TSTP Solution File: SYO053^2 by Vampire---4.9
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : SYO053^2 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d THM
% Computer : n026.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 21:00:20 EDT 2024
% Result : Theorem 0.21s 0.40s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SYO053^2 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.11 % Command : run_vampire %s %d THM
% 0.11/0.32 % Computer : n026.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Sun Jun 23 09:14:39 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.11/0.34 This is a TH0_THM_EQU_NAR problem
% 0.11/0.34 Running higher-order theorem proving
% 0.11/0.34 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
% 0.11/0.36 % (7281)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)
% 0.11/0.36 % (7281)Refutation not found, incomplete strategy
% 0.11/0.36 % (7281)------------------------------
% 0.11/0.36 % (7281)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.11/0.36 % (7281)Termination reason: Refutation not found, incomplete strategy
% 0.11/0.36
% 0.11/0.36
% 0.11/0.36 % (7281)Memory used [KB]: 5628
% 0.11/0.36 % (7281)Time elapsed: 0.004 s
% 0.11/0.36 % (7281)Instructions burned: 7 (million)
% 0.11/0.36 % (7281)------------------------------
% 0.11/0.36 % (7281)------------------------------
% 0.11/0.36 % (7279)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.11/0.37 % (7282)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.11/0.37 % (7284)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)
% 0.11/0.37 % (7280)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)
% 0.11/0.37 % (7283)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)
% 0.11/0.37 % (7285)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.11/0.37 % (7282)Instruction limit reached!
% 0.11/0.37 % (7282)------------------------------
% 0.11/0.37 % (7282)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.11/0.37 % (7282)Termination reason: Unknown
% 0.11/0.37 % (7282)Termination phase: shuffling
% 0.11/0.37
% 0.11/0.37 % (7282)Memory used [KB]: 1023
% 0.11/0.37 % (7282)Time elapsed: 0.004 s
% 0.11/0.37 % (7282)Instructions burned: 3 (million)
% 0.11/0.37 % (7282)------------------------------
% 0.11/0.37 % (7282)------------------------------
% 0.11/0.37 % (7283)Instruction limit reached!
% 0.11/0.37 % (7283)------------------------------
% 0.11/0.37 % (7283)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.11/0.37 % (7283)Termination reason: Unknown
% 0.11/0.37 % (7283)Termination phase: shuffling
% 0.11/0.37
% 0.11/0.37 % (7283)Memory used [KB]: 1023
% 0.11/0.37 % (7283)Time elapsed: 0.003 s
% 0.11/0.37 % (7283)Instructions burned: 2 (million)
% 0.11/0.37 % (7283)------------------------------
% 0.11/0.37 % (7283)------------------------------
% 0.11/0.37 % (7280)Instruction limit reached!
% 0.11/0.37 % (7280)------------------------------
% 0.11/0.37 % (7280)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.11/0.37 % (7280)Termination reason: Unknown
% 0.11/0.37 % (7280)Termination phase: Property scanning
% 0.11/0.37
% 0.11/0.37 % (7280)Memory used [KB]: 1023
% 0.11/0.37 % (7280)Time elapsed: 0.004 s
% 0.11/0.37 % (7280)Instructions burned: 4 (million)
% 0.11/0.37 % (7280)------------------------------
% 0.11/0.37 % (7280)------------------------------
% 0.11/0.37 % (7284)Refutation not found, incomplete strategy
% 0.11/0.37 % (7284)------------------------------
% 0.11/0.37 % (7284)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.11/0.37 % (7284)Termination reason: Refutation not found, incomplete strategy
% 0.11/0.37
% 0.11/0.37
% 0.11/0.37 % (7284)Memory used [KB]: 5628
% 0.11/0.37 % (7284)Time elapsed: 0.006 s
% 0.11/0.37 % (7284)Instructions burned: 6 (million)
% 0.11/0.37 % (7284)------------------------------
% 0.11/0.37 % (7284)------------------------------
% 0.11/0.37 % (7279)Refutation not found, incomplete strategy
% 0.11/0.37 % (7279)------------------------------
% 0.11/0.37 % (7279)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.11/0.37 % (7279)Termination reason: Refutation not found, incomplete strategy
% 0.11/0.37
% 0.11/0.37
% 0.11/0.37 % (7279)Memory used [KB]: 5628
% 0.11/0.37 % (7279)Time elapsed: 0.007 s
% 0.11/0.37 % (7279)Instructions burned: 8 (million)
% 0.11/0.37 % (7279)------------------------------
% 0.11/0.37 % (7279)------------------------------
% 0.11/0.37 % (7287)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)
% 0.11/0.37 % (7285)Refutation not found, incomplete strategy
% 0.11/0.37 % (7285)------------------------------
% 0.11/0.37 % (7285)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.11/0.37 % (7285)Termination reason: Refutation not found, incomplete strategy
% 0.11/0.37
% 0.11/0.37
% 0.11/0.37 % (7285)Memory used [KB]: 5628
% 0.11/0.37 % (7285)Time elapsed: 0.007 s
% 0.11/0.37 % (7285)Instructions burned: 8 (million)
% 0.11/0.37 % (7285)------------------------------
% 0.11/0.37 % (7285)------------------------------
% 0.11/0.37 % (7287)Instruction limit reached!
% 0.11/0.37 % (7287)------------------------------
% 0.11/0.37 % (7287)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.11/0.37 % (7287)Termination reason: Unknown
% 0.11/0.37 % (7287)Termination phase: shuffling
% 0.11/0.37
% 0.11/0.37 % (7287)Memory used [KB]: 1023
% 0.11/0.37 % (7287)Time elapsed: 0.002 s
% 0.11/0.37 % (7287)Instructions burned: 3 (million)
% 0.11/0.37 % (7287)------------------------------
% 0.11/0.37 % (7287)------------------------------
% 0.11/0.38 % (7298)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.11/0.38 % (7290)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)
% 0.11/0.38 % (7292)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)
% 0.11/0.38 % (7293)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)
% 0.11/0.38 % (7293)Instruction limit reached!
% 0.11/0.38 % (7293)------------------------------
% 0.11/0.38 % (7293)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.11/0.38 % (7293)Termination reason: Unknown
% 0.11/0.39 % (7293)Termination phase: shuffling
% 0.11/0.39
% 0.11/0.39 % (7293)Memory used [KB]: 1023
% 0.11/0.39 % (7293)Time elapsed: 0.004 s
% 0.11/0.39 % (7293)Instructions burned: 3 (million)
% 0.11/0.39 % (7293)------------------------------
% 0.11/0.39 % (7293)------------------------------
% 0.11/0.39 % (7298)Instruction limit reached!
% 0.11/0.39 % (7298)------------------------------
% 0.11/0.39 % (7298)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.11/0.39 % (7298)Termination reason: Unknown
% 0.11/0.39 % (7298)Termination phase: Saturation
% 0.11/0.39
% 0.11/0.39 % (7298)Memory used [KB]: 5756
% 0.11/0.39 % (7298)Time elapsed: 0.007 s
% 0.11/0.39 % (7298)Instructions burned: 16 (million)
% 0.11/0.39 % (7298)------------------------------
% 0.11/0.39 % (7298)------------------------------
% 0.11/0.39 % (7296)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.11/0.39 % (7295)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)
% 0.11/0.39 % (7299)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)
% 0.11/0.39 % (7292)Refutation not found, incomplete strategy
% 0.11/0.39 % (7292)------------------------------
% 0.11/0.39 % (7292)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.11/0.39 % (7292)Termination reason: Refutation not found, incomplete strategy
% 0.11/0.39
% 0.11/0.39
% 0.11/0.39 % (7292)Memory used [KB]: 5628
% 0.11/0.39 % (7292)Time elapsed: 0.007 s
% 0.11/0.39 % (7292)Instructions burned: 7 (million)
% 0.11/0.39 % (7292)------------------------------
% 0.11/0.39 % (7292)------------------------------
% 0.11/0.39 % (7296)Instruction limit reached!
% 0.11/0.39 % (7296)------------------------------
% 0.11/0.39 % (7296)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.11/0.39 % (7296)Termination reason: Unknown
% 0.11/0.39 % (7296)Termination phase: Function definition elimination
% 0.11/0.39
% 0.11/0.39 % (7296)Memory used [KB]: 1023
% 0.11/0.39 % (7296)Time elapsed: 0.006 s
% 0.11/0.39 % (7296)Instructions burned: 7 (million)
% 0.11/0.39 % (7296)------------------------------
% 0.11/0.39 % (7296)------------------------------
% 0.11/0.39 % (7299)Instruction limit reached!
% 0.11/0.39 % (7299)------------------------------
% 0.11/0.39 % (7299)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.11/0.39 % (7299)Termination reason: Unknown
% 0.11/0.39 % (7299)Termination phase: Property scanning
% 0.11/0.39
% 0.11/0.39 % (7299)Memory used [KB]: 1023
% 0.11/0.39 % (7299)Time elapsed: 0.004 s
% 0.11/0.39 % (7299)Instructions burned: 4 (million)
% 0.11/0.39 % (7299)------------------------------
% 0.11/0.39 % (7299)------------------------------
% 0.11/0.39 % (7307)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.11/0.39 % (7295)First to succeed.
% 0.11/0.40 % (7307)Instruction limit reached!
% 0.11/0.40 % (7307)------------------------------
% 0.11/0.40 % (7307)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.11/0.40 % (7307)Termination reason: Unknown
% 0.11/0.40 % (7307)Termination phase: Function definition elimination
% 0.11/0.40
% 0.11/0.40 % (7307)Memory used [KB]: 1023
% 0.11/0.40 % (7307)Time elapsed: 0.003 s
% 0.11/0.40 % (7307)Instructions burned: 7 (million)
% 0.11/0.40 % (7307)------------------------------
% 0.11/0.40 % (7307)------------------------------
% 0.21/0.40 % (7295)Refutation found. Thanks to Tanya!
% 0.21/0.40 % SZS status Theorem for theBenchmark
% 0.21/0.40 % SZS output start Proof for theBenchmark
% 0.21/0.40 thf(type_def_5, type, mu: $tType).
% 0.21/0.40 thf(func_def_0, type, mu: $tType).
% 0.21/0.40 thf(func_def_1, type, meq_ind: mu > mu > $i > $o).
% 0.21/0.40 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.40 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.21/0.40 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.40 thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.40 thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.40 thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.40 thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.40 thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.40 thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.21/0.40 thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.21/0.40 thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.21/0.40 thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.21/0.40 thf(func_def_15, type, mtrue: $i > $o).
% 0.21/0.40 thf(func_def_16, type, mfalse: $i > $o).
% 0.21/0.40 thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.21/0.40 thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.21/0.40 thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o).
% 0.21/0.40 thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o).
% 0.21/0.40 thf(func_def_21, type, mserial: ($i > $i > $o) > $o).
% 0.21/0.40 thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o).
% 0.21/0.40 thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o).
% 0.21/0.40 thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.21/0.40 thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o).
% 0.21/0.40 thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.21/0.40 thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.21/0.40 thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.21/0.40 thf(func_def_29, type, mvalid: ($i > $o) > $o).
% 0.21/0.40 thf(func_def_30, type, minvalid: ($i > $o) > $o).
% 0.21/0.40 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.21/0.40 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.21/0.40 thf(func_def_49, type, ph1: !>[X0: $tType]:(X0)).
% 0.21/0.40 thf(func_def_50, type, sK2: ($i > $i > $o) > $i > $i).
% 0.21/0.40 thf(f168,plain,(
% 0.21/0.40 $false),
% 0.21/0.40 inference(trivial_inequality_removal,[],[f167])).
% 0.21/0.40 thf(f167,plain,(
% 0.21/0.40 ($false = $true)),
% 0.21/0.40 inference(beta_eta_normalization,[],[f162])).
% 0.21/0.40 thf(f162,plain,(
% 0.21/0.40 ( ! [X2 : $i] : (($true = ((^[Y0 : $i]: ((^[Y1 : $i]: ($false)))) @ X2 @ (sK2 @ (^[Y0 : $i]: ((^[Y1 : $i]: ($false)))) @ X2)))) )),
% 0.21/0.40 inference(primitive_instantiation,[],[f156])).
% 0.21/0.40 thf(f156,plain,(
% 0.21/0.40 ( ! [X2 : $i,X1 : $i > $i > $o] : (((X1 @ X2 @ (sK2 @ X1 @ X2)) = $true)) )),
% 0.21/0.40 inference(not_proxy_clausification,[],[f155])).
% 0.21/0.40 thf(f155,plain,(
% 0.21/0.40 ( ! [X2 : $i,X1 : $i > $i > $o] : (($false = (~ (X1 @ X2 @ (sK2 @ X1 @ X2))))) )),
% 0.21/0.40 inference(beta_eta_normalization,[],[f154])).
% 0.21/0.40 thf(f154,plain,(
% 0.21/0.40 ( ! [X2 : $i,X1 : $i > $i > $o] : (($false = ((^[Y0 : $i]: (~ (X1 @ X2 @ Y0))) @ (sK2 @ X1 @ X2)))) )),
% 0.21/0.40 inference(sigma_clausification,[],[f151])).
% 0.21/0.40 thf(f151,plain,(
% 0.21/0.40 ( ! [X2 : $i,X1 : $i > $i > $o] : (($false = (!! @ $i @ (^[Y0 : $i]: (~ (X1 @ X2 @ Y0)))))) )),
% 0.21/0.40 inference(not_proxy_clausification,[],[f150])).
% 0.21/0.40 thf(f150,plain,(
% 0.21/0.40 ( ! [X2 : $i,X1 : $i > $i > $o] : (($true = (~ (!! @ $i @ (^[Y0 : $i]: (~ (X1 @ X2 @ Y0))))))) )),
% 0.21/0.40 inference(beta_eta_normalization,[],[f149])).
% 0.21/0.40 thf(f149,plain,(
% 0.21/0.40 ( ! [X2 : $i,X1 : $i > $i > $o] : (($true = ((^[Y0 : $i]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (X1 @ Y0 @ Y1)))))) @ X2))) )),
% 0.21/0.40 inference(pi_clausification,[],[f146])).
% 0.21/0.40 thf(f146,plain,(
% 0.21/0.40 ( ! [X1 : $i > $i > $o] : (((!! @ $i @ (^[Y0 : $i]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (X1 @ Y0 @ Y1))))))) = $true)) )),
% 0.21/0.40 inference(not_proxy_clausification,[],[f145])).
% 0.21/0.40 thf(f145,plain,(
% 0.21/0.40 ( ! [X1 : $i > $i > $o] : (($false = (~ (!! @ $i @ (^[Y0 : $i]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (X1 @ Y0 @ Y1)))))))))) )),
% 0.21/0.40 inference(beta_eta_normalization,[],[f144])).
% 0.21/0.40 thf(f144,plain,(
% 0.21/0.40 ( ! [X1 : $i > $i > $o] : (($false = ((^[Y0 : $i > $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2))))))))) @ X1))) )),
% 0.21/0.40 inference(pi_clausification,[],[f141])).
% 0.21/0.40 thf(f141,plain,(
% 0.21/0.40 ($false = (?? @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2)))))))))))),
% 0.21/0.40 inference(not_proxy_clausification,[],[f140])).
% 0.21/0.40 thf(f140,plain,(
% 0.21/0.40 ($true = (~ (?? @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2))))))))))))),
% 0.21/0.40 inference(boolean_simplification,[],[f139])).
% 0.21/0.40 thf(f139,plain,(
% 0.21/0.40 ($true = (~ (?? @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | $false)))))))))))),
% 0.21/0.40 inference(boolean_simplification,[],[f138])).
% 0.21/0.40 thf(f138,plain,(
% 0.21/0.40 ($true = (~ (?? @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (~ $true))))))))))))),
% 0.21/0.40 inference(beta_eta_normalization,[],[f137])).
% 0.21/0.40 thf(f137,plain,(
% 0.21/0.40 ($true = (~ (?? @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (~ ((^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: (Y1 @ Y2)))) @ ((^[Y1 : $i > $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (~ (Y3 @ Y4))))) @ ((^[Y3 : $i > $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y3 @ Y5 @ Y6)) | (Y4 @ Y6))))))))) @ Y1 @ ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (~ (Y3 @ Y4))))) @ Y2)))))) @ Y0 @ (^[Y1 : $i]: ($true)))))))))),
% 0.21/0.40 inference(definition_unfolding,[],[f107,f124,f136,f99])).
% 0.21/0.40 thf(f99,plain,(
% 0.21/0.40 (mtrue = (^[Y0 : $i]: ($true)))),
% 0.21/0.40 inference(cnf_transformation,[],[f66])).
% 0.21/0.40 thf(f66,plain,(
% 0.21/0.40 (mtrue = (^[Y0 : $i]: ($true)))),
% 0.21/0.40 inference(fool_elimination,[],[f65])).
% 0.21/0.40 thf(f65,plain,(
% 0.21/0.40 ((^[X0 : $i] : ($true)) = mtrue)),
% 0.21/0.40 inference(rectify,[],[f14])).
% 0.21/0.40 thf(f14,axiom,(
% 0.21/0.40 ((^[X2 : $i] : ($true)) = mtrue)),
% 0.21/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mtrue)).
% 0.21/0.40 thf(f136,plain,(
% 0.21/0.40 (mdia = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y2 @ Y4 @ Y5)) | (Y3 @ Y5))))))))) @ Y0 @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))))),
% 0.21/0.40 inference(definition_unfolding,[],[f108,f109,f101,f109])).
% 0.21/0.40 thf(f101,plain,(
% 0.21/0.40 (mbox = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y3))))))))))),
% 0.21/0.40 inference(cnf_transformation,[],[f64])).
% 0.21/0.40 thf(f64,plain,(
% 0.21/0.40 (mbox = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y3))))))))))),
% 0.21/0.40 inference(fool_elimination,[],[f63])).
% 0.21/0.40 thf(f63,plain,(
% 0.21/0.40 ((^[X0 : $i > $i > $o, X1 : $i > $o, X2 : $i] : (! [X3] : ((X1 @ X3) | ~(X0 @ X2 @ X3)))) = mbox)),
% 0.21/0.40 inference(rectify,[],[f16])).
% 0.21/0.40 thf(f16,axiom,(
% 0.21/0.40 ((^[X6 : $i > $i > $o, X3 : $i > $o, X2 : $i] : (! [X7] : ((X3 @ X7) | ~(X6 @ X2 @ X7)))) = mbox)),
% 0.21/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox)).
% 0.21/0.40 thf(f109,plain,(
% 0.21/0.40 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.21/0.40 inference(cnf_transformation,[],[f61])).
% 0.21/0.40 thf(f61,plain,(
% 0.21/0.40 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.21/0.40 inference(fool_elimination,[],[f60])).
% 0.21/0.40 thf(f60,plain,(
% 0.21/0.40 ((^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))) = mnot)),
% 0.21/0.40 inference(rectify,[],[f3])).
% 0.21/0.40 thf(f3,axiom,(
% 0.21/0.40 ((^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))) = mnot)),
% 0.21/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot)).
% 0.21/0.40 thf(f108,plain,(
% 0.21/0.40 (mdia = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mbox @ Y0 @ (mnot @ Y1)))))))),
% 0.21/0.40 inference(cnf_transformation,[],[f51])).
% 0.21/0.40 thf(f51,plain,(
% 0.21/0.40 (mdia = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mbox @ Y0 @ (mnot @ Y1)))))))),
% 0.21/0.40 inference(fool_elimination,[],[f50])).
% 0.21/0.40 thf(f50,plain,(
% 0.21/0.40 ((^[X0 : $i > $i > $o, X1 : $i > $o] : (mnot @ (mbox @ X0 @ (mnot @ X1)))) = mdia)),
% 0.21/0.40 inference(rectify,[],[f17])).
% 0.21/0.40 thf(f17,axiom,(
% 0.21/0.40 ((^[X6 : $i > $i > $o, X3 : $i > $o] : (mnot @ (mbox @ X6 @ (mnot @ X3)))) = mdia)),
% 0.21/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mdia)).
% 0.21/0.40 thf(f124,plain,(
% 0.21/0.40 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.21/0.40 inference(cnf_transformation,[],[f45])).
% 0.21/0.40 thf(f45,plain,(
% 0.21/0.40 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.21/0.40 inference(fool_elimination,[],[f44])).
% 0.21/0.40 thf(f44,plain,(
% 0.21/0.40 ((^[X0 : $i > $o] : (! [X1] : (X0 @ X1))) = mvalid)),
% 0.21/0.40 inference(rectify,[],[f28])).
% 0.21/0.40 thf(f28,axiom,(
% 0.21/0.40 ((^[X3 : $i > $o] : (! [X2] : (X3 @ X2))) = mvalid)),
% 0.21/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mvalid)).
% 0.21/0.40 thf(f107,plain,(
% 0.21/0.40 ((~ (?? @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (~ (mvalid @ (mdia @ Y0 @ mtrue)))))) = $true)),
% 0.21/0.40 inference(cnf_transformation,[],[f76])).
% 0.21/0.40 thf(f76,plain,(
% 0.21/0.40 ((~ (?? @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (~ (mvalid @ (mdia @ Y0 @ mtrue)))))) = $true)),
% 0.21/0.40 inference(fool_elimination,[],[f75])).
% 0.21/0.40 thf(f75,plain,(
% 0.21/0.40 ~? [X0 : $i > $i > $o] : ~(mvalid @ (mdia @ X0 @ mtrue))),
% 0.21/0.40 inference(rectify,[],[f33])).
% 0.21/0.40 thf(f33,negated_conjecture,(
% 0.21/0.40 ~? [X6 : $i > $i > $o] : ~(mvalid @ (mdia @ X6 @ mtrue))),
% 0.21/0.40 inference(negated_conjecture,[],[f32])).
% 0.21/0.40 thf(f32,conjecture,(
% 0.21/0.40 ? [X6 : $i > $i > $o] : ~(mvalid @ (mdia @ X6 @ mtrue))),
% 0.21/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj)).
% 0.21/0.40 % SZS output end Proof for theBenchmark
% 0.21/0.40 % (7295)------------------------------
% 0.21/0.40 % (7295)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.40 % (7295)Termination reason: Refutation
% 0.21/0.40
% 0.21/0.40 % (7295)Memory used [KB]: 5628
% 0.21/0.40 % (7295)Time elapsed: 0.011 s
% 0.21/0.40 % (7295)Instructions burned: 10 (million)
% 0.21/0.40 % (7295)------------------------------
% 0.21/0.40 % (7295)------------------------------
% 0.21/0.40 % (7278)Success in time 0.042 s
%------------------------------------------------------------------------------