TSTP Solution File: SEU361+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SEU361+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n019.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 0.74s 1.07s
% Output : Refutation 0.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SEU361+1 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.35 % Computer : n019.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sun Jun 19 22:47:54 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.74/1.05 ============================== Prover9 ===============================
% 0.74/1.05 Prover9 (32) version 2009-11A, November 2009.
% 0.74/1.05 Process 8620 was started by sandbox2 on n019.cluster.edu,
% 0.74/1.05 Sun Jun 19 22:47:55 2022
% 0.74/1.05 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_8467_n019.cluster.edu".
% 0.74/1.05 ============================== end of head ===========================
% 0.74/1.05
% 0.74/1.05 ============================== INPUT =================================
% 0.74/1.05
% 0.74/1.05 % Reading from file /tmp/Prover9_8467_n019.cluster.edu
% 0.74/1.05
% 0.74/1.05 set(prolog_style_variables).
% 0.74/1.05 set(auto2).
% 0.74/1.05 % set(auto2) -> set(auto).
% 0.74/1.05 % set(auto) -> set(auto_inference).
% 0.74/1.05 % set(auto) -> set(auto_setup).
% 0.74/1.05 % set(auto_setup) -> set(predicate_elim).
% 0.74/1.05 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.74/1.05 % set(auto) -> set(auto_limits).
% 0.74/1.05 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.74/1.05 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.74/1.05 % set(auto) -> set(auto_denials).
% 0.74/1.05 % set(auto) -> set(auto_process).
% 0.74/1.05 % set(auto2) -> assign(new_constants, 1).
% 0.74/1.05 % set(auto2) -> assign(fold_denial_max, 3).
% 0.74/1.05 % set(auto2) -> assign(max_weight, "200.000").
% 0.74/1.05 % set(auto2) -> assign(max_hours, 1).
% 0.74/1.05 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.74/1.05 % set(auto2) -> assign(max_seconds, 0).
% 0.74/1.05 % set(auto2) -> assign(max_minutes, 5).
% 0.74/1.05 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.74/1.05 % set(auto2) -> set(sort_initial_sos).
% 0.74/1.05 % set(auto2) -> assign(sos_limit, -1).
% 0.74/1.05 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.74/1.05 % set(auto2) -> assign(max_megs, 400).
% 0.74/1.05 % set(auto2) -> assign(stats, some).
% 0.74/1.05 % set(auto2) -> clear(echo_input).
% 0.74/1.05 % set(auto2) -> set(quiet).
% 0.74/1.05 % set(auto2) -> clear(print_initial_clauses).
% 0.74/1.05 % set(auto2) -> clear(print_given).
% 0.74/1.05 assign(lrs_ticks,-1).
% 0.74/1.05 assign(sos_limit,10000).
% 0.74/1.05 assign(order,kbo).
% 0.74/1.05 set(lex_order_vars).
% 0.74/1.05 clear(print_given).
% 0.74/1.05
% 0.74/1.05 % formulas(sos). % not echoed (28 formulas)
% 0.74/1.05
% 0.74/1.05 ============================== end of input ==========================
% 0.74/1.05
% 0.74/1.05 % From the command line: assign(max_seconds, 300).
% 0.74/1.05
% 0.74/1.05 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.74/1.05
% 0.74/1.05 % Formulas that are not ordinary clauses:
% 0.74/1.05 1 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.05 2 (all A (empty(A) -> finite(A))) # label(cc1_finset_1) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.05 3 (all A (rel_str(A) -> bottom_of_relstr(A) = join_on_relstr(A,empty_set))) # label(d11_yellow_0) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.05 4 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.05 5 (all A all B (rel_str(A) -> element(join_on_relstr(A,B),the_carrier(A)))) # label(dt_k1_yellow_0) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.05 6 (all A (rel_str(A) -> element(bottom_of_relstr(A),the_carrier(A)))) # label(dt_k3_yellow_0) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.05 7 (all A (rel_str(A) -> one_sorted_str(A))) # label(dt_l1_orders_2) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.05 8 $T # label(dt_l1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.05 9 $T # label(dt_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.05 10 $T # label(dt_u1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.05 11 (exists A rel_str(A)) # label(existence_l1_orders_2) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.05 12 (exists A one_sorted_str(A)) # label(existence_l1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.05 13 (all A exists B element(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.05 14 (all A (-empty_carrier(A) & one_sorted_str(A) -> -empty(the_carrier(A)))) # label(fc1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.05 15 (exists A (-empty(A) & finite(A))) # label(rc1_finset_1) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.05 16 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.05 17 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.05 18 (exists A (one_sorted_str(A) & -empty_carrier(A))) # label(rc3_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.05 19 (all A all B (in(A,B) -> element(A,B))) # label(t1_subset) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.05 20 (all A all B (element(A,B) -> empty(B) | in(A,B))) # label(t2_subset) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.05 21 (all A (antisymmetric_relstr(A) & rel_str(A) -> (all B (element(B,the_carrier(A)) -> (all C ((B = join_on_relstr(A,C) & ex_sup_of_relstr_set(A,C) -> relstr_set_smaller(A,C,B) & (all D (element(D,the_carrier(A)) -> (relstr_set_smaller(A,C,D) -> related(A,B,D))))) & (relstr_set_smaller(A,C,B) & (all D (element(D,the_carrier(A)) -> (relstr_set_smaller(A,C,D) -> related(A,B,D)))) -> B = join_on_relstr(A,C) & ex_sup_of_relstr_set(A,C)))))))) # label(t30_yellow_0) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.05 22 (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(axiom) # label(non_clause). [assumption].
% 0.74/1.05 23 (all A (empty(A) -> A = empty_set)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.05 24 (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].
% 0.74/1.05 25 (all A all B -(in(A,B) & empty(B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.05 26 (all A all B -(empty(A) & A != B & empty(B))) # label(t8_boole) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.05 27 -(all A (-empty_carrier(A) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A) -> (all B (element(B,the_carrier(A)) -> related(A,bottom_of_relstr(A),B))))) # label(t44_yellow_0) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.74/1.05
% 0.74/1.05 ============================== end of process non-clausal formulas ===
% 0.74/1.05
% 0.74/1.05 ============================== PROCESS INITIAL CLAUSES ===============
% 0.74/1.05
% 0.74/1.05 ============================== PREDICATE ELIMINATION =================
% 0.74/1.05 28 -rel_str(A) | one_sorted_str(A) # label(dt_l1_orders_2) # label(axiom). [clausify(7)].
% 0.74/1.05 29 rel_str(c1) # label(existence_l1_orders_2) # label(axiom). [clausify(11)].
% 0.74/1.05 30 rel_str(c7) # label(t44_yellow_0) # label(negated_conjecture). [clausify(27)].
% 0.74/1.05 Derived: one_sorted_str(c1). [resolve(28,a,29,a)].
% 0.74/1.05 Derived: one_sorted_str(c7). [resolve(28,a,30,a)].
% 0.74/1.05 31 -rel_str(A) | element(bottom_of_relstr(A),the_carrier(A)) # label(dt_k3_yellow_0) # label(axiom). [clausify(6)].
% 0.74/1.05 Derived: element(bottom_of_relstr(c1),the_carrier(c1)). [resolve(31,a,29,a)].
% 0.74/1.05 Derived: element(bottom_of_relstr(c7),the_carrier(c7)). [resolve(31,a,30,a)].
% 0.74/1.05 32 -rel_str(A) | join_on_relstr(A,empty_set) = bottom_of_relstr(A) # label(d11_yellow_0) # label(axiom). [clausify(3)].
% 0.74/1.05 Derived: join_on_relstr(c1,empty_set) = bottom_of_relstr(c1). [resolve(32,a,29,a)].
% 0.74/1.05 Derived: join_on_relstr(c7,empty_set) = bottom_of_relstr(c7). [resolve(32,a,30,a)].
% 0.74/1.05 33 -rel_str(A) | element(join_on_relstr(A,B),the_carrier(A)) # label(dt_k1_yellow_0) # label(axiom). [clausify(5)].
% 0.74/1.05 Derived: element(join_on_relstr(c1,A),the_carrier(c1)). [resolve(33,a,29,a)].
% 0.74/1.05 Derived: element(join_on_relstr(c7,A),the_carrier(c7)). [resolve(33,a,30,a)].
% 0.74/1.05 34 -rel_str(A) | -element(B,the_carrier(A)) | relstr_set_smaller(A,empty_set,B) # label(t6_yellow_0) # label(axiom). [clausify(24)].
% 0.74/1.05 Derived: -element(A,the_carrier(c1)) | relstr_set_smaller(c1,empty_set,A). [resolve(34,a,29,a)].
% 0.74/1.05 Derived: -element(A,the_carrier(c7)) | relstr_set_smaller(c7,empty_set,A). [resolve(34,a,30,a)].
% 0.74/1.05 35 -rel_str(A) | -element(B,the_carrier(A)) | relstr_element_smaller(A,empty_set,B) # label(t6_yellow_0) # label(axiom). [clausify(24)].
% 0.74/1.05 Derived: -element(A,the_carrier(c1)) | relstr_element_smaller(c1,empty_set,A). [resolve(35,a,29,a)].
% 0.74/1.05 Derived: -element(A,the_carrier(c7)) | relstr_element_smaller(c7,empty_set,A). [resolve(35,a,30,a)].
% 0.74/1.05 36 empty_carrier(A) | -antisymmetric_relstr(A) | -lower_bounded_relstr(A) | -rel_str(A) | ex_sup_of_relstr_set(A,empty_set) # label(t42_yellow_0) # label(axiom). [clausify(22)].
% 0.74/1.06 Derived: empty_carrier(c1) | -antisymmetric_relstr(c1) | -lower_bounded_relstr(c1) | ex_sup_of_relstr_set(c1,empty_set). [resolve(36,d,29,a)].
% 0.74/1.06 Derived: empty_carrier(c7) | -antisymmetric_relstr(c7) | -lower_bounded_relstr(c7) | ex_sup_of_relstr_set(c7,empty_set). [resolve(36,d,30,a)].
% 0.74/1.06 37 empty_carrier(A) | -antisymmetric_relstr(A) | -lower_bounded_relstr(A) | -rel_str(A) | ex_inf_of_relstr_set(A,the_carrier(A)) # label(t42_yellow_0) # label(axiom). [clausify(22)].
% 0.74/1.06 Derived: empty_carrier(c1) | -antisymmetric_relstr(c1) | -lower_bounded_relstr(c1) | ex_inf_of_relstr_set(c1,the_carrier(c1)). [resolve(37,d,29,a)].
% 0.74/1.06 Derived: empty_carrier(c7) | -antisymmetric_relstr(c7) | -lower_bounded_relstr(c7) | ex_inf_of_relstr_set(c7,the_carrier(c7)). [resolve(37,d,30,a)].
% 0.74/1.06 38 -antisymmetric_relstr(A) | -rel_str(A) | -element(B,the_carrier(A)) | join_on_relstr(A,C) != B | -ex_sup_of_relstr_set(A,C) | relstr_set_smaller(A,C,B) # label(t30_yellow_0) # label(axiom). [clausify(21)].
% 0.74/1.06 Derived: -antisymmetric_relstr(c1) | -element(A,the_carrier(c1)) | join_on_relstr(c1,B) != A | -ex_sup_of_relstr_set(c1,B) | relstr_set_smaller(c1,B,A). [resolve(38,b,29,a)].
% 0.74/1.06 Derived: -antisymmetric_relstr(c7) | -element(A,the_carrier(c7)) | join_on_relstr(c7,B) != A | -ex_sup_of_relstr_set(c7,B) | relstr_set_smaller(c7,B,A). [resolve(38,b,30,a)].
% 0.74/1.06 39 -antisymmetric_relstr(A) | -rel_str(A) | -element(B,the_carrier(A)) | -relstr_set_smaller(A,C,B) | element(f2(A,B,C),the_carrier(A)) | ex_sup_of_relstr_set(A,C) # label(t30_yellow_0) # label(axiom). [clausify(21)].
% 0.74/1.06 Derived: -antisymmetric_relstr(c1) | -element(A,the_carrier(c1)) | -relstr_set_smaller(c1,B,A) | element(f2(c1,A,B),the_carrier(c1)) | ex_sup_of_relstr_set(c1,B). [resolve(39,b,29,a)].
% 0.74/1.06 Derived: -antisymmetric_relstr(c7) | -element(A,the_carrier(c7)) | -relstr_set_smaller(c7,B,A) | element(f2(c7,A,B),the_carrier(c7)) | ex_sup_of_relstr_set(c7,B). [resolve(39,b,30,a)].
% 0.74/1.06 40 -antisymmetric_relstr(A) | -rel_str(A) | -element(B,the_carrier(A)) | -relstr_set_smaller(A,C,B) | relstr_set_smaller(A,C,f2(A,B,C)) | ex_sup_of_relstr_set(A,C) # label(t30_yellow_0) # label(axiom). [clausify(21)].
% 0.74/1.06 Derived: -antisymmetric_relstr(c1) | -element(A,the_carrier(c1)) | -relstr_set_smaller(c1,B,A) | relstr_set_smaller(c1,B,f2(c1,A,B)) | ex_sup_of_relstr_set(c1,B). [resolve(40,b,29,a)].
% 0.74/1.06 Derived: -antisymmetric_relstr(c7) | -element(A,the_carrier(c7)) | -relstr_set_smaller(c7,B,A) | relstr_set_smaller(c7,B,f2(c7,A,B)) | ex_sup_of_relstr_set(c7,B). [resolve(40,b,30,a)].
% 0.74/1.06 41 -antisymmetric_relstr(A) | -rel_str(A) | -element(B,the_carrier(A)) | -relstr_set_smaller(A,C,B) | -related(A,B,f2(A,B,C)) | ex_sup_of_relstr_set(A,C) # label(t30_yellow_0) # label(axiom). [clausify(21)].
% 0.74/1.06 Derived: -antisymmetric_relstr(c1) | -element(A,the_carrier(c1)) | -relstr_set_smaller(c1,B,A) | -related(c1,A,f2(c1,A,B)) | ex_sup_of_relstr_set(c1,B). [resolve(41,b,29,a)].
% 0.74/1.06 Derived: -antisymmetric_relstr(c7) | -element(A,the_carrier(c7)) | -relstr_set_smaller(c7,B,A) | -related(c7,A,f2(c7,A,B)) | ex_sup_of_relstr_set(c7,B). [resolve(41,b,30,a)].
% 0.74/1.06 42 -antisymmetric_relstr(A) | -rel_str(A) | -element(B,the_carrier(A)) | -relstr_set_smaller(A,C,B) | element(f2(A,B,C),the_carrier(A)) | join_on_relstr(A,C) = B # label(t30_yellow_0) # label(axiom). [clausify(21)].
% 0.74/1.06 Derived: -antisymmetric_relstr(c1) | -element(A,the_carrier(c1)) | -relstr_set_smaller(c1,B,A) | element(f2(c1,A,B),the_carrier(c1)) | join_on_relstr(c1,B) = A. [resolve(42,b,29,a)].
% 0.74/1.06 Derived: -antisymmetric_relstr(c7) | -element(A,the_carrier(c7)) | -relstr_set_smaller(c7,B,A) | element(f2(c7,A,B),the_carrier(c7)) | join_on_relstr(c7,B) = A. [resolve(42,b,30,a)].
% 0.74/1.06 43 -antisymmetric_relstr(A) | -rel_str(A) | -element(B,the_carrier(A)) | -relstr_set_smaller(A,C,B) | relstr_set_smaller(A,C,f2(A,B,C)) | join_on_relstr(A,C) = B # label(t30_yellow_0) # label(axiom). [clausify(21)].
% 0.74/1.06 Derived: -antisymmetric_relstr(c1) | -element(A,the_carrier(c1)) | -relstr_set_smaller(c1,B,A) | relstr_set_smaller(c1,B,f2(c1,A,B)) | join_on_relstr(c1,B) = A. [resolve(43,b,29,a)].
% 0.74/1.07 Derived: -antisymmetric_relstr(c7) | -element(A,the_carrier(c7)) | -relstr_set_smaller(c7,B,A) | relstr_set_smaller(c7,B,f2(c7,A,B)) | join_on_relstr(c7,B) = A. [resolve(43,b,30,a)].
% 0.74/1.07 44 -antisymmetric_relstr(A) | -rel_str(A) | -element(B,the_carrier(A)) | -relstr_set_smaller(A,C,B) | -related(A,B,f2(A,B,C)) | join_on_relstr(A,C) = B # label(t30_yellow_0) # label(axiom). [clausify(21)].
% 0.74/1.07 Derived: -antisymmetric_relstr(c1) | -element(A,the_carrier(c1)) | -relstr_set_smaller(c1,B,A) | -related(c1,A,f2(c1,A,B)) | join_on_relstr(c1,B) = A. [resolve(44,b,29,a)].
% 0.74/1.07 Derived: -antisymmetric_relstr(c7) | -element(A,the_carrier(c7)) | -relstr_set_smaller(c7,B,A) | -related(c7,A,f2(c7,A,B)) | join_on_relstr(c7,B) = A. [resolve(44,b,30,a)].
% 0.74/1.07 45 -antisymmetric_relstr(A) | -rel_str(A) | -element(B,the_carrier(A)) | join_on_relstr(A,C) != B | -ex_sup_of_relstr_set(A,C) | -element(D,the_carrier(A)) | -relstr_set_smaller(A,C,D) | related(A,B,D) # label(t30_yellow_0) # label(axiom). [clausify(21)].
% 0.74/1.07 Derived: -antisymmetric_relstr(c1) | -element(A,the_carrier(c1)) | join_on_relstr(c1,B) != A | -ex_sup_of_relstr_set(c1,B) | -element(C,the_carrier(c1)) | -relstr_set_smaller(c1,B,C) | related(c1,A,C). [resolve(45,b,29,a)].
% 0.74/1.07 Derived: -antisymmetric_relstr(c7) | -element(A,the_carrier(c7)) | join_on_relstr(c7,B) != A | -ex_sup_of_relstr_set(c7,B) | -element(C,the_carrier(c7)) | -relstr_set_smaller(c7,B,C) | related(c7,A,C). [resolve(45,b,30,a)].
% 0.74/1.07 46 empty_carrier(A) | -one_sorted_str(A) | -empty(the_carrier(A)) # label(fc1_struct_0) # label(axiom). [clausify(14)].
% 0.74/1.07 47 one_sorted_str(c2) # label(existence_l1_struct_0) # label(axiom). [clausify(12)].
% 0.74/1.07 48 one_sorted_str(c6) # label(rc3_struct_0) # label(axiom). [clausify(18)].
% 0.74/1.07 Derived: empty_carrier(c2) | -empty(the_carrier(c2)). [resolve(46,b,47,a)].
% 0.74/1.07 Derived: empty_carrier(c6) | -empty(the_carrier(c6)). [resolve(46,b,48,a)].
% 0.74/1.07 49 one_sorted_str(c1). [resolve(28,a,29,a)].
% 0.74/1.07 Derived: empty_carrier(c1) | -empty(the_carrier(c1)). [resolve(49,a,46,b)].
% 0.74/1.07 50 one_sorted_str(c7). [resolve(28,a,30,a)].
% 0.74/1.07 Derived: empty_carrier(c7) | -empty(the_carrier(c7)). [resolve(50,a,46,b)].
% 0.74/1.07
% 0.74/1.07 ============================== end predicate elimination =============
% 0.74/1.07
% 0.74/1.07 Auto_denials: (non-Horn, no changes).
% 0.74/1.07
% 0.74/1.07 Term ordering decisions:
% 0.74/1.07 Function symbol KB weights: empty_set=1. c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. c7=1. c8=1. join_on_relstr=1. the_carrier=1. bottom_of_relstr=1. f1=1. f2=1.
% 0.74/1.07
% 0.74/1.07 ============================== end of process initial clauses ========
% 0.74/1.07
% 0.74/1.07 ============================== CLAUSES FOR SEARCH ====================
% 0.74/1.07
% 0.74/1.07 ============================== end of clauses for search =============
% 0.74/1.07
% 0.74/1.07 ============================== SEARCH ================================
% 0.74/1.07
% 0.74/1.07 % Starting search at 0.02 seconds.
% 0.74/1.07
% 0.74/1.07 ============================== PROOF =================================
% 0.74/1.07 % SZS status Theorem
% 0.74/1.07 % SZS output start Refutation
% 0.74/1.07
% 0.74/1.07 % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.74/1.07 % Length of proof is 26.
% 0.74/1.07 % Level of proof is 4.
% 0.74/1.07 % Maximum clause weight is 24.000.
% 0.74/1.07 % Given clauses 43.
% 0.74/1.07
% 0.74/1.07 3 (all A (rel_str(A) -> bottom_of_relstr(A) = join_on_relstr(A,empty_set))) # label(d11_yellow_0) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.07 6 (all A (rel_str(A) -> element(bottom_of_relstr(A),the_carrier(A)))) # label(dt_k3_yellow_0) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.07 21 (all A (antisymmetric_relstr(A) & rel_str(A) -> (all B (element(B,the_carrier(A)) -> (all C ((B = join_on_relstr(A,C) & ex_sup_of_relstr_set(A,C) -> relstr_set_smaller(A,C,B) & (all D (element(D,the_carrier(A)) -> (relstr_set_smaller(A,C,D) -> related(A,B,D))))) & (relstr_set_smaller(A,C,B) & (all D (element(D,the_carrier(A)) -> (relstr_set_smaller(A,C,D) -> related(A,B,D)))) -> B = join_on_relstr(A,C) & ex_sup_of_relstr_set(A,C)))))))) # label(t30_yellow_0) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.07 22 (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(axiom) # label(non_clause). [assumption].
% 0.74/1.07 24 (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].
% 0.74/1.07 27 -(all A (-empty_carrier(A) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A) -> (all B (element(B,the_carrier(A)) -> related(A,bottom_of_relstr(A),B))))) # label(t44_yellow_0) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.74/1.07 30 rel_str(c7) # label(t44_yellow_0) # label(negated_conjecture). [clausify(27)].
% 0.74/1.07 31 -rel_str(A) | element(bottom_of_relstr(A),the_carrier(A)) # label(dt_k3_yellow_0) # label(axiom). [clausify(6)].
% 0.74/1.07 32 -rel_str(A) | join_on_relstr(A,empty_set) = bottom_of_relstr(A) # label(d11_yellow_0) # label(axiom). [clausify(3)].
% 0.74/1.07 34 -rel_str(A) | -element(B,the_carrier(A)) | relstr_set_smaller(A,empty_set,B) # label(t6_yellow_0) # label(axiom). [clausify(24)].
% 0.74/1.07 36 empty_carrier(A) | -antisymmetric_relstr(A) | -lower_bounded_relstr(A) | -rel_str(A) | ex_sup_of_relstr_set(A,empty_set) # label(t42_yellow_0) # label(axiom). [clausify(22)].
% 0.74/1.07 45 -antisymmetric_relstr(A) | -rel_str(A) | -element(B,the_carrier(A)) | join_on_relstr(A,C) != B | -ex_sup_of_relstr_set(A,C) | -element(D,the_carrier(A)) | -relstr_set_smaller(A,C,D) | related(A,B,D) # label(t30_yellow_0) # label(axiom). [clausify(21)].
% 0.74/1.07 53 antisymmetric_relstr(c7) # label(t44_yellow_0) # label(negated_conjecture). [clausify(27)].
% 0.74/1.07 54 lower_bounded_relstr(c7) # label(t44_yellow_0) # label(negated_conjecture). [clausify(27)].
% 0.74/1.07 56 element(c8,the_carrier(c7)) # label(t44_yellow_0) # label(negated_conjecture). [clausify(27)].
% 0.74/1.07 60 -empty_carrier(c7) # label(t44_yellow_0) # label(negated_conjecture). [clausify(27)].
% 0.74/1.07 62 -related(c7,bottom_of_relstr(c7),c8) # label(t44_yellow_0) # label(negated_conjecture). [clausify(27)].
% 0.74/1.07 69 element(bottom_of_relstr(c7),the_carrier(c7)). [resolve(31,a,30,a)].
% 0.74/1.07 71 join_on_relstr(c7,empty_set) = bottom_of_relstr(c7). [resolve(32,a,30,a)].
% 0.74/1.07 75 -element(A,the_carrier(c7)) | relstr_set_smaller(c7,empty_set,A). [resolve(34,a,30,a)].
% 0.74/1.07 77 empty_carrier(c7) | -antisymmetric_relstr(c7) | -lower_bounded_relstr(c7) | ex_sup_of_relstr_set(c7,empty_set). [resolve(36,d,30,a)].
% 0.74/1.07 78 ex_sup_of_relstr_set(c7,empty_set). [copy(77),unit_del(a,60),unit_del(b,53),unit_del(c,54)].
% 0.74/1.07 101 -antisymmetric_relstr(c7) | -element(A,the_carrier(c7)) | join_on_relstr(c7,B) != A | -ex_sup_of_relstr_set(c7,B) | -element(C,the_carrier(c7)) | -relstr_set_smaller(c7,B,C) | related(c7,A,C). [resolve(45,b,30,a)].
% 0.74/1.07 102 -element(A,the_carrier(c7)) | join_on_relstr(c7,B) != A | -ex_sup_of_relstr_set(c7,B) | -element(C,the_carrier(c7)) | -relstr_set_smaller(c7,B,C) | related(c7,A,C). [copy(101),unit_del(a,53)].
% 0.74/1.07 126 relstr_set_smaller(c7,empty_set,c8). [resolve(75,a,56,a)].
% 0.74/1.07 128 $F. [ur(102,a,69,a,b,71,a,c,78,a,d,56,a,f,62,a),unit_del(a,126)].
% 0.74/1.07
% 0.74/1.07 % SZS output end Refutation
% 0.74/1.07 ============================== end of proof ==========================
% 0.74/1.07
% 0.74/1.07 ============================== STATISTICS ============================
% 0.74/1.07
% 0.74/1.07 Given=43. Generated=78. Kept=66. proofs=1.
% 0.74/1.07 Usable=42. Sos=22. Demods=3. Limbo=0, Disabled=78. Hints=0.
% 0.74/1.07 Megabytes=0.15.
% 0.74/1.07 User_CPU=0.02, System_CPU=0.00, Wall_clock=0.
% 0.74/1.07
% 0.74/1.07 ============================== end of statistics =====================
% 0.74/1.07
% 0.74/1.07 ============================== end of search =========================
% 0.74/1.07
% 0.74/1.07 THEOREM PROVED
% 0.74/1.07 % SZS status Theorem
% 0.74/1.07
% 0.74/1.07 Exiting with 1 proof.
% 0.74/1.07
% 0.74/1.07 Process 8620 exit (max_proofs) Sun Jun 19 22:47:55 2022
% 0.74/1.07 Prover9 interrupted
%------------------------------------------------------------------------------