%------------------------------------------------------------------------------ % File : DT2H2X---1.9.5 % Problem : LCL948^10 : 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 : n011.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8046.5625MB % OS : Linux 6.8.0-71-generic % CPULimit : 300s % WCLimit : 300s % DateTime : Mon Sep 7 11:35:14 AM UTC 2026 % Result : CounterSatisfiable 0.09s 0.45s % Output : Saturation 0.09s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : LCL948^10 : TPTP v9.3.1. Released v8.1.0. % 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300 % 0.09/0.36 % Computer : n011.cluster.edu % 0.09/0.36 % Model : x86_64 x86_64 % 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.36 % Memory : 8046.5625MB % 0.09/0.36 % OS : Linux 6.8.0-71-generic % 0.09/0.36 % CPULimit : 300 % 0.09/0.36 % WCLimit : 300 % 0.09/0.36 % DateTime : Sat Sep 5 21:05:59 UTC 2026 % 0.09/0.36 % CPUTime : % 0.09/0.36 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300 % 0.09/0.39 ---- Original DTF file --- % 0.09/0.40 thf(spec,logic,$$dhol). % 0.09/0.40 %------------------------------------------------------------------------------ % 0.09/0.40 % File : LCL948^10 : TPTP v9.3.1. Released v8.1.0. % 0.09/0.40 % Domain : Logic Calculi % 0.09/0.40 % Problem : Goedel translation of SET002+4 (from TPTP-v5.0.0) % 0.09/0.40 % Version : [BP13] axioms. % 0.09/0.40 % English : % 0.09/0.40 % 0.09/0.40 % Refs : [RO12] Raths & Otten (2012), The QMLTP Problem Library for Fi % 0.09/0.40 % : [BP13] Benzmueller & Paulson (2013), Quantified Multimodal Lo % 0.09/0.40 % : [Ste22] Steen (2022), An Extensible Logic Embedding Tool for L % 0.09/0.40 % Source : [TPTP] % 0.09/0.40 % Names : GSE002+4 [QMLTP] % 0.09/0.40 % 0.09/0.40 % Status : CounterSatisfiable % 0.09/0.40 % Rating : 1.00 v9.0.0, 0.75 v8.2.0, 1.00 v8.1.0 % 0.09/0.40 % Syntax : Number of formulae : 73 ( 12 unt; 27 typ; 10 def) % 0.09/0.40 % Number of atoms : 571 ( 10 equ; 0 cnn) % 0.09/0.40 % Maximal formula atoms : 30 ( 12 avg) % 0.09/0.40 % Number of connectives : 832 ( 1 ~; 1 |; 4 &; 821 @) % 0.09/0.40 % ( 1 <=>; 4 =>; 0 <=; 0 <~>) % 0.09/0.40 % Maximal formula depth : 21 ( 13 avg) % 0.09/0.40 % Number of types : 3 ( 1 usr) % 0.09/0.40 % Number of type conns : 83 ( 83 >; 0 *; 0 +; 0 <<) % 0.09/0.40 % Number of symbols : 27 ( 26 usr; 2 con; 0-3 aty) % 0.09/0.40 % Number of variables : 121 ( 111 ^; 7 !; 3 ?; 121 :) % 0.09/0.40 % SPC : TH0_CSA_EQU_NAR_NDT % 0.09/0.40 % 0.09/0.40 % Comments : This output was generated by embedproblem, version 1.7.1 (library % 0.09/0.40 % version 1.3). Generated on Thu Apr 28 13:18:18 EDT 2022 using % 0.09/0.40 % 'modal' embedding, version 1.5.2. Logic specification used: % 0.09/0.40 % $modal == [$constants == $rigid,$quantification == $varying, % 0.09/0.40 % $modalities == $modal_system_S4]. % 0.09/0.40 %------------------------------------------------------------------------------ % 0.09/0.40 thf(mworld,type, % 0.09/0.40 mworld: $tType ). % 0.09/0.40 % 0.09/0.40 thf(mrel_type,type, % 0.09/0.40 mrel: mworld > mworld > $o ). % 0.09/0.40 % 0.09/0.40 thf(mactual_type,type, % 0.09/0.40 mactual: mworld ). % 0.09/0.40 % 0.09/0.40 thf(mlocal_type,type, % 0.09/0.40 mlocal: ( mworld > $o ) > $o ). % 0.09/0.40 % 0.09/0.40 thf(mlocal_def,definition, % 0.09/0.40 ( mlocal % 0.09/0.40 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(mnot_type,type, % 0.09/0.40 mnot: ( mworld > $o ) > mworld > $o ). % 0.09/0.40 % 0.09/0.40 thf(mand_type,type, % 0.09/0.40 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ). % 0.09/0.40 % 0.09/0.40 thf(mor_type,type, % 0.09/0.40 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ). % 0.09/0.40 % 0.09/0.40 thf(mimplies_type,type, % 0.09/0.40 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ). % 0.09/0.40 % 0.09/0.40 thf(mequiv_type,type, % 0.09/0.40 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ). % 0.09/0.40 % 0.09/0.40 thf(mnot_def,definition, % 0.09/0.40 ( mnot % 0.09/0.40 = ( ^ [A: mworld > $o,W: mworld] : % 0.09/0.40 ~ ( A @ W ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(mand_def,definition, % 0.09/0.40 ( mand % 0.09/0.40 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] : % 0.09/0.40 ( ( A @ W ) % 0.09/0.40 & ( B @ W ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(mor_def,definition, % 0.09/0.40 ( mor % 0.09/0.40 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] : % 0.09/0.40 ( ( A @ W ) % 0.09/0.40 | ( B @ W ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(mimplies_def,definition, % 0.09/0.40 ( mimplies % 0.09/0.40 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] : % 0.09/0.40 ( ( A @ W ) % 0.09/0.40 => ( B @ W ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(mequiv_def,definition, % 0.09/0.40 ( mequiv % 0.09/0.40 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] : % 0.09/0.40 ( ( A @ W ) % 0.09/0.40 <=> ( B @ W ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(mbox_type,type, % 0.09/0.40 mbox: ( mworld > $o ) > mworld > $o ). % 0.09/0.40 % 0.09/0.40 thf(mbox_def,definition, % 0.09/0.40 ( mbox % 0.09/0.40 = ( ^ [Phi: mworld > $o,W: mworld] : % 0.09/0.40 ! [V: mworld] : % 0.09/0.40 ( ( mrel @ W @ V ) % 0.09/0.40 => ( Phi @ V ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(mdia_type,type, % 0.09/0.40 mdia: ( mworld > $o ) > mworld > $o ). % 0.09/0.40 % 0.09/0.40 thf(mdia_def,definition, % 0.09/0.40 ( mdia % 0.09/0.40 = ( ^ [Phi: mworld > $o,W: mworld] : % 0.09/0.40 ? [V: mworld] : % 0.09/0.40 ( ( mrel @ W @ V ) % 0.09/0.40 & ( Phi @ V ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(mrel_reflexive,axiom, % 0.09/0.40 ! [W: mworld] : ( mrel @ W @ W ) ). % 0.09/0.40 % 0.09/0.40 thf(mrel_transitive,axiom, % 0.09/0.40 ! [W: mworld,V: mworld,U: mworld] : % 0.09/0.40 ( ( ( mrel @ W @ V ) % 0.09/0.40 & ( mrel @ V @ U ) ) % 0.09/0.40 => ( mrel @ W @ U ) ) ). % 0.09/0.40 % 0.09/0.40 thf(eiw_di_type,type, % 0.09/0.40 eiw_di: $i > mworld > $o ). % 0.09/0.40 % 0.09/0.40 thf(eiw_di_nonempty,axiom, % 0.09/0.40 ! [W: mworld] : % 0.09/0.40 ? [X: $i] : ( eiw_di @ X @ W ) ). % 0.09/0.40 % 0.09/0.40 thf(mforall_di_type,type, % 0.09/0.40 mforall_di: ( $i > mworld > $o ) > mworld > $o ). % 0.09/0.40 % 0.09/0.40 thf(mforall_di_def,definition, % 0.09/0.40 ( mforall_di % 0.09/0.40 = ( ^ [A: $i > mworld > $o,W: mworld] : % 0.09/0.40 ! [X: $i] : % 0.09/0.40 ( ( eiw_di @ X @ W ) % 0.09/0.40 => ( A @ X @ W ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(mexists_di_type,type, % 0.09/0.40 mexists_di: ( $i > mworld > $o ) > mworld > $o ). % 0.09/0.40 % 0.09/0.40 thf(mexists_di_def,definition, % 0.09/0.40 ( mexists_di % 0.09/0.40 = ( ^ [A: $i > mworld > $o,W: mworld] : % 0.09/0.40 ? [X: $i] : % 0.09/0.40 ( ( eiw_di @ X @ W ) % 0.09/0.40 & ( A @ X @ W ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(empty_set_decl,type, % 0.09/0.40 empty_set: $i ). % 0.09/0.40 % 0.09/0.40 thf(qmltpeq_decl,type, % 0.09/0.40 qmltpeq: $i > $i > mworld > $o ). % 0.09/0.40 % 0.09/0.40 thf(equal_set_decl,type, % 0.09/0.40 equal_set: $i > $i > mworld > $o ). % 0.09/0.40 % 0.09/0.40 thf(member_decl,type, % 0.09/0.40 member: $i > $i > mworld > $o ). % 0.09/0.40 % 0.09/0.40 thf(subset_decl,type, % 0.09/0.40 subset: $i > $i > mworld > $o ). % 0.09/0.40 % 0.09/0.40 thf(singleton_decl,type, % 0.09/0.40 singleton: $i > $i ). % 0.09/0.40 % 0.09/0.40 thf(product_decl,type, % 0.09/0.40 product: $i > $i ). % 0.09/0.40 % 0.09/0.40 thf(unordered_pair_decl,type, % 0.09/0.40 unordered_pair: $i > $i > $i ). % 0.09/0.40 % 0.09/0.40 thf(intersection_decl,type, % 0.09/0.40 intersection: $i > $i > $i ). % 0.09/0.40 % 0.09/0.40 thf(difference_decl,type, % 0.09/0.40 difference: $i > $i > $i ). % 0.09/0.40 % 0.09/0.40 thf(sum_decl,type, % 0.09/0.40 sum: $i > $i ). % 0.09/0.40 % 0.09/0.40 thf(union_decl,type, % 0.09/0.40 union: $i > $i > $i ). % 0.09/0.40 % 0.09/0.40 thf(power_set_decl,type, % 0.09/0.40 power_set: $i > $i ). % 0.09/0.40 % 0.09/0.40 thf(reflexivity,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [X: $i] : ( mbox @ ( qmltpeq @ X @ X ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(symmetry,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [X: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [Y: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ X @ Y ) ) @ ( mbox @ ( qmltpeq @ Y @ X ) ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(transitivity,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [X: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [Y: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [Z: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( qmltpeq @ X @ Y ) ) @ ( mbox @ ( qmltpeq @ Y @ Z ) ) ) @ ( mbox @ ( qmltpeq @ X @ Z ) ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(difference_substitution_1,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [A: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [B: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( difference @ A @ C ) @ ( difference @ B @ C ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(difference_substitution_2,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [A: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [B: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( difference @ C @ A ) @ ( difference @ C @ B ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(intersection_substitution_1,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [A: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [B: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( intersection @ A @ C ) @ ( intersection @ B @ C ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(intersection_substitution_2,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [A: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [B: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( intersection @ C @ A ) @ ( intersection @ C @ B ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(power_set_substitution_1,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [A: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [B: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( power_set @ A ) @ ( power_set @ B ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(product_substitution_1,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [A: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [B: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( product @ A ) @ ( product @ B ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(singleton_substitution_1,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [A: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [B: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( singleton @ A ) @ ( singleton @ B ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(sum_substitution_1,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [A: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [B: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( sum @ A ) @ ( sum @ B ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(union_substitution_1,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [A: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [B: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( union @ A @ C ) @ ( union @ B @ C ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(union_substitution_2,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [A: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [B: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( union @ C @ A ) @ ( union @ C @ B ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(unordered_pair_substitution_1,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [A: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [B: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( unordered_pair @ A @ C ) @ ( unordered_pair @ B @ C ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(unordered_pair_substitution_2,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [A: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [B: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( unordered_pair @ C @ A ) @ ( unordered_pair @ C @ B ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(equal_set_substitution_1,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [A: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [B: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( equal_set @ A @ C ) ) ) @ ( mbox @ ( equal_set @ B @ C ) ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(equal_set_substitution_2,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [A: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [B: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( equal_set @ C @ A ) ) ) @ ( mbox @ ( equal_set @ C @ B ) ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(member_substitution_1,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [A: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [B: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( member @ A @ C ) ) ) @ ( mbox @ ( member @ B @ C ) ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(member_substitution_2,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [A: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [B: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( member @ C @ A ) ) ) @ ( mbox @ ( member @ C @ B ) ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(subset_substitution_1,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [A: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [B: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( subset @ A @ C ) ) ) @ ( mbox @ ( subset @ B @ C ) ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(subset_substitution_2,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [A: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [B: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [C: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( subset @ C @ A ) ) ) @ ( mbox @ ( subset @ C @ B ) ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(subset_0,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [A: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [B: $i] : % 0.09/0.40 ( mand % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mimplies @ ( mbox @ ( subset @ A @ B ) ) % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [X: $i] : ( mbox @ ( mimplies @ ( mbox @ ( member @ X @ A ) ) @ ( mbox @ ( member @ X @ B ) ) ) ) ) ) ) ) % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mimplies % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [X: $i] : ( mbox @ ( mimplies @ ( mbox @ ( member @ X @ A ) ) @ ( mbox @ ( member @ X @ B ) ) ) ) ) ) % 0.09/0.40 @ ( mbox @ ( subset @ A @ B ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(equal_set_0,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [A: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [B: $i] : ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( equal_set @ A @ B ) ) @ ( mand @ ( mbox @ ( subset @ A @ B ) ) @ ( mbox @ ( subset @ B @ A ) ) ) ) ) @ ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( subset @ A @ B ) ) @ ( mbox @ ( subset @ B @ A ) ) ) @ ( mbox @ ( equal_set @ A @ B ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(power_set_0,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [X: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [A: $i] : ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( member @ X @ ( power_set @ A ) ) ) @ ( mbox @ ( subset @ X @ A ) ) ) ) @ ( mbox @ ( mimplies @ ( mbox @ ( subset @ X @ A ) ) @ ( mbox @ ( member @ X @ ( power_set @ A ) ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(intersection_0,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [X: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [A: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [B: $i] : ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( member @ X @ ( intersection @ A @ B ) ) ) @ ( mand @ ( mbox @ ( member @ X @ A ) ) @ ( mbox @ ( member @ X @ B ) ) ) ) ) @ ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( member @ X @ A ) ) @ ( mbox @ ( member @ X @ B ) ) ) @ ( mbox @ ( member @ X @ ( intersection @ A @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(union_0,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [X: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [A: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [B: $i] : ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( member @ X @ ( union @ A @ B ) ) ) @ ( mor @ ( mbox @ ( member @ X @ A ) ) @ ( mbox @ ( member @ X @ B ) ) ) ) ) @ ( mbox @ ( mimplies @ ( mor @ ( mbox @ ( member @ X @ A ) ) @ ( mbox @ ( member @ X @ B ) ) ) @ ( mbox @ ( member @ X @ ( union @ A @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(empty_set_0,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [X: $i] : ( mbox @ ( mnot @ ( mbox @ ( member @ X @ empty_set ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(difference_0,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [B: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [A: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [E: $i] : ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( member @ B @ ( difference @ E @ A ) ) ) @ ( mand @ ( mbox @ ( member @ B @ E ) ) @ ( mbox @ ( mnot @ ( mbox @ ( member @ B @ A ) ) ) ) ) ) ) @ ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( member @ B @ E ) ) @ ( mbox @ ( mnot @ ( mbox @ ( member @ B @ A ) ) ) ) ) @ ( mbox @ ( member @ B @ ( difference @ E @ A ) ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(singleton_0,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [X: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [A: $i] : ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( member @ X @ ( singleton @ A ) ) ) @ ( mbox @ ( qmltpeq @ X @ A ) ) ) ) @ ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ X @ A ) ) @ ( mbox @ ( member @ X @ ( singleton @ A ) ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(unordered_pair_0,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [X: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [A: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [B: $i] : ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( member @ X @ ( unordered_pair @ A @ B ) ) ) @ ( mor @ ( mbox @ ( qmltpeq @ X @ A ) ) @ ( mbox @ ( qmltpeq @ X @ B ) ) ) ) ) @ ( mbox @ ( mimplies @ ( mor @ ( mbox @ ( qmltpeq @ X @ A ) ) @ ( mbox @ ( qmltpeq @ X @ B ) ) ) @ ( mbox @ ( member @ X @ ( unordered_pair @ A @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(sum_0,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [X: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [A: $i] : % 0.09/0.40 ( mand % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mimplies @ ( mbox @ ( member @ X @ ( sum @ A ) ) ) % 0.09/0.40 @ ( mexists_di % 0.09/0.40 @ ^ [Y: $i] : ( mand @ ( mbox @ ( member @ Y @ A ) ) @ ( mbox @ ( member @ X @ Y ) ) ) ) ) ) % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mimplies % 0.09/0.40 @ ( mexists_di % 0.09/0.40 @ ^ [Y: $i] : ( mand @ ( mbox @ ( member @ Y @ A ) ) @ ( mbox @ ( member @ X @ Y ) ) ) ) % 0.09/0.40 @ ( mbox @ ( member @ X @ ( sum @ A ) ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(product_0,axiom, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [X: $i] : % 0.09/0.40 ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [A: $i] : % 0.09/0.40 ( mand % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mimplies @ ( mbox @ ( member @ X @ ( product @ A ) ) ) % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [Y: $i] : ( mbox @ ( mimplies @ ( mbox @ ( member @ Y @ A ) ) @ ( mbox @ ( member @ X @ Y ) ) ) ) ) ) ) ) % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mimplies % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [Y: $i] : ( mbox @ ( mimplies @ ( mbox @ ( member @ Y @ A ) ) @ ( mbox @ ( member @ X @ Y ) ) ) ) ) ) % 0.09/0.40 @ ( mbox @ ( member @ X @ ( product @ A ) ) ) ) ) ) ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 thf(thI14,conjecture, % 0.09/0.40 ( mlocal % 0.09/0.40 @ ( mbox % 0.09/0.40 @ ( mforall_di % 0.09/0.40 @ ^ [A: $i] : ( mbox @ ( equal_set @ ( union @ A @ A ) @ A ) ) ) ) ) ). % 0.09/0.40 % 0.09/0.40 %------------------------------------------------------------------------------ % 0.09/0.40 ------------------------ % 0.09/0.40 /starexec/sw/sutcliffe/jdk-11.0.2/bin/java: Command not found. % 0.09/0.40 ---- Embedded in THF --- % 0.09/0.40 ------------------------ % 0.09/0.42 ---- Cleaned THF --- % 0.09/0.42 ------------------------ % 0.09/0.45 % (1278441)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_1278422 for (3000ds/2Mi) % 0.09/0.45 % (1278441)First to succeed. % 0.09/0.45 % SZS status Satisfiable for DTF2THF_1278422 % 0.09/0.45 % (1278441)# SZS output start Saturation. % 0.09/0.45 % (1278441)# SZS output end Saturation. % 0.09/0.45 % (1278441)------------------------------ % 0.09/0.45 % (1278441)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) % 0.09/0.45 % (1278441)Termination reason: Satisfiable % 0.09/0.45 % 0.09/0.45 % (1278441)Memory used [KB]: 5373 % 0.09/0.45 % (1278441)Time elapsed: 0.002 s % 0.09/0.45 % (1278441)Instructions burned: 1 (million) % 0.09/0.45 % (1278441)------------------------------ % 0.09/0.45 % (1278441)------------------------------ % 0.09/0.45 % (1278437)Success in time 0.011 s %------------------------------------------------------------------------------