TSTP Solution File: SYO448^1 by Vampire---4.9
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : SYO448^1 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d THM
% Computer : n025.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 : Mon Jun 24 21:02:14 EDT 2024
% Result : Theorem 0.19s 0.41s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SYO448^1 : TPTP v8.2.0. Released v4.0.0.
% 0.12/0.13 % Command : run_vampire %s %d THM
% 0.12/0.34 % Computer : n025.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sun Jun 23 10:53:24 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.19/0.36 This is a TH0_THM_EQU_NAR problem
% 0.19/0.36 Running higher-order theorem proving
% 0.19/0.36 Running /export/starexec/sandbox/solver/bin/vampire_ho --cores 7 --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox/benchmark/theBenchmark.p -m 16384 -t 300
% 0.19/0.38 % (23808)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.19/0.38 % (23810)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)
% 0.19/0.38 % (23806)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)
% 0.19/0.38 % (23807)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)
% 0.19/0.38 % (23811)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.19/0.38 % (23805)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.19/0.38 % (23808)Instruction limit reached!
% 0.19/0.38 % (23808)------------------------------
% 0.19/0.38 % (23808)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.19/0.38 % (23808)Termination reason: Unknown
% 0.19/0.38 % (23808)Termination phase: shuffling
% 0.19/0.38
% 0.19/0.38 % (23808)Memory used [KB]: 1023
% 0.19/0.38 % (23808)Time elapsed: 0.004 s
% 0.19/0.38 % (23808)Instructions burned: 3 (million)
% 0.19/0.38 % (23808)------------------------------
% 0.19/0.38 % (23808)------------------------------
% 0.19/0.39 % (23809)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)
% 0.19/0.39 % (23806)Instruction limit reached!
% 0.19/0.39 % (23806)------------------------------
% 0.19/0.39 % (23806)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.19/0.39 % (23806)Termination reason: Unknown
% 0.19/0.39 % (23806)Termination phase: Property scanning
% 0.19/0.39
% 0.19/0.39 % (23806)Memory used [KB]: 1023
% 0.19/0.39 % (23806)Time elapsed: 0.005 s
% 0.19/0.39 % (23806)Instructions burned: 4 (million)
% 0.19/0.39 % (23806)------------------------------
% 0.19/0.39 % (23806)------------------------------
% 0.19/0.39 % (23809)Instruction limit reached!
% 0.19/0.39 % (23809)------------------------------
% 0.19/0.39 % (23809)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.19/0.39 % (23809)Termination reason: Unknown
% 0.19/0.39 % (23809)Termination phase: shuffling
% 0.19/0.39
% 0.19/0.39 % (23809)Memory used [KB]: 1023
% 0.19/0.39 % (23809)Time elapsed: 0.003 s
% 0.19/0.39 % (23809)Instructions burned: 2 (million)
% 0.19/0.39 % (23809)------------------------------
% 0.19/0.39 % (23809)------------------------------
% 0.19/0.39 % (23810)Refutation not found, incomplete strategy
% 0.19/0.39 % (23810)------------------------------
% 0.19/0.39 % (23810)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.19/0.39 % (23810)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.39
% 0.19/0.39
% 0.19/0.39 % (23810)Memory used [KB]: 5628
% 0.19/0.39 % (23810)Time elapsed: 0.009 s
% 0.19/0.39 % (23810)Instructions burned: 10 (million)
% 0.19/0.39 % (23810)------------------------------
% 0.19/0.39 % (23810)------------------------------
% 0.19/0.39 % (23811)Instruction limit reached!
% 0.19/0.39 % (23811)------------------------------
% 0.19/0.39 % (23811)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.19/0.39 % (23811)Termination reason: Unknown
% 0.19/0.39 % (23811)Termination phase: Saturation
% 0.19/0.39
% 0.19/0.39 % (23811)Memory used [KB]: 5628
% 0.19/0.39 % (23811)Time elapsed: 0.011 s
% 0.19/0.39 % (23811)Instructions burned: 18 (million)
% 0.19/0.39 % (23811)------------------------------
% 0.19/0.39 % (23811)------------------------------
% 0.19/0.40 % (23807)Instruction limit reached!
% 0.19/0.40 % (23807)------------------------------
% 0.19/0.40 % (23807)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.19/0.40 % (23807)Termination reason: Unknown
% 0.19/0.40 % (23807)Termination phase: Saturation
% 0.19/0.40
% 0.19/0.40 % (23807)Memory used [KB]: 5756
% 0.19/0.40 % (23807)Time elapsed: 0.020 s
% 0.19/0.40 % (23807)Instructions burned: 27 (million)
% 0.19/0.40 % (23807)------------------------------
% 0.19/0.40 % (23807)------------------------------
% 0.19/0.40 % (23812)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)
% 0.19/0.40 % (23814)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)
% 0.19/0.40 % (23813)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)
% 0.19/0.40 % (23812)Instruction limit reached!
% 0.19/0.40 % (23812)------------------------------
% 0.19/0.40 % (23812)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.19/0.40 % (23812)Termination reason: Unknown
% 0.19/0.40 % (23812)Termination phase: shuffling
% 0.19/0.40
% 0.19/0.40 % (23812)Memory used [KB]: 1023
% 0.19/0.40 % (23812)Time elapsed: 0.004 s
% 0.19/0.40 % (23812)Instructions burned: 3 (million)
% 0.19/0.40 % (23812)------------------------------
% 0.19/0.40 % (23812)------------------------------
% 0.19/0.41 % (23805)First to succeed.
% 0.19/0.41 % (23814)Refutation not found, incomplete strategy
% 0.19/0.41 % (23814)------------------------------
% 0.19/0.41 % (23814)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.19/0.41 % (23814)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.41
% 0.19/0.41
% 0.19/0.41 % (23814)Memory used [KB]: 5756
% 0.19/0.41 % (23814)Time elapsed: 0.011 s
% 0.19/0.41 % (23814)Instructions burned: 13 (million)
% 0.19/0.41 % (23814)------------------------------
% 0.19/0.41 % (23814)------------------------------
% 0.19/0.41 % (23805)Refutation found. Thanks to Tanya!
% 0.19/0.41 % SZS status Theorem for theBenchmark
% 0.19/0.41 % SZS output start Proof for theBenchmark
% 0.19/0.41 thf(type_def_5, type, mu: $tType).
% 0.19/0.41 thf(func_def_0, type, mu: $tType).
% 0.19/0.41 thf(func_def_1, type, meq_ind: mu > mu > $i > $o).
% 0.19/0.41 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.19/0.41 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.19/0.41 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.19/0.41 thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.19/0.41 thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.19/0.41 thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.19/0.41 thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.19/0.41 thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.19/0.41 thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.19/0.41 thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.19/0.41 thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.19/0.41 thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.19/0.41 thf(func_def_15, type, mtrue: $i > $o).
% 0.19/0.41 thf(func_def_16, type, mfalse: $i > $o).
% 0.19/0.41 thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.19/0.41 thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.19/0.41 thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o).
% 0.19/0.41 thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o).
% 0.19/0.41 thf(func_def_21, type, mserial: ($i > $i > $o) > $o).
% 0.19/0.41 thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o).
% 0.19/0.41 thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o).
% 0.19/0.41 thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.19/0.41 thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o).
% 0.19/0.41 thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.19/0.41 thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.19/0.41 thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.19/0.41 thf(func_def_29, type, mvalid: ($i > $o) > $o).
% 0.19/0.41 thf(func_def_30, type, minvalid: ($i > $o) > $o).
% 0.19/0.41 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.19/0.41 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.19/0.41 thf(func_def_33, type, rel_s5: $i > $i > $o).
% 0.19/0.41 thf(func_def_34, type, mbox_s5: ($i > $o) > $i > $o).
% 0.19/0.41 thf(func_def_35, type, mdia_s5: ($i > $o) > $i > $o).
% 0.19/0.41 thf(func_def_36, type, p: $i > $o).
% 0.19/0.41 thf(func_def_37, type, q: $i > $o).
% 0.19/0.41 thf(f606,plain,(
% 0.19/0.41 $false),
% 0.19/0.41 inference(trivial_inequality_removal,[],[f605])).
% 0.19/0.41 thf(f605,plain,(
% 0.19/0.41 ($false = $true)),
% 0.19/0.41 inference(superposition,[],[f201,f543])).
% 0.19/0.41 thf(f543,plain,(
% 0.19/0.41 ($true = (p @ sK5))),
% 0.19/0.41 inference(trivial_inequality_removal,[],[f533])).
% 0.19/0.41 thf(f533,plain,(
% 0.19/0.41 ($true = (p @ sK5)) | ($false = $true)),
% 0.19/0.41 inference(superposition,[],[f531,f310])).
% 0.19/0.41 thf(f310,plain,(
% 0.19/0.41 ( ! [X0 : $i] : (($false = (rel_s5 @ sK1 @ X0)) | ((p @ X0) = $true)) )),
% 0.19/0.41 inference(trivial_inequality_removal,[],[f295])).
% 0.19/0.41 thf(f295,plain,(
% 0.19/0.41 ( ! [X0 : $i] : (((p @ X0) = $true) | ($false = $true) | ($false = (rel_s5 @ sK1 @ X0))) )),
% 0.19/0.41 inference(superposition,[],[f290,f245])).
% 0.19/0.41 thf(f245,plain,(
% 0.19/0.41 ((rel_s5 @ sK2 @ sK1) = $true)),
% 0.19/0.41 inference(trivial_inequality_removal,[],[f228])).
% 0.19/0.41 thf(f228,plain,(
% 0.19/0.41 ((rel_s5 @ sK2 @ sK1) = $true) | ($false = $true)),
% 0.19/0.41 inference(superposition,[],[f218,f186])).
% 0.19/0.41 thf(f186,plain,(
% 0.19/0.41 ((rel_s5 @ sK1 @ sK2) = $true)),
% 0.19/0.41 inference(not_proxy_clausification,[],[f172])).
% 0.19/0.41 thf(f172,plain,(
% 0.19/0.41 ($false = (~ (rel_s5 @ sK1 @ sK2)))),
% 0.19/0.41 inference(binary_proxy_clausification,[],[f171])).
% 0.19/0.41 thf(f171,plain,(
% 0.19/0.41 ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_s5 @ sK2 @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s5 @ sK2 @ Y0)))))) | (~ (rel_s5 @ sK1 @ sK2))))),
% 0.19/0.41 inference(beta_eta_normalization,[],[f170])).
% 0.19/0.41 thf(f170,plain,(
% 0.19/0.41 ($false = ((^[Y0 : $i]: (((~ (!! @ $i @ (^[Y1 : $i]: ((p @ Y1) | (~ (rel_s5 @ Y0 @ Y1)))))) | (!! @ $i @ (^[Y1 : $i]: ((q @ Y1) | (~ (rel_s5 @ Y0 @ Y1)))))) | (~ (rel_s5 @ sK1 @ Y0)))) @ sK2))),
% 0.19/0.41 inference(sigma_clausification,[],[f169])).
% 0.19/0.41 thf(f169,plain,(
% 0.19/0.41 ($false = (!! @ $i @ (^[Y0 : $i]: (((~ (!! @ $i @ (^[Y1 : $i]: ((p @ Y1) | (~ (rel_s5 @ Y0 @ Y1)))))) | (!! @ $i @ (^[Y1 : $i]: ((q @ Y1) | (~ (rel_s5 @ Y0 @ Y1)))))) | (~ (rel_s5 @ sK1 @ Y0))))))),
% 0.19/0.41 inference(binary_proxy_clausification,[],[f167])).
% 0.19/0.41 thf(f167,plain,(
% 0.19/0.41 ($false = ((!! @ $i @ (^[Y0 : $i]: (((~ (!! @ $i @ (^[Y1 : $i]: ((p @ Y1) | (~ (rel_s5 @ Y0 @ Y1)))))) | (!! @ $i @ (^[Y1 : $i]: ((q @ Y1) | (~ (rel_s5 @ Y0 @ Y1)))))) | (~ (rel_s5 @ sK1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: (((~ (!! @ $i @ (^[Y1 : $i]: ((q @ Y1) | (~ (rel_s5 @ Y0 @ Y1)))))) | (!! @ $i @ (^[Y1 : $i]: ((p @ Y1) | (~ (rel_s5 @ Y0 @ Y1)))))) | (~ (rel_s5 @ sK1 @ Y0)))))))),
% 0.19/0.41 inference(beta_eta_normalization,[],[f166])).
% 0.19/0.41 thf(f166,plain,(
% 0.19/0.41 ($false = ((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (((~ (!! @ $i @ (^[Y2 : $i]: ((p @ Y2) | (~ (rel_s5 @ Y1 @ Y2)))))) | (!! @ $i @ (^[Y2 : $i]: ((q @ Y2) | (~ (rel_s5 @ Y1 @ Y2)))))) | (~ (rel_s5 @ Y0 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: (((~ (!! @ $i @ (^[Y2 : $i]: ((q @ Y2) | (~ (rel_s5 @ Y1 @ Y2)))))) | (!! @ $i @ (^[Y2 : $i]: ((p @ Y2) | (~ (rel_s5 @ Y1 @ Y2)))))) | (~ (rel_s5 @ Y0 @ Y1))))))) @ sK1))),
% 0.19/0.41 inference(sigma_clausification,[],[f165])).
% 0.19/0.41 thf(f165,plain,(
% 0.19/0.41 ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (((~ (!! @ $i @ (^[Y2 : $i]: ((p @ Y2) | (~ (rel_s5 @ Y1 @ Y2)))))) | (!! @ $i @ (^[Y2 : $i]: ((q @ Y2) | (~ (rel_s5 @ Y1 @ Y2)))))) | (~ (rel_s5 @ Y0 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: (((~ (!! @ $i @ (^[Y2 : $i]: ((q @ Y2) | (~ (rel_s5 @ Y1 @ Y2)))))) | (!! @ $i @ (^[Y2 : $i]: ((p @ Y2) | (~ (rel_s5 @ Y1 @ Y2)))))) | (~ (rel_s5 @ Y0 @ Y1)))))))) != $true)),
% 0.19/0.41 inference(beta_eta_normalization,[],[f159])).
% 0.19/0.41 thf(f159,plain,(
% 0.19/0.41 (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s5 @ Y1 @ Y2)))))))) @ ((^[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_s5 @ Y1 @ Y2)))))))) @ p) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s5 @ Y1 @ Y2)))))))) @ q))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s5 @ Y1 @ Y2)))))))) @ ((^[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_s5 @ Y1 @ Y2)))))))) @ q) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s5 @ Y1 @ Y2)))))))) @ p))))) != $true)),
% 0.19/0.41 inference(definition_unfolding,[],[f123,f136,f145,f120,f149,f120,f120,f120,f149,f120,f120])).
% 0.19/0.41 thf(f149,plain,(
% 0.19/0.41 (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)))))),
% 0.19/0.41 inference(definition_unfolding,[],[f142,f145,f119])).
% 0.19/0.41 thf(f119,plain,(
% 0.19/0.41 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.19/0.41 inference(cnf_transformation,[],[f55])).
% 0.19/0.41 thf(f55,plain,(
% 0.19/0.41 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.19/0.41 inference(fool_elimination,[],[f54])).
% 0.19/0.41 thf(f54,plain,(
% 0.19/0.41 (mnot = (^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))))),
% 0.19/0.41 inference(rectify,[],[f3])).
% 0.19/0.41 thf(f3,axiom,(
% 0.19/0.41 (mnot = (^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))))),
% 0.19/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot)).
% 0.19/0.41 thf(f142,plain,(
% 0.19/0.41 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.19/0.41 inference(cnf_transformation,[],[f98])).
% 0.19/0.41 thf(f98,plain,(
% 0.19/0.41 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.19/0.41 inference(fool_elimination,[],[f97])).
% 0.19/0.41 thf(f97,plain,(
% 0.19/0.41 (mimplies = (^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)))),
% 0.19/0.41 inference(rectify,[],[f6])).
% 0.19/0.41 thf(f6,axiom,(
% 0.19/0.41 (mimplies = (^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)))),
% 0.19/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies)).
% 0.19/0.41 thf(f120,plain,(
% 0.19/0.41 (mbox_s5 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s5 @ Y1 @ Y2)))))))))),
% 0.19/0.41 inference(cnf_transformation,[],[f72])).
% 0.19/0.41 thf(f72,plain,(
% 0.19/0.41 (mbox_s5 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s5 @ Y1 @ Y2)))))))))),
% 0.19/0.41 inference(fool_elimination,[],[f71])).
% 0.19/0.41 thf(f71,plain,(
% 0.19/0.41 ((^[X0 : $i > $o, X1 : $i] : (! [X2] : (~(rel_s5 @ X1 @ X2) | (X0 @ X2)))) = mbox_s5)),
% 0.19/0.41 inference(rectify,[],[f32])).
% 0.19/0.41 thf(f32,axiom,(
% 0.19/0.41 ((^[X3 : $i > $o, X2 : $i] : (! [X7] : (~(rel_s5 @ X2 @ X7) | (X3 @ X7)))) = mbox_s5)),
% 0.19/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox_s5)).
% 0.19/0.41 thf(f145,plain,(
% 0.19/0.41 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.19/0.41 inference(cnf_transformation,[],[f109])).
% 0.19/0.41 thf(f109,plain,(
% 0.19/0.41 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.19/0.41 inference(fool_elimination,[],[f108])).
% 0.19/0.41 thf(f108,plain,(
% 0.19/0.41 (mor = (^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X1 @ X2) | (X0 @ X2))))),
% 0.19/0.41 inference(rectify,[],[f4])).
% 0.19/0.41 thf(f4,axiom,(
% 0.19/0.41 (mor = (^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X4 @ X2) | (X3 @ X2))))),
% 0.19/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor)).
% 0.19/0.41 thf(f136,plain,(
% 0.19/0.41 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.19/0.41 inference(cnf_transformation,[],[f68])).
% 0.19/0.41 thf(f68,plain,(
% 0.19/0.41 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.19/0.41 inference(fool_elimination,[],[f67])).
% 0.19/0.41 thf(f67,plain,(
% 0.19/0.41 ((^[X0 : $i > $o] : (! [X1] : (X0 @ X1))) = mvalid)),
% 0.19/0.41 inference(rectify,[],[f28])).
% 0.19/0.41 thf(f28,axiom,(
% 0.19/0.41 ((^[X3 : $i > $o] : (! [X2] : (X3 @ X2))) = mvalid)),
% 0.19/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mvalid)).
% 0.19/0.41 thf(f123,plain,(
% 0.19/0.41 ((mvalid @ (mor @ (mbox_s5 @ (mimplies @ (mbox_s5 @ p) @ (mbox_s5 @ q))) @ (mbox_s5 @ (mimplies @ (mbox_s5 @ q) @ (mbox_s5 @ p))))) != $true)),
% 0.19/0.41 inference(cnf_transformation,[],[f110])).
% 0.19/0.41 thf(f110,plain,(
% 0.19/0.41 ((mvalid @ (mor @ (mbox_s5 @ (mimplies @ (mbox_s5 @ p) @ (mbox_s5 @ q))) @ (mbox_s5 @ (mimplies @ (mbox_s5 @ q) @ (mbox_s5 @ p))))) != $true)),
% 0.19/0.41 inference(flattening,[],[f62])).
% 0.19/0.41 thf(f62,plain,(
% 0.19/0.41 ~((mvalid @ (mor @ (mbox_s5 @ (mimplies @ (mbox_s5 @ p) @ (mbox_s5 @ q))) @ (mbox_s5 @ (mimplies @ (mbox_s5 @ q) @ (mbox_s5 @ p))))) = $true)),
% 0.19/0.41 inference(fool_elimination,[],[f61])).
% 0.19/0.41 thf(f61,plain,(
% 0.19/0.41 ~(mvalid @ (mor @ (mbox_s5 @ (mimplies @ (mbox_s5 @ p) @ (mbox_s5 @ q))) @ (mbox_s5 @ (mimplies @ (mbox_s5 @ q) @ (mbox_s5 @ p)))))),
% 0.19/0.41 inference(rectify,[],[f38])).
% 0.19/0.41 thf(f38,negated_conjecture,(
% 0.19/0.41 ~(mvalid @ (mor @ (mbox_s5 @ (mimplies @ (mbox_s5 @ p) @ (mbox_s5 @ q))) @ (mbox_s5 @ (mimplies @ (mbox_s5 @ q) @ (mbox_s5 @ p)))))),
% 0.19/0.41 inference(negated_conjecture,[],[f37])).
% 0.19/0.41 thf(f37,conjecture,(
% 0.19/0.41 (mvalid @ (mor @ (mbox_s5 @ (mimplies @ (mbox_s5 @ p) @ (mbox_s5 @ q))) @ (mbox_s5 @ (mimplies @ (mbox_s5 @ q) @ (mbox_s5 @ p)))))),
% 0.19/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove)).
% 0.19/0.41 thf(f218,plain,(
% 0.19/0.41 ( ! [X2 : $i,X1 : $i] : (($false = (rel_s5 @ X1 @ X2)) | ((rel_s5 @ X2 @ X1) = $true)) )),
% 0.19/0.41 inference(binary_proxy_clausification,[],[f217])).
% 0.19/0.41 thf(f217,plain,(
% 0.19/0.41 ( ! [X2 : $i,X1 : $i] : ((((rel_s5 @ X1 @ X2) => (rel_s5 @ X2 @ X1)) = $true)) )),
% 0.19/0.41 inference(beta_eta_normalization,[],[f216])).
% 0.19/0.41 thf(f216,plain,(
% 0.19/0.41 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((rel_s5 @ X1 @ Y0) => (rel_s5 @ Y0 @ X1))) @ X2) = $true)) )),
% 0.19/0.41 inference(pi_clausification,[],[f215])).
% 0.19/0.41 thf(f215,plain,(
% 0.19/0.41 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((rel_s5 @ X1 @ Y0) => (rel_s5 @ Y0 @ X1)))) = $true)) )),
% 0.19/0.41 inference(beta_eta_normalization,[],[f214])).
% 0.19/0.41 thf(f214,plain,(
% 0.19/0.41 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((rel_s5 @ Y0 @ Y1) => (rel_s5 @ Y1 @ Y0))))) @ X1) = $true)) )),
% 0.19/0.41 inference(pi_clausification,[],[f213])).
% 0.19/0.41 thf(f213,plain,(
% 0.19/0.41 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((rel_s5 @ Y0 @ Y1) => (rel_s5 @ Y1 @ Y0)))))) = $true)),
% 0.19/0.41 inference(beta_eta_normalization,[],[f160])).
% 0.19/0.41 thf(f160,plain,(
% 0.19/0.41 (((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1))))))) @ rel_s5) = $true)),
% 0.19/0.41 inference(definition_unfolding,[],[f143,f140])).
% 0.19/0.41 thf(f140,plain,(
% 0.19/0.41 (msymmetric = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1))))))))),
% 0.19/0.41 inference(cnf_transformation,[],[f92])).
% 0.19/0.41 thf(f92,plain,(
% 0.19/0.41 (msymmetric = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1))))))))),
% 0.19/0.41 inference(fool_elimination,[],[f91])).
% 0.19/0.41 thf(f91,plain,(
% 0.19/0.41 (msymmetric = (^[X0 : $i > $i > $o] : (! [X1,X2] : ((X0 @ X2 @ X1) => (X0 @ X1 @ X2)))))),
% 0.19/0.41 inference(rectify,[],[f19])).
% 0.19/0.41 thf(f19,axiom,(
% 0.19/0.41 (msymmetric = (^[X6 : $i > $i > $o] : (! [X9,X8] : ((X6 @ X8 @ X9) => (X6 @ X9 @ X8)))))),
% 0.19/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',msymmetric)).
% 0.19/0.41 thf(f143,plain,(
% 0.19/0.41 ((msymmetric @ rel_s5) = $true)),
% 0.19/0.41 inference(cnf_transformation,[],[f80])).
% 0.19/0.41 thf(f80,plain,(
% 0.19/0.41 ((msymmetric @ rel_s5) = $true)),
% 0.19/0.41 inference(fool_elimination,[],[f79])).
% 0.19/0.41 thf(f79,plain,(
% 0.19/0.41 (msymmetric @ rel_s5)),
% 0.19/0.41 inference(rectify,[],[f36])).
% 0.19/0.41 thf(f36,axiom,(
% 0.19/0.41 (msymmetric @ rel_s5)),
% 0.19/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',a3)).
% 0.19/0.41 thf(f290,plain,(
% 0.19/0.41 ( ! [X0 : $i,X1 : $i] : (($false = (rel_s5 @ sK2 @ X1)) | ($false = (rel_s5 @ X1 @ X0)) | ((p @ X0) = $true)) )),
% 0.19/0.41 inference(trivial_inequality_removal,[],[f282])).
% 0.19/0.41 thf(f282,plain,(
% 0.19/0.41 ( ! [X0 : $i,X1 : $i] : (((p @ X0) = $true) | ($false = $true) | ($false = (rel_s5 @ sK2 @ X1)) | ($false = (rel_s5 @ X1 @ X0))) )),
% 0.19/0.41 inference(superposition,[],[f180,f212])).
% 0.19/0.41 thf(f212,plain,(
% 0.19/0.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (rel_s5 @ X1 @ X3)) | ($false = (rel_s5 @ X1 @ X2)) | ($false = (rel_s5 @ X2 @ X3))) )),
% 0.19/0.41 inference(binary_proxy_clausification,[],[f211])).
% 0.19/0.41 thf(f211,plain,(
% 0.19/0.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((rel_s5 @ X2 @ X3) & (rel_s5 @ X1 @ X2))) | ($true = (rel_s5 @ X1 @ X3))) )),
% 0.19/0.41 inference(binary_proxy_clausification,[],[f210])).
% 0.19/0.41 thf(f210,plain,(
% 0.19/0.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((((rel_s5 @ X2 @ X3) & (rel_s5 @ X1 @ X2)) => (rel_s5 @ X1 @ X3)) = $true)) )),
% 0.19/0.41 inference(beta_eta_normalization,[],[f209])).
% 0.19/0.41 thf(f209,plain,(
% 0.19/0.41 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: (((rel_s5 @ X2 @ Y0) & (rel_s5 @ X1 @ X2)) => (rel_s5 @ X1 @ Y0))) @ X3) = $true)) )),
% 0.19/0.41 inference(pi_clausification,[],[f208])).
% 0.19/0.41 thf(f208,plain,(
% 0.19/0.41 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (((rel_s5 @ X2 @ Y0) & (rel_s5 @ X1 @ X2)) => (rel_s5 @ X1 @ Y0)))))) )),
% 0.19/0.41 inference(beta_eta_normalization,[],[f207])).
% 0.19/0.41 thf(f207,plain,(
% 0.19/0.41 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((rel_s5 @ Y0 @ Y1) & (rel_s5 @ X1 @ Y0)) => (rel_s5 @ X1 @ Y1))))) @ X2))) )),
% 0.19/0.41 inference(pi_clausification,[],[f206])).
% 0.19/0.41 thf(f206,plain,(
% 0.19/0.41 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((rel_s5 @ Y0 @ Y1) & (rel_s5 @ X1 @ Y0)) => (rel_s5 @ X1 @ Y1)))))) = $true)) )),
% 0.19/0.41 inference(beta_eta_normalization,[],[f205])).
% 0.19/0.41 thf(f205,plain,(
% 0.19/0.41 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((rel_s5 @ Y1 @ Y2) & (rel_s5 @ Y0 @ Y1)) => (rel_s5 @ Y0 @ Y2))))))) @ X1))) )),
% 0.19/0.41 inference(pi_clausification,[],[f204])).
% 0.19/0.41 thf(f204,plain,(
% 0.19/0.41 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((rel_s5 @ Y1 @ Y2) & (rel_s5 @ Y0 @ Y1)) => (rel_s5 @ Y0 @ Y2)))))))))),
% 0.19/0.41 inference(beta_eta_normalization,[],[f161])).
% 0.19/0.41 thf(f161,plain,(
% 0.19/0.41 (((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y3))))))))) @ rel_s5) = $true)),
% 0.19/0.41 inference(definition_unfolding,[],[f147,f115])).
% 0.19/0.41 thf(f115,plain,(
% 0.19/0.41 (mtransitive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y3))))))))))),
% 0.19/0.41 inference(cnf_transformation,[],[f66])).
% 0.19/0.41 thf(f66,plain,(
% 0.19/0.41 (mtransitive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y1 @ Y2)) => (Y0 @ Y1 @ Y3))))))))))),
% 0.19/0.41 inference(fool_elimination,[],[f65])).
% 0.19/0.41 thf(f65,plain,(
% 0.19/0.41 ((^[X0 : $i > $i > $o] : (! [X1,X2,X3] : (((X0 @ X3 @ X2) & (X0 @ X2 @ X1)) => (X0 @ X3 @ X1)))) = mtransitive)),
% 0.19/0.41 inference(rectify,[],[f21])).
% 0.19/0.41 thf(f21,axiom,(
% 0.19/0.41 ((^[X6 : $i > $i > $o] : (! [X10,X9,X8] : (((X6 @ X8 @ X9) & (X6 @ X9 @ X10)) => (X6 @ X8 @ X10)))) = mtransitive)),
% 0.19/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mtransitive)).
% 0.19/0.41 thf(f147,plain,(
% 0.19/0.41 ((mtransitive @ rel_s5) = $true)),
% 0.19/0.41 inference(cnf_transformation,[],[f76])).
% 0.19/0.41 thf(f76,plain,(
% 0.19/0.41 ((mtransitive @ rel_s5) = $true)),
% 0.19/0.41 inference(fool_elimination,[],[f75])).
% 0.19/0.41 thf(f75,plain,(
% 0.19/0.41 (mtransitive @ rel_s5)),
% 0.19/0.41 inference(rectify,[],[f35])).
% 0.19/0.41 thf(f35,axiom,(
% 0.19/0.41 (mtransitive @ rel_s5)),
% 0.19/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2)).
% 0.19/0.41 thf(f180,plain,(
% 0.19/0.41 ( ! [X1 : $i] : (($false = (rel_s5 @ sK2 @ X1)) | ($true = (p @ X1))) )),
% 0.19/0.41 inference(not_proxy_clausification,[],[f179])).
% 0.19/0.41 thf(f179,plain,(
% 0.19/0.41 ( ! [X1 : $i] : (((~ (rel_s5 @ sK2 @ X1)) = $true) | ($true = (p @ X1))) )),
% 0.19/0.41 inference(binary_proxy_clausification,[],[f178])).
% 0.19/0.41 thf(f178,plain,(
% 0.19/0.41 ( ! [X1 : $i] : ((((p @ X1) | (~ (rel_s5 @ sK2 @ X1))) = $true)) )),
% 0.19/0.41 inference(beta_eta_normalization,[],[f177])).
% 0.19/0.41 thf(f177,plain,(
% 0.19/0.41 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((p @ Y0) | (~ (rel_s5 @ sK2 @ Y0)))) @ X1) = $true)) )),
% 0.19/0.41 inference(pi_clausification,[],[f176])).
% 0.19/0.41 thf(f176,plain,(
% 0.19/0.41 ((!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_s5 @ sK2 @ Y0))))) = $true)),
% 0.19/0.41 inference(not_proxy_clausification,[],[f175])).
% 0.19/0.41 thf(f175,plain,(
% 0.19/0.41 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_s5 @ sK2 @ Y0)))))))),
% 0.19/0.41 inference(binary_proxy_clausification,[],[f173])).
% 0.19/0.41 thf(f173,plain,(
% 0.19/0.41 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_s5 @ sK2 @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s5 @ sK2 @ Y0)))))))),
% 0.19/0.41 inference(binary_proxy_clausification,[],[f171])).
% 0.19/0.41 thf(f531,plain,(
% 0.19/0.41 ((rel_s5 @ sK1 @ sK5) = $true)),
% 0.19/0.41 inference(trivial_inequality_removal,[],[f509])).
% 0.19/0.41 thf(f509,plain,(
% 0.19/0.41 ($false = $true) | ((rel_s5 @ sK1 @ sK5) = $true)),
% 0.19/0.41 inference(superposition,[],[f404,f239])).
% 0.19/0.41 thf(f239,plain,(
% 0.19/0.41 ($true = (rel_s5 @ sK5 @ sK4))),
% 0.19/0.41 inference(trivial_inequality_removal,[],[f231])).
% 0.19/0.41 thf(f231,plain,(
% 0.19/0.41 ($false = $true) | ($true = (rel_s5 @ sK5 @ sK4))),
% 0.19/0.41 inference(superposition,[],[f218,f202])).
% 0.19/0.41 thf(f202,plain,(
% 0.19/0.41 ((rel_s5 @ sK4 @ sK5) = $true)),
% 0.19/0.41 inference(not_proxy_clausification,[],[f200])).
% 0.19/0.41 thf(f200,plain,(
% 0.19/0.41 ($false = (~ (rel_s5 @ sK4 @ sK5)))),
% 0.19/0.41 inference(binary_proxy_clausification,[],[f199])).
% 0.19/0.41 thf(f199,plain,(
% 0.19/0.41 ($false = ((p @ sK5) | (~ (rel_s5 @ sK4 @ sK5))))),
% 0.19/0.41 inference(beta_eta_normalization,[],[f198])).
% 0.19/0.41 thf(f198,plain,(
% 0.19/0.41 ($false = ((^[Y0 : $i]: ((p @ Y0) | (~ (rel_s5 @ sK4 @ Y0)))) @ sK5))),
% 0.19/0.41 inference(sigma_clausification,[],[f191])).
% 0.19/0.41 thf(f191,plain,(
% 0.19/0.41 ($false = (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_s5 @ sK4 @ Y0))))))),
% 0.19/0.41 inference(binary_proxy_clausification,[],[f190])).
% 0.19/0.41 thf(f190,plain,(
% 0.19/0.41 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s5 @ sK4 @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_s5 @ sK4 @ Y0)))))))),
% 0.19/0.41 inference(binary_proxy_clausification,[],[f188])).
% 0.19/0.41 thf(f188,plain,(
% 0.19/0.41 ((((~ (!! @ $i @ (^[Y0 : $i]: ((q @ Y0) | (~ (rel_s5 @ sK4 @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((p @ Y0) | (~ (rel_s5 @ sK4 @ Y0)))))) | (~ (rel_s5 @ sK1 @ sK4))) = $false)),
% 0.19/0.41 inference(beta_eta_normalization,[],[f187])).
% 0.19/0.41 thf(f187,plain,(
% 0.19/0.41 ($false = ((^[Y0 : $i]: (((~ (!! @ $i @ (^[Y1 : $i]: ((q @ Y1) | (~ (rel_s5 @ Y0 @ Y1)))))) | (!! @ $i @ (^[Y1 : $i]: ((p @ Y1) | (~ (rel_s5 @ Y0 @ Y1)))))) | (~ (rel_s5 @ sK1 @ Y0)))) @ sK4))),
% 0.19/0.41 inference(sigma_clausification,[],[f168])).
% 0.19/0.41 thf(f168,plain,(
% 0.19/0.41 ((!! @ $i @ (^[Y0 : $i]: (((~ (!! @ $i @ (^[Y1 : $i]: ((q @ Y1) | (~ (rel_s5 @ Y0 @ Y1)))))) | (!! @ $i @ (^[Y1 : $i]: ((p @ Y1) | (~ (rel_s5 @ Y0 @ Y1)))))) | (~ (rel_s5 @ sK1 @ Y0))))) = $false)),
% 0.19/0.41 inference(binary_proxy_clausification,[],[f167])).
% 0.19/0.41 thf(f404,plain,(
% 0.19/0.41 ( ! [X0 : $i] : (($false = (rel_s5 @ X0 @ sK4)) | ((rel_s5 @ sK1 @ X0) = $true)) )),
% 0.19/0.41 inference(trivial_inequality_removal,[],[f372])).
% 0.19/0.41 thf(f372,plain,(
% 0.19/0.41 ( ! [X0 : $i] : (($false = (rel_s5 @ X0 @ sK4)) | ((rel_s5 @ sK1 @ X0) = $true) | ($false = $true)) )),
% 0.19/0.41 inference(superposition,[],[f292,f246])).
% 0.19/0.41 thf(f246,plain,(
% 0.19/0.41 ($true = (rel_s5 @ sK4 @ sK1))),
% 0.19/0.41 inference(trivial_inequality_removal,[],[f230])).
% 0.19/0.41 thf(f230,plain,(
% 0.19/0.41 ($true = (rel_s5 @ sK4 @ sK1)) | ($false = $true)),
% 0.19/0.41 inference(superposition,[],[f218,f203])).
% 0.19/0.41 thf(f203,plain,(
% 0.19/0.41 ((rel_s5 @ sK1 @ sK4) = $true)),
% 0.19/0.41 inference(not_proxy_clausification,[],[f189])).
% 0.19/0.41 thf(f189,plain,(
% 0.19/0.41 ($false = (~ (rel_s5 @ sK1 @ sK4)))),
% 0.19/0.41 inference(binary_proxy_clausification,[],[f188])).
% 0.19/0.41 thf(f292,plain,(
% 0.19/0.41 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($false = (rel_s5 @ X2 @ X1)) | ((rel_s5 @ X1 @ X0) = $true) | ($false = (rel_s5 @ X0 @ X2))) )),
% 0.19/0.41 inference(trivial_inequality_removal,[],[f281])).
% 0.19/0.41 thf(f281,plain,(
% 0.19/0.41 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($false = (rel_s5 @ X2 @ X1)) | ($false = $true) | ((rel_s5 @ X1 @ X0) = $true) | ($false = (rel_s5 @ X0 @ X2))) )),
% 0.19/0.41 inference(superposition,[],[f212,f218])).
% 0.19/0.41 thf(f201,plain,(
% 0.19/0.41 ($false = (p @ sK5))),
% 0.19/0.41 inference(binary_proxy_clausification,[],[f199])).
% 0.19/0.41 % SZS output end Proof for theBenchmark
% 0.19/0.41 % (23805)------------------------------
% 0.19/0.41 % (23805)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.19/0.41 % (23805)Termination reason: Refutation
% 0.19/0.41
% 0.19/0.41 % (23805)Memory used [KB]: 5884
% 0.19/0.41 % (23805)Time elapsed: 0.029 s
% 0.19/0.41 % (23805)Instructions burned: 48 (million)
% 0.19/0.41 % (23805)------------------------------
% 0.19/0.41 % (23805)------------------------------
% 0.19/0.41 % (23804)Success in time 0.044 s
%------------------------------------------------------------------------------