TSTP Solution File: SEU494^1 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU494^1 : TPTP v8.2.0. Released v3.6.0.
% 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 03:49:08 EDT 2024
% Result : Theorem 0.08s 0.31s
% Output : Refutation 0.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.08 % Problem : SEU494^1 : TPTP v8.2.0. Released v3.6.0.
% 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
% 0.08/0.28 % Computer : n032.cluster.edu
% 0.08/0.28 % Model : x86_64 x86_64
% 0.08/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.28 % Memory : 8042.1875MB
% 0.08/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.28 % CPULimit : 300
% 0.08/0.28 % WCLimit : 300
% 0.08/0.28 % DateTime : Sun May 19 17:11:53 EDT 2024
% 0.08/0.28 % CPUTime :
% 0.08/0.28 This is a TH0_THM_EQU_NAR problem
% 0.08/0.28 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
% 0.08/0.30 % (31715)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)
% 0.08/0.30 % (31714)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)
% 0.08/0.30 % (31719)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.08/0.30 % (31714)Instruction limit reached!
% 0.08/0.30 % (31714)------------------------------
% 0.08/0.30 % (31714)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.08/0.30 % (31714)Termination reason: Unknown
% 0.08/0.30 % (31714)Termination phase: Unused predicate definition removal
% 0.08/0.30
% 0.08/0.30 % (31714)Memory used [KB]: 1023
% 0.08/0.30 % (31714)Time elapsed: 0.003 s
% 0.08/0.30 % (31714)Instructions burned: 6 (million)
% 0.08/0.30 % (31714)------------------------------
% 0.08/0.30 % (31714)------------------------------
% 0.08/0.30 % (31717)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)
% 0.08/0.30 % (31716)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.08/0.30 % (31718)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)
% 0.08/0.30 % (31716)Instruction limit reached!
% 0.08/0.30 % (31716)------------------------------
% 0.08/0.30 % (31716)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.08/0.30 % (31716)Termination reason: Unknown
% 0.08/0.30 % (31716)Termination phase: shuffling
% 0.08/0.30
% 0.08/0.30 % (31716)Memory used [KB]: 1023
% 0.08/0.30 % (31716)Time elapsed: 0.002 s
% 0.08/0.30 % (31716)Instructions burned: 2 (million)
% 0.08/0.30 % (31716)------------------------------
% 0.08/0.30 % (31716)------------------------------
% 0.08/0.30 % (31717)Instruction limit reached!
% 0.08/0.30 % (31717)------------------------------
% 0.08/0.30 % (31717)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.08/0.30 % (31717)Termination reason: Unknown
% 0.08/0.30 % (31717)Termination phase: shuffling
% 0.08/0.30
% 0.08/0.30 % (31717)Memory used [KB]: 1023
% 0.08/0.30 % (31717)Time elapsed: 0.003 s
% 0.08/0.30 % (31717)Instructions burned: 2 (million)
% 0.08/0.30 % (31717)------------------------------
% 0.08/0.30 % (31717)------------------------------
% 0.08/0.30 % (31719)Instruction limit reached!
% 0.08/0.30 % (31719)------------------------------
% 0.08/0.30 % (31719)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.08/0.30 % (31719)Termination reason: Unknown
% 0.08/0.30 % (31719)Termination phase: Saturation
% 0.08/0.30
% 0.08/0.30 % (31719)Memory used [KB]: 5756
% 0.08/0.30 % (31719)Time elapsed: 0.008 s
% 0.08/0.30 % (31719)Instructions burned: 19 (million)
% 0.08/0.30 % (31719)------------------------------
% 0.08/0.30 % (31719)------------------------------
% 0.08/0.30 % (31720)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)
% 0.08/0.30 % (31713)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.08/0.30 % (31715)First to succeed.
% 0.08/0.30 % (31720)Instruction limit reached!
% 0.08/0.30 % (31720)------------------------------
% 0.08/0.30 % (31720)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.08/0.30 % (31720)Termination reason: Unknown
% 0.08/0.30 % (31720)Termination phase: shuffling
% 0.08/0.30
% 0.08/0.30 % (31720)Memory used [KB]: 1023
% 0.08/0.30 % (31720)Time elapsed: 0.003 s
% 0.08/0.30 % (31720)Instructions burned: 4 (million)
% 0.08/0.30 % (31720)------------------------------
% 0.08/0.30 % (31720)------------------------------
% 0.08/0.31 % (31715)Refutation found. Thanks to Tanya!
% 0.08/0.31 % SZS status Theorem for theBenchmark
% 0.08/0.31 % SZS output start Proof for theBenchmark
% 0.08/0.31 thf(func_def_0, type, subrel: ($i > $i > $o) > ($i > $i > $o) > $o).
% 0.08/0.31 thf(func_def_2, type, inv: ($i > $i > $o) > $i > $i > $o).
% 0.08/0.31 thf(func_def_3, type, idem: (($i > $i > $o) > $i > $i > $o) > $o).
% 0.08/0.31 thf(func_def_4, type, infl: (($i > $i > $o) > $i > $i > $o) > $o).
% 0.08/0.31 thf(func_def_5, type, mono: (($i > $i > $o) > $i > $i > $o) > $o).
% 0.08/0.31 thf(func_def_6, type, refl: ($i > $i > $o) > $o).
% 0.08/0.31 thf(func_def_7, type, irrefl: ($i > $i > $o) > $o).
% 0.08/0.31 thf(func_def_8, type, rc: ($i > $i > $o) > $i > $i > $o).
% 0.08/0.31 thf(func_def_9, type, symm: ($i > $i > $o) > $o).
% 0.08/0.31 thf(func_def_10, type, antisymm: ($i > $i > $o) > $o).
% 0.08/0.31 thf(func_def_11, type, asymm: ($i > $i > $o) > $o).
% 0.08/0.31 thf(func_def_12, type, sc: ($i > $i > $o) > $i > $i > $o).
% 0.08/0.31 thf(func_def_13, type, trans: ($i > $i > $o) > $o).
% 0.08/0.31 thf(func_def_14, type, tc: ($i > $i > $o) > $i > $i > $o).
% 0.08/0.31 thf(func_def_15, type, trc: ($i > $i > $o) > $i > $i > $o).
% 0.08/0.31 thf(func_def_16, type, trsc: ($i > $i > $o) > $i > $i > $o).
% 0.08/0.31 thf(func_def_17, type, po: ($i > $i > $o) > $o).
% 0.08/0.31 thf(func_def_18, type, so: ($i > $i > $o) > $o).
% 0.08/0.31 thf(func_def_19, type, total: ($i > $i > $o) > $o).
% 0.08/0.31 thf(func_def_20, type, term: ($i > $i > $o) > $o).
% 0.08/0.31 thf(func_def_21, type, ind: ($i > $i > $o) > $o).
% 0.08/0.31 thf(func_def_22, type, innf: ($i > $i > $o) > $i > $o).
% 0.08/0.31 thf(func_def_23, type, nfof: ($i > $i > $o) > $i > $i > $o).
% 0.08/0.31 thf(func_def_24, type, norm: ($i > $i > $o) > $o).
% 0.08/0.31 thf(func_def_25, type, join: ($i > $i > $o) > $i > $i > $o).
% 0.08/0.31 thf(func_def_26, type, lconfl: ($i > $i > $o) > $o).
% 0.08/0.31 thf(func_def_27, type, sconfl: ($i > $i > $o) > $o).
% 0.08/0.31 thf(func_def_28, type, confl: ($i > $i > $o) > $o).
% 0.08/0.31 thf(func_def_29, type, cr: ($i > $i > $o) > $o).
% 0.08/0.31 thf(func_def_30, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 0.08/0.31 thf(func_def_45, type, sK0: $i > $i > $o).
% 0.08/0.31 thf(f282,plain,(
% 0.08/0.31 $false),
% 0.08/0.31 inference(avatar_sat_refutation,[],[f192,f197,f202,f203,f208,f209,f249,f281])).
% 0.08/0.31 thf(f281,plain,(
% 0.08/0.31 ~spl1_1 | ~spl1_3),
% 0.08/0.31 inference(avatar_contradiction_clause,[],[f280])).
% 0.08/0.31 thf(f280,plain,(
% 0.08/0.31 $false | (~spl1_1 | ~spl1_3)),
% 0.08/0.31 inference(trivial_inequality_removal,[],[f279])).
% 0.08/0.31 thf(f279,plain,(
% 0.08/0.31 ($true = $false) | (~spl1_1 | ~spl1_3)),
% 0.08/0.31 inference(backward_demodulation,[],[f196,f256])).
% 0.08/0.31 thf(f256,plain,(
% 0.08/0.31 ($false = (sK0 @ sK5 @ sK6)) | ~spl1_1),
% 0.08/0.31 inference(trivial_inequality_removal,[],[f253])).
% 0.08/0.31 thf(f253,plain,(
% 0.08/0.31 ($true = $false) | ($false = (sK0 @ sK5 @ sK6)) | ~spl1_1),
% 0.08/0.31 inference(superposition,[],[f175,f187])).
% 0.08/0.31 thf(f187,plain,(
% 0.08/0.31 ($true = (sK0 @ sK6 @ sK5)) | ~spl1_1),
% 0.08/0.31 inference(avatar_component_clause,[],[f185])).
% 0.08/0.31 thf(f185,plain,(
% 0.08/0.31 spl1_1 <=> ($true = (sK0 @ sK6 @ sK5))),
% 0.08/0.31 introduced(avatar_definition,[new_symbols(naming,[spl1_1])])).
% 0.08/0.31 thf(f175,plain,(
% 0.08/0.31 ( ! [X2 : $i,X1 : $i] : (($false = (sK0 @ X2 @ X1)) | ((sK0 @ X1 @ X2) = $false)) )),
% 0.08/0.31 inference(not_proxy_clausification,[],[f174])).
% 0.08/0.31 thf(f174,plain,(
% 0.08/0.31 ( ! [X2 : $i,X1 : $i] : (($true = (~ (sK0 @ X1 @ X2))) | ($false = (sK0 @ X2 @ X1))) )),
% 0.08/0.31 inference(binary_proxy_clausification,[],[f173])).
% 0.08/0.31 thf(f173,plain,(
% 0.08/0.31 ( ! [X2 : $i,X1 : $i] : (($true = ((sK0 @ X2 @ X1) => (~ (sK0 @ X1 @ X2))))) )),
% 0.08/0.31 inference(beta_eta_normalization,[],[f172])).
% 0.08/0.31 thf(f172,plain,(
% 0.08/0.31 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((sK0 @ Y0 @ X1) => (~ (sK0 @ X1 @ Y0)))) @ X2))) )),
% 0.08/0.31 inference(pi_clausification,[],[f171])).
% 0.08/0.31 thf(f171,plain,(
% 0.08/0.31 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((sK0 @ Y0 @ X1) => (~ (sK0 @ X1 @ Y0))))))) )),
% 0.08/0.31 inference(beta_eta_normalization,[],[f170])).
% 0.08/0.31 thf(f170,plain,(
% 0.08/0.31 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y1 @ Y0) => (~ (sK0 @ Y0 @ Y1)))))) @ X1))) )),
% 0.08/0.31 inference(pi_clausification,[],[f169])).
% 0.08/0.31 thf(f169,plain,(
% 0.08/0.31 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y1 @ Y0) => (~ (sK0 @ Y0 @ Y1))))))))),
% 0.08/0.31 inference(binary_proxy_clausification,[],[f167])).
% 0.08/0.31 thf(f167,plain,(
% 0.08/0.31 ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y1 @ Y0) => (~ (sK0 @ Y0 @ Y1))))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK0 @ Y2 @ Y1) & (sK0 @ Y0 @ Y2)) => (sK0 @ Y0 @ Y1))))))))))),
% 0.08/0.31 inference(beta_eta_normalization,[],[f140])).
% 0.08/0.31 thf(f140,plain,(
% 0.08/0.31 ($true = ((^[Y0 : $i > $i > $o]: (((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3 @ Y2) => (~ (Y1 @ Y2 @ Y3)))))))) @ Y0) & ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y4 @ Y3) & (Y1 @ Y2 @ Y4)) => (Y1 @ Y2 @ Y3))))))))) @ Y0))) @ sK0))),
% 0.08/0.31 inference(definition_unfolding,[],[f115,f131])).
% 0.08/0.31 thf(f131,plain,(
% 0.08/0.31 (so = (^[Y0 : $i > $i > $o]: (((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3 @ Y2) => (~ (Y1 @ Y2 @ Y3)))))))) @ Y0) & ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y4 @ Y3) & (Y1 @ Y2 @ Y4)) => (Y1 @ Y2 @ Y3))))))))) @ Y0))))),
% 0.08/0.31 inference(definition_unfolding,[],[f98,f100,f123])).
% 0.08/0.31 thf(f123,plain,(
% 0.08/0.31 (trans = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y1 @ Y2))))))))))),
% 0.08/0.31 inference(cnf_transformation,[],[f86])).
% 0.08/0.31 thf(f86,plain,(
% 0.08/0.31 (trans = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y3 @ Y2) & (Y0 @ Y1 @ Y3)) => (Y0 @ Y1 @ Y2))))))))))),
% 0.08/0.31 inference(fool_elimination,[],[f85])).
% 0.08/0.31 thf(f85,plain,(
% 0.08/0.31 ((^[X0 : $i > $i > $o] : (! [X1,X2,X3] : (((X0 @ X3 @ X1) & (X0 @ X1 @ X2)) => (X0 @ X3 @ X2)))) = trans)),
% 0.08/0.31 inference(rectify,[],[f13])).
% 0.08/0.31 thf(f13,axiom,(
% 0.08/0.31 ((^[X0 : $i > $i > $o] : (! [X3,X5,X2] : (((X0 @ X2 @ X3) & (X0 @ X3 @ X5)) => (X0 @ X2 @ X5)))) = trans)),
% 0.08/0.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitive)).
% 0.08/0.31 thf(f100,plain,(
% 0.08/0.31 (asymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) => (~ (Y0 @ Y1 @ Y2)))))))))),
% 0.08/0.31 inference(cnf_transformation,[],[f72])).
% 0.08/0.31 thf(f72,plain,(
% 0.08/0.31 (asymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) => (~ (Y0 @ Y1 @ Y2)))))))))),
% 0.08/0.31 inference(fool_elimination,[],[f71])).
% 0.08/0.31 thf(f71,plain,(
% 0.08/0.31 ((^[X0 : $i > $i > $o] : (! [X1,X2] : ((X0 @ X1 @ X2) => ~(X0 @ X2 @ X1)))) = asymm)),
% 0.08/0.31 inference(rectify,[],[f11])).
% 0.08/0.31 thf(f11,axiom,(
% 0.08/0.31 ((^[X0 : $i > $i > $o] : (! [X2,X3] : ((X0 @ X2 @ X3) => ~(X0 @ X3 @ X2)))) = asymm)),
% 0.08/0.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',asymmetric)).
% 0.08/0.31 thf(f98,plain,(
% 0.08/0.31 (so = (^[Y0 : $i > $i > $o]: ((asymm @ Y0) & (trans @ Y0))))),
% 0.08/0.31 inference(cnf_transformation,[],[f65])).
% 0.08/0.31 thf(f65,plain,(
% 0.08/0.31 (so = (^[Y0 : $i > $i > $o]: ((asymm @ Y0) & (trans @ Y0))))),
% 0.08/0.31 inference(fool_elimination,[],[f64])).
% 0.08/0.31 thf(f64,plain,(
% 0.08/0.31 (so = (^[X0 : $i > $i > $o] : ((trans @ X0) & (asymm @ X0))))),
% 0.08/0.31 inference(rectify,[],[f18])).
% 0.08/0.31 thf(f18,axiom,(
% 0.08/0.31 (so = (^[X0 : $i > $i > $o] : ((trans @ X0) & (asymm @ X0))))),
% 0.08/0.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',strict_order)).
% 0.08/0.31 thf(f115,plain,(
% 0.08/0.31 ($true = (so @ sK0))),
% 0.08/0.31 inference(cnf_transformation,[],[f93])).
% 0.08/0.31 thf(f93,plain,(
% 0.08/0.31 ($true = (so @ sK0)) & ($true != (so @ (inv @ sK0)))),
% 0.08/0.31 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f91,f92])).
% 0.08/0.31 thf(f92,plain,(
% 0.08/0.31 ? [X0 : $i > $i > $o] : (((so @ X0) = $true) & ((so @ (inv @ X0)) != $true)) => (($true = (so @ sK0)) & ($true != (so @ (inv @ sK0))))),
% 0.08/0.31 introduced(choice_axiom,[])).
% 0.08/0.31 thf(f91,plain,(
% 0.08/0.31 ? [X0 : $i > $i > $o] : (((so @ X0) = $true) & ((so @ (inv @ X0)) != $true))),
% 0.08/0.31 inference(ennf_transformation,[],[f59])).
% 0.08/0.31 thf(f59,plain,(
% 0.08/0.31 ~! [X0 : $i > $i > $o] : (((so @ X0) = $true) => ((so @ (inv @ X0)) = $true))),
% 0.08/0.31 inference(fool_elimination,[],[f58])).
% 0.08/0.31 thf(f58,plain,(
% 0.08/0.31 ~! [X0 : $i > $i > $o] : ((so @ X0) => (so @ (inv @ X0)))),
% 0.08/0.31 inference(rectify,[],[f31])).
% 0.08/0.31 thf(f31,negated_conjecture,(
% 0.08/0.31 ~! [X0 : $i > $i > $o] : ((so @ X0) => (so @ (inv @ X0)))),
% 0.08/0.31 inference(negated_conjecture,[],[f30])).
% 0.08/0.31 thf(f30,conjecture,(
% 0.08/0.31 ! [X0 : $i > $i > $o] : ((so @ X0) => (so @ (inv @ X0)))),
% 0.08/0.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_of_strict_order_is_strict_order)).
% 0.08/0.31 thf(f196,plain,(
% 0.08/0.31 ($true = (sK0 @ sK5 @ sK6)) | ~spl1_3),
% 0.08/0.31 inference(avatar_component_clause,[],[f194])).
% 0.08/0.31 thf(f194,plain,(
% 0.08/0.31 spl1_3 <=> ($true = (sK0 @ sK5 @ sK6))),
% 0.08/0.31 introduced(avatar_definition,[new_symbols(naming,[spl1_3])])).
% 0.08/0.31 thf(f249,plain,(
% 0.08/0.31 ~spl1_2 | ~spl1_4 | ~spl1_5),
% 0.08/0.31 inference(avatar_contradiction_clause,[],[f248])).
% 0.08/0.31 thf(f248,plain,(
% 0.08/0.31 $false | (~spl1_2 | ~spl1_4 | ~spl1_5)),
% 0.08/0.31 inference(trivial_inequality_removal,[],[f247])).
% 0.08/0.31 thf(f247,plain,(
% 0.08/0.31 ($true = $false) | (~spl1_2 | ~spl1_4 | ~spl1_5)),
% 0.08/0.31 inference(backward_demodulation,[],[f207,f242])).
% 0.08/0.31 thf(f242,plain,(
% 0.08/0.31 ($false = (sK0 @ sK3 @ sK4)) | (~spl1_2 | ~spl1_4)),
% 0.08/0.31 inference(trivial_inequality_removal,[],[f235])).
% 0.08/0.31 thf(f235,plain,(
% 0.08/0.31 ($false = (sK0 @ sK3 @ sK4)) | ($true = $false) | (~spl1_2 | ~spl1_4)),
% 0.08/0.31 inference(superposition,[],[f191,f221])).
% 0.08/0.31 thf(f221,plain,(
% 0.08/0.31 ( ! [X0 : $i] : (($true = (sK0 @ X0 @ sK2)) | ($false = (sK0 @ X0 @ sK4))) ) | ~spl1_4),
% 0.08/0.31 inference(trivial_inequality_removal,[],[f216])).
% 0.08/0.31 thf(f216,plain,(
% 0.08/0.31 ( ! [X0 : $i] : (($true = $false) | ($true = (sK0 @ X0 @ sK2)) | ($false = (sK0 @ X0 @ sK4))) ) | ~spl1_4),
% 0.08/0.31 inference(superposition,[],[f183,f201])).
% 0.08/0.31 thf(f201,plain,(
% 0.08/0.31 ((sK0 @ sK4 @ sK2) = $true) | ~spl1_4),
% 0.08/0.31 inference(avatar_component_clause,[],[f199])).
% 0.08/0.31 thf(f199,plain,(
% 0.08/0.31 spl1_4 <=> ((sK0 @ sK4 @ sK2) = $true)),
% 0.08/0.31 introduced(avatar_definition,[new_symbols(naming,[spl1_4])])).
% 0.08/0.31 thf(f183,plain,(
% 0.08/0.31 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (sK0 @ X3 @ X2)) | ($false = (sK0 @ X1 @ X3)) | ((sK0 @ X1 @ X2) = $true)) )),
% 0.08/0.31 inference(binary_proxy_clausification,[],[f182])).
% 0.08/0.31 thf(f182,plain,(
% 0.08/0.31 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((sK0 @ X1 @ X2) = $true) | ($false = ((sK0 @ X3 @ X2) & (sK0 @ X1 @ X3)))) )),
% 0.08/0.31 inference(binary_proxy_clausification,[],[f181])).
% 0.08/0.31 thf(f181,plain,(
% 0.08/0.31 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((sK0 @ X3 @ X2) & (sK0 @ X1 @ X3)) => (sK0 @ X1 @ X2)))) )),
% 0.08/0.31 inference(beta_eta_normalization,[],[f180])).
% 0.08/0.31 thf(f180,plain,(
% 0.08/0.31 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (((sK0 @ Y0 @ X2) & (sK0 @ X1 @ Y0)) => (sK0 @ X1 @ X2))) @ X3))) )),
% 0.08/0.31 inference(pi_clausification,[],[f179])).
% 0.08/0.31 thf(f179,plain,(
% 0.08/0.31 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (((sK0 @ Y0 @ X2) & (sK0 @ X1 @ Y0)) => (sK0 @ X1 @ X2)))))) )),
% 0.08/0.31 inference(beta_eta_normalization,[],[f178])).
% 0.08/0.31 thf(f178,plain,(
% 0.08/0.31 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((sK0 @ Y1 @ Y0) & (sK0 @ X1 @ Y1)) => (sK0 @ X1 @ Y0))))) @ X2))) )),
% 0.08/0.31 inference(pi_clausification,[],[f177])).
% 0.08/0.31 thf(f177,plain,(
% 0.08/0.31 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((sK0 @ Y1 @ Y0) & (sK0 @ X1 @ Y1)) => (sK0 @ X1 @ Y0)))))) = $true)) )),
% 0.08/0.31 inference(beta_eta_normalization,[],[f176])).
% 0.08/0.31 thf(f176,plain,(
% 0.08/0.31 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK0 @ Y2 @ Y1) & (sK0 @ Y0 @ Y2)) => (sK0 @ Y0 @ Y1))))))) @ X1))) )),
% 0.08/0.31 inference(pi_clausification,[],[f168])).
% 0.08/0.31 thf(f168,plain,(
% 0.08/0.31 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK0 @ Y2 @ Y1) & (sK0 @ Y0 @ Y2)) => (sK0 @ Y0 @ Y1)))))))))),
% 0.08/0.31 inference(binary_proxy_clausification,[],[f167])).
% 0.08/0.31 thf(f191,plain,(
% 0.08/0.31 ($false = (sK0 @ sK3 @ sK2)) | ~spl1_2),
% 0.08/0.31 inference(avatar_component_clause,[],[f189])).
% 0.08/0.31 thf(f189,plain,(
% 0.08/0.31 spl1_2 <=> ($false = (sK0 @ sK3 @ sK2))),
% 0.08/0.31 introduced(avatar_definition,[new_symbols(naming,[spl1_2])])).
% 0.08/0.31 thf(f207,plain,(
% 0.08/0.31 ($true = (sK0 @ sK3 @ sK4)) | ~spl1_5),
% 0.08/0.31 inference(avatar_component_clause,[],[f205])).
% 0.08/0.31 thf(f205,plain,(
% 0.08/0.31 spl1_5 <=> ($true = (sK0 @ sK3 @ sK4))),
% 0.08/0.31 introduced(avatar_definition,[new_symbols(naming,[spl1_5])])).
% 0.08/0.31 thf(f209,plain,(
% 0.08/0.31 spl1_5 | spl1_3),
% 0.08/0.31 inference(avatar_split_clause,[],[f159,f194,f205])).
% 0.08/0.31 thf(f159,plain,(
% 0.08/0.31 ($true = (sK0 @ sK5 @ sK6)) | ($true = (sK0 @ sK3 @ sK4))),
% 0.08/0.31 inference(binary_proxy_clausification,[],[f157])).
% 0.08/0.31 thf(f157,plain,(
% 0.08/0.31 ($false = ((sK0 @ sK5 @ sK6) => (~ (sK0 @ sK6 @ sK5)))) | ($true = (sK0 @ sK3 @ sK4))),
% 0.08/0.31 inference(binary_proxy_clausification,[],[f155])).
% 0.08/0.31 thf(f155,plain,(
% 0.08/0.31 ($true = ((sK0 @ sK3 @ sK4) & (sK0 @ sK4 @ sK2))) | ($false = ((sK0 @ sK5 @ sK6) => (~ (sK0 @ sK6 @ sK5))))),
% 0.08/0.31 inference(binary_proxy_clausification,[],[f153])).
% 0.08/0.31 thf(f153,plain,(
% 0.08/0.31 ($false = (((sK0 @ sK3 @ sK4) & (sK0 @ sK4 @ sK2)) => (sK0 @ sK3 @ sK2))) | ($false = ((sK0 @ sK5 @ sK6) => (~ (sK0 @ sK6 @ sK5))))),
% 0.08/0.31 inference(beta_eta_normalization,[],[f152])).
% 0.08/0.31 thf(f152,plain,(
% 0.08/0.31 ($false = (((sK0 @ sK3 @ sK4) & (sK0 @ sK4 @ sK2)) => (sK0 @ sK3 @ sK2))) | ($false = ((^[Y0 : $i]: ((sK0 @ sK5 @ Y0) => (~ (sK0 @ Y0 @ sK5)))) @ sK6))),
% 0.08/0.31 inference(sigma_clausification,[],[f151])).
% 0.08/0.31 thf(f151,plain,(
% 0.08/0.31 ($false = (!! @ $i @ (^[Y0 : $i]: ((sK0 @ sK5 @ Y0) => (~ (sK0 @ Y0 @ sK5)))))) | ($false = (((sK0 @ sK3 @ sK4) & (sK0 @ sK4 @ sK2)) => (sK0 @ sK3 @ sK2)))),
% 0.08/0.31 inference(beta_eta_normalization,[],[f150])).
% 0.08/0.31 thf(f150,plain,(
% 0.08/0.31 ($false = (((sK0 @ sK3 @ sK4) & (sK0 @ sK4 @ sK2)) => (sK0 @ sK3 @ sK2))) | ($false = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y0 @ Y1) => (~ (sK0 @ Y1 @ Y0)))))) @ sK5))),
% 0.08/0.31 inference(sigma_clausification,[],[f149])).
% 0.08/0.31 thf(f149,plain,(
% 0.08/0.31 ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y0 @ Y1) => (~ (sK0 @ Y1 @ Y0)))))))) | ($false = (((sK0 @ sK3 @ sK4) & (sK0 @ sK4 @ sK2)) => (sK0 @ sK3 @ sK2)))),
% 0.08/0.31 inference(beta_eta_normalization,[],[f148])).
% 0.08/0.31 thf(f148,plain,(
% 0.08/0.31 ($false = ((^[Y0 : $i]: (((sK0 @ sK3 @ Y0) & (sK0 @ Y0 @ sK2)) => (sK0 @ sK3 @ sK2))) @ sK4)) | ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y0 @ Y1) => (~ (sK0 @ Y1 @ Y0))))))))),
% 0.08/0.31 inference(sigma_clausification,[],[f147])).
% 0.08/0.31 thf(f147,plain,(
% 0.08/0.31 ($false = (!! @ $i @ (^[Y0 : $i]: (((sK0 @ sK3 @ Y0) & (sK0 @ Y0 @ sK2)) => (sK0 @ sK3 @ sK2))))) | ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y0 @ Y1) => (~ (sK0 @ Y1 @ Y0))))))))),
% 0.08/0.31 inference(beta_eta_normalization,[],[f146])).
% 0.08/0.31 thf(f146,plain,(
% 0.08/0.31 ($false = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((sK0 @ Y0 @ Y1) & (sK0 @ Y1 @ sK2)) => (sK0 @ Y0 @ sK2))))) @ sK3)) | ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y0 @ Y1) => (~ (sK0 @ Y1 @ Y0))))))))),
% 0.08/0.31 inference(sigma_clausification,[],[f145])).
% 0.08/0.31 thf(f145,plain,(
% 0.08/0.31 ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((sK0 @ Y0 @ Y1) & (sK0 @ Y1 @ sK2)) => (sK0 @ Y0 @ sK2))))))) | ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y0 @ Y1) => (~ (sK0 @ Y1 @ Y0))))))))),
% 0.08/0.31 inference(beta_eta_normalization,[],[f144])).
% 0.08/0.31 thf(f144,plain,(
% 0.08/0.31 ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y0 @ Y1) => (~ (sK0 @ Y1 @ Y0)))))))) | ($false = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK0 @ Y1 @ Y2) & (sK0 @ Y2 @ Y0)) => (sK0 @ Y1 @ Y0))))))) @ sK2))),
% 0.08/0.31 inference(sigma_clausification,[],[f143])).
% 0.08/0.31 thf(f143,plain,(
% 0.08/0.31 ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK0 @ Y1 @ Y2) & (sK0 @ Y2 @ Y0)) => (sK0 @ Y1 @ Y0))))))))) | ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y0 @ Y1) => (~ (sK0 @ Y1 @ Y0))))))))),
% 0.08/0.31 inference(binary_proxy_clausification,[],[f142])).
% 0.08/0.31 thf(f142,plain,(
% 0.08/0.31 ($true != ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y0 @ Y1) => (~ (sK0 @ Y1 @ Y0))))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK0 @ Y1 @ Y2) & (sK0 @ Y2 @ Y0)) => (sK0 @ Y1 @ Y0))))))))))),
% 0.08/0.31 inference(beta_eta_normalization,[],[f141])).
% 0.08/0.31 thf(f141,plain,(
% 0.08/0.31 ($true != ((^[Y0 : $i > $i > $o]: (((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3 @ Y2) => (~ (Y1 @ Y2 @ Y3)))))))) @ Y0) & ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y4 @ Y3) & (Y1 @ Y2 @ Y4)) => (Y1 @ Y2 @ Y3))))))))) @ Y0))) @ ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))) @ sK0)))),
% 0.08/0.31 inference(definition_unfolding,[],[f114,f131,f96])).
% 0.08/0.31 thf(f96,plain,(
% 0.08/0.31 (inv = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))))),
% 0.08/0.31 inference(cnf_transformation,[],[f47])).
% 0.08/0.31 thf(f47,plain,(
% 0.08/0.31 (inv = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))))),
% 0.08/0.31 inference(fool_elimination,[],[f46])).
% 0.08/0.31 thf(f46,plain,(
% 0.08/0.31 ((^[X0 : $i > $i > $o, X1 : $i, X2 : $i] : (X0 @ X2 @ X1)) = inv)),
% 0.08/0.31 inference(rectify,[],[f2])).
% 0.08/0.31 thf(f2,axiom,(
% 0.08/0.31 ((^[X0 : $i > $i > $o, X2 : $i, X3 : $i] : (X0 @ X3 @ X2)) = inv)),
% 0.08/0.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse)).
% 0.08/0.31 thf(f114,plain,(
% 0.08/0.31 ($true != (so @ (inv @ sK0)))),
% 0.08/0.31 inference(cnf_transformation,[],[f93])).
% 0.08/0.31 thf(f208,plain,(
% 0.08/0.31 spl1_1 | spl1_5),
% 0.08/0.31 inference(avatar_split_clause,[],[f160,f205,f185])).
% 0.08/0.31 thf(f160,plain,(
% 0.08/0.31 ($true = (sK0 @ sK6 @ sK5)) | ($true = (sK0 @ sK3 @ sK4))),
% 0.08/0.31 inference(not_proxy_clausification,[],[f158])).
% 0.08/0.31 thf(f158,plain,(
% 0.08/0.31 ($true = (sK0 @ sK3 @ sK4)) | ($false = (~ (sK0 @ sK6 @ sK5)))),
% 0.08/0.31 inference(binary_proxy_clausification,[],[f157])).
% 0.08/0.31 thf(f203,plain,(
% 0.08/0.31 spl1_3 | spl1_4),
% 0.08/0.31 inference(avatar_split_clause,[],[f162,f199,f194])).
% 0.08/0.31 thf(f162,plain,(
% 0.08/0.31 ((sK0 @ sK4 @ sK2) = $true) | ($true = (sK0 @ sK5 @ sK6))),
% 0.08/0.31 inference(binary_proxy_clausification,[],[f156])).
% 0.08/0.31 thf(f156,plain,(
% 0.08/0.31 ((sK0 @ sK4 @ sK2) = $true) | ($false = ((sK0 @ sK5 @ sK6) => (~ (sK0 @ sK6 @ sK5))))),
% 0.08/0.31 inference(binary_proxy_clausification,[],[f155])).
% 0.08/0.31 thf(f202,plain,(
% 0.08/0.31 spl1_4 | spl1_1),
% 0.08/0.31 inference(avatar_split_clause,[],[f163,f185,f199])).
% 0.08/0.31 thf(f163,plain,(
% 0.08/0.31 ($true = (sK0 @ sK6 @ sK5)) | ((sK0 @ sK4 @ sK2) = $true)),
% 0.08/0.31 inference(not_proxy_clausification,[],[f161])).
% 0.08/0.31 thf(f161,plain,(
% 0.08/0.31 ((sK0 @ sK4 @ sK2) = $true) | ($false = (~ (sK0 @ sK6 @ sK5)))),
% 0.08/0.31 inference(binary_proxy_clausification,[],[f156])).
% 0.08/0.31 thf(f197,plain,(
% 0.08/0.31 spl1_3 | spl1_2),
% 0.08/0.31 inference(avatar_split_clause,[],[f165,f189,f194])).
% 0.08/0.31 thf(f165,plain,(
% 0.08/0.31 ($true = (sK0 @ sK5 @ sK6)) | ($false = (sK0 @ sK3 @ sK2))),
% 0.08/0.31 inference(binary_proxy_clausification,[],[f154])).
% 0.08/0.31 thf(f154,plain,(
% 0.08/0.31 ($false = ((sK0 @ sK5 @ sK6) => (~ (sK0 @ sK6 @ sK5)))) | ($false = (sK0 @ sK3 @ sK2))),
% 0.08/0.31 inference(binary_proxy_clausification,[],[f153])).
% 0.08/0.31 thf(f192,plain,(
% 0.08/0.31 spl1_1 | spl1_2),
% 0.08/0.31 inference(avatar_split_clause,[],[f166,f189,f185])).
% 0.08/0.31 thf(f166,plain,(
% 0.08/0.31 ($false = (sK0 @ sK3 @ sK2)) | ($true = (sK0 @ sK6 @ sK5))),
% 0.08/0.31 inference(not_proxy_clausification,[],[f164])).
% 0.08/0.31 thf(f164,plain,(
% 0.08/0.31 ($false = (~ (sK0 @ sK6 @ sK5))) | ($false = (sK0 @ sK3 @ sK2))),
% 0.08/0.31 inference(binary_proxy_clausification,[],[f154])).
% 0.08/0.31 % SZS output end Proof for theBenchmark
% 0.08/0.31 % (31715)------------------------------
% 0.08/0.31 % (31715)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.08/0.31 % (31715)Termination reason: Refutation
% 0.08/0.31
% 0.08/0.31 % (31715)Memory used [KB]: 5756
% 0.08/0.31 % (31715)Time elapsed: 0.011 s
% 0.08/0.31 % (31715)Instructions burned: 21 (million)
% 0.08/0.31 % (31715)------------------------------
% 0.08/0.31 % (31715)------------------------------
% 0.08/0.31 % (31704)Success in time 0.019 s
% 0.08/0.31 % Vampire---4.8 exiting
%------------------------------------------------------------------------------