%------------------------------------------------------------------------------ % File : DT2H2X---1.9.5 % Problem : LCL942^2 : 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 : n026.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 0.18s 0.46s % Output : Saturation 0.18s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL942^2 : 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 % 0.12/0.37 % Computer : n026.cluster.edu % 0.12/0.37 % Model : x86_64 x86_64 % 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.37 % Memory : 8046.5625MB % 0.12/0.37 % OS : Linux 6.8.0-71-generic % 0.12/0.37 % CPULimit : 300 % 0.12/0.37 % WCLimit : 300 % 0.12/0.37 % DateTime : Fri Sep 4 16:02:25 UTC 2026 % 0.12/0.38 % CPUTime : % 0.12/0.38 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300 % 0.12/0.40 ---- Original DTF file --- % 0.12/0.40 thf(spec,logic,$$dhol). % 0.12/0.40 %------------------------------------------------------------------------------ % 0.12/0.40 % File : LCL942^2 : TPTP v9.3.1. Released v8.1.0. % 0.12/0.40 % Domain : Logic Calculi % 0.12/0.40 % Problem : Goedel translation of ALG017+1 (from TPTP-v5.0.0) % 0.12/0.40 % Version : [BP13] axioms. % 0.12/0.40 % English : % 0.12/0.40 % 0.12/0.40 % Refs : [RO12] Raths & Otten (2012), The QMLTP Problem Library for Fi % 0.12/0.40 % : [BP13] Benzmueller & Paulson (2013), Quantified Multimodal Lo % 0.12/0.40 % : [Ste22] Steen (2022), An Extensible Logic Embedding Tool for L % 0.12/0.40 % Source : [TPTP] % 0.12/0.40 % Names : GAL017+1 [QMLTP] % 0.12/0.40 % 0.12/0.40 % Status : Theorem % 0.12/0.40 % Rating : 0.50 v9.3.0, 0.33 v9.1.0, 0.38 v9.0.0, 0.60 v8.2.0, 0.62 v8.1.0 % 0.12/0.40 % Syntax : Number of formulae : 50 ( 11 unt; 21 typ; 10 def) % 0.12/0.40 % Number of atoms : 1117 ( 10 equ; 0 cnn) % 0.12/0.40 % Maximal formula atoms : 240 ( 38 avg) % 0.12/0.40 % Number of connectives : 2738 ( 1 ~; 1 |; 2 &;2731 @) % 0.12/0.40 % ( 1 <=>; 2 =>; 0 <=; 0 <~>) % 0.12/0.40 % Maximal formula depth : 73 ( 14 avg) % 0.12/0.40 % Number of types : 3 ( 1 usr) % 0.12/0.40 % Number of type conns : 63 ( 63 >; 0 *; 0 +; 0 <<) % 0.12/0.40 % Number of symbols : 21 ( 20 usr; 6 con; 0-3 aty) % 0.12/0.40 % Number of variables : 42 ( 37 ^; 3 !; 2 ?; 42 :) % 0.12/0.40 % SPC : TH0_THM_EQU_NAR_NDT % 0.12/0.40 % 0.12/0.40 % Comments : This output was generated by embedproblem, version 1.7.1 (library % 0.12/0.40 % version 1.3). Generated on Thu Apr 28 13:18:18 EDT 2022 using % 0.12/0.40 % 'modal' embedding, version 1.5.2. Logic specification used: % 0.12/0.40 % $modal == [$constants == $rigid,$quantification == $constant, % 0.12/0.40 % $modalities == $modal_system_T]. % 0.12/0.40 %------------------------------------------------------------------------------ % 0.12/0.40 thf(mworld,type, % 0.12/0.40 mworld: $tType ). % 0.12/0.40 % 0.12/0.40 thf(mrel_type,type, % 0.12/0.40 mrel: mworld > mworld > $o ). % 0.12/0.40 % 0.12/0.40 thf(mactual_type,type, % 0.12/0.40 mactual: mworld ). % 0.12/0.40 % 0.12/0.40 thf(mlocal_type,type, % 0.12/0.40 mlocal: ( mworld > $o ) > $o ). % 0.12/0.40 % 0.12/0.40 thf(mlocal_def,definition, % 0.12/0.40 ( mlocal % 0.12/0.40 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ). % 0.12/0.40 % 0.12/0.40 thf(mnot_type,type, % 0.12/0.40 mnot: ( mworld > $o ) > mworld > $o ). % 0.12/0.40 % 0.12/0.40 thf(mand_type,type, % 0.12/0.40 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ). % 0.12/0.40 % 0.12/0.40 thf(mor_type,type, % 0.12/0.40 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ). % 0.12/0.40 % 0.12/0.40 thf(mimplies_type,type, % 0.12/0.40 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ). % 0.12/0.40 % 0.12/0.40 thf(mequiv_type,type, % 0.12/0.40 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ). % 0.12/0.40 % 0.12/0.40 thf(mnot_def,definition, % 0.12/0.40 ( mnot % 0.12/0.40 = ( ^ [A: mworld > $o,W: mworld] : % 0.12/0.40 ~ ( A @ W ) ) ) ). % 0.12/0.40 % 0.12/0.40 thf(mand_def,definition, % 0.12/0.40 ( mand % 0.12/0.40 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] : % 0.12/0.40 ( ( A @ W ) % 0.12/0.40 & ( B @ W ) ) ) ) ). % 0.12/0.40 % 0.12/0.40 thf(mor_def,definition, % 0.12/0.40 ( mor % 0.12/0.40 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] : % 0.12/0.40 ( ( A @ W ) % 0.12/0.40 | ( B @ W ) ) ) ) ). % 0.12/0.40 % 0.12/0.40 thf(mimplies_def,definition, % 0.12/0.40 ( mimplies % 0.12/0.40 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] : % 0.12/0.40 ( ( A @ W ) % 0.12/0.40 => ( B @ W ) ) ) ) ). % 0.12/0.40 % 0.12/0.40 thf(mequiv_def,definition, % 0.12/0.40 ( mequiv % 0.12/0.40 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] : % 0.12/0.40 ( ( A @ W ) % 0.12/0.40 <=> ( B @ W ) ) ) ) ). % 0.12/0.40 % 0.12/0.40 thf(mbox_type,type, % 0.12/0.40 mbox: ( mworld > $o ) > mworld > $o ). % 0.12/0.40 % 0.12/0.40 thf(mbox_def,definition, % 0.12/0.40 ( mbox % 0.12/0.40 = ( ^ [Phi: mworld > $o,W: mworld] : % 0.12/0.40 ! [V: mworld] : % 0.12/0.40 ( ( mrel @ W @ V ) % 0.12/0.40 => ( Phi @ V ) ) ) ) ). % 0.12/0.40 % 0.12/0.40 thf(mdia_type,type, % 0.12/0.40 mdia: ( mworld > $o ) > mworld > $o ). % 0.12/0.40 % 0.12/0.40 thf(mdia_def,definition, % 0.12/0.40 ( mdia % 0.12/0.40 = ( ^ [Phi: mworld > $o,W: mworld] : % 0.12/0.40 ? [V: mworld] : % 0.12/0.40 ( ( mrel @ W @ V ) % 0.12/0.40 & ( Phi @ V ) ) ) ) ). % 0.12/0.40 % 0.12/0.40 thf(mrel_reflexive,axiom, % 0.12/0.40 ! [W: mworld] : ( mrel @ W @ W ) ). % 0.12/0.40 % 0.12/0.40 thf(mforall_di_type,type, % 0.12/0.40 mforall_di: ( $i > mworld > $o ) > mworld > $o ). % 0.12/0.40 % 0.12/0.40 thf(mforall_di_def,definition, % 0.12/0.40 ( mforall_di % 0.12/0.40 = ( ^ [A: $i > mworld > $o,W: mworld] : % 0.12/0.40 ! [X: $i] : ( A @ X @ W ) ) ) ). % 0.12/0.40 % 0.12/0.40 thf(mexists_di_type,type, % 0.12/0.40 mexists_di: ( $i > mworld > $o ) > mworld > $o ). % 0.12/0.40 % 0.12/0.40 thf(mexists_di_def,definition, % 0.12/0.40 ( mexists_di % 0.12/0.40 = ( ^ [A: $i > mworld > $o,W: mworld] : % 0.12/0.40 ? [X: $i] : ( A @ X @ W ) ) ) ). % 0.12/0.40 % 0.12/0.40 thf(unit_decl,type, % 0.12/0.40 unit: $i ). % 0.12/0.40 % 0.12/0.40 thf(e0_decl,type, % 0.12/0.40 e0: $i ). % 0.12/0.40 % 0.12/0.40 thf(e1_decl,type, % 0.12/0.40 e1: $i ). % 0.12/0.40 % 0.12/0.40 thf(e2_decl,type, % 0.12/0.40 e2: $i ). % 0.12/0.40 % 0.12/0.40 thf(e3_decl,type, % 0.12/0.40 e3: $i ). % 0.12/0.40 % 0.12/0.40 thf(qmltpeq_decl,type, % 0.12/0.40 qmltpeq: $i > $i > mworld > $o ). % 0.12/0.40 % 0.12/0.40 thf(inv_decl,type, % 0.12/0.40 inv: $i > $i ). % 0.12/0.40 % 0.12/0.40 thf(op_decl,type, % 0.12/0.40 op: $i > $i > $i ). % 0.12/0.40 % 0.12/0.40 thf(reflexivity,axiom, % 0.12/0.40 ( mlocal % 0.12/0.40 @ ( mbox % 0.12/0.40 @ ( mforall_di % 0.12/0.40 @ ^ [X: $i] : ( mbox @ ( qmltpeq @ X @ X ) ) ) ) ) ). % 0.12/0.40 % 0.12/0.40 thf(symmetry,axiom, % 0.12/0.40 ( mlocal % 0.12/0.40 @ ( mbox % 0.12/0.40 @ ( mforall_di % 0.12/0.40 @ ^ [X: $i] : % 0.12/0.40 ( mbox % 0.12/0.40 @ ( mforall_di % 0.12/0.40 @ ^ [Y: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ X @ Y ) ) @ ( mbox @ ( qmltpeq @ Y @ X ) ) ) ) ) ) ) ) ) ). % 0.12/0.40 % 0.12/0.40 thf(transitivity,axiom, % 0.12/0.40 ( mlocal % 0.12/0.40 @ ( mbox % 0.12/0.40 @ ( mforall_di % 0.12/0.40 @ ^ [X: $i] : % 0.12/0.40 ( mbox % 0.12/0.40 @ ( mforall_di % 0.12/0.40 @ ^ [Y: $i] : % 0.12/0.40 ( mbox % 0.12/0.40 @ ( mforall_di % 0.12/0.40 @ ^ [Z: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( qmltpeq @ X @ Y ) ) @ ( mbox @ ( qmltpeq @ Y @ Z ) ) ) @ ( mbox @ ( qmltpeq @ X @ Z ) ) ) ) ) ) ) ) ) ) ) ). % 0.12/0.40 % 0.12/0.40 thf(inv_substitution_1,axiom, % 0.12/0.40 ( mlocal % 0.12/0.40 @ ( mbox % 0.12/0.40 @ ( mforall_di % 0.12/0.40 @ ^ [A: $i] : % 0.12/0.40 ( mbox % 0.12/0.40 @ ( mforall_di % 0.12/0.40 @ ^ [B: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( inv @ A ) @ ( inv @ B ) ) ) ) ) ) ) ) ) ) ). % 0.12/0.40 % 0.12/0.40 thf(op_substitution_1,axiom, % 0.12/0.40 ( mlocal % 0.12/0.40 @ ( mbox % 0.12/0.40 @ ( mforall_di % 0.12/0.40 @ ^ [A: $i] : % 0.12/0.40 ( mbox % 0.12/0.40 @ ( mforall_di % 0.12/0.40 @ ^ [B: $i] : % 0.12/0.40 ( mbox % 0.12/0.40 @ ( mforall_di % 0.12/0.40 @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( op @ A @ C ) @ ( op @ B @ C ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.12/0.40 % 0.12/0.40 thf(op_substitution_2,axiom, % 0.12/0.40 ( mlocal % 0.12/0.40 @ ( mbox % 0.12/0.40 @ ( mforall_di % 0.12/0.40 @ ^ [A: $i] : % 0.12/0.40 ( mbox % 0.12/0.40 @ ( mforall_di % 0.12/0.40 @ ^ [B: $i] : % 0.12/0.40 ( mbox % 0.12/0.40 @ ( mforall_di % 0.12/0.40 @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( op @ C @ A ) @ ( op @ C @ B ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.12/0.40 % 0.12/0.40 thf(ax1,axiom, % 0.12/0.40 mlocal @ ( mand @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 ) ) ) ) ) @ ( mand @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e1 ) @ e0 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e1 ) @ e1 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e1 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e1 ) @ e3 ) ) ) ) ) @ ( mand @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e2 ) @ e0 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e2 ) @ e1 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e2 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e2 ) @ e3 ) ) ) ) ) @ ( mand @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e3 ) @ e0 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e3 ) @ e1 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e3 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e3 ) @ e3 ) ) ) ) ) @ ( mand @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e0 ) @ e0 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e0 ) @ e1 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e0 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e0 ) @ e3 ) ) ) ) ) @ ( mand @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 ) ) ) ) ) @ ( mand @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e2 ) @ e0 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e2 ) @ e1 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e2 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e2 ) @ e3 ) ) ) ) ) @ ( mand @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e3 ) @ e0 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e3 ) @ e1 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e3 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e3 ) @ e3 ) ) ) ) ) @ ( mand @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e0 ) @ e0 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e0 ) @ e1 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e0 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e0 ) @ e3 ) ) ) ) ) @ ( mand @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e1 ) @ e0 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e1 ) @ e1 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e1 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e1 ) @ e3 ) ) ) ) ) @ ( mand @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 ) ) ) ) ) @ ( mand @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e3 ) @ e0 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e3 ) @ e1 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e3 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e3 ) @ e3 ) ) ) ) ) @ ( mand @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e0 ) @ e0 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e0 ) @ e1 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e0 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e0 ) @ e3 ) ) ) ) ) @ ( mand @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e1 ) @ e0 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e1 ) @ e1 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e1 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e1 ) @ e3 ) ) ) ) ) @ ( mand @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e2 ) @ e0 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e2 ) @ e1 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e2 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e2 ) @ e3 ) ) ) ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.12/0.40 % 0.12/0.40 thf(ax2,axiom, % 0.12/0.40 mlocal @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e0 @ e0 ) @ e0 ) @ ( op @ e0 @ ( op @ e0 @ e0 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e0 @ e0 ) @ e1 ) @ ( op @ e0 @ ( op @ e0 @ e1 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e0 @ e0 ) @ e2 ) @ ( op @ e0 @ ( op @ e0 @ e2 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e0 @ e0 ) @ e3 ) @ ( op @ e0 @ ( op @ e0 @ e3 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e0 @ e1 ) @ e0 ) @ ( op @ e0 @ ( op @ e1 @ e0 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e0 @ e1 ) @ e1 ) @ ( op @ e0 @ ( op @ e1 @ e1 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e0 @ e1 ) @ e2 ) @ ( op @ e0 @ ( op @ e1 @ e2 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e0 @ e1 ) @ e3 ) @ ( op @ e0 @ ( op @ e1 @ e3 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e0 @ e2 ) @ e0 ) @ ( op @ e0 @ ( op @ e2 @ e0 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e0 @ e2 ) @ e1 ) @ ( op @ e0 @ ( op @ e2 @ e1 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e0 @ e2 ) @ e2 ) @ ( op @ e0 @ ( op @ e2 @ e2 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e0 @ e2 ) @ e3 ) @ ( op @ e0 @ ( op @ e2 @ e3 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e0 @ e3 ) @ e0 ) @ ( op @ e0 @ ( op @ e3 @ e0 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e0 @ e3 ) @ e1 ) @ ( op @ e0 @ ( op @ e3 @ e1 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e0 @ e3 ) @ e2 ) @ ( op @ e0 @ ( op @ e3 @ e2 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e0 @ e3 ) @ e3 ) @ ( op @ e0 @ ( op @ e3 @ e3 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e1 @ e0 ) @ e0 ) @ ( op @ e1 @ ( op @ e0 @ e0 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e1 @ e0 ) @ e1 ) @ ( op @ e1 @ ( op @ e0 @ e1 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e1 @ e0 ) @ e2 ) @ ( op @ e1 @ ( op @ e0 @ e2 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e1 @ e0 ) @ e3 ) @ ( op @ e1 @ ( op @ e0 @ e3 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e1 @ e1 ) @ e0 ) @ ( op @ e1 @ ( op @ e1 @ e0 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e1 @ e1 ) @ e1 ) @ ( op @ e1 @ ( op @ e1 @ e1 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e1 @ e1 ) @ e2 ) @ ( op @ e1 @ ( op @ e1 @ e2 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e1 @ e1 ) @ e3 ) @ ( op @ e1 @ ( op @ e1 @ e3 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e1 @ e2 ) @ e0 ) @ ( op @ e1 @ ( op @ e2 @ e0 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e1 @ e2 ) @ e1 ) @ ( op @ e1 @ ( op @ e2 @ e1 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e1 @ e2 ) @ e2 ) @ ( op @ e1 @ ( op @ e2 @ e2 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e1 @ e2 ) @ e3 ) @ ( op @ e1 @ ( op @ e2 @ e3 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e1 @ e3 ) @ e0 ) @ ( op @ e1 @ ( op @ e3 @ e0 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e1 @ e3 ) @ e1 ) @ ( op @ e1 @ ( op @ e3 @ e1 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e1 @ e3 ) @ e2 ) @ ( op @ e1 @ ( op @ e3 @ e2 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e1 @ e3 ) @ e3 ) @ ( op @ e1 @ ( op @ e3 @ e3 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e2 @ e0 ) @ e0 ) @ ( op @ e2 @ ( op @ e0 @ e0 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e2 @ e0 ) @ e1 ) @ ( op @ e2 @ ( op @ e0 @ e1 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e2 @ e0 ) @ e2 ) @ ( op @ e2 @ ( op @ e0 @ e2 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e2 @ e0 ) @ e3 ) @ ( op @ e2 @ ( op @ e0 @ e3 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e2 @ e1 ) @ e0 ) @ ( op @ e2 @ ( op @ e1 @ e0 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e2 @ e1 ) @ e1 ) @ ( op @ e2 @ ( op @ e1 @ e1 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e2 @ e1 ) @ e2 ) @ ( op @ e2 @ ( op @ e1 @ e2 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e2 @ e1 ) @ e3 ) @ ( op @ e2 @ ( op @ e1 @ e3 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e2 @ e2 ) @ e0 ) @ ( op @ e2 @ ( op @ e2 @ e0 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e2 @ e2 ) @ e1 ) @ ( op @ e2 @ ( op @ e2 @ e1 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e2 @ e2 ) @ e2 ) @ ( op @ e2 @ ( op @ e2 @ e2 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e2 @ e2 ) @ e3 ) @ ( op @ e2 @ ( op @ e2 @ e3 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e2 @ e3 ) @ e0 ) @ ( op @ e2 @ ( op @ e3 @ e0 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e2 @ e3 ) @ e1 ) @ ( op @ e2 @ ( op @ e3 @ e1 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e2 @ e3 ) @ e2 ) @ ( op @ e2 @ ( op @ e3 @ e2 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e2 @ e3 ) @ e3 ) @ ( op @ e2 @ ( op @ e3 @ e3 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e3 @ e0 ) @ e0 ) @ ( op @ e3 @ ( op @ e0 @ e0 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e3 @ e0 ) @ e1 ) @ ( op @ e3 @ ( op @ e0 @ e1 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e3 @ e0 ) @ e2 ) @ ( op @ e3 @ ( op @ e0 @ e2 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e3 @ e0 ) @ e3 ) @ ( op @ e3 @ ( op @ e0 @ e3 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e3 @ e1 ) @ e0 ) @ ( op @ e3 @ ( op @ e1 @ e0 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e3 @ e1 ) @ e1 ) @ ( op @ e3 @ ( op @ e1 @ e1 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e3 @ e1 ) @ e2 ) @ ( op @ e3 @ ( op @ e1 @ e2 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e3 @ e1 ) @ e3 ) @ ( op @ e3 @ ( op @ e1 @ e3 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e3 @ e2 ) @ e0 ) @ ( op @ e3 @ ( op @ e2 @ e0 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e3 @ e2 ) @ e1 ) @ ( op @ e3 @ ( op @ e2 @ e1 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e3 @ e2 ) @ e2 ) @ ( op @ e3 @ ( op @ e2 @ e2 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e3 @ e2 ) @ e3 ) @ ( op @ e3 @ ( op @ e2 @ e3 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e3 @ e3 ) @ e0 ) @ ( op @ e3 @ ( op @ e3 @ e0 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e3 @ e3 ) @ e1 ) @ ( op @ e3 @ ( op @ e3 @ e1 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e3 @ e3 ) @ e2 ) @ ( op @ e3 @ ( op @ e3 @ e2 ) ) ) ) @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e3 @ e3 ) @ e3 ) @ ( op @ e3 @ ( op @ e3 @ e3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.12/0.40 % 0.12/0.40 thf(ax3,axiom, % 0.12/0.40 mlocal @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ unit @ e0 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ unit ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ unit @ e1 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ unit ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ unit @ e2 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ unit ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ unit @ e3 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e3 @ unit ) @ e3 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ unit @ e0 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ unit @ e1 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ unit @ e2 ) ) @ ( mbox @ ( qmltpeq @ unit @ e3 ) ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.12/0.40 % 0.12/0.40 thf(ax4,axiom, % 0.12/0.40 mlocal @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ ( inv @ e0 ) ) @ unit ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( inv @ e0 ) @ e0 ) @ unit ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ ( inv @ e1 ) ) @ unit ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( inv @ e1 ) @ e1 ) @ unit ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ ( inv @ e2 ) ) @ unit ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( inv @ e2 ) @ e2 ) @ unit ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e3 @ ( inv @ e3 ) ) @ unit ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( inv @ e3 ) @ e3 ) @ unit ) ) @ ( mand @ ( mor @ ( mbox @ ( qmltpeq @ ( inv @ e0 ) @ e0 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( inv @ e0 ) @ e1 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( inv @ e0 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( inv @ e0 ) @ e3 ) ) ) ) ) @ ( mand @ ( mor @ ( mbox @ ( qmltpeq @ ( inv @ e1 ) @ e0 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( inv @ e1 ) @ e1 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( inv @ e1 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( inv @ e1 ) @ e3 ) ) ) ) ) @ ( mand @ ( mor @ ( mbox @ ( qmltpeq @ ( inv @ e2 ) @ e0 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( inv @ e2 ) @ e1 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( inv @ e2 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( inv @ e2 ) @ e3 ) ) ) ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( inv @ e3 ) @ e0 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( inv @ e3 ) @ e1 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( inv @ e3 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( inv @ e3 ) @ e3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.12/0.40 % 0.12/0.40 thf(ax5,axiom, % 0.12/0.40 mlocal @ ( mbox @ ( qmltpeq @ ( inv @ unit ) @ unit ) ) ). % 0.12/0.40 % 0.12/0.40 thf(ax6,axiom, % 0.12/0.40 mlocal @ ( mand @ ( mbox @ ( qmltpeq @ ( inv @ ( inv @ e0 ) ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( inv @ ( inv @ e1 ) ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( inv @ ( inv @ e2 ) ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( inv @ ( inv @ e3 ) ) @ e3 ) ) ) ) ) ). % 0.12/0.40 % 0.12/0.40 thf(ax7,axiom, % 0.12/0.40 mlocal @ ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ ( inv @ e0 ) @ e0 ) ) @ ( mbox @ ( qmltpeq @ ( inv @ e0 ) @ e0 ) ) ) ) @ ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ ( inv @ e0 ) @ e1 ) ) @ ( mbox @ ( qmltpeq @ ( inv @ e1 ) @ e0 ) ) ) ) @ ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ ( inv @ e0 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( inv @ e2 ) @ e0 ) ) ) ) @ ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ ( inv @ e0 ) @ e3 ) ) @ ( mbox @ ( qmltpeq @ ( inv @ e3 ) @ e0 ) ) ) ) @ ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ ( inv @ e1 ) @ e0 ) ) @ ( mbox @ ( qmltpeq @ ( inv @ e0 ) @ e1 ) ) ) ) @ ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ ( inv @ e1 ) @ e1 ) ) @ ( mbox @ ( qmltpeq @ ( inv @ e1 ) @ e1 ) ) ) ) @ ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ ( inv @ e1 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( inv @ e2 ) @ e1 ) ) ) ) @ ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ ( inv @ e1 ) @ e3 ) ) @ ( mbox @ ( qmltpeq @ ( inv @ e3 ) @ e1 ) ) ) ) @ ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ ( inv @ e2 ) @ e0 ) ) @ ( mbox @ ( qmltpeq @ ( inv @ e0 ) @ e2 ) ) ) ) @ ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ ( inv @ e2 ) @ e1 ) ) @ ( mbox @ ( qmltpeq @ ( inv @ e1 ) @ e2 ) ) ) ) @ ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ ( inv @ e2 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( inv @ e2 ) @ e2 ) ) ) ) @ ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ ( inv @ e2 ) @ e3 ) ) @ ( mbox @ ( qmltpeq @ ( inv @ e3 ) @ e2 ) ) ) ) @ ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ ( inv @ e3 ) @ e0 ) ) @ ( mbox @ ( qmltpeq @ ( inv @ e0 ) @ e3 ) ) ) ) @ ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ ( inv @ e3 ) @ e1 ) ) @ ( mbox @ ( qmltpeq @ ( inv @ e1 ) @ e3 ) ) ) ) @ ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ ( inv @ e3 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( inv @ e2 ) @ e3 ) ) ) ) @ ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ ( inv @ e3 ) @ e3 ) ) @ ( mbox @ ( qmltpeq @ ( inv @ e3 ) @ e3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.12/0.40 % 0.12/0.40 thf(ax8,axiom, % 0.12/0.40 mlocal @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( inv @ e0 ) @ ( inv @ e1 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( inv @ e0 ) @ ( inv @ e2 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( inv @ e0 ) @ ( inv @ e3 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( inv @ e1 ) @ ( inv @ e2 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( inv @ e1 ) @ ( inv @ e3 ) ) ) ) ) @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( inv @ e2 ) @ ( inv @ e3 ) ) ) ) ) ) ) ) ) ) ). % 0.12/0.40 % 0.12/0.40 thf(ax9,axiom, % 0.12/0.40 mlocal @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ ( op @ e1 @ e0 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ ( op @ e2 @ e0 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ ( op @ e3 @ e0 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e0 ) @ ( op @ e2 @ e0 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e0 ) @ ( op @ e3 @ e0 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e0 ) @ ( op @ e3 @ e0 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e1 ) @ ( op @ e1 @ e1 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e1 ) @ ( op @ e2 @ e1 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e1 ) @ ( op @ e3 @ e1 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ ( op @ e2 @ e1 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ ( op @ e3 @ e1 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e1 ) @ ( op @ e3 @ e1 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e2 ) @ ( op @ e1 @ e2 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e2 ) @ ( op @ e2 @ e2 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e2 ) @ ( op @ e3 @ e2 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e2 ) @ ( op @ e2 @ e2 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e2 ) @ ( op @ e3 @ e2 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ ( op @ e3 @ e2 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e3 ) @ ( op @ e1 @ e3 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e3 ) @ ( op @ e2 @ e3 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e3 ) @ ( op @ e3 @ e3 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e3 ) @ ( op @ e2 @ e3 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e3 ) @ ( op @ e3 @ e3 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e3 ) @ ( op @ e3 @ e3 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ ( op @ e0 @ e1 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ ( op @ e0 @ e2 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ ( op @ e0 @ e3 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e1 ) @ ( op @ e0 @ e2 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e1 ) @ ( op @ e0 @ e3 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e2 ) @ ( op @ e0 @ e3 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e0 ) @ ( op @ e1 @ e1 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e0 ) @ ( op @ e1 @ e2 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e0 ) @ ( op @ e1 @ e3 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ ( op @ e1 @ e2 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ ( op @ e1 @ e3 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e2 ) @ ( op @ e1 @ e3 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e0 ) @ ( op @ e2 @ e1 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e0 ) @ ( op @ e2 @ e2 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e0 ) @ ( op @ e2 @ e3 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e1 ) @ ( op @ e2 @ e2 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e1 ) @ ( op @ e2 @ e3 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ ( op @ e2 @ e3 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e0 ) @ ( op @ e3 @ e1 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e0 ) @ ( op @ e3 @ e2 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e0 ) @ ( op @ e3 @ e3 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e1 ) @ ( op @ e3 @ e2 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e1 ) @ ( op @ e3 @ e3 ) ) ) ) ) @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e2 ) @ ( op @ e3 @ e3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.12/0.40 % 0.12/0.40 thf(ax10,axiom, % 0.12/0.40 mlocal @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ e0 @ e1 ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ e0 @ e2 ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ e0 @ e3 ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ e1 @ e2 ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ e1 @ e3 ) ) ) ) @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ e2 @ e3 ) ) ) ) ) ) ) ) ) ). % 0.12/0.40 % 0.12/0.40 thf(ax11,axiom, % 0.12/0.40 mlocal @ ( mand @ ( mbox @ ( qmltpeq @ e0 @ ( op @ e3 @ e3 ) ) ) @ ( mbox @ ( qmltpeq @ e1 @ ( op @ e2 @ e3 ) ) ) ) ). % 0.12/0.40 % 0.12/0.40 thf(co1,conjecture, % 0.12/0.40 mlocal @ ( mbox @ ( mnot @ ( mand @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 ) ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 ) ) ) ) ) ) ) ) @ ( mbox @ ( mnot @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 ) ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 ) ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.12/0.40 % 0.12/0.40 %------------------------------------------------------------------------------ % 0.12/0.40 ------------------------ % 0.12/0.40 /starexec/sw/sutcliffe/jdk-11.0.2/bin/java: Command not found. % 0.12/0.40 ---- Embedded in THF --- % 0.12/0.41 ------------------------ % 0.12/0.43 ---- Cleaned THF --- % 0.12/0.43 ------------------------ % 0.12/0.45 % (781863)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_781818 for (2999ds/2Mi) % 0.12/0.45 % (781863)Refutation not found, incomplete strategy % 0.12/0.45 % (781863)------------------------------ % 0.12/0.45 % (781863)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) % 0.12/0.45 % (781863)Termination reason: Refutation not found, incomplete strategy % 0.12/0.45 % 0.12/0.45 % 0.12/0.45 % (781863)Memory used [KB]: 5373 % 0.12/0.45 % (781863)Time elapsed: 0.002 s % 0.12/0.45 % (781863)Instructions burned: 1 (million) % 0.12/0.45 % (781863)------------------------------ % 0.12/0.45 % (781863)------------------------------ % 0.12/0.46 % (781858)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_781818 for (2999ds/183Mi) % 0.12/0.46 % (781859)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_781818 for (2999ds/4Mi) % 0.12/0.46 % (781860)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_781818 for (2999ds/27Mi) % 0.12/0.46 % (781858)First to succeed. % 0.12/0.46 % (781862)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_781818 for (2999ds/2Mi) % 0.12/0.46 % (781860)Refutation not found, incomplete strategy % 0.12/0.46 % (781860)------------------------------ % 0.12/0.46 % (781860)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) % 0.12/0.46 % (781860)Termination reason: Refutation not found, incomplete strategy % 0.12/0.46 % 0.12/0.46 % 0.12/0.46 % (781860)Memory used [KB]: 5373 % 0.12/0.46 % (781860)Time elapsed: 0.003 s % 0.12/0.46 % (781860)------------------------------ % 0.12/0.46 % (781860)------------------------------ % 0.12/0.46 % (781864)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_781818 for (2999ds/275Mi) % 0.18/0.46 % (781859)Also succeeded, but the first one will report. % 0.18/0.46 % (781864)Refutation not found, incomplete strategy % 0.18/0.46 % (781864)------------------------------ % 0.18/0.46 % (781864)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) % 0.18/0.46 % (781864)Termination reason: Refutation not found, incomplete strategy % 0.18/0.46 % 0.18/0.46 % 0.18/0.46 % (781864)Memory used [KB]: 5373 % 0.18/0.46 % (781864)Time elapsed: 0.002 s % 0.18/0.46 % (781864)------------------------------ % 0.18/0.46 % (781864)------------------------------ % 0.18/0.46 % SZS status Satisfiable for DTF2THF_781818 % 0.18/0.46 % (781858)# SZS output start Saturation. % 0.18/0.46 % (781858)# SZS output end Saturation. % 0.18/0.46 % (781858)------------------------------ % 0.18/0.46 % (781858)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) % 0.18/0.46 % (781858)Termination reason: Satisfiable % 0.18/0.46 % 0.18/0.46 % (781858)Memory used [KB]: 5373 % 0.18/0.46 % (781858)Time elapsed: 0.002 s % 0.18/0.46 % (781858)Instructions burned: 1 (million) % 0.18/0.46 % (781858)------------------------------ % 0.18/0.46 % (781858)------------------------------ % 0.18/0.46 % (781857)Success in time 0.017 s %------------------------------------------------------------------------------