%------------------------------------------------------------------------------ % File : DT2H2X---1.9.5 % Problem : LCL954^19 : TPTP v9.3.1. Released v8.1.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300 % Computer : n002.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 11:35:15 AM UTC 2026 % Result : CounterSatisfiable 0.11s 0.45s % Output : Saturation 0.11s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL954^19 : TPTP v9.3.1. Released v8.1.0. % 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300 % 0.11/0.37 % Computer : n002.cluster.edu % 0.11/0.37 % Model : x86_64 x86_64 % 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.37 % Memory : 8046.5625MB % 0.11/0.37 % OS : Linux 6.8.0-71-generic % 0.11/0.37 % CPULimit : 300 % 0.11/0.37 % WCLimit : 300 % 0.11/0.37 % DateTime : Fri Sep 4 14:30:05 UTC 2026 % 0.11/0.37 % CPUTime : % 0.11/0.37 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300 % 0.11/0.39 ---- Original DTF file --- % 0.11/0.40 thf(spec,logic,$$dhol). % 0.11/0.40 %------------------------------------------------------------------------------ % 0.11/0.40 % File : LCL954^19 : TPTP v9.3.1. Released v8.1.0. % 0.11/0.40 % Domain : Logic Calculi % 0.11/0.40 % Problem : Goedel translation of SWV060+1 (from TPTP-v5.0.0) % 0.11/0.40 % Version : [BP13] axioms. % 0.11/0.40 % English : % 0.11/0.40 % 0.11/0.40 % Refs : [RO12] Raths & Otten (2012), The QMLTP Problem Library for Fi % 0.11/0.40 % : [BP13] Benzmueller & Paulson (2013), Quantified Multimodal Lo % 0.11/0.40 % : [Ste22] Steen (2022), An Extensible Logic Embedding Tool for L % 0.11/0.40 % Source : [TPTP] % 0.11/0.40 % Names : GSV060+1 [QMLTP] % 0.11/0.40 % 0.11/0.40 % Status : Theorem % 0.11/0.40 % Rating : 0.17 v9.3.0, 0.22 v9.1.0, 0.25 v9.0.0, 0.20 v8.2.0, 0.31 v8.1.0 % 0.11/0.40 % Syntax : Number of formulae : 195 ( 12 unt; 48 typ; 10 def) % 0.11/0.40 % Number of atoms : 1906 ( 10 equ; 0 cnn) % 0.11/0.40 % Maximal formula atoms : 97 ( 12 avg) % 0.11/0.40 % Number of connectives : 3056 ( 1 ~; 1 |; 4 &;3045 @) % 0.11/0.40 % ( 1 <=>; 4 =>; 0 <=; 0 <~>) % 0.11/0.40 % Maximal formula depth : 51 ( 15 avg) % 0.11/0.40 % Number of types : 3 ( 1 usr) % 0.11/0.40 % Number of type conns : 113 ( 113 >; 0 *; 0 +; 0 <<) % 0.11/0.40 % Number of symbols : 48 ( 47 usr; 11 con; 0-4 aty) % 0.11/0.40 % Number of variables : 361 ( 351 ^; 7 !; 3 ?; 361 :) % 0.11/0.40 % SPC : TH0_THM_EQU_NAR_NDT % 0.11/0.40 % 0.11/0.40 % Comments : This output was generated by embedproblem, version 1.7.1 (library % 0.11/0.40 % version 1.3). Generated on Thu Apr 28 13:18:18 EDT 2022 using % 0.11/0.40 % 'modal' embedding, version 1.5.2. Logic specification used: % 0.11/0.40 % $modal == [$constants == $rigid,$quantification == $varying, % 0.11/0.40 % $modalities == $modal_system_S4]. % 0.11/0.40 %------------------------------------------------------------------------------ % 0.11/0.40 thf(mworld,type, % 0.11/0.40 mworld: $tType ). % 0.11/0.40 % 0.11/0.40 thf(mrel_type,type, % 0.11/0.40 mrel: mworld > mworld > $o ). % 0.11/0.40 % 0.11/0.40 thf(mactual_type,type, % 0.11/0.40 mactual: mworld ). % 0.11/0.40 % 0.11/0.40 thf(mlocal_type,type, % 0.11/0.40 mlocal: ( mworld > $o ) > $o ). % 0.11/0.40 % 0.11/0.40 thf(mlocal_def,definition, % 0.11/0.40 ( mlocal % 0.11/0.40 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(mnot_type,type, % 0.11/0.40 mnot: ( mworld > $o ) > mworld > $o ). % 0.11/0.40 % 0.11/0.40 thf(mand_type,type, % 0.11/0.40 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ). % 0.11/0.40 % 0.11/0.40 thf(mor_type,type, % 0.11/0.40 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ). % 0.11/0.40 % 0.11/0.40 thf(mimplies_type,type, % 0.11/0.40 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ). % 0.11/0.40 % 0.11/0.40 thf(mequiv_type,type, % 0.11/0.40 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ). % 0.11/0.40 % 0.11/0.40 thf(mnot_def,definition, % 0.11/0.40 ( mnot % 0.11/0.40 = ( ^ [A: mworld > $o,W: mworld] : % 0.11/0.40 ~ ( A @ W ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(mand_def,definition, % 0.11/0.40 ( mand % 0.11/0.40 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] : % 0.11/0.40 ( ( A @ W ) % 0.11/0.40 & ( B @ W ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(mor_def,definition, % 0.11/0.40 ( mor % 0.11/0.40 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] : % 0.11/0.40 ( ( A @ W ) % 0.11/0.40 | ( B @ W ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(mimplies_def,definition, % 0.11/0.40 ( mimplies % 0.11/0.40 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] : % 0.11/0.40 ( ( A @ W ) % 0.11/0.40 => ( B @ W ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(mequiv_def,definition, % 0.11/0.40 ( mequiv % 0.11/0.40 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] : % 0.11/0.40 ( ( A @ W ) % 0.11/0.40 <=> ( B @ W ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(mbox_type,type, % 0.11/0.40 mbox: ( mworld > $o ) > mworld > $o ). % 0.11/0.40 % 0.11/0.40 thf(mbox_def,definition, % 0.11/0.40 ( mbox % 0.11/0.40 = ( ^ [Phi: mworld > $o,W: mworld] : % 0.11/0.40 ! [V: mworld] : % 0.11/0.40 ( ( mrel @ W @ V ) % 0.11/0.40 => ( Phi @ V ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(mdia_type,type, % 0.11/0.40 mdia: ( mworld > $o ) > mworld > $o ). % 0.11/0.40 % 0.11/0.40 thf(mdia_def,definition, % 0.11/0.40 ( mdia % 0.11/0.40 = ( ^ [Phi: mworld > $o,W: mworld] : % 0.11/0.40 ? [V: mworld] : % 0.11/0.40 ( ( mrel @ W @ V ) % 0.11/0.40 & ( Phi @ V ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(mrel_reflexive,axiom, % 0.11/0.40 ! [W: mworld] : ( mrel @ W @ W ) ). % 0.11/0.40 % 0.11/0.40 thf(mrel_transitive,axiom, % 0.11/0.40 ! [W: mworld,V: mworld,U: mworld] : % 0.11/0.40 ( ( ( mrel @ W @ V ) % 0.11/0.40 & ( mrel @ V @ U ) ) % 0.11/0.40 => ( mrel @ W @ U ) ) ). % 0.11/0.40 % 0.11/0.40 thf(eiw_di_type,type, % 0.11/0.40 eiw_di: $i > mworld > $o ). % 0.11/0.40 % 0.11/0.40 thf(eiw_di_nonempty,axiom, % 0.11/0.40 ! [W: mworld] : % 0.11/0.40 ? [X: $i] : ( eiw_di @ X @ W ) ). % 0.11/0.40 % 0.11/0.40 thf(mforall_di_type,type, % 0.11/0.40 mforall_di: ( $i > mworld > $o ) > mworld > $o ). % 0.11/0.40 % 0.11/0.40 thf(mforall_di_def,definition, % 0.11/0.40 ( mforall_di % 0.11/0.40 = ( ^ [A: $i > mworld > $o,W: mworld] : % 0.11/0.40 ! [X: $i] : % 0.11/0.40 ( ( eiw_di @ X @ W ) % 0.11/0.40 => ( A @ X @ W ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(mexists_di_type,type, % 0.11/0.40 mexists_di: ( $i > mworld > $o ) > mworld > $o ). % 0.11/0.40 % 0.11/0.40 thf(mexists_di_def,definition, % 0.11/0.40 ( mexists_di % 0.11/0.40 = ( ^ [A: $i > mworld > $o,W: mworld] : % 0.11/0.40 ? [X: $i] : % 0.11/0.40 ( ( eiw_di @ X @ W ) % 0.11/0.40 & ( A @ X @ W ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(typedecl_customqmltpeq,type, % 0.11/0.40 customqmltpeq: $i > $i > mworld > $o ). % 0.11/0.40 % 0.11/0.40 thf(true_decl,type, % 0.11/0.40 true: mworld > $o ). % 0.11/0.40 % 0.11/0.40 thf(def_decl,type, % 0.11/0.40 def: $i ). % 0.11/0.40 % 0.11/0.40 thf(tptp_minus_1_decl,type, % 0.11/0.40 tptp_minus_1: $i ). % 0.11/0.40 % 0.11/0.40 thf(tptp_float_0_0_decl,type, % 0.11/0.40 tptp_float_0_0: $i ). % 0.11/0.40 % 0.11/0.40 thf(n0_decl,type, % 0.11/0.40 n0: $i ). % 0.11/0.40 % 0.11/0.40 thf(n1_decl,type, % 0.11/0.40 n1: $i ). % 0.11/0.40 % 0.11/0.40 thf(n2_decl,type, % 0.11/0.40 n2: $i ). % 0.11/0.40 % 0.11/0.40 thf(n3_decl,type, % 0.11/0.40 n3: $i ). % 0.11/0.40 % 0.11/0.40 thf(n4_decl,type, % 0.11/0.40 n4: $i ). % 0.11/0.40 % 0.11/0.40 thf(use_decl,type, % 0.11/0.40 use: $i ). % 0.11/0.40 % 0.11/0.40 thf(n5_decl,type, % 0.11/0.40 n5: $i ). % 0.11/0.40 % 0.11/0.40 thf(geq_decl,type, % 0.11/0.40 geq: $i > $i > mworld > $o ). % 0.11/0.40 % 0.11/0.40 thf(lt_decl,type, % 0.11/0.40 lt: $i > $i > mworld > $o ). % 0.11/0.40 % 0.11/0.40 thf(leq_decl,type, % 0.11/0.40 leq: $i > $i > mworld > $o ). % 0.11/0.40 % 0.11/0.40 thf(gt_decl,type, % 0.11/0.40 gt: $i > $i > mworld > $o ). % 0.11/0.40 % 0.11/0.40 thf(minus_decl,type, % 0.11/0.40 minus: $i > $i > $i ). % 0.11/0.40 % 0.11/0.40 thf(dim_decl,type, % 0.11/0.40 dim: $i > $i > $i ). % 0.11/0.40 % 0.11/0.40 thf(sum_decl,type, % 0.11/0.40 sum: $i > $i > $i > $i ). % 0.11/0.40 % 0.11/0.40 thf(plus_decl,type, % 0.11/0.40 plus: $i > $i > $i ). % 0.11/0.40 % 0.11/0.40 thf(inv_decl,type, % 0.11/0.40 inv: $i > $i ). % 0.11/0.40 % 0.11/0.40 thf(uniform_int_rnd_decl,type, % 0.11/0.40 uniform_int_rnd: $i > $i > $i ). % 0.11/0.40 % 0.11/0.40 thf(succ_decl,type, % 0.11/0.40 succ: $i > $i ). % 0.11/0.40 % 0.11/0.40 thf(pred_decl,type, % 0.11/0.40 pred: $i > $i ). % 0.11/0.40 % 0.11/0.40 thf(tptp_update3_decl,type, % 0.11/0.40 tptp_update3: $i > $i > $i > $i > $i ). % 0.11/0.40 % 0.11/0.40 thf(tptp_update2_decl,type, % 0.11/0.40 tptp_update2: $i > $i > $i > $i ). % 0.11/0.40 % 0.11/0.40 thf(tptp_const_array1_decl,type, % 0.11/0.40 tptp_const_array1: $i > $i > $i ). % 0.11/0.40 % 0.11/0.40 thf(tptp_mmul_decl,type, % 0.11/0.40 tptp_mmul: $i > $i > $i ). % 0.11/0.40 % 0.11/0.40 thf(a_select3_decl,type, % 0.11/0.40 a_select3: $i > $i > $i > $i ). % 0.11/0.40 % 0.11/0.40 thf(tptp_const_array2_decl,type, % 0.11/0.40 tptp_const_array2: $i > $i > $i > $i ). % 0.11/0.40 % 0.11/0.40 thf(a_select2_decl,type, % 0.11/0.40 a_select2: $i > $i > $i ). % 0.11/0.40 % 0.11/0.40 thf(tptp_madd_decl,type, % 0.11/0.40 tptp_madd: $i > $i > $i ). % 0.11/0.40 % 0.11/0.40 thf(tptp_msub_decl,type, % 0.11/0.40 tptp_msub: $i > $i > $i ). % 0.11/0.40 % 0.11/0.40 thf(trans_decl,type, % 0.11/0.40 trans: $i > $i ). % 0.11/0.40 % 0.11/0.40 thf(reflexivity,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [X: $i] : ( mbox @ ( customqmltpeq @ X @ X ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(symmetry,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [X: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [Y: $i] : ( mbox @ ( mimplies @ ( mbox @ ( customqmltpeq @ X @ Y ) ) @ ( mbox @ ( customqmltpeq @ Y @ X ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(transitivity,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [X: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [Y: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [Z: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( customqmltpeq @ X @ Y ) ) @ ( mbox @ ( customqmltpeq @ Y @ Z ) ) ) @ ( mbox @ ( customqmltpeq @ X @ Z ) ) ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(a_select2_substitution_1,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [A: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [B: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( customqmltpeq @ A @ B ) ) @ ( mbox @ ( customqmltpeq @ ( a_select2 @ A @ C ) @ ( a_select2 @ B @ C ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(a_select2_substitution_2,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [A: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [B: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( customqmltpeq @ A @ B ) ) @ ( mbox @ ( customqmltpeq @ ( a_select2 @ C @ A ) @ ( a_select2 @ C @ B ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(a_select3_substitution_1,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [A: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [B: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [C: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [D: $i] : ( mbox @ ( mimplies @ ( mbox @ ( customqmltpeq @ A @ B ) ) @ ( mbox @ ( customqmltpeq @ ( a_select3 @ A @ C @ D ) @ ( a_select3 @ B @ C @ D ) ) ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(a_select3_substitution_2,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [A: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [B: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [C: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [D: $i] : ( mbox @ ( mimplies @ ( mbox @ ( customqmltpeq @ A @ B ) ) @ ( mbox @ ( customqmltpeq @ ( a_select3 @ C @ A @ D ) @ ( a_select3 @ C @ B @ D ) ) ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(a_select3_substitution_3,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [A: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [B: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [C: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [D: $i] : ( mbox @ ( mimplies @ ( mbox @ ( customqmltpeq @ A @ B ) ) @ ( mbox @ ( customqmltpeq @ ( a_select3 @ C @ D @ A ) @ ( a_select3 @ C @ D @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(dim_substitution_1,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [A: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [B: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( customqmltpeq @ A @ B ) ) @ ( mbox @ ( customqmltpeq @ ( dim @ A @ C ) @ ( dim @ B @ C ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(dim_substitution_2,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [A: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [B: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( customqmltpeq @ A @ B ) ) @ ( mbox @ ( customqmltpeq @ ( dim @ C @ A ) @ ( dim @ C @ B ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(inv_substitution_1,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [A: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [B: $i] : ( mbox @ ( mimplies @ ( mbox @ ( customqmltpeq @ A @ B ) ) @ ( mbox @ ( customqmltpeq @ ( inv @ A ) @ ( inv @ B ) ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(minus_substitution_1,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [A: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [B: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( customqmltpeq @ A @ B ) ) @ ( mbox @ ( customqmltpeq @ ( minus @ A @ C ) @ ( minus @ B @ C ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(minus_substitution_2,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [A: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [B: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( customqmltpeq @ A @ B ) ) @ ( mbox @ ( customqmltpeq @ ( minus @ C @ A ) @ ( minus @ C @ B ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(plus_substitution_1,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [A: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [B: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( customqmltpeq @ A @ B ) ) @ ( mbox @ ( customqmltpeq @ ( plus @ A @ C ) @ ( plus @ B @ C ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(plus_substitution_2,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [A: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [B: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( customqmltpeq @ A @ B ) ) @ ( mbox @ ( customqmltpeq @ ( plus @ C @ A ) @ ( plus @ C @ B ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(pred_substitution_1,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [A: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [B: $i] : ( mbox @ ( mimplies @ ( mbox @ ( customqmltpeq @ A @ B ) ) @ ( mbox @ ( customqmltpeq @ ( pred @ A ) @ ( pred @ B ) ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(succ_substitution_1,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [A: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [B: $i] : ( mbox @ ( mimplies @ ( mbox @ ( customqmltpeq @ A @ B ) ) @ ( mbox @ ( customqmltpeq @ ( succ @ A ) @ ( succ @ B ) ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(sum_substitution_1,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [A: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [B: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [C: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [D: $i] : ( mbox @ ( mimplies @ ( mbox @ ( customqmltpeq @ A @ B ) ) @ ( mbox @ ( customqmltpeq @ ( sum @ A @ C @ D ) @ ( sum @ B @ C @ D ) ) ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(sum_substitution_2,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [A: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [B: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [C: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [D: $i] : ( mbox @ ( mimplies @ ( mbox @ ( customqmltpeq @ A @ B ) ) @ ( mbox @ ( customqmltpeq @ ( sum @ C @ A @ D ) @ ( sum @ C @ B @ D ) ) ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(sum_substitution_3,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [A: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [B: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [C: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [D: $i] : ( mbox @ ( mimplies @ ( mbox @ ( customqmltpeq @ A @ B ) ) @ ( mbox @ ( customqmltpeq @ ( sum @ C @ D @ A ) @ ( sum @ C @ D @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(tptp_const_array1_substitution_1,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [A: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [B: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( customqmltpeq @ A @ B ) ) @ ( mbox @ ( customqmltpeq @ ( tptp_const_array1 @ A @ C ) @ ( tptp_const_array1 @ B @ C ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(tptp_const_array1_substitution_2,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [A: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [B: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( customqmltpeq @ A @ B ) ) @ ( mbox @ ( customqmltpeq @ ( tptp_const_array1 @ C @ A ) @ ( tptp_const_array1 @ C @ B ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(tptp_const_array2_substitution_1,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [A: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [B: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [C: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [D: $i] : ( mbox @ ( mimplies @ ( mbox @ ( customqmltpeq @ A @ B ) ) @ ( mbox @ ( customqmltpeq @ ( tptp_const_array2 @ A @ C @ D ) @ ( tptp_const_array2 @ B @ C @ D ) ) ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(tptp_const_array2_substitution_2,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [A: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [B: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [C: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [D: $i] : ( mbox @ ( mimplies @ ( mbox @ ( customqmltpeq @ A @ B ) ) @ ( mbox @ ( customqmltpeq @ ( tptp_const_array2 @ C @ A @ D ) @ ( tptp_const_array2 @ C @ B @ D ) ) ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(tptp_const_array2_substitution_3,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [A: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [B: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [C: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [D: $i] : ( mbox @ ( mimplies @ ( mbox @ ( customqmltpeq @ A @ B ) ) @ ( mbox @ ( customqmltpeq @ ( tptp_const_array2 @ C @ D @ A ) @ ( tptp_const_array2 @ C @ D @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(tptp_madd_substitution_1,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [A: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [B: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( customqmltpeq @ A @ B ) ) @ ( mbox @ ( customqmltpeq @ ( tptp_madd @ A @ C ) @ ( tptp_madd @ B @ C ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(tptp_madd_substitution_2,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [A: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [B: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( customqmltpeq @ A @ B ) ) @ ( mbox @ ( customqmltpeq @ ( tptp_madd @ C @ A ) @ ( tptp_madd @ C @ B ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(tptp_mmul_substitution_1,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [A: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [B: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( customqmltpeq @ A @ B ) ) @ ( mbox @ ( customqmltpeq @ ( tptp_mmul @ A @ C ) @ ( tptp_mmul @ B @ C ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(tptp_mmul_substitution_2,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [A: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [B: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( customqmltpeq @ A @ B ) ) @ ( mbox @ ( customqmltpeq @ ( tptp_mmul @ C @ A ) @ ( tptp_mmul @ C @ B ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(tptp_msub_substitution_1,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [A: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [B: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( customqmltpeq @ A @ B ) ) @ ( mbox @ ( customqmltpeq @ ( tptp_msub @ A @ C ) @ ( tptp_msub @ B @ C ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(tptp_msub_substitution_2,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [A: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [B: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( customqmltpeq @ A @ B ) ) @ ( mbox @ ( customqmltpeq @ ( tptp_msub @ C @ A ) @ ( tptp_msub @ C @ B ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(tptp_update2_substitution_1,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [A: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [B: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [C: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [D: $i] : ( mbox @ ( mimplies @ ( mbox @ ( customqmltpeq @ A @ B ) ) @ ( mbox @ ( customqmltpeq @ ( tptp_update2 @ A @ C @ D ) @ ( tptp_update2 @ B @ C @ D ) ) ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(tptp_update2_substitution_2,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [A: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [B: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [C: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [D: $i] : ( mbox @ ( mimplies @ ( mbox @ ( customqmltpeq @ A @ B ) ) @ ( mbox @ ( customqmltpeq @ ( tptp_update2 @ C @ A @ D ) @ ( tptp_update2 @ C @ B @ D ) ) ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(tptp_update2_substitution_3,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [A: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [B: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [C: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [D: $i] : ( mbox @ ( mimplies @ ( mbox @ ( customqmltpeq @ A @ B ) ) @ ( mbox @ ( customqmltpeq @ ( tptp_update2 @ C @ D @ A ) @ ( tptp_update2 @ C @ D @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(tptp_update3_substitution_1,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [A: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [B: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [C: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [D: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [E: $i] : ( mbox @ ( mimplies @ ( mbox @ ( customqmltpeq @ A @ B ) ) @ ( mbox @ ( customqmltpeq @ ( tptp_update3 @ A @ C @ D @ E ) @ ( tptp_update3 @ B @ C @ D @ E ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(tptp_update3_substitution_2,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [A: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [B: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [C: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [D: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [E: $i] : ( mbox @ ( mimplies @ ( mbox @ ( customqmltpeq @ A @ B ) ) @ ( mbox @ ( customqmltpeq @ ( tptp_update3 @ C @ A @ D @ E ) @ ( tptp_update3 @ C @ B @ D @ E ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(tptp_update3_substitution_3,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [A: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [B: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [C: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [D: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [E: $i] : ( mbox @ ( mimplies @ ( mbox @ ( customqmltpeq @ A @ B ) ) @ ( mbox @ ( customqmltpeq @ ( tptp_update3 @ C @ D @ A @ E ) @ ( tptp_update3 @ C @ D @ B @ E ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(tptp_update3_substitution_4,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [A: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [B: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [C: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [D: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [E: $i] : ( mbox @ ( mimplies @ ( mbox @ ( customqmltpeq @ A @ B ) ) @ ( mbox @ ( customqmltpeq @ ( tptp_update3 @ C @ D @ E @ A ) @ ( tptp_update3 @ C @ D @ E @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(trans_substitution_1,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [A: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [B: $i] : ( mbox @ ( mimplies @ ( mbox @ ( customqmltpeq @ A @ B ) ) @ ( mbox @ ( customqmltpeq @ ( trans @ A ) @ ( trans @ B ) ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(uniform_int_rnd_substitution_1,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [A: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [B: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( customqmltpeq @ A @ B ) ) @ ( mbox @ ( customqmltpeq @ ( uniform_int_rnd @ A @ C ) @ ( uniform_int_rnd @ B @ C ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(uniform_int_rnd_substitution_2,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [A: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [B: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( customqmltpeq @ A @ B ) ) @ ( mbox @ ( customqmltpeq @ ( uniform_int_rnd @ C @ A ) @ ( uniform_int_rnd @ C @ B ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(geq_substitution_1,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [A: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [B: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( customqmltpeq @ A @ B ) ) @ ( mbox @ ( geq @ A @ C ) ) ) @ ( mbox @ ( geq @ B @ C ) ) ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(geq_substitution_2,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [A: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [B: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( customqmltpeq @ A @ B ) ) @ ( mbox @ ( geq @ C @ A ) ) ) @ ( mbox @ ( geq @ C @ B ) ) ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(gt_substitution_1,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [A: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [B: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( customqmltpeq @ A @ B ) ) @ ( mbox @ ( gt @ A @ C ) ) ) @ ( mbox @ ( gt @ B @ C ) ) ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(gt_substitution_2,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [A: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [B: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( customqmltpeq @ A @ B ) ) @ ( mbox @ ( gt @ C @ A ) ) ) @ ( mbox @ ( gt @ C @ B ) ) ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(leq_substitution_1,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [A: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [B: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( customqmltpeq @ A @ B ) ) @ ( mbox @ ( leq @ A @ C ) ) ) @ ( mbox @ ( leq @ B @ C ) ) ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(leq_substitution_2,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [A: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [B: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( customqmltpeq @ A @ B ) ) @ ( mbox @ ( leq @ C @ A ) ) ) @ ( mbox @ ( leq @ C @ B ) ) ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(lt_substitution_1,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [A: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [B: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( customqmltpeq @ A @ B ) ) @ ( mbox @ ( lt @ A @ C ) ) ) @ ( mbox @ ( lt @ B @ C ) ) ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(lt_substitution_2,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [A: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [B: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( customqmltpeq @ A @ B ) ) @ ( mbox @ ( lt @ C @ A ) ) ) @ ( mbox @ ( lt @ C @ B ) ) ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(totality,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [X: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [Y: $i] : ( mor @ ( mbox @ ( gt @ X @ Y ) ) @ ( mor @ ( mbox @ ( gt @ Y @ X ) ) @ ( mbox @ ( customqmltpeq @ X @ Y ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(transitivity_gt,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [X: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [Y: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [Z: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( gt @ X @ Y ) ) @ ( mbox @ ( gt @ Y @ Z ) ) ) @ ( mbox @ ( gt @ X @ Z ) ) ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(irreflexivity_gt,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [X: $i] : ( mbox @ ( mnot @ ( mbox @ ( gt @ X @ X ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(reflexivity_leq,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [X: $i] : ( mbox @ ( leq @ X @ X ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(transitivity_leq,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [X: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [Y: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [Z: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( leq @ X @ Y ) ) @ ( mbox @ ( leq @ Y @ Z ) ) ) @ ( mbox @ ( leq @ X @ Z ) ) ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(lt_gt,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [X: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [Y: $i] : ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( lt @ X @ Y ) ) @ ( mbox @ ( gt @ Y @ X ) ) ) ) @ ( mbox @ ( mimplies @ ( mbox @ ( gt @ Y @ X ) ) @ ( mbox @ ( lt @ X @ Y ) ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(leq_geq,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [X: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [Y: $i] : ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( geq @ X @ Y ) ) @ ( mbox @ ( leq @ Y @ X ) ) ) ) @ ( mbox @ ( mimplies @ ( mbox @ ( leq @ Y @ X ) ) @ ( mbox @ ( geq @ X @ Y ) ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(leq_gt1,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [X: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [Y: $i] : ( mbox @ ( mimplies @ ( mbox @ ( gt @ Y @ X ) ) @ ( mbox @ ( leq @ X @ Y ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(leq_gt2,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [X: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [Y: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( leq @ X @ Y ) ) @ ( mbox @ ( mnot @ ( mbox @ ( customqmltpeq @ X @ Y ) ) ) ) ) @ ( mbox @ ( gt @ Y @ X ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(leq_gt_pred,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [X: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [Y: $i] : ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( leq @ X @ ( pred @ Y ) ) ) @ ( mbox @ ( gt @ Y @ X ) ) ) ) @ ( mbox @ ( mimplies @ ( mbox @ ( gt @ Y @ X ) ) @ ( mbox @ ( leq @ X @ ( pred @ Y ) ) ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(gt_succ,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [X: $i] : ( mbox @ ( gt @ ( succ @ X ) @ X ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(leq_succ,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [X: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [Y: $i] : ( mbox @ ( mimplies @ ( mbox @ ( leq @ X @ Y ) ) @ ( mbox @ ( leq @ X @ ( succ @ Y ) ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(leq_succ_gt_equiv,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [X: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [Y: $i] : ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( leq @ X @ Y ) ) @ ( mbox @ ( gt @ ( succ @ Y ) @ X ) ) ) ) @ ( mbox @ ( mimplies @ ( mbox @ ( gt @ ( succ @ Y ) @ X ) ) @ ( mbox @ ( leq @ X @ Y ) ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(uniform_int_rand_ranges_hi,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [X: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( leq @ n0 @ X ) ) @ ( mbox @ ( leq @ ( uniform_int_rnd @ C @ X ) @ X ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(uniform_int_rand_ranges_lo,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [X: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( leq @ n0 @ X ) ) @ ( mbox @ ( leq @ n0 @ ( uniform_int_rnd @ C @ X ) ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(const_array1_select,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [I: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [L: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [U: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [Val: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( leq @ L @ I ) ) @ ( mbox @ ( leq @ I @ U ) ) ) @ ( mbox @ ( customqmltpeq @ ( a_select2 @ ( tptp_const_array1 @ ( dim @ L @ U ) @ Val ) @ I ) @ Val ) ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(const_array2_select,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [I: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [L1: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [U1: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [J: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [L2: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [U2: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [Val: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( leq @ L1 @ I ) ) @ ( mand @ ( mbox @ ( leq @ I @ U1 ) ) @ ( mand @ ( mbox @ ( leq @ L2 @ J ) ) @ ( mbox @ ( leq @ J @ U2 ) ) ) ) ) @ ( mbox @ ( customqmltpeq @ ( a_select3 @ ( tptp_const_array2 @ ( dim @ L1 @ U1 ) @ ( dim @ L2 @ U2 ) @ Val ) @ I @ J ) @ Val ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(matrix_symm_trans,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [A: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [N: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mimplies % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [I: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [J: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( leq @ n0 @ I ) ) @ ( mand @ ( mbox @ ( leq @ I @ N ) ) @ ( mand @ ( mbox @ ( leq @ n0 @ J ) ) @ ( mbox @ ( leq @ J @ N ) ) ) ) ) @ ( mbox @ ( customqmltpeq @ ( a_select3 @ A @ I @ J ) @ ( a_select3 @ A @ J @ I ) ) ) ) ) ) ) ) ) % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [I: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [J: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( leq @ n0 @ I ) ) @ ( mand @ ( mbox @ ( leq @ I @ N ) ) @ ( mand @ ( mbox @ ( leq @ n0 @ J ) ) @ ( mbox @ ( leq @ J @ N ) ) ) ) ) @ ( mbox @ ( customqmltpeq @ ( a_select3 @ ( trans @ A ) @ I @ J ) @ ( a_select3 @ ( trans @ A ) @ J @ I ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(matrix_symm_inv,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [A: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [N: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mimplies % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [I: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [J: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( leq @ n0 @ I ) ) @ ( mand @ ( mbox @ ( leq @ I @ N ) ) @ ( mand @ ( mbox @ ( leq @ n0 @ J ) ) @ ( mbox @ ( leq @ J @ N ) ) ) ) ) @ ( mbox @ ( customqmltpeq @ ( a_select3 @ A @ I @ J ) @ ( a_select3 @ A @ J @ I ) ) ) ) ) ) ) ) ) % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [I: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [J: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( leq @ n0 @ I ) ) @ ( mand @ ( mbox @ ( leq @ I @ N ) ) @ ( mand @ ( mbox @ ( leq @ n0 @ J ) ) @ ( mbox @ ( leq @ J @ N ) ) ) ) ) @ ( mbox @ ( customqmltpeq @ ( a_select3 @ ( inv @ A ) @ I @ J ) @ ( a_select3 @ ( inv @ A ) @ J @ I ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(matrix_symm_update_diagonal,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [A: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [N: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mimplies % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [I: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [J: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( leq @ n0 @ I ) ) @ ( mand @ ( mbox @ ( leq @ I @ N ) ) @ ( mand @ ( mbox @ ( leq @ n0 @ J ) ) @ ( mbox @ ( leq @ J @ N ) ) ) ) ) @ ( mbox @ ( customqmltpeq @ ( a_select3 @ A @ I @ J ) @ ( a_select3 @ A @ J @ I ) ) ) ) ) ) ) ) ) % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [I: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [J: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [K: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [VAL: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( leq @ n0 @ I ) ) @ ( mand @ ( mbox @ ( leq @ I @ N ) ) @ ( mand @ ( mbox @ ( leq @ n0 @ J ) ) @ ( mand @ ( mbox @ ( leq @ J @ N ) ) @ ( mand @ ( mbox @ ( leq @ n0 @ K ) ) @ ( mbox @ ( leq @ K @ N ) ) ) ) ) ) ) @ ( mbox @ ( customqmltpeq @ ( a_select3 @ ( tptp_update3 @ A @ K @ K @ VAL ) @ I @ J ) @ ( a_select3 @ ( tptp_update3 @ A @ K @ K @ VAL ) @ J @ I ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(matrix_symm_add,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [A: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [B: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [N: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mimplies % 0.11/0.40 @ ( mand % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [I: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [J: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( leq @ n0 @ I ) ) @ ( mand @ ( mbox @ ( leq @ I @ N ) ) @ ( mand @ ( mbox @ ( leq @ n0 @ J ) ) @ ( mbox @ ( leq @ J @ N ) ) ) ) ) @ ( mbox @ ( customqmltpeq @ ( a_select3 @ A @ I @ J ) @ ( a_select3 @ A @ J @ I ) ) ) ) ) ) ) ) ) % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [I: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [J: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( leq @ n0 @ I ) ) @ ( mand @ ( mbox @ ( leq @ I @ N ) ) @ ( mand @ ( mbox @ ( leq @ n0 @ J ) ) @ ( mbox @ ( leq @ J @ N ) ) ) ) ) @ ( mbox @ ( customqmltpeq @ ( a_select3 @ B @ I @ J ) @ ( a_select3 @ B @ J @ I ) ) ) ) ) ) ) ) ) ) % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [I: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [J: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( leq @ n0 @ I ) ) @ ( mand @ ( mbox @ ( leq @ I @ N ) ) @ ( mand @ ( mbox @ ( leq @ n0 @ J ) ) @ ( mbox @ ( leq @ J @ N ) ) ) ) ) @ ( mbox @ ( customqmltpeq @ ( a_select3 @ ( tptp_madd @ A @ B ) @ I @ J ) @ ( a_select3 @ ( tptp_madd @ A @ B ) @ J @ I ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(matrix_symm_sub,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [A: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [B: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [N: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mimplies % 0.11/0.40 @ ( mand % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [I: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [J: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( leq @ n0 @ I ) ) @ ( mand @ ( mbox @ ( leq @ I @ N ) ) @ ( mand @ ( mbox @ ( leq @ n0 @ J ) ) @ ( mbox @ ( leq @ J @ N ) ) ) ) ) @ ( mbox @ ( customqmltpeq @ ( a_select3 @ A @ I @ J ) @ ( a_select3 @ A @ J @ I ) ) ) ) ) ) ) ) ) % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [I: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [J: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( leq @ n0 @ I ) ) @ ( mand @ ( mbox @ ( leq @ I @ N ) ) @ ( mand @ ( mbox @ ( leq @ n0 @ J ) ) @ ( mbox @ ( leq @ J @ N ) ) ) ) ) @ ( mbox @ ( customqmltpeq @ ( a_select3 @ B @ I @ J ) @ ( a_select3 @ B @ J @ I ) ) ) ) ) ) ) ) ) ) % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [I: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [J: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( leq @ n0 @ I ) ) @ ( mand @ ( mbox @ ( leq @ I @ N ) ) @ ( mand @ ( mbox @ ( leq @ n0 @ J ) ) @ ( mbox @ ( leq @ J @ N ) ) ) ) ) @ ( mbox @ ( customqmltpeq @ ( a_select3 @ ( tptp_msub @ A @ B ) @ I @ J ) @ ( a_select3 @ ( tptp_msub @ A @ B ) @ J @ I ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(matrix_symm_aba1,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [A: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [B: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [N: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mimplies % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [I: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [J: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( leq @ n0 @ I ) ) @ ( mand @ ( mbox @ ( leq @ I @ N ) ) @ ( mand @ ( mbox @ ( leq @ n0 @ J ) ) @ ( mbox @ ( leq @ J @ N ) ) ) ) ) @ ( mbox @ ( customqmltpeq @ ( a_select3 @ B @ I @ J ) @ ( a_select3 @ B @ J @ I ) ) ) ) ) ) ) ) ) % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [I: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [J: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( leq @ n0 @ I ) ) @ ( mand @ ( mbox @ ( leq @ I @ N ) ) @ ( mand @ ( mbox @ ( leq @ n0 @ J ) ) @ ( mbox @ ( leq @ J @ N ) ) ) ) ) @ ( mbox @ ( customqmltpeq @ ( a_select3 @ ( tptp_mmul @ A @ ( tptp_mmul @ B @ ( trans @ A ) ) ) @ I @ J ) @ ( a_select3 @ ( tptp_mmul @ A @ ( tptp_mmul @ B @ ( trans @ A ) ) ) @ J @ I ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(matrix_symm_aba2,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [A: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [B: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [N: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [M: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mimplies % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [I: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [J: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( leq @ n0 @ I ) ) @ ( mand @ ( mbox @ ( leq @ I @ M ) ) @ ( mand @ ( mbox @ ( leq @ n0 @ J ) ) @ ( mbox @ ( leq @ J @ M ) ) ) ) ) @ ( mbox @ ( customqmltpeq @ ( a_select3 @ B @ I @ J ) @ ( a_select3 @ B @ J @ I ) ) ) ) ) ) ) ) ) % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [I: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [J: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( leq @ n0 @ I ) ) @ ( mand @ ( mbox @ ( leq @ I @ N ) ) @ ( mand @ ( mbox @ ( leq @ n0 @ J ) ) @ ( mbox @ ( leq @ J @ N ) ) ) ) ) @ ( mbox @ ( customqmltpeq @ ( a_select3 @ ( tptp_mmul @ A @ ( tptp_mmul @ B @ ( trans @ A ) ) ) @ I @ J ) @ ( a_select3 @ ( tptp_mmul @ A @ ( tptp_mmul @ B @ ( trans @ A ) ) ) @ J @ I ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(matrix_symm_joseph_update,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [A: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [B: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [C: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [D: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [E: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [F: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [N: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [M: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mimplies % 0.11/0.40 @ ( mand % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [I: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [J: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( leq @ n0 @ I ) ) @ ( mand @ ( mbox @ ( leq @ I @ M ) ) @ ( mand @ ( mbox @ ( leq @ n0 @ J ) ) @ ( mbox @ ( leq @ J @ M ) ) ) ) ) @ ( mbox @ ( customqmltpeq @ ( a_select3 @ D @ I @ J ) @ ( a_select3 @ D @ J @ I ) ) ) ) ) ) ) ) ) % 0.11/0.40 @ ( mand % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [I: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [J: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( leq @ n0 @ I ) ) @ ( mand @ ( mbox @ ( leq @ I @ N ) ) @ ( mand @ ( mbox @ ( leq @ n0 @ J ) ) @ ( mbox @ ( leq @ J @ N ) ) ) ) ) @ ( mbox @ ( customqmltpeq @ ( a_select3 @ A @ I @ J ) @ ( a_select3 @ A @ J @ I ) ) ) ) ) ) ) ) ) % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [I: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [J: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( leq @ n0 @ I ) ) @ ( mand @ ( mbox @ ( leq @ I @ N ) ) @ ( mand @ ( mbox @ ( leq @ n0 @ J ) ) @ ( mbox @ ( leq @ J @ N ) ) ) ) ) @ ( mbox @ ( customqmltpeq @ ( a_select3 @ F @ I @ J ) @ ( a_select3 @ F @ J @ I ) ) ) ) ) ) ) ) ) ) ) % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [I: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [J: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( leq @ n0 @ I ) ) @ ( mand @ ( mbox @ ( leq @ I @ N ) ) @ ( mand @ ( mbox @ ( leq @ n0 @ J ) ) @ ( mbox @ ( leq @ J @ N ) ) ) ) ) @ ( mbox @ ( customqmltpeq @ ( a_select3 @ ( tptp_madd @ A @ ( tptp_mmul @ B @ ( tptp_mmul @ ( tptp_madd @ ( tptp_mmul @ C @ ( tptp_mmul @ D @ ( trans @ C ) ) ) @ ( tptp_mmul @ E @ ( tptp_mmul @ F @ ( trans @ E ) ) ) ) @ ( trans @ B ) ) ) ) @ I @ J ) @ ( a_select3 @ ( tptp_madd @ A @ ( tptp_mmul @ B @ ( tptp_mmul @ ( tptp_madd @ ( tptp_mmul @ C @ ( tptp_mmul @ D @ ( trans @ C ) ) ) @ ( tptp_mmul @ E @ ( tptp_mmul @ F @ ( trans @ E ) ) ) ) @ ( trans @ B ) ) ) ) @ J @ I ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(sum_plus_base,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [Body: $i] : ( mbox @ ( customqmltpeq @ ( sum @ n0 @ tptp_minus_1 @ Body ) @ n0 ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(sum_plus_base_float,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [Body: $i] : ( mbox @ ( customqmltpeq @ tptp_float_0_0 @ ( sum @ n0 @ tptp_minus_1 @ Body ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(succ_tptp_minus_1,axiom, % 0.11/0.40 mlocal @ ( mbox @ ( customqmltpeq @ ( succ @ tptp_minus_1 ) @ n0 ) ) ). % 0.11/0.40 % 0.11/0.40 thf(succ_plus_1_r,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [X: $i] : ( mbox @ ( customqmltpeq @ ( plus @ X @ n1 ) @ ( succ @ X ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(succ_plus_1_l,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [X: $i] : ( mbox @ ( customqmltpeq @ ( plus @ n1 @ X ) @ ( succ @ X ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(succ_plus_2_r,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [X: $i] : ( mbox @ ( customqmltpeq @ ( plus @ X @ n2 ) @ ( succ @ ( succ @ X ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(succ_plus_2_l,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [X: $i] : ( mbox @ ( customqmltpeq @ ( plus @ n2 @ X ) @ ( succ @ ( succ @ X ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(succ_plus_3_r,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [X: $i] : ( mbox @ ( customqmltpeq @ ( plus @ X @ n3 ) @ ( succ @ ( succ @ ( succ @ X ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(succ_plus_3_l,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [X: $i] : ( mbox @ ( customqmltpeq @ ( plus @ n3 @ X ) @ ( succ @ ( succ @ ( succ @ X ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(succ_plus_4_r,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [X: $i] : ( mbox @ ( customqmltpeq @ ( plus @ X @ n4 ) @ ( succ @ ( succ @ ( succ @ ( succ @ X ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(succ_plus_4_l,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [X: $i] : ( mbox @ ( customqmltpeq @ ( plus @ n4 @ X ) @ ( succ @ ( succ @ ( succ @ ( succ @ X ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(succ_plus_5_r,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [X: $i] : ( mbox @ ( customqmltpeq @ ( plus @ X @ n5 ) @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ X ) ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(succ_plus_5_l,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [X: $i] : ( mbox @ ( customqmltpeq @ ( plus @ n5 @ X ) @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ X ) ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(pred_minus_1,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [X: $i] : ( mbox @ ( customqmltpeq @ ( minus @ X @ n1 ) @ ( pred @ X ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(pred_succ,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [X: $i] : ( mbox @ ( customqmltpeq @ ( pred @ ( succ @ X ) ) @ X ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(succ_pred,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [X: $i] : ( mbox @ ( customqmltpeq @ ( succ @ ( pred @ X ) ) @ X ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(leq_succ_succ,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [X: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [Y: $i] : ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( leq @ ( succ @ X ) @ ( succ @ Y ) ) ) @ ( mbox @ ( leq @ X @ Y ) ) ) ) @ ( mbox @ ( mimplies @ ( mbox @ ( leq @ X @ Y ) ) @ ( mbox @ ( leq @ ( succ @ X ) @ ( succ @ Y ) ) ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(leq_succ_gt,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [X: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [Y: $i] : ( mbox @ ( mimplies @ ( mbox @ ( leq @ ( succ @ X ) @ Y ) ) @ ( mbox @ ( gt @ Y @ X ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(leq_minus,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [X: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [Y: $i] : ( mbox @ ( mimplies @ ( mbox @ ( leq @ ( minus @ X @ Y ) @ X ) ) @ ( mbox @ ( leq @ n0 @ Y ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(sel3_update_1,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [X: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [U: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [V: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [VAL: $i] : ( mbox @ ( customqmltpeq @ ( a_select3 @ ( tptp_update3 @ X @ U @ V @ VAL ) @ U @ V ) @ VAL ) ) ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(sel3_update_2,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [I: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [J: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [U: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [V: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [X: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [VAL: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [VAL2: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( customqmltpeq @ I @ U ) ) ) ) @ ( mand @ ( mbox @ ( customqmltpeq @ J @ V ) ) @ ( mbox @ ( customqmltpeq @ ( a_select3 @ X @ U @ V ) @ VAL ) ) ) ) @ ( mbox @ ( customqmltpeq @ ( a_select3 @ ( tptp_update3 @ X @ I @ J @ VAL2 ) @ U @ V ) @ VAL ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(sel3_update_3,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [I: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [J: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [U: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [V: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [X: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [VAL: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mimplies % 0.11/0.40 @ ( mand % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [I0: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [J0: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( leq @ n0 @ I0 ) ) @ ( mand @ ( mbox @ ( leq @ n0 @ J0 ) ) @ ( mand @ ( mbox @ ( leq @ I0 @ U ) ) @ ( mbox @ ( leq @ J0 @ V ) ) ) ) ) @ ( mbox @ ( customqmltpeq @ ( a_select3 @ X @ I0 @ J0 ) @ VAL ) ) ) ) ) ) ) ) % 0.11/0.40 @ ( mand @ ( mbox @ ( leq @ n0 @ I ) ) @ ( mand @ ( mbox @ ( leq @ I @ U ) ) @ ( mand @ ( mbox @ ( leq @ n0 @ J ) ) @ ( mbox @ ( leq @ J @ V ) ) ) ) ) ) % 0.11/0.40 @ ( mbox @ ( customqmltpeq @ ( a_select3 @ ( tptp_update3 @ X @ U @ V @ VAL ) @ I @ J ) @ VAL ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(sel2_update_1,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [X: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [U: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [VAL: $i] : ( mbox @ ( customqmltpeq @ ( a_select2 @ ( tptp_update2 @ X @ U @ VAL ) @ U ) @ VAL ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(sel2_update_2,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [I: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [U: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [X: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [VAL: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [VAL2: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( customqmltpeq @ I @ U ) ) ) ) @ ( mbox @ ( customqmltpeq @ ( a_select2 @ X @ U ) @ VAL ) ) ) @ ( mbox @ ( customqmltpeq @ ( a_select2 @ ( tptp_update2 @ X @ I @ VAL2 ) @ U ) @ VAL ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(sel2_update_3,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [I: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [U: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [X: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [VAL: $i] : % 0.11/0.40 ( mbox % 0.11/0.40 @ ( mimplies % 0.11/0.40 @ ( mand % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [I0: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( leq @ n0 @ I0 ) ) @ ( mbox @ ( leq @ I0 @ U ) ) ) @ ( mbox @ ( customqmltpeq @ ( a_select2 @ X @ I0 ) @ VAL ) ) ) ) ) ) % 0.11/0.40 @ ( mand @ ( mbox @ ( leq @ n0 @ I ) ) @ ( mbox @ ( leq @ I @ U ) ) ) ) % 0.11/0.40 @ ( mbox @ ( customqmltpeq @ ( a_select2 @ ( tptp_update2 @ X @ U @ VAL ) @ I ) @ VAL ) ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(ttrue,axiom, % 0.11/0.40 mlocal @ ( mbox @ true ) ). % 0.11/0.40 % 0.11/0.40 thf(defuse,axiom, % 0.11/0.40 mlocal @ ( mbox @ ( mnot @ ( mbox @ ( customqmltpeq @ def @ use ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(cl5_nebula_array_0001,conjecture, % 0.11/0.40 mlocal @ ( mbox @ ( mimplies @ ( mbox @ true ) @ ( mbox @ true ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(gt_5_4,axiom, % 0.11/0.40 mlocal @ ( mbox @ ( gt @ n5 @ n4 ) ) ). % 0.11/0.40 % 0.11/0.40 thf(gt_4_tptp_minus_1,axiom, % 0.11/0.40 mlocal @ ( mbox @ ( gt @ n4 @ tptp_minus_1 ) ) ). % 0.11/0.40 % 0.11/0.40 thf(gt_5_tptp_minus_1,axiom, % 0.11/0.40 mlocal @ ( mbox @ ( gt @ n5 @ tptp_minus_1 ) ) ). % 0.11/0.40 % 0.11/0.40 thf(gt_0_tptp_minus_1,axiom, % 0.11/0.40 mlocal @ ( mbox @ ( gt @ n0 @ tptp_minus_1 ) ) ). % 0.11/0.40 % 0.11/0.40 thf(gt_1_tptp_minus_1,axiom, % 0.11/0.40 mlocal @ ( mbox @ ( gt @ n1 @ tptp_minus_1 ) ) ). % 0.11/0.40 % 0.11/0.40 thf(gt_2_tptp_minus_1,axiom, % 0.11/0.40 mlocal @ ( mbox @ ( gt @ n2 @ tptp_minus_1 ) ) ). % 0.11/0.40 % 0.11/0.40 thf(gt_3_tptp_minus_1,axiom, % 0.11/0.40 mlocal @ ( mbox @ ( gt @ n3 @ tptp_minus_1 ) ) ). % 0.11/0.40 % 0.11/0.40 thf(gt_4_0,axiom, % 0.11/0.40 mlocal @ ( mbox @ ( gt @ n4 @ n0 ) ) ). % 0.11/0.40 % 0.11/0.40 thf(gt_5_0,axiom, % 0.11/0.40 mlocal @ ( mbox @ ( gt @ n5 @ n0 ) ) ). % 0.11/0.40 % 0.11/0.40 thf(gt_1_0,axiom, % 0.11/0.40 mlocal @ ( mbox @ ( gt @ n1 @ n0 ) ) ). % 0.11/0.40 % 0.11/0.40 thf(gt_2_0,axiom, % 0.11/0.40 mlocal @ ( mbox @ ( gt @ n2 @ n0 ) ) ). % 0.11/0.40 % 0.11/0.40 thf(gt_3_0,axiom, % 0.11/0.40 mlocal @ ( mbox @ ( gt @ n3 @ n0 ) ) ). % 0.11/0.40 % 0.11/0.40 thf(gt_4_1,axiom, % 0.11/0.40 mlocal @ ( mbox @ ( gt @ n4 @ n1 ) ) ). % 0.11/0.40 % 0.11/0.40 thf(gt_5_1,axiom, % 0.11/0.40 mlocal @ ( mbox @ ( gt @ n5 @ n1 ) ) ). % 0.11/0.40 % 0.11/0.40 thf(gt_2_1,axiom, % 0.11/0.40 mlocal @ ( mbox @ ( gt @ n2 @ n1 ) ) ). % 0.11/0.40 % 0.11/0.40 thf(gt_3_1,axiom, % 0.11/0.40 mlocal @ ( mbox @ ( gt @ n3 @ n1 ) ) ). % 0.11/0.40 % 0.11/0.40 thf(gt_4_2,axiom, % 0.11/0.40 mlocal @ ( mbox @ ( gt @ n4 @ n2 ) ) ). % 0.11/0.40 % 0.11/0.40 thf(gt_5_2,axiom, % 0.11/0.40 mlocal @ ( mbox @ ( gt @ n5 @ n2 ) ) ). % 0.11/0.40 % 0.11/0.40 thf(gt_3_2,axiom, % 0.11/0.40 mlocal @ ( mbox @ ( gt @ n3 @ n2 ) ) ). % 0.11/0.40 % 0.11/0.40 thf(gt_4_3,axiom, % 0.11/0.40 mlocal @ ( mbox @ ( gt @ n4 @ n3 ) ) ). % 0.11/0.40 % 0.11/0.40 thf(gt_5_3,axiom, % 0.11/0.40 mlocal @ ( mbox @ ( gt @ n5 @ n3 ) ) ). % 0.11/0.40 % 0.11/0.40 thf(finite_domain_4,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [X: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( leq @ n0 @ X ) ) @ ( mbox @ ( leq @ X @ n4 ) ) ) @ ( mor @ ( mbox @ ( customqmltpeq @ X @ n0 ) ) @ ( mor @ ( mbox @ ( customqmltpeq @ X @ n1 ) ) @ ( mor @ ( mbox @ ( customqmltpeq @ X @ n2 ) ) @ ( mor @ ( mbox @ ( customqmltpeq @ X @ n3 ) ) @ ( mbox @ ( customqmltpeq @ X @ n4 ) ) ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(finite_domain_5,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [X: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( leq @ n0 @ X ) ) @ ( mbox @ ( leq @ X @ n5 ) ) ) @ ( mor @ ( mbox @ ( customqmltpeq @ X @ n0 ) ) @ ( mor @ ( mbox @ ( customqmltpeq @ X @ n1 ) ) @ ( mor @ ( mbox @ ( customqmltpeq @ X @ n2 ) ) @ ( mor @ ( mbox @ ( customqmltpeq @ X @ n3 ) ) @ ( mor @ ( mbox @ ( customqmltpeq @ X @ n4 ) ) @ ( mbox @ ( customqmltpeq @ X @ n5 ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(finite_domain_0,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [X: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( leq @ n0 @ X ) ) @ ( mbox @ ( leq @ X @ n0 ) ) ) @ ( mbox @ ( customqmltpeq @ X @ n0 ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(finite_domain_1,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [X: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( leq @ n0 @ X ) ) @ ( mbox @ ( leq @ X @ n1 ) ) ) @ ( mor @ ( mbox @ ( customqmltpeq @ X @ n0 ) ) @ ( mbox @ ( customqmltpeq @ X @ n1 ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(finite_domain_2,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [X: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( leq @ n0 @ X ) ) @ ( mbox @ ( leq @ X @ n2 ) ) ) @ ( mor @ ( mbox @ ( customqmltpeq @ X @ n0 ) ) @ ( mor @ ( mbox @ ( customqmltpeq @ X @ n1 ) ) @ ( mbox @ ( customqmltpeq @ X @ n2 ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(finite_domain_3,axiom, % 0.11/0.40 ( mlocal % 0.11/0.40 @ ( mbox % 0.11/0.40 @ ( mforall_di % 0.11/0.40 @ ^ [X: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( leq @ n0 @ X ) ) @ ( mbox @ ( leq @ X @ n3 ) ) ) @ ( mor @ ( mbox @ ( customqmltpeq @ X @ n0 ) ) @ ( mor @ ( mbox @ ( customqmltpeq @ X @ n1 ) ) @ ( mor @ ( mbox @ ( customqmltpeq @ X @ n2 ) ) @ ( mbox @ ( customqmltpeq @ X @ n3 ) ) ) ) ) ) ) ) ) ) ). % 0.11/0.40 % 0.11/0.40 thf(successor_4,axiom, % 0.11/0.40 mlocal @ ( mbox @ ( customqmltpeq @ ( succ @ ( succ @ ( succ @ ( succ @ n0 ) ) ) ) @ n4 ) ) ). % 0.11/0.40 % 0.11/0.40 thf(successor_5,axiom, % 0.11/0.40 mlocal @ ( mbox @ ( customqmltpeq @ ( succ @ ( succ @ ( succ @ ( succ @ ( succ @ n0 ) ) ) ) ) @ n5 ) ) ). % 0.11/0.40 % 0.11/0.40 thf(successor_1,axiom, % 0.11/0.40 mlocal @ ( mbox @ ( customqmltpeq @ ( succ @ n0 ) @ n1 ) ) ). % 0.11/0.40 % 0.11/0.40 thf(successor_2,axiom, % 0.11/0.40 mlocal @ ( mbox @ ( customqmltpeq @ ( succ @ ( succ @ n0 ) ) @ n2 ) ) ). % 0.11/0.40 % 0.11/0.40 thf(successor_3,axiom, % 0.11/0.40 mlocal @ ( mbox @ ( customqmltpeq @ ( succ @ ( succ @ ( succ @ n0 ) ) ) @ n3 ) ) ). % 0.11/0.40 % 0.11/0.40 %------------------------------------------------------------------------------ % 0.11/0.40 ------------------------ % 0.11/0.40 /starexec/sw/sutcliffe/jdk-11.0.2/bin/java: Command not found. % 0.11/0.40 ---- Embedded in THF --- % 0.11/0.40 ------------------------ % 0.11/0.42 ---- Cleaned THF --- % 0.11/0.42 ------------------------ % 0.11/0.45 % (1795217)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_1795198 for (2999ds/2Mi) % 0.11/0.45 % (1795217)First to succeed. % 0.11/0.45 % SZS status Satisfiable for DTF2THF_1795198 % 0.11/0.45 % (1795217)# SZS output start Saturation. % 0.11/0.45 % (1795217)# SZS output end Saturation. % 0.11/0.45 % (1795217)------------------------------ % 0.11/0.45 % (1795217)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) % 0.11/0.45 % (1795217)Termination reason: Satisfiable % 0.11/0.45 % 0.11/0.45 % (1795217)Memory used [KB]: 5373 % 0.11/0.45 % (1795217)Time elapsed: 0.002 s % 0.11/0.45 % (1795217)Instructions burned: 1 (million) % 0.11/0.45 % (1795217)------------------------------ % 0.11/0.45 % (1795217)------------------------------ % 0.11/0.45 % (1795213)Success in time 0.012 s %------------------------------------------------------------------------------