TSTP Solution File: SEU339+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SEU339+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n028.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 13:31:05 EDT 2022
% Result : Theorem 0.96s 1.22s
% Output : Refutation 0.96s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU339+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.34 % Computer : n028.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Mon Jun 20 03:34:31 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.46/1.03 ============================== Prover9 ===============================
% 0.46/1.03 Prover9 (32) version 2009-11A, November 2009.
% 0.46/1.03 Process 11973 was started by sandbox on n028.cluster.edu,
% 0.46/1.03 Mon Jun 20 03:34:32 2022
% 0.46/1.03 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_11820_n028.cluster.edu".
% 0.46/1.03 ============================== end of head ===========================
% 0.46/1.03
% 0.46/1.03 ============================== INPUT =================================
% 0.46/1.03
% 0.46/1.03 % Reading from file /tmp/Prover9_11820_n028.cluster.edu
% 0.46/1.03
% 0.46/1.03 set(prolog_style_variables).
% 0.46/1.03 set(auto2).
% 0.46/1.03 % set(auto2) -> set(auto).
% 0.46/1.03 % set(auto) -> set(auto_inference).
% 0.46/1.03 % set(auto) -> set(auto_setup).
% 0.46/1.03 % set(auto_setup) -> set(predicate_elim).
% 0.46/1.03 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.46/1.03 % set(auto) -> set(auto_limits).
% 0.46/1.03 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.46/1.03 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.46/1.03 % set(auto) -> set(auto_denials).
% 0.46/1.03 % set(auto) -> set(auto_process).
% 0.46/1.03 % set(auto2) -> assign(new_constants, 1).
% 0.46/1.03 % set(auto2) -> assign(fold_denial_max, 3).
% 0.46/1.03 % set(auto2) -> assign(max_weight, "200.000").
% 0.46/1.03 % set(auto2) -> assign(max_hours, 1).
% 0.46/1.03 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.46/1.03 % set(auto2) -> assign(max_seconds, 0).
% 0.46/1.03 % set(auto2) -> assign(max_minutes, 5).
% 0.46/1.03 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.46/1.03 % set(auto2) -> set(sort_initial_sos).
% 0.46/1.03 % set(auto2) -> assign(sos_limit, -1).
% 0.46/1.03 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.46/1.03 % set(auto2) -> assign(max_megs, 400).
% 0.46/1.03 % set(auto2) -> assign(stats, some).
% 0.46/1.03 % set(auto2) -> clear(echo_input).
% 0.46/1.03 % set(auto2) -> set(quiet).
% 0.46/1.03 % set(auto2) -> clear(print_initial_clauses).
% 0.46/1.03 % set(auto2) -> clear(print_given).
% 0.46/1.03 assign(lrs_ticks,-1).
% 0.46/1.03 assign(sos_limit,10000).
% 0.46/1.03 assign(order,kbo).
% 0.46/1.03 set(lex_order_vars).
% 0.46/1.03 clear(print_given).
% 0.46/1.03
% 0.46/1.03 % formulas(sos). % not echoed (46 formulas)
% 0.46/1.03
% 0.46/1.03 ============================== end of input ==========================
% 0.46/1.03
% 0.46/1.03 % From the command line: assign(max_seconds, 300).
% 0.46/1.03
% 0.46/1.03 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.46/1.03
% 0.46/1.03 % Formulas that are not ordinary clauses:
% 0.46/1.03 1 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.03 2 (all A all B all C (element(C,powerset(cartesian_product2(A,B))) -> relation(C))) # label(cc1_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.03 3 (all A all B unordered_pair(A,B) = unordered_pair(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.03 4 (all A (relation(A) -> (all B (is_antisymmetric_in(A,B) <-> (all C all D (in(C,B) & in(D,B) & in(ordered_pair(C,D),A) & in(ordered_pair(D,C),A) -> C = D)))))) # label(d4_relat_2) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.03 5 (all A all B ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A))) # label(d5_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.03 6 (all A (rel_str(A) -> (antisymmetric_relstr(A) <-> is_antisymmetric_in(the_InternalRel(A),the_carrier(A))))) # label(d6_orders_2) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.03 7 (all A (rel_str(A) -> (all B (element(B,the_carrier(A)) -> (all C (element(C,the_carrier(A)) -> (related(A,B,C) <-> in(ordered_pair(B,C),the_InternalRel(A))))))))) # label(d9_orders_2) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.03 8 $T # label(dt_k1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.03 9 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.03 10 $T # label(dt_k1_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.03 11 $T # label(dt_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.03 12 $T # label(dt_k2_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.03 13 $T # label(dt_k4_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.03 14 (all A (rel_str(A) -> one_sorted_str(A))) # label(dt_l1_orders_2) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.03 15 $T # label(dt_l1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.03 16 $T # label(dt_m1_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.03 17 $T # label(dt_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.03 18 (all A all B all C (relation_of2_as_subset(C,A,B) -> element(C,powerset(cartesian_product2(A,B))))) # label(dt_m2_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.03 19 (all A (rel_str(A) -> relation_of2_as_subset(the_InternalRel(A),the_carrier(A),the_carrier(A)))) # label(dt_u1_orders_2) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.03 20 $T # label(dt_u1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.03 21 (exists A rel_str(A)) # label(existence_l1_orders_2) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.03 22 (exists A one_sorted_str(A)) # label(existence_l1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.03 23 (all A all B exists C relation_of2(C,A,B)) # label(existence_m1_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.03 24 (all A exists B element(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.03 25 (all A all B exists C relation_of2_as_subset(C,A,B)) # label(existence_m2_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.03 26 (all A -empty(powerset(A))) # label(fc1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.03 27 (all A -empty(singleton(A))) # label(fc2_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.03 28 (all A all B -empty(unordered_pair(A,B))) # label(fc3_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.03 29 (all A all B (-empty(A) & -empty(B) -> -empty(cartesian_product2(A,B)))) # label(fc4_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.03 30 (all A (-empty(A) -> (exists B (element(B,powerset(A)) & -empty(B))))) # label(rc1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.03 31 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.03 32 (all A exists B (element(B,powerset(A)) & empty(B))) # label(rc2_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.03 33 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.03 34 (all A all B all C (relation_of2_as_subset(C,A,B) <-> relation_of2(C,A,B))) # label(redefinition_m2_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.03 35 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.03 36 (all A all B all C all D (in(ordered_pair(A,B),cartesian_product2(C,D)) <-> in(A,C) & in(B,D))) # label(t106_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.03 37 (all A all B (in(A,B) -> element(A,B))) # label(t1_subset) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.03 38 (all A all B (element(A,B) -> empty(B) | in(A,B))) # label(t2_subset) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.03 39 (all A all B (element(A,powerset(B)) <-> subset(A,B))) # label(t3_subset) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.03 40 (all A all B all C (in(A,B) & element(B,powerset(C)) -> element(A,C))) # label(t4_subset) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.03 41 (all A all B all C -(in(A,B) & element(B,powerset(C)) & empty(C))) # label(t5_subset) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.03 42 (all A (empty(A) -> A = empty_set)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.03 43 (all A all B -(in(A,B) & empty(B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.03 44 (all A all B -(empty(A) & A != B & empty(B))) # label(t8_boole) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.03 45 -(all A (antisymmetric_relstr(A) & rel_str(A) -> (all B (element(B,the_carrier(A)) -> (all C (element(C,the_carrier(A)) -> (related(A,B,C) & related(A,C,B) -> B = C))))))) # label(t25_orders_2) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.46/1.03
% 0.46/1.03 ============================== end of process non-clausal formulas ===
% 0.46/1.03
% 0.46/1.03 ============================== PROCESS INITIAL CLAUSES ===============
% 0.46/1.03
% 0.46/1.03 ============================== PREDICATE ELIMINATION =================
% 0.46/1.03 46 -rel_str(A) | one_sorted_str(A) # label(dt_l1_orders_2) # label(axiom). [clausify(14)].
% 0.46/1.03 47 rel_str(c1) # label(existence_l1_orders_2) # label(axiom). [clausify(21)].
% 0.46/1.03 48 rel_str(c5) # label(t25_orders_2) # label(negated_conjecture). [clausify(45)].
% 0.46/1.03 Derived: one_sorted_str(c1). [resolve(46,a,47,a)].
% 0.46/1.03 Derived: one_sorted_str(c5). [resolve(46,a,48,a)].
% 0.46/1.03 49 -rel_str(A) | -antisymmetric_relstr(A) | is_antisymmetric_in(the_InternalRel(A),the_carrier(A)) # label(d6_orders_2) # label(axiom). [clausify(6)].
% 0.46/1.03 Derived: -antisymmetric_relstr(c1) | is_antisymmetric_in(the_InternalRel(c1),the_carrier(c1)). [resolve(49,a,47,a)].
% 0.46/1.03 Derived: -antisymmetric_relstr(c5) | is_antisymmetric_in(the_InternalRel(c5),the_carrier(c5)). [resolve(49,a,48,a)].
% 0.46/1.03 50 -rel_str(A) | antisymmetric_relstr(A) | -is_antisymmetric_in(the_InternalRel(A),the_carrier(A)) # label(d6_orders_2) # label(axiom). [clausify(6)].
% 0.46/1.03 Derived: antisymmetric_relstr(c1) | -is_antisymmetric_in(the_InternalRel(c1),the_carrier(c1)). [resolve(50,a,47,a)].
% 0.46/1.03 Derived: antisymmetric_relstr(c5) | -is_antisymmetric_in(the_InternalRel(c5),the_carrier(c5)). [resolve(50,a,48,a)].
% 0.46/1.03 51 -rel_str(A) | relation_of2_as_subset(the_InternalRel(A),the_carrier(A),the_carrier(A)) # label(dt_u1_orders_2) # label(axiom). [clausify(19)].
% 0.46/1.03 Derived: relation_of2_as_subset(the_InternalRel(c1),the_carrier(c1),the_carrier(c1)). [resolve(51,a,47,a)].
% 0.46/1.03 Derived: relation_of2_as_subset(the_InternalRel(c5),the_carrier(c5),the_carrier(c5)). [resolve(51,a,48,a)].
% 0.46/1.03 52 -rel_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | -related(A,B,C) | in(ordered_pair(B,C),the_InternalRel(A)) # label(d9_orders_2) # label(axiom). [clausify(7)].
% 0.46/1.03 Derived: -element(A,the_carrier(c1)) | -element(B,the_carrier(c1)) | -related(c1,A,B) | in(ordered_pair(A,B),the_InternalRel(c1)). [resolve(52,a,47,a)].
% 0.46/1.03 Derived: -element(A,the_carrier(c5)) | -element(B,the_carrier(c5)) | -related(c5,A,B) | in(ordered_pair(A,B),the_InternalRel(c5)). [resolve(52,a,48,a)].
% 0.46/1.03 53 -rel_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | related(A,B,C) | -in(ordered_pair(B,C),the_InternalRel(A)) # label(d9_orders_2) # label(axiom). [clausify(7)].
% 0.46/1.03 Derived: -element(A,the_carrier(c1)) | -element(B,the_carrier(c1)) | related(c1,A,B) | -in(ordered_pair(A,B),the_InternalRel(c1)). [resolve(53,a,47,a)].
% 0.46/1.03 Derived: -element(A,the_carrier(c5)) | -element(B,the_carrier(c5)) | related(c5,A,B) | -in(ordered_pair(A,B),the_InternalRel(c5)). [resolve(53,a,48,a)].
% 0.46/1.03 54 element(A,powerset(B)) | -subset(A,B) # label(t3_subset) # label(axiom). [clausify(39)].
% 0.46/1.03 55 subset(A,A) # label(reflexivity_r1_tarski) # label(axiom). [clausify(35)].
% 0.46/1.03 56 -element(A,powerset(B)) | subset(A,B) # label(t3_subset) # label(axiom). [clausify(39)].
% 0.46/1.03 Derived: element(A,powerset(A)). [resolve(54,b,55,a)].
% 0.46/1.03 57 relation_of2_as_subset(A,B,C) | -relation_of2(A,B,C) # label(redefinition_m2_relset_1) # label(axiom). [clausify(34)].
% 0.46/1.03 58 relation_of2(f3(A,B),A,B) # label(existence_m1_relset_1) # label(axiom). [clausify(23)].
% 0.46/1.03 59 -relation_of2_as_subset(A,B,C) | relation_of2(A,B,C) # label(redefinition_m2_relset_1) # label(axiom). [clausify(34)].
% 0.46/1.03 Derived: relation_of2_as_subset(f3(A,B),A,B). [resolve(57,b,58,a)].
% 0.46/1.03 60 -relation_of2_as_subset(A,B,C) | element(A,powerset(cartesian_product2(B,C))) # label(dt_m2_relset_1) # label(axiom). [clausify(18)].
% 0.46/1.03 61 relation_of2_as_subset(f5(A,B),A,B) # label(existence_m2_relset_1) # label(axiom). [clausify(25)].
% 0.46/1.03 Derived: element(f5(A,B),powerset(cartesian_product2(A,B))). [resolve(60,a,61,a)].
% 0.46/1.03 62 relation_of2_as_subset(the_InternalRel(c1),the_carrier(c1),the_carrier(c1)). [resolve(51,a,47,a)].
% 0.46/1.03 Derived: element(the_InternalRel(c1),powerset(cartesian_product2(the_carrier(c1),the_carrier(c1)))). [resolve(62,a,60,a)].
% 0.46/1.03 63 relation_of2_as_subset(the_InternalRel(c5),the_carrier(c5),the_carrier(c5)). [resolve(51,a,48,a)].
% 0.46/1.03 Derived: element(the_InternalRel(c5),powerset(cartesian_product2(the_carrier(c5),the_carrier(c5)))). [resolve(63,a,60,a)].
% 0.46/1.03 64 relation_of2_as_subset(f3(A,B),A,B). [resolve(57,b,58,a)].
% 0.46/1.03 Derived: element(f3(A,B),powerset(cartesian_product2(A,B))). [resolve(64,a,60,a)].
% 0.46/1.03 65 -relation(A) | is_antisymmetric_in(A,B) | in(f1(A,B),B) # label(d4_relat_2) # label(axiom). [clausify(4)].
% 0.96/1.22 66 -element(A,powerset(cartesian_product2(B,C))) | relation(A) # label(cc1_relset_1) # label(axiom). [clausify(2)].
% 0.96/1.22 Derived: is_antisymmetric_in(A,B) | in(f1(A,B),B) | -element(A,powerset(cartesian_product2(C,D))). [resolve(65,a,66,b)].
% 0.96/1.22 67 -relation(A) | is_antisymmetric_in(A,B) | in(f2(A,B),B) # label(d4_relat_2) # label(axiom). [clausify(4)].
% 0.96/1.22 Derived: is_antisymmetric_in(A,B) | in(f2(A,B),B) | -element(A,powerset(cartesian_product2(C,D))). [resolve(67,a,66,b)].
% 0.96/1.22 68 -relation(A) | is_antisymmetric_in(A,B) | f2(A,B) != f1(A,B) # label(d4_relat_2) # label(axiom). [clausify(4)].
% 0.96/1.22 Derived: is_antisymmetric_in(A,B) | f2(A,B) != f1(A,B) | -element(A,powerset(cartesian_product2(C,D))). [resolve(68,a,66,b)].
% 0.96/1.22 69 -relation(A) | is_antisymmetric_in(A,B) | in(ordered_pair(f1(A,B),f2(A,B)),A) # label(d4_relat_2) # label(axiom). [clausify(4)].
% 0.96/1.22 Derived: is_antisymmetric_in(A,B) | in(ordered_pair(f1(A,B),f2(A,B)),A) | -element(A,powerset(cartesian_product2(C,D))). [resolve(69,a,66,b)].
% 0.96/1.22 70 -relation(A) | is_antisymmetric_in(A,B) | in(ordered_pair(f2(A,B),f1(A,B)),A) # label(d4_relat_2) # label(axiom). [clausify(4)].
% 0.96/1.22 Derived: is_antisymmetric_in(A,B) | in(ordered_pair(f2(A,B),f1(A,B)),A) | -element(A,powerset(cartesian_product2(C,D))). [resolve(70,a,66,b)].
% 0.96/1.22 71 -relation(A) | -is_antisymmetric_in(A,B) | -in(C,B) | -in(D,B) | -in(ordered_pair(C,D),A) | -in(ordered_pair(D,C),A) | D = C # label(d4_relat_2) # label(axiom). [clausify(4)].
% 0.96/1.22 Derived: -is_antisymmetric_in(A,B) | -in(C,B) | -in(D,B) | -in(ordered_pair(C,D),A) | -in(ordered_pair(D,C),A) | D = C | -element(A,powerset(cartesian_product2(E,F))). [resolve(71,a,66,b)].
% 0.96/1.22
% 0.96/1.22 ============================== end predicate elimination =============
% 0.96/1.22
% 0.96/1.22 Auto_denials: (non-Horn, no changes).
% 0.96/1.22
% 0.96/1.22 Term ordering decisions:
% 0.96/1.22 Function symbol KB weights: empty_set=1. c1=1. c3=1. c4=1. c5=1. c6=1. c7=1. cartesian_product2=1. ordered_pair=1. unordered_pair=1. f1=1. f2=1. f3=1. f5=1. the_carrier=1. powerset=1. the_InternalRel=1. singleton=1. f4=1. f6=1. f7=1.
% 0.96/1.22
% 0.96/1.22 ============================== end of process initial clauses ========
% 0.96/1.22
% 0.96/1.22 ============================== CLAUSES FOR SEARCH ====================
% 0.96/1.22
% 0.96/1.22 ============================== end of clauses for search =============
% 0.96/1.22
% 0.96/1.22 ============================== SEARCH ================================
% 0.96/1.22
% 0.96/1.22 % Starting search at 0.02 seconds.
% 0.96/1.22
% 0.96/1.22 Low Water (keep): wt=13.000, iters=3555
% 0.96/1.22
% 0.96/1.22 Low Water (keep): wt=12.000, iters=3384
% 0.96/1.22
% 0.96/1.22 ============================== PROOF =================================
% 0.96/1.22 % SZS status Theorem
% 0.96/1.22 % SZS output start Refutation
% 0.96/1.22
% 0.96/1.22 % Proof 1 at 0.19 (+ 0.01) seconds.
% 0.96/1.22 % Length of proof is 53.
% 0.96/1.22 % Level of proof is 9.
% 0.96/1.22 % Maximum clause weight is 34.000.
% 0.96/1.22 % Given clauses 244.
% 0.96/1.22
% 0.96/1.22 2 (all A all B all C (element(C,powerset(cartesian_product2(A,B))) -> relation(C))) # label(cc1_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.22 3 (all A all B unordered_pair(A,B) = unordered_pair(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.22 4 (all A (relation(A) -> (all B (is_antisymmetric_in(A,B) <-> (all C all D (in(C,B) & in(D,B) & in(ordered_pair(C,D),A) & in(ordered_pair(D,C),A) -> C = D)))))) # label(d4_relat_2) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.22 5 (all A all B ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A))) # label(d5_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.22 6 (all A (rel_str(A) -> (antisymmetric_relstr(A) <-> is_antisymmetric_in(the_InternalRel(A),the_carrier(A))))) # label(d6_orders_2) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.22 7 (all A (rel_str(A) -> (all B (element(B,the_carrier(A)) -> (all C (element(C,the_carrier(A)) -> (related(A,B,C) <-> in(ordered_pair(B,C),the_InternalRel(A))))))))) # label(d9_orders_2) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.22 18 (all A all B all C (relation_of2_as_subset(C,A,B) -> element(C,powerset(cartesian_product2(A,B))))) # label(dt_m2_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.22 19 (all A (rel_str(A) -> relation_of2_as_subset(the_InternalRel(A),the_carrier(A),the_carrier(A)))) # label(dt_u1_orders_2) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.22 36 (all A all B all C all D (in(ordered_pair(A,B),cartesian_product2(C,D)) <-> in(A,C) & in(B,D))) # label(t106_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.22 38 (all A all B (element(A,B) -> empty(B) | in(A,B))) # label(t2_subset) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.22 40 (all A all B all C (in(A,B) & element(B,powerset(C)) -> element(A,C))) # label(t4_subset) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.22 41 (all A all B all C -(in(A,B) & element(B,powerset(C)) & empty(C))) # label(t5_subset) # label(axiom) # label(non_clause). [assumption].
% 0.96/1.22 45 -(all A (antisymmetric_relstr(A) & rel_str(A) -> (all B (element(B,the_carrier(A)) -> (all C (element(C,the_carrier(A)) -> (related(A,B,C) & related(A,C,B) -> B = C))))))) # label(t25_orders_2) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.96/1.22 48 rel_str(c5) # label(t25_orders_2) # label(negated_conjecture). [clausify(45)].
% 0.96/1.22 49 -rel_str(A) | -antisymmetric_relstr(A) | is_antisymmetric_in(the_InternalRel(A),the_carrier(A)) # label(d6_orders_2) # label(axiom). [clausify(6)].
% 0.96/1.22 51 -rel_str(A) | relation_of2_as_subset(the_InternalRel(A),the_carrier(A),the_carrier(A)) # label(dt_u1_orders_2) # label(axiom). [clausify(19)].
% 0.96/1.22 52 -rel_str(A) | -element(B,the_carrier(A)) | -element(C,the_carrier(A)) | -related(A,B,C) | in(ordered_pair(B,C),the_InternalRel(A)) # label(d9_orders_2) # label(axiom). [clausify(7)].
% 0.96/1.22 60 -relation_of2_as_subset(A,B,C) | element(A,powerset(cartesian_product2(B,C))) # label(dt_m2_relset_1) # label(axiom). [clausify(18)].
% 0.96/1.22 63 relation_of2_as_subset(the_InternalRel(c5),the_carrier(c5),the_carrier(c5)). [resolve(51,a,48,a)].
% 0.96/1.22 66 -element(A,powerset(cartesian_product2(B,C))) | relation(A) # label(cc1_relset_1) # label(axiom). [clausify(2)].
% 0.96/1.22 71 -relation(A) | -is_antisymmetric_in(A,B) | -in(C,B) | -in(D,B) | -in(ordered_pair(C,D),A) | -in(ordered_pair(D,C),A) | D = C # label(d4_relat_2) # label(axiom). [clausify(4)].
% 0.96/1.22 74 antisymmetric_relstr(c5) # label(t25_orders_2) # label(negated_conjecture). [clausify(45)].
% 0.96/1.22 77 element(c6,the_carrier(c5)) # label(t25_orders_2) # label(negated_conjecture). [clausify(45)].
% 0.96/1.22 78 element(c7,the_carrier(c5)) # label(t25_orders_2) # label(negated_conjecture). [clausify(45)].
% 0.96/1.22 79 related(c5,c6,c7) # label(t25_orders_2) # label(negated_conjecture). [clausify(45)].
% 0.96/1.22 80 related(c5,c7,c6) # label(t25_orders_2) # label(negated_conjecture). [clausify(45)].
% 0.96/1.22 82 unordered_pair(A,B) = unordered_pair(B,A) # label(commutativity_k2_tarski) # label(axiom). [clausify(3)].
% 0.96/1.22 84 ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)) # label(d5_tarski) # label(axiom). [clausify(5)].
% 0.96/1.22 85 ordered_pair(A,B) = unordered_pair(singleton(A),unordered_pair(A,B)). [copy(84),rewrite([82(4)])].
% 0.96/1.22 89 c7 != c6 # label(t25_orders_2) # label(negated_conjecture). [clausify(45)].
% 0.96/1.22 93 -in(A,B) | -element(B,powerset(C)) | -empty(C) # label(t5_subset) # label(axiom). [clausify(41)].
% 0.96/1.22 99 -element(A,B) | empty(B) | in(A,B) # label(t2_subset) # label(axiom). [clausify(38)].
% 0.96/1.22 100 -in(ordered_pair(A,B),cartesian_product2(C,D)) | in(A,C) # label(t106_zfmisc_1) # label(axiom). [clausify(36)].
% 0.96/1.22 101 -in(unordered_pair(singleton(A),unordered_pair(A,B)),cartesian_product2(C,D)) | in(A,C). [copy(100),rewrite([85(1)])].
% 0.96/1.22 102 -in(ordered_pair(A,B),cartesian_product2(C,D)) | in(B,D) # label(t106_zfmisc_1) # label(axiom). [clausify(36)].
% 0.96/1.22 103 -in(unordered_pair(singleton(A),unordered_pair(A,B)),cartesian_product2(C,D)) | in(B,D). [copy(102),rewrite([85(1)])].
% 0.96/1.22 104 -in(A,B) | -element(B,powerset(C)) | element(A,C) # label(t4_subset) # label(axiom). [clausify(40)].
% 0.96/1.22 108 -antisymmetric_relstr(c5) | is_antisymmetric_in(the_InternalRel(c5),the_carrier(c5)). [resolve(49,a,48,a)].
% 0.96/1.22 109 is_antisymmetric_in(the_InternalRel(c5),the_carrier(c5)). [copy(108),unit_del(a,74)].
% 0.96/1.22 114 -element(A,the_carrier(c5)) | -element(B,the_carrier(c5)) | -related(c5,A,B) | in(ordered_pair(A,B),the_InternalRel(c5)). [resolve(52,a,48,a)].
% 0.96/1.22 115 -element(A,the_carrier(c5)) | -element(B,the_carrier(c5)) | -related(c5,A,B) | in(unordered_pair(singleton(A),unordered_pair(A,B)),the_InternalRel(c5)). [copy(114),rewrite([85(9)])].
% 0.96/1.22 123 element(the_InternalRel(c5),powerset(cartesian_product2(the_carrier(c5),the_carrier(c5)))). [resolve(63,a,60,a)].
% 0.96/1.22 132 -is_antisymmetric_in(A,B) | -in(C,B) | -in(D,B) | -in(ordered_pair(C,D),A) | -in(ordered_pair(D,C),A) | D = C | -element(A,powerset(cartesian_product2(E,F))). [resolve(71,a,66,b)].
% 0.96/1.22 133 -is_antisymmetric_in(A,B) | -in(C,B) | -in(D,B) | -in(unordered_pair(singleton(C),unordered_pair(C,D)),A) | -in(unordered_pair(singleton(D),unordered_pair(C,D)),A) | D = C | -element(A,powerset(cartesian_product2(E,F))). [copy(132),rewrite([85(4),85(8),82(9)])].
% 0.96/1.22 174 in(unordered_pair(singleton(c7),unordered_pair(c6,c7)),the_InternalRel(c5)). [resolve(115,c,80,a),rewrite([82(13)]),unit_del(a,78),unit_del(b,77)].
% 0.96/1.22 175 in(unordered_pair(singleton(c6),unordered_pair(c6,c7)),the_InternalRel(c5)). [resolve(115,c,79,a),unit_del(a,77),unit_del(b,78)].
% 0.96/1.22 1074 -empty(cartesian_product2(the_carrier(c5),the_carrier(c5))). [ur(93,a,174,a,b,123,a)].
% 0.96/1.22 1078 -element(the_InternalRel(c5),powerset(A)) | element(unordered_pair(singleton(c6),unordered_pair(c6,c7)),A). [resolve(175,a,104,a)].
% 0.96/1.22 4126 element(unordered_pair(singleton(c6),unordered_pair(c6,c7)),cartesian_product2(the_carrier(c5),the_carrier(c5))). [resolve(1078,a,123,a)].
% 0.96/1.22 4182 in(unordered_pair(singleton(c6),unordered_pair(c6,c7)),cartesian_product2(the_carrier(c5),the_carrier(c5))). [resolve(4126,a,99,a),unit_del(a,1074)].
% 0.96/1.22 4187 in(c7,the_carrier(c5)). [resolve(4182,a,103,a)].
% 0.96/1.22 4188 in(c6,the_carrier(c5)). [resolve(4182,a,101,a)].
% 0.96/1.22 4196 $F. [ur(133,a,109,a,c,4187,a,d,175,a,e,174,a,f,89,a,g,123,a),unit_del(a,4188)].
% 0.96/1.22
% 0.96/1.22 % SZS output end Refutation
% 0.96/1.22 ============================== end of proof ==========================
% 0.96/1.22
% 0.96/1.22 ============================== STATISTICS ============================
% 0.96/1.22
% 0.96/1.22 Given=244. Generated=5164. Kept=4111. proofs=1.
% 0.96/1.22 Usable=236. Sos=3815. Demods=6. Limbo=7, Disabled=132. Hints=0.
% 0.96/1.22 Megabytes=2.67.
% 0.96/1.22 User_CPU=0.19, System_CPU=0.01, Wall_clock=0.
% 0.96/1.22
% 0.96/1.22 ============================== end of statistics =====================
% 0.96/1.22
% 0.96/1.22 ============================== end of search =========================
% 0.96/1.22
% 0.96/1.22 THEOREM PROVED
% 0.96/1.22 % SZS status Theorem
% 0.96/1.22
% 0.96/1.22 Exiting with 1 proof.
% 0.96/1.22
% 0.96/1.22 Process 11973 exit (max_proofs) Mon Jun 20 03:34:32 2022
% 0.96/1.22 Prover9 interrupted
%------------------------------------------------------------------------------