TSTP Solution File: SYO440^1 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SYO440^1 : 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 : n011.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
% 0.07/0.12 % Problem : SYO440^1 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.13 % 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
% 0.14/0.34 % Computer : n011.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon May 20 09:49:53 EDT 2024
% 0.14/0.34 % CPUTime :
% 0.14/0.34 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 % (27803)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 % (27802)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 % (27802)Instruction limit reached!
% 0.14/0.37 % (27802)------------------------------
% 0.14/0.37 % (27802)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (27802)Termination reason: Unknown
% 0.14/0.37 % (27802)Termination phase: shuffling
% 0.14/0.37
% 0.14/0.37 % (27802)Memory used [KB]: 1023
% 0.14/0.37 % (27802)Time elapsed: 0.003 s
% 0.14/0.37 % (27802)Instructions burned: 3 (million)
% 0.14/0.37 % (27802)------------------------------
% 0.14/0.37 % (27802)------------------------------
% 0.14/0.37 % (27803)Refutation not found, incomplete strategy
% 0.14/0.37 % (27803)------------------------------
% 0.14/0.37 % (27803)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (27803)Termination reason: Refutation not found, incomplete strategy
% 0.14/0.37
% 0.14/0.37
% 0.14/0.37 % (27803)Memory used [KB]: 5628
% 0.14/0.38 % (27803)Time elapsed: 0.010 s
% 0.14/0.38 % (27803)Instructions burned: 14 (million)
% 0.14/0.38 % (27803)------------------------------
% 0.14/0.38 % (27803)------------------------------
% 0.14/0.38 % (27805)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 % (27804)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 % (27799)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)
% 0.14/0.38 % (27798)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 % (27805)Instruction limit reached!
% 0.14/0.38 % (27805)------------------------------
% 0.14/0.38 % (27805)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (27805)Termination reason: Unknown
% 0.14/0.38 % (27805)Termination phase: shuffling
% 0.14/0.38
% 0.14/0.38 % (27805)Memory used [KB]: 1023
% 0.14/0.38 % (27805)Time elapsed: 0.003 s
% 0.14/0.38 % (27805)Instructions burned: 4 (million)
% 0.14/0.38 % (27805)------------------------------
% 0.14/0.38 % (27805)------------------------------
% 0.14/0.38 % (27801)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.38 % (27800)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 % (27801)Instruction limit reached!
% 0.14/0.38 % (27801)------------------------------
% 0.14/0.38 % (27801)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (27801)Termination reason: Unknown
% 0.14/0.38 % (27801)Termination phase: shuffling
% 0.14/0.38
% 0.14/0.38 % (27801)Memory used [KB]: 1023
% 0.14/0.38 % (27801)Time elapsed: 0.003 s
% 0.14/0.38 % (27801)Instructions burned: 2 (million)
% 0.14/0.38 % (27801)------------------------------
% 0.14/0.38 % (27801)------------------------------
% 0.14/0.39 % (27806)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 % (27807)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 % (27804)Instruction limit reached!
% 0.14/0.39 % (27804)------------------------------
% 0.14/0.39 % (27804)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (27804)Termination reason: Unknown
% 0.14/0.39 % (27804)Termination phase: Saturation
% 0.14/0.39
% 0.14/0.39 % (27804)Memory used [KB]: 5628
% 0.14/0.39 % (27804)Time elapsed: 0.013 s
% 0.14/0.39 % (27804)Instructions burned: 19 (million)
% 0.14/0.39 % (27804)------------------------------
% 0.14/0.39 % (27804)------------------------------
% 0.14/0.39 % (27799)Instruction limit reached!
% 0.14/0.39 % (27799)------------------------------
% 0.14/0.39 % (27799)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (27799)Termination reason: Unknown
% 0.14/0.39 % (27799)Termination phase: Property scanning
% 0.14/0.39
% 0.14/0.39 % (27799)Memory used [KB]: 1023
% 0.14/0.39 % (27799)Time elapsed: 0.005 s
% 0.14/0.39 % (27799)Instructions burned: 5 (million)
% 0.14/0.39 % (27799)------------------------------
% 0.14/0.39 % (27799)------------------------------
% 0.14/0.40 % (27808)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)
% 0.14/0.40 % (27807)Instruction limit reached!
% 0.14/0.40 % (27807)------------------------------
% 0.14/0.40 % (27807)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40 % (27807)Termination reason: Unknown
% 0.14/0.40 % (27807)Termination phase: Saturation
% 0.14/0.40
% 0.14/0.40 % (27807)Memory used [KB]: 5628
% 0.14/0.40 % (27807)Time elapsed: 0.009 s
% 0.14/0.40 % (27807)Instructions burned: 15 (million)
% 0.14/0.40 % (27807)------------------------------
% 0.14/0.40 % (27807)------------------------------
% 0.14/0.40 % (27808)Instruction limit reached!
% 0.14/0.40 % (27808)------------------------------
% 0.14/0.40 % (27808)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40 % (27808)Termination reason: Unknown
% 0.14/0.40 % (27808)Termination phase: shuffling
% 0.14/0.40
% 0.21/0.40 % (27808)Memory used [KB]: 1023
% 0.21/0.40 % (27808)Time elapsed: 0.003 s
% 0.21/0.40 % (27808)Instructions burned: 3 (million)
% 0.21/0.40 % (27808)------------------------------
% 0.21/0.40 % (27808)------------------------------
% 0.21/0.40 % (27809)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)
% 0.21/0.40 % (27800)Instruction limit reached!
% 0.21/0.40 % (27800)------------------------------
% 0.21/0.40 % (27800)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.40 % (27800)Termination reason: Unknown
% 0.21/0.40 % (27800)Termination phase: Saturation
% 0.21/0.40
% 0.21/0.40 % (27800)Memory used [KB]: 5756
% 0.21/0.40 % (27800)Time elapsed: 0.040 s
% 0.21/0.40 % (27800)Instructions burned: 27 (million)
% 0.21/0.40 % (27800)------------------------------
% 0.21/0.40 % (27800)------------------------------
% 0.21/0.40 % (27810)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.21/0.41 % (27811)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.21/0.41 % (27810)Instruction limit reached!
% 0.21/0.41 % (27810)------------------------------
% 0.21/0.41 % (27810)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.41 % (27810)Termination reason: Unknown
% 0.21/0.41 % (27810)Termination phase: Function definition elimination
% 0.21/0.41
% 0.21/0.41 % (27810)Memory used [KB]: 1023
% 0.21/0.41 % (27810)Time elapsed: 0.006 s
% 0.21/0.41 % (27810)Instructions burned: 8 (million)
% 0.21/0.41 % (27810)------------------------------
% 0.21/0.41 % (27810)------------------------------
% 0.21/0.41 % (27813)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 % (27813)Instruction limit reached!
% 0.21/0.41 % (27813)------------------------------
% 0.21/0.41 % (27813)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.41 % (27813)Termination reason: Unknown
% 0.21/0.41 % (27813)Termination phase: shuffling
% 0.21/0.41
% 0.21/0.41 % (27813)Memory used [KB]: 1023
% 0.21/0.41 % (27813)Time elapsed: 0.003 s
% 0.21/0.41 % (27813)Instructions burned: 3 (million)
% 0.21/0.41 % (27813)------------------------------
% 0.21/0.41 % (27813)------------------------------
% 0.21/0.41 % (27806)Instruction limit reached!
% 0.21/0.41 % (27806)------------------------------
% 0.21/0.41 % (27806)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.41 % (27806)Termination reason: Unknown
% 0.21/0.41 % (27806)Termination phase: Saturation
% 0.21/0.41
% 0.21/0.41 % (27806)Memory used [KB]: 5756
% 0.21/0.41 % (27806)Time elapsed: 0.025 s
% 0.21/0.41 % (27806)Instructions burned: 37 (million)
% 0.21/0.41 % (27806)------------------------------
% 0.21/0.41 % (27806)------------------------------
% 0.21/0.41 % (27812)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 % (27809)First to succeed.
% 0.21/0.41 % (27812)Instruction limit reached!
% 0.21/0.41 % (27812)------------------------------
% 0.21/0.41 % (27812)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.41 % (27812)Termination reason: Unknown
% 0.21/0.41 % (27812)Termination phase: shuffling
% 0.21/0.41
% 0.21/0.41 % (27812)Memory used [KB]: 1023
% 0.21/0.41 % (27812)Time elapsed: 0.003 s
% 0.21/0.41 % (27812)Instructions burned: 3 (million)
% 0.21/0.41 % (27812)------------------------------
% 0.21/0.41 % (27812)------------------------------
% 0.21/0.42 % (27811)Instruction limit reached!
% 0.21/0.42 % (27811)------------------------------
% 0.21/0.42 % (27811)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.42 % (27811)Termination reason: Unknown
% 0.21/0.42 % (27811)Termination phase: Saturation
% 0.21/0.42
% 0.21/0.42 % (27811)Memory used [KB]: 5756
% 0.21/0.42 % (27811)Time elapsed: 0.010 s
% 0.21/0.42 % (27811)Instructions burned: 16 (million)
% 0.21/0.42 % (27811)------------------------------
% 0.21/0.42 % (27811)------------------------------
% 0.21/0.42 % (27809)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_53, type, ph1: !>[X0: $tType]:(X0)).
% 0.21/0.42 thf(f314,plain,(
% 0.21/0.42 $false),
% 0.21/0.42 inference(trivial_inequality_removal,[],[f313])).
% 0.21/0.42 thf(f313,plain,(
% 0.21/0.42 ($true = $false)),
% 0.21/0.42 inference(boolean_simplification,[],[f312])).
% 0.21/0.42 thf(f312,plain,(
% 0.21/0.42 ($true = (~ $true))),
% 0.21/0.42 inference(backward_demodulation,[],[f298,f306])).
% 0.21/0.42 thf(f306,plain,(
% 0.21/0.42 ($true = (rel_s4 @ sK2 @ sK4))),
% 0.21/0.42 inference(boolean_simplification,[],[f301])).
% 0.21/0.42 thf(f301,plain,(
% 0.21/0.42 ($true = ($true => (rel_s4 @ sK2 @ sK4)))),
% 0.21/0.42 inference(superposition,[],[f209,f291])).
% 0.21/0.42 thf(f291,plain,(
% 0.21/0.42 ($true = (rel_s4 @ sK3 @ sK4))),
% 0.21/0.42 inference(not_proxy_clausification,[],[f288])).
% 0.21/0.42 thf(f288,plain,(
% 0.21/0.42 ((~ (rel_s4 @ sK3 @ sK4)) = $false)),
% 0.21/0.42 inference(binary_proxy_clausification,[],[f269])).
% 0.21/0.42 thf(f269,plain,(
% 0.21/0.42 (((~ (rel_s4 @ sK3 @ sK4)) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (p @ Y0)))))) = $false)),
% 0.21/0.42 inference(beta_eta_normalization,[],[f265])).
% 0.21/0.42 thf(f265,plain,(
% 0.21/0.42 (((^[Y0 : $i]: ((~ (rel_s4 @ sK3 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))))) @ sK4) = $false)),
% 0.21/0.42 inference(sigma_clausification,[],[f251])).
% 0.21/0.42 thf(f251,plain,(
% 0.21/0.42 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK3 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1)))))))) = $false)),
% 0.21/0.42 inference(not_proxy_clausification,[],[f225])).
% 0.21/0.42 thf(f225,plain,(
% 0.21/0.42 ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK3 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))))))) = $true)),
% 0.21/0.42 inference(boolean_simplification,[],[f224])).
% 0.21/0.42 thf(f224,plain,(
% 0.21/0.42 ($true = ($false | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK3 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1)))))))))))),
% 0.21/0.42 inference(boolean_simplification,[],[f221])).
% 0.21/0.42 thf(f221,plain,(
% 0.21/0.42 ($true = ((~ $true) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK3 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1)))))))))))),
% 0.21/0.42 inference(superposition,[],[f211,f162])).
% 0.21/0.42 thf(f162,plain,(
% 0.21/0.42 ( ! [X1 : $i] : (($true = (rel_s4 @ X1 @ X1))) )),
% 0.21/0.42 inference(beta_eta_normalization,[],[f161])).
% 0.21/0.42 thf(f161,plain,(
% 0.21/0.42 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (rel_s4 @ Y0 @ Y0)) @ X1))) )),
% 0.21/0.42 inference(pi_clausification,[],[f157])).
% 0.21/0.42 thf(f157,plain,(
% 0.21/0.42 ($true = (!! @ $i @ (^[Y0 : $i]: (rel_s4 @ Y0 @ Y0))))),
% 0.21/0.42 inference(beta_eta_normalization,[],[f154])).
% 0.21/0.42 thf(f154,plain,(
% 0.21/0.42 ($true = ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) @ rel_s4))),
% 0.21/0.42 inference(definition_unfolding,[],[f110,f142])).
% 0.21/0.42 thf(f142,plain,(
% 0.21/0.42 (mreflexive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))),
% 0.21/0.42 inference(cnf_transformation,[],[f75])).
% 0.21/0.42 thf(f75,plain,(
% 0.21/0.42 (mreflexive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))),
% 0.21/0.42 inference(fool_elimination,[],[f74])).
% 0.21/0.42 thf(f74,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(f110,plain,(
% 0.21/0.42 ((mreflexive @ rel_s4) = $true)),
% 0.21/0.42 inference(cnf_transformation,[],[f45])).
% 0.21/0.42 thf(f45,plain,(
% 0.21/0.42 ((mreflexive @ rel_s4) = $true)),
% 0.21/0.42 inference(fool_elimination,[],[f44])).
% 0.21/0.42 thf(f44,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(f211,plain,(
% 0.21/0.42 ( ! [X1 : $i] : (($true = ((~ (rel_s4 @ sK3 @ X1)) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1)))))))))))) )),
% 0.21/0.42 inference(beta_eta_normalization,[],[f210])).
% 0.21/0.42 thf(f210,plain,(
% 0.21/0.42 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((~ (rel_s4 @ sK3 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (p @ Y2))))))))))) @ X1))) )),
% 0.21/0.42 inference(pi_clausification,[],[f201])).
% 0.21/0.42 thf(f201,plain,(
% 0.21/0.42 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK3 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (p @ Y2)))))))))))) = $true)),
% 0.21/0.42 inference(not_proxy_clausification,[],[f197])).
% 0.21/0.42 thf(f197,plain,(
% 0.21/0.42 ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK3 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (p @ Y2))))))))))))) = $false)),
% 0.21/0.42 inference(boolean_simplification,[],[f196])).
% 0.21/0.42 thf(f196,plain,(
% 0.21/0.42 ($false = ($false | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK3 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (p @ Y2)))))))))))))))),
% 0.21/0.42 inference(backward_demodulation,[],[f191,f195])).
% 0.21/0.42 thf(f195,plain,(
% 0.21/0.42 ((~ (rel_s4 @ sK2 @ sK3)) = $false)),
% 0.21/0.42 inference(binary_proxy_clausification,[],[f191])).
% 0.21/0.42 thf(f191,plain,(
% 0.21/0.42 (((~ (rel_s4 @ sK2 @ sK3)) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK3 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (p @ Y2)))))))))))))) = $false)),
% 0.21/0.42 inference(beta_eta_normalization,[],[f190])).
% 0.21/0.42 thf(f190,plain,(
% 0.21/0.42 (((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (p @ Y3))))))))))))))) @ sK3) = $false)),
% 0.21/0.42 inference(sigma_clausification,[],[f186])).
% 0.21/0.42 thf(f186,plain,(
% 0.21/0.42 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (p @ Y3)))))))))))))))) = $false)),
% 0.21/0.42 inference(boolean_simplification,[],[f185])).
% 0.21/0.42 thf(f185,plain,(
% 0.21/0.42 (($false | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ 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)),
% 0.21/0.42 inference(backward_demodulation,[],[f182,f184])).
% 0.21/0.42 thf(f184,plain,(
% 0.21/0.42 ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))))))) = $false)),
% 0.21/0.42 inference(binary_proxy_clausification,[],[f182])).
% 0.21/0.42 thf(f182,plain,(
% 0.21/0.42 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (p @ Y3))))))))))))))))))),
% 0.21/0.42 inference(beta_eta_normalization,[],[f181])).
% 0.21/0.42 thf(f181,plain,(
% 0.21/0.42 (((^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (p @ Y2))))))))) | (!! @ $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)))))))))))))))))) @ sK2) = $false)),
% 0.21/0.42 inference(sigma_clausification,[],[f178])).
% 0.21/0.42 thf(f178,plain,(
% 0.21/0.42 ((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (p @ Y2))))))))) | (!! @ $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))))))))))))))))))) = $false)),
% 0.21/0.42 inference(not_proxy_clausification,[],[f160])).
% 0.21/0.42 thf(f160,plain,(
% 0.21/0.42 ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (p @ Y2))))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s4 @ Y3 @ Y4)) | (p @ Y4)))))))))))))))))))))),
% 0.21/0.42 inference(boolean_simplification,[],[f159])).
% 0.21/0.42 thf(f159,plain,(
% 0.21/0.42 ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (p @ Y2))))))))) | (~ (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s4 @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (rel_s4 @ Y3 @ Y4)) | (p @ Y4)))))))))))))))))))))))),
% 0.21/0.42 inference(beta_eta_normalization,[],[f155])).
% 0.21/0.42 thf(f155,plain,(
% 0.21/0.42 ($true = (~ ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) | (Y2 @ 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))))))),
% 0.21/0.42 inference(definition_unfolding,[],[f117,f126,f145,f153,f130,f153,f130,f153,f130])).
% 0.21/0.42 thf(f130,plain,(
% 0.21/0.42 (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 0.21/0.42 inference(cnf_transformation,[],[f91])).
% 0.21/0.42 thf(f91,plain,(
% 0.21/0.42 (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s4 @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 0.21/0.42 inference(fool_elimination,[],[f90])).
% 0.21/0.42 thf(f90,plain,(
% 0.21/0.42 ((^[X0 : $i > $o, X1 : $i] : (! [X2] : ((X0 @ X2) | ~(rel_s4 @ X1 @ X2)))) = mbox_s4)),
% 0.21/0.42 inference(rectify,[],[f32])).
% 0.21/0.42 thf(f32,axiom,(
% 0.21/0.42 ((^[X3 : $i > $o, X2 : $i] : (! [X7] : ((X3 @ X7) | ~(rel_s4 @ X2 @ X7)))) = mbox_s4)),
% 0.21/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_s4)).
% 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]: ((~ (rel_s4 @ Y2 @ Y3)) | (Y1 @ Y3))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))))),
% 0.21/0.42 inference(definition_unfolding,[],[f141,f140,f130,f140])).
% 0.21/0.42 thf(f140,plain,(
% 0.21/0.42 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.21/0.42 inference(cnf_transformation,[],[f103])).
% 0.21/0.42 thf(f103,plain,(
% 0.21/0.42 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.21/0.42 inference(fool_elimination,[],[f102])).
% 0.21/0.42 thf(f102,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(f141,plain,(
% 0.21/0.42 (mdia_s4 = (^[Y0 : $i > $o]: (mnot @ (mbox_s4 @ (mnot @ Y0)))))),
% 0.21/0.42 inference(cnf_transformation,[],[f89])).
% 0.21/0.42 thf(f89,plain,(
% 0.21/0.42 (mdia_s4 = (^[Y0 : $i > $o]: (mnot @ (mbox_s4 @ (mnot @ Y0)))))),
% 0.21/0.42 inference(fool_elimination,[],[f88])).
% 0.21/0.42 thf(f88,plain,(
% 0.21/0.42 ((^[X0 : $i > $o] : (mnot @ (mbox_s4 @ (mnot @ X0)))) = mdia_s4)),
% 0.21/0.42 inference(rectify,[],[f33])).
% 0.21/0.42 thf(f33,axiom,(
% 0.21/0.42 ((^[X3 : $i > $o] : (mnot @ (mbox_s4 @ (mnot @ X3)))) = mdia_s4)),
% 0.21/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mdia_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]: ((Y3 @ Y4) | (Y2 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))))),
% 0.21/0.42 inference(definition_unfolding,[],[f127,f111,f140])).
% 0.21/0.42 thf(f111,plain,(
% 0.21/0.42 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.21/0.42 inference(cnf_transformation,[],[f97])).
% 0.21/0.42 thf(f97,plain,(
% 0.21/0.42 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.21/0.42 inference(fool_elimination,[],[f96])).
% 0.21/0.42 thf(f96,plain,(
% 0.21/0.42 ((^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X0 @ X2) | (X1 @ X2))) = mor)),
% 0.21/0.42 inference(rectify,[],[f4])).
% 0.21/0.42 thf(f4,axiom,(
% 0.21/0.42 ((^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X3 @ X2) | (X4 @ X2))) = mor)),
% 0.21/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor)).
% 0.21/0.42 thf(f127,plain,(
% 0.21/0.42 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.21/0.42 inference(cnf_transformation,[],[f83])).
% 0.21/0.42 thf(f83,plain,(
% 0.21/0.42 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.21/0.42 inference(fool_elimination,[],[f82])).
% 0.21/0.42 thf(f82,plain,(
% 0.21/0.42 ((^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)) = mimplies)),
% 0.21/0.42 inference(rectify,[],[f6])).
% 0.21/0.42 thf(f6,axiom,(
% 0.21/0.42 ((^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)) = mimplies)),
% 0.21/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies)).
% 0.21/0.42 thf(f126,plain,(
% 0.21/0.42 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.21/0.42 inference(cnf_transformation,[],[f81])).
% 0.21/0.42 thf(f81,plain,(
% 0.21/0.42 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.21/0.42 inference(fool_elimination,[],[f80])).
% 0.21/0.42 thf(f80,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 > $o] : (! [X2] : (X3 @ X2))) = mvalid)),
% 0.21/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mvalid)).
% 0.21/0.42 thf(f117,plain,(
% 0.21/0.42 ($true = (~ (mvalid @ (mimplies @ (mdia_s4 @ (mbox_s4 @ (mdia_s4 @ (mbox_s4 @ p)))) @ (mdia_s4 @ (mbox_s4 @ p))))))),
% 0.21/0.42 inference(cnf_transformation,[],[f56])).
% 0.21/0.42 thf(f56,plain,(
% 0.21/0.42 ($true = (~ (mvalid @ (mimplies @ (mdia_s4 @ (mbox_s4 @ (mdia_s4 @ (mbox_s4 @ p)))) @ (mdia_s4 @ (mbox_s4 @ p))))))),
% 0.21/0.42 inference(fool_elimination,[],[f55])).
% 0.21/0.42 thf(f55,plain,(
% 0.21/0.42 ~(mvalid @ (mimplies @ (mdia_s4 @ (mbox_s4 @ (mdia_s4 @ (mbox_s4 @ p)))) @ (mdia_s4 @ (mbox_s4 @ p))))),
% 0.21/0.42 inference(rectify,[],[f37])).
% 0.21/0.42 thf(f37,negated_conjecture,(
% 0.21/0.42 ~(mvalid @ (mimplies @ (mdia_s4 @ (mbox_s4 @ (mdia_s4 @ (mbox_s4 @ p)))) @ (mdia_s4 @ (mbox_s4 @ p))))),
% 0.21/0.42 inference(negated_conjecture,[],[f36])).
% 0.21/0.42 thf(f36,conjecture,(
% 0.21/0.42 (mvalid @ (mimplies @ (mdia_s4 @ (mbox_s4 @ (mdia_s4 @ (mbox_s4 @ p)))) @ (mdia_s4 @ (mbox_s4 @ p))))),
% 0.21/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove)).
% 0.21/0.42 thf(f209,plain,(
% 0.21/0.42 ( ! [X0 : $i] : ((((rel_s4 @ sK3 @ X0) => (rel_s4 @ sK2 @ X0)) = $true)) )),
% 0.21/0.42 inference(boolean_simplification,[],[f205])).
% 0.21/0.42 thf(f205,plain,(
% 0.21/0.42 ( ! [X0 : $i] : (($true = (((rel_s4 @ sK3 @ X0) & $true) => (rel_s4 @ sK2 @ X0)))) )),
% 0.21/0.42 inference(superposition,[],[f168,f198])).
% 0.21/0.42 thf(f198,plain,(
% 0.21/0.42 ($true = (rel_s4 @ sK2 @ sK3))),
% 0.21/0.42 inference(not_proxy_clausification,[],[f195])).
% 0.21/0.42 thf(f168,plain,(
% 0.21/0.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((rel_s4 @ X3 @ X1) & (rel_s4 @ X2 @ X3)) => (rel_s4 @ X2 @ X1)))) )),
% 0.21/0.42 inference(beta_eta_normalization,[],[f167])).
% 0.21/0.42 thf(f167,plain,(
% 0.21/0.42 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (((rel_s4 @ Y0 @ X1) & (rel_s4 @ X2 @ Y0)) => (rel_s4 @ X2 @ X1))) @ X3))) )),
% 0.21/0.42 inference(pi_clausification,[],[f166])).
% 0.21/0.42 thf(f166,plain,(
% 0.21/0.42 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (((rel_s4 @ Y0 @ X1) & (rel_s4 @ X2 @ Y0)) => (rel_s4 @ X2 @ X1)))))) )),
% 0.21/0.42 inference(beta_eta_normalization,[],[f165])).
% 0.21/0.42 thf(f165,plain,(
% 0.21/0.42 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((rel_s4 @ Y1 @ X1) & (rel_s4 @ Y0 @ Y1)) => (rel_s4 @ Y0 @ X1))))) @ X2))) )),
% 0.21/0.42 inference(pi_clausification,[],[f164])).
% 0.21/0.42 thf(f164,plain,(
% 0.21/0.42 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((rel_s4 @ Y1 @ X1) & (rel_s4 @ Y0 @ Y1)) => (rel_s4 @ Y0 @ X1)))))))) )),
% 0.21/0.42 inference(beta_eta_normalization,[],[f163])).
% 0.21/0.42 thf(f163,plain,(
% 0.21/0.42 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((rel_s4 @ Y2 @ Y0) & (rel_s4 @ Y1 @ Y2)) => (rel_s4 @ Y1 @ Y0))))))) @ X1))) )),
% 0.21/0.42 inference(pi_clausification,[],[f158])).
% 0.21/0.42 thf(f158,plain,(
% 0.21/0.42 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((rel_s4 @ Y2 @ Y0) & (rel_s4 @ Y1 @ Y2)) => (rel_s4 @ Y1 @ Y0)))))))))),
% 0.21/0.42 inference(beta_eta_normalization,[],[f156])).
% 0.21/0.42 thf(f156,plain,(
% 0.21/0.42 (((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y2 @ Y1))))))))) @ rel_s4) = $true)),
% 0.21/0.42 inference(definition_unfolding,[],[f135,f133])).
% 0.21/0.42 thf(f133,plain,(
% 0.21/0.42 (mtransitive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y2 @ Y1))))))))))),
% 0.21/0.42 inference(cnf_transformation,[],[f43])).
% 0.21/0.42 thf(f43,plain,(
% 0.21/0.42 (mtransitive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y1) & (Y0 @ Y2 @ Y3)) => (Y0 @ Y2 @ Y1))))))))))),
% 0.21/0.42 inference(fool_elimination,[],[f42])).
% 0.21/0.42 thf(f42,plain,(
% 0.21/0.42 ((^[X0 : $i > $i > $o] : (! [X1,X2,X3] : (((X0 @ X2 @ X1) & (X0 @ X1 @ X3)) => (X0 @ X2 @ X3)))) = mtransitive)),
% 0.21/0.42 inference(rectify,[],[f21])).
% 0.21/0.42 thf(f21,axiom,(
% 0.21/0.42 ((^[X6 : $i > $i > $o] : (! [X9,X8,X10] : (((X6 @ X8 @ X9) & (X6 @ X9 @ X10)) => (X6 @ X8 @ X10)))) = mtransitive)),
% 0.21/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mtransitive)).
% 0.21/0.42 thf(f135,plain,(
% 0.21/0.42 ((mtransitive @ rel_s4) = $true)),
% 0.21/0.42 inference(cnf_transformation,[],[f51])).
% 0.21/0.42 thf(f51,plain,(
% 0.21/0.42 ((mtransitive @ rel_s4) = $true)),
% 0.21/0.42 inference(fool_elimination,[],[f50])).
% 0.21/0.42 thf(f50,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 thf(f298,plain,(
% 0.21/0.42 ((~ (rel_s4 @ sK2 @ sK4)) = $true)),
% 0.21/0.42 inference(boolean_simplification,[],[f297])).
% 0.21/0.42 thf(f297,plain,(
% 0.21/0.42 ($true = ((~ (rel_s4 @ sK2 @ sK4)) | $false))),
% 0.21/0.42 inference(superposition,[],[f193,f290])).
% 0.21/0.42 thf(f290,plain,(
% 0.21/0.42 ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (p @ Y0))))) = $false)),
% 0.21/0.42 inference(boolean_simplification,[],[f289])).
% 0.21/0.42 thf(f289,plain,(
% 0.21/0.42 (($false | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK4 @ Y0)) | (p @ Y0)))))) = $false)),
% 0.21/0.42 inference(backward_demodulation,[],[f269,f288])).
% 0.21/0.42 thf(f193,plain,(
% 0.21/0.42 ( ! [X1 : $i] : (($true = ((~ (rel_s4 @ sK2 @ X1)) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ X1 @ Y0)) | (p @ Y0)))))))) )),
% 0.21/0.42 inference(beta_eta_normalization,[],[f192])).
% 0.21/0.42 thf(f192,plain,(
% 0.21/0.42 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1))))))) @ X1))) )),
% 0.21/0.42 inference(pi_clausification,[],[f187])).
% 0.21/0.42 thf(f187,plain,(
% 0.21/0.42 ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s4 @ sK2 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s4 @ Y0 @ Y1)) | (p @ Y1)))))))))),
% 0.21/0.42 inference(not_proxy_clausification,[],[f184])).
% 0.21/0.42 % SZS output end Proof for theBenchmark
% 0.21/0.42 % (27809)------------------------------
% 0.21/0.42 % (27809)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.42 % (27809)Termination reason: Refutation
% 0.21/0.42
% 0.21/0.42 % (27809)Memory used [KB]: 5884
% 0.21/0.42 % (27809)Time elapsed: 0.022 s
% 0.21/0.42 % (27809)Instructions burned: 33 (million)
% 0.21/0.42 % (27809)------------------------------
% 0.21/0.42 % (27809)------------------------------
% 0.21/0.42 % (27797)Success in time 0.059 s
% 0.21/0.42 % Vampire---4.8 exiting
%------------------------------------------------------------------------------