TSTP Solution File: SYO415^1 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SYO415^1 : 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 : n006.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 09:04:21 EDT 2024
% Result : Theorem 0.16s 0.40s
% Output : Refutation 0.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SYO415^1 : TPTP v8.2.0. Released v4.0.0.
% 0.13/0.15 % 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
% 0.16/0.36 % Computer : n006.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Mon May 20 08:48:53 EDT 2024
% 0.16/0.36 % CPUTime :
% 0.16/0.36 This is a TH0_THM_EQU_NAR problem
% 0.16/0.36 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
% 0.16/0.38 % (19341)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.16/0.38 % (19342)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)
% 0.16/0.38 % (19343)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)
% 0.16/0.38 % (19344)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.16/0.38 % (19346)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)
% 0.16/0.38 % (19347)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.16/0.38 % (19344)Instruction limit reached!
% 0.16/0.38 % (19344)------------------------------
% 0.16/0.38 % (19344)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.38 % (19344)Termination reason: Unknown
% 0.16/0.38 % (19344)Termination phase: shuffling
% 0.16/0.38
% 0.16/0.38 % (19344)Memory used [KB]: 1023
% 0.16/0.38 % (19344)Time elapsed: 0.003 s
% 0.16/0.38 % (19344)Instructions burned: 2 (million)
% 0.16/0.38 % (19344)------------------------------
% 0.16/0.38 % (19344)------------------------------
% 0.16/0.38 % (19342)Instruction limit reached!
% 0.16/0.38 % (19342)------------------------------
% 0.16/0.38 % (19342)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.38 % (19342)Termination reason: Unknown
% 0.16/0.38 % (19342)Termination phase: shuffling
% 0.16/0.38
% 0.16/0.39 % (19342)Memory used [KB]: 1023
% 0.16/0.39 % (19342)Time elapsed: 0.004 s
% 0.16/0.39 % (19342)Instructions burned: 4 (million)
% 0.16/0.39 % (19342)------------------------------
% 0.16/0.39 % (19342)------------------------------
% 0.16/0.39 % (19346)Refutation not found, incomplete strategy
% 0.16/0.39 % (19346)------------------------------
% 0.16/0.39 % (19346)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.39 % (19346)Termination reason: Refutation not found, incomplete strategy
% 0.16/0.39
% 0.16/0.39
% 0.16/0.39 % (19346)Memory used [KB]: 5628
% 0.16/0.39 % (19346)Time elapsed: 0.007 s
% 0.16/0.39 % (19346)Instructions burned: 8 (million)
% 0.16/0.39 % (19346)------------------------------
% 0.16/0.39 % (19346)------------------------------
% 0.16/0.39 % (19345)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)
% 0.16/0.39 % (19345)Instruction limit reached!
% 0.16/0.39 % (19345)------------------------------
% 0.16/0.39 % (19345)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.39 % (19345)Termination reason: Unknown
% 0.16/0.39 % (19345)Termination phase: shuffling
% 0.16/0.39
% 0.16/0.39 % (19345)Memory used [KB]: 1023
% 0.16/0.39 % (19345)Time elapsed: 0.003 s
% 0.16/0.39 % (19345)Instructions burned: 2 (million)
% 0.16/0.39 % (19345)------------------------------
% 0.16/0.39 % (19345)------------------------------
% 0.16/0.39 % (19347)First to succeed.
% 0.16/0.40 % (19348)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)
% 0.16/0.40 % (19341)Also succeeded, but the first one will report.
% 0.16/0.40 % (19348)Instruction limit reached!
% 0.16/0.40 % (19348)------------------------------
% 0.16/0.40 % (19348)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.40 % (19348)Termination reason: Unknown
% 0.16/0.40 % (19348)Termination phase: shuffling
% 0.16/0.40
% 0.16/0.40 % (19348)Memory used [KB]: 1023
% 0.16/0.40 % (19348)Time elapsed: 0.004 s
% 0.16/0.40 % (19348)Instructions burned: 4 (million)
% 0.16/0.40 % (19348)------------------------------
% 0.16/0.40 % (19348)------------------------------
% 0.16/0.40 % (19347)Refutation found. Thanks to Tanya!
% 0.16/0.40 % SZS status Theorem for theBenchmark
% 0.16/0.40 % SZS output start Proof for theBenchmark
% 0.16/0.40 thf(type_def_5, type, mu: $tType).
% 0.16/0.40 thf(func_def_0, type, mu: $tType).
% 0.16/0.40 thf(func_def_1, type, meq_ind: mu > mu > $i > $o).
% 0.16/0.40 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.16/0.40 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.16/0.40 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.16/0.40 thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.16/0.40 thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.16/0.40 thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.16/0.40 thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.16/0.40 thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.16/0.40 thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.16/0.40 thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.16/0.40 thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.16/0.40 thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.16/0.40 thf(func_def_15, type, mtrue: $i > $o).
% 0.16/0.40 thf(func_def_16, type, mfalse: $i > $o).
% 0.16/0.40 thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.16/0.40 thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.16/0.40 thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o).
% 0.16/0.40 thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o).
% 0.16/0.40 thf(func_def_21, type, mserial: ($i > $i > $o) > $o).
% 0.16/0.40 thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o).
% 0.16/0.40 thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o).
% 0.16/0.40 thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.16/0.40 thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o).
% 0.16/0.40 thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.16/0.40 thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.16/0.40 thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.16/0.40 thf(func_def_29, type, mvalid: ($i > $o) > $o).
% 0.16/0.40 thf(func_def_30, type, minvalid: ($i > $o) > $o).
% 0.16/0.40 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.16/0.40 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.16/0.40 thf(func_def_33, type, rel_k: $i > $i > $o).
% 0.16/0.40 thf(func_def_34, type, mbox_k: ($i > $o) > $i > $o).
% 0.16/0.40 thf(func_def_35, type, mdia_k: ($i > $o) > $i > $o).
% 0.16/0.40 thf(func_def_36, type, p: $i > $o).
% 0.16/0.40 thf(func_def_37, type, q: $i > $o).
% 0.16/0.40 thf(func_def_56, type, sK3: $i > $i).
% 0.16/0.40 thf(f225,plain,(
% 0.16/0.40 $false),
% 0.16/0.40 inference(trivial_inequality_removal,[],[f224])).
% 0.16/0.40 thf(f224,plain,(
% 0.16/0.40 ($false = $true)),
% 0.16/0.40 inference(forward_demodulation,[],[f223,f221])).
% 0.16/0.40 thf(f221,plain,(
% 0.16/0.40 ($false = (q @ (sK3 @ sK2)))),
% 0.16/0.40 inference(trivial_inequality_removal,[],[f215])).
% 0.16/0.40 thf(f215,plain,(
% 0.16/0.40 ($false = (q @ (sK3 @ sK2))) | ($false = $true)),
% 0.16/0.40 inference(superposition,[],[f213,f205])).
% 0.16/0.40 thf(f205,plain,(
% 0.16/0.40 ( ! [X0 : $i] : (((rel_k @ sK2 @ X0) = $false) | ((q @ X0) = $false)) )),
% 0.16/0.40 inference(trivial_inequality_removal,[],[f202])).
% 0.16/0.40 thf(f202,plain,(
% 0.16/0.40 ( ! [X0 : $i] : (((rel_k @ sK2 @ X0) = $false) | ((q @ X0) = $false) | ($false = $true)) )),
% 0.16/0.40 inference(superposition,[],[f171,f164])).
% 0.16/0.40 thf(f164,plain,(
% 0.16/0.40 ( ! [X2 : $i,X1 : $i] : (((rel_k @ sK1 @ X1) = $false) | ($false = (rel_k @ X1 @ X2)) | ((q @ X2) = $false)) )),
% 0.16/0.40 inference(not_proxy_clausification,[],[f163])).
% 0.16/0.40 thf(f163,plain,(
% 0.16/0.40 ( ! [X2 : $i,X1 : $i] : (((~ (q @ X2)) = $true) | ((rel_k @ sK1 @ X1) = $false) | ($false = (rel_k @ X1 @ X2))) )),
% 0.16/0.40 inference(not_proxy_clausification,[],[f162])).
% 0.16/0.40 thf(f162,plain,(
% 0.16/0.40 ( ! [X2 : $i,X1 : $i] : (($false = (rel_k @ X1 @ X2)) | ($true = (~ (rel_k @ sK1 @ X1))) | ((~ (q @ X2)) = $true)) )),
% 0.16/0.40 inference(not_proxy_clausification,[],[f161])).
% 0.16/0.40 thf(f161,plain,(
% 0.16/0.40 ( ! [X2 : $i,X1 : $i] : (((~ (rel_k @ X1 @ X2)) = $true) | ((~ (q @ X2)) = $true) | ($true = (~ (rel_k @ sK1 @ X1)))) )),
% 0.16/0.40 inference(binary_proxy_clausification,[],[f160])).
% 0.16/0.40 thf(f160,plain,(
% 0.16/0.40 ( ! [X2 : $i,X1 : $i] : ((((~ (rel_k @ X1 @ X2)) | (~ (q @ X2))) = $true) | ($true = (~ (rel_k @ sK1 @ X1)))) )),
% 0.16/0.40 inference(beta_eta_normalization,[],[f159])).
% 0.16/0.40 thf(f159,plain,(
% 0.16/0.40 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((~ (rel_k @ X1 @ Y0)) | (~ (q @ Y0)))) @ X2) = $true) | ($true = (~ (rel_k @ sK1 @ X1)))) )),
% 0.16/0.40 inference(pi_clausification,[],[f158])).
% 0.16/0.40 thf(f158,plain,(
% 0.16/0.40 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ X1 @ Y0)) | (~ (q @ Y0))))) = $true) | ($true = (~ (rel_k @ sK1 @ X1)))) )),
% 0.16/0.40 inference(binary_proxy_clausification,[],[f157])).
% 0.16/0.40 thf(f157,plain,(
% 0.16/0.40 ( ! [X1 : $i] : ((((~ (rel_k @ sK1 @ X1)) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ X1 @ Y0)) | (~ (q @ Y0)))))) = $true)) )),
% 0.16/0.40 inference(beta_eta_normalization,[],[f156])).
% 0.16/0.40 thf(f156,plain,(
% 0.16/0.40 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | (~ (q @ Y1))))))) @ X1))) )),
% 0.16/0.40 inference(pi_clausification,[],[f155])).
% 0.16/0.40 thf(f155,plain,(
% 0.16/0.40 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | (~ (q @ Y1)))))))) = $true)),
% 0.16/0.40 inference(not_proxy_clausification,[],[f154])).
% 0.16/0.40 thf(f154,plain,(
% 0.16/0.40 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | (~ (q @ Y1))))))))))),
% 0.16/0.40 inference(binary_proxy_clausification,[],[f152])).
% 0.16/0.40 thf(f152,plain,(
% 0.16/0.40 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | (~ (q @ Y1))))))))) | ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | ((q @ Y1) | (~ (p @ Y1)))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | (~ (p @ Y1)))))))))))))),
% 0.16/0.40 inference(beta_eta_normalization,[],[f151])).
% 0.16/0.40 thf(f151,plain,(
% 0.16/0.40 ($false = ((^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_k @ Y1 @ Y2)) | (~ (q @ Y2))))))))) | ((!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_k @ Y1 @ Y2)) | ((q @ Y2) | (~ (p @ Y2)))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_k @ Y1 @ Y2)) | (~ (p @ Y2))))))))))))) @ sK1))),
% 0.16/0.40 inference(sigma_clausification,[],[f150])).
% 0.16/0.40 thf(f150,plain,(
% 0.16/0.40 ($true != (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (rel_k @ Y1 @ Y2)) | (~ (q @ Y2))))))))) | ((!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_k @ Y1 @ Y2)) | ((q @ Y2) | (~ (p @ Y2)))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_k @ Y1 @ Y2)) | (~ (p @ Y2)))))))))))))))),
% 0.16/0.40 inference(boolean_simplification,[],[f149])).
% 0.16/0.40 thf(f149,plain,(
% 0.16/0.40 ((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | (~ (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_k @ Y1 @ Y2)) | (~ (q @ Y2))))))))))) | ((!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_k @ Y1 @ Y2)) | ((q @ Y2) | (~ (p @ Y2)))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_k @ Y1 @ Y2)) | (~ (p @ Y2)))))))))))))) != $true)),
% 0.16/0.40 inference(boolean_simplification,[],[f148])).
% 0.16/0.40 thf(f148,plain,(
% 0.16/0.40 ((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | (~ (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_k @ Y1 @ Y2)) | (~ (q @ Y2))))))))))) | ((~ (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_k @ Y1 @ Y2)) | ((q @ Y2) | (~ (p @ Y2)))))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_k @ Y1 @ Y2)) | (~ (p @ Y2)))))))))))))) != $true)),
% 0.16/0.40 inference(boolean_simplification,[],[f147])).
% 0.16/0.40 thf(f147,plain,(
% 0.16/0.40 ((!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | (~ (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_k @ Y1 @ Y2)) | (~ (q @ Y2))))))))))) | (~ (~ ((~ (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_k @ Y1 @ Y2)) | ((q @ Y2) | (~ (p @ Y2)))))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_k @ Y1 @ Y2)) | (~ (p @ Y2)))))))))))))))) != $true)),
% 0.16/0.40 inference(beta_eta_normalization,[],[f146])).
% 0.16/0.40 thf(f146,plain,(
% 0.16/0.40 (((^[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 > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) | (Y2 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_k @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (rel_k @ Y2 @ Y3)) | (Y1 @ Y3))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))) @ p)) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (rel_k @ Y2 @ Y3)) | (Y1 @ Y3))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_k @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ ((^[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)))) @ p @ q)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (rel_k @ Y2 @ Y3)) | (Y1 @ Y3))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (rel_k @ Y2 @ Y3)) | (Y1 @ Y3))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))) @ q)))) != $true)),
% 0.16/0.40 inference(definition_unfolding,[],[f132,f124,f137,f136,f106,f145,f145,f106,f137,f145,f145])).
% 0.16/0.40 thf(f145,plain,(
% 0.16/0.40 (mdia_k = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (rel_k @ Y2 @ Y3)) | (Y1 @ Y3))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))))),
% 0.16/0.40 inference(definition_unfolding,[],[f134,f119,f106,f119])).
% 0.16/0.40 thf(f119,plain,(
% 0.16/0.40 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.16/0.40 inference(cnf_transformation,[],[f78])).
% 0.16/0.40 thf(f78,plain,(
% 0.16/0.40 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.16/0.40 inference(fool_elimination,[],[f77])).
% 0.16/0.40 thf(f77,plain,(
% 0.16/0.40 (mnot = (^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))))),
% 0.16/0.40 inference(rectify,[],[f3])).
% 0.16/0.40 thf(f3,axiom,(
% 0.16/0.40 (mnot = (^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))))),
% 0.16/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot)).
% 0.16/0.40 thf(f134,plain,(
% 0.16/0.40 (mdia_k = (^[Y0 : $i > $o]: (mnot @ (mbox_k @ (mnot @ Y0)))))),
% 0.16/0.40 inference(cnf_transformation,[],[f68])).
% 0.16/0.40 thf(f68,plain,(
% 0.16/0.40 (mdia_k = (^[Y0 : $i > $o]: (mnot @ (mbox_k @ (mnot @ Y0)))))),
% 0.16/0.40 inference(fool_elimination,[],[f67])).
% 0.16/0.40 thf(f67,plain,(
% 0.16/0.40 ((^[X0 : $i > $o] : (mnot @ (mbox_k @ (mnot @ X0)))) = mdia_k)),
% 0.16/0.40 inference(rectify,[],[f33])).
% 0.16/0.40 thf(f33,axiom,(
% 0.16/0.40 ((^[X3 : $i > $o] : (mnot @ (mbox_k @ (mnot @ X3)))) = mdia_k)),
% 0.16/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mdia_k)).
% 0.16/0.40 thf(f106,plain,(
% 0.16/0.40 (mbox_k = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_k @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 0.16/0.40 inference(cnf_transformation,[],[f46])).
% 0.16/0.40 thf(f46,plain,(
% 0.16/0.40 (mbox_k = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_k @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 0.16/0.40 inference(fool_elimination,[],[f45])).
% 0.16/0.40 thf(f45,plain,(
% 0.16/0.40 ((^[X0 : $i > $o, X1 : $i] : (! [X2] : ((X0 @ X2) | ~(rel_k @ X1 @ X2)))) = mbox_k)),
% 0.16/0.40 inference(rectify,[],[f32])).
% 0.16/0.40 thf(f32,axiom,(
% 0.16/0.40 ((^[X3 : $i > $o, X2 : $i] : (! [X7] : ((X3 @ X7) | ~(rel_k @ X2 @ X7)))) = mbox_k)),
% 0.16/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_k)).
% 0.16/0.40 thf(f136,plain,(
% 0.16/0.40 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) | (Y2 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))))),
% 0.16/0.40 inference(definition_unfolding,[],[f108,f119,f114,f119,f119])).
% 0.16/0.40 thf(f114,plain,(
% 0.16/0.40 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.16/0.40 inference(cnf_transformation,[],[f40])).
% 0.16/0.40 thf(f40,plain,(
% 0.16/0.40 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.16/0.40 inference(fool_elimination,[],[f39])).
% 0.16/0.40 thf(f39,plain,(
% 0.16/0.40 ((^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X0 @ X2) | (X1 @ X2))) = mor)),
% 0.16/0.40 inference(rectify,[],[f4])).
% 0.16/0.40 thf(f4,axiom,(
% 0.16/0.40 ((^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X3 @ X2) | (X4 @ X2))) = mor)),
% 0.16/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor)).
% 0.16/0.40 thf(f108,plain,(
% 0.16/0.40 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.16/0.40 inference(cnf_transformation,[],[f50])).
% 0.16/0.40 thf(f50,plain,(
% 0.16/0.40 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.16/0.40 inference(fool_elimination,[],[f49])).
% 0.16/0.40 thf(f49,plain,(
% 0.16/0.40 ((^[X0 : $i > $o, X1 : $i > $o] : (mnot @ (mor @ (mnot @ X0) @ (mnot @ X1)))) = mand)),
% 0.16/0.40 inference(rectify,[],[f5])).
% 0.16/0.40 thf(f5,axiom,(
% 0.16/0.40 ((^[X3 : $i > $o, X4 : $i > $o] : (mnot @ (mor @ (mnot @ X3) @ (mnot @ X4)))) = mand)),
% 0.16/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mand)).
% 0.16/0.40 thf(f137,plain,(
% 0.16/0.40 (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)))))),
% 0.16/0.40 inference(definition_unfolding,[],[f129,f114,f119])).
% 0.16/0.40 thf(f129,plain,(
% 0.16/0.40 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.16/0.40 inference(cnf_transformation,[],[f80])).
% 0.16/0.40 thf(f80,plain,(
% 0.16/0.40 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.16/0.40 inference(fool_elimination,[],[f79])).
% 0.16/0.40 thf(f79,plain,(
% 0.16/0.40 ((^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)) = mimplies)),
% 0.16/0.40 inference(rectify,[],[f6])).
% 0.16/0.40 thf(f6,axiom,(
% 0.16/0.40 ((^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)) = mimplies)),
% 0.16/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies)).
% 0.16/0.40 thf(f124,plain,(
% 0.16/0.40 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.16/0.40 inference(cnf_transformation,[],[f91])).
% 0.16/0.40 thf(f91,plain,(
% 0.16/0.40 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.16/0.40 inference(fool_elimination,[],[f90])).
% 0.16/0.40 thf(f90,plain,(
% 0.16/0.40 (mvalid = (^[X0 : $i > $o] : (! [X1] : (X0 @ X1))))),
% 0.16/0.40 inference(rectify,[],[f28])).
% 0.16/0.40 thf(f28,axiom,(
% 0.16/0.40 (mvalid = (^[X3 : $i > $o] : (! [X2] : (X3 @ X2))))),
% 0.16/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mvalid)).
% 0.16/0.40 thf(f132,plain,(
% 0.16/0.40 ((mvalid @ (mimplies @ (mand @ (mbox_k @ (mdia_k @ p)) @ (mdia_k @ (mbox_k @ (mimplies @ p @ q)))) @ (mdia_k @ (mdia_k @ q)))) != $true)),
% 0.16/0.40 inference(cnf_transformation,[],[f101])).
% 0.16/0.40 thf(f101,plain,(
% 0.16/0.40 ((mvalid @ (mimplies @ (mand @ (mbox_k @ (mdia_k @ p)) @ (mdia_k @ (mbox_k @ (mimplies @ p @ q)))) @ (mdia_k @ (mdia_k @ q)))) != $true)),
% 0.16/0.40 inference(flattening,[],[f42])).
% 0.16/0.40 thf(f42,plain,(
% 0.16/0.40 ~((mvalid @ (mimplies @ (mand @ (mbox_k @ (mdia_k @ p)) @ (mdia_k @ (mbox_k @ (mimplies @ p @ q)))) @ (mdia_k @ (mdia_k @ q)))) = $true)),
% 0.16/0.40 inference(fool_elimination,[],[f41])).
% 0.16/0.40 thf(f41,plain,(
% 0.16/0.40 ~(mvalid @ (mimplies @ (mand @ (mbox_k @ (mdia_k @ p)) @ (mdia_k @ (mbox_k @ (mimplies @ p @ q)))) @ (mdia_k @ (mdia_k @ q))))),
% 0.16/0.40 inference(rectify,[],[f35])).
% 0.16/0.40 thf(f35,negated_conjecture,(
% 0.16/0.40 ~(mvalid @ (mimplies @ (mand @ (mbox_k @ (mdia_k @ p)) @ (mdia_k @ (mbox_k @ (mimplies @ p @ q)))) @ (mdia_k @ (mdia_k @ q))))),
% 0.16/0.40 inference(negated_conjecture,[],[f34])).
% 0.16/0.40 thf(f34,conjecture,(
% 0.16/0.40 (mvalid @ (mimplies @ (mand @ (mbox_k @ (mdia_k @ p)) @ (mdia_k @ (mbox_k @ (mimplies @ p @ q)))) @ (mdia_k @ (mdia_k @ q))))),
% 0.16/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove)).
% 0.16/0.40 thf(f171,plain,(
% 0.16/0.40 ($true = (rel_k @ sK1 @ sK2))),
% 0.16/0.40 inference(not_proxy_clausification,[],[f170])).
% 0.16/0.40 thf(f170,plain,(
% 0.16/0.40 ((~ (rel_k @ sK1 @ sK2)) = $false)),
% 0.16/0.40 inference(binary_proxy_clausification,[],[f168])).
% 0.16/0.40 thf(f168,plain,(
% 0.16/0.40 (((~ (rel_k @ sK1 @ sK2)) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK2 @ Y0)) | ((q @ Y0) | (~ (p @ Y0)))))))) = $false)),
% 0.16/0.40 inference(beta_eta_normalization,[],[f167])).
% 0.16/0.40 thf(f167,plain,(
% 0.16/0.40 (((^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | ((q @ Y1) | (~ (p @ Y1))))))))) @ sK2) = $false)),
% 0.16/0.40 inference(sigma_clausification,[],[f166])).
% 0.16/0.40 thf(f166,plain,(
% 0.16/0.40 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | ((q @ Y1) | (~ (p @ Y1)))))))))) = $false)),
% 0.16/0.40 inference(binary_proxy_clausification,[],[f153])).
% 0.16/0.40 thf(f153,plain,(
% 0.16/0.40 (((!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | ((q @ Y1) | (~ (p @ Y1)))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | (~ (p @ Y1))))))))))) = $false)),
% 0.16/0.40 inference(binary_proxy_clausification,[],[f152])).
% 0.16/0.40 thf(f213,plain,(
% 0.16/0.40 ((rel_k @ sK2 @ (sK3 @ sK2)) = $true)),
% 0.16/0.40 inference(trivial_inequality_removal,[],[f210])).
% 0.16/0.40 thf(f210,plain,(
% 0.16/0.40 ((rel_k @ sK2 @ (sK3 @ sK2)) = $true) | ($false = $true)),
% 0.16/0.40 inference(superposition,[],[f189,f171])).
% 0.16/0.40 thf(f189,plain,(
% 0.16/0.40 ( ! [X1 : $i] : (((rel_k @ sK1 @ X1) = $false) | ((rel_k @ X1 @ (sK3 @ X1)) = $true)) )),
% 0.16/0.40 inference(not_proxy_clausification,[],[f188])).
% 0.16/0.40 thf(f188,plain,(
% 0.16/0.40 ( ! [X1 : $i] : (((~ (rel_k @ X1 @ (sK3 @ X1))) = $false) | ((rel_k @ sK1 @ X1) = $false)) )),
% 0.16/0.40 inference(binary_proxy_clausification,[],[f186])).
% 0.16/0.40 thf(f186,plain,(
% 0.16/0.40 ( ! [X1 : $i] : (($false = ((~ (rel_k @ X1 @ (sK3 @ X1))) | (~ (p @ (sK3 @ X1))))) | ((rel_k @ sK1 @ X1) = $false)) )),
% 0.16/0.40 inference(beta_eta_normalization,[],[f185])).
% 0.16/0.40 thf(f185,plain,(
% 0.16/0.40 ( ! [X1 : $i] : (((rel_k @ sK1 @ X1) = $false) | ($false = ((^[Y0 : $i]: ((~ (rel_k @ X1 @ Y0)) | (~ (p @ Y0)))) @ (sK3 @ X1)))) )),
% 0.16/0.40 inference(sigma_clausification,[],[f184])).
% 0.16/0.40 thf(f184,plain,(
% 0.16/0.40 ( ! [X1 : $i] : (((rel_k @ sK1 @ X1) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ X1 @ Y0)) | (~ (p @ Y0))))))) )),
% 0.16/0.40 inference(not_proxy_clausification,[],[f183])).
% 0.16/0.40 thf(f183,plain,(
% 0.16/0.40 ( ! [X1 : $i] : (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ X1 @ Y0)) | (~ (p @ Y0)))))) = $true) | ((rel_k @ sK1 @ X1) = $false)) )),
% 0.16/0.40 inference(not_proxy_clausification,[],[f182])).
% 0.16/0.40 thf(f182,plain,(
% 0.16/0.40 ( ! [X1 : $i] : (($true = (~ (rel_k @ sK1 @ X1))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ X1 @ Y0)) | (~ (p @ Y0)))))) = $true)) )),
% 0.16/0.40 inference(binary_proxy_clausification,[],[f181])).
% 0.16/0.40 thf(f181,plain,(
% 0.16/0.40 ( ! [X1 : $i] : ((((~ (rel_k @ sK1 @ X1)) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ X1 @ Y0)) | (~ (p @ Y0))))))) = $true)) )),
% 0.16/0.40 inference(beta_eta_normalization,[],[f180])).
% 0.16/0.40 thf(f180,plain,(
% 0.16/0.40 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | (~ (p @ Y1)))))))) @ X1) = $true)) )),
% 0.16/0.40 inference(pi_clausification,[],[f179])).
% 0.16/0.40 thf(f179,plain,(
% 0.16/0.40 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | (~ (p @ Y1))))))))) = $true)),
% 0.16/0.40 inference(not_proxy_clausification,[],[f165])).
% 0.16/0.40 thf(f165,plain,(
% 0.16/0.40 ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | (~ (p @ Y1)))))))))) = $false)),
% 0.16/0.40 inference(binary_proxy_clausification,[],[f153])).
% 0.16/0.40 thf(f223,plain,(
% 0.16/0.40 ($true = (q @ (sK3 @ sK2)))),
% 0.16/0.40 inference(trivial_inequality_removal,[],[f222])).
% 0.16/0.40 thf(f222,plain,(
% 0.16/0.40 ($false = $true) | ($true = (q @ (sK3 @ sK2)))),
% 0.16/0.40 inference(forward_demodulation,[],[f220,f209])).
% 0.16/0.40 thf(f209,plain,(
% 0.16/0.40 ($true = (p @ (sK3 @ sK2)))),
% 0.16/0.40 inference(trivial_inequality_removal,[],[f206])).
% 0.16/0.40 thf(f206,plain,(
% 0.16/0.40 ($false = $true) | ($true = (p @ (sK3 @ sK2)))),
% 0.16/0.40 inference(superposition,[],[f190,f171])).
% 0.16/0.40 thf(f190,plain,(
% 0.16/0.40 ( ! [X1 : $i] : (((rel_k @ sK1 @ X1) = $false) | ($true = (p @ (sK3 @ X1)))) )),
% 0.16/0.40 inference(not_proxy_clausification,[],[f187])).
% 0.16/0.40 thf(f187,plain,(
% 0.16/0.40 ( ! [X1 : $i] : (((~ (p @ (sK3 @ X1))) = $false) | ((rel_k @ sK1 @ X1) = $false)) )),
% 0.16/0.40 inference(binary_proxy_clausification,[],[f186])).
% 0.16/0.40 thf(f220,plain,(
% 0.16/0.40 ($false = (p @ (sK3 @ sK2))) | ($true = (q @ (sK3 @ sK2)))),
% 0.16/0.40 inference(trivial_inequality_removal,[],[f216])).
% 0.16/0.40 thf(f216,plain,(
% 0.16/0.40 ($false = (p @ (sK3 @ sK2))) | ($true = (q @ (sK3 @ sK2))) | ($false = $true)),
% 0.16/0.40 inference(superposition,[],[f178,f213])).
% 0.16/0.40 thf(f178,plain,(
% 0.16/0.40 ( ! [X1 : $i] : (((rel_k @ sK2 @ X1) = $false) | ((p @ X1) = $false) | ((q @ X1) = $true)) )),
% 0.16/0.40 inference(not_proxy_clausification,[],[f177])).
% 0.16/0.40 thf(f177,plain,(
% 0.16/0.40 ( ! [X1 : $i] : (($true = (~ (rel_k @ sK2 @ X1))) | ((q @ X1) = $true) | ((p @ X1) = $false)) )),
% 0.16/0.40 inference(not_proxy_clausification,[],[f176])).
% 0.16/0.40 thf(f176,plain,(
% 0.16/0.40 ( ! [X1 : $i] : (($true = (~ (p @ X1))) | ((q @ X1) = $true) | ($true = (~ (rel_k @ sK2 @ X1)))) )),
% 0.16/0.40 inference(binary_proxy_clausification,[],[f175])).
% 0.16/0.40 thf(f175,plain,(
% 0.16/0.40 ( ! [X1 : $i] : ((((q @ X1) | (~ (p @ X1))) = $true) | ($true = (~ (rel_k @ sK2 @ X1)))) )),
% 0.16/0.40 inference(binary_proxy_clausification,[],[f174])).
% 0.16/0.40 thf(f174,plain,(
% 0.16/0.40 ( ! [X1 : $i] : ((((~ (rel_k @ sK2 @ X1)) | ((q @ X1) | (~ (p @ X1)))) = $true)) )),
% 0.16/0.40 inference(beta_eta_normalization,[],[f173])).
% 0.16/0.40 thf(f173,plain,(
% 0.16/0.40 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((~ (rel_k @ sK2 @ Y0)) | ((q @ Y0) | (~ (p @ Y0))))) @ X1) = $true)) )),
% 0.16/0.40 inference(pi_clausification,[],[f172])).
% 0.16/0.40 thf(f172,plain,(
% 0.16/0.40 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK2 @ Y0)) | ((q @ Y0) | (~ (p @ Y0)))))) = $true)),
% 0.16/0.40 inference(not_proxy_clausification,[],[f169])).
% 0.16/0.40 thf(f169,plain,(
% 0.16/0.40 ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK2 @ Y0)) | ((q @ Y0) | (~ (p @ Y0))))))) = $false)),
% 0.16/0.40 inference(binary_proxy_clausification,[],[f168])).
% 0.16/0.40 % SZS output end Proof for theBenchmark
% 0.16/0.40 % (19347)------------------------------
% 0.16/0.40 % (19347)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.40 % (19347)Termination reason: Refutation
% 0.16/0.40
% 0.16/0.40 % (19347)Memory used [KB]: 5756
% 0.16/0.40 % (19347)Time elapsed: 0.015 s
% 0.16/0.40 % (19347)Instructions burned: 16 (million)
% 0.16/0.40 % (19347)------------------------------
% 0.16/0.40 % (19347)------------------------------
% 0.16/0.40 % (19340)Success in time 0.018 s
% 0.16/0.40 % Vampire---4.8 exiting
%------------------------------------------------------------------------------