%------------------------------------------------------------------------------ % File : DT2H2X---1.9.5 % Problem : LCL634^1 : TPTP v9.3.1. Bugfixed v5.2.0. % 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 11:34:27 AM UTC 2026 % Result : CounterSatisfiable 0.09s 0.46s % Output : Saturation 0.09s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : LCL634^1 : TPTP v9.3.1. Bugfixed v5.2.0. % 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 : Fri Sep 4 14:07:13 UTC 2026 % 0.09/0.37 % CPUTime : % 0.09/0.37 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300 % 0.09/0.39 ---- Original DTF file --- % 0.09/0.39 thf(spec,logic,$$dhol). % 0.09/0.39 %------------------------------------------------------------------------------ % 0.09/0.39 % File : LCL634^1 : TPTP v9.3.1. Bugfixed v5.2.0. % 0.09/0.39 % Domain : Logical Calculi % 0.09/0.39 % Problem : Goedel's ontological argument on the existence of God % 0.09/0.39 % Version : [Ben08] axioms. % 0.09/0.39 % English : % 0.09/0.39 % 0.09/0.39 % Refs : [Fit00] Fitting (2000), Higher-Order Modal Logic - A Sketch % 0.09/0.39 % : [Ben08] Benzmueller (2008), Email to G. Sutcliffe % 0.09/0.39 % Source : [Ben08] % 0.09/0.39 % Names : Fitting-HOLML-Ex-God-alternative-b [Ben08] % 0.09/0.39 % 0.09/0.39 % Status : CounterSatisfiable % 0.09/0.39 % Rating : 1.00 v9.3.0, 0.67 v9.0.0, 1.00 v8.1.0, 0.80 v7.4.0, 0.75 v7.2.0, 0.67 v5.4.0, 1.00 v5.2.0 % 0.09/0.39 % Syntax : Number of formulae : 26 ( 10 unt; 12 typ; 9 def) % 0.09/0.39 % Number of atoms : 48 ( 9 equ; 0 cnn) % 0.09/0.39 % Maximal formula atoms : 7 ( 3 avg) % 0.09/0.39 % Number of connectives : 64 ( 1 ~; 1 |; 1 &; 58 @) % 0.09/0.39 % ( 0 <=>; 3 =>; 0 <=; 0 <~>) % 0.09/0.39 % Maximal formula depth : 9 ( 3 avg) % 0.09/0.39 % Number of types : 3 ( 1 usr) % 0.09/0.39 % Number of type conns : 69 ( 69 >; 0 *; 0 +; 0 <<) % 0.09/0.39 % Number of symbols : 12 ( 11 usr; 0 con; 1-3 aty) % 0.09/0.39 % Number of variables : 34 ( 24 ^; 10 !; 0 ?; 34 :) % 0.09/0.39 % SPC : TH0_CSA_EQU_NAR_NDT % 0.09/0.39 % 0.09/0.39 % Comments : % 0.09/0.39 % Bugfixes : v4.0.0 - Complete overhaul. % 0.09/0.39 % : v5.2.0 - Added missing types % 0.09/0.39 %------------------------------------------------------------------------------ % 0.09/0.39 %----Some higher-order multimodal operators are needed % 0.09/0.39 %----Base type individuals; corresponds to type 0 in [Fit00] % 0.09/0.39 thf(individuals_decl,type, % 0.09/0.39 individuals: $tType ). % 0.09/0.39 % 0.09/0.39 thf(e_type,type, % 0.09/0.39 e: ( individuals > $i > $o ) > individuals > $i > $o ). % 0.09/0.39 % 0.09/0.39 thf(g_type,type, % 0.09/0.39 g: individuals > $i > $o ). % 0.09/0.39 % 0.09/0.39 thf(mall_ind_type,type, % 0.09/0.39 mall_ind: ( individuals > $i > $o ) > $i > $o ). % 0.09/0.39 % 0.09/0.39 thf(mall_indset_type,type, % 0.09/0.39 mall_indset: ( ( individuals > $i > $o ) > $i > $o ) > $i > $o ). % 0.09/0.39 % 0.09/0.39 thf(mbox_type,type, % 0.09/0.39 mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ). % 0.09/0.39 % 0.09/0.39 thf(mimplies_type,type, % 0.09/0.39 mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ). % 0.09/0.39 % 0.09/0.39 thf(mnot_type,type, % 0.09/0.39 mnot: ( $i > $o ) > $i > $o ). % 0.09/0.39 % 0.09/0.39 thf(mor_type,type, % 0.09/0.39 mor: ( $i > $o ) > ( $i > $o ) > $i > $o ). % 0.09/0.39 % 0.09/0.39 thf(mvalid_type,type, % 0.09/0.39 mvalid: ( $i > $o ) > $o ). % 0.09/0.39 % 0.09/0.39 %----mnot corresponds to set complement % 0.09/0.39 thf(mnot,definition, % 0.09/0.39 ( mnot % 0.09/0.39 = ( ^ [Phi: $i > $o,W: $i] : % 0.09/0.39 ~ ( Phi @ W ) ) ) ). % 0.09/0.39 % 0.09/0.39 thf(mor,definition, % 0.09/0.39 ( mor % 0.09/0.39 = ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] : % 0.09/0.39 ( ( Phi @ W ) % 0.09/0.39 | ( Psi @ W ) ) ) ) ). % 0.09/0.39 % 0.09/0.39 %----mimplies defined via mnot and mor % 0.09/0.39 thf(mimplies,definition, % 0.09/0.39 ( mimplies % 0.09/0.39 = ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Phi ) @ Psi ) ) ) ). % 0.09/0.39 % 0.09/0.39 %----mbox % 0.09/0.39 thf(mbox,definition, % 0.09/0.39 ( mbox % 0.09/0.39 = ( ^ [R: $i > $i > $o,Phi: $i > $o,W: $i] : % 0.09/0.39 ! [U: $i] : % 0.09/0.39 ( ( R @ W @ U ) % 0.09/0.39 => ( Phi @ U ) ) ) ) ). % 0.09/0.39 % 0.09/0.39 %----mall_ind (for individuals) % 0.09/0.39 thf(mall_ind,definition, % 0.09/0.39 ( mall_ind % 0.09/0.39 = ( ^ [Phi: individuals > $i > $o,W: $i] : % 0.09/0.39 ! [X: individuals] : ( Phi @ X @ W ) ) ) ). % 0.09/0.39 % 0.09/0.39 %----mall_indset (for sets of individuals) % 0.09/0.39 thf(mall_indset,definition, % 0.09/0.39 ( mall_indset % 0.09/0.39 = ( ^ [Phi: ( individuals > $i > $o ) > $i > $o,W: $i] : % 0.09/0.39 ! [X: individuals > $i > $o] : ( Phi @ X @ W ) ) ) ). % 0.09/0.39 % 0.09/0.39 %----Validity of a multi modal logic formula can now be encoded as % 0.09/0.39 thf(mvalid,definition, % 0.09/0.39 ( mvalid % 0.09/0.39 = ( ^ [Phi: $i > $o] : % 0.09/0.39 ! [W: $i] : ( Phi @ W ) ) ) ). % 0.09/0.39 % 0.09/0.39 %----The encoding of the example % 0.09/0.39 %----r is an S5 accessibility relation: reflexive, transitive and symmetric % 0.09/0.39 thf(r_type,type, % 0.09/0.39 r: $i > $i > $o ). % 0.09/0.39 % 0.09/0.39 thf(r_refl,axiom, % 0.09/0.39 ! [X: $i] : ( r @ X @ X ) ). % 0.09/0.39 % 0.09/0.39 thf(r_trans,axiom, % 0.09/0.39 ! [X: $i,Y: $i,Z: $i] : % 0.09/0.39 ( ( ( r @ X @ Y ) % 0.09/0.39 & ( r @ Y @ Z ) ) % 0.09/0.39 => ( r @ X @ Z ) ) ). % 0.09/0.39 % 0.09/0.39 thf(r_sym,axiom, % 0.09/0.39 ! [X: $i,Y: $i] : % 0.09/0.39 ( ( r @ X @ Y ) % 0.09/0.39 => ( r @ Y @ X ) ) ). % 0.09/0.39 % 0.09/0.39 %----The axioms of the example % 0.09/0.39 %----Positiveness: p % 0.09/0.39 thf(p_type,type, % 0.09/0.39 p: ( individuals > $i > $o ) > $i > $o ). % 0.09/0.39 % 0.09/0.39 thf(positiveness,axiom, % 0.09/0.39 ( mvalid % 0.09/0.39 @ ( mall_indset % 0.09/0.39 @ ^ [X: individuals > $i > $o] : % 0.09/0.39 ( mimplies @ ( mnot @ ( p @ X ) ) % 0.09/0.39 @ ( p % 0.09/0.39 @ ^ [Z: individuals] : ( mnot @ ( X @ Z ) ) ) ) ) ) ). % 0.09/0.39 % 0.09/0.39 %----Being God: g % 0.09/0.39 thf(g,definition, % 0.09/0.39 ( g % 0.09/0.39 = ( ^ [Z: individuals] : % 0.09/0.39 ( mall_indset % 0.09/0.39 @ ^ [X: individuals > $i > $o] : ( mimplies @ ( p @ X ) @ ( X @ Z ) ) ) ) ) ). % 0.09/0.39 % 0.09/0.39 %----Essence: e % 0.09/0.39 thf(e,definition, % 0.09/0.39 ( e % 0.09/0.39 = ( ^ [X: individuals > $i > $o,Z: individuals] : % 0.09/0.39 ( mall_indset % 0.09/0.39 @ ^ [Y: individuals > $i > $o] : % 0.09/0.39 ( mimplies @ ( Y @ Z ) % 0.09/0.39 @ ( mbox @ r % 0.09/0.39 @ ( mall_ind % 0.09/0.39 @ ^ [U: individuals] : ( mimplies @ ( X @ U ) @ ( Y @ U ) ) ) ) ) ) ) ) ). % 0.09/0.39 % 0.09/0.39 %----Conjecture: Being God is the essence of anything that is, in fact, God. % 0.09/0.39 thf(thm,conjecture, % 0.09/0.39 ( mvalid % 0.09/0.39 @ ( mall_ind % 0.09/0.39 @ ^ [Z: individuals] : ( mimplies @ ( g @ Z ) @ ( e @ g @ Z ) ) ) ) ). % 0.09/0.39 % 0.09/0.39 %------------------------------------------------------------------------------ % 0.09/0.39 ------------------------ % 0.09/0.39 /starexec/sw/sutcliffe/jdk-11.0.2/bin/java: Command not found. % 0.09/0.39 ---- Embedded in THF --- % 0.09/0.39 ------------------------ % 0.09/0.41 ---- Cleaned THF --- % 0.09/0.42 ------------------------ % 0.09/0.46 % (3951442)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_3951395 for (3000ds/18Mi) % 0.09/0.46 % (3951442)First to succeed. % 0.09/0.46 % (3951436)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_3951395 for (3000ds/183Mi) % 0.09/0.46 % SZS status Satisfiable for DTF2THF_3951395 % 0.09/0.46 % (3951442)# SZS output start Saturation. % 0.09/0.46 % (3951442)# SZS output end Saturation. % 0.09/0.46 % (3951442)------------------------------ % 0.09/0.46 % (3951442)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) % 0.09/0.46 % (3951442)Termination reason: Satisfiable % 0.09/0.46 % 0.09/0.46 % (3951442)Memory used [KB]: 5373 % 0.09/0.46 % (3951442)Time elapsed: 0.001 s % 0.09/0.46 % (3951442)------------------------------ % 0.09/0.46 % (3951442)------------------------------ % 0.09/0.46 % (3951433)Success in time 0.015 s %------------------------------------------------------------------------------