%------------------------------------------------------------------------------ % File : DT2H2X---1.9.5 % Problem : LCL944^8 : 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 : n005.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 11:35:13 AM UTC 2026 % Result : CounterSatisfiable 0.21s 0.48s % Output : Saturation 0.21s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL944^8 : TPTP v9.3.1. Released v8.1.0. % 0.00/0.05 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300 % 0.12/0.38 % Computer : n005.cluster.edu % 0.12/0.38 % Model : x86_64 x86_64 % 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.38 % Memory : 8046.5625MB % 0.12/0.38 % OS : Linux 6.8.0-71-generic % 0.12/0.38 % CPULimit : 300 % 0.12/0.38 % WCLimit : 300 % 0.12/0.38 % DateTime : Sat Sep 5 05:31:50 UTC 2026 % 0.12/0.39 % CPUTime : % 0.12/0.39 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300 % 0.12/0.41 ---- Original DTF file --- % 0.12/0.42 thf(spec,logic,$$dhol). % 0.12/0.42 %------------------------------------------------------------------------------ % 0.12/0.42 % File : LCL944^8 : TPTP v9.3.1. Released v8.1.0. % 0.12/0.42 % Domain : Logic Calculi % 0.12/0.42 % Problem : Goedel translation of LCL455+1 (from TPTP-v5.0.0) % 0.12/0.42 % Version : [BP13] axioms. % 0.12/0.42 % English : % 0.12/0.42 % 0.12/0.42 % Refs : [RO12] Raths & Otten (2012), The QMLTP Problem Library for Fi % 0.12/0.42 % : [BP13] Benzmueller & Paulson (2013), Quantified Multimodal Lo % 0.12/0.42 % : [Ste22] Steen (2022), An Extensible Logic Embedding Tool for L % 0.12/0.42 % Source : [TPTP] % 0.12/0.42 % Names : GLC455+1 [QMLTP] % 0.12/0.42 % 0.12/0.42 % Status : Theorem % 0.12/0.42 % Rating : 0.33 v9.3.0, 0.44 v9.1.0, 0.38 v9.0.0, 0.40 v8.2.0, 0.46 v8.1.0 % 0.12/0.42 % Syntax : Number of formulae : 130 ( 12 unt; 52 typ; 10 def) % 0.12/0.42 % Number of atoms : 914 ( 10 equ; 0 cnn) % 0.12/0.42 % Maximal formula atoms : 36 ( 11 avg) % 0.12/0.42 % Number of connectives : 1376 ( 1 ~; 1 |; 3 &;1367 @) % 0.12/0.42 % ( 1 <=>; 3 =>; 0 <=; 0 <~>) % 0.12/0.42 % Maximal formula depth : 23 ( 11 avg) % 0.12/0.42 % Number of types : 3 ( 1 usr) % 0.12/0.42 % Number of type conns : 104 ( 104 >; 0 *; 0 +; 0 <<) % 0.12/0.42 % Number of symbols : 52 ( 51 usr; 1 con; 0-3 aty) % 0.12/0.42 % Number of variables : 184 ( 177 ^; 4 !; 3 ?; 184 :) % 0.12/0.42 % SPC : TH0_THM_EQU_NAR_NDT % 0.12/0.42 % 0.12/0.42 % Comments : This output was generated by embedproblem, version 1.7.1 (library % 0.12/0.42 % version 1.3). Generated on Thu Apr 28 13:18:18 EDT 2022 using % 0.12/0.42 % 'modal' embedding, version 1.5.2. Logic specification used: % 0.12/0.42 % $modal == [$constants == $rigid,$quantification == $varying, % 0.12/0.42 % $modalities == $modal_system_T]. % 0.12/0.42 %------------------------------------------------------------------------------ % 0.12/0.42 thf(mworld,type, % 0.12/0.42 mworld: $tType ). % 0.12/0.42 % 0.12/0.42 thf(mrel_type,type, % 0.12/0.42 mrel: mworld > mworld > $o ). % 0.12/0.42 % 0.12/0.42 thf(mactual_type,type, % 0.12/0.42 mactual: mworld ). % 0.12/0.42 % 0.12/0.42 thf(mlocal_type,type, % 0.12/0.42 mlocal: ( mworld > $o ) > $o ). % 0.12/0.42 % 0.12/0.42 thf(mlocal_def,definition, % 0.12/0.42 ( mlocal % 0.12/0.42 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ). % 0.12/0.42 % 0.12/0.42 thf(mnot_type,type, % 0.12/0.42 mnot: ( mworld > $o ) > mworld > $o ). % 0.12/0.42 % 0.12/0.42 thf(mand_type,type, % 0.12/0.42 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ). % 0.12/0.42 % 0.12/0.42 thf(mor_type,type, % 0.12/0.42 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ). % 0.12/0.42 % 0.12/0.42 thf(mimplies_type,type, % 0.12/0.42 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ). % 0.12/0.42 % 0.12/0.42 thf(mequiv_type,type, % 0.12/0.42 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ). % 0.12/0.42 % 0.12/0.42 thf(mnot_def,definition, % 0.12/0.42 ( mnot % 0.12/0.42 = ( ^ [A: mworld > $o,W: mworld] : % 0.12/0.42 ~ ( A @ W ) ) ) ). % 0.12/0.42 % 0.12/0.42 thf(mand_def,definition, % 0.12/0.42 ( mand % 0.12/0.42 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] : % 0.12/0.42 ( ( A @ W ) % 0.12/0.42 & ( B @ W ) ) ) ) ). % 0.12/0.42 % 0.12/0.42 thf(mor_def,definition, % 0.12/0.42 ( mor % 0.12/0.42 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] : % 0.12/0.42 ( ( A @ W ) % 0.12/0.42 | ( B @ W ) ) ) ) ). % 0.12/0.42 % 0.12/0.42 thf(mimplies_def,definition, % 0.12/0.42 ( mimplies % 0.12/0.42 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] : % 0.12/0.42 ( ( A @ W ) % 0.12/0.42 => ( B @ W ) ) ) ) ). % 0.12/0.42 % 0.12/0.42 thf(mequiv_def,definition, % 0.12/0.42 ( mequiv % 0.12/0.42 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] : % 0.12/0.42 ( ( A @ W ) % 0.12/0.42 <=> ( B @ W ) ) ) ) ). % 0.12/0.42 % 0.12/0.42 thf(mbox_type,type, % 0.12/0.42 mbox: ( mworld > $o ) > mworld > $o ). % 0.12/0.42 % 0.12/0.42 thf(mbox_def,definition, % 0.12/0.42 ( mbox % 0.12/0.42 = ( ^ [Phi: mworld > $o,W: mworld] : % 0.12/0.42 ! [V: mworld] : % 0.12/0.42 ( ( mrel @ W @ V ) % 0.12/0.42 => ( Phi @ V ) ) ) ) ). % 0.12/0.42 % 0.12/0.42 thf(mdia_type,type, % 0.12/0.42 mdia: ( mworld > $o ) > mworld > $o ). % 0.12/0.42 % 0.12/0.42 thf(mdia_def,definition, % 0.12/0.42 ( mdia % 0.12/0.42 = ( ^ [Phi: mworld > $o,W: mworld] : % 0.12/0.42 ? [V: mworld] : % 0.12/0.42 ( ( mrel @ W @ V ) % 0.12/0.42 & ( Phi @ V ) ) ) ) ). % 0.12/0.42 % 0.12/0.42 thf(mrel_reflexive,axiom, % 0.12/0.42 ! [W: mworld] : ( mrel @ W @ W ) ). % 0.12/0.42 % 0.12/0.42 thf(eiw_di_type,type, % 0.12/0.42 eiw_di: $i > mworld > $o ). % 0.12/0.42 % 0.12/0.42 thf(eiw_di_nonempty,axiom, % 0.12/0.42 ! [W: mworld] : % 0.12/0.42 ? [X: $i] : ( eiw_di @ X @ W ) ). % 0.12/0.42 % 0.12/0.42 thf(mforall_di_type,type, % 0.12/0.42 mforall_di: ( $i > mworld > $o ) > mworld > $o ). % 0.12/0.42 % 0.12/0.42 thf(mforall_di_def,definition, % 0.12/0.42 ( mforall_di % 0.12/0.42 = ( ^ [A: $i > mworld > $o,W: mworld] : % 0.12/0.42 ! [X: $i] : % 0.12/0.42 ( ( eiw_di @ X @ W ) % 0.12/0.42 => ( A @ X @ W ) ) ) ) ). % 0.12/0.42 % 0.12/0.42 thf(mexists_di_type,type, % 0.12/0.42 mexists_di: ( $i > mworld > $o ) > mworld > $o ). % 0.12/0.42 % 0.12/0.42 thf(mexists_di_def,definition, % 0.12/0.42 ( mexists_di % 0.12/0.42 = ( ^ [A: $i > mworld > $o,W: mworld] : % 0.12/0.42 ? [X: $i] : % 0.12/0.42 ( ( eiw_di @ X @ W ) % 0.12/0.42 & ( A @ X @ W ) ) ) ) ). % 0.12/0.42 % 0.12/0.42 thf(r2_decl,type, % 0.12/0.42 r2: mworld > $o ). % 0.12/0.42 % 0.12/0.42 thf(r3_decl,type, % 0.12/0.42 r3: mworld > $o ). % 0.12/0.42 % 0.12/0.42 thf(r4_decl,type, % 0.12/0.42 r4: mworld > $o ). % 0.12/0.42 % 0.12/0.42 thf(r5_decl,type, % 0.12/0.42 r5: mworld > $o ). % 0.12/0.42 % 0.12/0.42 thf(equivalence_1_decl,type, % 0.12/0.42 equivalence_1: mworld > $o ). % 0.12/0.42 % 0.12/0.42 thf(equivalence_2_decl,type, % 0.12/0.42 equivalence_2: mworld > $o ). % 0.12/0.42 % 0.12/0.42 thf(cn2_decl,type, % 0.12/0.42 cn2: mworld > $o ). % 0.12/0.42 % 0.12/0.42 thf(cn1_decl,type, % 0.12/0.42 cn1: mworld > $o ). % 0.12/0.42 % 0.12/0.42 thf(cn3_decl,type, % 0.12/0.42 cn3: mworld > $o ). % 0.12/0.42 % 0.12/0.42 thf(kn2_decl,type, % 0.12/0.42 kn2: mworld > $o ). % 0.12/0.42 % 0.12/0.42 thf(kn1_decl,type, % 0.12/0.42 kn1: mworld > $o ). % 0.12/0.42 % 0.12/0.42 thf(kn3_decl,type, % 0.12/0.42 kn3: mworld > $o ). % 0.12/0.42 % 0.12/0.42 thf(equivalence_3_decl,type, % 0.12/0.42 equivalence_3: mworld > $o ). % 0.12/0.42 % 0.12/0.42 thf(op_implies_or_decl,type, % 0.12/0.42 op_implies_or: mworld > $o ). % 0.12/0.42 % 0.12/0.42 thf(op_and_decl,type, % 0.12/0.42 op_and: mworld > $o ). % 0.12/0.42 % 0.12/0.42 thf(and_2_decl,type, % 0.12/0.42 and_2: mworld > $o ). % 0.12/0.42 % 0.12/0.42 thf(and_3_decl,type, % 0.12/0.42 and_3: mworld > $o ). % 0.12/0.42 % 0.12/0.42 thf(and_1_decl,type, % 0.12/0.42 and_1: mworld > $o ). % 0.12/0.42 % 0.12/0.42 thf(implies_2_decl,type, % 0.12/0.42 implies_2: mworld > $o ). % 0.12/0.42 % 0.12/0.42 thf(implies_3_decl,type, % 0.12/0.42 implies_3: mworld > $o ). % 0.12/0.42 % 0.12/0.42 thf(op_implies_and_decl,type, % 0.12/0.42 op_implies_and: mworld > $o ). % 0.12/0.42 % 0.12/0.42 thf(implies_1_decl,type, % 0.12/0.42 implies_1: mworld > $o ). % 0.12/0.42 % 0.12/0.42 thf(substitution_of_equivalents_decl,type, % 0.12/0.42 substitution_of_equivalents: mworld > $o ). % 0.12/0.42 % 0.12/0.42 thf(op_or_decl,type, % 0.12/0.42 op_or: mworld > $o ). % 0.12/0.42 % 0.12/0.42 thf(modus_tollens_decl,type, % 0.12/0.42 modus_tollens: mworld > $o ). % 0.12/0.42 % 0.12/0.42 thf(or_1_decl,type, % 0.12/0.42 or_1: mworld > $o ). % 0.12/0.42 % 0.12/0.42 thf(or_2_decl,type, % 0.12/0.42 or_2: mworld > $o ). % 0.12/0.42 % 0.12/0.42 thf(or_3_decl,type, % 0.12/0.42 or_3: mworld > $o ). % 0.12/0.42 % 0.12/0.42 thf(op_equiv_decl,type, % 0.12/0.42 op_equiv: mworld > $o ). % 0.12/0.42 % 0.12/0.42 thf(modus_ponens_decl,type, % 0.12/0.42 modus_ponens: mworld > $o ). % 0.12/0.42 % 0.12/0.42 thf(r1_decl,type, % 0.12/0.42 r1: mworld > $o ). % 0.12/0.42 % 0.12/0.42 thf(qmltpeq_decl,type, % 0.12/0.42 qmltpeq: $i > $i > mworld > $o ). % 0.12/0.42 % 0.12/0.42 thf(is_a_theorem_decl,type, % 0.12/0.42 is_a_theorem: $i > mworld > $o ). % 0.12/0.42 % 0.12/0.42 thf(equiv_decl,type, % 0.12/0.42 equiv: $i > $i > $i ). % 0.12/0.42 % 0.12/0.42 thf(not_decl,type, % 0.12/0.42 not: $i > $i ). % 0.12/0.42 % 0.12/0.42 thf(or_decl,type, % 0.12/0.42 or: $i > $i > $i ). % 0.12/0.42 % 0.12/0.42 thf(and_decl,type, % 0.12/0.42 and: $i > $i > $i ). % 0.12/0.42 % 0.12/0.42 thf(implies_decl,type, % 0.12/0.42 implies: $i > $i > $i ). % 0.12/0.42 % 0.12/0.42 thf(reflexivity,axiom, % 0.12/0.42 ( mlocal % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [X: $i] : ( mbox @ ( qmltpeq @ X @ X ) ) ) ) ) ). % 0.12/0.42 % 0.12/0.42 thf(symmetry,axiom, % 0.12/0.42 ( mlocal % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [X: $i] : % 0.12/0.42 ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [Y: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ X @ Y ) ) @ ( mbox @ ( qmltpeq @ Y @ X ) ) ) ) ) ) ) ) ) ). % 0.12/0.42 % 0.12/0.42 thf(transitivity,axiom, % 0.12/0.42 ( mlocal % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [X: $i] : % 0.12/0.42 ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [Y: $i] : % 0.12/0.42 ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [Z: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( qmltpeq @ X @ Y ) ) @ ( mbox @ ( qmltpeq @ Y @ Z ) ) ) @ ( mbox @ ( qmltpeq @ X @ Z ) ) ) ) ) ) ) ) ) ) ) ). % 0.12/0.42 % 0.12/0.42 thf(and_substitution_1,axiom, % 0.12/0.42 ( mlocal % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [A: $i] : % 0.12/0.42 ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [B: $i] : % 0.12/0.42 ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( and @ A @ C ) @ ( and @ B @ C ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.12/0.42 % 0.12/0.42 thf(and_substitution_2,axiom, % 0.12/0.42 ( mlocal % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [A: $i] : % 0.12/0.42 ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [B: $i] : % 0.12/0.42 ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( and @ C @ A ) @ ( and @ C @ B ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.12/0.42 % 0.12/0.42 thf(equiv_substitution_1,axiom, % 0.12/0.42 ( mlocal % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [A: $i] : % 0.12/0.42 ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [B: $i] : % 0.12/0.42 ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( equiv @ A @ C ) @ ( equiv @ B @ C ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.12/0.42 % 0.12/0.42 thf(equiv_substitution_2,axiom, % 0.12/0.42 ( mlocal % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [A: $i] : % 0.12/0.42 ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [B: $i] : % 0.12/0.42 ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( equiv @ C @ A ) @ ( equiv @ C @ B ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.12/0.42 % 0.12/0.42 thf(implies_substitution_1,axiom, % 0.12/0.42 ( mlocal % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [A: $i] : % 0.12/0.42 ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [B: $i] : % 0.12/0.42 ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( implies @ A @ C ) @ ( implies @ B @ C ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.12/0.42 % 0.12/0.42 thf(implies_substitution_2,axiom, % 0.12/0.42 ( mlocal % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [A: $i] : % 0.12/0.42 ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [B: $i] : % 0.12/0.42 ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( implies @ C @ A ) @ ( implies @ C @ B ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.12/0.42 % 0.12/0.42 thf(not_substitution_1,axiom, % 0.12/0.42 ( mlocal % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [A: $i] : % 0.12/0.42 ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [B: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( not @ A ) @ ( not @ B ) ) ) ) ) ) ) ) ) ) ). % 0.12/0.42 % 0.12/0.42 thf(or_substitution_1,axiom, % 0.12/0.42 ( mlocal % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [A: $i] : % 0.12/0.42 ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [B: $i] : % 0.12/0.42 ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( or @ A @ C ) @ ( or @ B @ C ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.12/0.42 % 0.12/0.42 thf(or_substitution_2,axiom, % 0.12/0.42 ( mlocal % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [A: $i] : % 0.12/0.42 ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [B: $i] : % 0.12/0.42 ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( or @ C @ A ) @ ( or @ C @ B ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.12/0.42 % 0.12/0.42 thf(is_a_theorem_substitution_1,axiom, % 0.12/0.42 ( mlocal % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [A: $i] : % 0.12/0.42 ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [B: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( is_a_theorem @ A ) ) ) @ ( mbox @ ( is_a_theorem @ B ) ) ) ) ) ) ) ) ) ). % 0.12/0.42 % 0.12/0.42 thf(modus_ponens_0,axiom, % 0.12/0.42 ( mlocal % 0.12/0.42 @ ( mand % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mimplies @ ( mbox @ modus_ponens ) % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [X: $i] : % 0.12/0.42 ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [Y: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( is_a_theorem @ X ) ) @ ( mbox @ ( is_a_theorem @ ( implies @ X @ Y ) ) ) ) @ ( mbox @ ( is_a_theorem @ Y ) ) ) ) ) ) ) ) ) ) % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mimplies % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [X: $i] : % 0.12/0.42 ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [Y: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( is_a_theorem @ X ) ) @ ( mbox @ ( is_a_theorem @ ( implies @ X @ Y ) ) ) ) @ ( mbox @ ( is_a_theorem @ Y ) ) ) ) ) ) ) ) % 0.12/0.42 @ ( mbox @ modus_ponens ) ) ) ) ) ). % 0.12/0.42 % 0.12/0.42 thf(substitution_of_equivalents_0,axiom, % 0.12/0.42 ( mlocal % 0.12/0.42 @ ( mand % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mimplies @ ( mbox @ substitution_of_equivalents ) % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [X: $i] : % 0.12/0.42 ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [Y: $i] : ( mbox @ ( mimplies @ ( mbox @ ( is_a_theorem @ ( equiv @ X @ Y ) ) ) @ ( mbox @ ( qmltpeq @ X @ Y ) ) ) ) ) ) ) ) ) ) % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mimplies % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [X: $i] : % 0.12/0.42 ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [Y: $i] : ( mbox @ ( mimplies @ ( mbox @ ( is_a_theorem @ ( equiv @ X @ Y ) ) ) @ ( mbox @ ( qmltpeq @ X @ Y ) ) ) ) ) ) ) ) % 0.12/0.42 @ ( mbox @ substitution_of_equivalents ) ) ) ) ) ). % 0.12/0.42 % 0.12/0.42 thf(modus_tollens_0,axiom, % 0.12/0.42 ( mlocal % 0.12/0.42 @ ( mand % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mimplies @ ( mbox @ modus_tollens ) % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [X: $i] : % 0.12/0.42 ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [Y: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( implies @ ( not @ Y ) @ ( not @ X ) ) @ ( implies @ X @ Y ) ) ) ) ) ) ) ) ) ) % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mimplies % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [X: $i] : % 0.12/0.42 ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [Y: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( implies @ ( not @ Y ) @ ( not @ X ) ) @ ( implies @ X @ Y ) ) ) ) ) ) ) ) % 0.12/0.42 @ ( mbox @ modus_tollens ) ) ) ) ) ). % 0.12/0.42 % 0.12/0.42 thf(implies_1_0,axiom, % 0.12/0.42 ( mlocal % 0.12/0.42 @ ( mand % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mimplies @ ( mbox @ implies_1 ) % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [X: $i] : % 0.12/0.42 ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [Y: $i] : ( mbox @ ( is_a_theorem @ ( implies @ X @ ( implies @ Y @ X ) ) ) ) ) ) ) ) ) ) % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mimplies % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [X: $i] : % 0.12/0.42 ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [Y: $i] : ( mbox @ ( is_a_theorem @ ( implies @ X @ ( implies @ Y @ X ) ) ) ) ) ) ) ) % 0.12/0.42 @ ( mbox @ implies_1 ) ) ) ) ) ). % 0.12/0.42 % 0.12/0.42 thf(implies_2_0,axiom, % 0.12/0.42 ( mlocal % 0.12/0.42 @ ( mand % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mimplies @ ( mbox @ implies_2 ) % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [X: $i] : % 0.12/0.42 ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [Y: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( implies @ X @ ( implies @ X @ Y ) ) @ ( implies @ X @ Y ) ) ) ) ) ) ) ) ) ) % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mimplies % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [X: $i] : % 0.12/0.42 ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [Y: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( implies @ X @ ( implies @ X @ Y ) ) @ ( implies @ X @ Y ) ) ) ) ) ) ) ) % 0.12/0.42 @ ( mbox @ implies_2 ) ) ) ) ) ). % 0.12/0.42 % 0.12/0.42 thf(implies_3_0,axiom, % 0.12/0.42 ( mlocal % 0.12/0.42 @ ( mand % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mimplies @ ( mbox @ implies_3 ) % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [X: $i] : % 0.12/0.42 ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [Y: $i] : % 0.12/0.42 ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [Z: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( implies @ X @ Y ) @ ( implies @ ( implies @ Y @ Z ) @ ( implies @ X @ Z ) ) ) ) ) ) ) ) ) ) ) ) ) % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mimplies % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [X: $i] : % 0.12/0.42 ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [Y: $i] : % 0.12/0.42 ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [Z: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( implies @ X @ Y ) @ ( implies @ ( implies @ Y @ Z ) @ ( implies @ X @ Z ) ) ) ) ) ) ) ) ) ) ) % 0.12/0.42 @ ( mbox @ implies_3 ) ) ) ) ) ). % 0.12/0.42 % 0.12/0.42 thf(and_1_0,axiom, % 0.12/0.42 ( mlocal % 0.12/0.42 @ ( mand % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mimplies @ ( mbox @ and_1 ) % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [X: $i] : % 0.12/0.42 ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [Y: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( and @ X @ Y ) @ X ) ) ) ) ) ) ) ) ) % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mimplies % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [X: $i] : % 0.12/0.42 ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [Y: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( and @ X @ Y ) @ X ) ) ) ) ) ) ) % 0.12/0.42 @ ( mbox @ and_1 ) ) ) ) ) ). % 0.12/0.42 % 0.12/0.42 thf(and_2_0,axiom, % 0.12/0.42 ( mlocal % 0.12/0.42 @ ( mand % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mimplies @ ( mbox @ and_2 ) % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [X: $i] : % 0.12/0.42 ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [Y: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( and @ X @ Y ) @ Y ) ) ) ) ) ) ) ) ) % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mimplies % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [X: $i] : % 0.12/0.42 ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [Y: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( and @ X @ Y ) @ Y ) ) ) ) ) ) ) % 0.12/0.42 @ ( mbox @ and_2 ) ) ) ) ) ). % 0.12/0.42 % 0.12/0.42 thf(and_3_0,axiom, % 0.12/0.42 ( mlocal % 0.12/0.42 @ ( mand % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mimplies @ ( mbox @ and_3 ) % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [X: $i] : % 0.12/0.42 ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [Y: $i] : ( mbox @ ( is_a_theorem @ ( implies @ X @ ( implies @ Y @ ( and @ X @ Y ) ) ) ) ) ) ) ) ) ) ) % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mimplies % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [X: $i] : % 0.12/0.42 ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [Y: $i] : ( mbox @ ( is_a_theorem @ ( implies @ X @ ( implies @ Y @ ( and @ X @ Y ) ) ) ) ) ) ) ) ) % 0.12/0.42 @ ( mbox @ and_3 ) ) ) ) ) ). % 0.12/0.42 % 0.12/0.42 thf(or_1_0,axiom, % 0.12/0.42 ( mlocal % 0.12/0.42 @ ( mand % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mimplies @ ( mbox @ or_1 ) % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [X: $i] : % 0.12/0.42 ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [Y: $i] : ( mbox @ ( is_a_theorem @ ( implies @ X @ ( or @ X @ Y ) ) ) ) ) ) ) ) ) ) % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mimplies % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [X: $i] : % 0.12/0.42 ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [Y: $i] : ( mbox @ ( is_a_theorem @ ( implies @ X @ ( or @ X @ Y ) ) ) ) ) ) ) ) % 0.12/0.42 @ ( mbox @ or_1 ) ) ) ) ) ). % 0.12/0.42 % 0.12/0.42 thf(or_2_0,axiom, % 0.12/0.42 ( mlocal % 0.12/0.42 @ ( mand % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mimplies @ ( mbox @ or_2 ) % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [X: $i] : % 0.12/0.42 ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [Y: $i] : ( mbox @ ( is_a_theorem @ ( implies @ Y @ ( or @ X @ Y ) ) ) ) ) ) ) ) ) ) % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mimplies % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [X: $i] : % 0.12/0.42 ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [Y: $i] : ( mbox @ ( is_a_theorem @ ( implies @ Y @ ( or @ X @ Y ) ) ) ) ) ) ) ) % 0.12/0.42 @ ( mbox @ or_2 ) ) ) ) ) ). % 0.12/0.42 % 0.12/0.42 thf(or_3_0,axiom, % 0.12/0.42 ( mlocal % 0.12/0.42 @ ( mand % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mimplies @ ( mbox @ or_3 ) % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [X: $i] : % 0.12/0.42 ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [Y: $i] : % 0.12/0.42 ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [Z: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( implies @ X @ Z ) @ ( implies @ ( implies @ Y @ Z ) @ ( implies @ ( or @ X @ Y ) @ Z ) ) ) ) ) ) ) ) ) ) ) ) ) % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mimplies % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [X: $i] : % 0.12/0.42 ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [Y: $i] : % 0.12/0.42 ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [Z: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( implies @ X @ Z ) @ ( implies @ ( implies @ Y @ Z ) @ ( implies @ ( or @ X @ Y ) @ Z ) ) ) ) ) ) ) ) ) ) ) % 0.12/0.42 @ ( mbox @ or_3 ) ) ) ) ) ). % 0.12/0.42 % 0.12/0.42 thf(equivalence_1_0,axiom, % 0.12/0.42 ( mlocal % 0.12/0.42 @ ( mand % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mimplies @ ( mbox @ equivalence_1 ) % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [X: $i] : % 0.12/0.42 ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [Y: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( equiv @ X @ Y ) @ ( implies @ X @ Y ) ) ) ) ) ) ) ) ) ) % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mimplies % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [X: $i] : % 0.12/0.42 ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [Y: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( equiv @ X @ Y ) @ ( implies @ X @ Y ) ) ) ) ) ) ) ) % 0.12/0.42 @ ( mbox @ equivalence_1 ) ) ) ) ) ). % 0.12/0.42 % 0.12/0.42 thf(equivalence_2_0,axiom, % 0.12/0.42 ( mlocal % 0.12/0.42 @ ( mand % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mimplies @ ( mbox @ equivalence_2 ) % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [X: $i] : % 0.12/0.42 ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [Y: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( equiv @ X @ Y ) @ ( implies @ Y @ X ) ) ) ) ) ) ) ) ) ) % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mimplies % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [X: $i] : % 0.12/0.42 ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [Y: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( equiv @ X @ Y ) @ ( implies @ Y @ X ) ) ) ) ) ) ) ) % 0.12/0.42 @ ( mbox @ equivalence_2 ) ) ) ) ) ). % 0.12/0.42 % 0.12/0.42 thf(equivalence_3_0,axiom, % 0.12/0.42 ( mlocal % 0.12/0.42 @ ( mand % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mimplies @ ( mbox @ equivalence_3 ) % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [X: $i] : % 0.12/0.42 ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [Y: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( implies @ X @ Y ) @ ( implies @ ( implies @ Y @ X ) @ ( equiv @ X @ Y ) ) ) ) ) ) ) ) ) ) ) % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mimplies % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [X: $i] : % 0.12/0.42 ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [Y: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( implies @ X @ Y ) @ ( implies @ ( implies @ Y @ X ) @ ( equiv @ X @ Y ) ) ) ) ) ) ) ) ) % 0.12/0.42 @ ( mbox @ equivalence_3 ) ) ) ) ) ). % 0.12/0.42 % 0.12/0.42 thf(kn1_0,axiom, % 0.12/0.42 ( mlocal % 0.12/0.42 @ ( mand % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mimplies @ ( mbox @ kn1 ) % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [P: $i] : ( mbox @ ( is_a_theorem @ ( implies @ P @ ( and @ P @ P ) ) ) ) ) ) ) ) % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mimplies % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [P: $i] : ( mbox @ ( is_a_theorem @ ( implies @ P @ ( and @ P @ P ) ) ) ) ) ) % 0.12/0.42 @ ( mbox @ kn1 ) ) ) ) ) ). % 0.12/0.42 % 0.12/0.42 thf(kn2_0,axiom, % 0.12/0.42 ( mlocal % 0.12/0.42 @ ( mand % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mimplies @ ( mbox @ kn2 ) % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [P: $i] : % 0.12/0.42 ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [Q: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( and @ P @ Q ) @ P ) ) ) ) ) ) ) ) ) % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mimplies % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [P: $i] : % 0.12/0.42 ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [Q: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( and @ P @ Q ) @ P ) ) ) ) ) ) ) % 0.12/0.42 @ ( mbox @ kn2 ) ) ) ) ) ). % 0.12/0.42 % 0.12/0.42 thf(kn3_0,axiom, % 0.12/0.42 ( mlocal % 0.12/0.42 @ ( mand % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mimplies @ ( mbox @ kn3 ) % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [P: $i] : % 0.12/0.42 ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [Q: $i] : % 0.12/0.42 ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [R: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( implies @ P @ Q ) @ ( implies @ ( not @ ( and @ Q @ R ) ) @ ( not @ ( and @ R @ P ) ) ) ) ) ) ) ) ) ) ) ) ) ) % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mimplies % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [P: $i] : % 0.12/0.42 ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [Q: $i] : % 0.12/0.42 ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [R: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( implies @ P @ Q ) @ ( implies @ ( not @ ( and @ Q @ R ) ) @ ( not @ ( and @ R @ P ) ) ) ) ) ) ) ) ) ) ) ) % 0.12/0.42 @ ( mbox @ kn3 ) ) ) ) ) ). % 0.12/0.42 % 0.12/0.42 thf(cn1_0,axiom, % 0.12/0.42 ( mlocal % 0.12/0.42 @ ( mand % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mimplies @ ( mbox @ cn1 ) % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [P: $i] : % 0.12/0.42 ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [Q: $i] : % 0.12/0.42 ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [R: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( implies @ P @ Q ) @ ( implies @ ( implies @ Q @ R ) @ ( implies @ P @ R ) ) ) ) ) ) ) ) ) ) ) ) ) % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mimplies % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [P: $i] : % 0.12/0.42 ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [Q: $i] : % 0.12/0.42 ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [R: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( implies @ P @ Q ) @ ( implies @ ( implies @ Q @ R ) @ ( implies @ P @ R ) ) ) ) ) ) ) ) ) ) ) % 0.12/0.42 @ ( mbox @ cn1 ) ) ) ) ) ). % 0.12/0.42 % 0.12/0.42 thf(cn2_0,axiom, % 0.12/0.42 ( mlocal % 0.12/0.42 @ ( mand % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mimplies @ ( mbox @ cn2 ) % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [P: $i] : % 0.12/0.42 ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [Q: $i] : ( mbox @ ( is_a_theorem @ ( implies @ P @ ( implies @ ( not @ P ) @ Q ) ) ) ) ) ) ) ) ) ) % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mimplies % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [P: $i] : % 0.12/0.42 ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [Q: $i] : ( mbox @ ( is_a_theorem @ ( implies @ P @ ( implies @ ( not @ P ) @ Q ) ) ) ) ) ) ) ) % 0.12/0.42 @ ( mbox @ cn2 ) ) ) ) ) ). % 0.12/0.42 % 0.12/0.42 thf(cn3_0,axiom, % 0.12/0.42 ( mlocal % 0.12/0.42 @ ( mand % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mimplies @ ( mbox @ cn3 ) % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [P: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( implies @ ( not @ P ) @ P ) @ P ) ) ) ) ) ) ) % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mimplies % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [P: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( implies @ ( not @ P ) @ P ) @ P ) ) ) ) ) % 0.12/0.42 @ ( mbox @ cn3 ) ) ) ) ) ). % 0.12/0.42 % 0.12/0.42 thf(r1_0,axiom, % 0.12/0.42 ( mlocal % 0.12/0.42 @ ( mand % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mimplies @ ( mbox @ r1 ) % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [P: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( or @ P @ P ) @ P ) ) ) ) ) ) ) % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mimplies % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [P: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( or @ P @ P ) @ P ) ) ) ) ) % 0.12/0.42 @ ( mbox @ r1 ) ) ) ) ) ). % 0.12/0.42 % 0.12/0.42 thf(r2_0,axiom, % 0.12/0.42 ( mlocal % 0.12/0.42 @ ( mand % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mimplies @ ( mbox @ r2 ) % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [P: $i] : % 0.12/0.42 ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [Q: $i] : ( mbox @ ( is_a_theorem @ ( implies @ Q @ ( or @ P @ Q ) ) ) ) ) ) ) ) ) ) % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mimplies % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [P: $i] : % 0.12/0.42 ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [Q: $i] : ( mbox @ ( is_a_theorem @ ( implies @ Q @ ( or @ P @ Q ) ) ) ) ) ) ) ) % 0.12/0.42 @ ( mbox @ r2 ) ) ) ) ) ). % 0.12/0.42 % 0.12/0.42 thf(r3_0,axiom, % 0.12/0.42 ( mlocal % 0.12/0.42 @ ( mand % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mimplies @ ( mbox @ r3 ) % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [P: $i] : % 0.12/0.42 ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [Q: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( or @ P @ Q ) @ ( or @ Q @ P ) ) ) ) ) ) ) ) ) ) % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mimplies % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [P: $i] : % 0.12/0.42 ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [Q: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( or @ P @ Q ) @ ( or @ Q @ P ) ) ) ) ) ) ) ) % 0.12/0.42 @ ( mbox @ r3 ) ) ) ) ) ). % 0.12/0.42 % 0.12/0.42 thf(r4_0,axiom, % 0.12/0.42 ( mlocal % 0.12/0.42 @ ( mand % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mimplies @ ( mbox @ r4 ) % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [P: $i] : % 0.12/0.42 ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [Q: $i] : % 0.12/0.42 ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [R: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( or @ P @ ( or @ Q @ R ) ) @ ( or @ Q @ ( or @ P @ R ) ) ) ) ) ) ) ) ) ) ) ) ) % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mimplies % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [P: $i] : % 0.12/0.42 ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [Q: $i] : % 0.12/0.42 ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [R: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( or @ P @ ( or @ Q @ R ) ) @ ( or @ Q @ ( or @ P @ R ) ) ) ) ) ) ) ) ) ) ) % 0.12/0.42 @ ( mbox @ r4 ) ) ) ) ) ). % 0.12/0.42 % 0.12/0.42 thf(r5_0,axiom, % 0.12/0.42 ( mlocal % 0.12/0.42 @ ( mand % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mimplies @ ( mbox @ r5 ) % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [P: $i] : % 0.12/0.42 ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [Q: $i] : % 0.12/0.42 ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [R: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( implies @ Q @ R ) @ ( implies @ ( or @ P @ Q ) @ ( or @ P @ R ) ) ) ) ) ) ) ) ) ) ) ) ) % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mimplies % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [P: $i] : % 0.12/0.42 ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [Q: $i] : % 0.12/0.42 ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [R: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( implies @ Q @ R ) @ ( implies @ ( or @ P @ Q ) @ ( or @ P @ R ) ) ) ) ) ) ) ) ) ) ) % 0.12/0.42 @ ( mbox @ r5 ) ) ) ) ) ). % 0.12/0.42 % 0.12/0.42 thf(op_or_0,axiom, % 0.12/0.42 ( mlocal % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mimplies @ ( mbox @ op_or ) % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [X: $i] : % 0.12/0.42 ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [Y: $i] : ( mbox @ ( qmltpeq @ ( or @ X @ Y ) @ ( not @ ( and @ ( not @ X ) @ ( not @ Y ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.12/0.42 % 0.12/0.42 thf(op_and_0,axiom, % 0.12/0.42 ( mlocal % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mimplies @ ( mbox @ op_and ) % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [X: $i] : % 0.12/0.42 ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [Y: $i] : ( mbox @ ( qmltpeq @ ( and @ X @ Y ) @ ( not @ ( or @ ( not @ X ) @ ( not @ Y ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.12/0.42 % 0.12/0.42 thf(op_implies_and_0,axiom, % 0.12/0.42 ( mlocal % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mimplies @ ( mbox @ op_implies_and ) % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [X: $i] : % 0.12/0.42 ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [Y: $i] : ( mbox @ ( qmltpeq @ ( implies @ X @ Y ) @ ( not @ ( and @ X @ ( not @ Y ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.12/0.42 % 0.12/0.42 thf(op_implies_or_0,axiom, % 0.12/0.42 ( mlocal % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mimplies @ ( mbox @ op_implies_or ) % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [X: $i] : % 0.12/0.42 ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [Y: $i] : ( mbox @ ( qmltpeq @ ( implies @ X @ Y ) @ ( or @ ( not @ X ) @ Y ) ) ) ) ) ) ) ) ) ) ). % 0.12/0.42 % 0.12/0.42 thf(op_equiv_0,axiom, % 0.12/0.42 ( mlocal % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mimplies @ ( mbox @ op_equiv ) % 0.12/0.42 @ ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [X: $i] : % 0.12/0.42 ( mbox % 0.12/0.42 @ ( mforall_di % 0.12/0.42 @ ^ [Y: $i] : ( mbox @ ( qmltpeq @ ( equiv @ X @ Y ) @ ( and @ ( implies @ X @ Y ) @ ( implies @ Y @ X ) ) ) ) ) ) ) ) ) ) ) ). % 0.12/0.42 % 0.12/0.42 thf(hilbert_op_or,axiom, % 0.12/0.42 mlocal @ ( mbox @ op_or ) ). % 0.12/0.42 % 0.12/0.42 thf(hilbert_op_implies_and,axiom, % 0.12/0.42 mlocal @ ( mbox @ op_implies_and ) ). % 0.12/0.42 % 0.12/0.42 thf(hilbert_op_equiv,axiom, % 0.12/0.42 mlocal @ ( mbox @ op_equiv ) ). % 0.12/0.42 % 0.12/0.42 thf(hilbert_modus_ponens,axiom, % 0.12/0.42 mlocal @ ( mbox @ modus_ponens ) ). % 0.12/0.42 % 0.12/0.42 thf(hilbert_modus_tollens,axiom, % 0.12/0.42 mlocal @ ( mbox @ modus_tollens ) ). % 0.12/0.42 % 0.12/0.42 thf(hilbert_implies_1,axiom, % 0.12/0.42 mlocal @ ( mbox @ implies_1 ) ). % 0.12/0.42 % 0.12/0.42 thf(hilbert_implies_2,axiom, % 0.12/0.42 mlocal @ ( mbox @ implies_2 ) ). % 0.12/0.42 % 0.12/0.42 thf(hilbert_implies_3,axiom, % 0.12/0.42 mlocal @ ( mbox @ implies_3 ) ). % 0.12/0.42 % 0.12/0.42 thf(hilbert_and_1,axiom, % 0.12/0.42 mlocal @ ( mbox @ and_1 ) ). % 0.12/0.42 % 0.12/0.42 thf(hilbert_and_2,axiom, % 0.12/0.42 mlocal @ ( mbox @ and_2 ) ). % 0.12/0.42 % 0.12/0.42 thf(hilbert_and_3,axiom, % 0.12/0.42 mlocal @ ( mbox @ and_3 ) ). % 0.12/0.42 % 0.12/0.42 thf(hilbert_or_1,axiom, % 0.12/0.42 mlocal @ ( mbox @ or_1 ) ). % 0.12/0.42 % 0.12/0.42 thf(hilbert_or_2,axiom, % 0.12/0.42 mlocal @ ( mbox @ or_2 ) ). % 0.12/0.42 % 0.12/0.42 thf(hilbert_or_3,axiom, % 0.12/0.42 mlocal @ ( mbox @ or_3 ) ). % 0.12/0.42 % 0.12/0.42 thf(hilbert_equivalence_1,axiom, % 0.12/0.42 mlocal @ ( mbox @ equivalence_1 ) ). % 0.12/0.42 % 0.12/0.42 thf(hilbert_equivalence_2,axiom, % 0.12/0.42 mlocal @ ( mbox @ equivalence_2 ) ). % 0.12/0.42 % 0.12/0.42 thf(hilbert_equivalence_3,axiom, % 0.12/0.42 mlocal @ ( mbox @ equivalence_3 ) ). % 0.12/0.42 % 0.12/0.42 thf(substitution_of_equivalents_1,axiom, % 0.12/0.42 mlocal @ ( mbox @ substitution_of_equivalents ) ). % 0.12/0.42 % 0.12/0.42 thf(principia_op_implies_or,axiom, % 0.12/0.42 mlocal @ ( mbox @ op_implies_or ) ). % 0.12/0.42 % 0.12/0.42 thf(principia_op_and,axiom, % 0.12/0.42 mlocal @ ( mbox @ op_and ) ). % 0.12/0.42 % 0.12/0.42 thf(principia_op_equiv,axiom, % 0.12/0.42 mlocal @ ( mbox @ op_equiv ) ). % 0.12/0.42 % 0.12/0.42 thf(principia_r2,conjecture, % 0.12/0.42 mlocal @ ( mbox @ r2 ) ). % 0.12/0.42 % 0.12/0.42 %------------------------------------------------------------------------------ % 0.12/0.42 ------------------------ % 0.12/0.42 /starexec/sw/sutcliffe/jdk-11.0.2/bin/java: Command not found. % 0.12/0.42 ---- Embedded in THF --- % 0.12/0.42 ------------------------ % 0.12/0.44 ---- Cleaned THF --- % 0.12/0.45 ------------------------ % 0.21/0.47 % (2235932)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_2235913 for (3000ds/2Mi) % 0.21/0.47 % (2235932)First to succeed. % 0.21/0.48 % SZS status Satisfiable for DTF2THF_2235913 % 0.21/0.48 % (2235932)# SZS output start Saturation. % 0.21/0.48 % (2235932)# SZS output end Saturation. % 0.21/0.48 % (2235932)------------------------------ % 0.21/0.48 % (2235932)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) % 0.21/0.48 % (2235932)Termination reason: Satisfiable % 0.21/0.48 % 0.21/0.48 % (2235932)Memory used [KB]: 5373 % 0.21/0.48 % (2235932)Time elapsed: 0.002 s % 0.21/0.48 % (2235932)Instructions burned: 1 (million) % 0.21/0.48 % (2235932)------------------------------ % 0.21/0.48 % (2235932)------------------------------ % 0.21/0.48 % (2235928)Success in time 0.011 s %------------------------------------------------------------------------------