TSTP Solution File: LCL626^1 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : LCL626^1 : TPTP v8.2.0. Bugfixed v7.3.0.
% 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 : n032.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 00:16:15 EDT 2024
% Result : Theorem 0.13s 0.32s
% Output : Refutation 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.08 % Problem : LCL626^1 : TPTP v8.2.0. Bugfixed v7.3.0.
% 0.02/0.09 % 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
% 0.09/0.28 % Computer : n032.cluster.edu
% 0.09/0.28 % Model : x86_64 x86_64
% 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28 % Memory : 8042.1875MB
% 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28 % CPULimit : 300
% 0.09/0.28 % WCLimit : 300
% 0.09/0.28 % DateTime : Mon May 20 03:25:23 EDT 2024
% 0.09/0.28 % CPUTime :
% 0.09/0.28 This is a TH0_THM_EQU_NAR problem
% 0.09/0.28 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
% 0.09/0.30 % (15252)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.09/0.30 % (15254)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)
% 0.09/0.30 % (15253)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)
% 0.09/0.30 % (15250)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)
% 0.09/0.30 % (15252)Instruction limit reached!
% 0.09/0.30 % (15252)------------------------------
% 0.09/0.30 % (15252)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.09/0.30 % (15252)Termination reason: Unknown
% 0.09/0.30 % (15252)Termination phase: shuffling
% 0.09/0.30
% 0.09/0.30 % (15253)Instruction limit reached!
% 0.09/0.30 % (15253)------------------------------
% 0.09/0.30 % (15253)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.09/0.30 % (15253)Termination reason: Unknown
% 0.09/0.30 % (15253)Termination phase: shuffling
% 0.09/0.30
% 0.09/0.30 % (15253)Memory used [KB]: 1023
% 0.09/0.30 % (15253)Time elapsed: 0.003 s
% 0.09/0.30 % (15253)Instructions burned: 4 (million)
% 0.09/0.30 % (15253)------------------------------
% 0.09/0.30 % (15253)------------------------------
% 0.09/0.30 % (15252)Memory used [KB]: 1023
% 0.09/0.30 % (15252)Time elapsed: 0.003 s
% 0.09/0.30 % (15252)Instructions burned: 3 (million)
% 0.09/0.30 % (15252)------------------------------
% 0.09/0.30 % (15252)------------------------------
% 0.09/0.30 % (15250)Instruction limit reached!
% 0.09/0.30 % (15250)------------------------------
% 0.09/0.30 % (15250)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.09/0.30 % (15250)Termination reason: Unknown
% 0.09/0.30 % (15250)Termination phase: Property scanning
% 0.09/0.30
% 0.09/0.30 % (15250)Memory used [KB]: 1023
% 0.09/0.30 % (15250)Time elapsed: 0.003 s
% 0.09/0.30 % (15250)Instructions burned: 4 (million)
% 0.09/0.30 % (15250)------------------------------
% 0.09/0.30 % (15250)------------------------------
% 0.09/0.30 % (15255)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.09/0.30 % (15249)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.09/0.30 % (15251)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)
% 0.09/0.30 % (15254)Refutation not found, incomplete strategy
% 0.09/0.30 % (15254)------------------------------
% 0.09/0.30 % (15254)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.09/0.30 % (15254)Termination reason: Refutation not found, incomplete strategy
% 0.09/0.30
% 0.09/0.30
% 0.09/0.30 % (15254)Memory used [KB]: 5628
% 0.09/0.30 % (15254)Time elapsed: 0.005 s
% 0.09/0.30 % (15254)Instructions burned: 8 (million)
% 0.09/0.30 % (15254)------------------------------
% 0.09/0.30 % (15254)------------------------------
% 0.13/0.31 % (15256)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)
% 0.13/0.31 % (15255)Instruction limit reached!
% 0.13/0.31 % (15255)------------------------------
% 0.13/0.31 % (15255)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.31 % (15255)Termination reason: Unknown
% 0.13/0.31 % (15256)Instruction limit reached!
% 0.13/0.31 % (15256)------------------------------
% 0.13/0.31 % (15256)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.31 % (15256)Termination reason: Unknown
% 0.13/0.31 % (15256)Termination phase: shuffling
% 0.13/0.31
% 0.13/0.31 % (15256)Memory used [KB]: 1023
% 0.13/0.31 % (15256)Time elapsed: 0.002 s
% 0.13/0.31 % (15256)Instructions burned: 3 (million)
% 0.13/0.31 % (15256)------------------------------
% 0.13/0.31 % (15256)------------------------------
% 0.13/0.31 % (15255)Termination phase: Saturation
% 0.13/0.31
% 0.13/0.31 % (15255)Memory used [KB]: 5756
% 0.13/0.31 % (15255)Time elapsed: 0.010 s
% 0.13/0.31 % (15255)Instructions burned: 18 (million)
% 0.13/0.31 % (15255)------------------------------
% 0.13/0.31 % (15255)------------------------------
% 0.13/0.31 % (15257)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)
% 0.13/0.31 % (15259)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)
% 0.13/0.31 % (15260)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)
% 0.13/0.31 % (15259)Instruction limit reached!
% 0.13/0.31 % (15259)------------------------------
% 0.13/0.31 % (15259)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.31 % (15259)Termination reason: Unknown
% 0.13/0.31 % (15259)Termination phase: Property scanning
% 0.13/0.31
% 0.13/0.31 % (15259)Memory used [KB]: 1023
% 0.13/0.31 % (15259)Time elapsed: 0.003 s
% 0.13/0.31 % (15259)Instructions burned: 5 (million)
% 0.13/0.31 % (15259)------------------------------
% 0.13/0.31 % (15259)------------------------------
% 0.13/0.31 % (15258)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)
% 0.13/0.31 % (15251)First to succeed.
% 0.13/0.32 % (15261)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.13/0.32 % (15251)Refutation found. Thanks to Tanya!
% 0.13/0.32 % SZS status Theorem for theBenchmark
% 0.13/0.32 % SZS output start Proof for theBenchmark
% 0.13/0.32 thf(type_def_6, type, individuals: $tType).
% 0.13/0.32 thf(func_def_1, type, prop_a: $i > $o).
% 0.13/0.32 thf(func_def_2, type, prop_b: $i > $o).
% 0.13/0.32 thf(func_def_3, type, prop_c: $i > $o).
% 0.13/0.32 thf(func_def_4, type, mfalse: $i > $o).
% 0.13/0.32 thf(func_def_5, type, mtrue: $i > $o).
% 0.13/0.32 thf(func_def_6, type, mnot: ($i > $o) > $i > $o).
% 0.13/0.32 thf(func_def_8, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.13/0.32 thf(func_def_9, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.13/0.32 thf(func_def_10, type, mimpl: ($i > $o) > ($i > $o) > $i > $o).
% 0.13/0.32 thf(func_def_11, type, miff: ($i > $o) > ($i > $o) > $i > $o).
% 0.13/0.32 thf(func_def_12, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.13/0.32 thf(func_def_13, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.13/0.32 thf(func_def_14, type, individuals: $tType).
% 0.13/0.32 thf(func_def_15, type, mall: (individuals > $i > $o) > $i > $o).
% 0.13/0.32 thf(func_def_16, type, mexists: (individuals > $i > $o) > $i > $o).
% 0.13/0.32 thf(func_def_17, type, mvalid: ($i > $o) > $o).
% 0.13/0.32 thf(func_def_18, type, msatisfiable: ($i > $o) > $o).
% 0.13/0.32 thf(func_def_19, type, mcountersatisfiable: ($i > $o) > $o).
% 0.13/0.32 thf(func_def_20, type, minvalid: ($i > $o) > $o).
% 0.13/0.32 thf(func_def_21, type, cartesian_product: ($i > $o) > ($i > $o) > $i > $i > $o).
% 0.13/0.32 thf(func_def_22, type, pair_rel: $i > $i > $i > $i > $o).
% 0.13/0.32 thf(func_def_23, type, id_rel: ($i > $o) > $i > $i > $o).
% 0.13/0.32 thf(func_def_24, type, sub_rel: ($i > $i > $o) > ($i > $i > $o) > $o).
% 0.13/0.32 thf(func_def_25, type, is_rel_on: ($i > $i > $o) > ($i > $o) > ($i > $o) > $o).
% 0.13/0.32 thf(func_def_26, type, restrict_rel_domain: ($i > $i > $o) > ($i > $o) > $i > $i > $o).
% 0.13/0.32 thf(func_def_27, type, rel_diagonal: $i > $i > $o).
% 0.13/0.32 thf(func_def_28, type, rel_composition: ($i > $i > $o) > ($i > $i > $o) > $i > $i > $o).
% 0.13/0.32 thf(func_def_29, type, reflexive: ($i > $i > $o) > $o).
% 0.13/0.32 thf(func_def_30, type, irreflexive: ($i > $i > $o) > $o).
% 0.13/0.32 thf(func_def_31, type, symmetric: ($i > $i > $o) > $o).
% 0.13/0.32 thf(func_def_32, type, transitive: ($i > $i > $o) > $o).
% 0.13/0.32 thf(func_def_33, type, equiv_rel: ($i > $i > $o) > $o).
% 0.13/0.32 thf(func_def_34, type, rel_codomain: ($i > $i > $o) > $i > $o).
% 0.13/0.32 thf(func_def_35, type, rel_domain: ($i > $i > $o) > $i > $o).
% 0.13/0.32 thf(func_def_36, type, rel_inverse: ($i > $i > $o) > $i > $i > $o).
% 0.13/0.32 thf(func_def_37, type, equiv_classes: ($i > $i > $o) > ($i > $o) > $o).
% 0.13/0.32 thf(func_def_38, type, restrict_rel_codomain: ($i > $i > $o) > ($i > $o) > $i > $i > $o).
% 0.13/0.32 thf(func_def_39, type, rel_field: ($i > $i > $o) > $i > $o).
% 0.13/0.32 thf(func_def_40, type, well_founded: ($i > $i > $o) > $o).
% 0.13/0.32 thf(func_def_41, type, upwards_well_founded: ($i > $i > $o) > $o).
% 0.13/0.32 thf(func_def_42, type, r: $i > $i > $o).
% 0.13/0.32 thf(func_def_43, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 0.13/0.32 thf(func_def_60, type, sK0: $i > $o).
% 0.13/0.32 thf(func_def_62, type, sK2: ($i > $o) > $i).
% 0.13/0.32 thf(f321,plain,(
% 0.13/0.32 $false),
% 0.13/0.32 inference(avatar_sat_refutation,[],[f264,f320])).
% 0.13/0.32 thf(f320,plain,(
% 0.13/0.32 spl1_2),
% 0.13/0.32 inference(avatar_split_clause,[],[f315,f241])).
% 0.13/0.32 thf(f241,plain,(
% 0.13/0.32 spl1_2 <=> ($false = (r @ sK3 @ sK4))),
% 0.13/0.32 introduced(avatar_definition,[new_symbols(naming,[spl1_2])])).
% 0.13/0.32 thf(f315,plain,(
% 0.13/0.32 ($false = (r @ sK3 @ sK4))),
% 0.13/0.32 inference(trivial_inequality_removal,[],[f313])).
% 0.13/0.32 thf(f313,plain,(
% 0.13/0.32 ($false = (r @ sK3 @ sK4)) | ($true = $false)),
% 0.13/0.32 inference(superposition,[],[f199,f308])).
% 0.13/0.32 thf(f308,plain,(
% 0.13/0.32 ( ! [X0 : $i] : (($false = (r @ X0 @ sK5)) | ((r @ sK3 @ X0) = $false)) )),
% 0.13/0.32 inference(trivial_inequality_removal,[],[f307])).
% 0.13/0.32 thf(f307,plain,(
% 0.13/0.32 ( ! [X0 : $i] : (((r @ sK3 @ X0) = $false) | ($false = (r @ X0 @ sK5)) | ($true = $false)) )),
% 0.13/0.32 inference(forward_demodulation,[],[f305,f202])).
% 0.13/0.32 thf(f202,plain,(
% 0.13/0.32 ((sK0 @ sK6) = $false)),
% 0.13/0.32 inference(binary_proxy_clausification,[],[f201])).
% 0.13/0.32 thf(f201,plain,(
% 0.13/0.32 ($false = ((r @ sK5 @ sK6) => (sK0 @ sK6)))),
% 0.13/0.32 inference(beta_eta_normalization,[],[f200])).
% 0.13/0.32 thf(f200,plain,(
% 0.13/0.32 (((^[Y0 : $i]: ((r @ sK5 @ Y0) => (sK0 @ Y0))) @ sK6) = $false)),
% 0.13/0.32 inference(sigma_clausification,[],[f198])).
% 0.13/0.32 thf(f198,plain,(
% 0.13/0.32 ((!! @ $i @ (^[Y0 : $i]: ((r @ sK5 @ Y0) => (sK0 @ Y0)))) = $false)),
% 0.13/0.32 inference(binary_proxy_clausification,[],[f197])).
% 0.13/0.32 thf(f197,plain,(
% 0.13/0.32 ($false = ((r @ sK4 @ sK5) => (!! @ $i @ (^[Y0 : $i]: ((r @ sK5 @ Y0) => (sK0 @ Y0))))))),
% 0.13/0.32 inference(beta_eta_normalization,[],[f196])).
% 0.13/0.32 thf(f196,plain,(
% 0.13/0.32 (((^[Y0 : $i]: ((r @ sK4 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((r @ Y0 @ Y1) => (sK0 @ Y1)))))) @ sK5) = $false)),
% 0.13/0.32 inference(sigma_clausification,[],[f194])).
% 0.13/0.32 thf(f194,plain,(
% 0.13/0.32 ((!! @ $i @ (^[Y0 : $i]: ((r @ sK4 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((r @ Y0 @ Y1) => (sK0 @ Y1))))))) = $false)),
% 0.13/0.32 inference(binary_proxy_clausification,[],[f193])).
% 0.13/0.32 thf(f193,plain,(
% 0.13/0.32 (((r @ sK3 @ sK4) => (!! @ $i @ (^[Y0 : $i]: ((r @ sK4 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((r @ Y0 @ Y1) => (sK0 @ Y1)))))))) = $false)),
% 0.13/0.32 inference(beta_eta_normalization,[],[f192])).
% 0.13/0.32 thf(f192,plain,(
% 0.13/0.32 ($false = ((^[Y0 : $i]: ((r @ sK3 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((r @ Y0 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((r @ Y1 @ Y2) => (sK0 @ Y2))))))))) @ sK4))),
% 0.13/0.32 inference(sigma_clausification,[],[f191])).
% 0.13/0.32 thf(f191,plain,(
% 0.13/0.32 ($false = (!! @ $i @ (^[Y0 : $i]: ((r @ sK3 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((r @ Y0 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((r @ Y1 @ Y2) => (sK0 @ Y2)))))))))))),
% 0.13/0.32 inference(binary_proxy_clausification,[],[f189])).
% 0.13/0.32 thf(f189,plain,(
% 0.13/0.32 ($false = ((!! @ $i @ (^[Y0 : $i]: ((r @ sK3 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((r @ Y0 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((r @ Y1 @ Y2) => (sK0 @ Y2)))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((r @ sK3 @ Y0) => (sK0 @ Y0)))))))),
% 0.13/0.32 inference(beta_eta_normalization,[],[f188])).
% 0.13/0.32 thf(f188,plain,(
% 0.13/0.32 (((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((r @ Y0 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((r @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((r @ Y2 @ Y3) => (sK0 @ Y3)))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((r @ Y0 @ Y1) => (sK0 @ Y1))))))) @ sK3) = $false)),
% 0.13/0.32 inference(sigma_clausification,[],[f187])).
% 0.13/0.32 thf(f187,plain,(
% 0.13/0.32 ($true != (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((r @ Y0 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((r @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((r @ Y2 @ Y3) => (sK0 @ Y3)))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((r @ Y0 @ Y1) => (sK0 @ Y1)))))))))),
% 0.13/0.32 inference(beta_eta_normalization,[],[f163])).
% 0.13/0.32 thf(f163,plain,(
% 0.13/0.32 ($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 > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (Y1 @ Y3))))))))) @ r @ sK0) @ ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (Y1 @ Y3))))))))) @ r @ ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (Y1 @ Y3))))))))) @ r @ ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (Y1 @ Y3))))))))) @ r @ sK0))))))),
% 0.13/0.32 inference(definition_unfolding,[],[f129,f145,f157,f144,f144,f144,f144])).
% 0.13/0.32 thf(f144,plain,(
% 0.13/0.32 (mbox = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (Y1 @ Y3))))))))))),
% 0.13/0.32 inference(cnf_transformation,[],[f62])).
% 0.13/0.32 thf(f62,plain,(
% 0.13/0.32 (mbox = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (Y1 @ Y3))))))))))),
% 0.13/0.32 inference(fool_elimination,[],[f61])).
% 0.13/0.32 thf(f61,plain,(
% 0.13/0.32 ((^[X0 : $i > $i > $o, X1 : $i > $o, X2 : $i] : (! [X3] : ((X0 @ X2 @ X3) => (X1 @ X3)))) = mbox)),
% 0.13/0.32 inference(rectify,[],[f8])).
% 0.13/0.32 thf(f8,axiom,(
% 0.13/0.32 ((^[X4 : $i > $i > $o, X5 : $i > $o, X0 : $i] : (! [X2] : ((X4 @ X0 @ X2) => (X5 @ X2)))) = mbox)),
% 0.13/0.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox)).
% 0.13/0.32 thf(f157,plain,(
% 0.13/0.32 (mimpl = (^[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)))))),
% 0.13/0.32 inference(definition_unfolding,[],[f143,f147,f149])).
% 0.13/0.32 thf(f149,plain,(
% 0.13/0.32 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.13/0.32 inference(cnf_transformation,[],[f44])).
% 0.13/0.32 thf(f44,plain,(
% 0.13/0.32 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.13/0.32 inference(fool_elimination,[],[f43])).
% 0.13/0.32 thf(f43,plain,(
% 0.13/0.32 (mnot = (^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))))),
% 0.13/0.32 inference(rectify,[],[f3])).
% 0.13/0.32 thf(f3,axiom,(
% 0.13/0.32 (mnot = (^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))))),
% 0.13/0.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot)).
% 0.13/0.32 thf(f147,plain,(
% 0.13/0.32 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.13/0.32 inference(cnf_transformation,[],[f114])).
% 0.13/0.32 thf(f114,plain,(
% 0.13/0.32 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.13/0.32 inference(fool_elimination,[],[f113])).
% 0.13/0.32 thf(f113,plain,(
% 0.13/0.32 (mor = (^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X0 @ X2) | (X1 @ X2))))),
% 0.13/0.32 inference(rectify,[],[f4])).
% 0.13/0.32 thf(f4,axiom,(
% 0.13/0.32 (mor = (^[X0 : $i > $o, X2 : $i > $o, X1 : $i] : ((X0 @ X1) | (X2 @ X1))))),
% 0.13/0.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor)).
% 0.13/0.32 thf(f143,plain,(
% 0.13/0.32 (mimpl = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.13/0.32 inference(cnf_transformation,[],[f68])).
% 0.13/0.32 thf(f68,plain,(
% 0.13/0.32 (mimpl = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.13/0.32 inference(fool_elimination,[],[f67])).
% 0.13/0.32 thf(f67,plain,(
% 0.13/0.32 (mimpl = (^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)))),
% 0.13/0.32 inference(rectify,[],[f6])).
% 0.13/0.32 thf(f6,axiom,(
% 0.13/0.32 (mimpl = (^[X1 : $i > $o, X3 : $i > $o] : (mor @ (mnot @ X1) @ X3)))),
% 0.13/0.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimpl)).
% 0.13/0.32 thf(f145,plain,(
% 0.13/0.32 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.13/0.32 inference(cnf_transformation,[],[f85])).
% 0.13/0.32 thf(f85,plain,(
% 0.13/0.32 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.13/0.32 inference(fool_elimination,[],[f84])).
% 0.13/0.32 thf(f84,plain,(
% 0.13/0.32 ((^[X0 : $i > $o] : (! [X1] : (X0 @ X1))) = mvalid)),
% 0.13/0.32 inference(rectify,[],[f12])).
% 0.13/0.32 thf(f12,axiom,(
% 0.13/0.32 ((^[X5 : $i > $o] : (! [X6] : (X5 @ X6))) = mvalid)),
% 0.13/0.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mvalid)).
% 0.13/0.32 thf(f129,plain,(
% 0.13/0.32 ($true != (mvalid @ (mimpl @ (mbox @ r @ sK0) @ (mbox @ r @ (mbox @ r @ (mbox @ r @ sK0))))))),
% 0.13/0.32 inference(cnf_transformation,[],[f117])).
% 0.13/0.32 thf(f117,plain,(
% 0.13/0.32 ($true != (mvalid @ (mimpl @ (mbox @ r @ sK0) @ (mbox @ r @ (mbox @ r @ (mbox @ r @ sK0))))))),
% 0.13/0.32 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f115,f116])).
% 0.13/0.32 thf(f116,plain,(
% 0.13/0.32 ? [X0 : $i > $o] : ((mvalid @ (mimpl @ (mbox @ r @ X0) @ (mbox @ r @ (mbox @ r @ (mbox @ r @ X0))))) != $true) => ($true != (mvalid @ (mimpl @ (mbox @ r @ sK0) @ (mbox @ r @ (mbox @ r @ (mbox @ r @ sK0))))))),
% 0.13/0.32 introduced(choice_axiom,[])).
% 0.13/0.32 thf(f115,plain,(
% 0.13/0.32 ? [X0 : $i > $o] : ((mvalid @ (mimpl @ (mbox @ r @ X0) @ (mbox @ r @ (mbox @ r @ (mbox @ r @ X0))))) != $true)),
% 0.13/0.32 inference(ennf_transformation,[],[f101])).
% 0.13/0.32 thf(f101,plain,(
% 0.13/0.32 ~! [X0 : $i > $o] : ((mvalid @ (mimpl @ (mbox @ r @ X0) @ (mbox @ r @ (mbox @ r @ (mbox @ r @ X0))))) = $true)),
% 0.13/0.32 inference(fool_elimination,[],[f100])).
% 0.13/0.32 thf(f100,plain,(
% 0.13/0.32 ~! [X0 : $i > $o] : (mvalid @ (mimpl @ (mbox @ r @ X0) @ (mbox @ r @ (mbox @ r @ (mbox @ r @ X0)))))),
% 0.13/0.32 inference(rectify,[],[f39])).
% 0.13/0.32 thf(f39,negated_conjecture,(
% 0.13/0.32 ~! [X0 : $i > $o] : (mvalid @ (mimpl @ (mbox @ r @ X0) @ (mbox @ r @ (mbox @ r @ (mbox @ r @ X0)))))),
% 0.13/0.32 inference(negated_conjecture,[],[f38])).
% 0.13/0.32 thf(f38,conjecture,(
% 0.13/0.32 ! [X0 : $i > $o] : (mvalid @ (mimpl @ (mbox @ r @ X0) @ (mbox @ r @ (mbox @ r @ (mbox @ r @ X0)))))),
% 0.13/0.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k4)).
% 0.13/0.32 thf(f305,plain,(
% 0.13/0.32 ( ! [X0 : $i] : (((r @ sK3 @ X0) = $false) | ((sK0 @ sK6) = $true) | ($false = (r @ X0 @ sK5))) )),
% 0.13/0.32 inference(trivial_inequality_removal,[],[f288])).
% 0.13/0.32 thf(f288,plain,(
% 0.13/0.32 ( ! [X0 : $i] : (($true = $false) | ((sK0 @ sK6) = $true) | ($false = (r @ X0 @ sK5)) | ((r @ sK3 @ X0) = $false)) )),
% 0.13/0.32 inference(superposition,[],[f223,f203])).
% 0.13/0.32 thf(f203,plain,(
% 0.13/0.32 ($true = (r @ sK5 @ sK6))),
% 0.13/0.32 inference(binary_proxy_clausification,[],[f201])).
% 0.13/0.32 thf(f223,plain,(
% 0.13/0.32 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($false = (r @ X2 @ X1)) | ((r @ sK3 @ X0) = $false) | ((r @ X0 @ X2) = $false) | ((sK0 @ X1) = $true)) )),
% 0.13/0.32 inference(trivial_inequality_removal,[],[f221])).
% 0.13/0.32 thf(f221,plain,(
% 0.13/0.32 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = $false) | ((r @ X0 @ X2) = $false) | ($false = (r @ X2 @ X1)) | ((r @ sK3 @ X0) = $false) | ((sK0 @ X1) = $true)) )),
% 0.13/0.32 inference(superposition,[],[f172,f214])).
% 0.13/0.32 thf(f214,plain,(
% 0.13/0.32 ( ! [X0 : $i,X1 : $i] : (($false = (r @ X1 @ X0)) | ($true = (sK0 @ X0)) | ((r @ sK3 @ X1) = $false)) )),
% 0.13/0.32 inference(trivial_inequality_removal,[],[f211])).
% 0.13/0.32 thf(f211,plain,(
% 0.13/0.32 ( ! [X0 : $i,X1 : $i] : (($true = $false) | ($false = (r @ X1 @ X0)) | ($true = (sK0 @ X0)) | ((r @ sK3 @ X1) = $false)) )),
% 0.13/0.32 inference(superposition,[],[f207,f172])).
% 0.13/0.32 thf(f207,plain,(
% 0.13/0.32 ( ! [X1 : $i] : (((r @ sK3 @ X1) = $false) | ((sK0 @ X1) = $true)) )),
% 0.13/0.32 inference(binary_proxy_clausification,[],[f206])).
% 0.13/0.32 thf(f206,plain,(
% 0.13/0.32 ( ! [X1 : $i] : ((((r @ sK3 @ X1) => (sK0 @ X1)) = $true)) )),
% 0.13/0.32 inference(beta_eta_normalization,[],[f205])).
% 0.13/0.32 thf(f205,plain,(
% 0.13/0.32 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((r @ sK3 @ Y0) => (sK0 @ Y0))) @ X1) = $true)) )),
% 0.13/0.32 inference(pi_clausification,[],[f204])).
% 0.13/0.32 thf(f204,plain,(
% 0.13/0.32 ($true = (!! @ $i @ (^[Y0 : $i]: ((r @ sK3 @ Y0) => (sK0 @ Y0)))))),
% 0.13/0.32 inference(not_proxy_clausification,[],[f190])).
% 0.13/0.32 thf(f190,plain,(
% 0.13/0.32 ((~ (!! @ $i @ (^[Y0 : $i]: ((r @ sK3 @ Y0) => (sK0 @ Y0))))) = $false)),
% 0.13/0.32 inference(binary_proxy_clausification,[],[f189])).
% 0.13/0.32 thf(f172,plain,(
% 0.13/0.32 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (r @ X1 @ X2)) | ((r @ X3 @ X2) = $false) | ($false = (r @ X1 @ X3))) )),
% 0.13/0.32 inference(binary_proxy_clausification,[],[f171])).
% 0.13/0.32 thf(f171,plain,(
% 0.13/0.32 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((r @ X1 @ X3) & (r @ X3 @ X2))) | ($true = (r @ X1 @ X2))) )),
% 0.13/0.32 inference(binary_proxy_clausification,[],[f170])).
% 0.13/0.32 thf(f170,plain,(
% 0.13/0.32 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((r @ X1 @ X3) & (r @ X3 @ X2)) => (r @ X1 @ X2)))) )),
% 0.13/0.32 inference(beta_eta_normalization,[],[f169])).
% 0.13/0.32 thf(f169,plain,(
% 0.13/0.32 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (((r @ X1 @ Y0) & (r @ Y0 @ X2)) => (r @ X1 @ X2))) @ X3))) )),
% 0.13/0.32 inference(pi_clausification,[],[f168])).
% 0.13/0.32 thf(f168,plain,(
% 0.13/0.32 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (((r @ X1 @ Y0) & (r @ Y0 @ X2)) => (r @ X1 @ X2)))))) )),
% 0.13/0.32 inference(beta_eta_normalization,[],[f167])).
% 0.13/0.32 thf(f167,plain,(
% 0.13/0.32 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((r @ X1 @ Y1) & (r @ Y1 @ Y0)) => (r @ X1 @ Y0))))) @ X2))) )),
% 0.13/0.32 inference(pi_clausification,[],[f166])).
% 0.13/0.32 thf(f166,plain,(
% 0.13/0.32 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((r @ X1 @ Y1) & (r @ Y1 @ Y0)) => (r @ X1 @ Y0)))))))) )),
% 0.13/0.32 inference(beta_eta_normalization,[],[f165])).
% 0.13/0.32 thf(f165,plain,(
% 0.13/0.32 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((r @ Y0 @ Y2) & (r @ Y2 @ Y1)) => (r @ Y0 @ Y1))))))) @ X1))) )),
% 0.13/0.32 inference(pi_clausification,[],[f164])).
% 0.13/0.32 thf(f164,plain,(
% 0.13/0.32 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((r @ Y0 @ Y2) & (r @ Y2 @ Y1)) => (r @ Y0 @ Y1)))))))) = $true)),
% 0.13/0.32 inference(beta_eta_normalization,[],[f162])).
% 0.13/0.32 thf(f162,plain,(
% 0.13/0.32 ($true = ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y1 @ Y2))))))))) @ r))),
% 0.13/0.32 inference(definition_unfolding,[],[f125,f124])).
% 0.13/0.32 thf(f124,plain,(
% 0.13/0.32 (transitive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y1 @ Y2))))))))))),
% 0.13/0.32 inference(cnf_transformation,[],[f70])).
% 0.13/0.32 thf(f70,plain,(
% 0.13/0.32 (transitive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y1 @ Y2))))))))))),
% 0.13/0.32 inference(fool_elimination,[],[f69])).
% 0.13/0.32 thf(f69,plain,(
% 0.13/0.32 (transitive = (^[X0 : $i > $i > $o] : (! [X1,X2,X3] : (((X0 @ X1 @ X2) & (X0 @ X3 @ X1)) => (X0 @ X3 @ X2)))))),
% 0.13/0.32 inference(rectify,[],[f27])).
% 0.13/0.32 thf(f27,axiom,(
% 0.13/0.32 (transitive = (^[X4 : $i > $i > $o] : (! [X2,X12,X0] : (((X4 @ X2 @ X12) & (X4 @ X0 @ X2)) => (X4 @ X0 @ X12)))))),
% 0.13/0.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitive)).
% 0.13/0.32 thf(f125,plain,(
% 0.13/0.32 ((transitive @ r) = $true)),
% 0.13/0.32 inference(cnf_transformation,[],[f60])).
% 0.13/0.32 thf(f60,plain,(
% 0.13/0.32 ((upwards_well_founded @ r) = $true) & ((transitive @ r) = $true)),
% 0.13/0.32 inference(fool_elimination,[],[f59])).
% 0.13/0.32 thf(f59,plain,(
% 0.13/0.32 (transitive @ r) & (upwards_well_founded @ r)),
% 0.13/0.32 inference(rectify,[],[f37])).
% 0.13/0.32 thf(f37,axiom,(
% 0.13/0.32 (transitive @ r) & (upwards_well_founded @ r)),
% 0.13/0.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upwf_trans)).
% 0.13/0.32 thf(f199,plain,(
% 0.13/0.32 ((r @ sK4 @ sK5) = $true)),
% 0.13/0.32 inference(binary_proxy_clausification,[],[f197])).
% 0.13/0.32 thf(f264,plain,(
% 0.13/0.32 ~spl1_2),
% 0.13/0.32 inference(avatar_contradiction_clause,[],[f263])).
% 0.13/0.32 thf(f263,plain,(
% 0.13/0.32 $false | ~spl1_2),
% 0.13/0.32 inference(trivial_inequality_removal,[],[f260])).
% 0.13/0.32 thf(f260,plain,(
% 0.13/0.32 ($true = $false) | ~spl1_2),
% 0.13/0.32 inference(backward_demodulation,[],[f195,f243])).
% 0.13/0.32 thf(f243,plain,(
% 0.13/0.32 ($false = (r @ sK3 @ sK4)) | ~spl1_2),
% 0.13/0.32 inference(avatar_component_clause,[],[f241])).
% 0.13/0.32 thf(f195,plain,(
% 0.13/0.32 ($true = (r @ sK3 @ sK4))),
% 0.13/0.32 inference(binary_proxy_clausification,[],[f193])).
% 0.13/0.32 % SZS output end Proof for theBenchmark
% 0.13/0.32 % (15251)------------------------------
% 0.13/0.32 % (15251)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.32 % (15251)Termination reason: Refutation
% 0.13/0.32
% 0.13/0.32 % (15251)Memory used [KB]: 5756
% 0.13/0.32 % (15251)Time elapsed: 0.018 s
% 0.13/0.32 % (15251)Instructions burned: 25 (million)
% 0.13/0.32 % (15251)------------------------------
% 0.13/0.32 % (15251)------------------------------
% 0.13/0.32 % (15248)Success in time 0.02 s
% 0.13/0.32 % Vampire---4.8 exiting
%------------------------------------------------------------------------------