TSTP Solution File: LCL957^6 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : LCL957^6 : TPTP v8.2.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n005.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 00:24:11 EDT 2024
% Result : Theorem 0.17s 0.39s
% Output : Refutation 0.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : LCL957^6 : TPTP v8.2.0. Released v8.1.0.
% 0.13/0.16 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.17/0.37 % Computer : n005.cluster.edu
% 0.17/0.37 % Model : x86_64 x86_64
% 0.17/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.37 % Memory : 8042.1875MB
% 0.17/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.37 % CPULimit : 300
% 0.17/0.37 % WCLimit : 300
% 0.17/0.37 % DateTime : Mon May 20 01:52:23 EDT 2024
% 0.17/0.37 % CPUTime :
% 0.17/0.37 This is a TH0_THM_EQU_NAR problem
% 0.17/0.37 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/sandbox/benchmark/theBenchmark.p
% 0.17/0.39 % (3212)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (3000ds/183Mi)
% 0.17/0.39 % (3219)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (3000ds/3Mi)
% 0.17/0.39 % (3219)Instruction limit reached!
% 0.17/0.39 % (3219)------------------------------
% 0.17/0.39 % (3219)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.39 % (3219)Termination reason: Unknown
% 0.17/0.39 % (3219)Termination phase: shuffling
% 0.17/0.39
% 0.17/0.39 % (3219)Memory used [KB]: 1023
% 0.17/0.39 % (3219)Time elapsed: 0.002 s
% 0.17/0.39 % (3219)Instructions burned: 3 (million)
% 0.17/0.39 % (3219)------------------------------
% 0.17/0.39 % (3219)------------------------------
% 0.17/0.39 % (3212)First to succeed.
% 0.17/0.39 % (3213)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 (3000ds/4Mi)
% 0.17/0.39 % (3214)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 (3000ds/27Mi)
% 0.17/0.39 % (3215)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (3000ds/2Mi)
% 0.17/0.39 % (3216)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 (3000ds/2Mi)
% 0.17/0.39 % (3217)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 (3000ds/275Mi)
% 0.17/0.39 % (3218)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (3000ds/18Mi)
% 0.17/0.39 % (3212)Refutation found. Thanks to Tanya!
% 0.17/0.39 % SZS status Theorem for theBenchmark
% 0.17/0.39 % SZS output start Proof for theBenchmark
% 0.17/0.39 thf(type_def_5, type, mworld: $tType).
% 0.17/0.39 thf(func_def_0, type, mworld: $tType).
% 0.17/0.39 thf(func_def_1, type, mrel: mworld > mworld > $o).
% 0.17/0.39 thf(func_def_2, type, mactual: mworld).
% 0.17/0.39 thf(func_def_3, type, mlocal: (mworld > $o) > $o).
% 0.17/0.39 thf(func_def_5, type, mnot: (mworld > $o) > mworld > $o).
% 0.17/0.39 thf(func_def_6, type, mand: (mworld > $o) > (mworld > $o) > mworld > $o).
% 0.17/0.39 thf(func_def_7, type, mor: (mworld > $o) > (mworld > $o) > mworld > $o).
% 0.17/0.39 thf(func_def_8, type, mimplies: (mworld > $o) > (mworld > $o) > mworld > $o).
% 0.17/0.39 thf(func_def_9, type, mequiv: (mworld > $o) > (mworld > $o) > mworld > $o).
% 0.17/0.39 thf(func_def_10, type, mbox: (mworld > $o) > mworld > $o).
% 0.17/0.39 thf(func_def_11, type, mdia: (mworld > $o) > mworld > $o).
% 0.17/0.39 thf(func_def_12, type, mforall_di: ($i > mworld > $o) > mworld > $o).
% 0.17/0.39 thf(func_def_13, type, mexists_di: ($i > mworld > $o) > mworld > $o).
% 0.17/0.39 thf(func_def_14, type, big_r: $i > $i > mworld > $o).
% 0.17/0.39 thf(func_def_32, type, sK1: mworld).
% 0.17/0.39 thf(func_def_33, type, sK2: $i > mworld > mworld).
% 0.17/0.39 thf(func_def_34, type, sK3: $i > mworld).
% 0.17/0.39 thf(func_def_35, type, sK4: $i > $i).
% 0.17/0.39 thf(func_def_36, type, sK5: $i > mworld).
% 0.17/0.39 thf(func_def_37, type, sK6: $i > mworld).
% 0.17/0.39 thf(f104,plain,(
% 0.17/0.39 $false),
% 0.17/0.39 inference(trivial_inequality_removal,[],[f102])).
% 0.17/0.39 thf(f102,plain,(
% 0.17/0.39 ($false = $true)),
% 0.17/0.39 inference(superposition,[],[f101,f48])).
% 0.17/0.39 thf(f48,plain,(
% 0.17/0.39 ( ! [X0 : mworld,X1 : mworld] : (($true = (mrel @ X1 @ X0))) )),
% 0.17/0.39 inference(cnf_transformation,[],[f33])).
% 0.17/0.39 thf(f33,plain,(
% 0.17/0.39 ! [X0 : mworld,X1 : mworld] : ($true = (mrel @ X1 @ X0))),
% 0.17/0.39 inference(fool_elimination,[],[f32])).
% 0.17/0.39 thf(f32,plain,(
% 0.17/0.39 ! [X0 : mworld,X1 : mworld] : (mrel @ X1 @ X0)),
% 0.17/0.39 inference(rectify,[],[f9])).
% 0.17/0.39 thf(f9,axiom,(
% 0.17/0.39 ! [X4 : mworld,X2 : mworld] : (mrel @ X2 @ X4)),
% 0.17/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_universal)).
% 0.17/0.39 thf(f101,plain,(
% 0.17/0.39 ( ! [X0 : $i] : (($false = (mrel @ (sK5 @ (sK4 @ X0)) @ (sK6 @ X0)))) )),
% 0.17/0.39 inference(trivial_inequality_removal,[],[f99])).
% 0.17/0.39 thf(f99,plain,(
% 0.17/0.39 ( ! [X0 : $i] : (($false = (mrel @ (sK5 @ (sK4 @ X0)) @ (sK6 @ X0))) | ($false = $true)) )),
% 0.17/0.39 inference(superposition,[],[f96,f93])).
% 0.17/0.39 thf(f93,plain,(
% 0.17/0.39 ( ! [X2 : mworld,X1 : $i] : (((big_r @ X1 @ X1 @ X2) = $true) | ($false = (mrel @ (sK5 @ X1) @ X2))) )),
% 0.17/0.39 inference(binary_proxy_clausification,[],[f92])).
% 0.17/0.39 thf(f92,plain,(
% 0.17/0.39 ( ! [X2 : mworld,X1 : $i] : ((((mrel @ (sK5 @ X1) @ X2) => (big_r @ X1 @ X1 @ X2)) = $true)) )),
% 0.17/0.39 inference(beta_eta_normalization,[],[f91])).
% 0.17/0.39 thf(f91,plain,(
% 0.17/0.39 ( ! [X2 : mworld,X1 : $i] : ((((^[Y0 : mworld]: ((mrel @ (sK5 @ X1) @ Y0) => (big_r @ X1 @ X1 @ Y0))) @ X2) = $true)) )),
% 0.17/0.39 inference(pi_clausification,[],[f90])).
% 0.17/0.39 thf(f90,plain,(
% 0.17/0.39 ( ! [X1 : $i] : (($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK5 @ X1) @ Y0) => (big_r @ X1 @ X1 @ Y0)))))) )),
% 0.17/0.39 inference(binary_proxy_clausification,[],[f87])).
% 0.17/0.39 thf(f87,plain,(
% 0.17/0.39 ( ! [X1 : $i] : (($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK5 @ X1) @ Y0) => (big_r @ X1 @ X1 @ Y0)))) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK5 @ X1) @ Y0) => (big_r @ (sK4 @ X1) @ (sK4 @ X1) @ Y0))))))) )),
% 0.17/0.39 inference(binary_proxy_clausification,[],[f86])).
% 0.17/0.39 thf(f86,plain,(
% 0.17/0.39 ( ! [X1 : $i] : (($false = ((mrel @ (sK3 @ X1) @ (sK5 @ X1)) => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK5 @ X1) @ Y0) => (big_r @ X1 @ X1 @ Y0)))) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK5 @ X1) @ Y0) => (big_r @ (sK4 @ X1) @ (sK4 @ X1) @ Y0)))))))) )),
% 0.17/0.39 inference(beta_eta_normalization,[],[f85])).
% 0.17/0.39 thf(f85,plain,(
% 0.17/0.39 ( ! [X1 : $i] : ((((^[Y0 : mworld]: ((mrel @ (sK3 @ X1) @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (big_r @ X1 @ X1 @ Y1)))) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (big_r @ (sK4 @ X1) @ (sK4 @ X1) @ Y1))))))) @ (sK5 @ X1)) = $false)) )),
% 0.17/0.39 inference(sigma_clausification,[],[f84])).
% 0.17/0.39 thf(f84,plain,(
% 0.17/0.39 ( ! [X1 : $i] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK3 @ X1) @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (big_r @ X1 @ X1 @ Y1)))) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (big_r @ (sK4 @ X1) @ (sK4 @ X1) @ Y1)))))))) = $false)) )),
% 0.17/0.39 inference(beta_eta_normalization,[],[f83])).
% 0.17/0.39 thf(f83,plain,(
% 0.17/0.39 ( ! [X1 : $i] : (($false = ((^[Y0 : $i]: (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ (sK3 @ X1) @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (big_r @ X1 @ X1 @ Y2)))) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (big_r @ Y0 @ Y0 @ Y2))))))))) @ (sK4 @ X1)))) )),
% 0.17/0.39 inference(sigma_clausification,[],[f81])).
% 0.17/0.39 thf(f81,plain,(
% 0.17/0.39 ( ! [X1 : $i] : (($false = (!! @ $i @ (^[Y0 : $i]: (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ (sK3 @ X1) @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (big_r @ X1 @ X1 @ Y2)))) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (big_r @ Y0 @ Y0 @ Y2)))))))))))) )),
% 0.17/0.39 inference(binary_proxy_clausification,[],[f80])).
% 0.17/0.39 thf(f80,plain,(
% 0.17/0.39 ( ! [X1 : $i] : ((((mrel @ sK1 @ (sK3 @ X1)) => (!! @ $i @ (^[Y0 : $i]: (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ (sK3 @ X1) @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (big_r @ X1 @ X1 @ Y2)))) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (big_r @ Y0 @ Y0 @ Y2))))))))))) = $false)) )),
% 0.17/0.39 inference(beta_eta_normalization,[],[f79])).
% 0.17/0.39 thf(f79,plain,(
% 0.17/0.39 ( ! [X1 : $i] : (($false = ((^[Y0 : mworld]: ((mrel @ sK1 @ Y0) => (!! @ $i @ (^[Y1 : $i]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y0 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (big_r @ X1 @ X1 @ Y3)))) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (big_r @ Y1 @ Y1 @ Y3)))))))))))) @ (sK3 @ X1)))) )),
% 0.17/0.39 inference(sigma_clausification,[],[f78])).
% 0.17/0.39 thf(f78,plain,(
% 0.17/0.39 ( ! [X1 : $i] : (($false = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK1 @ Y0) => (!! @ $i @ (^[Y1 : $i]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y0 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (big_r @ X1 @ X1 @ Y3)))) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (big_r @ Y1 @ Y1 @ Y3))))))))))))))) )),
% 0.17/0.39 inference(beta_eta_normalization,[],[f77])).
% 0.17/0.39 thf(f77,plain,(
% 0.17/0.39 ( ! [X1 : $i] : (($false = ((^[Y0 : $i]: (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ sK1 @ Y1) => (!! @ $i @ (^[Y2 : $i]: (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y1 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (big_r @ Y0 @ Y0 @ Y4)))) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (big_r @ Y2 @ Y2 @ Y4)))))))))))))) @ X1))) )),
% 0.17/0.39 inference(pi_clausification,[],[f57])).
% 0.17/0.39 thf(f57,plain,(
% 0.17/0.39 ($false = (?? @ $i @ (^[Y0 : $i]: (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ sK1 @ Y1) => (!! @ $i @ (^[Y2 : $i]: (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y1 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (big_r @ Y0 @ Y0 @ Y4)))) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (big_r @ Y2 @ Y2 @ Y4))))))))))))))))),
% 0.17/0.39 inference(binary_proxy_clausification,[],[f55])).
% 0.17/0.39 thf(f55,plain,(
% 0.17/0.39 ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK1 @ Y0) => ((?? @ $i @ (^[Y1 : $i]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y0 @ Y2) => (big_r @ Y1 @ Y1 @ Y2)))))) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ $i @ (^[Y2 : $i]: (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y1 @ Y3) => (big_r @ Y2 @ Y2 @ Y3))))))))))))) => (?? @ $i @ (^[Y0 : $i]: (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ sK1 @ Y1) => (!! @ $i @ (^[Y2 : $i]: (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y1 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (big_r @ Y0 @ Y0 @ Y4)))) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (big_r @ Y2 @ Y2 @ Y4)))))))))))))))))),
% 0.17/0.39 inference(binary_proxy_clausification,[],[f54])).
% 0.17/0.39 thf(f54,plain,(
% 0.17/0.39 ($false = ((mrel @ mactual @ sK1) => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK1 @ Y0) => ((?? @ $i @ (^[Y1 : $i]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y0 @ Y2) => (big_r @ Y1 @ Y1 @ Y2)))))) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ $i @ (^[Y2 : $i]: (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y1 @ Y3) => (big_r @ Y2 @ Y2 @ Y3))))))))))))) => (?? @ $i @ (^[Y0 : $i]: (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ sK1 @ Y1) => (!! @ $i @ (^[Y2 : $i]: (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y1 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (big_r @ Y0 @ Y0 @ Y4)))) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (big_r @ Y2 @ Y2 @ Y4))))))))))))))))))),
% 0.17/0.39 inference(beta_eta_normalization,[],[f53])).
% 0.17/0.39 thf(f53,plain,(
% 0.17/0.39 ($false = ((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((?? @ $i @ (^[Y2 : $i]: (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y1 @ Y3) => (big_r @ Y2 @ Y2 @ Y3)))))) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y2 @ Y4) => (big_r @ Y3 @ Y3 @ Y4))))))))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y2 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (big_r @ Y1 @ Y1 @ Y5)))) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (big_r @ Y3 @ Y3 @ Y5)))))))))))))))))) @ sK1))),
% 0.17/0.39 inference(sigma_clausification,[],[f52])).
% 0.17/0.39 thf(f52,plain,(
% 0.17/0.39 ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => ((?? @ $i @ (^[Y2 : $i]: (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y1 @ Y3) => (big_r @ Y2 @ Y2 @ Y3)))))) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y2 @ Y4) => (big_r @ Y3 @ Y3 @ Y4))))))))))))) => (?? @ $i @ (^[Y1 : $i]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y0 @ Y2) => (!! @ $i @ (^[Y3 : $i]: (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y2 @ Y4) => ((!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (big_r @ Y1 @ Y1 @ Y5)))) => (!! @ mworld @ (^[Y5 : mworld]: ((mrel @ Y4 @ Y5) => (big_r @ Y3 @ Y3 @ Y5))))))))))))))))))) != $true)),
% 0.17/0.39 inference(beta_eta_normalization,[],[f51])).
% 0.17/0.39 thf(f51,plain,(
% 0.17/0.39 ($true != ((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))) @ ((^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))) @ (^[Y0 : $i]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (Y1 @ Y3))))))) @ (big_r @ Y0 @ Y0)))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))) @ (^[Y0 : $i]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (Y1 @ Y3))))))) @ (big_r @ Y0 @ Y0))))))) @ ((^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))) @ (^[Y0 : $i]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (Y1 @ Y3))))))) @ ((^[Y1 : $i > mworld > $o]: ((^[Y2 : mworld]: (!! @ $i @ (^[Y3 : $i]: (Y1 @ Y3 @ Y2)))))) @ (^[Y1 : $i]: ((^[Y2 : mworld > $o]: ((^[Y3 : mworld]: (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ ((^[Y2 : mworld > $o]: ((^[Y3 : mworld > $o]: ((^[Y4 : mworld]: ((Y2 @ Y4) => (Y3 @ Y4))))))) @ ((^[Y2 : mworld > $o]: ((^[Y3 : mworld]: (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ (big_r @ Y0 @ Y0)) @ ((^[Y2 : mworld > $o]: ((^[Y3 : mworld]: (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ (big_r @ Y1 @ Y1)))))))))))))),
% 0.17/0.39 inference(definition_unfolding,[],[f44,f41,f46,f49,f46,f49,f43,f46,f46,f40,f46,f43,f46,f40,f46,f49,f46,f46])).
% 0.17/0.39 thf(f40,plain,(
% 0.17/0.39 (mforall_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))))),
% 0.17/0.39 inference(cnf_transformation,[],[f29])).
% 0.17/0.39 thf(f29,plain,(
% 0.17/0.39 (mforall_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))))),
% 0.17/0.39 inference(fool_elimination,[],[f28])).
% 0.17/0.39 thf(f28,plain,(
% 0.17/0.39 (mforall_di = (^[X0 : $i > mworld > $o, X1 : mworld] : (! [X2] : (X0 @ X2 @ X1))))),
% 0.17/0.39 inference(rectify,[],[f10])).
% 0.17/0.39 thf(f10,axiom,(
% 0.17/0.39 (mforall_di = (^[X1 : $i > mworld > $o, X2 : mworld] : (! [X5] : (X1 @ X5 @ X2))))),
% 0.17/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mforall_di_def)).
% 0.17/0.39 thf(f43,plain,(
% 0.17/0.39 (mexists_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))))),
% 0.17/0.39 inference(cnf_transformation,[],[f16])).
% 0.17/0.39 thf(f16,plain,(
% 0.17/0.39 (mexists_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))))),
% 0.17/0.39 inference(fool_elimination,[],[f15])).
% 0.17/0.39 thf(f15,plain,(
% 0.17/0.39 ((^[X0 : $i > mworld > $o, X1 : mworld] : (? [X2] : (X0 @ X2 @ X1))) = mexists_di)),
% 0.17/0.39 inference(rectify,[],[f11])).
% 0.17/0.39 thf(f11,axiom,(
% 0.17/0.39 ((^[X1 : $i > mworld > $o, X2 : mworld] : (? [X5] : (X1 @ X5 @ X2))) = mexists_di)),
% 0.17/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mexists_di_def)).
% 0.17/0.39 thf(f49,plain,(
% 0.17/0.39 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 0.17/0.39 inference(cnf_transformation,[],[f35])).
% 0.17/0.39 thf(f35,plain,(
% 0.17/0.39 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 0.17/0.39 inference(fool_elimination,[],[f34])).
% 0.17/0.39 thf(f34,plain,(
% 0.17/0.39 ((^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X0 @ X2) => (X1 @ X2))) = mimplies)),
% 0.17/0.39 inference(rectify,[],[f5])).
% 0.17/0.39 thf(f5,axiom,(
% 0.17/0.39 ((^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X1 @ X2) => (X3 @ X2))) = mimplies)),
% 0.17/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies_def)).
% 0.17/0.39 thf(f46,plain,(
% 0.17/0.39 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 0.17/0.39 inference(cnf_transformation,[],[f20])).
% 0.17/0.39 thf(f20,plain,(
% 0.17/0.39 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 0.17/0.39 inference(fool_elimination,[],[f19])).
% 0.17/0.39 thf(f19,plain,(
% 0.17/0.39 (mbox = (^[X0 : mworld > $o, X1 : mworld] : (! [X2 : mworld] : ((mrel @ X1 @ X2) => (X0 @ X2)))))),
% 0.17/0.39 inference(rectify,[],[f7])).
% 0.17/0.39 thf(f7,axiom,(
% 0.17/0.39 (mbox = (^[X0 : mworld > $o, X2 : mworld] : (! [X4 : mworld] : ((mrel @ X2 @ X4) => (X0 @ X4)))))),
% 0.17/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox_def)).
% 0.17/0.39 thf(f41,plain,(
% 0.17/0.39 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 0.17/0.39 inference(cnf_transformation,[],[f27])).
% 0.17/0.39 thf(f27,plain,(
% 0.17/0.39 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 0.17/0.39 inference(fool_elimination,[],[f1])).
% 0.17/0.39 thf(f1,axiom,(
% 0.17/0.39 ((^[X0 : mworld > $o] : (X0 @ mactual)) = mlocal)),
% 0.17/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mlocal_def)).
% 0.17/0.39 thf(f44,plain,(
% 0.17/0.39 ((mlocal @ (mbox @ (mimplies @ (mbox @ (mimplies @ (mexists_di @ (^[Y0 : $i]: (mbox @ (big_r @ Y0 @ Y0)))) @ (mbox @ (mforall_di @ (^[Y0 : $i]: (mbox @ (big_r @ Y0 @ Y0))))))) @ (mexists_di @ (^[Y0 : $i]: (mbox @ (mforall_di @ (^[Y1 : $i]: (mbox @ (mimplies @ (mbox @ (big_r @ Y0 @ Y0)) @ (mbox @ (big_r @ Y1 @ Y1)))))))))))) != $true)),
% 0.17/0.39 inference(cnf_transformation,[],[f38])).
% 0.17/0.39 thf(f38,plain,(
% 0.17/0.39 ((mlocal @ (mbox @ (mimplies @ (mbox @ (mimplies @ (mexists_di @ (^[Y0 : $i]: (mbox @ (big_r @ Y0 @ Y0)))) @ (mbox @ (mforall_di @ (^[Y0 : $i]: (mbox @ (big_r @ Y0 @ Y0))))))) @ (mexists_di @ (^[Y0 : $i]: (mbox @ (mforall_di @ (^[Y1 : $i]: (mbox @ (mimplies @ (mbox @ (big_r @ Y0 @ Y0)) @ (mbox @ (big_r @ Y1 @ Y1)))))))))))) != $true)),
% 0.17/0.39 inference(flattening,[],[f24])).
% 0.17/0.39 thf(f24,plain,(
% 0.17/0.39 ~((mlocal @ (mbox @ (mimplies @ (mbox @ (mimplies @ (mexists_di @ (^[Y0 : $i]: (mbox @ (big_r @ Y0 @ Y0)))) @ (mbox @ (mforall_di @ (^[Y0 : $i]: (mbox @ (big_r @ Y0 @ Y0))))))) @ (mexists_di @ (^[Y0 : $i]: (mbox @ (mforall_di @ (^[Y1 : $i]: (mbox @ (mimplies @ (mbox @ (big_r @ Y0 @ Y0)) @ (mbox @ (big_r @ Y1 @ Y1)))))))))))) = $true)),
% 0.17/0.39 inference(fool_elimination,[],[f23])).
% 0.17/0.39 thf(f23,plain,(
% 0.17/0.39 ~(mlocal @ (mbox @ (mimplies @ (mbox @ (mimplies @ (mexists_di @ (^[X0 : $i] : (mbox @ (big_r @ X0 @ X0)))) @ (mbox @ (mforall_di @ (^[X1 : $i] : (mbox @ (big_r @ X1 @ X1))))))) @ (mexists_di @ (^[X2 : $i] : (mbox @ (mforall_di @ (^[X3 : $i] : (mbox @ (mimplies @ (mbox @ (big_r @ X2 @ X2)) @ (mbox @ (big_r @ X3 @ X3))))))))))))),
% 0.17/0.39 inference(rectify,[],[f13])).
% 0.17/0.39 thf(f13,negated_conjecture,(
% 0.17/0.39 ~(mlocal @ (mbox @ (mimplies @ (mbox @ (mimplies @ (mexists_di @ (^[X5 : $i] : (mbox @ (big_r @ X5 @ X5)))) @ (mbox @ (mforall_di @ (^[X6 : $i] : (mbox @ (big_r @ X6 @ X6))))))) @ (mexists_di @ (^[X7 : $i] : (mbox @ (mforall_di @ (^[X4 : $i] : (mbox @ (mimplies @ (mbox @ (big_r @ X7 @ X7)) @ (mbox @ (big_r @ X4 @ X4))))))))))))),
% 0.17/0.39 inference(negated_conjecture,[],[f12])).
% 0.17/0.39 thf(f12,conjecture,(
% 0.17/0.39 (mlocal @ (mbox @ (mimplies @ (mbox @ (mimplies @ (mexists_di @ (^[X5 : $i] : (mbox @ (big_r @ X5 @ X5)))) @ (mbox @ (mforall_di @ (^[X6 : $i] : (mbox @ (big_r @ X6 @ X6))))))) @ (mexists_di @ (^[X7 : $i] : (mbox @ (mforall_di @ (^[X4 : $i] : (mbox @ (mimplies @ (mbox @ (big_r @ X7 @ X7)) @ (mbox @ (big_r @ X4 @ X4))))))))))))),
% 0.17/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',x2122)).
% 0.17/0.39 thf(f96,plain,(
% 0.17/0.39 ( ! [X1 : $i] : (($false = (big_r @ (sK4 @ X1) @ (sK4 @ X1) @ (sK6 @ X1)))) )),
% 0.17/0.39 inference(binary_proxy_clausification,[],[f95])).
% 0.17/0.39 thf(f95,plain,(
% 0.17/0.39 ( ! [X1 : $i] : (($false = ((mrel @ (sK5 @ X1) @ (sK6 @ X1)) => (big_r @ (sK4 @ X1) @ (sK4 @ X1) @ (sK6 @ X1))))) )),
% 0.17/0.39 inference(beta_eta_normalization,[],[f94])).
% 0.17/0.39 thf(f94,plain,(
% 0.17/0.39 ( ! [X1 : $i] : ((((^[Y0 : mworld]: ((mrel @ (sK5 @ X1) @ Y0) => (big_r @ (sK4 @ X1) @ (sK4 @ X1) @ Y0))) @ (sK6 @ X1)) = $false)) )),
% 0.17/0.39 inference(sigma_clausification,[],[f89])).
% 0.17/0.39 thf(f89,plain,(
% 0.17/0.39 ( ! [X1 : $i] : (($false = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK5 @ X1) @ Y0) => (big_r @ (sK4 @ X1) @ (sK4 @ X1) @ Y0)))))) )),
% 0.17/0.39 inference(binary_proxy_clausification,[],[f87])).
% 0.17/0.39 % SZS output end Proof for theBenchmark
% 0.17/0.39 % (3212)------------------------------
% 0.17/0.39 % (3212)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.17/0.39 % (3212)Termination reason: Refutation
% 0.17/0.39
% 0.17/0.39 % (3212)Memory used [KB]: 5628
% 0.17/0.39 % (3212)Time elapsed: 0.007 s
% 0.17/0.39 % (3212)Instructions burned: 11 (million)
% 0.17/0.39 % (3212)------------------------------
% 0.17/0.39 % (3212)------------------------------
% 0.17/0.39 % (3211)Success in time 0.014 s
% 0.17/0.39 % Vampire---4.8 exiting
%------------------------------------------------------------------------------