TSTP Solution File: SYO576^7 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SYO576^7 : TPTP v8.2.0. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 09:06:17 EDT 2024
% Result : Theorem 0.20s 0.42s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYO576^7 : TPTP v8.2.0. Released v5.5.0.
% 0.07/0.14 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.14/0.35 % Computer : n008.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon May 20 09:04:08 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 This is a TH0_THM_EQU_NAR problem
% 0.14/0.35 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.37 % (24302)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.37 % (24302)Instruction limit reached!
% 0.14/0.37 % (24302)------------------------------
% 0.14/0.37 % (24302)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (24302)Termination reason: Unknown
% 0.14/0.37 % (24302)Termination phase: shuffling
% 0.14/0.37
% 0.14/0.37 % (24302)Memory used [KB]: 1023
% 0.14/0.37 % (24302)Time elapsed: 0.003 s
% 0.14/0.37 % (24302)Instructions burned: 2 (million)
% 0.14/0.37 % (24302)------------------------------
% 0.14/0.37 % (24302)------------------------------
% 0.14/0.37 % (24299)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 theBenchmark for (2999ds/4Mi)
% 0.14/0.37 % (24298)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.14/0.37 % (24300)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 theBenchmark for (2999ds/27Mi)
% 0.14/0.37 % (24301)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.37 % (24303)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (2999ds/275Mi)
% 0.14/0.37 % (24304)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.14/0.37 % (24305)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.14/0.38 % (24301)Instruction limit reached!
% 0.14/0.38 % (24301)------------------------------
% 0.14/0.38 % (24301)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (24301)Termination reason: Unknown
% 0.14/0.38 % (24301)Termination phase: shuffling
% 0.14/0.38
% 0.14/0.38 % (24301)Memory used [KB]: 1023
% 0.14/0.38 % (24301)Time elapsed: 0.004 s
% 0.14/0.38 % (24301)Instructions burned: 3 (million)
% 0.14/0.38 % (24301)------------------------------
% 0.14/0.38 % (24301)------------------------------
% 0.14/0.38 % (24305)Instruction limit reached!
% 0.14/0.38 % (24305)------------------------------
% 0.14/0.38 % (24305)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (24305)Termination reason: Unknown
% 0.14/0.38 % (24305)Termination phase: shuffling
% 0.14/0.38
% 0.14/0.38 % (24305)Memory used [KB]: 1023
% 0.14/0.38 % (24305)Time elapsed: 0.003 s
% 0.14/0.38 % (24305)Instructions burned: 3 (million)
% 0.14/0.38 % (24305)------------------------------
% 0.14/0.38 % (24305)------------------------------
% 0.14/0.38 % (24299)Instruction limit reached!
% 0.14/0.38 % (24299)------------------------------
% 0.14/0.38 % (24299)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (24299)Termination reason: Unknown
% 0.14/0.38 % (24299)Termination phase: Property scanning
% 0.14/0.38
% 0.14/0.38 % (24299)Memory used [KB]: 1023
% 0.14/0.38 % (24299)Time elapsed: 0.005 s
% 0.14/0.38 % (24299)Instructions burned: 5 (million)
% 0.14/0.38 % (24299)------------------------------
% 0.14/0.38 % (24299)------------------------------
% 0.20/0.38 % (24303)Refutation not found, incomplete strategy
% 0.20/0.38 % (24303)------------------------------
% 0.20/0.38 % (24303)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.38 % (24303)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.38
% 0.20/0.38
% 0.20/0.38 % (24303)Memory used [KB]: 5628
% 0.20/0.38 % (24303)Time elapsed: 0.012 s
% 0.20/0.38 % (24303)Instructions burned: 15 (million)
% 0.20/0.38 % (24303)------------------------------
% 0.20/0.38 % (24303)------------------------------
% 0.20/0.38 % (24304)Instruction limit reached!
% 0.20/0.38 % (24304)------------------------------
% 0.20/0.38 % (24304)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.39 % (24304)Termination reason: Unknown
% 0.20/0.39 % (24304)Termination phase: Saturation
% 0.20/0.39
% 0.20/0.39 % (24304)Memory used [KB]: 5628
% 0.20/0.39 % (24304)Time elapsed: 0.013 s
% 0.20/0.39 % (24304)Instructions burned: 18 (million)
% 0.20/0.39 % (24304)------------------------------
% 0.20/0.39 % (24304)------------------------------
% 0.20/0.39 % (24306)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.20/0.39 % (24307)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.20/0.39 % (24300)Instruction limit reached!
% 0.20/0.39 % (24300)------------------------------
% 0.20/0.39 % (24300)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.39 % (24300)Termination reason: Unknown
% 0.20/0.39 % (24300)Termination phase: Saturation
% 0.20/0.39
% 0.20/0.39 % (24300)Memory used [KB]: 5756
% 0.20/0.39 % (24300)Time elapsed: 0.019 s
% 0.20/0.39 % (24300)Instructions burned: 27 (million)
% 0.20/0.39 % (24300)------------------------------
% 0.20/0.39 % (24300)------------------------------
% 0.20/0.39 % (24308)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.20/0.39 % (24309)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on theBenchmark for (2999ds/1041Mi)
% 0.20/0.39 % (24308)Instruction limit reached!
% 0.20/0.39 % (24308)------------------------------
% 0.20/0.39 % (24308)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.39 % (24308)Termination reason: Unknown
% 0.20/0.39 % (24308)Termination phase: shuffling
% 0.20/0.39
% 0.20/0.39 % (24308)Memory used [KB]: 1023
% 0.20/0.39 % (24308)Time elapsed: 0.004 s
% 0.20/0.39 % (24308)Instructions burned: 4 (million)
% 0.20/0.39 % (24308)------------------------------
% 0.20/0.39 % (24308)------------------------------
% 0.20/0.40 % (24307)Instruction limit reached!
% 0.20/0.40 % (24307)------------------------------
% 0.20/0.40 % (24307)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.40 % (24307)Termination reason: Unknown
% 0.20/0.40 % (24307)Termination phase: Saturation
% 0.20/0.40
% 0.20/0.40 % (24307)Memory used [KB]: 5628
% 0.20/0.40 % (24310)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.20/0.40 % (24307)Time elapsed: 0.011 s
% 0.20/0.40 % (24307)Instructions burned: 15 (million)
% 0.20/0.40 % (24307)------------------------------
% 0.20/0.40 % (24307)------------------------------
% 0.20/0.40 % (24311)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.20/0.40 % (24310)Instruction limit reached!
% 0.20/0.40 % (24310)------------------------------
% 0.20/0.40 % (24310)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.40 % (24310)Termination reason: Unknown
% 0.20/0.40 % (24310)Termination phase: Property scanning
% 0.20/0.40
% 0.20/0.40 % (24310)Memory used [KB]: 1023
% 0.20/0.40 % (24310)Time elapsed: 0.006 s
% 0.20/0.40 % (24310)Instructions burned: 8 (million)
% 0.20/0.40 % (24310)------------------------------
% 0.20/0.40 % (24310)------------------------------
% 0.20/0.41 % (24312)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.20/0.41 % (24312)Instruction limit reached!
% 0.20/0.41 % (24312)------------------------------
% 0.20/0.41 % (24312)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.41 % (24312)Termination reason: Unknown
% 0.20/0.41 % (24312)Termination phase: shuffling
% 0.20/0.41
% 0.20/0.41 % (24312)Memory used [KB]: 1023
% 0.20/0.41 % (24312)Time elapsed: 0.004 s
% 0.20/0.41 % (24312)Instructions burned: 4 (million)
% 0.20/0.41 % (24312)------------------------------
% 0.20/0.41 % (24312)------------------------------
% 0.20/0.41 % (24313)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.20/0.41 % (24306)Instruction limit reached!
% 0.20/0.41 % (24306)------------------------------
% 0.20/0.41 % (24306)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.41 % (24306)Termination reason: Unknown
% 0.20/0.41 % (24306)Termination phase: Saturation
% 0.20/0.41
% 0.20/0.41 % (24306)Memory used [KB]: 5756
% 0.20/0.41 % (24306)Time elapsed: 0.023 s
% 0.20/0.41 % (24306)Instructions burned: 38 (million)
% 0.20/0.41 % (24306)------------------------------
% 0.20/0.41 % (24306)------------------------------
% 0.20/0.41 % (24313)Instruction limit reached!
% 0.20/0.41 % (24313)------------------------------
% 0.20/0.41 % (24313)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.41 % (24313)Termination reason: Unknown
% 0.20/0.41 % (24313)Termination phase: shuffling
% 0.20/0.41
% 0.20/0.41 % (24313)Memory used [KB]: 1023
% 0.20/0.41 % (24313)Time elapsed: 0.004 s
% 0.20/0.41 % (24313)Instructions burned: 4 (million)
% 0.20/0.41 % (24313)------------------------------
% 0.20/0.41 % (24313)------------------------------
% 0.20/0.41 % (24311)Instruction limit reached!
% 0.20/0.41 % (24311)------------------------------
% 0.20/0.41 % (24311)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.41 % (24311)Termination reason: Unknown
% 0.20/0.41 % (24311)Termination phase: Saturation
% 0.20/0.41
% 0.20/0.41 % (24311)Memory used [KB]: 5756
% 0.20/0.41 % (24311)Time elapsed: 0.012 s
% 0.20/0.41 % (24311)Instructions burned: 16 (million)
% 0.20/0.41 % (24311)------------------------------
% 0.20/0.41 % (24311)------------------------------
% 0.20/0.41 % (24314)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.20/0.42 % (24314)Instruction limit reached!
% 0.20/0.42 % (24314)------------------------------
% 0.20/0.42 % (24314)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.42 % (24314)Termination reason: Unknown
% 0.20/0.42 % (24314)Termination phase: Function definition elimination
% 0.20/0.42
% 0.20/0.42 % (24315)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.20/0.42 % (24314)Memory used [KB]: 1023
% 0.20/0.42 % (24314)Time elapsed: 0.006 s
% 0.20/0.42 % (24314)Instructions burned: 8 (million)
% 0.20/0.42 % (24314)------------------------------
% 0.20/0.42 % (24314)------------------------------
% 0.20/0.42 % (24309)First to succeed.
% 0.20/0.42 % (24315)Instruction limit reached!
% 0.20/0.42 % (24315)------------------------------
% 0.20/0.42 % (24315)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.42 % (24315)Termination reason: Unknown
% 0.20/0.42 % (24315)Termination phase: shuffling
% 0.20/0.42
% 0.20/0.42 % (24315)Memory used [KB]: 1023
% 0.20/0.42 % (24315)Time elapsed: 0.004 s
% 0.20/0.42 % (24315)Instructions burned: 4 (million)
% 0.20/0.42 % (24315)------------------------------
% 0.20/0.42 % (24315)------------------------------
% 0.20/0.42 % (24316)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.20/0.42 % (24317)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.20/0.42 % (24309)Refutation found. Thanks to Tanya!
% 0.20/0.42 % SZS status Theorem for theBenchmark
% 0.20/0.42 % SZS output start Proof for theBenchmark
% 0.20/0.42 thf(type_def_5, type, mu: $tType).
% 0.20/0.42 thf(func_def_0, type, mu: $tType).
% 0.20/0.42 thf(func_def_1, type, qmltpeq: mu > mu > $i > $o).
% 0.20/0.42 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.42 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.20/0.42 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.42 thf(func_def_6, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.20/0.42 thf(func_def_7, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.20/0.42 thf(func_def_8, type, mtrue: $i > $o).
% 0.20/0.42 thf(func_def_9, type, mfalse: $i > $o).
% 0.20/0.42 thf(func_def_10, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.42 thf(func_def_11, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.42 thf(func_def_12, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.42 thf(func_def_13, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.42 thf(func_def_14, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.42 thf(func_def_15, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.20/0.42 thf(func_def_16, type, exists_in_world: mu > $i > $o).
% 0.20/0.42 thf(func_def_17, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.20/0.42 thf(func_def_18, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.20/0.42 thf(func_def_19, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.20/0.42 thf(func_def_20, type, mreflexive: ($i > $i > $o) > $o).
% 0.20/0.42 thf(func_def_21, type, msymmetric: ($i > $i > $o) > $o).
% 0.20/0.42 thf(func_def_22, type, mserial: ($i > $i > $o) > $o).
% 0.20/0.42 thf(func_def_23, type, mtransitive: ($i > $i > $o) > $o).
% 0.20/0.42 thf(func_def_24, type, meuclidean: ($i > $i > $o) > $o).
% 0.20/0.42 thf(func_def_25, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.20/0.42 thf(func_def_26, type, mfunctional: ($i > $i > $o) > $o).
% 0.20/0.42 thf(func_def_27, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.20/0.42 thf(func_def_28, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.20/0.42 thf(func_def_29, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.20/0.42 thf(func_def_30, type, mvalid: ($i > $o) > $o).
% 0.20/0.42 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.20/0.42 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.20/0.42 thf(func_def_33, type, minvalid: ($i > $o) > $o).
% 0.20/0.42 thf(func_def_34, type, rel_s4: $i > $i > $o).
% 0.20/0.42 thf(func_def_35, type, mbox_s4: ($i > $o) > $i > $o).
% 0.20/0.42 thf(func_def_36, type, mdia_s4: ($i > $o) > $i > $o).
% 0.20/0.42 thf(func_def_37, type, p: $i > $o).
% 0.20/0.42 thf(func_def_54, type, ph1: !>[X0: $tType]:(X0)).
% 0.20/0.42 thf(func_def_55, type, sK2: $i > mu).
% 0.20/0.42 thf(f353,plain,(
% 0.20/0.42 $false),
% 0.20/0.42 inference(trivial_inequality_removal,[],[f352])).
% 0.20/0.42 thf(f352,plain,(
% 0.20/0.42 ($false = $true)),
% 0.20/0.42 inference(forward_demodulation,[],[f350,f313])).
% 0.20/0.42 thf(f313,plain,(
% 0.20/0.42 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (p @ Y0))))))),
% 0.20/0.42 inference(binary_proxy_clausification,[],[f301])).
% 0.20/0.42 thf(f301,plain,(
% 0.20/0.42 ($false = ((~ (rel_s4 @ sK4 @ sK5)) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (p @ Y0)))))))),
% 0.20/0.42 inference(beta_eta_normalization,[],[f299])).
% 0.20/0.42 thf(f299,plain,(
% 0.20/0.42 ($false = ((^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))))) @ sK5))),
% 0.20/0.42 inference(sigma_clausification,[],[f285])).
% 0.20/0.42 thf(f285,plain,(
% 0.20/0.42 ($false = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1)))))))))),
% 0.20/0.42 inference(not_proxy_clausification,[],[f256])).
% 0.20/0.42 thf(f256,plain,(
% 0.20/0.42 ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))))))) = $true)),
% 0.20/0.42 inference(boolean_simplification,[],[f255])).
% 0.20/0.42 thf(f255,plain,(
% 0.20/0.42 ($true = ($false | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1)))))))))))),
% 0.20/0.42 inference(boolean_simplification,[],[f252])).
% 0.20/0.42 thf(f252,plain,(
% 0.20/0.42 ($true = ((~ $true) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1)))))))))))),
% 0.20/0.42 inference(superposition,[],[f243,f167])).
% 0.20/0.42 thf(f167,plain,(
% 0.20/0.42 ( ! [X1 : $i] : (($true = (rel_s4 @ X1 @ X1))) )),
% 0.20/0.42 inference(beta_eta_normalization,[],[f166])).
% 0.20/0.42 thf(f166,plain,(
% 0.20/0.42 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (rel_s4 @ Y0 @ Y0)) @ X1))) )),
% 0.20/0.42 inference(pi_clausification,[],[f162])).
% 0.20/0.42 thf(f162,plain,(
% 0.20/0.42 ((!! @ $i @ (^[Y0 : $i]: (rel_s4 @ Y0 @ Y0))) = $true)),
% 0.20/0.42 inference(beta_eta_normalization,[],[f161])).
% 0.20/0.42 thf(f161,plain,(
% 0.20/0.42 ($true = ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) @ rel_s4))),
% 0.20/0.42 inference(definition_unfolding,[],[f146,f132])).
% 0.20/0.42 thf(f132,plain,(
% 0.20/0.42 (mreflexive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))),
% 0.20/0.42 inference(cnf_transformation,[],[f71])).
% 0.20/0.42 thf(f71,plain,(
% 0.20/0.42 (mreflexive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))),
% 0.20/0.42 inference(fool_elimination,[],[f70])).
% 0.20/0.42 thf(f70,plain,(
% 0.20/0.42 (mreflexive = (^[X0 : $i > $i > $o] : (! [X1] : (X0 @ X1 @ X1))))),
% 0.20/0.42 inference(rectify,[],[f18])).
% 0.20/0.42 thf(f18,axiom,(
% 0.20/0.42 (mreflexive = (^[X5 : $i > $i > $o] : (! [X8] : (X5 @ X8 @ X8))))),
% 0.20/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mreflexive)).
% 0.20/0.42 thf(f146,plain,(
% 0.20/0.42 ((mreflexive @ rel_s4) = $true)),
% 0.20/0.42 inference(cnf_transformation,[],[f105])).
% 0.20/0.42 thf(f105,plain,(
% 0.20/0.42 ((mreflexive @ rel_s4) = $true)),
% 0.20/0.42 inference(fool_elimination,[],[f104])).
% 0.20/0.42 thf(f104,plain,(
% 0.20/0.42 (mreflexive @ rel_s4)),
% 0.20/0.42 inference(rectify,[],[f34])).
% 0.20/0.42 thf(f34,axiom,(
% 0.20/0.42 (mreflexive @ rel_s4)),
% 0.20/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',a1)).
% 0.20/0.42 thf(f243,plain,(
% 0.20/0.42 ( ! [X1 : $i] : ((((~ (rel_s4 @ sK4 @ X1)) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1)))))))))) = $true)) )),
% 0.20/0.42 inference(beta_eta_normalization,[],[f242])).
% 0.20/0.42 thf(f242,plain,(
% 0.20/0.42 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (p @ Y2))))))))))) @ X1) = $true)) )),
% 0.20/0.42 inference(pi_clausification,[],[f229])).
% 0.20/0.42 thf(f229,plain,(
% 0.20/0.42 ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (p @ Y2)))))))))))))),
% 0.20/0.42 inference(not_proxy_clausification,[],[f225])).
% 0.20/0.42 thf(f225,plain,(
% 0.20/0.42 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (p @ Y2))))))))))))))),
% 0.20/0.42 inference(boolean_simplification,[],[f224])).
% 0.20/0.42 thf(f224,plain,(
% 0.20/0.42 ($false = ($false | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (p @ Y2)))))))))))))))),
% 0.20/0.42 inference(backward_demodulation,[],[f219,f223])).
% 0.20/0.42 thf(f223,plain,(
% 0.20/0.42 ($false = (~ (rel_s4 @ sK3 @ sK4)))),
% 0.20/0.42 inference(binary_proxy_clausification,[],[f219])).
% 0.20/0.42 thf(f219,plain,(
% 0.20/0.42 ($false = ((~ (rel_s4 @ sK3 @ sK4)) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (p @ Y2)))))))))))))))),
% 0.20/0.42 inference(beta_eta_normalization,[],[f218])).
% 0.20/0.42 thf(f218,plain,(
% 0.20/0.42 ($false = ((^[Y0 : $i]: ((~ (rel_s4 @ sK3 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (p @ Y3))))))))))))))) @ sK4))),
% 0.20/0.42 inference(sigma_clausification,[],[f214])).
% 0.20/0.42 thf(f214,plain,(
% 0.20/0.42 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK3 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (p @ Y3)))))))))))))))) = $false)),
% 0.20/0.42 inference(boolean_simplification,[],[f213])).
% 0.20/0.42 thf(f213,plain,(
% 0.20/0.42 (((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK3 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (p @ Y3)))))))))))))))) | $false) = $false)),
% 0.20/0.42 inference(backward_demodulation,[],[f210,f211])).
% 0.20/0.42 thf(f211,plain,(
% 0.20/0.42 ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK3 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))))))) = $false)),
% 0.20/0.42 inference(binary_proxy_clausification,[],[f210])).
% 0.20/0.42 thf(f210,plain,(
% 0.20/0.42 ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK3 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (p @ Y3)))))))))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK3 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1)))))))))))),
% 0.20/0.42 inference(beta_eta_normalization,[],[f209])).
% 0.20/0.42 thf(f209,plain,(
% 0.20/0.42 ($false = ((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s4 @ Y3 @ Y4)) | (p @ Y4)))))))))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (p @ Y2))))))))))) @ sK3))),
% 0.20/0.42 inference(sigma_clausification,[],[f206])).
% 0.20/0.42 thf(f206,plain,(
% 0.20/0.42 ($false = (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s4 @ Y3 @ Y4)) | (p @ Y4)))))))))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (p @ Y2)))))))))))))),
% 0.20/0.42 inference(not_proxy_clausification,[],[f165])).
% 0.20/0.42 thf(f165,plain,(
% 0.20/0.42 ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s4 @ Y3 @ Y4)) | (p @ Y4)))))))))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (p @ Y2))))))))))))))),
% 0.20/0.42 inference(boolean_simplification,[],[f164])).
% 0.20/0.42 thf(f164,plain,(
% 0.20/0.42 ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s4 @ Y3 @ Y4)) | (p @ Y4)))))))))))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (p @ Y2))))))))))))) = $true)),
% 0.20/0.42 inference(beta_eta_normalization,[],[f159])).
% 0.20/0.42 thf(f159,plain,(
% 0.20/0.42 ((~ ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (Y1 @ Y3))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (Y1 @ Y3))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ p)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (Y1 @ Y3))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ p))))) = $true)),
% 0.20/0.42 inference(definition_unfolding,[],[f118,f144,f151,f158,f140,f158,f140,f158,f140])).
% 0.20/0.42 thf(f140,plain,(
% 0.20/0.42 (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 0.20/0.42 inference(cnf_transformation,[],[f75])).
% 0.20/0.42 thf(f75,plain,(
% 0.20/0.42 (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 0.20/0.42 inference(fool_elimination,[],[f74])).
% 0.20/0.42 thf(f74,plain,(
% 0.20/0.42 ((^[X0 : $i > $o, X1 : $i] : (! [X2] : ((X0 @ X2) | ~(rel_s4 @ X1 @ X2)))) = mbox_s4)),
% 0.20/0.42 inference(rectify,[],[f32])).
% 0.20/0.42 thf(f32,axiom,(
% 0.20/0.42 ((^[X3 : $i > $o, X2 : $i] : (! [X6] : ((X3 @ X6) | ~(rel_s4 @ X2 @ X6)))) = mbox_s4)),
% 0.20/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox_s4)).
% 0.20/0.42 thf(f158,plain,(
% 0.20/0.42 (mdia_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (Y1 @ Y3))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))))),
% 0.20/0.42 inference(definition_unfolding,[],[f120,f129,f140,f129])).
% 0.20/0.42 thf(f129,plain,(
% 0.20/0.42 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.20/0.42 inference(cnf_transformation,[],[f77])).
% 0.20/0.42 thf(f77,plain,(
% 0.20/0.42 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.20/0.42 inference(fool_elimination,[],[f76])).
% 0.20/0.42 thf(f76,plain,(
% 0.20/0.42 (mnot = (^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))))),
% 0.20/0.42 inference(rectify,[],[f2])).
% 0.20/0.42 thf(f2,axiom,(
% 0.20/0.42 (mnot = (^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))))),
% 0.20/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot)).
% 0.20/0.42 thf(f120,plain,(
% 0.20/0.42 (mdia_s4 = (^[Y0 : $i > $o]: (mnot @ (mbox_s4 @ (mnot @ Y0)))))),
% 0.20/0.42 inference(cnf_transformation,[],[f107])).
% 0.20/0.42 thf(f107,plain,(
% 0.20/0.42 (mdia_s4 = (^[Y0 : $i > $o]: (mnot @ (mbox_s4 @ (mnot @ Y0)))))),
% 0.20/0.42 inference(fool_elimination,[],[f106])).
% 0.20/0.42 thf(f106,plain,(
% 0.20/0.42 ((^[X0 : $i > $o] : (mnot @ (mbox_s4 @ (mnot @ X0)))) = mdia_s4)),
% 0.20/0.42 inference(rectify,[],[f33])).
% 0.20/0.42 thf(f33,axiom,(
% 0.20/0.42 ((^[X3 : $i > $o] : (mnot @ (mbox_s4 @ (mnot @ X3)))) = mdia_s4)),
% 0.20/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mdia_s4)).
% 0.20/0.42 thf(f151,plain,(
% 0.20/0.42 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))))),
% 0.20/0.42 inference(definition_unfolding,[],[f126,f122,f129])).
% 0.20/0.42 thf(f122,plain,(
% 0.20/0.42 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.20/0.42 inference(cnf_transformation,[],[f111])).
% 0.20/0.42 thf(f111,plain,(
% 0.20/0.42 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.20/0.42 inference(fool_elimination,[],[f110])).
% 0.20/0.42 thf(f110,plain,(
% 0.20/0.42 (mor = (^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X1 @ X2) | (X0 @ X2))))),
% 0.20/0.42 inference(rectify,[],[f3])).
% 0.20/0.42 thf(f3,axiom,(
% 0.20/0.42 (mor = (^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X4 @ X2) | (X3 @ X2))))),
% 0.20/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor)).
% 0.20/0.42 thf(f126,plain,(
% 0.20/0.42 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.20/0.42 inference(cnf_transformation,[],[f50])).
% 0.20/0.42 thf(f50,plain,(
% 0.20/0.42 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.20/0.42 inference(fool_elimination,[],[f49])).
% 0.20/0.42 thf(f49,plain,(
% 0.20/0.42 (mimplies = (^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)))),
% 0.20/0.42 inference(rectify,[],[f9])).
% 0.20/0.42 thf(f9,axiom,(
% 0.20/0.42 (mimplies = (^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)))),
% 0.20/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies)).
% 0.20/0.42 thf(f144,plain,(
% 0.20/0.42 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.20/0.42 inference(cnf_transformation,[],[f69])).
% 0.20/0.42 thf(f69,plain,(
% 0.20/0.42 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.20/0.42 inference(fool_elimination,[],[f68])).
% 0.20/0.42 thf(f68,plain,(
% 0.20/0.42 ((^[X0 : $i > $o] : (! [X1] : (X0 @ X1))) = mvalid)),
% 0.20/0.42 inference(rectify,[],[f28])).
% 0.20/0.42 thf(f28,axiom,(
% 0.20/0.42 ((^[X3 : $i > $o] : (! [X2] : (X3 @ X2))) = mvalid)),
% 0.20/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mvalid)).
% 0.20/0.42 thf(f118,plain,(
% 0.20/0.42 ($true = (~ (mvalid @ (mimplies @ (mdia_s4 @ (mbox_s4 @ (mdia_s4 @ (mbox_s4 @ p)))) @ (mdia_s4 @ (mbox_s4 @ p))))))),
% 0.20/0.42 inference(cnf_transformation,[],[f91])).
% 0.20/0.42 thf(f91,plain,(
% 0.20/0.42 ($true = (~ (mvalid @ (mimplies @ (mdia_s4 @ (mbox_s4 @ (mdia_s4 @ (mbox_s4 @ p)))) @ (mdia_s4 @ (mbox_s4 @ p))))))),
% 0.20/0.42 inference(fool_elimination,[],[f90])).
% 0.20/0.42 thf(f90,plain,(
% 0.20/0.42 ~(mvalid @ (mimplies @ (mdia_s4 @ (mbox_s4 @ (mdia_s4 @ (mbox_s4 @ p)))) @ (mdia_s4 @ (mbox_s4 @ p))))),
% 0.20/0.42 inference(rectify,[],[f38])).
% 0.20/0.42 thf(f38,negated_conjecture,(
% 0.20/0.42 ~(mvalid @ (mimplies @ (mdia_s4 @ (mbox_s4 @ (mdia_s4 @ (mbox_s4 @ p)))) @ (mdia_s4 @ (mbox_s4 @ p))))),
% 0.20/0.42 inference(negated_conjecture,[],[f37])).
% 0.20/0.42 thf(f37,conjecture,(
% 0.20/0.42 (mvalid @ (mimplies @ (mdia_s4 @ (mbox_s4 @ (mdia_s4 @ (mbox_s4 @ p)))) @ (mdia_s4 @ (mbox_s4 @ p))))),
% 0.20/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',con)).
% 0.20/0.42 thf(f350,plain,(
% 0.20/0.42 ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (p @ Y0))))) = $true)),
% 0.20/0.42 inference(boolean_simplification,[],[f349])).
% 0.20/0.42 thf(f349,plain,(
% 0.20/0.42 ($true = ($false | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (p @ Y0)))))))),
% 0.20/0.42 inference(boolean_simplification,[],[f338])).
% 0.20/0.42 thf(f338,plain,(
% 0.20/0.42 ($true = ((~ $true) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK5 @ Y0)) | (p @ Y0)))))))),
% 0.20/0.42 inference(superposition,[],[f221,f335])).
% 0.20/0.42 thf(f335,plain,(
% 0.20/0.42 ($true = (rel_s4 @ sK3 @ sK5))),
% 0.20/0.42 inference(boolean_simplification,[],[f322])).
% 0.20/0.42 thf(f322,plain,(
% 0.20/0.42 ($true = ($true => (rel_s4 @ sK3 @ sK5)))),
% 0.20/0.42 inference(superposition,[],[f238,f317])).
% 0.20/0.42 thf(f317,plain,(
% 0.20/0.42 ($true = (rel_s4 @ sK4 @ sK5))),
% 0.20/0.42 inference(not_proxy_clausification,[],[f316])).
% 0.20/0.42 thf(f316,plain,(
% 0.20/0.42 ((~ (rel_s4 @ sK4 @ sK5)) = $false)),
% 0.20/0.42 inference(boolean_simplification,[],[f315])).
% 0.20/0.42 thf(f315,plain,(
% 0.20/0.42 ($false = ((~ (rel_s4 @ sK4 @ sK5)) | $false))),
% 0.20/0.42 inference(backward_demodulation,[],[f301,f313])).
% 0.20/0.42 thf(f238,plain,(
% 0.20/0.42 ( ! [X0 : $i] : (($true = ((rel_s4 @ sK4 @ X0) => (rel_s4 @ sK3 @ X0)))) )),
% 0.20/0.42 inference(boolean_simplification,[],[f232])).
% 0.20/0.42 thf(f232,plain,(
% 0.20/0.42 ( ! [X0 : $i] : (((($true & (rel_s4 @ sK4 @ X0)) => (rel_s4 @ sK3 @ X0)) = $true)) )),
% 0.20/0.42 inference(superposition,[],[f196,f226])).
% 0.20/0.42 thf(f226,plain,(
% 0.20/0.42 ((rel_s4 @ sK3 @ sK4) = $true)),
% 0.20/0.42 inference(not_proxy_clausification,[],[f223])).
% 0.20/0.42 thf(f196,plain,(
% 0.20/0.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((rel_s4 @ X1 @ X3) & (rel_s4 @ X3 @ X2)) => (rel_s4 @ X1 @ X2)))) )),
% 0.20/0.42 inference(beta_eta_normalization,[],[f195])).
% 0.20/0.42 thf(f195,plain,(
% 0.20/0.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (((rel_s4 @ X1 @ Y0) & (rel_s4 @ Y0 @ X2)) => (rel_s4 @ X1 @ X2))) @ X3))) )),
% 0.20/0.42 inference(pi_clausification,[],[f194])).
% 0.20/0.42 thf(f194,plain,(
% 0.20/0.42 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (((rel_s4 @ X1 @ Y0) & (rel_s4 @ Y0 @ X2)) => (rel_s4 @ X1 @ X2)))))) )),
% 0.20/0.42 inference(beta_eta_normalization,[],[f193])).
% 0.20/0.42 thf(f193,plain,(
% 0.20/0.42 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((rel_s4 @ X1 @ Y1) & (rel_s4 @ Y1 @ Y0)) => (rel_s4 @ X1 @ Y0))))) @ X2))) )),
% 0.20/0.42 inference(pi_clausification,[],[f192])).
% 0.20/0.42 thf(f192,plain,(
% 0.20/0.42 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((rel_s4 @ X1 @ Y1) & (rel_s4 @ Y1 @ Y0)) => (rel_s4 @ X1 @ Y0)))))))) )),
% 0.20/0.42 inference(beta_eta_normalization,[],[f191])).
% 0.20/0.42 thf(f191,plain,(
% 0.20/0.42 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((rel_s4 @ Y0 @ Y2) & (rel_s4 @ Y2 @ Y1)) => (rel_s4 @ Y0 @ Y1))))))) @ X1))) )),
% 0.20/0.42 inference(pi_clausification,[],[f163])).
% 0.20/0.42 thf(f163,plain,(
% 0.20/0.42 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((rel_s4 @ Y0 @ Y2) & (rel_s4 @ Y2 @ Y1)) => (rel_s4 @ Y0 @ Y1)))))))))),
% 0.20/0.42 inference(beta_eta_normalization,[],[f160])).
% 0.20/0.42 thf(f160,plain,(
% 0.20/0.42 (((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y1 @ Y2))))))))) @ rel_s4) = $true)),
% 0.20/0.42 inference(definition_unfolding,[],[f134,f117])).
% 0.20/0.42 thf(f117,plain,(
% 0.20/0.42 (mtransitive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y1 @ Y2))))))))))),
% 0.20/0.42 inference(cnf_transformation,[],[f45])).
% 0.20/0.42 thf(f45,plain,(
% 0.20/0.42 (mtransitive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y1 @ Y2))))))))))),
% 0.20/0.42 inference(fool_elimination,[],[f44])).
% 0.20/0.42 thf(f44,plain,(
% 0.20/0.42 (mtransitive = (^[X0 : $i > $i > $o] : (! [X1,X2,X3] : (((X0 @ X1 @ X2) & (X0 @ X3 @ X1)) => (X0 @ X3 @ X2)))))),
% 0.20/0.42 inference(rectify,[],[f21])).
% 0.20/0.42 thf(f21,axiom,(
% 0.20/0.42 (mtransitive = (^[X5 : $i > $i > $o] : (! [X9,X10,X8] : (((X5 @ X9 @ X10) & (X5 @ X8 @ X9)) => (X5 @ X8 @ X10)))))),
% 0.20/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mtransitive)).
% 0.20/0.42 thf(f134,plain,(
% 0.20/0.42 ((mtransitive @ rel_s4) = $true)),
% 0.20/0.42 inference(cnf_transformation,[],[f61])).
% 0.20/0.42 thf(f61,plain,(
% 0.20/0.42 ((mtransitive @ rel_s4) = $true)),
% 0.20/0.42 inference(fool_elimination,[],[f60])).
% 0.20/0.42 thf(f60,plain,(
% 0.20/0.42 (mtransitive @ rel_s4)),
% 0.20/0.42 inference(rectify,[],[f35])).
% 0.20/0.42 thf(f35,axiom,(
% 0.20/0.42 (mtransitive @ rel_s4)),
% 0.20/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2)).
% 0.20/0.42 thf(f221,plain,(
% 0.20/0.42 ( ! [X1 : $i] : (($true = ((~ (rel_s4 @ sK3 @ X1)) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (p @ Y0)))))))) )),
% 0.20/0.42 inference(beta_eta_normalization,[],[f220])).
% 0.20/0.42 thf(f220,plain,(
% 0.20/0.42 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((~ (rel_s4 @ sK3 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))))) @ X1) = $true)) )),
% 0.20/0.42 inference(pi_clausification,[],[f215])).
% 0.20/0.42 thf(f215,plain,(
% 0.20/0.42 ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK3 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1)))))))))),
% 0.20/0.43 inference(not_proxy_clausification,[],[f211])).
% 0.20/0.43 % SZS output end Proof for theBenchmark
% 0.20/0.43 % (24309)------------------------------
% 0.20/0.43 % (24309)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.43 % (24309)Termination reason: Refutation
% 0.20/0.43
% 0.20/0.43 % (24309)Memory used [KB]: 5884
% 0.20/0.43 % (24309)Time elapsed: 0.053 s
% 0.20/0.43 % (24309)Instructions burned: 43 (million)
% 0.20/0.43 % (24309)------------------------------
% 0.20/0.43 % (24309)------------------------------
% 0.20/0.43 % (24297)Success in time 0.066 s
% 0.20/0.43 % Vampire---4.8 exiting
%------------------------------------------------------------------------------