closed_subset(A,c2) | -element(A,powerset(the_carrier(c2))) | open_subset(subset_complement(the_carrier(c2),A),c2). [resolve(31,b,23,a)].
% 0.73/1.02 Derived: -topological_space(c3) | -closed_subset(A,c3) | -element(A,powerset(the_carrier(c3))) | open_subset(subset_complement(the_carrier(c3),A),c3). [resolve(31,b,24,a)].
% 0.73/1.02 32 -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(10)].
% 0.73/1.02 Derived: -topological_space(c2) | -open_subset(A,c2) | -element(A,powerset(the_carrier(c2))) | closed_subset(subset_complement(the_carrier(c2),A),c2). [resolve(32,b,23,a)].
% 0.73/1.02 Derived: -topological_space(c3) | -open_subset(A,c3) | -element(A,powerset(the_carrier(c3))) | closed_subset(subset_complement(the_carrier(c3),A),c3). [resolve(32,b,24,a)].
% 0.73/1.02 33 -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(20)].
% 0.73/1.02 Derived: -element(A,powerset(the_carrier(c2))) | interior(c2,A) = subset_complement(the_carrier(c2),topstr_closure(c2,subset_complement(the_carrier(c2),A))). [resolve(33,a,23,a)].
% 0.73/1.02 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(33,a,24,a)].
% 0.73/1.02 34 element(A,powerset(B)) | -subset(A,B) # label(t3_subset) # label(axiom). [clausify(19)].
% 0.73/1.02 35 subset(A,A) # label(reflexivity_r1_tarski) # label(axiom). [clausify(4)].
% 0.73/1.02 36 -element(A,powerset(B)) | subset(A,B) # label(t3_subset) # label(axiom). [clausify(19)].
% 0.73/1.02 Derived: element(A,powerset(A)). [resolve(34,b,35,a)].
% 0.73/1.02
% 0.73/1.02 ============================== end predicate elimination =============
% 0.73/1.02
% 0.73/1.02 Auto_denials:
% 0.73/1.02 % copying label t51_tops_1 to answer in negative clause
% 0.73/1.02
% 0.73/1.02 Term ordering decisions:
% 0.73/1.02 Function symbol KB weights: c2=1. c3=1. c4=1. subset_complement=1. topstr_closure=1. interior=1. the_carrier=1. powerset=1. f1=1. f2=1. f3=1.
% 0.73/1.02
% 0.73/1.02 ============================== end of process initial clauses ========
% 0.73/1.02
% 0.73/1.02 ============================== CLAUSES FOR SEARCH ====================
% 0.73/1.02
% 0.73/1.02 ============================== end of clauses for search =============
% 0.73/1.02
% 0.73/1.02 ============================== SEARCH ================================
% 0.73/1.02
% 0.73/1.02 % Starting search at 0.01 seconds.
% 0.73/1.02
% 0.73/1.02 ============================== PROOF =================================
% 0.73/1.02 % SZS status Theorem
% 0.73/1.02 % SZS output start Refutation
% 0.73/1.02
% 0.73/1.02 % Proof 1 at 0.02 (+ 0.00) seconds: t51_tops_1.
% 0.73/1.02 % Length of proof is 26.
% 0.73/1.02 % Level of proof is 6.
% 0.73/1.02 % Maximum clause weight is 18.000.
% 0.73/1.02 % Given clauses 91.
% 0.73/1.02
% 0.73/1.02 1 (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].
% 0.73/1.02 6 (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].
% 0.73/1.02 7 (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].
% 0.73/1.02 9 (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].
% 0.73/1.02 20 (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].
% 0.73/1.02 21 -(all A (topological_space(A) & top_str(A) -> (all B (element(B,powerset(the_carrier(A))) -> open_subset(interior(A,B),A))))) # label(t51_tops_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.73/1.02 24 top_str(c3) # label(t51_tops_1) # label(negated_conjecture). [clausify(21)].
% 0.73/1.02 28 -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(7)].
% 0.73/1.02 29 -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(9)].
% 0.73/1.02 31 -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(1)].
% 0.73/1.02 33 -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(20)].
% 0.73/1.02 37 topological_space(c3) # label(t51_tops_1) # label(negated_conjecture). [clausify(21)].
% 0.73/1.02 39 element(c4,powerset(the_carrier(c3))) # label(t51_tops_1) # label(negated_conjecture). [clausify(21)].
% 0.73/1.02 40 -open_subset(interior(c3,c4),c3) # label(t51_tops_1) # label(negated_conjecture) # answer(t51_tops_1). [clausify(21)].
% 0.73/1.02 41 -element(A,powerset(B)) | element(subset_complement(B,A),powerset(B)) # label(dt_k3_subset_1) # label(axiom). [clausify(6)].
% 0.73/1.02 52 -element(A,powerset(the_carrier(c3))) | element(topstr_closure(c3,A),powerset(the_carrier(c3))). [resolve(28,a,24,a)].
% 0.73/1.02 54 -topological_space(c3) | -element(A,powerset(the_carrier(c3))) | closed_subset(topstr_closure(c3,A),c3). [resolve(29,b,24,a)].
% 0.73/1.02 58 -topological_space(c3) | -closed_subset(A,c3) | -element(A,powerset(the_carrier(c3))) | open_subset(subset_complement(the_carrier(c3),A),c3). [resolve(31,b,24,a)].
% 0.73/1.02 63 -element(A,powerset(the_carrier(c3))) | interior(c3,A) = subset_complement(the_carrier(c3),topstr_closure(c3,subset_complement(the_carrier(c3),A))). [resolve(33,a,24,a)].
% 0.73/1.02 64 -element(A,powerset(the_carrier(c3))) | subset_complement(the_carrier(c3),topstr_closure(c3,subset_complement(the_carrier(c3),A))) = interior(c3,A). [copy(63),flip(b)].
% 0.73/1.02 66 element(subset_complement(the_carrier(c3),c4),powerset(the_carrier(c3))). [hyper(41,a,39,a)].
% 0.73/1.02 83 subset_complement(the_carrier(c3),topstr_closure(c3,subset_complement(the_carrier(c3),c4))) = interior(c3,c4). [hyper(64,a,39,a)].
% 0.73/1.02 96 closed_subset(topstr_closure(c3,subset_complement(the_carrier(c3),c4)),c3). [hyper(54,a,37,a,b,66,a)].
% 0.73/1.02 97 element(topstr_closure(c3,subset_complement(the_carrier(c3),c4)),powerset(the_carrier(c3))). [hyper(52,a,66,a)].
% 0.73/1.02 242 open_subset(interior(c3,c4),c3). [hyper(58,a,37,a,b,96,a,c,97,a),rewrite([83(9)])].
% 0.73/1.02 243 $F # answer(t51_tops_1). [resolve(242,a,40,a)].
% 0.73/1.02
% 0.73/1.02 % SZS output end Refutation
% 0.73/1.02 ============================== end of proof ==========================
% 0.73/1.02
% 0.73/1.02 ============================== STATISTICS ============================
% 0.73/1.02
% 0.73/1.02 Given=91. Generated=235. Kept=204. proofs=1.
% 0.73/1.02 Usable=87. Sos=111. Demods=57. Limbo=1, Disabled=48. Hints=0.
% 0.73/1.02 Megabytes=0.27.
% 0.73/1.02 User_CPU=0.03, System_CPU=0.00, Wall_clock=0.
% 0.73/1.02
% 0.73/1.02 ============================== end of statistics =====================
% 0.73/1.02
% 0.73/1.02 ============================== end of search =========================
% 0.73/1.02
% 0.73/1.02 THEOREM PROVED
% 0.73/1.02 % SZS status Theorem
% 0.73/1.02
% 0.73/1.02 Exiting with 1 proof.
% 0.73/1.02
% 0.73/1.02 Process 21458 exit (max_proofs) Mon Jun 20 12:34:57 2022
% 0.73/1.02 Prover9 interrupted
%------------------------------------------------------------------------------