TSTP Solution File: SYO438^1 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SYO438^1 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n003.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 09:04:26 EDT 2024
% Result : Theorem 0.21s 0.42s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYO438^1 : TPTP v8.2.0. Released v4.0.0.
% 0.11/0.14 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.14/0.35 % Computer : n003.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 10:02:08 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/sandbox2/benchmark/theBenchmark.p
% 0.14/0.37 % (23536)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.37 % (23534)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 % (23537)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 % (23536)Instruction limit reached!
% 0.14/0.37 % (23536)------------------------------
% 0.14/0.37 % (23536)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (23536)Termination reason: Unknown
% 0.14/0.37 % (23536)Termination phase: shuffling
% 0.14/0.37 % (23537)Instruction limit reached!
% 0.14/0.37 % (23537)------------------------------
% 0.14/0.37 % (23537)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (23537)Termination reason: Unknown
% 0.14/0.37 % (23537)Termination phase: shuffling
% 0.14/0.37
% 0.14/0.37 % (23537)Memory used [KB]: 1023
% 0.14/0.37 % (23537)Time elapsed: 0.003 s
% 0.14/0.37 % (23537)Instructions burned: 2 (million)
% 0.14/0.37 % (23537)------------------------------
% 0.14/0.37 % (23537)------------------------------
% 0.14/0.38
% 0.14/0.38 % (23536)Memory used [KB]: 1023
% 0.14/0.38 % (23536)Time elapsed: 0.003 s
% 0.14/0.38 % (23536)Instructions burned: 2 (million)
% 0.14/0.38 % (23536)------------------------------
% 0.14/0.38 % (23536)------------------------------
% 0.14/0.38 % (23539)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.14/0.38 % (23538)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)
% 0.14/0.38 % (23540)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 % (23534)Instruction limit reached!
% 0.14/0.38 % (23534)------------------------------
% 0.14/0.38 % (23534)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (23534)Termination reason: Unknown
% 0.14/0.38 % (23534)Termination phase: shuffling
% 0.14/0.38
% 0.14/0.38 % (23534)Memory used [KB]: 1023
% 0.14/0.38 % (23534)Time elapsed: 0.005 s
% 0.14/0.38 % (23534)Instructions burned: 5 (million)
% 0.14/0.38 % (23534)------------------------------
% 0.14/0.38 % (23534)------------------------------
% 0.14/0.38 % (23540)Instruction limit reached!
% 0.14/0.38 % (23540)------------------------------
% 0.14/0.38 % (23540)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (23540)Termination reason: Unknown
% 0.14/0.38 % (23540)Termination phase: Property scanning
% 0.14/0.38
% 0.14/0.38 % (23540)Memory used [KB]: 1023
% 0.14/0.38 % (23540)Time elapsed: 0.004 s
% 0.14/0.38 % (23540)Instructions burned: 4 (million)
% 0.14/0.38 % (23540)------------------------------
% 0.14/0.38 % (23540)------------------------------
% 0.14/0.38 % (23535)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)
% 0.14/0.38 % (23533)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.14/0.38 % (23538)Refutation not found, incomplete strategy
% 0.14/0.38 % (23538)------------------------------
% 0.14/0.38 % (23538)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (23538)Termination reason: Refutation not found, incomplete strategy
% 0.14/0.39
% 0.14/0.39
% 0.14/0.39 % (23538)Memory used [KB]: 5628
% 0.14/0.39 % (23538)Time elapsed: 0.012 s
% 0.14/0.39 % (23538)Instructions burned: 15 (million)
% 0.14/0.39 % (23538)------------------------------
% 0.14/0.39 % (23538)------------------------------
% 0.14/0.39 % (23539)Instruction limit reached!
% 0.14/0.39 % (23539)------------------------------
% 0.14/0.39 % (23539)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (23539)Termination reason: Unknown
% 0.14/0.39 % (23539)Termination phase: Saturation
% 0.14/0.39
% 0.14/0.39 % (23539)Memory used [KB]: 5628
% 0.14/0.39 % (23539)Time elapsed: 0.012 s
% 0.14/0.39 % (23539)Instructions burned: 18 (million)
% 0.14/0.39 % (23539)------------------------------
% 0.14/0.39 % (23539)------------------------------
% 0.14/0.39 % (23541)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)
% 0.14/0.39 % (23543)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)
% 0.14/0.39 % (23543)Instruction limit reached!
% 0.14/0.39 % (23543)------------------------------
% 0.14/0.39 % (23543)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (23543)Termination reason: Unknown
% 0.14/0.39 % (23543)Termination phase: shuffling
% 0.14/0.39
% 0.14/0.39 % (23543)Memory used [KB]: 1023
% 0.14/0.39 % (23543)Time elapsed: 0.003 s
% 0.14/0.39 % (23543)Instructions burned: 3 (million)
% 0.14/0.39 % (23543)------------------------------
% 0.14/0.39 % (23543)------------------------------
% 0.14/0.39 % (23542)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)
% 0.14/0.39 % (23544)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)
% 0.14/0.40 % (23535)Instruction limit reached!
% 0.14/0.40 % (23535)------------------------------
% 0.14/0.40 % (23535)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40 % (23535)Termination reason: Unknown
% 0.14/0.40 % (23535)Termination phase: Saturation
% 0.14/0.40
% 0.14/0.40 % (23535)Memory used [KB]: 5628
% 0.14/0.40 % (23535)Time elapsed: 0.019 s
% 0.14/0.40 % (23535)Instructions burned: 28 (million)
% 0.14/0.40 % (23535)------------------------------
% 0.14/0.40 % (23535)------------------------------
% 0.14/0.40 % (23545)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.14/0.40 % (23546)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.14/0.40 % (23542)Instruction limit reached!
% 0.14/0.40 % (23542)------------------------------
% 0.14/0.40 % (23542)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40 % (23542)Termination reason: Unknown
% 0.14/0.40 % (23542)Termination phase: Saturation
% 0.14/0.40
% 0.14/0.40 % (23542)Memory used [KB]: 5628
% 0.14/0.40 % (23542)Time elapsed: 0.011 s
% 0.14/0.40 % (23542)Instructions burned: 16 (million)
% 0.14/0.40 % (23542)------------------------------
% 0.14/0.40 % (23542)------------------------------
% 0.14/0.40 % (23545)Instruction limit reached!
% 0.14/0.40 % (23545)------------------------------
% 0.14/0.40 % (23545)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40 % (23545)Termination reason: Unknown
% 0.14/0.40 % (23545)Termination phase: Function definition elimination
% 0.14/0.40
% 0.14/0.40 % (23545)Memory used [KB]: 1023
% 0.14/0.40 % (23545)Time elapsed: 0.006 s
% 0.14/0.40 % (23545)Instructions burned: 9 (million)
% 0.14/0.40 % (23545)------------------------------
% 0.14/0.40 % (23545)------------------------------
% 0.21/0.41 % (23547)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)
% 0.21/0.41 % (23547)Instruction limit reached!
% 0.21/0.41 % (23547)------------------------------
% 0.21/0.41 % (23547)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.41 % (23547)Termination reason: Unknown
% 0.21/0.41 % (23547)Termination phase: Property scanning
% 0.21/0.41
% 0.21/0.41 % (23547)Memory used [KB]: 1023
% 0.21/0.41 % (23547)Time elapsed: 0.004 s
% 0.21/0.41 % (23547)Instructions burned: 4 (million)
% 0.21/0.41 % (23547)------------------------------
% 0.21/0.41 % (23547)------------------------------
% 0.21/0.41 % (23546)Instruction limit reached!
% 0.21/0.41 % (23546)------------------------------
% 0.21/0.41 % (23546)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.41 % (23546)Termination reason: Unknown
% 0.21/0.41 % (23546)Termination phase: Saturation
% 0.21/0.41
% 0.21/0.41 % (23546)Memory used [KB]: 5756
% 0.21/0.41 % (23546)Time elapsed: 0.012 s
% 0.21/0.41 % (23546)Instructions burned: 16 (million)
% 0.21/0.41 % (23546)------------------------------
% 0.21/0.41 % (23546)------------------------------
% 0.21/0.41 % (23548)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)
% 0.21/0.41 % (23548)Instruction limit reached!
% 0.21/0.41 % (23548)------------------------------
% 0.21/0.41 % (23548)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.41 % (23548)Termination reason: Unknown
% 0.21/0.41 % (23548)Termination phase: shuffling
% 0.21/0.41
% 0.21/0.41 % (23548)Memory used [KB]: 1023
% 0.21/0.41 % (23548)Time elapsed: 0.004 s
% 0.21/0.41 % (23548)Instructions burned: 4 (million)
% 0.21/0.41 % (23548)------------------------------
% 0.21/0.41 % (23548)------------------------------
% 0.21/0.41 % (23541)Instruction limit reached!
% 0.21/0.41 % (23541)------------------------------
% 0.21/0.41 % (23541)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.41 % (23541)Termination reason: Unknown
% 0.21/0.41 % (23541)Termination phase: Saturation
% 0.21/0.41
% 0.21/0.41 % (23541)Memory used [KB]: 5756
% 0.21/0.41 % (23541)Time elapsed: 0.025 s
% 0.21/0.41 % (23541)Instructions burned: 38 (million)
% 0.21/0.41 % (23541)------------------------------
% 0.21/0.41 % (23541)------------------------------
% 0.21/0.41 % (23533)First to succeed.
% 0.21/0.42 % (23549)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)
% 0.21/0.42 % (23550)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)
% 0.21/0.42 % (23533)Refutation found. Thanks to Tanya!
% 0.21/0.42 % SZS status Theorem for theBenchmark
% 0.21/0.42 % SZS output start Proof for theBenchmark
% 0.21/0.42 thf(type_def_5, type, mu: $tType).
% 0.21/0.42 thf(func_def_0, type, mu: $tType).
% 0.21/0.42 thf(func_def_1, type, meq_ind: mu > mu > $i > $o).
% 0.21/0.42 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.42 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.21/0.42 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.42 thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.42 thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.42 thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.42 thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.42 thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.42 thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.21/0.42 thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.21/0.42 thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.21/0.42 thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.21/0.42 thf(func_def_15, type, mtrue: $i > $o).
% 0.21/0.42 thf(func_def_16, type, mfalse: $i > $o).
% 0.21/0.42 thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.21/0.42 thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.21/0.42 thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o).
% 0.21/0.42 thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o).
% 0.21/0.42 thf(func_def_21, type, mserial: ($i > $i > $o) > $o).
% 0.21/0.42 thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o).
% 0.21/0.42 thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o).
% 0.21/0.42 thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.21/0.42 thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o).
% 0.21/0.42 thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.21/0.42 thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.21/0.42 thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.21/0.42 thf(func_def_29, type, mvalid: ($i > $o) > $o).
% 0.21/0.42 thf(func_def_30, type, minvalid: ($i > $o) > $o).
% 0.21/0.42 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.21/0.42 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.21/0.42 thf(func_def_33, type, rel_s4: $i > $i > $o).
% 0.21/0.42 thf(func_def_34, type, mbox_s4: ($i > $o) > $i > $o).
% 0.21/0.42 thf(func_def_35, type, mdia_s4: ($i > $o) > $i > $o).
% 0.21/0.42 thf(func_def_36, type, p: $i > $o).
% 0.21/0.42 thf(func_def_54, type, sK2: $i > $i).
% 0.21/0.42 thf(func_def_55, type, sK3: $i > $i).
% 0.21/0.42 thf(f587,plain,(
% 0.21/0.42 $false),
% 0.21/0.42 inference(avatar_sat_refutation,[],[f250,f259,f526,f578,f586])).
% 0.21/0.42 thf(f586,plain,(
% 0.21/0.42 spl0_1 | ~spl0_21),
% 0.21/0.42 inference(avatar_contradiction_clause,[],[f585])).
% 0.21/0.42 thf(f585,plain,(
% 0.21/0.42 $false | (spl0_1 | ~spl0_21)),
% 0.21/0.42 inference(subsumption_resolution,[],[f581,f218])).
% 0.21/0.42 thf(f218,plain,(
% 0.21/0.42 ($false != (rel_s4 @ sK1 @ sK4)) | spl0_1),
% 0.21/0.42 inference(avatar_component_clause,[],[f217])).
% 0.21/0.42 thf(f217,plain,(
% 0.21/0.42 spl0_1 <=> ($false = (rel_s4 @ sK1 @ sK4))),
% 0.21/0.42 introduced(avatar_definition,[new_symbols(naming,[spl0_1])])).
% 0.21/0.42 thf(f581,plain,(
% 0.21/0.42 ($false = (rel_s4 @ sK1 @ sK4)) | ~spl0_21),
% 0.21/0.42 inference(trivial_inequality_removal,[],[f579])).
% 0.21/0.42 thf(f579,plain,(
% 0.21/0.42 ($false = (rel_s4 @ sK1 @ sK4)) | ($true = $false) | ~spl0_21),
% 0.21/0.42 inference(superposition,[],[f524,f361])).
% 0.21/0.42 thf(f361,plain,(
% 0.21/0.42 ( ! [X0 : $i] : (((p @ (sK3 @ (sK2 @ X0))) = $true) | ((rel_s4 @ sK1 @ X0) = $false)) )),
% 0.21/0.42 inference(trivial_inequality_removal,[],[f356])).
% 0.21/0.42 thf(f356,plain,(
% 0.21/0.42 ( ! [X0 : $i] : (((rel_s4 @ sK1 @ X0) = $false) | ((p @ (sK3 @ (sK2 @ X0))) = $true) | ($true = $false)) )),
% 0.21/0.42 inference(superposition,[],[f207,f191])).
% 0.21/0.42 thf(f191,plain,(
% 0.21/0.42 ( ! [X2 : $i,X1 : $i] : (((rel_s4 @ (sK2 @ X1) @ X2) = $false) | ((rel_s4 @ sK1 @ X1) = $false) | ($true = (p @ (sK3 @ X2)))) )),
% 0.21/0.42 inference(not_proxy_clausification,[],[f190])).
% 0.21/0.42 thf(f190,plain,(
% 0.21/0.42 ( ! [X2 : $i,X1 : $i] : (((rel_s4 @ (sK2 @ X1) @ X2) = $false) | ((~ (p @ (sK3 @ X2))) = $false) | ((rel_s4 @ sK1 @ X1) = $false)) )),
% 0.21/0.42 inference(binary_proxy_clausification,[],[f188])).
% 0.21/0.42 thf(f188,plain,(
% 0.21/0.42 ( ! [X2 : $i,X1 : $i] : (((rel_s4 @ (sK2 @ X1) @ X2) = $false) | ((rel_s4 @ sK1 @ X1) = $false) | (((~ (p @ (sK3 @ X2))) | (~ (rel_s4 @ X2 @ (sK3 @ X2)))) = $false)) )),
% 0.21/0.42 inference(beta_eta_normalization,[],[f187])).
% 0.21/0.42 thf(f187,plain,(
% 0.21/0.42 ( ! [X2 : $i,X1 : $i] : (((rel_s4 @ sK1 @ X1) = $false) | (((^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s4 @ X2 @ Y0)))) @ (sK3 @ X2)) = $false) | ((rel_s4 @ (sK2 @ X1) @ X2) = $false)) )),
% 0.21/0.42 inference(sigma_clausification,[],[f186])).
% 0.21/0.42 thf(f186,plain,(
% 0.21/0.42 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s4 @ X2 @ Y0))))) = $false) | ((rel_s4 @ (sK2 @ X1) @ X2) = $false) | ((rel_s4 @ sK1 @ X1) = $false)) )),
% 0.21/0.42 inference(not_proxy_clausification,[],[f185])).
% 0.21/0.42 thf(f185,plain,(
% 0.21/0.42 ( ! [X2 : $i,X1 : $i] : (((rel_s4 @ sK1 @ X1) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s4 @ X2 @ Y0)))))) = $true) | ((rel_s4 @ (sK2 @ X1) @ X2) = $false)) )),
% 0.21/0.42 inference(not_proxy_clausification,[],[f184])).
% 0.21/0.42 thf(f184,plain,(
% 0.21/0.42 ( ! [X2 : $i,X1 : $i] : (($true = (~ (rel_s4 @ (sK2 @ X1) @ X2))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s4 @ X2 @ Y0)))))) = $true) | ((rel_s4 @ sK1 @ X1) = $false)) )),
% 0.21/0.42 inference(binary_proxy_clausification,[],[f183])).
% 0.21/0.42 thf(f183,plain,(
% 0.21/0.42 ( ! [X2 : $i,X1 : $i] : (((rel_s4 @ sK1 @ X1) = $false) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s4 @ X2 @ Y0)))))) | (~ (rel_s4 @ (sK2 @ X1) @ X2))))) )),
% 0.21/0.42 inference(beta_eta_normalization,[],[f182])).
% 0.21/0.42 thf(f182,plain,(
% 0.21/0.42 ( ! [X2 : $i,X1 : $i] : (((rel_s4 @ sK1 @ X1) = $false) | (((^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (rel_s4 @ (sK2 @ X1) @ Y0)))) @ X2) = $true)) )),
% 0.21/0.42 inference(pi_clausification,[],[f181])).
% 0.21/0.42 thf(f181,plain,(
% 0.21/0.42 ( ! [X1 : $i] : (((rel_s4 @ sK1 @ X1) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (rel_s4 @ (sK2 @ X1) @ Y0))))) = $true)) )),
% 0.21/0.42 inference(not_proxy_clausification,[],[f180])).
% 0.21/0.42 thf(f180,plain,(
% 0.21/0.42 ( ! [X1 : $i] : (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (rel_s4 @ (sK2 @ X1) @ Y0)))))) = $false) | ((rel_s4 @ sK1 @ X1) = $false)) )),
% 0.21/0.42 inference(binary_proxy_clausification,[],[f178])).
% 0.21/0.42 thf(f178,plain,(
% 0.21/0.42 ( ! [X1 : $i] : (((rel_s4 @ sK1 @ X1) = $false) | (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (rel_s4 @ (sK2 @ X1) @ Y0)))))) | (~ (rel_s4 @ X1 @ (sK2 @ X1)))) = $false)) )),
% 0.21/0.42 inference(not_proxy_clausification,[],[f177])).
% 0.21/0.42 thf(f177,plain,(
% 0.21/0.42 ( ! [X1 : $i] : (($true = (~ (rel_s4 @ sK1 @ X1))) | (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (rel_s4 @ (sK2 @ X1) @ Y0)))))) | (~ (rel_s4 @ X1 @ (sK2 @ X1)))) = $false)) )),
% 0.21/0.42 inference(beta_eta_normalization,[],[f176])).
% 0.21/0.42 thf(f176,plain,(
% 0.21/0.42 ( ! [X1 : $i] : (($true = (~ (rel_s4 @ sK1 @ X1))) | (((^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (p @ Y2)) | (~ (rel_s4 @ Y1 @ Y2)))))) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (rel_s4 @ X1 @ Y0)))) @ (sK2 @ X1)) = $false)) )),
% 0.21/0.42 inference(sigma_clausification,[],[f175])).
% 0.21/0.42 thf(f175,plain,(
% 0.21/0.42 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (p @ Y2)) | (~ (rel_s4 @ Y1 @ Y2)))))) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (rel_s4 @ X1 @ Y0))))) = $false) | ($true = (~ (rel_s4 @ sK1 @ X1)))) )),
% 0.21/0.42 inference(not_proxy_clausification,[],[f174])).
% 0.21/0.42 thf(f174,plain,(
% 0.21/0.42 ( ! [X1 : $i] : (($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (p @ Y2)) | (~ (rel_s4 @ Y1 @ Y2)))))) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (rel_s4 @ X1 @ Y0))))))) | ($true = (~ (rel_s4 @ sK1 @ X1)))) )),
% 0.21/0.42 inference(binary_proxy_clausification,[],[f173])).
% 0.21/0.42 thf(f173,plain,(
% 0.21/0.42 ( ! [X1 : $i] : ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (p @ Y2)) | (~ (rel_s4 @ Y1 @ Y2)))))) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (rel_s4 @ X1 @ Y0)))))) | (~ (rel_s4 @ sK1 @ X1))) = $true)) )),
% 0.21/0.42 inference(beta_eta_normalization,[],[f172])).
% 0.21/0.42 thf(f172,plain,(
% 0.21/0.42 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (p @ Y3)) | (~ (rel_s4 @ Y2 @ Y3)))))) | (~ (rel_s4 @ Y1 @ Y2)))))) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (rel_s4 @ sK1 @ Y0)))) @ X1))) )),
% 0.21/0.42 inference(pi_clausification,[],[f171])).
% 0.21/0.42 thf(f171,plain,(
% 0.21/0.42 ((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (p @ Y3)) | (~ (rel_s4 @ Y2 @ Y3)))))) | (~ (rel_s4 @ Y1 @ Y2)))))) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (rel_s4 @ sK1 @ Y0))))) = $true)),
% 0.21/0.42 inference(not_proxy_clausification,[],[f170])).
% 0.21/0.42 thf(f170,plain,(
% 0.21/0.42 ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (p @ Y3)) | (~ (rel_s4 @ Y2 @ Y3)))))) | (~ (rel_s4 @ Y1 @ Y2)))))) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (rel_s4 @ sK1 @ Y0)))))) = $false)),
% 0.21/0.42 inference(binary_proxy_clausification,[],[f168])).
% 0.21/0.42 thf(f168,plain,(
% 0.21/0.42 (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (p @ Y3)) | (~ (rel_s4 @ Y2 @ Y3)))))) | (~ (rel_s4 @ Y1 @ Y2)))))) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (rel_s4 @ sK1 @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (rel_s4 @ sK1 @ Y0)))))) = $false)),
% 0.21/0.42 inference(beta_eta_normalization,[],[f167])).
% 0.21/0.42 thf(f167,plain,(
% 0.21/0.42 (((^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: ((~ (p @ Y4)) | (~ (rel_s4 @ Y3 @ Y4)))))) | (~ (rel_s4 @ Y2 @ Y3)))))) | (~ (rel_s4 @ Y1 @ Y2)))))) | (~ (rel_s4 @ Y0 @ Y1)))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (p @ Y2)) | (~ (rel_s4 @ Y1 @ Y2)))))) | (~ (rel_s4 @ Y0 @ Y1))))))) @ sK1) = $false)),
% 0.21/0.42 inference(sigma_clausification,[],[f166])).
% 0.21/0.42 thf(f166,plain,(
% 0.21/0.42 ($true != (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: ((~ (p @ Y4)) | (~ (rel_s4 @ Y3 @ Y4)))))) | (~ (rel_s4 @ Y2 @ Y3)))))) | (~ (rel_s4 @ Y1 @ Y2)))))) | (~ (rel_s4 @ Y0 @ Y1)))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (p @ Y2)) | (~ (rel_s4 @ Y1 @ Y2)))))) | (~ (rel_s4 @ Y0 @ Y1)))))))))),
% 0.21/0.42 inference(beta_eta_normalization,[],[f154])).
% 0.21/0.42 thf(f154,plain,(
% 0.21/0.42 ($true != ((^[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]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (rel_s4 @ Y2 @ Y3)))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (rel_s4 @ Y2 @ Y3)))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))) @ p)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (rel_s4 @ Y2 @ Y3)))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))) @ p)))))),
% 0.21/0.42 inference(definition_unfolding,[],[f113,f142,f145,f110,f153,f110,f153,f110,f153])).
% 0.21/0.42 thf(f153,plain,(
% 0.21/0.42 (mdia_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (rel_s4 @ Y2 @ Y3)))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))))),
% 0.21/0.42 inference(definition_unfolding,[],[f129,f138,f110,f138])).
% 0.21/0.42 thf(f138,plain,(
% 0.21/0.42 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.21/0.42 inference(cnf_transformation,[],[f90])).
% 0.21/0.42 thf(f90,plain,(
% 0.21/0.42 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.21/0.42 inference(fool_elimination,[],[f89])).
% 0.21/0.42 thf(f89,plain,(
% 0.21/0.42 (mnot = (^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))))),
% 0.21/0.42 inference(rectify,[],[f3])).
% 0.21/0.42 thf(f3,axiom,(
% 0.21/0.42 (mnot = (^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))))),
% 0.21/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot)).
% 0.21/0.42 thf(f129,plain,(
% 0.21/0.42 (mdia_s4 = (^[Y0 : $i > $o]: (mnot @ (mbox_s4 @ (mnot @ Y0)))))),
% 0.21/0.42 inference(cnf_transformation,[],[f102])).
% 0.21/0.42 thf(f102,plain,(
% 0.21/0.42 (mdia_s4 = (^[Y0 : $i > $o]: (mnot @ (mbox_s4 @ (mnot @ Y0)))))),
% 0.21/0.42 inference(fool_elimination,[],[f101])).
% 0.21/0.42 thf(f101,plain,(
% 0.21/0.42 (mdia_s4 = (^[X0 : $i > $o] : (mnot @ (mbox_s4 @ (mnot @ X0)))))),
% 0.21/0.42 inference(rectify,[],[f33])).
% 0.21/0.42 thf(f33,axiom,(
% 0.21/0.42 (mdia_s4 = (^[X3 : $i > $o] : (mnot @ (mbox_s4 @ (mnot @ X3)))))),
% 0.21/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mdia_s4)).
% 0.21/0.42 thf(f110,plain,(
% 0.21/0.42 (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))))))),
% 0.21/0.42 inference(cnf_transformation,[],[f48])).
% 0.21/0.42 thf(f48,plain,(
% 0.21/0.42 (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s4 @ Y1 @ Y2)))))))))),
% 0.21/0.42 inference(fool_elimination,[],[f47])).
% 0.21/0.42 thf(f47,plain,(
% 0.21/0.42 (mbox_s4 = (^[X0 : $i > $o, X1 : $i] : (! [X2] : (~(rel_s4 @ X1 @ X2) | (X0 @ X2)))))),
% 0.21/0.42 inference(rectify,[],[f32])).
% 0.21/0.42 thf(f32,axiom,(
% 0.21/0.42 (mbox_s4 = (^[X3 : $i > $o, X2 : $i] : (! [X7] : (~(rel_s4 @ X2 @ X7) | (X3 @ X7)))))),
% 0.21/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_s4)).
% 0.21/0.42 thf(f145,plain,(
% 0.21/0.42 (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)))))),
% 0.21/0.42 inference(definition_unfolding,[],[f112,f140,f138])).
% 0.21/0.42 thf(f140,plain,(
% 0.21/0.42 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.21/0.42 inference(cnf_transformation,[],[f52])).
% 0.21/0.42 thf(f52,plain,(
% 0.21/0.42 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.21/0.42 inference(fool_elimination,[],[f51])).
% 0.21/0.42 thf(f51,plain,(
% 0.21/0.42 (mor = (^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X1 @ X2) | (X0 @ X2))))),
% 0.21/0.42 inference(rectify,[],[f4])).
% 0.21/0.42 thf(f4,axiom,(
% 0.21/0.42 (mor = (^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X4 @ X2) | (X3 @ X2))))),
% 0.21/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor)).
% 0.21/0.42 thf(f112,plain,(
% 0.21/0.42 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.21/0.42 inference(cnf_transformation,[],[f77])).
% 0.21/0.42 thf(f77,plain,(
% 0.21/0.42 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.21/0.42 inference(fool_elimination,[],[f76])).
% 0.21/0.42 thf(f76,plain,(
% 0.21/0.42 (mimplies = (^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)))),
% 0.21/0.42 inference(rectify,[],[f6])).
% 0.21/0.42 thf(f6,axiom,(
% 0.21/0.42 (mimplies = (^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)))),
% 0.21/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies)).
% 0.21/0.42 thf(f142,plain,(
% 0.21/0.42 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.21/0.42 inference(cnf_transformation,[],[f54])).
% 0.21/0.42 thf(f54,plain,(
% 0.21/0.42 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.21/0.42 inference(fool_elimination,[],[f53])).
% 0.21/0.42 thf(f53,plain,(
% 0.21/0.42 ((^[X0 : $i > $o] : (! [X1] : (X0 @ X1))) = mvalid)),
% 0.21/0.42 inference(rectify,[],[f28])).
% 0.21/0.42 thf(f28,axiom,(
% 0.21/0.42 ((^[X3 : $i > $o] : (! [X2] : (X3 @ X2))) = mvalid)),
% 0.21/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mvalid)).
% 0.21/0.42 thf(f113,plain,(
% 0.21/0.42 ((mvalid @ (mimplies @ (mbox_s4 @ (mdia_s4 @ (mbox_s4 @ (mdia_s4 @ p)))) @ (mbox_s4 @ (mdia_s4 @ p)))) != $true)),
% 0.21/0.42 inference(cnf_transformation,[],[f107])).
% 0.21/0.42 thf(f107,plain,(
% 0.21/0.42 ((mvalid @ (mimplies @ (mbox_s4 @ (mdia_s4 @ (mbox_s4 @ (mdia_s4 @ p)))) @ (mbox_s4 @ (mdia_s4 @ p)))) != $true)),
% 0.21/0.42 inference(flattening,[],[f58])).
% 0.21/0.42 thf(f58,plain,(
% 0.21/0.42 ~((mvalid @ (mimplies @ (mbox_s4 @ (mdia_s4 @ (mbox_s4 @ (mdia_s4 @ p)))) @ (mbox_s4 @ (mdia_s4 @ p)))) = $true)),
% 0.21/0.42 inference(fool_elimination,[],[f57])).
% 0.21/0.42 thf(f57,plain,(
% 0.21/0.42 ~(mvalid @ (mimplies @ (mbox_s4 @ (mdia_s4 @ (mbox_s4 @ (mdia_s4 @ p)))) @ (mbox_s4 @ (mdia_s4 @ p))))),
% 0.21/0.42 inference(rectify,[],[f37])).
% 0.21/0.42 thf(f37,negated_conjecture,(
% 0.21/0.42 ~(mvalid @ (mimplies @ (mbox_s4 @ (mdia_s4 @ (mbox_s4 @ (mdia_s4 @ p)))) @ (mbox_s4 @ (mdia_s4 @ p))))),
% 0.21/0.42 inference(negated_conjecture,[],[f36])).
% 0.21/0.42 thf(f36,conjecture,(
% 0.21/0.42 (mvalid @ (mimplies @ (mbox_s4 @ (mdia_s4 @ (mbox_s4 @ (mdia_s4 @ p)))) @ (mbox_s4 @ (mdia_s4 @ p))))),
% 0.21/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove)).
% 0.21/0.42 thf(f207,plain,(
% 0.21/0.42 ( ! [X1 : $i] : (($true = (rel_s4 @ X1 @ X1))) )),
% 0.21/0.42 inference(beta_eta_normalization,[],[f206])).
% 0.21/0.42 thf(f206,plain,(
% 0.21/0.42 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (rel_s4 @ Y0 @ Y0)) @ X1))) )),
% 0.21/0.42 inference(pi_clausification,[],[f205])).
% 0.21/0.42 thf(f205,plain,(
% 0.21/0.42 ((!! @ $i @ (^[Y0 : $i]: (rel_s4 @ Y0 @ Y0))) = $true)),
% 0.21/0.42 inference(beta_eta_normalization,[],[f155])).
% 0.21/0.42 thf(f155,plain,(
% 0.21/0.42 ($true = ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) @ rel_s4))),
% 0.21/0.42 inference(definition_unfolding,[],[f123,f124])).
% 0.21/0.42 thf(f124,plain,(
% 0.21/0.42 (mreflexive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))),
% 0.21/0.42 inference(cnf_transformation,[],[f69])).
% 0.21/0.42 thf(f69,plain,(
% 0.21/0.42 (mreflexive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))),
% 0.21/0.42 inference(fool_elimination,[],[f68])).
% 0.21/0.42 thf(f68,plain,(
% 0.21/0.42 (mreflexive = (^[X0 : $i > $i > $o] : (! [X1] : (X0 @ X1 @ X1))))),
% 0.21/0.42 inference(rectify,[],[f18])).
% 0.21/0.42 thf(f18,axiom,(
% 0.21/0.42 (mreflexive = (^[X6 : $i > $i > $o] : (! [X8] : (X6 @ X8 @ X8))))),
% 0.21/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mreflexive)).
% 0.21/0.42 thf(f123,plain,(
% 0.21/0.42 ((mreflexive @ rel_s4) = $true)),
% 0.21/0.42 inference(cnf_transformation,[],[f92])).
% 0.21/0.42 thf(f92,plain,(
% 0.21/0.42 ((mreflexive @ rel_s4) = $true)),
% 0.21/0.42 inference(fool_elimination,[],[f91])).
% 0.21/0.42 thf(f91,plain,(
% 0.21/0.42 (mreflexive @ rel_s4)),
% 0.21/0.42 inference(rectify,[],[f34])).
% 0.21/0.42 thf(f34,axiom,(
% 0.21/0.42 (mreflexive @ rel_s4)),
% 0.21/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a1)).
% 0.21/0.42 thf(f524,plain,(
% 0.21/0.42 ((p @ (sK3 @ (sK2 @ sK4))) = $false) | ~spl0_21),
% 0.21/0.42 inference(avatar_component_clause,[],[f522])).
% 0.21/0.42 thf(f522,plain,(
% 0.21/0.42 spl0_21 <=> ((p @ (sK3 @ (sK2 @ sK4))) = $false)),
% 0.21/0.42 introduced(avatar_definition,[new_symbols(naming,[spl0_21])])).
% 0.21/0.42 thf(f578,plain,(
% 0.21/0.42 spl0_1 | ~spl0_20),
% 0.21/0.42 inference(avatar_contradiction_clause,[],[f577])).
% 0.21/0.42 thf(f577,plain,(
% 0.21/0.42 $false | (spl0_1 | ~spl0_20)),
% 0.21/0.42 inference(subsumption_resolution,[],[f572,f218])).
% 0.21/0.42 thf(f572,plain,(
% 0.21/0.42 ($false = (rel_s4 @ sK1 @ sK4)) | ~spl0_20),
% 0.21/0.42 inference(trivial_inequality_removal,[],[f569])).
% 0.21/0.42 thf(f569,plain,(
% 0.21/0.42 ($true = $false) | ($false = (rel_s4 @ sK1 @ sK4)) | ~spl0_20),
% 0.21/0.42 inference(superposition,[],[f207,f515])).
% 0.21/0.42 thf(f515,plain,(
% 0.21/0.42 ( ! [X0 : $i] : (((rel_s4 @ (sK2 @ X0) @ (sK2 @ sK4)) = $false) | ((rel_s4 @ sK1 @ X0) = $false)) ) | ~spl0_20),
% 0.21/0.42 inference(avatar_component_clause,[],[f514])).
% 0.21/0.42 thf(f514,plain,(
% 0.21/0.42 spl0_20 <=> ! [X0] : (((rel_s4 @ (sK2 @ X0) @ (sK2 @ sK4)) = $false) | ((rel_s4 @ sK1 @ X0) = $false))),
% 0.21/0.42 introduced(avatar_definition,[new_symbols(naming,[spl0_20])])).
% 0.21/0.42 thf(f526,plain,(
% 0.21/0.42 spl0_20 | spl0_21 | ~spl0_3),
% 0.21/0.42 inference(avatar_split_clause,[],[f460,f247,f522,f514])).
% 0.21/0.42 thf(f247,plain,(
% 0.21/0.42 spl0_3 <=> ! [X0] : (((p @ X0) = $false) | ((rel_s4 @ (sK2 @ sK4) @ X0) = $false))),
% 0.21/0.42 introduced(avatar_definition,[new_symbols(naming,[spl0_3])])).
% 0.21/0.42 thf(f460,plain,(
% 0.21/0.42 ( ! [X0 : $i] : (((rel_s4 @ (sK2 @ X0) @ (sK2 @ sK4)) = $false) | ((p @ (sK3 @ (sK2 @ sK4))) = $false) | ((rel_s4 @ sK1 @ X0) = $false)) ) | ~spl0_3),
% 0.21/0.42 inference(trivial_inequality_removal,[],[f452])).
% 0.21/0.42 thf(f452,plain,(
% 0.21/0.42 ( ! [X0 : $i] : (($true = $false) | ((rel_s4 @ sK1 @ X0) = $false) | ((p @ (sK3 @ (sK2 @ sK4))) = $false) | ((rel_s4 @ (sK2 @ X0) @ (sK2 @ sK4)) = $false)) ) | ~spl0_3),
% 0.21/0.42 inference(superposition,[],[f248,f192])).
% 0.21/0.42 thf(f192,plain,(
% 0.21/0.42 ( ! [X2 : $i,X1 : $i] : (($true = (rel_s4 @ X2 @ (sK3 @ X2))) | ((rel_s4 @ (sK2 @ X1) @ X2) = $false) | ((rel_s4 @ sK1 @ X1) = $false)) )),
% 0.21/0.42 inference(not_proxy_clausification,[],[f189])).
% 0.21/0.42 thf(f189,plain,(
% 0.21/0.42 ( ! [X2 : $i,X1 : $i] : (((~ (rel_s4 @ X2 @ (sK3 @ X2))) = $false) | ((rel_s4 @ sK1 @ X1) = $false) | ((rel_s4 @ (sK2 @ X1) @ X2) = $false)) )),
% 0.21/0.42 inference(binary_proxy_clausification,[],[f188])).
% 0.21/0.42 thf(f248,plain,(
% 0.21/0.42 ( ! [X0 : $i] : (((rel_s4 @ (sK2 @ sK4) @ X0) = $false) | ((p @ X0) = $false)) ) | ~spl0_3),
% 0.21/0.42 inference(avatar_component_clause,[],[f247])).
% 0.21/0.42 thf(f259,plain,(
% 0.21/0.42 ~spl0_1),
% 0.21/0.42 inference(avatar_contradiction_clause,[],[f258])).
% 0.21/0.42 thf(f258,plain,(
% 0.21/0.42 $false | ~spl0_1),
% 0.21/0.42 inference(trivial_inequality_removal,[],[f251])).
% 0.21/0.42 thf(f251,plain,(
% 0.21/0.42 ($true = $false) | ~spl0_1),
% 0.21/0.42 inference(superposition,[],[f219,f204])).
% 0.21/0.42 thf(f204,plain,(
% 0.21/0.42 ($true = (rel_s4 @ sK1 @ sK4))),
% 0.21/0.42 inference(not_proxy_clausification,[],[f196])).
% 0.21/0.42 thf(f196,plain,(
% 0.21/0.42 ((~ (rel_s4 @ sK1 @ sK4)) = $false)),
% 0.21/0.42 inference(binary_proxy_clausification,[],[f195])).
% 0.21/0.42 thf(f195,plain,(
% 0.21/0.42 (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s4 @ sK4 @ Y0)))))) | (~ (rel_s4 @ sK1 @ sK4))) = $false)),
% 0.21/0.42 inference(beta_eta_normalization,[],[f194])).
% 0.21/0.42 thf(f194,plain,(
% 0.21/0.42 (((^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (rel_s4 @ sK1 @ Y0)))) @ sK4) = $false)),
% 0.21/0.42 inference(sigma_clausification,[],[f169])).
% 0.21/0.42 thf(f169,plain,(
% 0.21/0.42 ((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_s4 @ Y0 @ Y1)))))) | (~ (rel_s4 @ sK1 @ Y0))))) = $false)),
% 0.21/0.42 inference(binary_proxy_clausification,[],[f168])).
% 0.21/0.42 thf(f219,plain,(
% 0.21/0.42 ($false = (rel_s4 @ sK1 @ sK4)) | ~spl0_1),
% 0.21/0.42 inference(avatar_component_clause,[],[f217])).
% 0.21/0.42 thf(f250,plain,(
% 0.21/0.42 spl0_3 | spl0_1),
% 0.21/0.42 inference(avatar_split_clause,[],[f239,f217,f247])).
% 0.21/0.42 thf(f239,plain,(
% 0.21/0.42 ( ! [X0 : $i] : (((rel_s4 @ (sK2 @ sK4) @ X0) = $false) | ($false = (rel_s4 @ sK1 @ sK4)) | ((p @ X0) = $false)) )),
% 0.21/0.42 inference(trivial_inequality_removal,[],[f233])).
% 0.21/0.42 thf(f233,plain,(
% 0.21/0.42 ( ! [X0 : $i] : (((p @ X0) = $false) | ($true = $false) | ((rel_s4 @ (sK2 @ sK4) @ X0) = $false) | ($false = (rel_s4 @ sK1 @ sK4))) )),
% 0.21/0.42 inference(superposition,[],[f231,f193])).
% 0.21/0.42 thf(f193,plain,(
% 0.21/0.42 ( ! [X1 : $i] : (($true = (rel_s4 @ X1 @ (sK2 @ X1))) | ((rel_s4 @ sK1 @ X1) = $false)) )),
% 0.21/0.42 inference(not_proxy_clausification,[],[f179])).
% 0.21/0.42 thf(f179,plain,(
% 0.21/0.42 ( ! [X1 : $i] : (((~ (rel_s4 @ X1 @ (sK2 @ X1))) = $false) | ((rel_s4 @ sK1 @ X1) = $false)) )),
% 0.21/0.42 inference(binary_proxy_clausification,[],[f178])).
% 0.21/0.42 thf(f231,plain,(
% 0.21/0.42 ( ! [X0 : $i,X1 : $i] : (($false = (rel_s4 @ sK4 @ X1)) | ((rel_s4 @ X1 @ X0) = $false) | ((p @ X0) = $false)) )),
% 0.21/0.42 inference(trivial_inequality_removal,[],[f226])).
% 0.21/0.42 thf(f226,plain,(
% 0.21/0.42 ( ! [X0 : $i,X1 : $i] : (($false = (rel_s4 @ sK4 @ X1)) | ($true = $false) | ((p @ X0) = $false) | ((rel_s4 @ X1 @ X0) = $false)) )),
% 0.21/0.42 inference(superposition,[],[f165,f203])).
% 0.21/0.42 thf(f203,plain,(
% 0.21/0.42 ( ! [X1 : $i] : (($false = (rel_s4 @ sK4 @ X1)) | ((p @ X1) = $false)) )),
% 0.21/0.42 inference(not_proxy_clausification,[],[f202])).
% 0.21/0.42 thf(f202,plain,(
% 0.21/0.42 ( ! [X1 : $i] : (($true = (~ (p @ X1))) | ($false = (rel_s4 @ sK4 @ X1))) )),
% 0.21/0.42 inference(not_proxy_clausification,[],[f201])).
% 0.21/0.42 thf(f201,plain,(
% 0.21/0.42 ( ! [X1 : $i] : (($true = (~ (rel_s4 @ sK4 @ X1))) | ($true = (~ (p @ X1)))) )),
% 0.21/0.42 inference(binary_proxy_clausification,[],[f200])).
% 0.21/0.42 thf(f200,plain,(
% 0.21/0.42 ( ! [X1 : $i] : (($true = ((~ (p @ X1)) | (~ (rel_s4 @ sK4 @ X1))))) )),
% 0.21/0.42 inference(beta_eta_normalization,[],[f199])).
% 0.21/0.42 thf(f199,plain,(
% 0.21/0.42 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s4 @ sK4 @ Y0)))) @ X1) = $true)) )),
% 0.21/0.42 inference(pi_clausification,[],[f198])).
% 0.21/0.42 thf(f198,plain,(
% 0.21/0.42 ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s4 @ sK4 @ Y0))))))),
% 0.21/0.42 inference(not_proxy_clausification,[],[f197])).
% 0.21/0.42 thf(f197,plain,(
% 0.21/0.42 ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s4 @ sK4 @ Y0)))))) = $false)),
% 0.21/0.42 inference(binary_proxy_clausification,[],[f195])).
% 0.21/0.42 thf(f165,plain,(
% 0.21/0.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((rel_s4 @ X3 @ X2) = $true) | ((rel_s4 @ X3 @ X1) = $false) | ((rel_s4 @ X1 @ X2) = $false)) )),
% 0.21/0.42 inference(binary_proxy_clausification,[],[f164])).
% 0.21/0.42 thf(f164,plain,(
% 0.21/0.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((rel_s4 @ X3 @ X2) = $true) | (((rel_s4 @ X3 @ X1) & (rel_s4 @ X1 @ X2)) = $false)) )),
% 0.21/0.42 inference(binary_proxy_clausification,[],[f163])).
% 0.21/0.42 thf(f163,plain,(
% 0.21/0.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((rel_s4 @ X3 @ X1) & (rel_s4 @ X1 @ X2)) => (rel_s4 @ X3 @ X2)))) )),
% 0.21/0.42 inference(beta_eta_normalization,[],[f162])).
% 0.21/0.42 thf(f162,plain,(
% 0.21/0.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (((rel_s4 @ Y0 @ X1) & (rel_s4 @ X1 @ X2)) => (rel_s4 @ Y0 @ X2))) @ X3))) )),
% 0.21/0.42 inference(pi_clausification,[],[f161])).
% 0.21/0.42 thf(f161,plain,(
% 0.21/0.42 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (((rel_s4 @ Y0 @ X1) & (rel_s4 @ X1 @ X2)) => (rel_s4 @ Y0 @ X2)))))) )),
% 0.21/0.42 inference(beta_eta_normalization,[],[f160])).
% 0.21/0.42 thf(f160,plain,(
% 0.21/0.42 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((rel_s4 @ Y1 @ X1) & (rel_s4 @ X1 @ Y0)) => (rel_s4 @ Y1 @ Y0))))) @ X2) = $true)) )),
% 0.21/0.42 inference(pi_clausification,[],[f159])).
% 0.21/0.42 thf(f159,plain,(
% 0.21/0.42 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((rel_s4 @ Y1 @ X1) & (rel_s4 @ X1 @ Y0)) => (rel_s4 @ Y1 @ Y0)))))))) )),
% 0.21/0.42 inference(beta_eta_normalization,[],[f158])).
% 0.21/0.42 thf(f158,plain,(
% 0.21/0.42 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((rel_s4 @ Y2 @ Y0) & (rel_s4 @ Y0 @ Y1)) => (rel_s4 @ Y2 @ Y1))))))) @ X1))) )),
% 0.21/0.42 inference(pi_clausification,[],[f157])).
% 0.21/0.42 thf(f157,plain,(
% 0.21/0.42 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((rel_s4 @ Y2 @ Y0) & (rel_s4 @ Y0 @ Y1)) => (rel_s4 @ Y2 @ Y1)))))))))),
% 0.21/0.42 inference(beta_eta_normalization,[],[f156])).
% 0.21/0.42 thf(f156,plain,(
% 0.21/0.42 ($true = ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y3 @ Y2))))))))) @ rel_s4))),
% 0.21/0.42 inference(definition_unfolding,[],[f126,f143])).
% 0.21/0.42 thf(f143,plain,(
% 0.21/0.42 (mtransitive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y3 @ Y2))))))))))),
% 0.21/0.42 inference(cnf_transformation,[],[f42])).
% 0.21/0.42 thf(f42,plain,(
% 0.21/0.42 (mtransitive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y3 @ Y2))))))))))),
% 0.21/0.42 inference(fool_elimination,[],[f41])).
% 0.21/0.42 thf(f41,plain,(
% 0.21/0.42 (mtransitive = (^[X0 : $i > $i > $o] : (! [X1,X2,X3] : (((X0 @ X3 @ X2) & (X0 @ X1 @ X3)) => (X0 @ X1 @ X2)))))),
% 0.21/0.42 inference(rectify,[],[f21])).
% 0.21/0.42 thf(f21,axiom,(
% 0.21/0.42 (mtransitive = (^[X6 : $i > $i > $o] : (! [X8,X10,X9] : (((X6 @ X9 @ X10) & (X6 @ X8 @ X9)) => (X6 @ X8 @ X10)))))),
% 0.21/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mtransitive)).
% 0.21/0.42 thf(f126,plain,(
% 0.21/0.42 ((mtransitive @ rel_s4) = $true)),
% 0.21/0.42 inference(cnf_transformation,[],[f100])).
% 0.21/0.42 thf(f100,plain,(
% 0.21/0.42 ((mtransitive @ rel_s4) = $true)),
% 0.21/0.42 inference(fool_elimination,[],[f99])).
% 0.21/0.42 thf(f99,plain,(
% 0.21/0.42 (mtransitive @ rel_s4)),
% 0.21/0.42 inference(rectify,[],[f35])).
% 0.21/0.42 thf(f35,axiom,(
% 0.21/0.42 (mtransitive @ rel_s4)),
% 0.21/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2)).
% 0.21/0.42 % SZS output end Proof for theBenchmark
% 0.21/0.42 % (23533)------------------------------
% 0.21/0.42 % (23533)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.42 % (23533)Termination reason: Refutation
% 0.21/0.42
% 0.21/0.42 % (23533)Memory used [KB]: 6012
% 0.21/0.42 % (23533)Time elapsed: 0.038 s
% 0.21/0.42 % (23533)Instructions burned: 50 (million)
% 0.21/0.42 % (23533)------------------------------
% 0.21/0.42 % (23533)------------------------------
% 0.21/0.42 % (23532)Success in time 0.065 s
% 0.21/0.42 % Vampire---4.8 exiting
%------------------------------------------------------------------------------