TSTP Solution File: SET580^3 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SET580^3 : 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/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n028.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 03:12:10 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
% 0.03/0.12 % Problem : SET580^3 : TPTP v8.2.0. Released v3.6.0.
% 0.13/0.14 % 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 : n028.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 11:46:38 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
% 0.15/0.39 % (28765)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)
% 0.15/0.39 % (28765)First to succeed.
% 0.15/0.39 % (28766)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.15/0.39 % (28764)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)
% 0.15/0.39 % (28763)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.15/0.39 % (28766)Instruction limit reached!
% 0.15/0.39 % (28766)------------------------------
% 0.15/0.39 % (28766)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39 % (28766)Termination reason: Unknown
% 0.15/0.39 % (28766)Termination phase: Property scanning
% 0.15/0.39
% 0.15/0.39 % (28766)Memory used [KB]: 1023
% 0.15/0.39 % (28766)Time elapsed: 0.004 s
% 0.15/0.39 % (28766)Instructions burned: 2 (million)
% 0.15/0.39 % (28766)------------------------------
% 0.15/0.39 % (28766)------------------------------
% 0.15/0.39 % (28765)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(func_def_0, type, in: $i > ($i > $o) > $o).
% 0.15/0.39 thf(func_def_2, type, is_a: $i > ($i > $o) > $o).
% 0.15/0.39 thf(func_def_3, type, emptyset: $i > $o).
% 0.15/0.39 thf(func_def_4, type, unord_pair: $i > $i > $i > $o).
% 0.15/0.39 thf(func_def_5, type, singleton: $i > $i > $o).
% 0.15/0.39 thf(func_def_6, type, union: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.39 thf(func_def_7, type, excl_union: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.39 thf(func_def_8, type, intersection: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.39 thf(func_def_9, type, setminus: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.39 thf(func_def_10, type, complement: ($i > $o) > $i > $o).
% 0.15/0.39 thf(func_def_11, type, disjoint: ($i > $o) > ($i > $o) > $o).
% 0.15/0.39 thf(func_def_12, type, subset: ($i > $o) > ($i > $o) > $o).
% 0.15/0.39 thf(func_def_13, type, meets: ($i > $o) > ($i > $o) > $o).
% 0.15/0.39 thf(func_def_14, type, misses: ($i > $o) > ($i > $o) > $o).
% 0.15/0.39 thf(func_def_15, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 0.15/0.39 thf(func_def_29, type, sK0: $i > $o).
% 0.15/0.39 thf(func_def_30, type, sK1: $i > $o).
% 0.15/0.39 thf(f141,plain,(
% 0.15/0.39 $false),
% 0.15/0.39 inference(avatar_sat_refutation,[],[f124,f129,f131,f133,f134,f137,f140])).
% 0.15/0.39 thf(f140,plain,(
% 0.15/0.39 ~spl3_1 | ~spl3_3),
% 0.15/0.39 inference(avatar_contradiction_clause,[],[f139])).
% 0.15/0.39 thf(f139,plain,(
% 0.15/0.39 $false | (~spl3_1 | ~spl3_3)),
% 0.15/0.39 inference(trivial_inequality_removal,[],[f138])).
% 0.15/0.39 thf(f138,plain,(
% 0.15/0.39 ($true = $false) | (~spl3_1 | ~spl3_3)),
% 0.15/0.39 inference(forward_demodulation,[],[f122,f115])).
% 0.15/0.39 thf(f115,plain,(
% 0.15/0.39 ($false = (sK0 @ sK2)) | ~spl3_1),
% 0.15/0.39 inference(avatar_component_clause,[],[f113])).
% 0.15/0.39 thf(f113,plain,(
% 0.15/0.39 spl3_1 <=> ($false = (sK0 @ sK2))),
% 0.15/0.39 introduced(avatar_definition,[new_symbols(naming,[spl3_1])])).
% 0.15/0.39 thf(f122,plain,(
% 0.15/0.39 ($true = (sK0 @ sK2)) | ~spl3_3),
% 0.15/0.39 inference(avatar_component_clause,[],[f121])).
% 0.15/0.39 thf(f121,plain,(
% 0.15/0.39 spl3_3 <=> ($true = (sK0 @ sK2))),
% 0.15/0.39 introduced(avatar_definition,[new_symbols(naming,[spl3_3])])).
% 0.15/0.39 thf(f137,plain,(
% 0.15/0.39 ~spl3_2 | ~spl3_4),
% 0.15/0.39 inference(avatar_contradiction_clause,[],[f136])).
% 0.15/0.39 thf(f136,plain,(
% 0.15/0.39 $false | (~spl3_2 | ~spl3_4)),
% 0.15/0.39 inference(trivial_inequality_removal,[],[f135])).
% 0.15/0.39 thf(f135,plain,(
% 0.15/0.39 ($true = $false) | (~spl3_2 | ~spl3_4)),
% 0.15/0.39 inference(backward_demodulation,[],[f119,f128])).
% 0.15/0.39 thf(f128,plain,(
% 0.15/0.39 ($false = (sK1 @ sK2)) | ~spl3_4),
% 0.15/0.39 inference(avatar_component_clause,[],[f126])).
% 0.15/0.39 thf(f126,plain,(
% 0.15/0.39 spl3_4 <=> ($false = (sK1 @ sK2))),
% 0.15/0.39 introduced(avatar_definition,[new_symbols(naming,[spl3_4])])).
% 0.15/0.39 thf(f119,plain,(
% 0.15/0.39 ($true = (sK1 @ sK2)) | ~spl3_2),
% 0.15/0.39 inference(avatar_component_clause,[],[f117])).
% 0.15/0.39 thf(f117,plain,(
% 0.15/0.39 spl3_2 <=> ($true = (sK1 @ sK2))),
% 0.15/0.39 introduced(avatar_definition,[new_symbols(naming,[spl3_2])])).
% 0.15/0.39 thf(f134,plain,(
% 0.15/0.39 spl3_4 | spl3_3 | ~spl3_2),
% 0.15/0.39 inference(avatar_split_clause,[],[f78,f117,f121,f126])).
% 0.15/0.39 thf(f78,plain,(
% 0.15/0.39 ($true = (sK0 @ sK2)) | ($true != (sK1 @ sK2)) | ($false = (sK1 @ sK2))),
% 0.15/0.39 inference(duplicate_literal_removal,[],[f77])).
% 0.15/0.39 thf(f77,plain,(
% 0.15/0.39 ($true = (sK0 @ sK2)) | ($true = (sK0 @ sK2)) | ($false = (sK1 @ sK2)) | ($true != (sK1 @ sK2))),
% 0.15/0.39 inference(not_proxy_clausification,[],[f76])).
% 0.15/0.39 thf(f76,plain,(
% 0.15/0.39 ($false = (sK1 @ sK2)) | ($true = (sK0 @ sK2)) | ($true != (sK1 @ sK2)) | ($false = (~ (sK0 @ sK2)))),
% 0.15/0.39 inference(binary_proxy_clausification,[],[f75])).
% 0.15/0.39 thf(f75,plain,(
% 0.15/0.39 ($true = (sK0 @ sK2)) | ($true != (sK1 @ sK2)) | (((sK1 @ sK2) & (~ (sK0 @ sK2))) = $false)),
% 0.15/0.39 inference(binary_proxy_clausification,[],[f73])).
% 0.15/0.39 thf(f73,plain,(
% 0.15/0.39 ($true != (((sK1 @ sK2) & (~ (sK0 @ sK2))) | ((~ (sK1 @ sK2)) & (sK0 @ sK2)))) | ($true != (sK1 @ sK2)) | ($true = (sK0 @ sK2))),
% 0.15/0.39 inference(beta_eta_normalization,[],[f70])).
% 0.15/0.39 thf(f70,plain,(
% 0.15/0.39 ($true != (sK1 @ sK2)) | ($true != ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (((Y1 @ Y2) & (~ (Y0 @ Y2))) | ((~ (Y1 @ Y2)) & (Y0 @ Y2)))))))) @ sK0 @ sK1 @ sK2)) | ($true = (sK0 @ sK2))),
% 0.15/0.39 inference(definition_unfolding,[],[f54,f62])).
% 0.15/0.39 thf(f62,plain,(
% 0.15/0.39 (excl_union = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (((Y1 @ Y2) & (~ (Y0 @ Y2))) | ((~ (Y1 @ Y2)) & (Y0 @ Y2)))))))))),
% 0.15/0.39 inference(cnf_transformation,[],[f22])).
% 0.15/0.39 thf(f22,plain,(
% 0.15/0.39 (excl_union = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (((Y1 @ Y2) & (~ (Y0 @ Y2))) | ((~ (Y1 @ Y2)) & (Y0 @ Y2)))))))))),
% 0.15/0.39 inference(fool_elimination,[],[f21])).
% 0.15/0.39 thf(f21,plain,(
% 0.15/0.39 (excl_union = (^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : (((X0 @ X2) & ~(X1 @ X2)) | (~(X0 @ X2) & (X1 @ X2)))))),
% 0.15/0.39 inference(rectify,[],[f7])).
% 0.15/0.39 thf(f7,axiom,(
% 0.15/0.39 (excl_union = (^[X0 : $i > $o, X2 : $i > $o, X3 : $i] : (((X0 @ X3) & ~(X2 @ X3)) | (~(X0 @ X3) & (X2 @ X3)))))),
% 0.15/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',excl_union)).
% 0.15/0.39 thf(f54,plain,(
% 0.15/0.39 ($true = (sK0 @ sK2)) | ($true != (sK1 @ sK2)) | ((excl_union @ sK0 @ sK1 @ sK2) != $true)),
% 0.15/0.39 inference(cnf_transformation,[],[f49])).
% 0.15/0.39 thf(f49,plain,(
% 0.15/0.39 (((($true != (sK0 @ sK2)) | ($true = (sK1 @ sK2))) & (($true = (sK0 @ sK2)) | ($true != (sK1 @ sK2)))) | ((excl_union @ sK0 @ sK1 @ sK2) != $true)) & (((($true != (sK1 @ sK2)) | ($true != (sK0 @ sK2))) & (($true = (sK0 @ sK2)) | ($true = (sK1 @ sK2)))) | ((excl_union @ sK0 @ sK1 @ sK2) = $true))),
% 0.15/0.39 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f47,f48])).
% 0.15/0.39 thf(f48,plain,(
% 0.15/0.39 ? [X0 : $i > $o,X1 : $i > $o,X2] : ((((((X0 @ X2) != $true) | ($true = (X1 @ X2))) & (((X0 @ X2) = $true) | ($true != (X1 @ X2)))) | ($true != (excl_union @ X0 @ X1 @ X2))) & (((($true != (X1 @ X2)) | ((X0 @ X2) != $true)) & (((X0 @ X2) = $true) | ($true = (X1 @ X2)))) | ($true = (excl_union @ X0 @ X1 @ X2)))) => ((((($true != (sK0 @ sK2)) | ($true = (sK1 @ sK2))) & (($true = (sK0 @ sK2)) | ($true != (sK1 @ sK2)))) | ((excl_union @ sK0 @ sK1 @ sK2) != $true)) & (((($true != (sK1 @ sK2)) | ($true != (sK0 @ sK2))) & (($true = (sK0 @ sK2)) | ($true = (sK1 @ sK2)))) | ((excl_union @ sK0 @ sK1 @ sK2) = $true)))),
% 0.15/0.39 introduced(choice_axiom,[])).
% 0.15/0.39 thf(f47,plain,(
% 0.15/0.39 ? [X0 : $i > $o,X1 : $i > $o,X2] : ((((((X0 @ X2) != $true) | ($true = (X1 @ X2))) & (((X0 @ X2) = $true) | ($true != (X1 @ X2)))) | ($true != (excl_union @ X0 @ X1 @ X2))) & (((($true != (X1 @ X2)) | ((X0 @ X2) != $true)) & (((X0 @ X2) = $true) | ($true = (X1 @ X2)))) | ($true = (excl_union @ X0 @ X1 @ X2))))),
% 0.15/0.39 inference(nnf_transformation,[],[f46])).
% 0.15/0.39 thf(f46,plain,(
% 0.15/0.39 ? [X0 : $i > $o,X1 : $i > $o,X2] : (($true = (excl_union @ X0 @ X1 @ X2)) <~> (($true != (X1 @ X2)) <=> ((X0 @ X2) = $true)))),
% 0.15/0.39 inference(ennf_transformation,[],[f45])).
% 0.15/0.39 thf(f45,plain,(
% 0.15/0.39 ~! [X0 : $i > $o,X1 : $i > $o,X2] : (($true = (excl_union @ X0 @ X1 @ X2)) <=> (($true != (X1 @ X2)) <=> ((X0 @ X2) = $true)))),
% 0.15/0.39 inference(flattening,[],[f39])).
% 0.15/0.39 thf(f39,plain,(
% 0.15/0.39 ~! [X0 : $i > $o,X1 : $i > $o,X2] : (($true = (excl_union @ X0 @ X1 @ X2)) <=> (((X0 @ X2) = $true) <=> ~($true = (X1 @ X2))))),
% 0.15/0.39 inference(fool_elimination,[],[f38])).
% 0.15/0.39 thf(f38,plain,(
% 0.15/0.39 ~! [X0 : $i > $o,X1 : $i > $o,X2] : ((excl_union @ X0 @ X1 @ X2) <=> ((X0 @ X2) <=> ~(X1 @ X2)))),
% 0.15/0.39 inference(rectify,[],[f16])).
% 0.15/0.39 thf(f16,negated_conjecture,(
% 0.15/0.39 ~! [X0 : $i > $o,X2 : $i > $o,X3] : ((excl_union @ X0 @ X2 @ X3) <=> ((X0 @ X3) <=> ~(X2 @ X3)))),
% 0.15/0.39 inference(negated_conjecture,[],[f15])).
% 0.15/0.39 thf(f15,conjecture,(
% 0.15/0.39 ! [X0 : $i > $o,X2 : $i > $o,X3] : ((excl_union @ X0 @ X2 @ X3) <=> ((X0 @ X3) <=> ~(X2 @ X3)))),
% 0.15/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm)).
% 0.15/0.39 thf(f133,plain,(
% 0.15/0.39 spl3_4 | spl3_2 | spl3_3),
% 0.15/0.39 inference(avatar_split_clause,[],[f88,f121,f117,f126])).
% 0.15/0.39 thf(f88,plain,(
% 0.15/0.39 ($true = (sK1 @ sK2)) | ($false = (sK1 @ sK2)) | ($true = (sK0 @ sK2))),
% 0.15/0.39 inference(not_proxy_clausification,[],[f87])).
% 0.15/0.39 thf(f87,plain,(
% 0.15/0.39 ($true = (sK1 @ sK2)) | ($true = (~ (sK1 @ sK2))) | ($true = (sK0 @ sK2))),
% 0.15/0.39 inference(duplicate_literal_removal,[],[f86])).
% 0.15/0.39 thf(f86,plain,(
% 0.15/0.39 ($true = (sK1 @ sK2)) | ($true = (sK0 @ sK2)) | ($true = (sK1 @ sK2)) | ($true = (~ (sK1 @ sK2)))),
% 0.15/0.39 inference(binary_proxy_clausification,[],[f84])).
% 0.15/0.39 thf(f84,plain,(
% 0.15/0.39 ($true = (sK1 @ sK2)) | ($true = (sK0 @ sK2)) | (((sK1 @ sK2) & (~ (sK0 @ sK2))) = $true) | ($true = (~ (sK1 @ sK2)))),
% 0.15/0.39 inference(binary_proxy_clausification,[],[f82])).
% 0.15/0.39 thf(f82,plain,(
% 0.15/0.39 ($true = (sK1 @ sK2)) | ($true = (sK0 @ sK2)) | (((~ (sK1 @ sK2)) & (sK0 @ sK2)) = $true) | (((sK1 @ sK2) & (~ (sK0 @ sK2))) = $true)),
% 0.15/0.39 inference(binary_proxy_clausification,[],[f81])).
% 0.15/0.39 thf(f81,plain,(
% 0.15/0.39 ($true = (sK0 @ sK2)) | ($true = (((sK1 @ sK2) & (~ (sK0 @ sK2))) | ((~ (sK1 @ sK2)) & (sK0 @ sK2)))) | ($true = (sK1 @ sK2))),
% 0.15/0.39 inference(beta_eta_normalization,[],[f72])).
% 0.15/0.39 thf(f72,plain,(
% 0.15/0.39 ($true = (sK0 @ sK2)) | ($true = (sK1 @ sK2)) | ($true = ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (((Y1 @ Y2) & (~ (Y0 @ Y2))) | ((~ (Y1 @ Y2)) & (Y0 @ Y2)))))))) @ sK0 @ sK1 @ sK2))),
% 0.15/0.39 inference(definition_unfolding,[],[f52,f62])).
% 0.15/0.39 thf(f52,plain,(
% 0.15/0.39 ($true = (sK0 @ sK2)) | ($true = (sK1 @ sK2)) | ((excl_union @ sK0 @ sK1 @ sK2) = $true)),
% 0.15/0.39 inference(cnf_transformation,[],[f49])).
% 0.15/0.39 thf(f131,plain,(
% 0.15/0.39 spl3_2 | spl3_3),
% 0.15/0.39 inference(avatar_split_clause,[],[f94,f121,f117])).
% 0.15/0.39 thf(f94,plain,(
% 0.15/0.39 ($true = (sK0 @ sK2)) | ($true = (sK1 @ sK2))),
% 0.15/0.39 inference(duplicate_literal_removal,[],[f93])).
% 0.15/0.39 thf(f93,plain,(
% 0.15/0.39 ($true = (sK1 @ sK2)) | ($true = (sK0 @ sK2)) | ($true = (sK1 @ sK2))),
% 0.15/0.39 inference(binary_proxy_clausification,[],[f91])).
% 0.15/0.39 thf(f91,plain,(
% 0.15/0.39 (((sK1 @ sK2) & (~ (sK0 @ sK2))) = $true) | ($true = (sK1 @ sK2)) | ($true = (sK0 @ sK2))),
% 0.15/0.39 inference(duplicate_literal_removal,[],[f83])).
% 0.15/0.39 thf(f83,plain,(
% 0.15/0.39 ($true = (sK1 @ sK2)) | (((sK1 @ sK2) & (~ (sK0 @ sK2))) = $true) | ($true = (sK0 @ sK2)) | ($true = (sK0 @ sK2))),
% 0.15/0.39 inference(binary_proxy_clausification,[],[f82])).
% 0.15/0.39 thf(f129,plain,(
% 0.15/0.39 spl3_4 | ~spl3_3 | spl3_1 | ~spl3_2),
% 0.15/0.39 inference(avatar_split_clause,[],[f103,f117,f113,f121,f126])).
% 0.15/0.39 thf(f103,plain,(
% 0.15/0.39 ($false = (sK0 @ sK2)) | ($true != (sK0 @ sK2)) | ($false = (sK1 @ sK2)) | ($true != (sK1 @ sK2))),
% 0.15/0.39 inference(not_proxy_clausification,[],[f102])).
% 0.15/0.39 thf(f102,plain,(
% 0.15/0.39 ($true != (sK0 @ sK2)) | ($true = (~ (sK1 @ sK2))) | ($true != (sK1 @ sK2)) | ($false = (sK0 @ sK2))),
% 0.15/0.39 inference(not_proxy_clausification,[],[f100])).
% 0.15/0.39 thf(f100,plain,(
% 0.15/0.39 ($true = (~ (sK0 @ sK2))) | ($true != (sK1 @ sK2)) | ($true = (~ (sK1 @ sK2))) | ($true != (sK0 @ sK2))),
% 0.15/0.39 inference(binary_proxy_clausification,[],[f99])).
% 0.15/0.39 thf(f99,plain,(
% 0.15/0.39 (((sK1 @ sK2) & (~ (sK0 @ sK2))) = $true) | ($true != (sK0 @ sK2)) | ($true = (~ (sK1 @ sK2))) | ($true != (sK1 @ sK2))),
% 0.15/0.39 inference(binary_proxy_clausification,[],[f97])).
% 0.15/0.39 thf(f97,plain,(
% 0.15/0.39 (((~ (sK1 @ sK2)) & (sK0 @ sK2)) = $true) | ($true != (sK0 @ sK2)) | ($true != (sK1 @ sK2)) | (((sK1 @ sK2) & (~ (sK0 @ sK2))) = $true)),
% 0.15/0.39 inference(binary_proxy_clausification,[],[f96])).
% 0.15/0.39 thf(f96,plain,(
% 0.15/0.39 ($true = (((sK1 @ sK2) & (~ (sK0 @ sK2))) | ((~ (sK1 @ sK2)) & (sK0 @ sK2)))) | ($true != (sK0 @ sK2)) | ($true != (sK1 @ sK2))),
% 0.15/0.39 inference(beta_eta_normalization,[],[f71])).
% 0.15/0.39 thf(f71,plain,(
% 0.15/0.39 ($true != (sK1 @ sK2)) | ($true = ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (((Y1 @ Y2) & (~ (Y0 @ Y2))) | ((~ (Y1 @ Y2)) & (Y0 @ Y2)))))))) @ sK0 @ sK1 @ sK2)) | ($true != (sK0 @ sK2))),
% 0.15/0.39 inference(definition_unfolding,[],[f53,f62])).
% 0.15/0.39 thf(f53,plain,(
% 0.15/0.39 ($true != (sK1 @ sK2)) | ($true != (sK0 @ sK2)) | ((excl_union @ sK0 @ sK1 @ sK2) = $true)),
% 0.15/0.39 inference(cnf_transformation,[],[f49])).
% 0.15/0.39 thf(f124,plain,(
% 0.15/0.39 spl3_1 | spl3_2 | ~spl3_3),
% 0.15/0.39 inference(avatar_split_clause,[],[f111,f121,f117,f113])).
% 0.15/0.39 thf(f111,plain,(
% 0.15/0.39 ($true != (sK0 @ sK2)) | ($false = (sK0 @ sK2)) | ($true = (sK1 @ sK2))),
% 0.15/0.39 inference(duplicate_literal_removal,[],[f110])).
% 0.15/0.39 thf(f110,plain,(
% 0.15/0.39 ($true = (sK1 @ sK2)) | ($true != (sK0 @ sK2)) | ($true = (sK1 @ sK2)) | ($false = (sK0 @ sK2))),
% 0.15/0.39 inference(not_proxy_clausification,[],[f109])).
% 0.15/0.39 thf(f109,plain,(
% 0.15/0.39 ($true = (sK1 @ sK2)) | ($true != (sK0 @ sK2)) | ((~ (sK1 @ sK2)) = $false) | ($false = (sK0 @ sK2))),
% 0.15/0.39 inference(binary_proxy_clausification,[],[f105])).
% 0.15/0.39 thf(f105,plain,(
% 0.15/0.39 ($true != (sK0 @ sK2)) | (((~ (sK1 @ sK2)) & (sK0 @ sK2)) = $false) | ($true = (sK1 @ sK2))),
% 0.15/0.39 inference(binary_proxy_clausification,[],[f104])).
% 0.15/0.39 thf(f104,plain,(
% 0.15/0.39 ($true != (sK0 @ sK2)) | ($true != (((sK1 @ sK2) & (~ (sK0 @ sK2))) | ((~ (sK1 @ sK2)) & (sK0 @ sK2)))) | ($true = (sK1 @ sK2))),
% 0.15/0.39 inference(beta_eta_normalization,[],[f69])).
% 0.15/0.39 thf(f69,plain,(
% 0.15/0.39 ($true != (sK0 @ sK2)) | ($true = (sK1 @ sK2)) | ($true != ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (((Y1 @ Y2) & (~ (Y0 @ Y2))) | ((~ (Y1 @ Y2)) & (Y0 @ Y2)))))))) @ sK0 @ sK1 @ sK2))),
% 0.15/0.39 inference(definition_unfolding,[],[f55,f62])).
% 0.15/0.39 thf(f55,plain,(
% 0.15/0.39 ($true != (sK0 @ sK2)) | ($true = (sK1 @ sK2)) | ((excl_union @ sK0 @ sK1 @ sK2) != $true)),
% 0.15/0.39 inference(cnf_transformation,[],[f49])).
% 0.15/0.39 % SZS output end Proof for theBenchmark
% 0.15/0.39 % (28765)------------------------------
% 0.15/0.39 % (28765)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39 % (28765)Termination reason: Refutation
% 0.15/0.39
% 0.15/0.39 % (28765)Memory used [KB]: 5500
% 0.15/0.39 % (28765)Time elapsed: 0.008 s
% 0.15/0.39 % (28765)Instructions burned: 6 (million)
% 0.15/0.39 % (28765)------------------------------
% 0.15/0.39 % (28765)------------------------------
% 0.15/0.39 % (28762)Success in time 0.021 s
% 0.15/0.39 % Vampire---4.8 exiting
%------------------------------------------------------------------------------