TSTP Solution File: SEU360+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SEU360+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n024.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 13:31:15 EDT 2022
% Result : Theorem 0.72s 1.13s
% Output : Refutation 0.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU360+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n024.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 : 600
% 0.12/0.34 % DateTime : Mon Jun 20 13:18:17 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.43/0.98 ============================== Prover9 ===============================
% 0.43/0.98 Prover9 (32) version 2009-11A, November 2009.
% 0.43/0.98 Process 31476 was started by sandbox on n024.cluster.edu,
% 0.43/0.98 Mon Jun 20 13:18:17 2022
% 0.43/0.98 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_31323_n024.cluster.edu".
% 0.43/0.98 ============================== end of head ===========================
% 0.43/0.98
% 0.43/0.98 ============================== INPUT =================================
% 0.43/0.98
% 0.43/0.98 % Reading from file /tmp/Prover9_31323_n024.cluster.edu
% 0.43/0.98
% 0.43/0.98 set(prolog_style_variables).
% 0.43/0.98 set(auto2).
% 0.43/0.98 % set(auto2) -> set(auto).
% 0.43/0.98 % set(auto) -> set(auto_inference).
% 0.43/0.98 % set(auto) -> set(auto_setup).
% 0.43/0.98 % set(auto_setup) -> set(predicate_elim).
% 0.43/0.98 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.43/0.98 % set(auto) -> set(auto_limits).
% 0.43/0.98 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.43/0.98 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.43/0.98 % set(auto) -> set(auto_denials).
% 0.43/0.98 % set(auto) -> set(auto_process).
% 0.43/0.98 % set(auto2) -> assign(new_constants, 1).
% 0.43/0.98 % set(auto2) -> assign(fold_denial_max, 3).
% 0.43/0.98 % set(auto2) -> assign(max_weight, "200.000").
% 0.43/0.98 % set(auto2) -> assign(max_hours, 1).
% 0.43/0.98 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.43/0.98 % set(auto2) -> assign(max_seconds, 0).
% 0.43/0.98 % set(auto2) -> assign(max_minutes, 5).
% 0.43/0.98 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.43/0.98 % set(auto2) -> set(sort_initial_sos).
% 0.43/0.98 % set(auto2) -> assign(sos_limit, -1).
% 0.43/0.98 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.43/0.98 % set(auto2) -> assign(max_megs, 400).
% 0.43/0.98 % set(auto2) -> assign(stats, some).
% 0.43/0.98 % set(auto2) -> clear(echo_input).
% 0.43/0.98 % set(auto2) -> set(quiet).
% 0.43/0.98 % set(auto2) -> clear(print_initial_clauses).
% 0.43/0.98 % set(auto2) -> clear(print_given).
% 0.43/0.98 assign(lrs_ticks,-1).
% 0.43/0.98 assign(sos_limit,10000).
% 0.43/0.98 assign(order,kbo).
% 0.43/0.98 set(lex_order_vars).
% 0.43/0.98 clear(print_given).
% 0.43/0.98
% 0.43/0.98 % formulas(sos). % not echoed (27 formulas)
% 0.43/0.98
% 0.43/0.98 ============================== end of input ==========================
% 0.43/0.98
% 0.43/0.98 % From the command line: assign(max_seconds, 300).
% 0.43/0.98
% 0.43/0.98 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.43/0.98
% 0.43/0.98 % Formulas that are not ordinary clauses:
% 0.43/0.98 1 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.98 2 (all A (empty(A) -> finite(A))) # label(cc1_finset_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.98 3 (all A (rel_str(A) -> (lower_bounded_relstr(A) <-> (exists B (element(B,the_carrier(A)) & relstr_element_smaller(A,the_carrier(A),B)))))) # label(d4_yellow_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.98 4 (all A (rel_str(A) -> (all B all C (element(C,the_carrier(A)) -> (relstr_element_smaller(A,B,C) <-> (all D (element(D,the_carrier(A)) -> (in(D,B) -> related(A,C,D))))))))) # label(d8_lattice3) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.98 5 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.98 6 (all A (rel_str(A) -> one_sorted_str(A))) # label(dt_l1_orders_2) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.98 7 $T # label(dt_l1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.98 8 $T # label(dt_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.98 9 $T # label(dt_u1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.98 10 (exists A rel_str(A)) # label(existence_l1_orders_2) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.98 11 (exists A one_sorted_str(A)) # label(existence_l1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.98 12 (all A exists B element(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.98 13 (all A (-empty_carrier(A) & one_sorted_str(A) -> -empty(the_carrier(A)))) # label(fc1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.98 14 (exists A (-empty(A) & finite(A))) # label(rc1_finset_1) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.98 15 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.98 16 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.98 17 (exists A (one_sorted_str(A) & -empty_carrier(A))) # label(rc3_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 18 (all A (antisymmetric_relstr(A) & rel_str(A) -> (all B (ex_sup_of_relstr_set(A,B) <-> (exists C (element(C,the_carrier(A)) & relstr_set_smaller(A,B,C) & (all D (element(D,the_carrier(A)) -> (relstr_set_smaller(A,B,D) -> related(A,C,D)))))))))) # label(t15_yellow_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 19 (all A (antisymmetric_relstr(A) & rel_str(A) -> (all B (ex_inf_of_relstr_set(A,B) <-> (exists C (element(C,the_carrier(A)) & relstr_element_smaller(A,B,C) & (all D (element(D,the_carrier(A)) -> (relstr_element_smaller(A,B,D) -> related(A,D,C)))))))))) # label(t16_yellow_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 20 (all A all B (in(A,B) -> element(A,B))) # label(t1_subset) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 21 (all A all B (element(A,B) -> empty(B) | in(A,B))) # label(t2_subset) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 22 (all A (empty(A) -> A = empty_set)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 23 (all A (rel_str(A) -> (all B (element(B,the_carrier(A)) -> relstr_set_smaller(A,empty_set,B) & relstr_element_smaller(A,empty_set,B))))) # label(t6_yellow_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 24 (all A all B -(in(A,B) & empty(B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 25 (all A all B -(empty(A) & A != B & empty(B))) # label(t8_boole) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 26 -(all A (-empty_carrier(A) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A) -> ex_sup_of_relstr_set(A,empty_set) & ex_inf_of_relstr_set(A,the_carrier(A)))) # label(t42_yellow_0) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.43/0.99
% 0.43/0.99 ============================== end of process non-clausal formulas ===
% 0.43/0.99
% 0.43/0.99 ============================== PROCESS INITIAL CLAUSES ===============
% 0.43/0.99
% 0.43/0.99 ============================== PREDICATE ELIMINATION =================
% 0.43/0.99 27 -rel_str(A) | one_sorted_str(A) # label(dt_l1_orders_2) # label(axiom). [clausify(6)].
% 0.43/0.99 28 rel_str(c1) # label(existence_l1_orders_2) # label(axiom). [clausify(10)].
% 0.43/0.99 29 rel_str(c7) # label(t42_yellow_0) # label(negated_conjecture). [clausify(26)].
% 0.43/0.99 Derived: one_sorted_str(c1). [resolve(27,a,28,a)].
% 0.43/0.99 Derived: one_sorted_str(c7). [resolve(27,a,29,a)].
% 0.43/0.99 30 -rel_str(A) | -lower_bounded_relstr(A) | element(f1(A),the_carrier(A)) # label(d4_yellow_0) # label(axiom). [clausify(3)].
% 0.43/0.99 Derived: -lower_bounded_relstr(c1) | element(f1(c1),the_carrier(c1)). [resolve(30,a,28,a)].
% 0.43/0.99 Derived: -lower_bounded_relstr(c7) | element(f1(c7),the_carrier(c7)). [resolve(30,a,29,a)].
% 0.43/0.99 31 -rel_str(A) | -lower_bounded_relstr(A) | relstr_element_smaller(A,the_carrier(A),f1(A)) # label(d4_yellow_0) # label(axiom). [clausify(3)].
% 0.43/0.99 Derived: -lower_bounded_relstr(c1) | relstr_element_smaller(c1,the_carrier(c1),f1(c1)). [resolve(31,a,28,a)].
% 0.43/0.99 Derived: -lower_bounded_relstr(c7) | relstr_element_smaller(c7,the_carrier(c7),f1(c7)). [resolve(31,a,29,a)].
% 0.43/0.99 32 -rel_str(A) | -element(B,the_carrier(A)) | relstr_set_smaller(A,empty_set,B) # label(t6_yellow_0) # label(axiom). [clausify(23)].
% 0.43/0.99 Derived: -element(A,the_carrier(c1)) | relstr_set_smaller(c1,empty_set,A). [resolve(32,a,28,a)].
% 0.43/0.99 Derived: -element(A,the_carrier(c7)) | relstr_set_smaller(c7,empty_set,A). [resolve(32,a,29,a)].
% 0.43/0.99 33 -rel_str(A) | -element(B,the_carrier(A)) | relstr_element_smaller(A,empty_set,B) # label(t6_yellow_0) # label(axiom). [clausify(23)].
% 0.43/0.99 Derived: -element(A,the_carrier(c1)) | relstr_element_smaller(c1,empty_set,A). [resolve(33,a,28,a)].
% 0.43/0.99 Derived: -element(A,the_carrier(c7)) | relstr_element_smaller(c7,empty_set,A). [resolve(33,a,29,a)].
% 0.43/0.99 34 -rel_str(A) | lower_bounded_relstr(A) | -element(B,the_carrier(A)) | -relstr_element_smaller(A,the_carrier(A),B) # label(d4_yellow_0) # label(axiom). [clausify(3)].
% 0.43/0.99 Derived: lower_bounded_relstr(c1) | -element(A,the_carrier(c1)) | -relstr_element_smaller(c1,the_carrier(c1),A). [resolve(34,a,28,a)].
% 0.43/0.99 Derived: lower_bounded_relstr(c7) | -element(A,the_carrier(c7)) | -relstr_element_smaller(c7,the_carrier(c7),A). [resolve(34,a,29,a)].
% 0.43/0.99 35 -antisymmetric_relstr(A) | -rel_str(A) | -ex_sup_of_relstr_set(A,B) | element(f4(A,B),the_carrier(A)) # label(t15_yellow_0) # label(axiom). [clausify(18)].
% 0.43/0.99 Derived: -antisymmetric_relstr(c1) | -ex_sup_of_relstr_set(c1,A) | element(f4(c1,A),the_carrier(c1)). [resolve(35,b,28,a)].
% 0.43/0.99 Derived: -antisymmetric_relstr(c7) | -ex_sup_of_relstr_set(c7,A) | element(f4(c7,A),the_carrier(c7)). [resolve(35,b,29,a)].
% 0.43/0.99 36 -antisymmetric_relstr(A) | -rel_str(A) | -ex_sup_of_relstr_set(A,B) | relstr_set_smaller(A,B,f4(A,B)) # label(t15_yellow_0) # label(axiom). [clausify(18)].
% 0.43/0.99 Derived: -antisymmetric_relstr(c1) | -ex_sup_of_relstr_set(c1,A) | relstr_set_smaller(c1,A,f4(c1,A)). [resolve(36,b,28,a)].
% 0.43/0.99 Derived: -antisymmetric_relstr(c7) | -ex_sup_of_relstr_set(c7,A) | relstr_set_smaller(c7,A,f4(c7,A)). [resolve(36,b,29,a)].
% 0.43/0.99 37 -antisymmetric_relstr(A) | -rel_str(A) | -ex_inf_of_relstr_set(A,B) | element(f6(A,B),the_carrier(A)) # label(t16_yellow_0) # label(axiom). [clausify(19)].
% 0.43/0.99 Derived: -antisymmetric_relstr(c1) | -ex_inf_of_relstr_set(c1,A) | element(f6(c1,A),the_carrier(c1)). [resolve(37,b,28,a)].
% 0.43/0.99 Derived: -antisymmetric_relstr(c7) | -ex_inf_of_relstr_set(c7,A) | element(f6(c7,A),the_carrier(c7)). [resolve(37,b,29,a)].
% 0.43/0.99 38 -antisymmetric_relstr(A) | -rel_str(A) | -ex_inf_of_relstr_set(A,B) | relstr_element_smaller(A,B,f6(A,B)) # label(t16_yellow_0) # label(axiom). [clausify(19)].
% 0.43/0.99 Derived: -antisymmetric_relstr(c1) | -ex_inf_of_relstr_set(c1,A) | relstr_element_smaller(c1,A,f6(c1,A)). [resolve(38,b,28,a)].
% 0.43/0.99 Derived: -antisymmetric_relstr(c7) | -ex_inf_of_relstr_set(c7,A) | relstr_element_smaller(c7,A,f6(c7,A)). [resolve(38,b,29,a)].
% 0.43/0.99 39 -rel_str(A) | -element(B,the_carrier(A)) | relstr_element_smaller(A,C,B) | in(f2(A,C,B),C) # label(d8_lattice3) # label(axiom). [clausify(4)].
% 0.43/0.99 Derived: -element(A,the_carrier(c1)) | relstr_element_smaller(c1,B,A) | in(f2(c1,B,A),B). [resolve(39,a,28,a)].
% 0.43/0.99 Derived: -element(A,the_carrier(c7)) | relstr_element_smaller(c7,B,A) | in(f2(c7,B,A),B). [resolve(39,a,29,a)].
% 0.43/0.99 40 -rel_str(A) | -element(B,the_carrier(A)) | relstr_element_smaller(A,C,B) | element(f2(A,C,B),the_carrier(A)) # label(d8_lattice3) # label(axiom). [clausify(4)].
% 0.43/0.99 Derived: -element(A,the_carrier(c1)) | relstr_element_smaller(c1,B,A) | element(f2(c1,B,A),the_carrier(c1)). [resolve(40,a,28,a)].
% 0.43/0.99 Derived: -element(A,the_carrier(c7)) | relstr_element_smaller(c7,B,A) | element(f2(c7,B,A),the_carrier(c7)). [resolve(40,a,29,a)].
% 0.43/0.99 41 -rel_str(A) | -element(B,the_carrier(A)) | relstr_element_smaller(A,C,B) | -related(A,B,f2(A,C,B)) # label(d8_lattice3) # label(axiom). [clausify(4)].
% 0.43/0.99 Derived: -element(A,the_carrier(c1)) | relstr_element_smaller(c1,B,A) | -related(c1,A,f2(c1,B,A)). [resolve(41,a,28,a)].
% 0.43/0.99 Derived: -element(A,the_carrier(c7)) | relstr_element_smaller(c7,B,A) | -related(c7,A,f2(c7,B,A)). [resolve(41,a,29,a)].
% 0.43/0.99 42 -rel_str(A) | -element(B,the_carrier(A)) | -relstr_element_smaller(A,C,B) | -element(D,the_carrier(A)) | -in(D,C) | related(A,B,D) # label(d8_lattice3) # label(axiom). [clausify(4)].
% 0.43/0.99 Derived: -element(A,the_carrier(c1)) | -relstr_element_smaller(c1,B,A) | -element(C,the_carrier(c1)) | -in(C,B) | related(c1,A,C). [resolve(42,a,28,a)].
% 0.43/0.99 Derived: -element(A,the_carrier(c7)) | -relstr_element_smaller(c7,B,A) | -element(C,the_carrier(c7)) | -in(C,B) | related(c7,A,C). [resolve(42,a,29,a)].
% 0.43/0.99 43 -antisymmetric_relstr(A) | -rel_str(A) | -ex_sup_of_relstr_set(A,B) | -element(C,the_carrier(A)) | -relstr_set_smaller(A,B,C) | related(A,f4(A,B),C) # label(t15_yellow_0) # label(axiom). [clausify(18)].
% 0.43/0.99 Derived: -antisymmetric_relstr(c1) | -ex_sup_of_relstr_set(c1,A) | -element(B,the_carrier(c1)) | -relstr_set_smaller(c1,A,B) | related(c1,f4(c1,A),B). [resolve(43,b,28,a)].
% 0.43/0.99 Derived: -antisymmetric_relstr(c7) | -ex_sup_of_relstr_set(c7,A) | -element(B,the_carrier(c7)) | -relstr_set_smaller(c7,A,B) | related(c7,f4(c7,A),B). [resolve(43,b,29,a)].
% 0.43/0.99 44 -antisymmetric_relstr(A) | -rel_str(A) | -ex_inf_of_relstr_set(A,B) | -element(C,the_carrier(A)) | -relstr_element_smaller(A,B,C) | related(A,C,f6(A,B)) # label(t16_yellow_0) # label(axiom). [clausify(19)].
% 0.43/0.99 Derived: -antisymmetric_relstr(c1) | -ex_inf_of_relstr_set(c1,A) | -element(B,the_carrier(c1)) | -relstr_element_smaller(c1,A,B) | related(c1,B,f6(c1,A)). [resolve(44,b,28,a)].
% 0.43/0.99 Derived: -antisymmetric_relstr(c7) | -ex_inf_of_relstr_set(c7,A) | -element(B,the_carrier(c7)) | -relstr_element_smaller(c7,A,B) | related(c7,B,f6(c7,A)). [resolve(44,b,29,a)].
% 0.43/0.99 45 -antisymmetric_relstr(A) | -rel_str(A) | ex_sup_of_relstr_set(A,B) | -element(C,the_carrier(A)) | -relstr_set_smaller(A,B,C) | element(f5(A,B,C),the_carrier(A)) # label(t15_yellow_0) # label(axiom). [clausify(18)].
% 0.43/0.99 Derived: -antisymmetric_relstr(c1) | ex_sup_of_relstr_set(c1,A) | -element(B,the_carrier(c1)) | -relstr_set_smaller(c1,A,B) | element(f5(c1,A,B),the_carrier(c1)). [resolve(45,b,28,a)].
% 0.43/0.99 Derived: -antisymmetric_relstr(c7) | ex_sup_of_relstr_set(c7,A) | -element(B,the_carrier(c7)) | -relstr_set_smaller(c7,A,B) | element(f5(c7,A,B),the_carrier(c7)). [resolve(45,b,29,a)].
% 0.43/0.99 46 -antisymmetric_relstr(A) | -rel_str(A) | ex_sup_of_relstr_set(A,B) | -element(C,the_carrier(A)) | -relstr_set_smaller(A,B,C) | relstr_set_smaller(A,B,f5(A,B,C)) # label(t15_yellow_0) # label(axiom). [clausify(18)].
% 0.43/0.99 Derived: -antisymmetric_relstr(c1) | ex_sup_of_relstr_set(c1,A) | -element(B,the_carrier(c1)) | -relstr_set_smaller(c1,A,B) | relstr_set_smaller(c1,A,f5(c1,A,B)). [resolve(46,b,28,a)].
% 0.43/0.99 Derived: -antisymmetric_relstr(c7) | ex_sup_of_relstr_set(c7,A) | -element(B,the_carrier(c7)) | -relstr_set_smaller(c7,A,B) | relstr_set_smaller(c7,A,f5(c7,A,B)). [resolve(46,b,29,a)].
% 0.43/0.99 47 -antisymmetric_relstr(A) | -rel_str(A) | ex_sup_of_relstr_set(A,B) | -element(C,the_carrier(A)) | -relstr_set_smaller(A,B,C) | -related(A,C,f5(A,B,C)) # label(t15_yellow_0) # label(axiom). [clausify(18)].
% 0.43/0.99 Derived: -antisymmetric_relstr(c1) | ex_sup_of_relstr_set(c1,A) | -element(B,the_carrier(c1)) | -relstr_set_smaller(c1,A,B) | -related(c1,B,f5(c1,A,B)). [resolve(47,b,28,a)].
% 0.43/0.99 Derived: -antisymmetric_relstr(c7) | ex_sup_of_relstr_set(c7,A) | -element(B,the_carrier(c7)) | -relstr_set_smaller(c7,A,B) | -related(c7,B,f5(c7,A,B)). [resolve(47,b,29,a)].
% 0.43/0.99 48 -antisymmetric_relstr(A) | -rel_str(A) | ex_inf_of_relstr_set(A,B) | -element(C,the_carrier(A)) | -relstr_element_smaller(A,B,C) | element(f7(A,B,C),the_carrier(A)) # label(t16_yellow_0) # label(axiom). [clausify(19)].
% 0.43/0.99 Derived: -antisymmetric_relstr(c1) | ex_inf_of_relstr_set(c1,A) | -element(B,the_carrier(c1)) | -relstr_element_smaller(c1,A,B) | element(f7(c1,A,B),the_carrier(c1)). [resolve(48,b,28,a)].
% 0.43/0.99 Derived: -antisymmetric_relstr(c7) | ex_inf_of_relstr_set(c7,A) | -element(B,the_carrier(c7)) | -relstr_element_smaller(c7,A,B) | element(f7(c7,A,B),the_carrier(c7)). [resolve(48,b,29,a)].
% 0.43/0.99 49 -antisymmetric_relstr(A) | -rel_str(A) | ex_inf_of_relstr_set(A,B) | -element(C,the_carrier(A)) | -relstr_element_smaller(A,B,C) | relstr_element_smaller(A,B,f7(A,B,C)) # label(t16_yellow_0) # label(axiom). [clausify(19)].
% 0.43/0.99 Derived: -antisymmetric_relstr(c1) | ex_inf_of_relstr_set(c1,A) | -element(B,the_carrier(c1)) | -relstr_element_smaller(c1,A,B) | relstr_element_smaller(c1,A,f7(c1,A,B)). [resolve(49,b,28,a)].
% 0.43/0.99 Derived: -antisymmetric_relstr(c7) | ex_inf_of_relstr_set(c7,A) | -element(B,the_carrier(c7)) | -relstr_element_smaller(c7,A,B) | relstr_element_smaller(c7,A,f7(c7,A,B)). [resolve(49,b,29,a)].
% 0.43/0.99 50 -antisymmetric_relstr(A) | -rel_str(A) | ex_inf_of_relstr_set(A,B) | -element(C,the_carrier(A)) | -relstr_element_smaller(A,B,C) | -related(A,f7(A,B,C),C) # label(t16_yellow_0) # label(axiom). [clausify(19)].
% 0.43/0.99 Derived: -antisymmetric_relstr(c1) | ex_inf_of_relstr_set(c1,A) | -element(B,the_carrier(c1)) | -relstr_element_smaller(c1,A,B) | -related(c1,f7(c1,A,B),B). [resolve(50,b,28,a)].
% 0.43/0.99 Derived: -antisymmetric_relstr(c7) | ex_inf_of_relstr_set(c7,A) | -element(B,the_carrier(c7)) | -relstr_element_smaller(c7,A,B) | -related(c7,f7(c7,A,B),B). [resolve(50,b,29,a)].
% 0.43/0.99 51 empty_carrier(A) | -one_sorted_str(A) | -empty(the_carrier(A)) # label(fc1_struct_0) # label(axiom). [clausify(13)].
% 0.43/0.99 52 one_sorted_str(c2) # label(existence_l1_struct_0) # label(axiom). [clausify(11)].
% 0.72/1.13 53 one_sorted_str(c6) # label(rc3_struct_0) # label(axiom). [clausify(17)].
% 0.72/1.13 Derived: empty_carrier(c2) | -empty(the_carrier(c2)). [resolve(51,b,52,a)].
% 0.72/1.13 Derived: empty_carrier(c6) | -empty(the_carrier(c6)). [resolve(51,b,53,a)].
% 0.72/1.13 54 one_sorted_str(c1). [resolve(27,a,28,a)].
% 0.72/1.13 Derived: empty_carrier(c1) | -empty(the_carrier(c1)). [resolve(54,a,51,b)].
% 0.72/1.13 55 one_sorted_str(c7). [resolve(27,a,29,a)].
% 0.72/1.13 Derived: empty_carrier(c7) | -empty(the_carrier(c7)). [resolve(55,a,51,b)].
% 0.72/1.13
% 0.72/1.13 ============================== end predicate elimination =============
% 0.72/1.13
% 0.72/1.13 Auto_denials: (non-Horn, no changes).
% 0.72/1.13
% 0.72/1.13 Term ordering decisions:
% 0.72/1.13 Function symbol KB weights: empty_set=1. c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. c7=1. f4=1. f6=1. the_carrier=1. f1=1. f3=1. f2=1. f5=1. f7=1.
% 0.72/1.13
% 0.72/1.13 ============================== end of process initial clauses ========
% 0.72/1.13
% 0.72/1.13 ============================== CLAUSES FOR SEARCH ====================
% 0.72/1.13
% 0.72/1.13 ============================== end of clauses for search =============
% 0.72/1.13
% 0.72/1.13 ============================== SEARCH ================================
% 0.72/1.13
% 0.72/1.13 % Starting search at 0.02 seconds.
% 0.72/1.13
% 0.72/1.13 ============================== PROOF =================================
% 0.72/1.13 % SZS status Theorem
% 0.72/1.13 % SZS output start Refutation
% 0.72/1.13
% 0.72/1.13 % Proof 1 at 0.16 (+ 0.01) seconds.
% 0.72/1.13 % Length of proof is 66.
% 0.72/1.13 % Level of proof is 17.
% 0.72/1.13 % Maximum clause weight is 30.000.
% 0.72/1.13 % Given clauses 443.
% 0.72/1.13
% 0.72/1.13 3 (all A (rel_str(A) -> (lower_bounded_relstr(A) <-> (exists B (element(B,the_carrier(A)) & relstr_element_smaller(A,the_carrier(A),B)))))) # label(d4_yellow_0) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.13 4 (all A (rel_str(A) -> (all B all C (element(C,the_carrier(A)) -> (relstr_element_smaller(A,B,C) <-> (all D (element(D,the_carrier(A)) -> (in(D,B) -> related(A,C,D))))))))) # label(d8_lattice3) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.13 6 (all A (rel_str(A) -> one_sorted_str(A))) # label(dt_l1_orders_2) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.13 13 (all A (-empty_carrier(A) & one_sorted_str(A) -> -empty(the_carrier(A)))) # label(fc1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.13 18 (all A (antisymmetric_relstr(A) & rel_str(A) -> (all B (ex_sup_of_relstr_set(A,B) <-> (exists C (element(C,the_carrier(A)) & relstr_set_smaller(A,B,C) & (all D (element(D,the_carrier(A)) -> (relstr_set_smaller(A,B,D) -> related(A,C,D)))))))))) # label(t15_yellow_0) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.13 19 (all A (antisymmetric_relstr(A) & rel_str(A) -> (all B (ex_inf_of_relstr_set(A,B) <-> (exists C (element(C,the_carrier(A)) & relstr_element_smaller(A,B,C) & (all D (element(D,the_carrier(A)) -> (relstr_element_smaller(A,B,D) -> related(A,D,C)))))))))) # label(t16_yellow_0) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.13 21 (all A all B (element(A,B) -> empty(B) | in(A,B))) # label(t2_subset) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.13 23 (all A (rel_str(A) -> (all B (element(B,the_carrier(A)) -> relstr_set_smaller(A,empty_set,B) & relstr_element_smaller(A,empty_set,B))))) # label(t6_yellow_0) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.13 26 -(all A (-empty_carrier(A) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A) -> ex_sup_of_relstr_set(A,empty_set) & ex_inf_of_relstr_set(A,the_carrier(A)))) # label(t42_yellow_0) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.72/1.13 27 -rel_str(A) | one_sorted_str(A) # label(dt_l1_orders_2) # label(axiom). [clausify(6)].
% 0.72/1.13 29 rel_str(c7) # label(t42_yellow_0) # label(negated_conjecture). [clausify(26)].
% 0.72/1.13 30 -rel_str(A) | -lower_bounded_relstr(A) | element(f1(A),the_carrier(A)) # label(d4_yellow_0) # label(axiom). [clausify(3)].
% 0.72/1.13 31 -rel_str(A) | -lower_bounded_relstr(A) | relstr_element_smaller(A,the_carrier(A),f1(A)) # label(d4_yellow_0) # label(axiom). [clausify(3)].
% 0.72/1.13 32 -rel_str(A) | -element(B,the_carrier(A)) | relstr_set_smaller(A,empty_set,B) # label(t6_yellow_0) # label(axiom). [clausify(23)].
% 0.72/1.13 42 -rel_str(A) | -element(B,the_carrier(A)) | -relstr_element_smaller(A,C,B) | -element(D,the_carrier(A)) | -in(D,C) | related(A,B,D) # label(d8_lattice3) # label(axiom). [clausify(4)].
% 0.72/1.13 45 -antisymmetric_relstr(A) | -rel_str(A) | ex_sup_of_relstr_set(A,B) | -element(C,the_carrier(A)) | -relstr_set_smaller(A,B,C) | element(f5(A,B,C),the_carrier(A)) # label(t15_yellow_0) # label(axiom). [clausify(18)].
% 0.72/1.13 47 -antisymmetric_relstr(A) | -rel_str(A) | ex_sup_of_relstr_set(A,B) | -element(C,the_carrier(A)) | -relstr_set_smaller(A,B,C) | -related(A,C,f5(A,B,C)) # label(t15_yellow_0) # label(axiom). [clausify(18)].
% 0.72/1.13 48 -antisymmetric_relstr(A) | -rel_str(A) | ex_inf_of_relstr_set(A,B) | -element(C,the_carrier(A)) | -relstr_element_smaller(A,B,C) | element(f7(A,B,C),the_carrier(A)) # label(t16_yellow_0) # label(axiom). [clausify(19)].
% 0.72/1.13 49 -antisymmetric_relstr(A) | -rel_str(A) | ex_inf_of_relstr_set(A,B) | -element(C,the_carrier(A)) | -relstr_element_smaller(A,B,C) | relstr_element_smaller(A,B,f7(A,B,C)) # label(t16_yellow_0) # label(axiom). [clausify(19)].
% 0.72/1.13 50 -antisymmetric_relstr(A) | -rel_str(A) | ex_inf_of_relstr_set(A,B) | -element(C,the_carrier(A)) | -relstr_element_smaller(A,B,C) | -related(A,f7(A,B,C),C) # label(t16_yellow_0) # label(axiom). [clausify(19)].
% 0.72/1.13 51 empty_carrier(A) | -one_sorted_str(A) | -empty(the_carrier(A)) # label(fc1_struct_0) # label(axiom). [clausify(13)].
% 0.72/1.13 55 one_sorted_str(c7). [resolve(27,a,29,a)].
% 0.72/1.13 58 antisymmetric_relstr(c7) # label(t42_yellow_0) # label(negated_conjecture). [clausify(26)].
% 0.72/1.13 59 lower_bounded_relstr(c7) # label(t42_yellow_0) # label(negated_conjecture). [clausify(26)].
% 0.72/1.13 64 -empty_carrier(c7) # label(t42_yellow_0) # label(negated_conjecture). [clausify(26)].
% 0.72/1.13 67 -ex_sup_of_relstr_set(c7,empty_set) | -ex_inf_of_relstr_set(c7,the_carrier(c7)) # label(t42_yellow_0) # label(negated_conjecture). [clausify(26)].
% 0.72/1.13 71 -element(A,B) | empty(B) | in(A,B) # label(t2_subset) # label(axiom). [clausify(21)].
% 0.72/1.13 73 -lower_bounded_relstr(c7) | element(f1(c7),the_carrier(c7)). [resolve(30,a,29,a)].
% 0.72/1.13 74 element(f1(c7),the_carrier(c7)). [copy(73),unit_del(a,59)].
% 0.72/1.13 76 -lower_bounded_relstr(c7) | relstr_element_smaller(c7,the_carrier(c7),f1(c7)). [resolve(31,a,29,a)].
% 0.72/1.13 77 relstr_element_smaller(c7,the_carrier(c7),f1(c7)). [copy(76),unit_del(a,59)].
% 0.72/1.13 79 -element(A,the_carrier(c7)) | relstr_set_smaller(c7,empty_set,A). [resolve(32,a,29,a)].
% 0.72/1.13 102 -element(A,the_carrier(c7)) | -relstr_element_smaller(c7,B,A) | -element(C,the_carrier(c7)) | -in(C,B) | related(c7,A,C). [resolve(42,a,29,a)].
% 0.72/1.13 110 -antisymmetric_relstr(c7) | ex_sup_of_relstr_set(c7,A) | -element(B,the_carrier(c7)) | -relstr_set_smaller(c7,A,B) | element(f5(c7,A,B),the_carrier(c7)). [resolve(45,b,29,a)].
% 0.72/1.13 111 ex_sup_of_relstr_set(c7,A) | -element(B,the_carrier(c7)) | -relstr_set_smaller(c7,A,B) | element(f5(c7,A,B),the_carrier(c7)). [copy(110),unit_del(a,58)].
% 0.72/1.13 116 -antisymmetric_relstr(c7) | ex_sup_of_relstr_set(c7,A) | -element(B,the_carrier(c7)) | -relstr_set_smaller(c7,A,B) | -related(c7,B,f5(c7,A,B)). [resolve(47,b,29,a)].
% 0.72/1.13 117 ex_sup_of_relstr_set(c7,A) | -element(B,the_carrier(c7)) | -relstr_set_smaller(c7,A,B) | -related(c7,B,f5(c7,A,B)). [copy(116),unit_del(a,58)].
% 0.72/1.13 119 -antisymmetric_relstr(c7) | ex_inf_of_relstr_set(c7,A) | -element(B,the_carrier(c7)) | -relstr_element_smaller(c7,A,B) | element(f7(c7,A,B),the_carrier(c7)). [resolve(48,b,29,a)].
% 0.72/1.13 120 ex_inf_of_relstr_set(c7,A) | -element(B,the_carrier(c7)) | -relstr_element_smaller(c7,A,B) | element(f7(c7,A,B),the_carrier(c7)). [copy(119),unit_del(a,58)].
% 0.72/1.13 122 -antisymmetric_relstr(c7) | ex_inf_of_relstr_set(c7,A) | -element(B,the_carrier(c7)) | -relstr_element_smaller(c7,A,B) | relstr_element_smaller(c7,A,f7(c7,A,B)). [resolve(49,b,29,a)].
% 0.72/1.13 123 ex_inf_of_relstr_set(c7,A) | -element(B,the_carrier(c7)) | -relstr_element_smaller(c7,A,B) | relstr_element_smaller(c7,A,f7(c7,A,B)). [copy(122),unit_del(a,58)].
% 0.72/1.13 125 -antisymmetric_relstr(c7) | ex_inf_of_relstr_set(c7,A) | -element(B,the_carrier(c7)) | -relstr_element_smaller(c7,A,B) | -related(c7,f7(c7,A,B),B). [resolve(50,b,29,a)].
% 0.72/1.13 126 ex_inf_of_relstr_set(c7,A) | -element(B,the_carrier(c7)) | -relstr_element_smaller(c7,A,B) | -related(c7,f7(c7,A,B),B). [copy(125),unit_del(a,58)].
% 0.72/1.13 131 empty_carrier(c7) | -empty(the_carrier(c7)). [resolve(55,a,51,b)].
% 0.72/1.13 132 -empty(the_carrier(c7)). [copy(131),unit_del(a,64)].
% 0.72/1.13 140 in(f1(c7),the_carrier(c7)). [resolve(74,a,71,a),unit_del(a,132)].
% 0.72/1.13 142 relstr_set_smaller(c7,empty_set,f1(c7)). [resolve(79,a,74,a)].
% 0.72/1.13 153 -element(A,the_carrier(c7)) | -in(A,the_carrier(c7)) | related(c7,f1(c7),A). [resolve(102,b,77,a),unit_del(a,74)].
% 0.72/1.13 155 ex_inf_of_relstr_set(c7,the_carrier(c7)) | element(f7(c7,the_carrier(c7),f1(c7)),the_carrier(c7)). [resolve(120,c,77,a),unit_del(b,74)].
% 0.72/1.13 156 ex_inf_of_relstr_set(c7,the_carrier(c7)) | relstr_element_smaller(c7,the_carrier(c7),f7(c7,the_carrier(c7),f1(c7))). [resolve(123,c,77,a),unit_del(b,74)].
% 0.72/1.13 164 ex_sup_of_relstr_set(c7,empty_set) | element(f5(c7,empty_set,f1(c7)),the_carrier(c7)). [resolve(142,a,111,c),unit_del(b,74)].
% 0.72/1.13 201 element(f5(c7,empty_set,f1(c7)),the_carrier(c7)) | -ex_inf_of_relstr_set(c7,the_carrier(c7)). [resolve(164,a,67,a)].
% 0.72/1.13 255 element(f7(c7,the_carrier(c7),f1(c7)),the_carrier(c7)) | element(f5(c7,empty_set,f1(c7)),the_carrier(c7)). [resolve(155,a,201,b)].
% 0.72/1.13 263 ex_inf_of_relstr_set(c7,the_carrier(c7)) | -element(f7(c7,the_carrier(c7),f1(c7)),the_carrier(c7)) | -element(A,the_carrier(c7)) | -in(A,the_carrier(c7)) | related(c7,f7(c7,the_carrier(c7),f1(c7)),A). [resolve(156,b,102,b)].
% 0.72/1.13 720 ex_inf_of_relstr_set(c7,the_carrier(c7)) | -element(f7(c7,the_carrier(c7),f1(c7)),the_carrier(c7)) | related(c7,f7(c7,the_carrier(c7),f1(c7)),f1(c7)). [resolve(263,d,140,a),unit_del(c,74)].
% 0.72/1.13 909 ex_inf_of_relstr_set(c7,the_carrier(c7)) | related(c7,f7(c7,the_carrier(c7),f1(c7)),f1(c7)) | element(f5(c7,empty_set,f1(c7)),the_carrier(c7)). [resolve(720,b,255,a)].
% 0.72/1.13 1081 ex_inf_of_relstr_set(c7,the_carrier(c7)) | element(f5(c7,empty_set,f1(c7)),the_carrier(c7)). [resolve(909,b,126,d),merge(c),unit_del(c,74),unit_del(d,77)].
% 0.72/1.13 1087 element(f5(c7,empty_set,f1(c7)),the_carrier(c7)). [resolve(1081,a,201,b),merge(b)].
% 0.72/1.13 1099 in(f5(c7,empty_set,f1(c7)),the_carrier(c7)). [resolve(1087,a,71,a),unit_del(a,132)].
% 0.72/1.13 1114 related(c7,f1(c7),f5(c7,empty_set,f1(c7))). [resolve(1099,a,153,b),unit_del(a,1087)].
% 0.72/1.13 1121 ex_sup_of_relstr_set(c7,empty_set). [resolve(1114,a,117,d),unit_del(b,74),unit_del(c,142)].
% 0.72/1.13 1138 -ex_inf_of_relstr_set(c7,the_carrier(c7)). [back_unit_del(67),unit_del(a,1121)].
% 0.72/1.13 1150 -element(f7(c7,the_carrier(c7),f1(c7)),the_carrier(c7)) | related(c7,f7(c7,the_carrier(c7),f1(c7)),f1(c7)). [back_unit_del(720),unit_del(a,1138)].
% 0.72/1.13 1169 element(f7(c7,the_carrier(c7),f1(c7)),the_carrier(c7)). [back_unit_del(155),unit_del(a,1138)].
% 0.72/1.13 1184 related(c7,f7(c7,the_carrier(c7),f1(c7)),f1(c7)). [back_unit_del(1150),unit_del(a,1169)].
% 0.72/1.13 1215 $F. [ur(126,a,1138,a,b,74,a,c,77,a),unit_del(a,1184)].
% 0.72/1.13
% 0.72/1.13 % SZS output end Refutation
% 0.72/1.13 ============================== end of proof ==========================
% 0.72/1.13
% 0.72/1.13 ============================== STATISTICS ============================
% 0.72/1.13
% 0.72/1.13 Given=443. Generated=1612. Kept=1143. proofs=1.
% 0.72/1.13 Usable=310. Sos=313. Demods=1. Limbo=2, Disabled=611. Hints=0.
% 0.72/1.13 Megabytes=1.78.
% 0.72/1.13 User_CPU=0.16, System_CPU=0.01, Wall_clock=1.
% 0.72/1.13
% 0.72/1.13 ============================== end of statistics =====================
% 0.72/1.13
% 0.72/1.13 ============================== end of search =========================
% 0.72/1.13
% 0.72/1.13 THEOREM PROVED
% 0.72/1.13 % SZS status Theorem
% 0.72/1.13
% 0.72/1.13 Exiting with 1 proof.
% 0.72/1.13
% 0.72/1.13 Process 31476 exit (max_proofs) Mon Jun 20 13:18:18 2022
% 0.72/1.13 Prover9 interrupted
%------------------------------------------------------------------------------