TSTP Solution File: LCL958^18 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : LCL958^18 : 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 : n013.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 0.15s 0.39s
% Output : Refutation 0.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : LCL958^18 : TPTP v8.2.0. Released v8.1.0.
% 0.11/0.14 % 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
% 0.15/0.36 % Computer : n013.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Mon May 20 03:30:38 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 This is a TH0_THM_EQU_NAR problem
% 0.15/0.36 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.38 % (3586)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.15/0.38 % (3587)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)
% 0.15/0.38 % (3584)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)
% 0.15/0.38 % (3586)Instruction limit reached!
% 0.15/0.38 % (3586)------------------------------
% 0.15/0.38 % (3586)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (3586)Termination reason: Unknown
% 0.15/0.38 % (3586)Termination phase: Preprocessing 3
% 0.15/0.38
% 0.15/0.38 % (3586)Memory used [KB]: 1023
% 0.15/0.38 % (3586)Time elapsed: 0.003 s
% 0.15/0.38 % (3586)Instructions burned: 3 (million)
% 0.15/0.38 % (3586)------------------------------
% 0.15/0.38 % (3586)------------------------------
% 0.15/0.38 % (3585)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)
% 0.15/0.38 % (3587)Instruction limit reached!
% 0.15/0.38 % (3587)------------------------------
% 0.15/0.38 % (3587)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (3587)Termination reason: Unknown
% 0.15/0.38 % (3587)Termination phase: Property scanning
% 0.15/0.38
% 0.15/0.38 % (3587)Memory used [KB]: 1023
% 0.15/0.38 % (3587)Time elapsed: 0.003 s
% 0.15/0.38 % (3587)Instructions burned: 3 (million)
% 0.15/0.38 % (3583)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.15/0.38 % (3587)------------------------------
% 0.15/0.38 % (3587)------------------------------
% 0.15/0.38 % (3590)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)
% 0.15/0.38 % (3589)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.15/0.38 % (3584)Instruction limit reached!
% 0.15/0.38 % (3584)------------------------------
% 0.15/0.38 % (3584)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (3584)Termination reason: Unknown
% 0.15/0.38 % (3584)Termination phase: Property scanning
% 0.15/0.38
% 0.15/0.38 % (3584)Memory used [KB]: 1023
% 0.15/0.38 % (3584)Time elapsed: 0.004 s
% 0.15/0.38 % (3584)Instructions burned: 4 (million)
% 0.15/0.38 % (3584)------------------------------
% 0.15/0.38 % (3584)------------------------------
% 0.15/0.38 % (3590)Instruction limit reached!
% 0.15/0.38 % (3590)------------------------------
% 0.15/0.38 % (3590)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (3590)Termination reason: Unknown
% 0.15/0.38 % (3590)Termination phase: Function definition elimination
% 0.15/0.38
% 0.15/0.38 % (3590)Memory used [KB]: 1023
% 0.15/0.38 % (3590)Time elapsed: 0.004 s
% 0.15/0.38 % (3590)Instructions burned: 3 (million)
% 0.15/0.38 % (3590)------------------------------
% 0.15/0.38 % (3590)------------------------------
% 0.15/0.39 % (3583)First to succeed.
% 0.15/0.39 % (3589)Instruction limit reached!
% 0.15/0.39 % (3589)------------------------------
% 0.15/0.39 % (3589)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39 % (3589)Termination reason: Unknown
% 0.15/0.39 % (3589)Termination phase: Saturation
% 0.15/0.39
% 0.15/0.39 % (3589)Memory used [KB]: 5628
% 0.15/0.39 % (3589)Time elapsed: 0.012 s
% 0.15/0.39 % (3589)Instructions burned: 18 (million)
% 0.15/0.39 % (3589)------------------------------
% 0.15/0.39 % (3589)------------------------------
% 0.15/0.39 % (3588)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)
% 0.15/0.39 % (3585)Also succeeded, but the first one will report.
% 0.15/0.39 % (3583)Refutation found. Thanks to Tanya!
% 0.15/0.39 % SZS status Theorem for theBenchmark
% 0.15/0.39 % SZS output start Proof for theBenchmark
% 0.15/0.39 thf(type_def_5, type, mworld: $tType).
% 0.15/0.39 thf(func_def_0, type, mworld: $tType).
% 0.15/0.39 thf(func_def_1, type, mrel: mworld > mworld > $o).
% 0.15/0.39 thf(func_def_2, type, mactual: mworld).
% 0.15/0.39 thf(func_def_3, type, mlocal: (mworld > $o) > $o).
% 0.15/0.39 thf(func_def_5, type, mnot: (mworld > $o) > mworld > $o).
% 0.15/0.39 thf(func_def_6, type, mand: (mworld > $o) > (mworld > $o) > mworld > $o).
% 0.15/0.39 thf(func_def_7, type, mor: (mworld > $o) > (mworld > $o) > mworld > $o).
% 0.15/0.39 thf(func_def_8, type, mimplies: (mworld > $o) > (mworld > $o) > mworld > $o).
% 0.15/0.39 thf(func_def_9, type, mequiv: (mworld > $o) > (mworld > $o) > mworld > $o).
% 0.15/0.39 thf(func_def_10, type, mbox: (mworld > $o) > mworld > $o).
% 0.15/0.39 thf(func_def_11, type, mdia: (mworld > $o) > mworld > $o).
% 0.15/0.39 thf(func_def_12, type, eiw_di: $i > mworld > $o).
% 0.15/0.39 thf(func_def_13, type, mforall_di: ($i > mworld > $o) > mworld > $o).
% 0.15/0.39 thf(func_def_14, type, mexists_di: ($i > mworld > $o) > mworld > $o).
% 0.15/0.39 thf(func_def_15, type, big_q: $i > mworld > $o).
% 0.15/0.39 thf(func_def_16, type, big_p: $i > mworld > $o).
% 0.15/0.39 thf(func_def_30, type, sK0: mworld > $i).
% 0.15/0.39 thf(func_def_35, type, sK2: $i > mworld).
% 0.15/0.39 thf(func_def_36, type, sK3: $i > $i).
% 0.15/0.39 thf(func_def_37, type, sK4: $i > mworld).
% 0.15/0.39 thf(func_def_38, type, sK5: $i > mworld).
% 0.15/0.39 thf(func_def_39, type, sK6: $i > mworld).
% 0.15/0.39 thf(f126,plain,(
% 0.15/0.39 $false),
% 0.15/0.39 inference(trivial_inequality_removal,[],[f121])).
% 0.15/0.39 thf(f121,plain,(
% 0.15/0.39 ($true = $false)),
% 0.15/0.39 inference(superposition,[],[f118,f56])).
% 0.15/0.39 thf(f56,plain,(
% 0.15/0.39 ( ! [X0 : mworld] : (($true = (eiw_di @ (sK0 @ X0) @ X0))) )),
% 0.15/0.39 inference(cnf_transformation,[],[f48])).
% 0.15/0.39 thf(f48,plain,(
% 0.15/0.39 ! [X0 : mworld] : ($true = (eiw_di @ (sK0 @ X0) @ X0))),
% 0.15/0.39 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f20,f47])).
% 0.15/0.39 thf(f47,plain,(
% 0.15/0.39 ! [X0 : mworld] : (? [X1] : ($true = (eiw_di @ X1 @ X0)) => ($true = (eiw_di @ (sK0 @ X0) @ X0)))),
% 0.15/0.39 introduced(choice_axiom,[])).
% 0.15/0.39 thf(f20,plain,(
% 0.15/0.39 ! [X0 : mworld] : ? [X1] : ($true = (eiw_di @ X1 @ X0))),
% 0.15/0.39 inference(fool_elimination,[],[f19])).
% 0.15/0.40 thf(f19,plain,(
% 0.15/0.40 ! [X0 : mworld] : ? [X1] : (eiw_di @ X1 @ X0)),
% 0.15/0.40 inference(rectify,[],[f10])).
% 0.15/0.40 thf(f10,axiom,(
% 0.15/0.40 ! [X2 : mworld] : ? [X5] : (eiw_di @ X5 @ X2)),
% 0.15/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',eiw_di_nonempty)).
% 0.15/0.40 thf(f118,plain,(
% 0.15/0.40 ( ! [X0 : $i] : (($false = (eiw_di @ X0 @ mactual))) )),
% 0.15/0.40 inference(trivial_inequality_removal,[],[f117])).
% 0.15/0.40 thf(f117,plain,(
% 0.15/0.40 ( ! [X0 : $i] : (($true != $true) | ($false = (eiw_di @ X0 @ mactual))) )),
% 0.15/0.40 inference(duplicate_literal_removal,[],[f114])).
% 0.15/0.40 thf(f114,plain,(
% 0.15/0.40 ( ! [X0 : $i] : (($false = (eiw_di @ X0 @ mactual)) | ($true != $true) | ($false = (eiw_di @ X0 @ mactual))) )),
% 0.15/0.40 inference(superposition,[],[f113,f75])).
% 0.15/0.40 thf(f75,plain,(
% 0.15/0.40 ( ! [X1 : $i] : (($true = (eiw_di @ (sK3 @ X1) @ (sK2 @ X1))) | ($false = (eiw_di @ X1 @ mactual))) )),
% 0.15/0.40 inference(binary_proxy_clausification,[],[f73])).
% 0.15/0.40 thf(f73,plain,(
% 0.15/0.40 ( ! [X1 : $i] : (($false = (eiw_di @ X1 @ mactual)) | ($false = ((eiw_di @ (sK3 @ X1) @ (sK2 @ X1)) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK2 @ X1) @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (big_p @ X1 @ Y1)))) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (big_q @ X1 @ Y1)))) | (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (big_p @ (sK3 @ X1) @ Y1)))))))))))) )),
% 0.15/0.40 inference(beta_eta_normalization,[],[f72])).
% 0.15/0.40 thf(f72,plain,(
% 0.15/0.40 ( ! [X1 : $i] : (($false = (eiw_di @ X1 @ mactual)) | ($false = ((^[Y0 : $i]: ((eiw_di @ Y0 @ (sK2 @ X1)) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ (sK2 @ X1) @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (big_p @ X1 @ Y2)))) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (big_q @ X1 @ Y2)))) | (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (big_p @ Y0 @ Y2))))))))))) @ (sK3 @ X1)))) )),
% 0.15/0.40 inference(sigma_clausification,[],[f70])).
% 0.15/0.40 thf(f70,plain,(
% 0.15/0.40 ( ! [X1 : $i] : (($false = (eiw_di @ X1 @ mactual)) | ((!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ (sK2 @ X1)) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ (sK2 @ X1) @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (big_p @ X1 @ Y2)))) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (big_q @ X1 @ Y2)))) | (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (big_p @ Y0 @ Y2)))))))))))) = $false)) )),
% 0.15/0.40 inference(binary_proxy_clausification,[],[f69])).
% 0.15/0.40 thf(f69,plain,(
% 0.15/0.40 ( ! [X1 : $i] : (($false = (eiw_di @ X1 @ mactual)) | (((mrel @ mactual @ (sK2 @ X1)) => (!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ (sK2 @ X1)) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ (sK2 @ X1) @ Y1) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (big_p @ X1 @ Y2)))) => ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (big_q @ X1 @ Y2)))) | (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (big_p @ Y0 @ Y2))))))))))))) = $false)) )),
% 0.15/0.40 inference(beta_eta_normalization,[],[f68])).
% 0.15/0.40 thf(f68,plain,(
% 0.15/0.40 ( ! [X1 : $i] : ((((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y0 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (big_p @ X1 @ Y3)))) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (big_q @ X1 @ Y3)))) | (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (big_p @ Y1 @ Y3)))))))))))))) @ (sK2 @ X1)) = $false) | ($false = (eiw_di @ X1 @ mactual))) )),
% 0.15/0.40 inference(sigma_clausification,[],[f67])).
% 0.15/0.40 thf(f67,plain,(
% 0.15/0.40 ( ! [X1 : $i] : (($false = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y0 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (big_p @ X1 @ Y3)))) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (big_q @ X1 @ Y3)))) | (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (big_p @ Y1 @ Y3)))))))))))))))) | ($false = (eiw_di @ X1 @ mactual))) )),
% 0.15/0.40 inference(binary_proxy_clausification,[],[f66])).
% 0.15/0.40 thf(f66,plain,(
% 0.15/0.40 ( ! [X1 : $i] : (($false = ((eiw_di @ X1 @ mactual) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y0 @ Y2) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (big_p @ X1 @ Y3)))) => ((!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (big_q @ X1 @ Y3)))) | (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (big_p @ Y1 @ Y3)))))))))))))))))) )),
% 0.15/0.40 inference(beta_eta_normalization,[],[f65])).
% 0.15/0.40 thf(f65,plain,(
% 0.15/0.40 ( ! [X1 : $i] : (($false = ((^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ mactual @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y1 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (big_p @ Y0 @ Y4)))) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (big_q @ Y0 @ Y4)))) | (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (big_p @ Y2 @ Y4))))))))))))))))) @ X1))) )),
% 0.15/0.40 inference(pi_clausification,[],[f64])).
% 0.15/0.40 thf(f64,plain,(
% 0.15/0.40 ($true != (?? @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ mactual @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y1 @ Y3) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (big_p @ Y0 @ Y4)))) => ((!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (big_q @ Y0 @ Y4)))) | (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (big_p @ Y2 @ Y4)))))))))))))))))))),
% 0.15/0.40 inference(beta_eta_normalization,[],[f63])).
% 0.15/0.40 thf(f63,plain,(
% 0.15/0.40 ($true != ((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (?? @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) & (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]: ((eiw_di @ Y3 @ Y2) => (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_p @ Y0)) @ ((^[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_q @ Y0)) @ ((^[Y2 : mworld > $o]: ((^[Y3 : mworld]: (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ (big_p @ Y1))))))))))))),
% 0.15/0.40 inference(definition_unfolding,[],[f55,f58,f53,f49,f57,f49,f60,f49,f50,f49,f49])).
% 0.15/0.40 thf(f50,plain,(
% 0.15/0.40 (mor = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.15/0.40 inference(cnf_transformation,[],[f37])).
% 0.15/0.40 thf(f37,plain,(
% 0.15/0.40 (mor = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.15/0.40 inference(fool_elimination,[],[f36])).
% 0.15/0.40 thf(f36,plain,(
% 0.15/0.40 (mor = (^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X1 @ X2) | (X0 @ X2))))),
% 0.15/0.40 inference(rectify,[],[f4])).
% 0.15/0.40 thf(f4,axiom,(
% 0.15/0.40 (mor = (^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X3 @ X2) | (X1 @ X2))))),
% 0.15/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor_def)).
% 0.15/0.40 thf(f60,plain,(
% 0.15/0.40 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 0.15/0.40 inference(cnf_transformation,[],[f33])).
% 0.15/0.40 thf(f33,plain,(
% 0.15/0.40 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 0.15/0.40 inference(fool_elimination,[],[f32])).
% 0.15/0.40 thf(f32,plain,(
% 0.15/0.40 ((^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X0 @ X2) => (X1 @ X2))) = mimplies)),
% 0.15/0.40 inference(rectify,[],[f5])).
% 0.15/0.40 thf(f5,axiom,(
% 0.15/0.40 ((^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X1 @ X2) => (X3 @ X2))) = mimplies)),
% 0.15/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies_def)).
% 0.15/0.40 thf(f57,plain,(
% 0.15/0.40 (mforall_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))))),
% 0.15/0.40 inference(cnf_transformation,[],[f35])).
% 0.15/0.40 thf(f35,plain,(
% 0.15/0.40 (mforall_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))))),
% 0.15/0.40 inference(fool_elimination,[],[f34])).
% 0.15/0.40 thf(f34,plain,(
% 0.15/0.40 ((^[X0 : $i > mworld > $o, X1 : mworld] : (! [X2] : ((eiw_di @ X2 @ X1) => (X0 @ X2 @ X1)))) = mforall_di)),
% 0.15/0.40 inference(rectify,[],[f12])).
% 0.15/0.40 thf(f12,axiom,(
% 0.15/0.40 ((^[X1 : $i > mworld > $o, X2 : mworld] : (! [X5] : ((eiw_di @ X5 @ X2) => (X1 @ X5 @ X2)))) = mforall_di)),
% 0.15/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mforall_di_def)).
% 0.15/0.40 thf(f49,plain,(
% 0.15/0.40 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 0.15/0.40 inference(cnf_transformation,[],[f29])).
% 0.15/0.40 thf(f29,plain,(
% 0.15/0.40 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 0.15/0.40 inference(fool_elimination,[],[f28])).
% 0.15/0.40 thf(f28,plain,(
% 0.15/0.40 (mbox = (^[X0 : mworld > $o, X1 : mworld] : (! [X2 : mworld] : ((mrel @ X1 @ X2) => (X0 @ X2)))))),
% 0.15/0.40 inference(rectify,[],[f7])).
% 0.15/0.40 thf(f7,axiom,(
% 0.15/0.40 (mbox = (^[X0 : mworld > $o, X2 : mworld] : (! [X4 : mworld] : ((mrel @ X2 @ X4) => (X0 @ X4)))))),
% 0.15/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox_def)).
% 0.15/0.40 thf(f53,plain,(
% 0.15/0.40 (mexists_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (?? @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) & (Y0 @ Y2 @ Y1))))))))),
% 0.15/0.40 inference(cnf_transformation,[],[f24])).
% 0.15/0.40 thf(f24,plain,(
% 0.15/0.40 (mexists_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (?? @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) & (Y0 @ Y2 @ Y1))))))))),
% 0.15/0.40 inference(fool_elimination,[],[f23])).
% 0.15/0.40 thf(f23,plain,(
% 0.15/0.40 ((^[X0 : $i > mworld > $o, X1 : mworld] : (? [X2] : ((X0 @ X2 @ X1) & (eiw_di @ X2 @ X1)))) = mexists_di)),
% 0.15/0.40 inference(rectify,[],[f13])).
% 0.15/0.40 thf(f13,axiom,(
% 0.15/0.40 ((^[X1 : $i > mworld > $o, X2 : mworld] : (? [X5] : ((X1 @ X5 @ X2) & (eiw_di @ X5 @ X2)))) = mexists_di)),
% 0.15/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mexists_di_def)).
% 0.15/0.40 thf(f58,plain,(
% 0.15/0.40 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 0.15/0.40 inference(cnf_transformation,[],[f27])).
% 0.15/0.40 thf(f27,plain,(
% 0.15/0.40 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 0.15/0.40 inference(fool_elimination,[],[f1])).
% 0.15/0.40 thf(f1,axiom,(
% 0.15/0.40 ((^[X0 : mworld > $o] : (X0 @ mactual)) = mlocal)),
% 0.15/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mlocal_def)).
% 0.15/0.40 thf(f55,plain,(
% 0.15/0.40 ($true != (mlocal @ (mexists_di @ (^[Y0 : $i]: (mbox @ (mforall_di @ (^[Y1 : $i]: (mbox @ (mimplies @ (mbox @ (big_p @ Y0)) @ (mor @ (mbox @ (big_q @ Y0)) @ (mbox @ (big_p @ Y1))))))))))))),
% 0.15/0.40 inference(cnf_transformation,[],[f44])).
% 0.15/0.40 thf(f44,plain,(
% 0.15/0.40 ($true != (mlocal @ (mexists_di @ (^[Y0 : $i]: (mbox @ (mforall_di @ (^[Y1 : $i]: (mbox @ (mimplies @ (mbox @ (big_p @ Y0)) @ (mor @ (mbox @ (big_q @ Y0)) @ (mbox @ (big_p @ Y1))))))))))))),
% 0.15/0.40 inference(flattening,[],[f18])).
% 0.15/0.40 thf(f18,plain,(
% 0.15/0.40 ~($true = (mlocal @ (mexists_di @ (^[Y0 : $i]: (mbox @ (mforall_di @ (^[Y1 : $i]: (mbox @ (mimplies @ (mbox @ (big_p @ Y0)) @ (mor @ (mbox @ (big_q @ Y0)) @ (mbox @ (big_p @ Y1))))))))))))),
% 0.15/0.40 inference(fool_elimination,[],[f17])).
% 0.15/0.40 thf(f17,plain,(
% 0.15/0.40 ~(mlocal @ (mexists_di @ (^[X0 : $i] : (mbox @ (mforall_di @ (^[X1 : $i] : (mbox @ (mimplies @ (mbox @ (big_p @ X0)) @ (mor @ (mbox @ (big_q @ X0)) @ (mbox @ (big_p @ X1)))))))))))),
% 0.15/0.40 inference(rectify,[],[f15])).
% 0.15/0.40 thf(f15,negated_conjecture,(
% 0.15/0.40 ~(mlocal @ (mexists_di @ (^[X5 : $i] : (mbox @ (mforall_di @ (^[X6 : $i] : (mbox @ (mimplies @ (mbox @ (big_p @ X5)) @ (mor @ (mbox @ (big_q @ X5)) @ (mbox @ (big_p @ X6)))))))))))),
% 0.15/0.40 inference(negated_conjecture,[],[f14])).
% 0.15/0.40 thf(f14,conjecture,(
% 0.15/0.40 (mlocal @ (mexists_di @ (^[X5 : $i] : (mbox @ (mforall_di @ (^[X6 : $i] : (mbox @ (mimplies @ (mbox @ (big_p @ X5)) @ (mor @ (mbox @ (big_q @ X5)) @ (mbox @ (big_p @ X6)))))))))))),
% 0.15/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',x2137)).
% 0.15/0.40 thf(f113,plain,(
% 0.15/0.40 ( ! [X0 : $i,X1 : mworld] : (($true != (eiw_di @ (sK3 @ X0) @ X1)) | ($false = (eiw_di @ X0 @ mactual))) )),
% 0.15/0.40 inference(trivial_inequality_removal,[],[f111])).
% 0.15/0.40 thf(f111,plain,(
% 0.15/0.40 ( ! [X0 : $i,X1 : mworld] : (($true != (eiw_di @ (sK3 @ X0) @ X1)) | ($false = (eiw_di @ X0 @ mactual)) | ($true = $false)) )),
% 0.15/0.40 inference(superposition,[],[f95,f109])).
% 0.15/0.40 thf(f109,plain,(
% 0.15/0.40 ( ! [X0 : $i] : (($false = (eiw_di @ (sK3 @ X0) @ mactual)) | ($false = (eiw_di @ X0 @ mactual))) )),
% 0.15/0.40 inference(trivial_inequality_removal,[],[f107])).
% 0.15/0.40 thf(f107,plain,(
% 0.15/0.40 ( ! [X0 : $i] : (($false = (eiw_di @ (sK3 @ X0) @ mactual)) | ($true = $false) | ($false = (eiw_di @ X0 @ mactual))) )),
% 0.15/0.40 inference(superposition,[],[f93,f103])).
% 0.15/0.40 thf(f103,plain,(
% 0.15/0.40 ( ! [X0 : $i,X1 : mworld] : (($true = (big_p @ X0 @ X1)) | ($false = (eiw_di @ X0 @ mactual))) )),
% 0.15/0.40 inference(trivial_inequality_removal,[],[f99])).
% 0.15/0.40 thf(f99,plain,(
% 0.15/0.40 ( ! [X0 : $i,X1 : mworld] : (($false = (eiw_di @ X0 @ mactual)) | ($true = (big_p @ X0 @ X1)) | ($true = $false)) )),
% 0.15/0.40 inference(superposition,[],[f54,f84])).
% 0.15/0.40 thf(f84,plain,(
% 0.15/0.40 ( ! [X2 : mworld,X1 : $i] : (($false = (mrel @ (sK4 @ X1) @ X2)) | ($true = (big_p @ X1 @ X2)) | ($false = (eiw_di @ X1 @ mactual))) )),
% 0.15/0.40 inference(binary_proxy_clausification,[],[f83])).
% 0.15/0.40 thf(f83,plain,(
% 0.15/0.40 ( ! [X2 : mworld,X1 : $i] : (($false = (eiw_di @ X1 @ mactual)) | ($true = ((mrel @ (sK4 @ X1) @ X2) => (big_p @ X1 @ X2)))) )),
% 0.15/0.40 inference(beta_eta_normalization,[],[f82])).
% 0.15/0.40 thf(f82,plain,(
% 0.15/0.40 ( ! [X2 : mworld,X1 : $i] : (($false = (eiw_di @ X1 @ mactual)) | ($true = ((^[Y0 : mworld]: ((mrel @ (sK4 @ X1) @ Y0) => (big_p @ X1 @ Y0))) @ X2))) )),
% 0.15/0.40 inference(pi_clausification,[],[f81])).
% 0.15/0.40 thf(f81,plain,(
% 0.15/0.40 ( ! [X1 : $i] : (($false = (eiw_di @ X1 @ mactual)) | ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK4 @ X1) @ Y0) => (big_p @ X1 @ Y0)))))) )),
% 0.15/0.40 inference(binary_proxy_clausification,[],[f78])).
% 0.15/0.40 thf(f78,plain,(
% 0.15/0.40 ( ! [X1 : $i] : (($false = (eiw_di @ X1 @ mactual)) | (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK4 @ X1) @ Y0) => (big_p @ X1 @ Y0)))) => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK4 @ X1) @ Y0) => (big_q @ X1 @ Y0)))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK4 @ X1) @ Y0) => (big_p @ (sK3 @ X1) @ Y0)))))) = $false)) )),
% 0.15/0.40 inference(binary_proxy_clausification,[],[f77])).
% 0.15/0.40 thf(f77,plain,(
% 0.15/0.40 ( ! [X1 : $i] : (($false = ((mrel @ (sK2 @ X1) @ (sK4 @ X1)) => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK4 @ X1) @ Y0) => (big_p @ X1 @ Y0)))) => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK4 @ X1) @ Y0) => (big_q @ X1 @ Y0)))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK4 @ X1) @ Y0) => (big_p @ (sK3 @ X1) @ Y0)))))))) | ($false = (eiw_di @ X1 @ mactual))) )),
% 0.15/0.40 inference(beta_eta_normalization,[],[f76])).
% 0.15/0.40 thf(f76,plain,(
% 0.15/0.40 ( ! [X1 : $i] : (($false = ((^[Y0 : mworld]: ((mrel @ (sK2 @ X1) @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (big_p @ X1 @ Y1)))) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (big_q @ X1 @ Y1)))) | (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (big_p @ (sK3 @ X1) @ Y1)))))))) @ (sK4 @ X1))) | ($false = (eiw_di @ X1 @ mactual))) )),
% 0.15/0.40 inference(sigma_clausification,[],[f74])).
% 0.15/0.40 thf(f74,plain,(
% 0.15/0.40 ( ! [X1 : $i] : (($false = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK2 @ X1) @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (big_p @ X1 @ Y1)))) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (big_q @ X1 @ Y1)))) | (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (big_p @ (sK3 @ X1) @ Y1)))))))))) | ($false = (eiw_di @ X1 @ mactual))) )),
% 0.15/0.40 inference(binary_proxy_clausification,[],[f73])).
% 0.15/0.40 thf(f54,plain,(
% 0.15/0.40 ( ! [X0 : mworld,X1 : mworld] : (($true = (mrel @ X1 @ X0))) )),
% 0.15/0.40 inference(cnf_transformation,[],[f39])).
% 0.15/0.40 thf(f39,plain,(
% 0.15/0.40 ! [X0 : mworld,X1 : mworld] : ($true = (mrel @ X1 @ X0))),
% 0.15/0.40 inference(fool_elimination,[],[f38])).
% 0.15/0.40 thf(f38,plain,(
% 0.15/0.40 ! [X0 : mworld,X1 : mworld] : (mrel @ X1 @ X0)),
% 0.15/0.40 inference(rectify,[],[f9])).
% 0.15/0.40 thf(f9,axiom,(
% 0.15/0.40 ! [X4 : mworld,X2 : mworld] : (mrel @ X2 @ X4)),
% 0.15/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_universal)).
% 0.15/0.40 thf(f93,plain,(
% 0.15/0.40 ( ! [X1 : $i] : (($false = (big_p @ (sK3 @ X1) @ (sK6 @ X1))) | ($false = (eiw_di @ X1 @ mactual))) )),
% 0.15/0.40 inference(binary_proxy_clausification,[],[f92])).
% 0.15/0.40 thf(f92,plain,(
% 0.15/0.40 ( ! [X1 : $i] : (($false = ((mrel @ (sK4 @ X1) @ (sK6 @ X1)) => (big_p @ (sK3 @ X1) @ (sK6 @ X1)))) | ($false = (eiw_di @ X1 @ mactual))) )),
% 0.15/0.40 inference(beta_eta_normalization,[],[f91])).
% 0.15/0.40 thf(f91,plain,(
% 0.15/0.40 ( ! [X1 : $i] : (($false = ((^[Y0 : mworld]: ((mrel @ (sK4 @ X1) @ Y0) => (big_p @ (sK3 @ X1) @ Y0))) @ (sK6 @ X1))) | ($false = (eiw_di @ X1 @ mactual))) )),
% 0.15/0.40 inference(sigma_clausification,[],[f85])).
% 0.15/0.40 thf(f85,plain,(
% 0.15/0.40 ( ! [X1 : $i] : (($false = (eiw_di @ X1 @ mactual)) | ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK4 @ X1) @ Y0) => (big_p @ (sK3 @ X1) @ Y0)))) = $false)) )),
% 0.15/0.40 inference(binary_proxy_clausification,[],[f80])).
% 0.15/0.40 thf(f80,plain,(
% 0.15/0.40 ( ! [X1 : $i] : (($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK4 @ X1) @ Y0) => (big_q @ X1 @ Y0)))) | (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK4 @ X1) @ Y0) => (big_p @ (sK3 @ X1) @ Y0)))))) | ($false = (eiw_di @ X1 @ mactual))) )),
% 0.15/0.40 inference(binary_proxy_clausification,[],[f78])).
% 0.15/0.40 thf(f95,plain,(
% 0.15/0.40 ( ! [X2 : mworld,X0 : $i,X1 : mworld] : (($true = (eiw_di @ X0 @ X1)) | ($true != (eiw_di @ X0 @ X2))) )),
% 0.15/0.40 inference(subsumption_resolution,[],[f61,f54])).
% 0.15/0.40 thf(f61,plain,(
% 0.15/0.40 ( ! [X2 : mworld,X0 : $i,X1 : mworld] : (($true != (mrel @ X2 @ X1)) | ($true = (eiw_di @ X0 @ X1)) | ($true != (eiw_di @ X0 @ X2))) )),
% 0.15/0.40 inference(cnf_transformation,[],[f46])).
% 0.15/0.40 thf(f46,plain,(
% 0.15/0.40 ! [X0,X1 : mworld,X2 : mworld] : (($true != (eiw_di @ X0 @ X2)) | ($true != (mrel @ X2 @ X1)) | ($true = (eiw_di @ X0 @ X1)))),
% 0.15/0.40 inference(flattening,[],[f45])).
% 0.15/0.40 thf(f45,plain,(
% 0.15/0.40 ! [X0,X1 : mworld,X2 : mworld] : (($true = (eiw_di @ X0 @ X1)) | (($true != (eiw_di @ X0 @ X2)) | ($true != (mrel @ X2 @ X1))))),
% 0.15/0.40 inference(ennf_transformation,[],[f43])).
% 0.15/0.40 thf(f43,plain,(
% 0.15/0.40 ! [X0,X1 : mworld,X2 : mworld] : ((($true = (eiw_di @ X0 @ X2)) & ($true = (mrel @ X2 @ X1))) => ($true = (eiw_di @ X0 @ X1)))),
% 0.15/0.40 inference(fool_elimination,[],[f42])).
% 0.15/0.40 thf(f42,plain,(
% 0.15/0.40 ! [X0,X1 : mworld,X2 : mworld] : (((mrel @ X2 @ X1) & (eiw_di @ X0 @ X2)) => (eiw_di @ X0 @ X1))),
% 0.15/0.40 inference(rectify,[],[f11])).
% 0.15/0.40 thf(f11,axiom,(
% 0.15/0.40 ! [X5,X4 : mworld,X2 : mworld] : (((mrel @ X2 @ X4) & (eiw_di @ X5 @ X2)) => (eiw_di @ X5 @ X4))),
% 0.15/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',eiw_di_cumul)).
% 0.15/0.40 % SZS output end Proof for theBenchmark
% 0.15/0.40 % (3583)------------------------------
% 0.15/0.40 % (3583)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.40 % (3583)Termination reason: Refutation
% 0.15/0.40
% 0.15/0.40 % (3583)Memory used [KB]: 5628
% 0.15/0.40 % (3583)Time elapsed: 0.014 s
% 0.15/0.40 % (3583)Instructions burned: 13 (million)
% 0.15/0.40 % (3583)------------------------------
% 0.15/0.40 % (3583)------------------------------
% 0.15/0.40 % (3582)Success in time 0.026 s
% 0.15/0.40 % Vampire---4.8 exiting
%------------------------------------------------------------------------------