%------------------------------------------------------------------------------ % File : DT2H2X---1.9.5 % Problem : LCL949^4 : TPTP v9.3.1. Released v8.1.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300 % Computer : n013.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8046.5625MB % OS : Linux 6.8.0-71-generic % CPULimit : 300s % WCLimit : 300s % DateTime : Mon Sep 7 11:35:14 AM UTC 2026 % Result : CounterSatisfiable 0.09s 0.44s % Output : Saturation 0.09s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL949^4 : TPTP v9.3.1. Released v8.1.0. % 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300 % 0.09/0.36 % Computer : n013.cluster.edu % 0.09/0.36 % Model : x86_64 x86_64 % 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.36 % Memory : 8046.5625MB % 0.09/0.36 % OS : Linux 6.8.0-71-generic % 0.09/0.36 % CPULimit : 300 % 0.09/0.36 % WCLimit : 300 % 0.09/0.36 % DateTime : Sat Sep 5 21:07:05 UTC 2026 % 0.09/0.36 % CPUTime : % 0.09/0.36 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300 % 0.09/0.39 ---- Original DTF file --- % 0.09/0.39 thf(spec,logic,$$dhol). % 0.09/0.39 %------------------------------------------------------------------------------ % 0.09/0.39 % File : LCL949^4 : TPTP v9.3.1. Released v8.1.0. % 0.09/0.39 % Domain : Logic Calculi % 0.09/0.39 % Problem : Goedel translation of SET054+1 (from TPTP-v5.0.0) % 0.09/0.39 % Version : [BP13] axioms. % 0.09/0.39 % English : % 0.09/0.39 % 0.09/0.39 % Refs : [RO12] Raths & Otten (2012), The QMLTP Problem Library for Fi % 0.09/0.39 % : [BP13] Benzmueller & Paulson (2013), Quantified Multimodal Lo % 0.09/0.39 % : [Ste22] Steen (2022), An Extensible Logic Embedding Tool for L % 0.09/0.39 % Source : [TPTP] % 0.09/0.39 % Names : GSE054+1 [QMLTP] % 0.09/0.39 % 0.09/0.39 % Status : Theorem % 0.09/0.39 % Rating : 0.25 v9.3.0, 0.22 v9.1.0, 0.25 v9.0.0, 0.20 v8.2.0, 0.31 v8.1.0 % 0.09/0.39 % Syntax : Number of formulae : 141 ( 11 unt; 45 typ; 10 def) % 0.09/0.39 % Number of atoms : 1245 ( 10 equ; 0 cnn) % 0.09/0.39 % Maximal formula atoms : 32 ( 12 avg) % 0.09/0.39 % Number of connectives : 1970 ( 1 ~; 1 |; 3 &;1961 @) % 0.09/0.39 % ( 1 <=>; 3 =>; 0 <=; 0 <~>) % 0.09/0.39 % Maximal formula depth : 27 ( 14 avg) % 0.09/0.39 % Number of types : 3 ( 1 usr) % 0.09/0.39 % Number of type conns : 104 ( 104 >; 0 *; 0 +; 0 <<) % 0.09/0.39 % Number of symbols : 45 ( 44 usr; 6 con; 0-3 aty) % 0.09/0.39 % Number of variables : 229 ( 221 ^; 6 !; 2 ?; 229 :) % 0.09/0.39 % SPC : TH0_THM_EQU_NAR_NDT % 0.09/0.39 % 0.09/0.39 % Comments : This output was generated by embedproblem, version 1.7.1 (library % 0.09/0.39 % version 1.3). Generated on Thu Apr 28 13:18:18 EDT 2022 using % 0.09/0.39 % 'modal' embedding, version 1.5.2. Logic specification used: % 0.09/0.39 % $modal == [$constants == $rigid,$quantification == $constant, % 0.09/0.39 % $modalities == $modal_system_S4]. % 0.09/0.39 %------------------------------------------------------------------------------ % 0.09/0.39 thf(mworld,type, % 0.09/0.39 mworld: $tType ). % 0.09/0.39 % 0.09/0.39 thf(mrel_type,type, % 0.09/0.39 mrel: mworld > mworld > $o ). % 0.09/0.39 % 0.09/0.39 thf(mactual_type,type, % 0.09/0.39 mactual: mworld ). % 0.09/0.39 % 0.09/0.39 thf(mlocal_type,type, % 0.09/0.39 mlocal: ( mworld > $o ) > $o ). % 0.09/0.39 % 0.09/0.39 thf(mlocal_def,definition, % 0.09/0.39 ( mlocal % 0.09/0.39 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ). % 0.09/0.39 % 0.09/0.39 thf(mnot_type,type, % 0.09/0.39 mnot: ( mworld > $o ) > mworld > $o ). % 0.09/0.39 % 0.09/0.39 thf(mand_type,type, % 0.09/0.39 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ). % 0.09/0.39 % 0.09/0.39 thf(mor_type,type, % 0.09/0.39 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ). % 0.09/0.39 % 0.09/0.39 thf(mimplies_type,type, % 0.09/0.39 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ). % 0.09/0.39 % 0.09/0.39 thf(mequiv_type,type, % 0.09/0.39 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ). % 0.09/0.39 % 0.09/0.39 thf(mnot_def,definition, % 0.09/0.39 ( mnot % 0.09/0.39 = ( ^ [A: mworld > $o,W: mworld] : % 0.09/0.39 ~ ( A @ W ) ) ) ). % 0.09/0.39 % 0.09/0.39 thf(mand_def,definition, % 0.09/0.39 ( mand % 0.09/0.39 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] : % 0.09/0.39 ( ( A @ W ) % 0.09/0.39 & ( B @ W ) ) ) ) ). % 0.09/0.39 % 0.09/0.39 thf(mor_def,definition, % 0.09/0.39 ( mor % 0.09/0.39 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] : % 0.09/0.39 ( ( A @ W ) % 0.09/0.39 | ( B @ W ) ) ) ) ). % 0.09/0.39 % 0.09/0.39 thf(mimplies_def,definition, % 0.09/0.39 ( mimplies % 0.09/0.39 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] : % 0.09/0.39 ( ( A @ W ) % 0.09/0.39 => ( B @ W ) ) ) ) ). % 0.09/0.39 % 0.09/0.39 thf(mequiv_def,definition, % 0.09/0.39 ( mequiv % 0.09/0.39 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] : % 0.09/0.39 ( ( A @ W ) % 0.09/0.39 <=> ( B @ W ) ) ) ) ). % 0.09/0.39 % 0.09/0.39 thf(mbox_type,type, % 0.09/0.39 mbox: ( mworld > $o ) > mworld > $o ). % 0.09/0.39 % 0.09/0.39 thf(mbox_def,definition, % 0.09/0.39 ( mbox % 0.09/0.39 = ( ^ [Phi: mworld > $o,W: mworld] : % 0.09/0.39 ! [V: mworld] : % 0.09/0.39 ( ( mrel @ W @ V ) % 0.09/0.39 => ( Phi @ V ) ) ) ) ). % 0.09/0.39 % 0.09/0.39 thf(mdia_type,type, % 0.09/0.39 mdia: ( mworld > $o ) > mworld > $o ). % 0.09/0.39 % 0.09/0.39 thf(mdia_def,definition, % 0.09/0.39 ( mdia % 0.09/0.39 = ( ^ [Phi: mworld > $o,W: mworld] : % 0.09/0.39 ? [V: mworld] : % 0.09/0.39 ( ( mrel @ W @ V ) % 0.09/0.39 & ( Phi @ V ) ) ) ) ). % 0.09/0.39 % 0.09/0.39 thf(mrel_reflexive,axiom, % 0.09/0.39 ! [W: mworld] : ( mrel @ W @ W ) ). % 0.09/0.39 % 0.09/0.39 thf(mrel_transitive,axiom, % 0.09/0.39 ! [W: mworld,V: mworld,U: mworld] : % 0.09/0.39 ( ( ( mrel @ W @ V ) % 0.09/0.39 & ( mrel @ V @ U ) ) % 0.09/0.39 => ( mrel @ W @ U ) ) ). % 0.09/0.39 % 0.09/0.39 thf(mforall_di_type,type, % 0.09/0.39 mforall_di: ( $i > mworld > $o ) > mworld > $o ). % 0.09/0.39 % 0.09/0.39 thf(mforall_di_def,definition, % 0.09/0.39 ( mforall_di % 0.09/0.39 = ( ^ [A: $i > mworld > $o,W: mworld] : % 0.09/0.39 ! [X: $i] : ( A @ X @ W ) ) ) ). % 0.09/0.39 % 0.09/0.39 thf(mexists_di_type,type, % 0.09/0.39 mexists_di: ( $i > mworld > $o ) > mworld > $o ). % 0.09/0.39 % 0.09/0.39 thf(mexists_di_def,definition, % 0.09/0.39 ( mexists_di % 0.09/0.39 = ( ^ [A: $i > mworld > $o,W: mworld] : % 0.09/0.39 ? [X: $i] : ( A @ X @ W ) ) ) ). % 0.09/0.39 % 0.09/0.39 thf(universal_class_decl,type, % 0.09/0.39 universal_class: $i ). % 0.09/0.39 % 0.09/0.39 thf(identity_relation_decl,type, % 0.09/0.39 identity_relation: $i ). % 0.09/0.39 % 0.09/0.39 thf(successor_relation_decl,type, % 0.09/0.39 successor_relation: $i ). % 0.09/0.39 % 0.09/0.39 thf(element_relation_decl,type, % 0.09/0.39 element_relation: $i ). % 0.09/0.39 % 0.09/0.39 thf(null_class_decl,type, % 0.09/0.39 null_class: $i ). % 0.09/0.39 % 0.09/0.39 thf(qmltpeq_decl,type, % 0.09/0.39 qmltpeq: $i > $i > mworld > $o ). % 0.09/0.39 % 0.09/0.39 thf(inductive_decl,type, % 0.09/0.39 inductive: $i > mworld > $o ). % 0.09/0.39 % 0.09/0.39 thf(disjoint_decl,type, % 0.09/0.39 disjoint: $i > $i > mworld > $o ). % 0.09/0.39 % 0.09/0.39 thf(function_decl,type, % 0.09/0.39 function: $i > mworld > $o ). % 0.09/0.39 % 0.09/0.39 thf(member_decl,type, % 0.09/0.39 member: $i > $i > mworld > $o ). % 0.09/0.39 % 0.09/0.39 thf(subclass_decl,type, % 0.09/0.39 subclass: $i > $i > mworld > $o ). % 0.09/0.39 % 0.09/0.39 thf(singleton_decl,type, % 0.09/0.39 singleton: $i > $i ). % 0.09/0.39 % 0.09/0.39 thf(image_decl,type, % 0.09/0.39 image: $i > $i > $i ). % 0.09/0.39 % 0.09/0.39 thf(inverse_decl,type, % 0.09/0.39 inverse: $i > $i ). % 0.09/0.39 % 0.09/0.39 thf(rotate_decl,type, % 0.09/0.39 rotate: $i > $i ). % 0.09/0.39 % 0.09/0.39 thf(unordered_pair_decl,type, % 0.09/0.39 unordered_pair: $i > $i > $i ). % 0.09/0.39 % 0.09/0.39 thf(successor_decl,type, % 0.09/0.39 successor: $i > $i ). % 0.09/0.39 % 0.09/0.39 thf(apply_decl,type, % 0.09/0.39 apply: $i > $i > $i ). % 0.09/0.39 % 0.09/0.39 thf(power_class_decl,type, % 0.09/0.39 power_class: $i > $i ). % 0.09/0.39 % 0.09/0.39 thf(range_of_decl,type, % 0.09/0.39 range_of: $i > $i ). % 0.09/0.39 % 0.09/0.39 thf(union_decl,type, % 0.09/0.39 union: $i > $i > $i ). % 0.09/0.39 % 0.09/0.39 thf(restrict_decl,type, % 0.09/0.39 restrict: $i > $i > $i > $i ). % 0.09/0.39 % 0.09/0.39 thf(second_decl,type, % 0.09/0.39 second: $i > $i ). % 0.09/0.39 % 0.09/0.39 thf(ordered_pair_decl,type, % 0.09/0.39 ordered_pair: $i > $i > $i ). % 0.09/0.39 % 0.09/0.39 thf(domain_of_decl,type, % 0.09/0.39 domain_of: $i > $i ). % 0.09/0.39 % 0.09/0.39 thf(sum_class_decl,type, % 0.09/0.39 sum_class: $i > $i ). % 0.09/0.39 % 0.09/0.39 thf(compose_decl,type, % 0.09/0.39 compose: $i > $i > $i ). % 0.09/0.39 % 0.09/0.39 thf(intersection_decl,type, % 0.09/0.39 intersection: $i > $i > $i ). % 0.09/0.39 % 0.09/0.39 thf(cross_product_decl,type, % 0.09/0.39 cross_product: $i > $i > $i ). % 0.09/0.39 % 0.09/0.39 thf(complement_decl,type, % 0.09/0.39 complement: $i > $i ). % 0.09/0.39 % 0.09/0.39 thf(flip_decl,type, % 0.09/0.39 flip: $i > $i ). % 0.09/0.39 % 0.09/0.39 thf(first_decl,type, % 0.09/0.39 first: $i > $i ). % 0.09/0.39 % 0.09/0.39 thf(reflexivity,axiom, % 0.09/0.39 ( mlocal % 0.09/0.39 @ ( mbox % 0.09/0.39 @ ( mforall_di % 0.09/0.39 @ ^ [X: $i] : ( mbox @ ( qmltpeq @ X @ X ) ) ) ) ) ). % 0.09/0.39 % 0.09/0.39 thf(symmetry,axiom, % 0.09/0.39 ( mlocal % 0.09/0.39 @ ( mbox % 0.09/0.39 @ ( mforall_di % 0.09/0.39 @ ^ [X: $i] : % 0.09/0.39 ( mbox % 0.09/0.39 @ ( mforall_di % 0.09/0.39 @ ^ [Y: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ X @ Y ) ) @ ( mbox @ ( qmltpeq @ Y @ X ) ) ) ) ) ) ) ) ) ). % 0.09/0.39 % 0.09/0.39 thf(transitivity,axiom, % 0.09/0.39 ( mlocal % 0.09/0.39 @ ( mbox % 0.09/0.39 @ ( mforall_di % 0.09/0.39 @ ^ [X: $i] : % 0.09/0.39 ( mbox % 0.09/0.39 @ ( mforall_di % 0.09/0.39 @ ^ [Y: $i] : % 0.09/0.39 ( mbox % 0.09/0.39 @ ( mforall_di % 0.09/0.39 @ ^ [Z: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( qmltpeq @ X @ Y ) ) @ ( mbox @ ( qmltpeq @ Y @ Z ) ) ) @ ( mbox @ ( qmltpeq @ X @ Z ) ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.39 % 0.09/0.39 thf(apply_substitution_1,axiom, % 0.09/0.39 ( mlocal % 0.09/0.39 @ ( mbox % 0.09/0.39 @ ( mforall_di % 0.09/0.39 @ ^ [A: $i] : % 0.09/0.39 ( mbox % 0.09/0.39 @ ( mforall_di % 0.09/0.39 @ ^ [B: $i] : % 0.09/0.39 ( mbox % 0.09/0.39 @ ( mforall_di % 0.09/0.39 @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( apply @ A @ C ) @ ( apply @ B @ C ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.39 % 0.09/0.39 thf(apply_substitution_2,axiom, % 0.09/0.39 ( mlocal % 0.09/0.39 @ ( mbox % 0.09/0.39 @ ( mforall_di % 0.09/0.39 @ ^ [A: $i] : % 0.09/0.39 ( mbox % 0.09/0.39 @ ( mforall_di % 0.09/0.39 @ ^ [B: $i] : % 0.09/0.39 ( mbox % 0.09/0.39 @ ( mforall_di % 0.09/0.39 @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( apply @ C @ A ) @ ( apply @ C @ B ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.39 % 0.09/0.39 thf(complement_substitution_1,axiom, % 0.09/0.39 ( mlocal % 0.09/0.39 @ ( mbox % 0.09/0.39 @ ( mforall_di % 0.09/0.39 @ ^ [A: $i] : % 0.09/0.39 ( mbox % 0.09/0.39 @ ( mforall_di % 0.09/0.39 @ ^ [B: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( complement @ A ) @ ( complement @ B ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.39 % 0.09/0.39 thf(compose_substitution_1,axiom, % 0.09/0.39 ( mlocal % 0.09/0.39 @ ( mbox % 0.09/0.39 @ ( mforall_di % 0.09/0.39 @ ^ [A: $i] : % 0.09/0.39 ( mbox % 0.09/0.39 @ ( mforall_di % 0.09/0.39 @ ^ [B: $i] : % 0.09/0.39 ( mbox % 0.09/0.39 @ ( mforall_di % 0.09/0.39 @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( compose @ A @ C ) @ ( compose @ B @ C ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.39 % 0.09/0.39 thf(compose_substitution_2,axiom, % 0.09/0.39 ( mlocal % 0.09/0.39 @ ( mbox % 0.09/0.39 @ ( mforall_di % 0.09/0.39 @ ^ [A: $i] : % 0.09/0.39 ( mbox % 0.09/0.39 @ ( mforall_di % 0.09/0.39 @ ^ [B: $i] : % 0.09/0.39 ( mbox % 0.09/0.39 @ ( mforall_di % 0.09/0.39 @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( compose @ C @ A ) @ ( compose @ C @ B ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.39 % 0.09/0.39 thf(cross_product_substitution_1,axiom, % 0.09/0.39 ( mlocal % 0.09/0.39 @ ( mbox % 0.09/0.39 @ ( mforall_di % 0.09/0.39 @ ^ [A: $i] : % 0.09/0.39 ( mbox % 0.09/0.39 @ ( mforall_di % 0.09/0.39 @ ^ [B: $i] : % 0.09/0.39 ( mbox % 0.09/0.39 @ ( mforall_di % 0.09/0.39 @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( cross_product @ A @ C ) @ ( cross_product @ B @ C ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.39 % 0.09/0.39 thf(cross_product_substitution_2,axiom, % 0.09/0.39 ( mlocal % 0.09/0.39 @ ( mbox % 0.09/0.39 @ ( mforall_di % 0.09/0.39 @ ^ [A: $i] : % 0.09/0.39 ( mbox % 0.09/0.39 @ ( mforall_di % 0.09/0.39 @ ^ [B: $i] : % 0.09/0.39 ( mbox % 0.09/0.39 @ ( mforall_di % 0.09/0.39 @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( cross_product @ C @ A ) @ ( cross_product @ C @ B ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.39 % 0.09/0.39 thf(domain_of_substitution_1,axiom, % 0.09/0.39 ( mlocal % 0.09/0.39 @ ( mbox % 0.09/0.39 @ ( mforall_di % 0.09/0.39 @ ^ [A: $i] : % 0.09/0.39 ( mbox % 0.09/0.39 @ ( mforall_di % 0.09/0.39 @ ^ [B: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( domain_of @ A ) @ ( domain_of @ B ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.39 % 0.09/0.39 thf(first_substitution_1,axiom, % 0.09/0.39 ( mlocal % 0.09/0.39 @ ( mbox % 0.09/0.39 @ ( mforall_di % 0.09/0.39 @ ^ [A: $i] : % 0.09/0.39 ( mbox % 0.09/0.39 @ ( mforall_di % 0.09/0.39 @ ^ [B: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( first @ A ) @ ( first @ B ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.39 % 0.09/0.39 thf(flip_substitution_1,axiom, % 0.09/0.39 ( mlocal % 0.09/0.39 @ ( mbox % 0.09/0.39 @ ( mforall_di % 0.09/0.39 @ ^ [A: $i] : % 0.09/0.39 ( mbox % 0.09/0.39 @ ( mforall_di % 0.09/0.39 @ ^ [B: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( flip @ A ) @ ( flip @ B ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.39 % 0.09/0.39 thf(image_substitution_1,axiom, % 0.09/0.39 ( mlocal % 0.09/0.39 @ ( mbox % 0.09/0.39 @ ( mforall_di % 0.09/0.39 @ ^ [A: $i] : % 0.09/0.39 ( mbox % 0.09/0.39 @ ( mforall_di % 0.09/0.39 @ ^ [B: $i] : % 0.09/0.39 ( mbox % 0.09/0.39 @ ( mforall_di % 0.09/0.39 @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( image @ A @ C ) @ ( image @ B @ C ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.39 % 0.09/0.39 thf(image_substitution_2,axiom, % 0.09/0.39 ( mlocal % 0.09/0.39 @ ( mbox % 0.09/0.39 @ ( mforall_di % 0.09/0.39 @ ^ [A: $i] : % 0.09/0.39 ( mbox % 0.09/0.39 @ ( mforall_di % 0.09/0.39 @ ^ [B: $i] : % 0.09/0.39 ( mbox % 0.09/0.39 @ ( mforall_di % 0.09/0.39 @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( image @ C @ A ) @ ( image @ C @ B ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.39 % 0.09/0.39 thf(intersection_substitution_1,axiom, % 0.09/0.39 ( mlocal % 0.09/0.39 @ ( mbox % 0.09/0.39 @ ( mforall_di % 0.09/0.39 @ ^ [A: $i] : % 0.09/0.39 ( mbox % 0.09/0.39 @ ( mforall_di % 0.09/0.39 @ ^ [B: $i] : % 0.09/0.39 ( mbox % 0.09/0.39 @ ( mforall_di % 0.09/0.39 @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( intersection @ A @ C ) @ ( intersection @ B @ C ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.39 % 0.09/0.39 thf(intersection_substitution_2,axiom, % 0.09/0.39 ( mlocal % 0.09/0.39 @ ( mbox % 0.09/0.39 @ ( mforall_di % 0.09/0.39 @ ^ [A: $i] : % 0.09/0.39 ( mbox % 0.09/0.39 @ ( mforall_di % 0.09/0.39 @ ^ [B: $i] : % 0.09/0.39 ( mbox % 0.09/0.39 @ ( mforall_di % 0.09/0.39 @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( intersection @ C @ A ) @ ( intersection @ C @ B ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(inverse_substitution_1,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [A: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [B: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( inverse @ A ) @ ( inverse @ B ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(ordered_pair_substitution_1,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [A: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [B: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( ordered_pair @ A @ C ) @ ( ordered_pair @ B @ C ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(ordered_pair_substitution_2,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [A: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [B: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( ordered_pair @ C @ A ) @ ( ordered_pair @ C @ B ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(power_class_substitution_1,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [A: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [B: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( power_class @ A ) @ ( power_class @ B ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(range_of_substitution_1,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [A: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [B: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( range_of @ A ) @ ( range_of @ B ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(restrict_substitution_1,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [A: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [B: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [C: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [D: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( restrict @ A @ C @ D ) @ ( restrict @ B @ C @ D ) ) ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(restrict_substitution_2,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [A: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [B: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [C: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [D: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( restrict @ C @ A @ D ) @ ( restrict @ C @ B @ D ) ) ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(restrict_substitution_3,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [A: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [B: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [C: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [D: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( restrict @ C @ D @ A ) @ ( restrict @ C @ D @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(rotate_substitution_1,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [A: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [B: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( rotate @ A ) @ ( rotate @ B ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(second_substitution_1,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [A: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [B: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( second @ A ) @ ( second @ B ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(singleton_substitution_1,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [A: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [B: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( singleton @ A ) @ ( singleton @ B ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(successor_substitution_1,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [A: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [B: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( successor @ A ) @ ( successor @ B ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(sum_class_substitution_1,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [A: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [B: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( sum_class @ A ) @ ( sum_class @ B ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(union_substitution_1,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [A: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [B: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( union @ A @ C ) @ ( union @ B @ C ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(union_substitution_2,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [A: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [B: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( union @ C @ A ) @ ( union @ C @ B ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(unordered_pair_substitution_1,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [A: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [B: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( unordered_pair @ A @ C ) @ ( unordered_pair @ B @ C ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(unordered_pair_substitution_2,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [A: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [B: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( unordered_pair @ C @ A ) @ ( unordered_pair @ C @ B ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(disjoint_substitution_1,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [A: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [B: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( disjoint @ A @ C ) ) ) @ ( mbox @ ( disjoint @ B @ C ) ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(disjoint_substitution_2,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [A: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [B: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( disjoint @ C @ A ) ) ) @ ( mbox @ ( disjoint @ C @ B ) ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(function_substitution_1,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [A: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [B: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( function @ A ) ) ) @ ( mbox @ ( function @ B ) ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(inductive_substitution_1,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [A: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [B: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( inductive @ A ) ) ) @ ( mbox @ ( inductive @ B ) ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(member_substitution_1,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [A: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [B: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( member @ A @ C ) ) ) @ ( mbox @ ( member @ B @ C ) ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(member_substitution_2,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [A: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [B: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( member @ C @ A ) ) ) @ ( mbox @ ( member @ C @ B ) ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(subclass_substitution_1,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [A: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [B: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( subclass @ A @ C ) ) ) @ ( mbox @ ( subclass @ B @ C ) ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(subclass_substitution_2,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [A: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [B: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( subclass @ C @ A ) ) ) @ ( mbox @ ( subclass @ C @ B ) ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(subclass_defn,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [X: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [Y: $i] : % 0.09/0.40 ( mand % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mimplies @ ( mbox @ ( subclass @ X @ Y ) ) % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [U: $i] : ( mbox @ ( mimplies @ ( mbox @ ( member @ U @ X ) ) @ ( mbox @ ( member @ U @ Y ) ) ) ) ) ) ) ) % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mimplies % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [U: $i] : ( mbox @ ( mimplies @ ( mbox @ ( member @ U @ X ) ) @ ( mbox @ ( member @ U @ Y ) ) ) ) ) ) % 0.09/0.40 @ ( mbox @ ( subclass @ X @ Y ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(class_elements_are_sets,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [X: $i] : ( mbox @ ( subclass @ X @ universal_class ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(extensionality,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [X: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [Y: $i] : ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ X @ Y ) ) @ ( mand @ ( mbox @ ( subclass @ X @ Y ) ) @ ( mbox @ ( subclass @ Y @ X ) ) ) ) ) @ ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( subclass @ X @ Y ) ) @ ( mbox @ ( subclass @ Y @ X ) ) ) @ ( mbox @ ( qmltpeq @ X @ Y ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(unordered_pair_defn,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [U: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [X: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [Y: $i] : ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( member @ U @ ( unordered_pair @ X @ Y ) ) ) @ ( mand @ ( mbox @ ( member @ U @ universal_class ) ) @ ( mor @ ( mbox @ ( qmltpeq @ U @ X ) ) @ ( mbox @ ( qmltpeq @ U @ Y ) ) ) ) ) ) @ ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( member @ U @ universal_class ) ) @ ( mor @ ( mbox @ ( qmltpeq @ U @ X ) ) @ ( mbox @ ( qmltpeq @ U @ Y ) ) ) ) @ ( mbox @ ( member @ U @ ( unordered_pair @ X @ Y ) ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(unordered_pair_0,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [X: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [Y: $i] : ( mbox @ ( member @ ( unordered_pair @ X @ Y ) @ universal_class ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(singleton_set_defn,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [X: $i] : ( mbox @ ( qmltpeq @ ( singleton @ X ) @ ( unordered_pair @ X @ X ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(ordered_pair_defn,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [X: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [Y: $i] : ( mbox @ ( qmltpeq @ ( ordered_pair @ X @ Y ) @ ( unordered_pair @ ( singleton @ X ) @ ( unordered_pair @ X @ ( singleton @ Y ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(cross_product_defn,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [U: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [V: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [X: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [Y: $i] : ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( member @ ( ordered_pair @ U @ V ) @ ( cross_product @ X @ Y ) ) ) @ ( mand @ ( mbox @ ( member @ U @ X ) ) @ ( mbox @ ( member @ V @ Y ) ) ) ) ) @ ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( member @ U @ X ) ) @ ( mbox @ ( member @ V @ Y ) ) ) @ ( mbox @ ( member @ ( ordered_pair @ U @ V ) @ ( cross_product @ X @ Y ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(cross_product_0,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [X: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [Y: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [Z: $i] : ( mbox @ ( mimplies @ ( mbox @ ( member @ Z @ ( cross_product @ X @ Y ) ) ) @ ( mbox @ ( qmltpeq @ Z @ ( ordered_pair @ ( first @ Z ) @ ( second @ Z ) ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(element_relation_defn,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [X: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [Y: $i] : ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( member @ ( ordered_pair @ X @ Y ) @ element_relation ) ) @ ( mand @ ( mbox @ ( member @ Y @ universal_class ) ) @ ( mbox @ ( member @ X @ Y ) ) ) ) ) @ ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( member @ Y @ universal_class ) ) @ ( mbox @ ( member @ X @ Y ) ) ) @ ( mbox @ ( member @ ( ordered_pair @ X @ Y ) @ element_relation ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(element_relation_0,axiom, % 0.09/0.40 mlocal @ ( mbox @ ( subclass @ element_relation @ ( cross_product @ universal_class @ universal_class ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(intersection_0,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [X: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [Y: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [Z: $i] : ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( member @ Z @ ( intersection @ X @ Y ) ) ) @ ( mand @ ( mbox @ ( member @ Z @ X ) ) @ ( mbox @ ( member @ Z @ Y ) ) ) ) ) @ ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( member @ Z @ X ) ) @ ( mbox @ ( member @ Z @ Y ) ) ) @ ( mbox @ ( member @ Z @ ( intersection @ X @ Y ) ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(complement_0,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [X: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [Z: $i] : ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( member @ Z @ ( complement @ X ) ) ) @ ( mand @ ( mbox @ ( member @ Z @ universal_class ) ) @ ( mbox @ ( mnot @ ( mbox @ ( member @ Z @ X ) ) ) ) ) ) ) @ ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( member @ Z @ universal_class ) ) @ ( mbox @ ( mnot @ ( mbox @ ( member @ Z @ X ) ) ) ) ) @ ( mbox @ ( member @ Z @ ( complement @ X ) ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(restrict_defn,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [X: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [XR: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [Y: $i] : ( mbox @ ( qmltpeq @ ( restrict @ XR @ X @ Y ) @ ( intersection @ XR @ ( cross_product @ X @ Y ) ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(null_class_defn,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [X: $i] : ( mbox @ ( mnot @ ( mbox @ ( member @ X @ null_class ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(domain_of_0,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [X: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [Z: $i] : ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( member @ Z @ ( domain_of @ X ) ) ) @ ( mand @ ( mbox @ ( member @ Z @ universal_class ) ) @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( restrict @ X @ ( singleton @ Z ) @ universal_class ) @ null_class ) ) ) ) ) ) ) @ ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( member @ Z @ universal_class ) ) @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( restrict @ X @ ( singleton @ Z ) @ universal_class ) @ null_class ) ) ) ) ) @ ( mbox @ ( member @ Z @ ( domain_of @ X ) ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(rotate_defn,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [X: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [U: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [V: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [W: $i] : ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( member @ ( ordered_pair @ ( ordered_pair @ U @ V ) @ W ) @ ( rotate @ X ) ) ) @ ( mand @ ( mbox @ ( member @ ( ordered_pair @ ( ordered_pair @ U @ V ) @ W ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) ) @ ( mbox @ ( member @ ( ordered_pair @ ( ordered_pair @ V @ W ) @ U ) @ X ) ) ) ) ) @ ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( member @ ( ordered_pair @ ( ordered_pair @ U @ V ) @ W ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) ) @ ( mbox @ ( member @ ( ordered_pair @ ( ordered_pair @ V @ W ) @ U ) @ X ) ) ) @ ( mbox @ ( member @ ( ordered_pair @ ( ordered_pair @ U @ V ) @ W ) @ ( rotate @ X ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(rotate_0,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [X: $i] : ( mbox @ ( subclass @ ( rotate @ X ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(flip_defn,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [U: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [V: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [W: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [X: $i] : ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( member @ ( ordered_pair @ ( ordered_pair @ U @ V ) @ W ) @ ( flip @ X ) ) ) @ ( mand @ ( mbox @ ( member @ ( ordered_pair @ ( ordered_pair @ U @ V ) @ W ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) ) @ ( mbox @ ( member @ ( ordered_pair @ ( ordered_pair @ V @ U ) @ W ) @ X ) ) ) ) ) @ ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( member @ ( ordered_pair @ ( ordered_pair @ U @ V ) @ W ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) ) @ ( mbox @ ( member @ ( ordered_pair @ ( ordered_pair @ V @ U ) @ W ) @ X ) ) ) @ ( mbox @ ( member @ ( ordered_pair @ ( ordered_pair @ U @ V ) @ W ) @ ( flip @ X ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(flip_0,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [X: $i] : ( mbox @ ( subclass @ ( flip @ X ) @ ( cross_product @ ( cross_product @ universal_class @ universal_class ) @ universal_class ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(union_defn,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [X: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [Y: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [Z: $i] : ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( member @ Z @ ( union @ X @ Y ) ) ) @ ( mor @ ( mbox @ ( member @ Z @ X ) ) @ ( mbox @ ( member @ Z @ Y ) ) ) ) ) @ ( mbox @ ( mimplies @ ( mor @ ( mbox @ ( member @ Z @ X ) ) @ ( mbox @ ( member @ Z @ Y ) ) ) @ ( mbox @ ( member @ Z @ ( union @ X @ Y ) ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(successor_defn,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [X: $i] : ( mbox @ ( qmltpeq @ ( successor @ X ) @ ( union @ X @ ( singleton @ X ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(successor_relation_defn1,axiom, % 0.09/0.40 mlocal @ ( mbox @ ( subclass @ successor_relation @ ( cross_product @ universal_class @ universal_class ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(successor_relation_defn2,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [X: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [Y: $i] : ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( member @ ( ordered_pair @ X @ Y ) @ successor_relation ) ) @ ( mand @ ( mbox @ ( member @ X @ universal_class ) ) @ ( mand @ ( mbox @ ( member @ Y @ universal_class ) ) @ ( mbox @ ( qmltpeq @ ( successor @ X ) @ Y ) ) ) ) ) ) @ ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( member @ X @ universal_class ) ) @ ( mand @ ( mbox @ ( member @ Y @ universal_class ) ) @ ( mbox @ ( qmltpeq @ ( successor @ X ) @ Y ) ) ) ) @ ( mbox @ ( member @ ( ordered_pair @ X @ Y ) @ successor_relation ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(inverse_defn,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [Y: $i] : ( mbox @ ( qmltpeq @ ( inverse @ Y ) @ ( domain_of @ ( flip @ ( cross_product @ Y @ universal_class ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(range_of_defn,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [Z: $i] : ( mbox @ ( qmltpeq @ ( range_of @ Z ) @ ( domain_of @ ( inverse @ Z ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(image_defn,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [X: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [XR: $i] : ( mbox @ ( qmltpeq @ ( image @ XR @ X ) @ ( range_of @ ( restrict @ XR @ X @ universal_class ) ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(inductive_defn,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [X: $i] : ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( inductive @ X ) ) @ ( mand @ ( mbox @ ( member @ null_class @ X ) ) @ ( mbox @ ( subclass @ ( image @ successor_relation @ X ) @ X ) ) ) ) ) @ ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( member @ null_class @ X ) ) @ ( mbox @ ( subclass @ ( image @ successor_relation @ X ) @ X ) ) ) @ ( mbox @ ( inductive @ X ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(infinity,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mexists_di % 0.09/0.40 @ ^ [X: $i] : % 0.09/0.40 ( mand @ ( mbox @ ( member @ X @ universal_class ) ) % 0.09/0.40 @ ( mand @ ( mbox @ ( inductive @ X ) ) % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [Y: $i] : ( mbox @ ( mimplies @ ( mbox @ ( inductive @ Y ) ) @ ( mbox @ ( subclass @ X @ Y ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(sum_class_defn,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [U: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [X: $i] : % 0.09/0.40 ( mand % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mimplies @ ( mbox @ ( member @ U @ ( sum_class @ X ) ) ) % 0.09/0.40 @ ( mexists_di % 0.09/0.40 @ ^ [Y: $i] : ( mand @ ( mbox @ ( member @ U @ Y ) ) @ ( mbox @ ( member @ Y @ X ) ) ) ) ) ) % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mimplies % 0.09/0.40 @ ( mexists_di % 0.09/0.40 @ ^ [Y: $i] : ( mand @ ( mbox @ ( member @ U @ Y ) ) @ ( mbox @ ( member @ Y @ X ) ) ) ) % 0.09/0.40 @ ( mbox @ ( member @ U @ ( sum_class @ X ) ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(sum_class_0,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [X: $i] : ( mbox @ ( mimplies @ ( mbox @ ( member @ X @ universal_class ) ) @ ( mbox @ ( member @ ( sum_class @ X ) @ universal_class ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(power_class_defn,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [U: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [X: $i] : ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( member @ U @ ( power_class @ X ) ) ) @ ( mand @ ( mbox @ ( member @ U @ universal_class ) ) @ ( mbox @ ( subclass @ U @ X ) ) ) ) ) @ ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( member @ U @ universal_class ) ) @ ( mbox @ ( subclass @ U @ X ) ) ) @ ( mbox @ ( member @ U @ ( power_class @ X ) ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(power_class_0,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [U: $i] : ( mbox @ ( mimplies @ ( mbox @ ( member @ U @ universal_class ) ) @ ( mbox @ ( member @ ( power_class @ U ) @ universal_class ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(compose_defn1,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [XR: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [YR: $i] : ( mbox @ ( subclass @ ( compose @ YR @ XR ) @ ( cross_product @ universal_class @ universal_class ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(compose_defn2,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [XR: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [YR: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [U: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [V: $i] : ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( member @ ( ordered_pair @ U @ V ) @ ( compose @ YR @ XR ) ) ) @ ( mand @ ( mbox @ ( member @ U @ universal_class ) ) @ ( mbox @ ( member @ V @ ( image @ YR @ ( image @ YR @ ( singleton @ U ) ) ) ) ) ) ) ) @ ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( member @ U @ universal_class ) ) @ ( mbox @ ( member @ V @ ( image @ YR @ ( image @ YR @ ( singleton @ U ) ) ) ) ) ) @ ( mbox @ ( member @ ( ordered_pair @ U @ V ) @ ( compose @ YR @ XR ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(function_defn,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [XF: $i] : ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( function @ XF ) ) @ ( mand @ ( mbox @ ( subclass @ XF @ ( cross_product @ universal_class @ universal_class ) ) ) @ ( mbox @ ( subclass @ ( compose @ XF @ ( inverse @ XF ) ) @ identity_relation ) ) ) ) ) @ ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( subclass @ XF @ ( cross_product @ universal_class @ universal_class ) ) ) @ ( mbox @ ( subclass @ ( compose @ XF @ ( inverse @ XF ) ) @ identity_relation ) ) ) @ ( mbox @ ( function @ XF ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(replacement,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [X: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [XF: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( member @ X @ universal_class ) ) @ ( mbox @ ( function @ XF ) ) ) @ ( mbox @ ( member @ ( image @ XF @ X ) @ universal_class ) ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(disjoint_defn,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [X: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [Y: $i] : % 0.09/0.40 ( mand % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mimplies @ ( mbox @ ( disjoint @ X @ Y ) ) % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [U: $i] : ( mbox @ ( mnot @ ( mand @ ( mbox @ ( member @ U @ X ) ) @ ( mbox @ ( member @ U @ Y ) ) ) ) ) ) ) ) ) % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mimplies % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [U: $i] : ( mbox @ ( mnot @ ( mand @ ( mbox @ ( member @ U @ X ) ) @ ( mbox @ ( member @ U @ Y ) ) ) ) ) ) ) % 0.09/0.40 @ ( mbox @ ( disjoint @ X @ Y ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(regularity,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [X: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mimplies @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ X @ null_class ) ) ) ) % 0.09/0.40 @ ( mexists_di % 0.09/0.40 @ ^ [U: $i] : ( mand @ ( mbox @ ( member @ U @ universal_class ) ) @ ( mand @ ( mbox @ ( member @ U @ X ) ) @ ( mbox @ ( disjoint @ U @ X ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(apply_defn,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [XF: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [Y: $i] : ( mbox @ ( qmltpeq @ ( apply @ XF @ Y ) @ ( sum_class @ ( image @ XF @ ( singleton @ Y ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(choice,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mexists_di % 0.09/0.40 @ ^ [XF: $i] : % 0.09/0.40 ( mand @ ( mbox @ ( function @ XF ) ) % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [Y: $i] : ( mbox @ ( mimplies @ ( mbox @ ( member @ Y @ universal_class ) ) @ ( mor @ ( mbox @ ( qmltpeq @ Y @ null_class ) ) @ ( mbox @ ( member @ ( apply @ XF @ Y ) @ Y ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(reflexivity_of_subclass,conjecture, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [X: $i] : ( mbox @ ( subclass @ X @ X ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 %------------------------------------------------------------------------------ % 0.09/0.40 ------------------------ % 0.09/0.40 /starexec/sw/sutcliffe/jdk-11.0.2/bin/java: Command not found. % 0.09/0.40 ---- Embedded in THF --- % 0.09/0.40 ------------------------ % 0.09/0.42 ---- Cleaned THF --- % 0.09/0.42 ------------------------ % 0.09/0.44 % (1414794)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_1414767 for (3000ds/4Mi) % 0.09/0.44 % (1414794)First to succeed. % 0.09/0.44 % SZS status Satisfiable for DTF2THF_1414767 % 0.09/0.44 % (1414794)# SZS output start Saturation. % 0.09/0.44 % (1414794)# SZS output end Saturation. % 0.09/0.44 % (1414794)------------------------------ % 0.09/0.44 % (1414794)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) % 0.09/0.44 % (1414794)Termination reason: Satisfiable % 0.09/0.44 % 0.09/0.44 % (1414794)Memory used [KB]: 5373 % 0.09/0.44 % (1414794)Time elapsed: 0.001 s % 0.09/0.44 % (1414794)------------------------------ % 0.09/0.44 % (1414794)------------------------------ % 0.09/0.44 % (1414792)Success in time 0.008 s %------------------------------------------------------------------------------