%------------------------------------------------------------------------------ % File : DT2H2X---1.9.5 % Problem : LCL963^3 : TPTP v9.3.1. Released v8.1.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300 % Computer : n014.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 11:35:17 AM UTC 2026 % Result : CounterSatisfiable 0.10s 0.46s % Output : Saturation 0.10s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL963^3 : TPTP v9.3.1. Released v8.1.0. % 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300 % 0.10/0.37 % Computer : n014.cluster.edu % 0.10/0.37 % Model : x86_64 x86_64 % 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.37 % Memory : 8046.5625MB % 0.10/0.37 % OS : Linux 6.8.0-71-generic % 0.10/0.37 % CPULimit : 300 % 0.10/0.37 % WCLimit : 300 % 0.10/0.37 % DateTime : Fri Sep 4 23:48:57 UTC 2026 % 0.10/0.38 % CPUTime : % 0.10/0.38 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300 % 0.10/0.40 ---- Original DTF file --- % 0.10/0.40 thf(spec,logic,$$dhol). % 0.10/0.40 %------------------------------------------------------------------------------ % 0.10/0.40 % File : LCL963^3 : TPTP v9.3.1. Released v8.1.0. % 0.10/0.40 % Domain : Logic Calculi % 0.10/0.40 % Problem : Goedel translation of LCL451+1 (from TPTP-v5.0.0) % 0.10/0.40 % Version : [BP13] axioms. % 0.10/0.40 % English : % 0.10/0.40 % 0.10/0.40 % Refs : [RO12] Raths & Otten (2012), The QMLTP Problem Library for Fi % 0.10/0.40 % : [BP13] Benzmueller & Paulson (2013), Quantified Multimodal Lo % 0.10/0.40 % : [Ste22] Steen (2022), An Extensible Logic Embedding Tool for L % 0.10/0.40 % Source : [TPTP] % 0.10/0.40 % Names : GLC451+1 [QMLTP] % 0.10/0.40 % 0.10/0.40 % Status : CounterSatisfiable % 0.10/0.40 % Rating : 1.00 v9.0.0, 0.75 v8.2.0, 1.00 v8.1.0 % 0.10/0.40 % Syntax : Number of formulae : 129 ( 11 unt; 52 typ; 10 def) % 0.10/0.40 % Number of atoms : 911 ( 10 equ; 0 cnn) % 0.10/0.40 % Maximal formula atoms : 36 ( 11 avg) % 0.10/0.40 % Number of connectives : 1368 ( 1 ~; 1 |; 2 &;1361 @) % 0.10/0.40 % ( 1 <=>; 2 =>; 0 <=; 0 <~>) % 0.10/0.40 % Maximal formula depth : 23 ( 11 avg) % 0.10/0.40 % Number of types : 3 ( 1 usr) % 0.10/0.40 % Number of type conns : 103 ( 103 >; 0 *; 0 +; 0 <<) % 0.10/0.40 % Number of symbols : 52 ( 51 usr; 1 con; 0-3 aty) % 0.10/0.40 % Number of variables : 183 ( 177 ^; 3 !; 3 ?; 183 :) % 0.10/0.40 % SPC : TH0_CSA_EQU_NAR_NDT % 0.10/0.40 % 0.10/0.40 % Comments : This output was generated by embedproblem, version 1.7.1 (library % 0.10/0.40 % version 1.3). Generated on Thu Apr 28 13:18:18 EDT 2022 using % 0.10/0.40 % 'modal' embedding, version 1.5.2. Logic specification used: % 0.10/0.40 % $modal == [$constants == $rigid,$quantification == $constant, % 0.10/0.40 % $modalities == $modal_system_D]. % 0.10/0.40 %------------------------------------------------------------------------------ % 0.10/0.40 thf(mworld,type, % 0.10/0.40 mworld: $tType ). % 0.10/0.40 % 0.10/0.40 thf(mrel_type,type, % 0.10/0.40 mrel: mworld > mworld > $o ). % 0.10/0.40 % 0.10/0.40 thf(mactual_type,type, % 0.10/0.40 mactual: mworld ). % 0.10/0.40 % 0.10/0.40 thf(mlocal_type,type, % 0.10/0.40 mlocal: ( mworld > $o ) > $o ). % 0.10/0.40 % 0.10/0.40 thf(mlocal_def,definition, % 0.10/0.40 ( mlocal % 0.10/0.40 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ). % 0.10/0.40 % 0.10/0.40 thf(mnot_type,type, % 0.10/0.40 mnot: ( mworld > $o ) > mworld > $o ). % 0.10/0.40 % 0.10/0.40 thf(mand_type,type, % 0.10/0.40 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ). % 0.10/0.40 % 0.10/0.40 thf(mor_type,type, % 0.10/0.40 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ). % 0.10/0.40 % 0.10/0.40 thf(mimplies_type,type, % 0.10/0.40 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ). % 0.10/0.40 % 0.10/0.40 thf(mequiv_type,type, % 0.10/0.40 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ). % 0.10/0.40 % 0.10/0.40 thf(mnot_def,definition, % 0.10/0.40 ( mnot % 0.10/0.40 = ( ^ [A: mworld > $o,W: mworld] : % 0.10/0.40 ~ ( A @ W ) ) ) ). % 0.10/0.40 % 0.10/0.40 thf(mand_def,definition, % 0.10/0.40 ( mand % 0.10/0.40 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] : % 0.10/0.40 ( ( A @ W ) % 0.10/0.40 & ( B @ W ) ) ) ) ). % 0.10/0.40 % 0.10/0.40 thf(mor_def,definition, % 0.10/0.40 ( mor % 0.10/0.40 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] : % 0.10/0.40 ( ( A @ W ) % 0.10/0.40 | ( B @ W ) ) ) ) ). % 0.10/0.40 % 0.10/0.40 thf(mimplies_def,definition, % 0.10/0.40 ( mimplies % 0.10/0.40 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] : % 0.10/0.40 ( ( A @ W ) % 0.10/0.40 => ( B @ W ) ) ) ) ). % 0.10/0.40 % 0.10/0.40 thf(mequiv_def,definition, % 0.10/0.40 ( mequiv % 0.10/0.40 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] : % 0.10/0.40 ( ( A @ W ) % 0.10/0.40 <=> ( B @ W ) ) ) ) ). % 0.10/0.40 % 0.10/0.40 thf(mbox_type,type, % 0.10/0.40 mbox: ( mworld > $o ) > mworld > $o ). % 0.10/0.40 % 0.10/0.40 thf(mbox_def,definition, % 0.10/0.40 ( mbox % 0.10/0.40 = ( ^ [Phi: mworld > $o,W: mworld] : % 0.10/0.40 ! [V: mworld] : % 0.10/0.40 ( ( mrel @ W @ V ) % 0.10/0.40 => ( Phi @ V ) ) ) ) ). % 0.10/0.40 % 0.10/0.40 thf(mdia_type,type, % 0.10/0.40 mdia: ( mworld > $o ) > mworld > $o ). % 0.10/0.40 % 0.10/0.40 thf(mdia_def,definition, % 0.10/0.40 ( mdia % 0.10/0.40 = ( ^ [Phi: mworld > $o,W: mworld] : % 0.10/0.40 ? [V: mworld] : % 0.10/0.40 ( ( mrel @ W @ V ) % 0.10/0.40 & ( Phi @ V ) ) ) ) ). % 0.10/0.40 % 0.10/0.40 thf(mrel_serial,axiom, % 0.10/0.40 ! [W: mworld] : % 0.10/0.40 ? [V: mworld] : ( mrel @ W @ V ) ). % 0.10/0.40 % 0.10/0.40 thf(mforall_di_type,type, % 0.10/0.40 mforall_di: ( $i > mworld > $o ) > mworld > $o ). % 0.10/0.40 % 0.10/0.40 thf(mforall_di_def,definition, % 0.10/0.40 ( mforall_di % 0.10/0.40 = ( ^ [A: $i > mworld > $o,W: mworld] : % 0.10/0.40 ! [X: $i] : ( A @ X @ W ) ) ) ). % 0.10/0.40 % 0.10/0.40 thf(mexists_di_type,type, % 0.10/0.40 mexists_di: ( $i > mworld > $o ) > mworld > $o ). % 0.10/0.40 % 0.10/0.40 thf(mexists_di_def,definition, % 0.10/0.40 ( mexists_di % 0.10/0.40 = ( ^ [A: $i > mworld > $o,W: mworld] : % 0.10/0.40 ? [X: $i] : ( A @ X @ W ) ) ) ). % 0.10/0.40 % 0.10/0.40 thf(r2_decl,type, % 0.10/0.40 r2: mworld > $o ). % 0.10/0.40 % 0.10/0.40 thf(r3_decl,type, % 0.10/0.40 r3: mworld > $o ). % 0.10/0.40 % 0.10/0.40 thf(r4_decl,type, % 0.10/0.40 r4: mworld > $o ). % 0.10/0.40 % 0.10/0.40 thf(r5_decl,type, % 0.10/0.40 r5: mworld > $o ). % 0.10/0.40 % 0.10/0.40 thf(equivalence_1_decl,type, % 0.10/0.40 equivalence_1: mworld > $o ). % 0.10/0.40 % 0.10/0.40 thf(equivalence_2_decl,type, % 0.10/0.40 equivalence_2: mworld > $o ). % 0.10/0.40 % 0.10/0.40 thf(cn2_decl,type, % 0.10/0.40 cn2: mworld > $o ). % 0.10/0.40 % 0.10/0.40 thf(cn1_decl,type, % 0.10/0.40 cn1: mworld > $o ). % 0.10/0.40 % 0.10/0.40 thf(cn3_decl,type, % 0.10/0.40 cn3: mworld > $o ). % 0.10/0.40 % 0.10/0.40 thf(kn2_decl,type, % 0.10/0.40 kn2: mworld > $o ). % 0.10/0.40 % 0.10/0.40 thf(kn1_decl,type, % 0.10/0.40 kn1: mworld > $o ). % 0.10/0.40 % 0.10/0.40 thf(kn3_decl,type, % 0.10/0.40 kn3: mworld > $o ). % 0.10/0.40 % 0.10/0.40 thf(equivalence_3_decl,type, % 0.10/0.40 equivalence_3: mworld > $o ). % 0.10/0.40 % 0.10/0.40 thf(op_implies_or_decl,type, % 0.10/0.40 op_implies_or: mworld > $o ). % 0.10/0.40 % 0.10/0.40 thf(op_and_decl,type, % 0.10/0.40 op_and: mworld > $o ). % 0.10/0.40 % 0.10/0.40 thf(and_2_decl,type, % 0.10/0.40 and_2: mworld > $o ). % 0.10/0.40 % 0.10/0.40 thf(and_3_decl,type, % 0.10/0.40 and_3: mworld > $o ). % 0.10/0.40 % 0.10/0.40 thf(and_1_decl,type, % 0.10/0.40 and_1: mworld > $o ). % 0.10/0.40 % 0.10/0.40 thf(implies_2_decl,type, % 0.10/0.40 implies_2: mworld > $o ). % 0.10/0.40 % 0.10/0.40 thf(implies_3_decl,type, % 0.10/0.40 implies_3: mworld > $o ). % 0.10/0.40 % 0.10/0.40 thf(op_implies_and_decl,type, % 0.10/0.40 op_implies_and: mworld > $o ). % 0.10/0.40 % 0.10/0.40 thf(implies_1_decl,type, % 0.10/0.40 implies_1: mworld > $o ). % 0.10/0.40 % 0.10/0.40 thf(substitution_of_equivalents_decl,type, % 0.10/0.40 substitution_of_equivalents: mworld > $o ). % 0.10/0.40 % 0.10/0.40 thf(op_or_decl,type, % 0.10/0.40 op_or: mworld > $o ). % 0.10/0.40 % 0.10/0.40 thf(modus_tollens_decl,type, % 0.10/0.40 modus_tollens: mworld > $o ). % 0.10/0.40 % 0.10/0.40 thf(or_1_decl,type, % 0.10/0.40 or_1: mworld > $o ). % 0.10/0.40 % 0.10/0.40 thf(or_2_decl,type, % 0.10/0.40 or_2: mworld > $o ). % 0.10/0.40 % 0.10/0.40 thf(or_3_decl,type, % 0.10/0.40 or_3: mworld > $o ). % 0.10/0.40 % 0.10/0.40 thf(op_equiv_decl,type, % 0.10/0.40 op_equiv: mworld > $o ). % 0.10/0.40 % 0.10/0.40 thf(modus_ponens_decl,type, % 0.10/0.40 modus_ponens: mworld > $o ). % 0.10/0.40 % 0.10/0.40 thf(op_implies_decl,type, % 0.10/0.40 op_implies: mworld > $o ). % 0.10/0.40 % 0.10/0.40 thf(r1_decl,type, % 0.10/0.40 r1: mworld > $o ). % 0.10/0.40 % 0.10/0.40 thf(qmltpeq_decl,type, % 0.10/0.40 qmltpeq: $i > $i > mworld > $o ). % 0.10/0.40 % 0.10/0.40 thf(is_a_theorem_decl,type, % 0.10/0.40 is_a_theorem: $i > mworld > $o ). % 0.10/0.40 % 0.10/0.40 thf(equiv_decl,type, % 0.10/0.40 equiv: $i > $i > $i ). % 0.10/0.40 % 0.10/0.40 thf(not_decl,type, % 0.10/0.40 not: $i > $i ). % 0.10/0.40 % 0.10/0.40 thf(or_decl,type, % 0.10/0.40 or: $i > $i > $i ). % 0.10/0.40 % 0.10/0.40 thf(and_decl,type, % 0.10/0.40 and: $i > $i > $i ). % 0.10/0.40 % 0.10/0.40 thf(implies_decl,type, % 0.10/0.40 implies: $i > $i > $i ). % 0.10/0.40 % 0.10/0.40 thf(reflexivity,axiom, % 0.10/0.40 ( mlocal % 0.10/0.40 @ ( mbox % 0.10/0.40 @ ( mforall_di % 0.10/0.40 @ ^ [X: $i] : ( mbox @ ( qmltpeq @ X @ X ) ) ) ) ) ). % 0.10/0.40 % 0.10/0.40 thf(symmetry,axiom, % 0.10/0.40 ( mlocal % 0.10/0.40 @ ( mbox % 0.10/0.40 @ ( mforall_di % 0.10/0.40 @ ^ [X: $i] : % 0.10/0.40 ( mbox % 0.10/0.40 @ ( mforall_di % 0.10/0.40 @ ^ [Y: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ X @ Y ) ) @ ( mbox @ ( qmltpeq @ Y @ X ) ) ) ) ) ) ) ) ) ). % 0.10/0.40 % 0.10/0.40 thf(transitivity,axiom, % 0.10/0.40 ( mlocal % 0.10/0.40 @ ( mbox % 0.10/0.40 @ ( mforall_di % 0.10/0.40 @ ^ [X: $i] : % 0.10/0.40 ( mbox % 0.10/0.40 @ ( mforall_di % 0.10/0.40 @ ^ [Y: $i] : % 0.10/0.40 ( mbox % 0.10/0.40 @ ( mforall_di % 0.10/0.40 @ ^ [Z: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( qmltpeq @ X @ Y ) ) @ ( mbox @ ( qmltpeq @ Y @ Z ) ) ) @ ( mbox @ ( qmltpeq @ X @ Z ) ) ) ) ) ) ) ) ) ) ) ). % 0.10/0.40 % 0.10/0.40 thf(and_substitution_1,axiom, % 0.10/0.40 ( mlocal % 0.10/0.40 @ ( mbox % 0.10/0.40 @ ( mforall_di % 0.10/0.40 @ ^ [A: $i] : % 0.10/0.40 ( mbox % 0.10/0.40 @ ( mforall_di % 0.10/0.40 @ ^ [B: $i] : % 0.10/0.40 ( mbox % 0.10/0.40 @ ( mforall_di % 0.10/0.40 @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( and @ A @ C ) @ ( and @ B @ C ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.10/0.40 % 0.10/0.40 thf(and_substitution_2,axiom, % 0.10/0.40 ( mlocal % 0.10/0.40 @ ( mbox % 0.10/0.40 @ ( mforall_di % 0.10/0.40 @ ^ [A: $i] : % 0.10/0.40 ( mbox % 0.10/0.40 @ ( mforall_di % 0.10/0.40 @ ^ [B: $i] : % 0.10/0.40 ( mbox % 0.10/0.40 @ ( mforall_di % 0.10/0.40 @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( and @ C @ A ) @ ( and @ C @ B ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.10/0.40 % 0.10/0.40 thf(equiv_substitution_1,axiom, % 0.10/0.40 ( mlocal % 0.10/0.40 @ ( mbox % 0.10/0.40 @ ( mforall_di % 0.10/0.40 @ ^ [A: $i] : % 0.10/0.40 ( mbox % 0.10/0.40 @ ( mforall_di % 0.10/0.40 @ ^ [B: $i] : % 0.10/0.40 ( mbox % 0.10/0.40 @ ( mforall_di % 0.10/0.40 @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( equiv @ A @ C ) @ ( equiv @ B @ C ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.10/0.40 % 0.10/0.40 thf(equiv_substitution_2,axiom, % 0.10/0.40 ( mlocal % 0.10/0.40 @ ( mbox % 0.10/0.40 @ ( mforall_di % 0.10/0.40 @ ^ [A: $i] : % 0.10/0.40 ( mbox % 0.10/0.40 @ ( mforall_di % 0.10/0.40 @ ^ [B: $i] : % 0.10/0.40 ( mbox % 0.10/0.40 @ ( mforall_di % 0.10/0.40 @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( equiv @ C @ A ) @ ( equiv @ C @ B ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.10/0.40 % 0.10/0.40 thf(implies_substitution_1,axiom, % 0.10/0.40 ( mlocal % 0.10/0.40 @ ( mbox % 0.10/0.40 @ ( mforall_di % 0.10/0.40 @ ^ [A: $i] : % 0.10/0.40 ( mbox % 0.10/0.40 @ ( mforall_di % 0.10/0.40 @ ^ [B: $i] : % 0.10/0.40 ( mbox % 0.10/0.40 @ ( mforall_di % 0.10/0.40 @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( implies @ A @ C ) @ ( implies @ B @ C ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.10/0.40 % 0.10/0.40 thf(implies_substitution_2,axiom, % 0.10/0.40 ( mlocal % 0.10/0.40 @ ( mbox % 0.10/0.40 @ ( mforall_di % 0.10/0.40 @ ^ [A: $i] : % 0.10/0.40 ( mbox % 0.10/0.40 @ ( mforall_di % 0.10/0.40 @ ^ [B: $i] : % 0.10/0.40 ( mbox % 0.10/0.40 @ ( mforall_di % 0.10/0.40 @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( implies @ C @ A ) @ ( implies @ C @ B ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.10/0.40 % 0.10/0.40 thf(not_substitution_1,axiom, % 0.10/0.40 ( mlocal % 0.10/0.40 @ ( mbox % 0.10/0.40 @ ( mforall_di % 0.10/0.40 @ ^ [A: $i] : % 0.10/0.40 ( mbox % 0.10/0.40 @ ( mforall_di % 0.10/0.40 @ ^ [B: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( not @ A ) @ ( not @ B ) ) ) ) ) ) ) ) ) ) ). % 0.10/0.40 % 0.10/0.40 thf(or_substitution_1,axiom, % 0.10/0.40 ( mlocal % 0.10/0.40 @ ( mbox % 0.10/0.40 @ ( mforall_di % 0.10/0.40 @ ^ [A: $i] : % 0.10/0.40 ( mbox % 0.10/0.40 @ ( mforall_di % 0.10/0.40 @ ^ [B: $i] : % 0.10/0.40 ( mbox % 0.10/0.40 @ ( mforall_di % 0.10/0.40 @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( or @ A @ C ) @ ( or @ B @ C ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.10/0.40 % 0.10/0.40 thf(or_substitution_2,axiom, % 0.10/0.40 ( mlocal % 0.10/0.40 @ ( mbox % 0.10/0.40 @ ( mforall_di % 0.10/0.40 @ ^ [A: $i] : % 0.10/0.40 ( mbox % 0.10/0.40 @ ( mforall_di % 0.10/0.40 @ ^ [B: $i] : % 0.10/0.40 ( mbox % 0.10/0.40 @ ( mforall_di % 0.10/0.40 @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( or @ C @ A ) @ ( or @ C @ B ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.10/0.40 % 0.10/0.40 thf(is_a_theorem_substitution_1,axiom, % 0.10/0.40 ( mlocal % 0.10/0.40 @ ( mbox % 0.10/0.40 @ ( mforall_di % 0.10/0.40 @ ^ [A: $i] : % 0.10/0.40 ( mbox % 0.10/0.40 @ ( mforall_di % 0.10/0.40 @ ^ [B: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( is_a_theorem @ A ) ) ) @ ( mbox @ ( is_a_theorem @ B ) ) ) ) ) ) ) ) ) ). % 0.10/0.40 % 0.10/0.40 thf(modus_ponens_0,axiom, % 0.10/0.40 ( mlocal % 0.10/0.40 @ ( mand % 0.10/0.40 @ ( mbox % 0.10/0.40 @ ( mimplies @ ( mbox @ modus_ponens ) % 0.10/0.40 @ ( mbox % 0.10/0.40 @ ( mforall_di % 0.10/0.40 @ ^ [X: $i] : % 0.10/0.40 ( mbox % 0.10/0.40 @ ( mforall_di % 0.10/0.40 @ ^ [Y: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( is_a_theorem @ X ) ) @ ( mbox @ ( is_a_theorem @ ( implies @ X @ Y ) ) ) ) @ ( mbox @ ( is_a_theorem @ Y ) ) ) ) ) ) ) ) ) ) % 0.10/0.40 @ ( mbox % 0.10/0.40 @ ( mimplies % 0.10/0.40 @ ( mbox % 0.10/0.40 @ ( mforall_di % 0.10/0.40 @ ^ [X: $i] : % 0.10/0.40 ( mbox % 0.10/0.40 @ ( mforall_di % 0.10/0.40 @ ^ [Y: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( is_a_theorem @ X ) ) @ ( mbox @ ( is_a_theorem @ ( implies @ X @ Y ) ) ) ) @ ( mbox @ ( is_a_theorem @ Y ) ) ) ) ) ) ) ) % 0.10/0.40 @ ( mbox @ modus_ponens ) ) ) ) ) ). % 0.10/0.40 % 0.10/0.40 thf(substitution_of_equivalents_0,axiom, % 0.10/0.40 ( mlocal % 0.10/0.40 @ ( mand % 0.10/0.40 @ ( mbox % 0.10/0.40 @ ( mimplies @ ( mbox @ substitution_of_equivalents ) % 0.10/0.40 @ ( mbox % 0.10/0.40 @ ( mforall_di % 0.10/0.40 @ ^ [X: $i] : % 0.10/0.40 ( mbox % 0.10/0.40 @ ( mforall_di % 0.10/0.40 @ ^ [Y: $i] : ( mbox @ ( mimplies @ ( mbox @ ( is_a_theorem @ ( equiv @ X @ Y ) ) ) @ ( mbox @ ( qmltpeq @ X @ Y ) ) ) ) ) ) ) ) ) ) % 0.10/0.40 @ ( mbox % 0.10/0.40 @ ( mimplies % 0.10/0.40 @ ( mbox % 0.10/0.40 @ ( mforall_di % 0.10/0.40 @ ^ [X: $i] : % 0.10/0.40 ( mbox % 0.10/0.40 @ ( mforall_di % 0.10/0.40 @ ^ [Y: $i] : ( mbox @ ( mimplies @ ( mbox @ ( is_a_theorem @ ( equiv @ X @ Y ) ) ) @ ( mbox @ ( qmltpeq @ X @ Y ) ) ) ) ) ) ) ) % 0.10/0.40 @ ( mbox @ substitution_of_equivalents ) ) ) ) ) ). % 0.10/0.40 % 0.10/0.40 thf(modus_tollens_0,axiom, % 0.10/0.40 ( mlocal % 0.10/0.40 @ ( mand % 0.10/0.40 @ ( mbox % 0.10/0.40 @ ( mimplies @ ( mbox @ modus_tollens ) % 0.10/0.40 @ ( mbox % 0.10/0.40 @ ( mforall_di % 0.10/0.40 @ ^ [X: $i] : % 0.10/0.40 ( mbox % 0.10/0.40 @ ( mforall_di % 0.10/0.40 @ ^ [Y: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( implies @ ( not @ Y ) @ ( not @ X ) ) @ ( implies @ X @ Y ) ) ) ) ) ) ) ) ) ) % 0.10/0.40 @ ( mbox % 0.10/0.40 @ ( mimplies % 0.10/0.40 @ ( mbox % 0.10/0.40 @ ( mforall_di % 0.10/0.40 @ ^ [X: $i] : % 0.10/0.40 ( mbox % 0.10/0.40 @ ( mforall_di % 0.10/0.40 @ ^ [Y: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( implies @ ( not @ Y ) @ ( not @ X ) ) @ ( implies @ X @ Y ) ) ) ) ) ) ) ) % 0.10/0.40 @ ( mbox @ modus_tollens ) ) ) ) ) ). % 0.10/0.40 % 0.10/0.40 thf(implies_1_0,axiom, % 0.10/0.40 ( mlocal % 0.10/0.40 @ ( mand % 0.10/0.40 @ ( mbox % 0.10/0.40 @ ( mimplies @ ( mbox @ implies_1 ) % 0.10/0.40 @ ( mbox % 0.10/0.40 @ ( mforall_di % 0.10/0.40 @ ^ [X: $i] : % 0.10/0.40 ( mbox % 0.10/0.40 @ ( mforall_di % 0.10/0.40 @ ^ [Y: $i] : ( mbox @ ( is_a_theorem @ ( implies @ X @ ( implies @ Y @ X ) ) ) ) ) ) ) ) ) ) % 0.10/0.40 @ ( mbox % 0.10/0.40 @ ( mimplies % 0.10/0.40 @ ( mbox % 0.10/0.40 @ ( mforall_di % 0.10/0.40 @ ^ [X: $i] : % 0.10/0.40 ( mbox % 0.10/0.40 @ ( mforall_di % 0.10/0.40 @ ^ [Y: $i] : ( mbox @ ( is_a_theorem @ ( implies @ X @ ( implies @ Y @ X ) ) ) ) ) ) ) ) % 0.10/0.40 @ ( mbox @ implies_1 ) ) ) ) ) ). % 0.10/0.40 % 0.10/0.40 thf(implies_2_0,axiom, % 0.10/0.40 ( mlocal % 0.10/0.40 @ ( mand % 0.10/0.40 @ ( mbox % 0.10/0.40 @ ( mimplies @ ( mbox @ implies_2 ) % 0.10/0.40 @ ( mbox % 0.10/0.40 @ ( mforall_di % 0.10/0.40 @ ^ [X: $i] : % 0.10/0.40 ( mbox % 0.10/0.40 @ ( mforall_di % 0.10/0.40 @ ^ [Y: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( implies @ X @ ( implies @ X @ Y ) ) @ ( implies @ X @ Y ) ) ) ) ) ) ) ) ) ) % 0.10/0.40 @ ( mbox % 0.10/0.40 @ ( mimplies % 0.10/0.40 @ ( mbox % 0.10/0.40 @ ( mforall_di % 0.10/0.40 @ ^ [X: $i] : % 0.10/0.40 ( mbox % 0.10/0.40 @ ( mforall_di % 0.10/0.40 @ ^ [Y: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( implies @ X @ ( implies @ X @ Y ) ) @ ( implies @ X @ Y ) ) ) ) ) ) ) ) % 0.10/0.40 @ ( mbox @ implies_2 ) ) ) ) ) ). % 0.10/0.40 % 0.10/0.40 thf(implies_3_0,axiom, % 0.10/0.40 ( mlocal % 0.10/0.40 @ ( mand % 0.10/0.40 @ ( mbox % 0.10/0.40 @ ( mimplies @ ( mbox @ implies_3 ) % 0.10/0.40 @ ( mbox % 0.10/0.40 @ ( mforall_di % 0.10/0.40 @ ^ [X: $i] : % 0.10/0.40 ( mbox % 0.10/0.40 @ ( mforall_di % 0.10/0.40 @ ^ [Y: $i] : % 0.10/0.40 ( mbox % 0.10/0.40 @ ( mforall_di % 0.10/0.40 @ ^ [Z: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( implies @ X @ Y ) @ ( implies @ ( implies @ Y @ Z ) @ ( implies @ X @ Z ) ) ) ) ) ) ) ) ) ) ) ) ) % 0.10/0.40 @ ( mbox % 0.10/0.40 @ ( mimplies % 0.10/0.40 @ ( mbox % 0.10/0.40 @ ( mforall_di % 0.10/0.40 @ ^ [X: $i] : % 0.10/0.41 ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [Y: $i] : % 0.10/0.41 ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [Z: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( implies @ X @ Y ) @ ( implies @ ( implies @ Y @ Z ) @ ( implies @ X @ Z ) ) ) ) ) ) ) ) ) ) ) % 0.10/0.41 @ ( mbox @ implies_3 ) ) ) ) ) ). % 0.10/0.41 % 0.10/0.41 thf(and_1_0,axiom, % 0.10/0.41 ( mlocal % 0.10/0.41 @ ( mand % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mimplies @ ( mbox @ and_1 ) % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [X: $i] : % 0.10/0.41 ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [Y: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( and @ X @ Y ) @ X ) ) ) ) ) ) ) ) ) % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mimplies % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [X: $i] : % 0.10/0.41 ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [Y: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( and @ X @ Y ) @ X ) ) ) ) ) ) ) % 0.10/0.41 @ ( mbox @ and_1 ) ) ) ) ) ). % 0.10/0.41 % 0.10/0.41 thf(and_2_0,axiom, % 0.10/0.41 ( mlocal % 0.10/0.41 @ ( mand % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mimplies @ ( mbox @ and_2 ) % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [X: $i] : % 0.10/0.41 ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [Y: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( and @ X @ Y ) @ Y ) ) ) ) ) ) ) ) ) % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mimplies % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [X: $i] : % 0.10/0.41 ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [Y: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( and @ X @ Y ) @ Y ) ) ) ) ) ) ) % 0.10/0.41 @ ( mbox @ and_2 ) ) ) ) ) ). % 0.10/0.41 % 0.10/0.41 thf(and_3_0,axiom, % 0.10/0.41 ( mlocal % 0.10/0.41 @ ( mand % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mimplies @ ( mbox @ and_3 ) % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [X: $i] : % 0.10/0.41 ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [Y: $i] : ( mbox @ ( is_a_theorem @ ( implies @ X @ ( implies @ Y @ ( and @ X @ Y ) ) ) ) ) ) ) ) ) ) ) % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mimplies % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [X: $i] : % 0.10/0.41 ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [Y: $i] : ( mbox @ ( is_a_theorem @ ( implies @ X @ ( implies @ Y @ ( and @ X @ Y ) ) ) ) ) ) ) ) ) % 0.10/0.41 @ ( mbox @ and_3 ) ) ) ) ) ). % 0.10/0.41 % 0.10/0.41 thf(or_1_0,axiom, % 0.10/0.41 ( mlocal % 0.10/0.41 @ ( mand % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mimplies @ ( mbox @ or_1 ) % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [X: $i] : % 0.10/0.41 ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [Y: $i] : ( mbox @ ( is_a_theorem @ ( implies @ X @ ( or @ X @ Y ) ) ) ) ) ) ) ) ) ) % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mimplies % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [X: $i] : % 0.10/0.41 ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [Y: $i] : ( mbox @ ( is_a_theorem @ ( implies @ X @ ( or @ X @ Y ) ) ) ) ) ) ) ) % 0.10/0.41 @ ( mbox @ or_1 ) ) ) ) ) ). % 0.10/0.41 % 0.10/0.41 thf(or_2_0,axiom, % 0.10/0.41 ( mlocal % 0.10/0.41 @ ( mand % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mimplies @ ( mbox @ or_2 ) % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [X: $i] : % 0.10/0.41 ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [Y: $i] : ( mbox @ ( is_a_theorem @ ( implies @ Y @ ( or @ X @ Y ) ) ) ) ) ) ) ) ) ) % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mimplies % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [X: $i] : % 0.10/0.41 ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [Y: $i] : ( mbox @ ( is_a_theorem @ ( implies @ Y @ ( or @ X @ Y ) ) ) ) ) ) ) ) % 0.10/0.41 @ ( mbox @ or_2 ) ) ) ) ) ). % 0.10/0.41 % 0.10/0.41 thf(or_3_0,axiom, % 0.10/0.41 ( mlocal % 0.10/0.41 @ ( mand % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mimplies @ ( mbox @ or_3 ) % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [X: $i] : % 0.10/0.41 ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [Y: $i] : % 0.10/0.41 ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [Z: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( implies @ X @ Z ) @ ( implies @ ( implies @ Y @ Z ) @ ( implies @ ( or @ X @ Y ) @ Z ) ) ) ) ) ) ) ) ) ) ) ) ) % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mimplies % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [X: $i] : % 0.10/0.41 ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [Y: $i] : % 0.10/0.41 ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [Z: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( implies @ X @ Z ) @ ( implies @ ( implies @ Y @ Z ) @ ( implies @ ( or @ X @ Y ) @ Z ) ) ) ) ) ) ) ) ) ) ) % 0.10/0.41 @ ( mbox @ or_3 ) ) ) ) ) ). % 0.10/0.41 % 0.10/0.41 thf(equivalence_1_0,axiom, % 0.10/0.41 ( mlocal % 0.10/0.41 @ ( mand % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mimplies @ ( mbox @ equivalence_1 ) % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [X: $i] : % 0.10/0.41 ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [Y: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( equiv @ X @ Y ) @ ( implies @ X @ Y ) ) ) ) ) ) ) ) ) ) % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mimplies % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [X: $i] : % 0.10/0.41 ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [Y: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( equiv @ X @ Y ) @ ( implies @ X @ Y ) ) ) ) ) ) ) ) % 0.10/0.41 @ ( mbox @ equivalence_1 ) ) ) ) ) ). % 0.10/0.41 % 0.10/0.41 thf(equivalence_2_0,axiom, % 0.10/0.41 ( mlocal % 0.10/0.41 @ ( mand % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mimplies @ ( mbox @ equivalence_2 ) % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [X: $i] : % 0.10/0.41 ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [Y: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( equiv @ X @ Y ) @ ( implies @ Y @ X ) ) ) ) ) ) ) ) ) ) % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mimplies % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [X: $i] : % 0.10/0.41 ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [Y: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( equiv @ X @ Y ) @ ( implies @ Y @ X ) ) ) ) ) ) ) ) % 0.10/0.41 @ ( mbox @ equivalence_2 ) ) ) ) ) ). % 0.10/0.41 % 0.10/0.41 thf(equivalence_3_0,axiom, % 0.10/0.41 ( mlocal % 0.10/0.41 @ ( mand % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mimplies @ ( mbox @ equivalence_3 ) % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [X: $i] : % 0.10/0.41 ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [Y: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( implies @ X @ Y ) @ ( implies @ ( implies @ Y @ X ) @ ( equiv @ X @ Y ) ) ) ) ) ) ) ) ) ) ) % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mimplies % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [X: $i] : % 0.10/0.41 ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [Y: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( implies @ X @ Y ) @ ( implies @ ( implies @ Y @ X ) @ ( equiv @ X @ Y ) ) ) ) ) ) ) ) ) % 0.10/0.41 @ ( mbox @ equivalence_3 ) ) ) ) ) ). % 0.10/0.41 % 0.10/0.41 thf(kn1_0,axiom, % 0.10/0.41 ( mlocal % 0.10/0.41 @ ( mand % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mimplies @ ( mbox @ kn1 ) % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [P: $i] : ( mbox @ ( is_a_theorem @ ( implies @ P @ ( and @ P @ P ) ) ) ) ) ) ) ) % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mimplies % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [P: $i] : ( mbox @ ( is_a_theorem @ ( implies @ P @ ( and @ P @ P ) ) ) ) ) ) % 0.10/0.41 @ ( mbox @ kn1 ) ) ) ) ) ). % 0.10/0.41 % 0.10/0.41 thf(kn2_0,axiom, % 0.10/0.41 ( mlocal % 0.10/0.41 @ ( mand % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mimplies @ ( mbox @ kn2 ) % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [P: $i] : % 0.10/0.41 ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [Q: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( and @ P @ Q ) @ P ) ) ) ) ) ) ) ) ) % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mimplies % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [P: $i] : % 0.10/0.41 ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [Q: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( and @ P @ Q ) @ P ) ) ) ) ) ) ) % 0.10/0.41 @ ( mbox @ kn2 ) ) ) ) ) ). % 0.10/0.41 % 0.10/0.41 thf(kn3_0,axiom, % 0.10/0.41 ( mlocal % 0.10/0.41 @ ( mand % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mimplies @ ( mbox @ kn3 ) % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [P: $i] : % 0.10/0.41 ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [Q: $i] : % 0.10/0.41 ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [R: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( implies @ P @ Q ) @ ( implies @ ( not @ ( and @ Q @ R ) ) @ ( not @ ( and @ R @ P ) ) ) ) ) ) ) ) ) ) ) ) ) ) % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mimplies % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [P: $i] : % 0.10/0.41 ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [Q: $i] : % 0.10/0.41 ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [R: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( implies @ P @ Q ) @ ( implies @ ( not @ ( and @ Q @ R ) ) @ ( not @ ( and @ R @ P ) ) ) ) ) ) ) ) ) ) ) ) % 0.10/0.41 @ ( mbox @ kn3 ) ) ) ) ) ). % 0.10/0.41 % 0.10/0.41 thf(cn1_0,axiom, % 0.10/0.41 ( mlocal % 0.10/0.41 @ ( mand % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mimplies @ ( mbox @ cn1 ) % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [P: $i] : % 0.10/0.41 ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [Q: $i] : % 0.10/0.41 ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [R: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( implies @ P @ Q ) @ ( implies @ ( implies @ Q @ R ) @ ( implies @ P @ R ) ) ) ) ) ) ) ) ) ) ) ) ) % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mimplies % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [P: $i] : % 0.10/0.41 ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [Q: $i] : % 0.10/0.41 ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [R: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( implies @ P @ Q ) @ ( implies @ ( implies @ Q @ R ) @ ( implies @ P @ R ) ) ) ) ) ) ) ) ) ) ) % 0.10/0.41 @ ( mbox @ cn1 ) ) ) ) ) ). % 0.10/0.41 % 0.10/0.41 thf(cn2_0,axiom, % 0.10/0.41 ( mlocal % 0.10/0.41 @ ( mand % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mimplies @ ( mbox @ cn2 ) % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [P: $i] : % 0.10/0.41 ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [Q: $i] : ( mbox @ ( is_a_theorem @ ( implies @ P @ ( implies @ ( not @ P ) @ Q ) ) ) ) ) ) ) ) ) ) % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mimplies % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [P: $i] : % 0.10/0.41 ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [Q: $i] : ( mbox @ ( is_a_theorem @ ( implies @ P @ ( implies @ ( not @ P ) @ Q ) ) ) ) ) ) ) ) % 0.10/0.41 @ ( mbox @ cn2 ) ) ) ) ) ). % 0.10/0.41 % 0.10/0.41 thf(cn3_0,axiom, % 0.10/0.41 ( mlocal % 0.10/0.41 @ ( mand % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mimplies @ ( mbox @ cn3 ) % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [P: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( implies @ ( not @ P ) @ P ) @ P ) ) ) ) ) ) ) % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mimplies % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [P: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( implies @ ( not @ P ) @ P ) @ P ) ) ) ) ) % 0.10/0.41 @ ( mbox @ cn3 ) ) ) ) ) ). % 0.10/0.41 % 0.10/0.41 thf(r1_0,axiom, % 0.10/0.41 ( mlocal % 0.10/0.41 @ ( mand % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mimplies @ ( mbox @ r1 ) % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [P: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( or @ P @ P ) @ P ) ) ) ) ) ) ) % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mimplies % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [P: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( or @ P @ P ) @ P ) ) ) ) ) % 0.10/0.41 @ ( mbox @ r1 ) ) ) ) ) ). % 0.10/0.41 % 0.10/0.41 thf(r2_0,axiom, % 0.10/0.41 ( mlocal % 0.10/0.41 @ ( mand % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mimplies @ ( mbox @ r2 ) % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [P: $i] : % 0.10/0.41 ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [Q: $i] : ( mbox @ ( is_a_theorem @ ( implies @ Q @ ( or @ P @ Q ) ) ) ) ) ) ) ) ) ) % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mimplies % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [P: $i] : % 0.10/0.41 ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [Q: $i] : ( mbox @ ( is_a_theorem @ ( implies @ Q @ ( or @ P @ Q ) ) ) ) ) ) ) ) % 0.10/0.41 @ ( mbox @ r2 ) ) ) ) ) ). % 0.10/0.41 % 0.10/0.41 thf(r3_0,axiom, % 0.10/0.41 ( mlocal % 0.10/0.41 @ ( mand % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mimplies @ ( mbox @ r3 ) % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [P: $i] : % 0.10/0.41 ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [Q: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( or @ P @ Q ) @ ( or @ Q @ P ) ) ) ) ) ) ) ) ) ) % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mimplies % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [P: $i] : % 0.10/0.41 ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [Q: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( or @ P @ Q ) @ ( or @ Q @ P ) ) ) ) ) ) ) ) % 0.10/0.41 @ ( mbox @ r3 ) ) ) ) ) ). % 0.10/0.41 % 0.10/0.41 thf(r4_0,axiom, % 0.10/0.41 ( mlocal % 0.10/0.41 @ ( mand % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mimplies @ ( mbox @ r4 ) % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [P: $i] : % 0.10/0.41 ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [Q: $i] : % 0.10/0.41 ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [R: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( or @ P @ ( or @ Q @ R ) ) @ ( or @ Q @ ( or @ P @ R ) ) ) ) ) ) ) ) ) ) ) ) ) % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mimplies % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [P: $i] : % 0.10/0.41 ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [Q: $i] : % 0.10/0.41 ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [R: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( or @ P @ ( or @ Q @ R ) ) @ ( or @ Q @ ( or @ P @ R ) ) ) ) ) ) ) ) ) ) ) % 0.10/0.41 @ ( mbox @ r4 ) ) ) ) ) ). % 0.10/0.41 % 0.10/0.41 thf(r5_0,axiom, % 0.10/0.41 ( mlocal % 0.10/0.41 @ ( mand % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mimplies @ ( mbox @ r5 ) % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [P: $i] : % 0.10/0.41 ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [Q: $i] : % 0.10/0.41 ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [R: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( implies @ Q @ R ) @ ( implies @ ( or @ P @ Q ) @ ( or @ P @ R ) ) ) ) ) ) ) ) ) ) ) ) ) % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mimplies % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [P: $i] : % 0.10/0.41 ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [Q: $i] : % 0.10/0.41 ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [R: $i] : ( mbox @ ( is_a_theorem @ ( implies @ ( implies @ Q @ R ) @ ( implies @ ( or @ P @ Q ) @ ( or @ P @ R ) ) ) ) ) ) ) ) ) ) ) % 0.10/0.41 @ ( mbox @ r5 ) ) ) ) ) ). % 0.10/0.41 % 0.10/0.41 thf(op_or_0,axiom, % 0.10/0.41 ( mlocal % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mimplies @ ( mbox @ op_or ) % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [X: $i] : % 0.10/0.41 ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [Y: $i] : ( mbox @ ( qmltpeq @ ( or @ X @ Y ) @ ( not @ ( and @ ( not @ X ) @ ( not @ Y ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.10/0.41 % 0.10/0.41 thf(op_and_0,axiom, % 0.10/0.41 ( mlocal % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mimplies @ ( mbox @ op_and ) % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [X: $i] : % 0.10/0.41 ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [Y: $i] : ( mbox @ ( qmltpeq @ ( and @ X @ Y ) @ ( not @ ( or @ ( not @ X ) @ ( not @ Y ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.10/0.41 % 0.10/0.41 thf(op_implies_and_0,axiom, % 0.10/0.41 ( mlocal % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mimplies @ ( mbox @ op_implies_and ) % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [X: $i] : % 0.10/0.41 ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [Y: $i] : ( mbox @ ( qmltpeq @ ( implies @ X @ Y ) @ ( not @ ( and @ X @ ( not @ Y ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.10/0.41 % 0.10/0.41 thf(op_implies_or_0,axiom, % 0.10/0.41 ( mlocal % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mimplies @ ( mbox @ op_implies_or ) % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [X: $i] : % 0.10/0.41 ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [Y: $i] : ( mbox @ ( qmltpeq @ ( implies @ X @ Y ) @ ( or @ ( not @ X ) @ Y ) ) ) ) ) ) ) ) ) ) ). % 0.10/0.41 % 0.10/0.41 thf(op_equiv_0,axiom, % 0.10/0.41 ( mlocal % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mimplies @ ( mbox @ op_equiv ) % 0.10/0.41 @ ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [X: $i] : % 0.10/0.41 ( mbox % 0.10/0.41 @ ( mforall_di % 0.10/0.41 @ ^ [Y: $i] : ( mbox @ ( qmltpeq @ ( equiv @ X @ Y ) @ ( and @ ( implies @ X @ Y ) @ ( implies @ Y @ X ) ) ) ) ) ) ) ) ) ) ) ). % 0.10/0.41 % 0.10/0.41 thf(hilbert_op_or,axiom, % 0.10/0.41 mlocal @ ( mbox @ op_or ) ). % 0.10/0.41 % 0.10/0.41 thf(hilbert_op_implies_and,axiom, % 0.10/0.41 mlocal @ ( mbox @ op_implies_and ) ). % 0.10/0.41 % 0.10/0.41 thf(hilbert_op_equiv,axiom, % 0.10/0.41 mlocal @ ( mbox @ op_equiv ) ). % 0.10/0.41 % 0.10/0.41 thf(hilbert_modus_ponens,axiom, % 0.10/0.41 mlocal @ ( mbox @ modus_ponens ) ). % 0.10/0.41 % 0.10/0.41 thf(hilbert_modus_tollens,axiom, % 0.10/0.41 mlocal @ ( mbox @ modus_tollens ) ). % 0.10/0.41 % 0.10/0.41 thf(hilbert_implies_1,axiom, % 0.10/0.41 mlocal @ ( mbox @ implies_1 ) ). % 0.10/0.41 % 0.10/0.41 thf(hilbert_implies_2,axiom, % 0.10/0.41 mlocal @ ( mbox @ implies_2 ) ). % 0.10/0.41 % 0.10/0.41 thf(hilbert_implies_3,axiom, % 0.10/0.41 mlocal @ ( mbox @ implies_3 ) ). % 0.10/0.41 % 0.10/0.41 thf(hilbert_and_1,axiom, % 0.10/0.41 mlocal @ ( mbox @ and_1 ) ). % 0.10/0.41 % 0.10/0.41 thf(hilbert_and_2,axiom, % 0.10/0.41 mlocal @ ( mbox @ and_2 ) ). % 0.10/0.41 % 0.10/0.41 thf(hilbert_and_3,axiom, % 0.10/0.41 mlocal @ ( mbox @ and_3 ) ). % 0.10/0.41 % 0.10/0.41 thf(hilbert_or_1,axiom, % 0.10/0.41 mlocal @ ( mbox @ or_1 ) ). % 0.10/0.41 % 0.10/0.41 thf(hilbert_or_2,axiom, % 0.10/0.41 mlocal @ ( mbox @ or_2 ) ). % 0.10/0.41 % 0.10/0.41 thf(hilbert_or_3,axiom, % 0.10/0.41 mlocal @ ( mbox @ or_3 ) ). % 0.10/0.41 % 0.10/0.41 thf(hilbert_equivalence_1,axiom, % 0.10/0.41 mlocal @ ( mbox @ equivalence_1 ) ). % 0.10/0.41 % 0.10/0.41 thf(hilbert_equivalence_2,axiom, % 0.10/0.41 mlocal @ ( mbox @ equivalence_2 ) ). % 0.10/0.41 % 0.10/0.41 thf(hilbert_equivalence_3,axiom, % 0.10/0.41 mlocal @ ( mbox @ equivalence_3 ) ). % 0.10/0.41 % 0.10/0.41 thf(substitution_of_equivalents_1,axiom, % 0.10/0.41 mlocal @ ( mbox @ substitution_of_equivalents ) ). % 0.10/0.41 % 0.10/0.41 thf(luka_op_or,axiom, % 0.10/0.41 mlocal @ ( mbox @ op_or ) ). % 0.10/0.41 % 0.10/0.41 thf(luka_op_implies,axiom, % 0.10/0.41 mlocal @ ( mbox @ op_implies ) ). % 0.10/0.41 % 0.10/0.41 thf(luka_op_equiv,axiom, % 0.10/0.41 mlocal @ ( mbox @ op_equiv ) ). % 0.10/0.41 % 0.10/0.41 thf(luka_cn1,conjecture, % 0.10/0.41 mlocal @ ( mbox @ cn1 ) ). % 0.10/0.41 % 0.10/0.41 %------------------------------------------------------------------------------ % 0.10/0.41 ------------------------ % 0.10/0.41 /starexec/sw/sutcliffe/jdk-11.0.2/bin/java: Command not found. % 0.10/0.41 ---- Embedded in THF --- % 0.10/0.41 ------------------------ % 0.10/0.43 ---- Cleaned THF --- % 0.10/0.43 ------------------------ % 0.10/0.46 % (2641403)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_2641384 for (2999ds/2Mi) % 0.10/0.46 % (2641403)First to succeed. % 0.10/0.46 % SZS status Satisfiable for DTF2THF_2641384 % 0.10/0.46 % (2641403)# SZS output start Saturation. % 0.10/0.46 % (2641403)# SZS output end Saturation. % 0.10/0.46 % (2641403)------------------------------ % 0.10/0.46 % (2641403)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) % 0.10/0.46 % (2641403)Termination reason: Satisfiable % 0.10/0.46 % 0.10/0.46 % (2641403)Memory used [KB]: 5373 % 0.10/0.46 % (2641403)Time elapsed: 0.002 s % 0.10/0.46 % (2641403)Instructions burned: 1 (million) % 0.10/0.46 % (2641403)------------------------------ % 0.10/0.46 % (2641403)------------------------------ % 0.19/0.46 % (2641399)Success in time 0.012 s %------------------------------------------------------------------------------