TSTP Solution File: SEU353+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SEU353+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n004.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 13:31:12 EDT 2022
% Result : Theorem 0.82s 1.09s
% Output : Refutation 0.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU353+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n004.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 20 11:45:38 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.44/1.01 ============================== Prover9 ===============================
% 0.44/1.01 Prover9 (32) version 2009-11A, November 2009.
% 0.44/1.01 Process 7471 was started by sandbox on n004.cluster.edu,
% 0.44/1.01 Mon Jun 20 11:45:39 2022
% 0.44/1.01 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_7318_n004.cluster.edu".
% 0.44/1.01 ============================== end of head ===========================
% 0.44/1.01
% 0.44/1.01 ============================== INPUT =================================
% 0.44/1.01
% 0.44/1.01 % Reading from file /tmp/Prover9_7318_n004.cluster.edu
% 0.44/1.01
% 0.44/1.01 set(prolog_style_variables).
% 0.44/1.01 set(auto2).
% 0.44/1.01 % set(auto2) -> set(auto).
% 0.44/1.01 % set(auto) -> set(auto_inference).
% 0.44/1.01 % set(auto) -> set(auto_setup).
% 0.44/1.01 % set(auto_setup) -> set(predicate_elim).
% 0.44/1.01 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.44/1.01 % set(auto) -> set(auto_limits).
% 0.44/1.01 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.44/1.01 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.44/1.01 % set(auto) -> set(auto_denials).
% 0.44/1.01 % set(auto) -> set(auto_process).
% 0.44/1.01 % set(auto2) -> assign(new_constants, 1).
% 0.44/1.01 % set(auto2) -> assign(fold_denial_max, 3).
% 0.44/1.01 % set(auto2) -> assign(max_weight, "200.000").
% 0.44/1.01 % set(auto2) -> assign(max_hours, 1).
% 0.44/1.01 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.44/1.01 % set(auto2) -> assign(max_seconds, 0).
% 0.44/1.01 % set(auto2) -> assign(max_minutes, 5).
% 0.44/1.01 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.44/1.01 % set(auto2) -> set(sort_initial_sos).
% 0.44/1.01 % set(auto2) -> assign(sos_limit, -1).
% 0.44/1.01 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.44/1.01 % set(auto2) -> assign(max_megs, 400).
% 0.44/1.01 % set(auto2) -> assign(stats, some).
% 0.44/1.01 % set(auto2) -> clear(echo_input).
% 0.44/1.01 % set(auto2) -> set(quiet).
% 0.44/1.01 % set(auto2) -> clear(print_initial_clauses).
% 0.44/1.01 % set(auto2) -> clear(print_given).
% 0.44/1.01 assign(lrs_ticks,-1).
% 0.44/1.01 assign(sos_limit,10000).
% 0.44/1.01 assign(order,kbo).
% 0.44/1.01 set(lex_order_vars).
% 0.44/1.01 clear(print_given).
% 0.44/1.01
% 0.44/1.01 % formulas(sos). % not echoed (57 formulas)
% 0.44/1.01
% 0.44/1.01 ============================== end of input ==========================
% 0.44/1.01
% 0.44/1.01 % From the command line: assign(max_seconds, 300).
% 0.44/1.01
% 0.44/1.01 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.44/1.01
% 0.44/1.01 % Formulas that are not ordinary clauses:
% 0.44/1.01 1 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 2 (all A all B all C (relation_of2(C,A,B) -> (function(C) & v1_partfun1(C,A,B) -> function(C) & quasi_total(C,A,B)))) # label(cc1_funct_2) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 3 (all A (relation(A) & symmetric(A) & transitive(A) -> relation(A) & reflexive(A))) # label(cc1_partfun1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 4 (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].
% 0.44/1.01 5 (all A all B all C (relation_of2(C,A,B) -> (function(C) & quasi_total(C,A,B) & bijective(C,A,B) -> function(C) & one_to_one(C) & quasi_total(C,A,B) & onto(C,A,B)))) # label(cc2_funct_2) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 6 (all A all B all C (relation_of2(C,A,B) -> (function(C) & one_to_one(C) & quasi_total(C,A,B) & onto(C,A,B) -> function(C) & quasi_total(C,A,B) & bijective(C,A,B)))) # label(cc3_funct_2) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 7 (all A all B (relation_of2(B,A,A) -> (function(B) & v1_partfun1(B,A,A) & reflexive(B) & quasi_total(B,A,A) -> function(B) & one_to_one(B) & quasi_total(B,A,A) & onto(B,A,A) & bijective(B,A,A)))) # label(cc4_funct_2) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 8 (all A all B (-empty(B) -> (all C (relation_of2(C,A,B) -> (function(C) & quasi_total(C,A,B) -> function(C) & v1_partfun1(C,A,B) & quasi_total(C,A,B)))))) # label(cc5_funct_2) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 9 (all A all B (-empty(A) & -empty(B) -> (all C (relation_of2(C,A,B) -> (function(C) & quasi_total(C,A,B) -> function(C) & -empty(C) & v1_partfun1(C,A,B) & quasi_total(C,A,B)))))) # label(cc6_funct_2) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 10 (all A (one_sorted_str(A) -> identity_on_carrier(A) = identity_as_relation_of(the_carrier(A)))) # label(d11_grcat_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 11 $T # label(dt_k1_funct_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 12 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 13 $T # label(dt_k1_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 14 $T # label(dt_k2_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 15 (all A (v1_partfun1(identity_as_relation_of(A),A,A) & relation_of2_as_subset(identity_as_relation_of(A),A,A))) # label(dt_k6_partfun1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 16 (all A relation(identity_relation(A))) # label(dt_k6_relat_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 17 (all A (one_sorted_str(A) -> function(identity_on_carrier(A)) & quasi_total(identity_on_carrier(A),the_carrier(A),the_carrier(A)) & relation_of2_as_subset(identity_on_carrier(A),the_carrier(A),the_carrier(A)))) # label(dt_k7_grcat_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 18 (all A all B all C all D (-empty(A) & function(C) & quasi_total(C,A,B) & relation_of2(C,A,B) & element(D,A) -> element(apply_as_element(A,B,C,D),B))) # label(dt_k8_funct_2) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 19 $T # label(dt_l1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 20 $T # label(dt_m1_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 21 $T # label(dt_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 22 (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].
% 0.44/1.01 23 $T # label(dt_u1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 24 (exists A one_sorted_str(A)) # label(existence_l1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 25 (all A all B exists C relation_of2(C,A,B)) # label(existence_m1_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 26 (all A exists B element(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 27 (all A all B exists C relation_of2_as_subset(C,A,B)) # label(existence_m2_relset_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 28 (all A (-empty_carrier(A) & one_sorted_str(A) -> -empty(the_carrier(A)))) # label(fc1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 29 (all A -empty(powerset(A))) # label(fc1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 30 (all A (relation(identity_relation(A)) & function(identity_relation(A)) & reflexive(identity_relation(A)) & symmetric(identity_relation(A)) & antisymmetric(identity_relation(A)) & transitive(identity_relation(A)))) # label(fc2_partfun1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 31 (all A all B (-empty(A) & -empty(B) -> -empty(cartesian_product2(A,B)))) # label(fc4_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 32 (all A all B exists C (relation_of2(C,A,B) & relation(C) & function(C) & quasi_total(C,A,B))) # label(rc1_funct_2) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 33 (exists A (relation(A) & function(A) & one_to_one(A) & empty(A))) # label(rc1_partfun1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 34 (all A (-empty(A) -> (exists B (element(B,powerset(A)) & -empty(B))))) # label(rc1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 35 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 36 (all A exists B (relation_of2(B,A,A) & relation(B) & function(B) & one_to_one(B) & quasi_total(B,A,A) & onto(B,A,A) & bijective(B,A,A))) # label(rc2_funct_2) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 37 (all A all B exists C (relation_of2(C,A,B) & relation(C) & function(C))) # label(rc2_partfun1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 38 (all A exists B (element(B,powerset(A)) & empty(B))) # label(rc2_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 39 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 40 (all A exists B (relation_of2(B,A,A) & relation(B) & reflexive(B) & symmetric(B) & antisymmetric(B) & transitive(B) & v1_partfun1(B,A,A))) # label(rc3_partfun1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 41 (exists A (one_sorted_str(A) & -empty_carrier(A))) # label(rc3_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 42 (all A (-empty_carrier(A) & one_sorted_str(A) -> (exists B (element(B,powerset(the_carrier(A))) & -empty(B))))) # label(rc5_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 43 (all A identity_as_relation_of(A) = identity_relation(A)) # label(redefinition_k6_partfun1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 44 (all A all B all C all D (-empty(A) & function(C) & quasi_total(C,A,B) & relation_of2(C,A,B) & element(D,A) -> apply_as_element(A,B,C,D) = apply(C,D))) # label(redefinition_k8_funct_2) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 45 (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].
% 0.44/1.01 46 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 47 (all A all B (in(A,B) -> element(A,B))) # label(t1_subset) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 48 (all A all B (element(A,B) -> empty(B) | in(A,B))) # label(t2_subset) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 49 (all A all B (in(B,A) -> apply(identity_relation(A),B) = B)) # label(t35_funct_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 50 (all A all B (element(A,powerset(B)) <-> subset(A,B))) # label(t3_subset) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 51 (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].
% 0.44/1.01 52 (all A all B all C -(in(A,B) & element(B,powerset(C)) & empty(C))) # label(t5_subset) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 53 (all A (empty(A) -> A = empty_set)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 54 (all A all B -(in(A,B) & empty(B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 55 (all A all B -(empty(A) & A != B & empty(B))) # label(t8_boole) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 56 -(all A (-empty_carrier(A) & one_sorted_str(A) -> (all B (element(B,the_carrier(A)) -> apply_as_element(the_carrier(A),the_carrier(A),identity_on_carrier(A),B) = B)))) # label(t91_tmap_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.44/1.01
% 0.44/1.01 ============================== end of process non-clausal formulas ===
% 0.44/1.01
% 0.44/1.01 ============================== PROCESS INITIAL CLAUSES ===============
% 0.44/1.01
% 0.44/1.01 ============================== PREDICATE ELIMINATION =================
% 0.44/1.01 57 -one_sorted_str(A) | function(identity_on_carrier(A)) # label(dt_k7_grcat_1) # label(axiom). [clausify(17)].
% 0.44/1.01 58 one_sorted_str(c1) # label(existence_l1_struct_0) # label(axiom). [clausify(24)].
% 0.44/1.01 59 one_sorted_str(c5) # label(rc3_struct_0) # label(axiom). [clausify(41)].
% 0.44/1.01 60 one_sorted_str(c6) # label(t91_tmap_1) # label(negated_conjecture). [clausify(56)].
% 0.44/1.01 Derived: function(identity_on_carrier(c1)). [resolve(57,a,58,a)].
% 0.44/1.01 Derived: function(identity_on_carrier(c5)). [resolve(57,a,59,a)].
% 0.44/1.01 Derived: function(identity_on_carrier(c6)). [resolve(57,a,60,a)].
% 0.44/1.01 61 empty_carrier(A) | -one_sorted_str(A) | -empty(the_carrier(A)) # label(fc1_struct_0) # label(axiom). [clausify(28)].
% 0.44/1.01 Derived: empty_carrier(c1) | -empty(the_carrier(c1)). [resolve(61,b,58,a)].
% 0.44/1.01 Derived: empty_carrier(c5) | -empty(the_carrier(c5)). [resolve(61,b,59,a)].
% 0.44/1.01 Derived: empty_carrier(c6) | -empty(the_carrier(c6)). [resolve(61,b,60,a)].
% 0.44/1.01 62 empty_carrier(A) | -one_sorted_str(A) | -empty(f10(A)) # label(rc5_struct_0) # label(axiom). [clausify(42)].
% 0.44/1.01 Derived: empty_carrier(c1) | -empty(f10(c1)). [resolve(62,b,58,a)].
% 0.44/1.01 Derived: empty_carrier(c5) | -empty(f10(c5)). [resolve(62,b,59,a)].
% 0.44/1.01 Derived: empty_carrier(c6) | -empty(f10(c6)). [resolve(62,b,60,a)].
% 0.44/1.01 63 -one_sorted_str(A) | identity_as_relation_of(the_carrier(A)) = identity_on_carrier(A) # label(d11_grcat_1) # label(axiom). [clausify(10)].
% 0.44/1.02 Derived: identity_as_relation_of(the_carrier(c1)) = identity_on_carrier(c1). [resolve(63,a,58,a)].
% 0.44/1.02 Derived: identity_as_relation_of(the_carrier(c5)) = identity_on_carrier(c5). [resolve(63,a,59,a)].
% 0.44/1.02 Derived: identity_as_relation_of(the_carrier(c6)) = identity_on_carrier(c6). [resolve(63,a,60,a)].
% 0.44/1.02 64 -one_sorted_str(A) | quasi_total(identity_on_carrier(A),the_carrier(A),the_carrier(A)) # label(dt_k7_grcat_1) # label(axiom). [clausify(17)].
% 0.44/1.02 Derived: quasi_total(identity_on_carrier(c1),the_carrier(c1),the_carrier(c1)). [resolve(64,a,58,a)].
% 0.44/1.02 Derived: quasi_total(identity_on_carrier(c5),the_carrier(c5),the_carrier(c5)). [resolve(64,a,59,a)].
% 0.44/1.02 Derived: quasi_total(identity_on_carrier(c6),the_carrier(c6),the_carrier(c6)). [resolve(64,a,60,a)].
% 0.44/1.02 65 -one_sorted_str(A) | relation_of2_as_subset(identity_on_carrier(A),the_carrier(A),the_carrier(A)) # label(dt_k7_grcat_1) # label(axiom). [clausify(17)].
% 0.44/1.02 Derived: relation_of2_as_subset(identity_on_carrier(c1),the_carrier(c1),the_carrier(c1)). [resolve(65,a,58,a)].
% 0.44/1.02 Derived: relation_of2_as_subset(identity_on_carrier(c5),the_carrier(c5),the_carrier(c5)). [resolve(65,a,59,a)].
% 0.44/1.02 Derived: relation_of2_as_subset(identity_on_carrier(c6),the_carrier(c6),the_carrier(c6)). [resolve(65,a,60,a)].
% 0.44/1.02 66 empty_carrier(A) | -one_sorted_str(A) | element(f10(A),powerset(the_carrier(A))) # label(rc5_struct_0) # label(axiom). [clausify(42)].
% 0.44/1.02 Derived: empty_carrier(c1) | element(f10(c1),powerset(the_carrier(c1))). [resolve(66,b,58,a)].
% 0.44/1.02 Derived: empty_carrier(c5) | element(f10(c5),powerset(the_carrier(c5))). [resolve(66,b,59,a)].
% 0.44/1.02 Derived: empty_carrier(c6) | element(f10(c6),powerset(the_carrier(c6))). [resolve(66,b,60,a)].
% 0.44/1.02 67 -relation(A) | -symmetric(A) | -transitive(A) | reflexive(A) # label(cc1_partfun1) # label(axiom). [clausify(3)].
% 0.44/1.02 68 relation(c2) # label(rc1_partfun1) # label(axiom). [clausify(33)].
% 0.44/1.02 69 relation(identity_relation(A)) # label(dt_k6_relat_1) # label(axiom). [clausify(16)].
% 0.44/1.02 70 relation(identity_relation(A)) # label(fc2_partfun1) # label(axiom). [clausify(30)].
% 0.44/1.02 71 relation(f6(A)) # label(rc2_funct_2) # label(axiom). [clausify(36)].
% 0.44/1.02 72 relation(f9(A)) # label(rc3_partfun1) # label(axiom). [clausify(40)].
% 0.44/1.02 73 relation(f4(A,B)) # label(rc1_funct_2) # label(axiom). [clausify(32)].
% 0.44/1.02 74 relation(f7(A,B)) # label(rc2_partfun1) # label(axiom). [clausify(37)].
% 0.44/1.02 Derived: -symmetric(c2) | -transitive(c2) | reflexive(c2). [resolve(67,a,68,a)].
% 0.44/1.02 Derived: -symmetric(identity_relation(A)) | -transitive(identity_relation(A)) | reflexive(identity_relation(A)). [resolve(67,a,69,a)].
% 0.44/1.02 Derived: -symmetric(f6(A)) | -transitive(f6(A)) | reflexive(f6(A)). [resolve(67,a,71,a)].
% 0.44/1.02 Derived: -symmetric(f9(A)) | -transitive(f9(A)) | reflexive(f9(A)). [resolve(67,a,72,a)].
% 0.44/1.02 Derived: -symmetric(f4(A,B)) | -transitive(f4(A,B)) | reflexive(f4(A,B)). [resolve(67,a,73,a)].
% 0.44/1.02 Derived: -symmetric(f7(A,B)) | -transitive(f7(A,B)) | reflexive(f7(A,B)). [resolve(67,a,74,a)].
% 0.44/1.02 75 -element(A,powerset(cartesian_product2(B,C))) | relation(A) # label(cc1_relset_1) # label(axiom). [clausify(4)].
% 0.44/1.02 Derived: -element(A,powerset(cartesian_product2(B,C))) | -symmetric(A) | -transitive(A) | reflexive(A). [resolve(75,b,67,a)].
% 0.44/1.02 76 -relation_of2(A,B,C) | -function(A) | -v1_partfun1(A,B,C) | quasi_total(A,B,C) # label(cc1_funct_2) # label(axiom). [clausify(2)].
% 0.44/1.02 77 function(c2) # label(rc1_partfun1) # label(axiom). [clausify(33)].
% 0.44/1.02 78 function(identity_relation(A)) # label(fc2_partfun1) # label(axiom). [clausify(30)].
% 0.44/1.02 79 function(f6(A)) # label(rc2_funct_2) # label(axiom). [clausify(36)].
% 0.44/1.02 80 function(f4(A,B)) # label(rc1_funct_2) # label(axiom). [clausify(32)].
% 0.44/1.02 81 function(f7(A,B)) # label(rc2_partfun1) # label(axiom). [clausify(37)].
% 0.44/1.02 Derived: -relation_of2(c2,A,B) | -v1_partfun1(c2,A,B) | quasi_total(c2,A,B). [resolve(76,b,77,a)].
% 0.44/1.02 Derived: -relation_of2(identity_relation(A),B,C) | -v1_partfun1(identity_relation(A),B,C) | quasi_total(identity_relation(A),B,C). [resolve(76,b,78,a)].
% 0.44/1.02 Derived: -relation_of2(f6(A),B,C) | -v1_partfun1(f6(A),B,C) | quasi_total(f6(A),B,C). [resolve(76,b,79,a)].
% 0.44/1.02 Derived: -relation_of2(f4(A,B),C,D) | -v1_partfun1(f4(A,B),C,D) | quasi_total(f4(A,B),C,D). [resolve(76,b,80,a)].
% 0.44/1.02 Derived: -relation_of2(f7(A,B),C,D) | -v1_partfun1(f7(A,B),C,D) | quasi_total(f7(A,B),C,D). [resolve(76,b,81,a)].
% 0.44/1.02 82 -relation_of2(A,B,C) | -function(A) | -quasi_total(A,B,C) | -bijective(A,B,C) | one_to_one(A) # label(cc2_funct_2) # label(axiom). [clausify(5)].
% 0.44/1.02 Derived: -relation_of2(c2,A,B) | -quasi_total(c2,A,B) | -bijective(c2,A,B) | one_to_one(c2). [resolve(82,b,77,a)].
% 0.44/1.02 Derived: -relation_of2(identity_relation(A),B,C) | -quasi_total(identity_relation(A),B,C) | -bijective(identity_relation(A),B,C) | one_to_one(identity_relation(A)). [resolve(82,b,78,a)].
% 0.44/1.02 Derived: -relation_of2(f6(A),B,C) | -quasi_total(f6(A),B,C) | -bijective(f6(A),B,C) | one_to_one(f6(A)). [resolve(82,b,79,a)].
% 0.44/1.02 Derived: -relation_of2(f4(A,B),C,D) | -quasi_total(f4(A,B),C,D) | -bijective(f4(A,B),C,D) | one_to_one(f4(A,B)). [resolve(82,b,80,a)].
% 0.44/1.02 Derived: -relation_of2(f7(A,B),C,D) | -quasi_total(f7(A,B),C,D) | -bijective(f7(A,B),C,D) | one_to_one(f7(A,B)). [resolve(82,b,81,a)].
% 0.44/1.02 83 empty(A) | -relation_of2(B,C,A) | -function(B) | -quasi_total(B,C,A) | v1_partfun1(B,C,A) # label(cc5_funct_2) # label(axiom). [clausify(8)].
% 0.44/1.02 Derived: empty(A) | -relation_of2(c2,B,A) | -quasi_total(c2,B,A) | v1_partfun1(c2,B,A). [resolve(83,c,77,a)].
% 0.44/1.02 Derived: empty(A) | -relation_of2(identity_relation(B),C,A) | -quasi_total(identity_relation(B),C,A) | v1_partfun1(identity_relation(B),C,A). [resolve(83,c,78,a)].
% 0.44/1.02 Derived: empty(A) | -relation_of2(f6(B),C,A) | -quasi_total(f6(B),C,A) | v1_partfun1(f6(B),C,A). [resolve(83,c,79,a)].
% 0.44/1.02 Derived: empty(A) | -relation_of2(f4(B,C),D,A) | -quasi_total(f4(B,C),D,A) | v1_partfun1(f4(B,C),D,A). [resolve(83,c,80,a)].
% 0.44/1.02 Derived: empty(A) | -relation_of2(f7(B,C),D,A) | -quasi_total(f7(B,C),D,A) | v1_partfun1(f7(B,C),D,A). [resolve(83,c,81,a)].
% 0.44/1.02 84 empty(A) | empty(B) | -relation_of2(C,A,B) | -function(C) | -quasi_total(C,A,B) | -empty(C) # label(cc6_funct_2) # label(axiom). [clausify(9)].
% 0.44/1.02 Derived: empty(A) | empty(B) | -relation_of2(c2,A,B) | -quasi_total(c2,A,B) | -empty(c2). [resolve(84,d,77,a)].
% 0.44/1.02 Derived: empty(A) | empty(B) | -relation_of2(identity_relation(C),A,B) | -quasi_total(identity_relation(C),A,B) | -empty(identity_relation(C)). [resolve(84,d,78,a)].
% 0.44/1.02 Derived: empty(A) | empty(B) | -relation_of2(f6(C),A,B) | -quasi_total(f6(C),A,B) | -empty(f6(C)). [resolve(84,d,79,a)].
% 0.44/1.02 Derived: empty(A) | empty(B) | -relation_of2(f4(C,D),A,B) | -quasi_total(f4(C,D),A,B) | -empty(f4(C,D)). [resolve(84,d,80,a)].
% 0.44/1.02 Derived: empty(A) | empty(B) | -relation_of2(f7(C,D),A,B) | -quasi_total(f7(C,D),A,B) | -empty(f7(C,D)). [resolve(84,d,81,a)].
% 0.44/1.02 85 -relation_of2(A,B,C) | -function(A) | -quasi_total(A,B,C) | -bijective(A,B,C) | onto(A,B,C) # label(cc2_funct_2) # label(axiom). [clausify(5)].
% 0.44/1.02 Derived: -relation_of2(c2,A,B) | -quasi_total(c2,A,B) | -bijective(c2,A,B) | onto(c2,A,B). [resolve(85,b,77,a)].
% 0.44/1.02 Derived: -relation_of2(identity_relation(A),B,C) | -quasi_total(identity_relation(A),B,C) | -bijective(identity_relation(A),B,C) | onto(identity_relation(A),B,C). [resolve(85,b,78,a)].
% 0.44/1.02 Derived: -relation_of2(f6(A),B,C) | -quasi_total(f6(A),B,C) | -bijective(f6(A),B,C) | onto(f6(A),B,C). [resolve(85,b,79,a)].
% 0.44/1.02 Derived: -relation_of2(f4(A,B),C,D) | -quasi_total(f4(A,B),C,D) | -bijective(f4(A,B),C,D) | onto(f4(A,B),C,D). [resolve(85,b,80,a)].
% 0.44/1.02 Derived: -relation_of2(f7(A,B),C,D) | -quasi_total(f7(A,B),C,D) | -bijective(f7(A,B),C,D) | onto(f7(A,B),C,D). [resolve(85,b,81,a)].
% 0.44/1.02 86 -relation_of2(A,B,B) | -function(A) | -v1_partfun1(A,B,B) | -reflexive(A) | -quasi_total(A,B,B) | one_to_one(A) # label(cc4_funct_2) # label(axiom). [clausify(7)].
% 0.44/1.02 Derived: -relation_of2(c2,A,A) | -v1_partfun1(c2,A,A) | -reflexive(c2) | -quasi_total(c2,A,A) | one_to_one(c2). [resolve(86,b,77,a)].
% 0.44/1.02 Derived: -relation_of2(identity_relation(A),B,B) | -v1_partfun1(identity_relation(A),B,B) | -reflexive(identity_relation(A)) | -quasi_total(identity_relation(A),B,B) | one_to_one(identity_relation(A)). [resolve(86,b,78,a)].
% 0.44/1.02 Derived: -relation_of2(f6(A),B,B) | -v1_partfun1(f6(A),B,B) | -reflexive(f6(A)) | -quasi_total(f6(A),B,B) | one_to_one(f6(A)). [resolve(86,b,79,a)].
% 0.44/1.02 Derived: -relation_of2(f4(A,B),C,C) | -v1_partfun1(f4(A,B),C,C) | -reflexive(f4(A,B)) | -quasi_total(f4(A,B),C,C) | one_to_one(f4(A,B)). [resolve(86,b,80,a)].
% 0.44/1.02 Derived: -relation_of2(f7(A,B),C,C) | -v1_partfun1(f7(A,B),C,C) | -reflexive(f7(A,B)) | -quasi_total(f7(A,B),C,C) | one_to_one(f7(A,B)). [resolve(86,b,81,a)].
% 0.44/1.02 87 empty(A) | empty(B) | -relation_of2(C,A,B) | -function(C) | -quasi_total(C,A,B) | v1_partfun1(C,A,B) # label(cc6_funct_2) # label(axiom). [clausify(9)].
% 0.44/1.02 88 -relation_of2(A,B,C) | -function(A) | -one_to_one(A) | -quasi_total(A,B,C) | -onto(A,B,C) | bijective(A,B,C) # label(cc3_funct_2) # label(axiom). [clausify(6)].
% 0.44/1.02 Derived: -relation_of2(c2,A,B) | -one_to_one(c2) | -quasi_total(c2,A,B) | -onto(c2,A,B) | bijective(c2,A,B). [resolve(88,b,77,a)].
% 0.44/1.02 Derived: -relation_of2(identity_relation(A),B,C) | -one_to_one(identity_relation(A)) | -quasi_total(identity_relation(A),B,C) | -onto(identity_relation(A),B,C) | bijective(identity_relation(A),B,C). [resolve(88,b,78,a)].
% 0.44/1.02 Derived: -relation_of2(f6(A),B,C) | -one_to_one(f6(A)) | -quasi_total(f6(A),B,C) | -onto(f6(A),B,C) | bijective(f6(A),B,C). [resolve(88,b,79,a)].
% 0.44/1.02 Derived: -relation_of2(f4(A,B),C,D) | -one_to_one(f4(A,B)) | -quasi_total(f4(A,B),C,D) | -onto(f4(A,B),C,D) | bijective(f4(A,B),C,D). [resolve(88,b,80,a)].
% 0.44/1.02 Derived: -relation_of2(f7(A,B),C,D) | -one_to_one(f7(A,B)) | -quasi_total(f7(A,B),C,D) | -onto(f7(A,B),C,D) | bijective(f7(A,B),C,D). [resolve(88,b,81,a)].
% 0.44/1.02 89 -relation_of2(A,B,B) | -function(A) | -v1_partfun1(A,B,B) | -reflexive(A) | -quasi_total(A,B,B) | onto(A,B,B) # label(cc4_funct_2) # label(axiom). [clausify(7)].
% 0.44/1.02 Derived: -relation_of2(c2,A,A) | -v1_partfun1(c2,A,A) | -reflexive(c2) | -quasi_total(c2,A,A) | onto(c2,A,A). [resolve(89,b,77,a)].
% 0.44/1.02 Derived: -relation_of2(identity_relation(A),B,B) | -v1_partfun1(identity_relation(A),B,B) | -reflexive(identity_relation(A)) | -quasi_total(identity_relation(A),B,B) | onto(identity_relation(A),B,B). [resolve(89,b,78,a)].
% 0.44/1.02 Derived: -relation_of2(f6(A),B,B) | -v1_partfun1(f6(A),B,B) | -reflexive(f6(A)) | -quasi_total(f6(A),B,B) | onto(f6(A),B,B). [resolve(89,b,79,a)].
% 0.44/1.02 Derived: -relation_of2(f4(A,B),C,C) | -v1_partfun1(f4(A,B),C,C) | -reflexive(f4(A,B)) | -quasi_total(f4(A,B),C,C) | onto(f4(A,B),C,C). [resolve(89,b,80,a)].
% 0.44/1.02 Derived: -relation_of2(f7(A,B),C,C) | -v1_partfun1(f7(A,B),C,C) | -reflexive(f7(A,B)) | -quasi_total(f7(A,B),C,C) | onto(f7(A,B),C,C). [resolve(89,b,81,a)].
% 0.44/1.02 90 -relation_of2(A,B,B) | -function(A) | -v1_partfun1(A,B,B) | -reflexive(A) | -quasi_total(A,B,B) | bijective(A,B,B) # label(cc4_funct_2) # label(axiom). [clausify(7)].
% 0.44/1.02 Derived: -relation_of2(c2,A,A) | -v1_partfun1(c2,A,A) | -reflexive(c2) | -quasi_total(c2,A,A) | bijective(c2,A,A). [resolve(90,b,77,a)].
% 0.44/1.02 Derived: -relation_of2(identity_relation(A),B,B) | -v1_partfun1(identity_relation(A),B,B) | -reflexive(identity_relation(A)) | -quasi_total(identity_relation(A),B,B) | bijective(identity_relation(A),B,B). [resolve(90,b,78,a)].
% 0.44/1.02 Derived: -relation_of2(f6(A),B,B) | -v1_partfun1(f6(A),B,B) | -reflexive(f6(A)) | -quasi_total(f6(A),B,B) | bijective(f6(A),B,B). [resolve(90,b,79,a)].
% 0.44/1.02 Derived: -relation_of2(f4(A,B),C,C) | -v1_partfun1(f4(A,B),C,C) | -reflexive(f4(A,B)) | -quasi_total(f4(A,B),C,C) | bijective(f4(A,B),C,C). [resolve(90,b,80,a)].
% 0.44/1.02 Derived: -relation_of2(f7(A,B),C,C) | -v1_partfun1(f7(A,B),C,C) | -reflexive(f7(A,B)) | -quasi_total(f7(A,B),C,C) | bijective(f7(A,B),C,C). [resolve(90,b,81,a)].
% 0.44/1.02 91 empty(A) | -function(B) | -quasi_total(B,A,C) | -relation_of2(B,A,C) | -element(D,A) | element(apply_as_element(A,C,B,D),C) # label(dt_k8_funct_2) # label(axiom). [clausify(18)].
% 0.44/1.02 Derived: empty(A) | -quasi_total(c2,A,B) | -relation_of2(c2,A,B) | -element(C,A) | element(apply_as_element(A,B,c2,C),B). [resolve(91,b,77,a)].
% 0.44/1.02 Derived: empty(A) | -quasi_total(identity_relation(B),A,C) | -relation_of2(identity_relation(B),A,C) | -element(D,A) | element(apply_as_element(A,C,identity_relation(B),D),C). [resolve(91,b,78,a)].
% 0.44/1.02 Derived: empty(A) | -quasi_total(f6(B),A,C) | -relation_of2(f6(B),A,C) | -element(D,A) | element(apply_as_element(A,C,f6(B),D),C). [resolve(91,b,79,a)].
% 0.44/1.02 Derived: empty(A) | -quasi_total(f4(B,C),A,D) | -relation_of2(f4(B,C),A,D) | -element(E,A) | element(apply_as_element(A,D,f4(B,C),E),D). [resolve(91,b,80,a)].
% 0.44/1.02 Derived: empty(A) | -quasi_total(f7(B,C),A,D) | -relation_of2(f7(B,C),A,D) | -element(E,A) | element(apply_as_element(A,D,f7(B,C),E),D). [resolve(91,b,81,a)].
% 0.44/1.02 92 empty(A) | -function(B) | -quasi_total(B,A,C) | -relation_of2(B,A,C) | -element(D,A) | apply(B,D) = apply_as_element(A,C,B,D) # label(redefinition_k8_funct_2) # label(axiom). [clausify(44)].
% 0.44/1.02 Derived: empty(A) | -quasi_total(c2,A,B) | -relation_of2(c2,A,B) | -element(C,A) | apply(c2,C) = apply_as_element(A,B,c2,C). [resolve(92,b,77,a)].
% 0.44/1.02 Derived: empty(A) | -quasi_total(identity_relation(B),A,C) | -relation_of2(identity_relation(B),A,C) | -element(D,A) | apply(identity_relation(B),D) = apply_as_element(A,C,identity_relation(B),D). [resolve(92,b,78,a)].
% 0.44/1.02 Derived: empty(A) | -quasi_total(f6(B),A,C) | -relation_of2(f6(B),A,C) | -element(D,A) | apply(f6(B),D) = apply_as_element(A,C,f6(B),D). [resolve(92,b,79,a)].
% 0.44/1.02 Derived: empty(A) | -quasi_total(f4(B,C),A,D) | -relation_of2(f4(B,C),A,D) | -element(E,A) | apply(f4(B,C),E) = apply_as_element(A,D,f4(B,C),E). [resolve(92,b,80,a)].
% 0.44/1.02 Derived: empty(A) | -quasi_total(f7(B,C),A,D) | -relation_of2(f7(B,C),A,D) | -element(E,A) | apply(f7(B,C),E) = apply_as_element(A,D,f7(B,C),E). [resolve(92,b,81,a)].
% 0.44/1.02 93 function(identity_on_carrier(c1)). [resolve(57,a,58,a)].
% 0.44/1.02 Derived: -relation_of2(identity_on_carrier(c1),A,B) | -v1_partfun1(identity_on_carrier(c1),A,B) | quasi_total(identity_on_carrier(c1),A,B). [resolve(93,a,76,b)].
% 0.44/1.02 Derived: -relation_of2(identity_on_carrier(c1),A,B) | -quasi_total(identity_on_carrier(c1),A,B) | -bijective(identity_on_carrier(c1),A,B) | one_to_one(identity_on_carrier(c1)). [resolve(93,a,82,b)].
% 0.44/1.02 Derived: empty(A) | -relation_of2(identity_on_carrier(c1),B,A) | -quasi_total(identity_on_carrier(c1),B,A) | v1_partfun1(identity_on_carrier(c1),B,A). [resolve(93,a,83,c)].
% 0.44/1.02 Derived: empty(A) | empty(B) | -relation_of2(identity_on_carrier(c1),A,B) | -quasi_total(identity_on_carrier(c1),A,B) | -empty(identity_on_carrier(c1)). [resolve(93,a,84,d)].
% 0.44/1.02 Derived: -relation_of2(identity_on_carrier(c1),A,B) | -quasi_total(identity_on_carrier(c1),A,B) | -bijective(identity_on_carrier(c1),A,B) | onto(identity_on_carrier(c1),A,B). [resolve(93,a,85,b)].
% 0.44/1.02 Derived: -relation_of2(identity_on_carrier(c1),A,A) | -v1_partfun1(identity_on_carrier(c1),A,A) | -reflexive(identity_on_carrier(c1)) | -quasi_total(identity_on_carrier(c1),A,A) | one_to_one(identity_on_carrier(c1)). [resolve(93,a,86,b)].
% 0.44/1.02 Derived: -relation_of2(identity_on_carrier(c1),A,B) | -one_to_one(identity_on_carrier(c1)) | -quasi_total(identity_on_carrier(c1),A,B) | -onto(identity_on_carrier(c1),A,B) | bijective(identity_on_carrier(c1),A,B). [resolve(93,a,88,b)].
% 0.44/1.02 Derived: -relation_of2(identity_on_carrier(c1),A,A) | -v1_partfun1(identity_on_carrier(c1),A,A) | -reflexive(identity_on_carrier(c1)) | -quasi_total(identity_on_carrier(c1),A,A) | onto(identity_on_carrier(c1),A,A). [resolve(93,a,89,b)].
% 0.44/1.02 Derived: -relation_of2(identity_on_carrier(c1),A,A) | -v1_partfun1(identity_on_carrier(c1),A,A) | -reflexive(identity_on_carrier(c1)) | -quasi_total(identity_on_carrier(c1),A,A) | bijective(identity_on_carrier(c1),A,A). [resolve(93,a,90,b)].
% 0.44/1.02 Derived: empty(A) | -quasi_total(identity_on_carrier(c1),A,B) | -relation_of2(identity_on_carrier(c1),A,B) | -element(C,A) | element(apply_as_element(A,B,identity_on_carrier(c1),C),B). [resolve(93,a,91,b)].
% 0.44/1.02 Derived: empty(A) | -quasi_total(identity_on_carrier(c1),A,B) | -relation_of2(identity_on_carrier(c1),A,B) | -element(C,A) | apply(identity_on_carrier(c1),C) = apply_as_element(A,B,identity_on_carrier(c1),C). [resolve(93,a,92,b)].
% 0.44/1.02 94 function(identity_on_carrier(c5)). [resolve(57,a,59,a)].
% 0.44/1.02 Derived: -relation_of2(identity_on_carrier(c5),A,B) | -v1_partfun1(identity_on_carrier(c5),A,B) | quasi_total(identity_on_carrier(c5),A,B). [resolve(94,a,76,b)].
% 0.44/1.02 Derived: -relation_of2(identity_on_carrier(c5),A,B) | -quasi_total(identity_on_carrier(c5),A,B) | -bijective(identity_on_carrier(c5),A,B) | one_to_one(identity_on_carrier(c5)). [resolve(94,a,82,b)].
% 0.44/1.02 Derived: empty(A) | -relation_of2(identity_on_carrier(c5),B,A) | -quasi_total(identity_on_carrier(c5),B,A) | v1_partfun1(identity_on_carrier(c5),B,A). [resolve(94,a,83,c)].
% 0.44/1.02 Derived: empty(A) | empty(B) | -relation_of2(identity_on_carrier(c5),A,B) | -quasi_total(identity_on_carrier(c5),A,B) | -empty(identity_on_carrier(c5)). [resolve(94,a,84,d)].
% 0.44/1.02 Derived: -relation_of2(identity_on_carrier(c5),A,B) | -quasi_total(identity_on_carrier(c5),A,B) | -bijective(identity_on_carrier(c5),A,B) | onto(identity_on_carrier(c5),A,B). [resolve(94,a,85,b)].
% 0.44/1.02 Derived: -relation_of2(identity_on_carrier(c5),A,A) | -v1_partfun1(identity_on_carrier(c5),A,A) | -reflexive(identity_on_carrier(c5)) | -quasi_total(identity_on_carrier(c5),A,A) | one_to_one(identity_on_carrier(c5)). [resolve(94,a,86,b)].
% 0.44/1.02 Derived: -relation_of2(identity_on_carrier(c5),A,B) | -one_to_one(identity_on_carrier(c5)) | -quasi_total(identity_on_carrier(c5),A,B) | -onto(identity_on_carrier(c5),A,B) | bijective(identity_on_carrier(c5),A,B). [resolve(94,a,88,b)].
% 0.44/1.02 Derived: -relation_of2(identity_on_carrier(c5),A,A) | -v1_partfun1(identity_on_carrier(c5),A,A) | -reflexive(identity_on_carrier(c5)) | -quasi_total(identity_on_carrier(c5),A,A) | onto(identity_on_carrier(c5),A,A). [resolve(94,a,89,b)].
% 0.44/1.02 Derived: -relation_of2(identity_on_carrier(c5),A,A) | -v1_partfun1(identity_on_carrier(c5),A,A) | -reflexive(identity_on_carrier(c5)) | -quasi_total(identity_on_carrier(c5),A,A) | bijective(identity_on_carrier(c5),A,A). [resolve(94,a,90,b)].
% 0.44/1.02 Derived: empty(A) | -quasi_total(identity_on_carrier(c5),A,B) | -relation_of2(identity_on_carrier(c5),A,B) | -element(C,A) | element(apply_as_element(A,B,identity_on_carrier(c5),C),B). [resolve(94,a,91,b)].
% 0.44/1.02 Derived: empty(A) | -quasi_total(identity_on_carrier(c5),A,B) | -relation_of2(identity_on_carrier(c5),A,B) | -element(C,A) | apply(identity_on_carrier(c5),C) = apply_as_element(A,B,identity_on_carrier(c5),C). [resolve(94,a,92,b)].
% 0.44/1.02 95 function(identity_on_carrier(c6)). [resolve(57,a,60,a)].
% 0.44/1.02 Derived: -relation_of2(identity_on_carrier(c6),A,B) | -v1_partfun1(identity_on_carrier(c6),A,B) | quasi_total(identity_on_carrier(c6),A,B). [resolve(95,a,76,b)].
% 0.44/1.02 Derived: -relation_of2(identity_on_carrier(c6),A,B) | -quasi_total(identity_on_carrier(c6),A,B) | -bijective(identity_on_carrier(c6),A,B) | one_to_one(identity_on_carrier(c6)). [resolve(95,a,82,b)].
% 0.44/1.02 Derived: empty(A) | -relation_of2(identity_on_carrier(c6),B,A) | -quasi_total(identity_on_carrier(c6),B,A) | v1_partfun1(identity_on_carrier(c6),B,A). [resolve(95,a,83,c)].
% 0.44/1.02 Derived: empty(A) | empty(B) | -relation_of2(identity_on_carrier(c6),A,B) | -quasi_total(identity_on_carrier(c6),A,B) | -empty(identity_on_carrier(c6)). [resolve(95,a,84,d)].
% 0.44/1.02 Derived: -relation_of2(identity_on_carrier(c6),A,B) | -quasi_total(identity_on_carrier(c6),A,B) | -bijective(identity_on_carrier(c6),A,B) | onto(identity_on_carrier(c6),A,B). [resolve(95,a,85,b)].
% 0.44/1.02 Derived: -relation_of2(identity_on_carrier(c6),A,A) | -v1_partfun1(identity_on_carrier(c6),A,A) | -reflexive(identity_on_carrier(c6)) | -quasi_total(identity_on_carrier(c6),A,A) | one_to_one(identity_on_carrier(c6)). [resolve(95,a,86,b)].
% 0.44/1.02 Derived: -relation_of2(identity_on_carrier(c6),A,B) | -one_to_one(identity_on_carrier(c6)) | -quasi_total(identity_on_carrier(c6),A,B) | -onto(identity_on_carrier(c6),A,B) | bijective(identity_on_carrier(c6),A,B). [resolve(95,a,88,b)].
% 0.44/1.02 Derived: -relation_of2(identity_on_carrier(c6),A,A) | -v1_partfun1(identity_on_carrier(c6),A,A) | -reflexive(identity_on_carrier(c6)) | -quasi_total(identity_on_carrier(c6),A,A) | onto(identity_on_carrier(c6),A,A). [resolve(95,a,89,b)].
% 0.44/1.02 Derived: -relation_of2(identity_on_carrier(c6),A,A) | -v1_partfun1(identity_on_carrier(c6),A,A) | -reflexive(identity_on_carrier(c6)) | -quasi_total(identity_on_carrier(c6),A,A) | bijective(identity_on_carrier(c6),A,A). [resolve(95,a,90,b)].
% 0.44/1.02 Derived: empty(A) | -quasi_total(identity_on_carrier(c6),A,B) | -relation_of2(identity_on_carrier(c6),A,B) | -element(C,A) | element(apply_as_element(A,B,identity_on_carrier(c6),C),B). [resolve(95,a,91,b)].
% 0.82/1.09 Derived: empty(A) | -quasi_total(identity_on_carrier(c6),A,B) | -relation_of2(identity_on_carrier(c6),A,B) | -element(C,A) | apply(identity_on_carrier(c6),C) = apply_as_element(A,B,identity_on_carrier(c6),C). [resolve(95,a,92,b)].
% 0.82/1.09 96 element(A,powerset(B)) | -subset(A,B) # label(t3_subset) # label(axiom). [clausify(50)].
% 0.82/1.09 97 subset(A,A) # label(reflexivity_r1_tarski) # label(axiom). [clausify(46)].
% 0.82/1.09 98 -element(A,powerset(B)) | subset(A,B) # label(t3_subset) # label(axiom). [clausify(50)].
% 0.82/1.09 Derived: element(A,powerset(A)). [resolve(96,b,97,a)].
% 0.82/1.09 99 -relation_of2_as_subset(A,B,C) | relation_of2(A,B,C) # label(redefinition_m2_relset_1) # label(axiom). [clausify(45)].
% 0.82/1.09 100 relation_of2_as_subset(identity_as_relation_of(A),A,A) # label(dt_k6_partfun1) # label(axiom). [clausify(15)].
% 0.82/1.09 101 relation_of2_as_subset(f3(A,B),A,B) # label(existence_m2_relset_1) # label(axiom). [clausify(27)].
% 0.82/1.09 Derived: relation_of2(identity_as_relation_of(A),A,A). [resolve(99,a,100,a)].
% 0.82/1.09 Derived: relation_of2(f3(A,B),A,B). [resolve(99,a,101,a)].
% 0.82/1.09 102 relation_of2_as_subset(A,B,C) | -relation_of2(A,B,C) # label(redefinition_m2_relset_1) # label(axiom). [clausify(45)].
% 0.82/1.09 103 -relation_of2_as_subset(A,B,C) | element(A,powerset(cartesian_product2(B,C))) # label(dt_m2_relset_1) # label(axiom). [clausify(22)].
% 0.82/1.09 Derived: element(identity_as_relation_of(A),powerset(cartesian_product2(A,A))). [resolve(103,a,100,a)].
% 0.82/1.09 Derived: element(f3(A,B),powerset(cartesian_product2(A,B))). [resolve(103,a,101,a)].
% 0.82/1.09 Derived: element(A,powerset(cartesian_product2(B,C))) | -relation_of2(A,B,C). [resolve(103,a,102,a)].
% 0.82/1.09 104 relation_of2_as_subset(identity_on_carrier(c1),the_carrier(c1),the_carrier(c1)). [resolve(65,a,58,a)].
% 0.82/1.09 Derived: relation_of2(identity_on_carrier(c1),the_carrier(c1),the_carrier(c1)). [resolve(104,a,99,a)].
% 0.82/1.09 Derived: element(identity_on_carrier(c1),powerset(cartesian_product2(the_carrier(c1),the_carrier(c1)))). [resolve(104,a,103,a)].
% 0.82/1.09 105 relation_of2_as_subset(identity_on_carrier(c5),the_carrier(c5),the_carrier(c5)). [resolve(65,a,59,a)].
% 0.82/1.09 Derived: relation_of2(identity_on_carrier(c5),the_carrier(c5),the_carrier(c5)). [resolve(105,a,99,a)].
% 0.82/1.09 Derived: element(identity_on_carrier(c5),powerset(cartesian_product2(the_carrier(c5),the_carrier(c5)))). [resolve(105,a,103,a)].
% 0.82/1.09 106 relation_of2_as_subset(identity_on_carrier(c6),the_carrier(c6),the_carrier(c6)). [resolve(65,a,60,a)].
% 0.82/1.09 Derived: relation_of2(identity_on_carrier(c6),the_carrier(c6),the_carrier(c6)). [resolve(106,a,99,a)].
% 0.82/1.09 Derived: element(identity_on_carrier(c6),powerset(cartesian_product2(the_carrier(c6),the_carrier(c6)))). [resolve(106,a,103,a)].
% 0.82/1.09
% 0.82/1.09 ============================== end predicate elimination =============
% 0.82/1.09
% 0.82/1.09 Auto_denials: (non-Horn, no changes).
% 0.82/1.09
% 0.82/1.09 Term ordering decisions:
% 0.82/1.09 Function symbol KB weights: empty_set=1. c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. c7=1. apply=1. cartesian_product2=1. f1=1. f3=1. f4=1. f7=1. identity_on_carrier=1. identity_relation=1. the_carrier=1. powerset=1. identity_as_relation_of=1. f2=1. f5=1. f6=1. f8=1. f9=1. f10=1. apply_as_element=1.
% 0.82/1.09
% 0.82/1.09 ============================== end of process initial clauses ========
% 0.82/1.09
% 0.82/1.09 ============================== CLAUSES FOR SEARCH ====================
% 0.82/1.09
% 0.82/1.09 ============================== end of clauses for search =============
% 0.82/1.09
% 0.82/1.09 ============================== SEARCH ================================
% 0.82/1.09
% 0.82/1.09 % Starting search at 0.05 seconds.
% 0.82/1.09
% 0.82/1.09 ============================== PROOF =================================
% 0.82/1.09 % SZS status Theorem
% 0.82/1.09 % SZS output start Refutation
% 0.82/1.09
% 0.82/1.09 % Proof 1 at 0.09 (+ 0.00) seconds.
% 0.82/1.09 % Length of proof is 37.
% 0.82/1.09 % Level of proof is 6.
% 0.82/1.09 % Maximum clause weight is 26.000.
% 0.82/1.09 % Given clauses 302.
% 0.82/1.09
% 0.82/1.09 10 (all A (one_sorted_str(A) -> identity_on_carrier(A) = identity_as_relation_of(the_carrier(A)))) # label(d11_grcat_1) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 17 (all A (one_sorted_str(A) -> function(identity_on_carrier(A)) & quasi_total(identity_on_carrier(A),the_carrier(A),the_carrier(A)) & relation_of2_as_subset(identity_on_carrier(A),the_carrier(A),the_carrier(A)))) # label(dt_k7_grcat_1) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 28 (all A (-empty_carrier(A) & one_sorted_str(A) -> -empty(the_carrier(A)))) # label(fc1_struct_0) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 43 (all A identity_as_relation_of(A) = identity_relation(A)) # label(redefinition_k6_partfun1) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 44 (all A all B all C all D (-empty(A) & function(C) & quasi_total(C,A,B) & relation_of2(C,A,B) & element(D,A) -> apply_as_element(A,B,C,D) = apply(C,D))) # label(redefinition_k8_funct_2) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 45 (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].
% 0.82/1.09 48 (all A all B (element(A,B) -> empty(B) | in(A,B))) # label(t2_subset) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 49 (all A all B (in(B,A) -> apply(identity_relation(A),B) = B)) # label(t35_funct_1) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 56 -(all A (-empty_carrier(A) & one_sorted_str(A) -> (all B (element(B,the_carrier(A)) -> apply_as_element(the_carrier(A),the_carrier(A),identity_on_carrier(A),B) = B)))) # label(t91_tmap_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.82/1.09 57 -one_sorted_str(A) | function(identity_on_carrier(A)) # label(dt_k7_grcat_1) # label(axiom). [clausify(17)].
% 0.82/1.09 60 one_sorted_str(c6) # label(t91_tmap_1) # label(negated_conjecture). [clausify(56)].
% 0.82/1.09 61 empty_carrier(A) | -one_sorted_str(A) | -empty(the_carrier(A)) # label(fc1_struct_0) # label(axiom). [clausify(28)].
% 0.82/1.09 63 -one_sorted_str(A) | identity_as_relation_of(the_carrier(A)) = identity_on_carrier(A) # label(d11_grcat_1) # label(axiom). [clausify(10)].
% 0.82/1.09 64 -one_sorted_str(A) | quasi_total(identity_on_carrier(A),the_carrier(A),the_carrier(A)) # label(dt_k7_grcat_1) # label(axiom). [clausify(17)].
% 0.82/1.09 65 -one_sorted_str(A) | relation_of2_as_subset(identity_on_carrier(A),the_carrier(A),the_carrier(A)) # label(dt_k7_grcat_1) # label(axiom). [clausify(17)].
% 0.82/1.09 92 empty(A) | -function(B) | -quasi_total(B,A,C) | -relation_of2(B,A,C) | -element(D,A) | apply(B,D) = apply_as_element(A,C,B,D) # label(redefinition_k8_funct_2) # label(axiom). [clausify(44)].
% 0.82/1.09 95 function(identity_on_carrier(c6)). [resolve(57,a,60,a)].
% 0.82/1.09 99 -relation_of2_as_subset(A,B,C) | relation_of2(A,B,C) # label(redefinition_m2_relset_1) # label(axiom). [clausify(45)].
% 0.82/1.09 106 relation_of2_as_subset(identity_on_carrier(c6),the_carrier(c6),the_carrier(c6)). [resolve(65,a,60,a)].
% 0.82/1.09 120 element(c7,the_carrier(c6)) # label(t91_tmap_1) # label(negated_conjecture). [clausify(56)].
% 0.82/1.09 129 identity_relation(A) = identity_as_relation_of(A) # label(redefinition_k6_partfun1) # label(axiom). [clausify(43)].
% 0.82/1.09 137 -empty_carrier(c6) # label(t91_tmap_1) # label(negated_conjecture). [clausify(56)].
% 0.82/1.09 142 apply_as_element(the_carrier(c6),the_carrier(c6),identity_on_carrier(c6),c7) != c7 # label(t91_tmap_1) # label(negated_conjecture). [clausify(56)].
% 0.82/1.09 148 -element(A,B) | empty(B) | in(A,B) # label(t2_subset) # label(axiom). [clausify(48)].
% 0.82/1.09 149 -in(A,B) | apply(identity_relation(B),A) = A # label(t35_funct_1) # label(axiom). [clausify(49)].
% 0.82/1.09 150 -in(A,B) | apply(identity_as_relation_of(B),A) = A. [copy(149),rewrite([129(2)])].
% 0.82/1.09 155 empty_carrier(c6) | -empty(the_carrier(c6)). [resolve(61,b,60,a)].
% 0.82/1.09 156 -empty(the_carrier(c6)). [copy(155),unit_del(a,137)].
% 0.82/1.09 164 identity_as_relation_of(the_carrier(c6)) = identity_on_carrier(c6). [resolve(63,a,60,a)].
% 0.82/1.09 167 quasi_total(identity_on_carrier(c6),the_carrier(c6),the_carrier(c6)). [resolve(64,a,60,a)].
% 0.82/1.09 284 empty(A) | -quasi_total(identity_on_carrier(c6),A,B) | -relation_of2(identity_on_carrier(c6),A,B) | -element(C,A) | apply(identity_on_carrier(c6),C) = apply_as_element(A,B,identity_on_carrier(c6),C). [resolve(95,a,92,b)].
% 0.82/1.09 285 empty(A) | -quasi_total(identity_on_carrier(c6),A,B) | -relation_of2(identity_on_carrier(c6),A,B) | -element(C,A) | apply_as_element(A,B,identity_on_carrier(c6),C) = apply(identity_on_carrier(c6),C). [copy(284),flip(e)].
% 0.82/1.09 296 relation_of2(identity_on_carrier(c6),the_carrier(c6),the_carrier(c6)). [resolve(106,a,99,a)].
% 0.82/1.09 331 in(c7,the_carrier(c6)). [resolve(148,a,120,a),unit_del(a,156)].
% 0.82/1.09 359 -element(A,the_carrier(c6)) | apply_as_element(the_carrier(c6),the_carrier(c6),identity_on_carrier(c6),A) = apply(identity_on_carrier(c6),A). [resolve(285,b,167,a),unit_del(a,156),unit_del(b,296)].
% 0.82/1.09 409 apply(identity_on_carrier(c6),c7) = c7. [resolve(331,a,150,a),rewrite([164(3)])].
% 0.82/1.09 723 $F. [resolve(359,a,120,a),rewrite([409(12)]),unit_del(a,142)].
% 0.82/1.09
% 0.82/1.09 % SZS output end Refutation
% 0.82/1.09 ============================== end of proof ==========================
% 0.82/1.09
% 0.82/1.09 ============================== STATISTICS ============================
% 0.82/1.09
% 0.82/1.09 Given=302. Generated=823. Kept=586. proofs=1.
% 0.82/1.09 Usable=275. Sos=209. Demods=78. Limbo=5, Disabled=315. Hints=0.
% 0.82/1.09 Megabytes=0.89.
% 0.82/1.09 User_CPU=0.09, System_CPU=0.00, Wall_clock=0.
% 0.82/1.09
% 0.82/1.09 ============================== end of statistics =====================
% 0.82/1.09
% 0.82/1.09 ============================== end of search =========================
% 0.82/1.09
% 0.82/1.09 THEOREM PROVED
% 0.82/1.09 % SZS status Theorem
% 0.82/1.09
% 0.82/1.09 Exiting with 1 proof.
% 0.82/1.09
% 0.82/1.09 Process 7471 exit (max_proofs) Mon Jun 20 11:45:39 2022
% 0.82/1.09 Prover9 interrupted
%------------------------------------------------------------------------------