TSTP Solution File: SEU630^2 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU630^2 : TPTP v8.2.0. Released v3.7.0.
% 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 : n029.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 03:50:08 EDT 2024
% Result : Theorem 0.13s 0.37s
% Output : Refutation 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SEU630^2 : TPTP v8.2.0. Released v3.7.0.
% 0.07/0.13 % 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
% 0.13/0.33 % Computer : n029.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sun May 19 16:06:23 EDT 2024
% 0.13/0.33 % CPUTime :
% 0.13/0.33 This is a TH0_THM_EQU_NAR problem
% 0.13/0.33 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
% 0.13/0.35 % (28164)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.13/0.35 % (28164)Instruction limit reached!
% 0.13/0.35 % (28164)------------------------------
% 0.13/0.35 % (28164)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.35 % (28164)Termination reason: Unknown
% 0.13/0.35 % (28164)Termination phase: Function definition elimination
% 0.13/0.35
% 0.13/0.35 % (28164)Memory used [KB]: 1023
% 0.13/0.35 % (28164)Time elapsed: 0.003 s
% 0.13/0.35 % (28164)Instructions burned: 3 (million)
% 0.13/0.35 % (28164)------------------------------
% 0.13/0.35 % (28164)------------------------------
% 0.13/0.35 % (28166)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)
% 0.13/0.35 % (28162)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)
% 0.13/0.35 % (28161)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.13/0.35 % (28167)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.13/0.35 % (28165)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)
% 0.13/0.35 % (28168)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.13/0.35 % (28165)Instruction limit reached!
% 0.13/0.35 % (28165)------------------------------
% 0.13/0.35 % (28165)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.35 % (28165)Termination reason: Unknown
% 0.13/0.35 % (28165)Termination phase: Property scanning
% 0.13/0.35
% 0.13/0.35 % (28165)Memory used [KB]: 1023
% 0.13/0.35 % (28165)Time elapsed: 0.003 s
% 0.13/0.35 % (28165)Instructions burned: 3 (million)
% 0.13/0.35 % (28165)------------------------------
% 0.13/0.35 % (28165)------------------------------
% 0.13/0.36 % (28163)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)
% 0.13/0.36 % (28162)Instruction limit reached!
% 0.13/0.36 % (28162)------------------------------
% 0.13/0.36 % (28162)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.36 % (28162)Termination reason: Unknown
% 0.13/0.36 % (28162)Termination phase: Saturation
% 0.13/0.36
% 0.13/0.36 % (28162)Memory used [KB]: 1023
% 0.13/0.36 % (28162)Time elapsed: 0.004 s
% 0.13/0.36 % (28162)Instructions burned: 4 (million)
% 0.13/0.36 % (28162)------------------------------
% 0.13/0.36 % (28162)------------------------------
% 0.13/0.36 % (28168)Instruction limit reached!
% 0.13/0.36 % (28168)------------------------------
% 0.13/0.36 % (28168)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.36 % (28168)Termination reason: Unknown
% 0.13/0.36 % (28168)Termination phase: Saturation
% 0.13/0.36
% 0.13/0.36 % (28168)Memory used [KB]: 1023
% 0.13/0.36 % (28168)Time elapsed: 0.004 s
% 0.13/0.36 % (28168)Instructions burned: 4 (million)
% 0.13/0.36 % (28168)------------------------------
% 0.13/0.36 % (28168)------------------------------
% 0.13/0.36 % (28166)Refutation not found, incomplete strategy
% 0.13/0.36 % (28166)------------------------------
% 0.13/0.36 % (28166)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.36 % (28166)Termination reason: Refutation not found, incomplete strategy
% 0.13/0.36
% 0.13/0.36
% 0.13/0.36 % (28166)Memory used [KB]: 5500
% 0.13/0.36 % (28166)Time elapsed: 0.005 s
% 0.13/0.36 % (28166)Instructions burned: 5 (million)
% 0.13/0.36 % (28166)------------------------------
% 0.13/0.36 % (28166)------------------------------
% 0.13/0.36 % (28161)First to succeed.
% 0.13/0.36 % (28169)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.13/0.36 % (28167)Instruction limit reached!
% 0.13/0.36 % (28167)------------------------------
% 0.13/0.36 % (28167)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.36 % (28167)Termination reason: Unknown
% 0.13/0.36 % (28167)Termination phase: Saturation
% 0.13/0.36
% 0.13/0.36 % (28167)Memory used [KB]: 5628
% 0.13/0.36 % (28167)Time elapsed: 0.013 s
% 0.13/0.36 % (28167)Instructions burned: 18 (million)
% 0.13/0.36 % (28167)------------------------------
% 0.13/0.36 % (28167)------------------------------
% 0.13/0.37 % (28163)Also succeeded, but the first one will report.
% 0.13/0.37 % (28161)Refutation found. Thanks to Tanya!
% 0.13/0.37 % SZS status Theorem for theBenchmark
% 0.13/0.37 % SZS output start Proof for theBenchmark
% 0.13/0.37 thf(func_def_0, type, in: $i > $i > $o).
% 0.13/0.37 thf(func_def_2, type, setadjoin: $i > $i > $i).
% 0.13/0.37 thf(func_def_3, type, powerset: $i > $i).
% 0.13/0.37 thf(func_def_4, type, dsetconstr: $i > ($i > $o) > $i).
% 0.13/0.37 thf(func_def_7, type, binunion: $i > $i > $i).
% 0.13/0.37 thf(func_def_8, type, kpair: $i > $i > $i).
% 0.13/0.37 thf(func_def_9, type, cartprod: $i > $i > $i).
% 0.13/0.37 thf(func_def_29, type, ph5: !>[X0: $tType]:(X0)).
% 0.13/0.37 thf(f110,plain,(
% 0.13/0.37 $false),
% 0.13/0.37 inference(avatar_sat_refutation,[],[f76,f90,f96,f103,f109])).
% 0.13/0.37 thf(f109,plain,(
% 0.13/0.37 ~spl4_1 | spl4_3 | spl4_4),
% 0.13/0.37 inference(avatar_contradiction_clause,[],[f108])).
% 0.13/0.37 thf(f108,plain,(
% 0.13/0.37 $false | (~spl4_1 | spl4_3 | spl4_4)),
% 0.13/0.37 inference(subsumption_resolution,[],[f107,f87])).
% 0.13/0.37 thf(f87,plain,(
% 0.13/0.37 ($false != (in @ sK3 @ sK0)) | spl4_4),
% 0.13/0.37 inference(avatar_component_clause,[],[f86])).
% 0.13/0.37 thf(f86,plain,(
% 0.13/0.37 spl4_4 <=> ($false = (in @ sK3 @ sK0))),
% 0.13/0.37 introduced(avatar_definition,[new_symbols(naming,[spl4_4])])).
% 0.13/0.37 thf(f107,plain,(
% 0.13/0.37 ($false = (in @ sK3 @ sK0)) | (~spl4_1 | spl4_3)),
% 0.13/0.37 inference(subsumption_resolution,[],[f106,f83])).
% 0.13/0.37 thf(f83,plain,(
% 0.13/0.37 ($false != (in @ sK1 @ sK2)) | spl4_3),
% 0.13/0.37 inference(avatar_component_clause,[],[f82])).
% 0.13/0.37 thf(f82,plain,(
% 0.13/0.37 spl4_3 <=> ($false = (in @ sK1 @ sK2))),
% 0.13/0.37 introduced(avatar_definition,[new_symbols(naming,[spl4_3])])).
% 0.13/0.37 thf(f106,plain,(
% 0.13/0.37 ($false = (in @ sK1 @ sK2)) | ($false = (in @ sK3 @ sK0)) | ~spl4_1),
% 0.13/0.37 inference(equality_resolution,[],[f71])).
% 0.13/0.37 thf(f71,plain,(
% 0.13/0.37 ( ! [X2 : $i,X1 : $i] : (((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) != (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK3 @ emptyset)) @ emptyset))) | ($false = (in @ X2 @ sK0)) | ((in @ X1 @ sK2) = $false)) ) | ~spl4_1),
% 0.13/0.37 inference(avatar_component_clause,[],[f70])).
% 0.13/0.37 thf(f70,plain,(
% 0.13/0.37 spl4_1 <=> ! [X2,X1] : (((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) != (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK3 @ emptyset)) @ emptyset))) | ((in @ X1 @ sK2) = $false) | ($false = (in @ X2 @ sK0)))),
% 0.13/0.37 introduced(avatar_definition,[new_symbols(naming,[spl4_1])])).
% 0.13/0.37 thf(f103,plain,(
% 0.13/0.37 ~spl4_4),
% 0.13/0.37 inference(avatar_contradiction_clause,[],[f102])).
% 0.13/0.37 thf(f102,plain,(
% 0.13/0.37 $false | ~spl4_4),
% 0.13/0.37 inference(trivial_inequality_removal,[],[f99])).
% 0.13/0.37 thf(f99,plain,(
% 0.13/0.37 ($false = $true) | ~spl4_4),
% 0.13/0.37 inference(superposition,[],[f25,f88])).
% 0.13/0.37 thf(f88,plain,(
% 0.13/0.37 ($false = (in @ sK3 @ sK0)) | ~spl4_4),
% 0.13/0.37 inference(avatar_component_clause,[],[f86])).
% 0.13/0.37 thf(f25,plain,(
% 0.13/0.37 ((in @ sK3 @ sK0) = $true)),
% 0.13/0.37 inference(cnf_transformation,[],[f22])).
% 0.13/0.37 thf(f22,plain,(
% 0.13/0.37 (ubforcartprodlem3 = $true) & (dsetconstrI = $true) & (((in @ sK1 @ sK2) = $true) & (((in @ sK3 @ sK0) = $true) & ((in @ (kpair @ sK1 @ sK3) @ (cartprod @ sK2 @ sK0)) != $true)))),
% 0.13/0.37 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f19,f21,f20])).
% 0.13/0.37 thf(f20,plain,(
% 0.13/0.37 ? [X0,X1,X2] : (((in @ X1 @ X2) = $true) & ? [X3] : (((in @ X3 @ X0) = $true) & ($true != (in @ (kpair @ X1 @ X3) @ (cartprod @ X2 @ X0))))) => (((in @ sK1 @ sK2) = $true) & ? [X3] : (((in @ X3 @ sK0) = $true) & ((in @ (kpair @ sK1 @ X3) @ (cartprod @ sK2 @ sK0)) != $true)))),
% 0.13/0.37 introduced(choice_axiom,[])).
% 0.13/0.37 thf(f21,plain,(
% 0.13/0.37 ? [X3] : (((in @ X3 @ sK0) = $true) & ((in @ (kpair @ sK1 @ X3) @ (cartprod @ sK2 @ sK0)) != $true)) => (((in @ sK3 @ sK0) = $true) & ((in @ (kpair @ sK1 @ sK3) @ (cartprod @ sK2 @ sK0)) != $true))),
% 0.13/0.37 introduced(choice_axiom,[])).
% 0.13/0.37 thf(f19,plain,(
% 0.13/0.37 (ubforcartprodlem3 = $true) & (dsetconstrI = $true) & ? [X0,X1,X2] : (((in @ X1 @ X2) = $true) & ? [X3] : (((in @ X3 @ X0) = $true) & ($true != (in @ (kpair @ X1 @ X3) @ (cartprod @ X2 @ X0)))))),
% 0.13/0.37 inference(flattening,[],[f18])).
% 0.13/0.37 thf(f18,plain,(
% 0.13/0.37 (? [X0,X1,X2] : (((in @ X1 @ X2) = $true) & ? [X3] : (((in @ X3 @ X0) = $true) & ($true != (in @ (kpair @ X1 @ X3) @ (cartprod @ X2 @ X0))))) & (ubforcartprodlem3 = $true)) & (dsetconstrI = $true)),
% 0.13/0.37 inference(ennf_transformation,[],[f17])).
% 0.13/0.37 thf(f17,plain,(
% 0.13/0.37 ~((dsetconstrI = $true) => ((ubforcartprodlem3 = $true) => ! [X0,X1,X2] : (((in @ X1 @ X2) = $true) => ! [X3] : (((in @ X3 @ X0) = $true) => ($true = (in @ (kpair @ X1 @ X3) @ (cartprod @ X2 @ X0)))))))),
% 0.13/0.37 inference(fool_elimination,[],[f16])).
% 0.13/0.37 thf(f16,plain,(
% 0.13/0.37 ~(dsetconstrI => (ubforcartprodlem3 => ! [X0,X1,X2] : ((in @ X1 @ X2) => ! [X3] : ((in @ X3 @ X0) => (in @ (kpair @ X1 @ X3) @ (cartprod @ X2 @ X0))))))),
% 0.13/0.37 inference(rectify,[],[f6])).
% 0.13/0.37 thf(f6,negated_conjecture,(
% 0.13/0.37 ~(dsetconstrI => (ubforcartprodlem3 => ! [X4,X2,X0] : ((in @ X2 @ X0) => ! [X3] : ((in @ X3 @ X4) => (in @ (kpair @ X2 @ X3) @ (cartprod @ X0 @ X4))))))),
% 0.13/0.37 inference(negated_conjecture,[],[f5])).
% 0.13/0.37 thf(f5,conjecture,(
% 0.13/0.37 dsetconstrI => (ubforcartprodlem3 => ! [X4,X2,X0] : ((in @ X2 @ X0) => ! [X3] : ((in @ X3 @ X4) => (in @ (kpair @ X2 @ X3) @ (cartprod @ X0 @ X4)))))),
% 0.13/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairin)).
% 0.13/0.37 thf(f96,plain,(
% 0.13/0.37 ~spl4_3),
% 0.13/0.37 inference(avatar_contradiction_clause,[],[f95])).
% 0.13/0.37 thf(f95,plain,(
% 0.13/0.37 $false | ~spl4_3),
% 0.13/0.37 inference(trivial_inequality_removal,[],[f92])).
% 0.13/0.37 thf(f92,plain,(
% 0.13/0.37 ($false = $true) | ~spl4_3),
% 0.13/0.37 inference(superposition,[],[f26,f84])).
% 0.13/0.37 thf(f84,plain,(
% 0.13/0.37 ($false = (in @ sK1 @ sK2)) | ~spl4_3),
% 0.13/0.37 inference(avatar_component_clause,[],[f82])).
% 0.13/0.37 thf(f26,plain,(
% 0.13/0.37 ((in @ sK1 @ sK2) = $true)),
% 0.13/0.37 inference(cnf_transformation,[],[f22])).
% 0.13/0.37 thf(f90,plain,(
% 0.13/0.37 spl4_3 | spl4_4 | ~spl4_2),
% 0.13/0.37 inference(avatar_split_clause,[],[f79,f73,f86,f82])).
% 0.13/0.37 thf(f73,plain,(
% 0.13/0.37 spl4_2 <=> ((in @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ sK2 @ sK0)))) = $false)),
% 0.13/0.37 introduced(avatar_definition,[new_symbols(naming,[spl4_2])])).
% 0.13/0.37 thf(f79,plain,(
% 0.13/0.37 ($false = (in @ sK1 @ sK2)) | ($false = (in @ sK3 @ sK0)) | ~spl4_2),
% 0.13/0.37 inference(trivial_inequality_removal,[],[f77])).
% 0.13/0.37 thf(f77,plain,(
% 0.13/0.37 ($false = (in @ sK1 @ sK2)) | ($false = (in @ sK3 @ sK0)) | ($false = $true) | ~spl4_2),
% 0.13/0.37 inference(superposition,[],[f75,f47])).
% 0.13/0.37 thf(f47,plain,(
% 0.13/0.37 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X4 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X3 @ X1)))) = $true) | ($false = (in @ X2 @ X3)) | ($false = (in @ X4 @ X1))) )),
% 0.13/0.37 inference(binary_proxy_clausification,[],[f46])).
% 0.13/0.37 thf(f46,plain,(
% 0.13/0.37 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : ((((in @ X4 @ X1) => (in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X4 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X3 @ X1))))) = $true) | ($false = (in @ X2 @ X3))) )),
% 0.13/0.37 inference(beta_eta_normalization,[],[f45])).
% 0.13/0.37 thf(f45,plain,(
% 0.13/0.37 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = (in @ X2 @ X3)) | (((^[Y0 : $i]: ((in @ Y0 @ X1) => (in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X3 @ X1)))))) @ X4) = $true)) )),
% 0.13/0.37 inference(pi_clausification,[],[f44])).
% 0.13/0.37 thf(f44,plain,(
% 0.13/0.37 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (in @ X2 @ X3)) | ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X3 @ X1))))))) = $true)) )),
% 0.13/0.37 inference(binary_proxy_clausification,[],[f43])).
% 0.13/0.37 thf(f43,plain,(
% 0.13/0.37 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((in @ X2 @ X3) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X3 @ X1)))))))) = $true)) )),
% 0.13/0.37 inference(beta_eta_normalization,[],[f42])).
% 0.13/0.37 thf(f42,plain,(
% 0.13/0.37 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: ((in @ X2 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y0 @ X1))))))))) @ X3) = $true)) )),
% 0.13/0.37 inference(pi_clausification,[],[f41])).
% 0.13/0.37 thf(f41,plain,(
% 0.13/0.37 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((in @ X2 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y0 @ X1)))))))))) = $true)) )),
% 0.13/0.37 inference(beta_eta_normalization,[],[f40])).
% 0.13/0.37 thf(f40,plain,(
% 0.13/0.37 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => (in @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y1 @ X1))))))))))) @ X2) = $true)) )),
% 0.13/0.37 inference(pi_clausification,[],[f39])).
% 0.13/0.37 thf(f39,plain,(
% 0.13/0.37 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => (in @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y1 @ X1)))))))))))) = $true)) )),
% 0.13/0.37 inference(beta_eta_normalization,[],[f38])).
% 0.13/0.37 thf(f38,plain,(
% 0.13/0.37 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y2 @ Y0))))))))))))) @ X1))) )),
% 0.13/0.37 inference(pi_clausification,[],[f37])).
% 0.13/0.37 thf(f37,plain,(
% 0.13/0.37 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y2 @ Y0)))))))))))))))),
% 0.13/0.37 inference(beta_eta_normalization,[],[f35])).
% 0.13/0.37 thf(f35,plain,(
% 0.13/0.37 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ ((^[Y4 : $i]: ((^[Y5 : $i]: (setadjoin @ (setadjoin @ Y4 @ emptyset) @ (setadjoin @ (setadjoin @ Y4 @ (setadjoin @ Y5 @ emptyset)) @ emptyset))))) @ Y1 @ Y3) @ (powerset @ (powerset @ (binunion @ Y2 @ Y0)))))))))))))) = $true)),
% 0.13/0.37 inference(definition_unfolding,[],[f31,f28,f30])).
% 0.13/0.37 thf(f30,plain,(
% 0.13/0.37 (kpair = (^[Y0 : $i]: ((^[Y1 : $i]: (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))))),
% 0.13/0.37 inference(cnf_transformation,[],[f13])).
% 0.13/0.37 thf(f13,plain,(
% 0.13/0.37 (kpair = (^[Y0 : $i]: ((^[Y1 : $i]: (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))))),
% 0.13/0.37 inference(fool_elimination,[],[f12])).
% 0.13/0.37 thf(f12,plain,(
% 0.13/0.37 (kpair = (^[X0 : $i, X1 : $i] : (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))))),
% 0.13/0.37 inference(rectify,[],[f2])).
% 0.13/0.37 thf(f2,axiom,(
% 0.13/0.37 (kpair = (^[X2 : $i, X3 : $i] : (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))),
% 0.13/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpair)).
% 0.13/0.37 thf(f28,plain,(
% 0.13/0.37 (ubforcartprodlem3 = $true)),
% 0.13/0.37 inference(cnf_transformation,[],[f22])).
% 0.13/0.37 thf(f31,plain,(
% 0.13/0.37 (ubforcartprodlem3 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (kpair @ Y1 @ Y3) @ (powerset @ (powerset @ (binunion @ Y2 @ Y0)))))))))))))))),
% 0.13/0.37 inference(cnf_transformation,[],[f9])).
% 0.13/0.37 thf(f9,plain,(
% 0.13/0.37 (ubforcartprodlem3 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (kpair @ Y1 @ Y3) @ (powerset @ (powerset @ (binunion @ Y2 @ Y0)))))))))))))))),
% 0.13/0.37 inference(fool_elimination,[],[f8])).
% 0.13/0.37 thf(f8,plain,(
% 0.13/0.37 (ubforcartprodlem3 = ! [X0,X1,X2] : ((in @ X1 @ X0) => ! [X3] : ((in @ X3 @ X2) => (in @ (kpair @ X1 @ X3) @ (powerset @ (powerset @ (binunion @ X0 @ X2)))))))),
% 0.13/0.37 inference(rectify,[],[f4])).
% 0.13/0.37 thf(f4,axiom,(
% 0.13/0.37 (ubforcartprodlem3 = ! [X0,X2,X4] : ((in @ X2 @ X0) => ! [X3] : ((in @ X3 @ X4) => (in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X0 @ X4)))))))),
% 0.13/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ubforcartprodlem3)).
% 0.13/0.37 thf(f75,plain,(
% 0.13/0.37 ((in @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ sK2 @ sK0)))) = $false) | ~spl4_2),
% 0.13/0.37 inference(avatar_component_clause,[],[f73])).
% 0.13/0.37 thf(f76,plain,(
% 0.13/0.37 spl4_1 | spl4_2),
% 0.13/0.37 inference(avatar_split_clause,[],[f68,f73,f70])).
% 0.13/0.37 thf(f68,plain,(
% 0.13/0.37 ( ! [X2 : $i,X1 : $i] : (((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) != (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK3 @ emptyset)) @ emptyset))) | ($false = (in @ X2 @ sK0)) | ((in @ X1 @ sK2) = $false) | ((in @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ sK2 @ sK0)))) = $false)) )),
% 0.13/0.37 inference(equality_proxy_clausification,[],[f67])).
% 0.13/0.37 thf(f67,plain,(
% 0.13/0.37 ( ! [X2 : $i,X1 : $i] : (((in @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ sK2 @ sK0)))) = $false) | (((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK3 @ emptyset)) @ emptyset))) = $false) | ((in @ X1 @ sK2) = $false) | ($false = (in @ X2 @ sK0))) )),
% 0.13/0.37 inference(binary_proxy_clausification,[],[f66])).
% 0.13/0.37 thf(f66,plain,(
% 0.13/0.37 ( ! [X2 : $i,X1 : $i] : (((in @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ sK2 @ sK0)))) = $false) | ((in @ X1 @ sK2) = $false) | ((((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK3 @ emptyset)) @ emptyset))) & (in @ X2 @ sK0)) = $false)) )),
% 0.13/0.37 inference(beta_eta_normalization,[],[f65])).
% 0.13/0.37 thf(f65,plain,(
% 0.13/0.37 ( ! [X2 : $i,X1 : $i] : (((in @ X1 @ sK2) = $false) | ($false = ((^[Y0 : $i]: (((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK3 @ emptyset)) @ emptyset))) & (in @ Y0 @ sK0))) @ X2)) | ((in @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ sK2 @ sK0)))) = $false)) )),
% 0.13/0.37 inference(pi_clausification,[],[f64])).
% 0.13/0.37 thf(f64,plain,(
% 0.13/0.37 ( ! [X1 : $i] : (($false = (?? @ $i @ (^[Y0 : $i]: (((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK3 @ emptyset)) @ emptyset))) & (in @ Y0 @ sK0))))) | ((in @ X1 @ sK2) = $false) | ((in @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ sK2 @ sK0)))) = $false)) )),
% 0.13/0.37 inference(binary_proxy_clausification,[],[f63])).
% 0.13/0.37 thf(f63,plain,(
% 0.13/0.37 ( ! [X1 : $i] : (($false = ((?? @ $i @ (^[Y0 : $i]: (((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK3 @ emptyset)) @ emptyset))) & (in @ Y0 @ sK0)))) & (in @ X1 @ sK2))) | ((in @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ sK2 @ sK0)))) = $false)) )),
% 0.13/0.37 inference(beta_eta_normalization,[],[f62])).
% 0.13/0.37 thf(f62,plain,(
% 0.13/0.37 ( ! [X1 : $i] : (((in @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ sK2 @ sK0)))) = $false) | ($false = ((^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (((setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK3 @ emptyset)) @ emptyset))) & (in @ Y1 @ sK0)))) & (in @ Y0 @ sK2))) @ X1))) )),
% 0.13/0.37 inference(pi_clausification,[],[f61])).
% 0.13/0.37 thf(f61,plain,(
% 0.13/0.37 ($false = (?? @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (((setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK3 @ emptyset)) @ emptyset))) & (in @ Y1 @ sK0)))) & (in @ Y0 @ sK2))))) | ((in @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ sK2 @ sK0)))) = $false)),
% 0.13/0.37 inference(beta_eta_normalization,[],[f60])).
% 0.13/0.37 thf(f60,plain,(
% 0.13/0.37 ($false = ((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0) & (in @ Y2 @ sK0)))) & (in @ Y1 @ sK2))))) @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)))) | ((in @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ sK2 @ sK0)))) = $false)),
% 0.13/0.37 inference(trivial_inequality_removal,[],[f59])).
% 0.13/0.37 thf(f59,plain,(
% 0.13/0.37 ($false = ((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0) & (in @ Y2 @ sK0)))) & (in @ Y1 @ sK2))))) @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)))) | ((in @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ sK2 @ sK0)))) = $false) | ($true != $true)),
% 0.13/0.37 inference(superposition,[],[f36,f56])).
% 0.13/0.37 thf(f56,plain,(
% 0.13/0.37 ( ! [X2 : $i,X3 : $i,X1 : $i > $o] : (((in @ X3 @ (dsetconstr @ X2 @ X1)) = $true) | ($false = (in @ X3 @ X2)) | ((X1 @ X3) = $false)) )),
% 0.13/0.37 inference(binary_proxy_clausification,[],[f55])).
% 0.13/0.37 thf(f55,plain,(
% 0.13/0.37 ( ! [X2 : $i,X3 : $i,X1 : $i > $o] : (($false = (in @ X3 @ X2)) | (((X1 @ X3) => (in @ X3 @ (dsetconstr @ X2 @ X1))) = $true)) )),
% 0.13/0.37 inference(binary_proxy_clausification,[],[f54])).
% 0.13/0.37 thf(f54,plain,(
% 0.13/0.37 ( ! [X2 : $i,X3 : $i,X1 : $i > $o] : ((((in @ X3 @ X2) => ((X1 @ X3) => (in @ X3 @ (dsetconstr @ X2 @ X1)))) = $true)) )),
% 0.13/0.37 inference(beta_eta_normalization,[],[f53])).
% 0.13/0.37 thf(f53,plain,(
% 0.13/0.37 ( ! [X2 : $i,X3 : $i,X1 : $i > $o] : ((((^[Y0 : $i]: ((in @ Y0 @ X2) => ((X1 @ Y0) => (in @ Y0 @ (dsetconstr @ X2 @ X1))))) @ X3) = $true)) )),
% 0.13/0.37 inference(pi_clausification,[],[f52])).
% 0.13/0.37 thf(f52,plain,(
% 0.13/0.37 ( ! [X2 : $i,X1 : $i > $o] : (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => ((X1 @ Y0) => (in @ Y0 @ (dsetconstr @ X2 @ X1)))))) = $true)) )),
% 0.13/0.37 inference(beta_eta_normalization,[],[f51])).
% 0.13/0.37 thf(f51,plain,(
% 0.13/0.37 ( ! [X2 : $i,X1 : $i > $o] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => ((X1 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ X1))))))) @ X2) = $true)) )),
% 0.13/0.37 inference(pi_clausification,[],[f50])).
% 0.13/0.37 thf(f50,plain,(
% 0.13/0.37 ( ! [X1 : $i > $o] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => ((X1 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ X1)))))))) = $true)) )),
% 0.13/0.37 inference(beta_eta_normalization,[],[f49])).
% 0.13/0.37 thf(f49,plain,(
% 0.13/0.37 ( ! [X1 : $i > $o] : ((((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))) @ X1) = $true)) )),
% 0.13/0.37 inference(pi_clausification,[],[f48])).
% 0.13/0.37 thf(f48,plain,(
% 0.13/0.37 ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))) = $true)),
% 0.13/0.37 inference(beta_eta_normalization,[],[f33])).
% 0.13/0.37 thf(f33,plain,(
% 0.13/0.37 ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => (in @ Y2 @ (dsetconstr @ Y1 @ (^[Y3 : $i]: (Y0 @ Y3)))))))))))) = $true)),
% 0.13/0.37 inference(definition_unfolding,[],[f27,f23])).
% 0.13/0.37 thf(f23,plain,(
% 0.13/0.37 (dsetconstrI = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => (in @ Y2 @ (dsetconstr @ Y1 @ (^[Y3 : $i]: (Y0 @ Y3)))))))))))))),
% 0.13/0.37 inference(cnf_transformation,[],[f15])).
% 0.13/0.37 thf(f15,plain,(
% 0.13/0.37 (dsetconstrI = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => (in @ Y2 @ (dsetconstr @ Y1 @ (^[Y3 : $i]: (Y0 @ Y3)))))))))))))),
% 0.13/0.37 inference(fool_elimination,[],[f14])).
% 0.13/0.37 thf(f14,plain,(
% 0.13/0.37 (! [X0,X1,X2 : $i > $o] : ((in @ X0 @ X1) => ((X2 @ X0) => (in @ X0 @ (dsetconstr @ X1 @ (^[X3 : $i] : (X2 @ X3)))))) = dsetconstrI)),
% 0.13/0.37 inference(rectify,[],[f1])).
% 0.13/0.37 thf(f1,axiom,(
% 0.13/0.37 (! [X2,X0,X1 : $i > $o] : ((in @ X2 @ X0) => ((X1 @ X2) => (in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))))) = dsetconstrI)),
% 0.13/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrI)).
% 0.13/0.37 thf(f27,plain,(
% 0.13/0.37 (dsetconstrI = $true)),
% 0.13/0.37 inference(cnf_transformation,[],[f22])).
% 0.13/0.37 thf(f36,plain,(
% 0.13/0.37 ((in @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (dsetconstr @ (powerset @ (powerset @ (binunion @ sK2 @ sK0))) @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0) & (in @ Y2 @ sK0)))) & (in @ Y1 @ sK2))))))) != $true)),
% 0.13/0.37 inference(beta_eta_normalization,[],[f34])).
% 0.13/0.37 thf(f34,plain,(
% 0.13/0.37 ((in @ ((^[Y0 : $i]: ((^[Y1 : $i]: (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))) @ sK1 @ sK3) @ ((^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ (powerset @ (powerset @ (binunion @ Y0 @ Y1))) @ (^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((?? @ $i @ (^[Y4 : $i]: ((((^[Y5 : $i]: ((^[Y6 : $i]: (setadjoin @ (setadjoin @ Y5 @ emptyset) @ (setadjoin @ (setadjoin @ Y5 @ (setadjoin @ Y6 @ emptyset)) @ emptyset))))) @ Y3 @ Y4) = Y2) & (in @ Y4 @ Y1)))) & (in @ Y3 @ Y0))))))))) @ sK2 @ sK0)) != $true)),
% 0.13/0.37 inference(definition_unfolding,[],[f24,f30,f32])).
% 0.13/0.37 thf(f32,plain,(
% 0.13/0.37 (cartprod = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ (powerset @ (powerset @ (binunion @ Y0 @ Y1))) @ (^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((?? @ $i @ (^[Y4 : $i]: ((((^[Y5 : $i]: ((^[Y6 : $i]: (setadjoin @ (setadjoin @ Y5 @ emptyset) @ (setadjoin @ (setadjoin @ Y5 @ (setadjoin @ Y6 @ emptyset)) @ emptyset))))) @ Y3 @ Y4) = Y2) & (in @ Y4 @ Y1)))) & (in @ Y3 @ Y0))))))))))),
% 0.13/0.37 inference(definition_unfolding,[],[f29,f30])).
% 0.13/0.37 thf(f29,plain,(
% 0.13/0.37 (cartprod = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ (powerset @ (powerset @ (binunion @ Y0 @ Y1))) @ (^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((?? @ $i @ (^[Y4 : $i]: (((kpair @ Y3 @ Y4) = Y2) & (in @ Y4 @ Y1)))) & (in @ Y3 @ Y0))))))))))),
% 0.13/0.37 inference(cnf_transformation,[],[f11])).
% 0.13/0.37 thf(f11,plain,(
% 0.13/0.37 (cartprod = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ (powerset @ (powerset @ (binunion @ Y0 @ Y1))) @ (^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((?? @ $i @ (^[Y4 : $i]: (((kpair @ Y3 @ Y4) = Y2) & (in @ Y4 @ Y1)))) & (in @ Y3 @ Y0))))))))))),
% 0.13/0.37 inference(fool_elimination,[],[f10])).
% 0.13/0.37 thf(f10,plain,(
% 0.13/0.37 ((^[X0 : $i, X1 : $i] : (dsetconstr @ (powerset @ (powerset @ (binunion @ X0 @ X1))) @ (^[X2 : $i] : (? [X3] : ((in @ X3 @ X0) & ? [X4] : ((in @ X4 @ X1) & ((kpair @ X3 @ X4) = X2))))))) = cartprod)),
% 0.13/0.37 inference(rectify,[],[f3])).
% 0.13/0.37 thf(f3,axiom,(
% 0.13/0.37 ((^[X0 : $i, X4 : $i] : (dsetconstr @ (powerset @ (powerset @ (binunion @ X0 @ X4))) @ (^[X2 : $i] : (? [X3] : ((in @ X3 @ X0) & ? [X5] : ((in @ X5 @ X4) & ((kpair @ X3 @ X5) = X2))))))) = cartprod)),
% 0.13/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprod)).
% 0.13/0.37 thf(f24,plain,(
% 0.13/0.37 ((in @ (kpair @ sK1 @ sK3) @ (cartprod @ sK2 @ sK0)) != $true)),
% 0.13/0.37 inference(cnf_transformation,[],[f22])).
% 0.13/0.37 % SZS output end Proof for theBenchmark
% 0.13/0.37 % (28161)------------------------------
% 0.13/0.37 % (28161)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.37 % (28161)Termination reason: Refutation
% 0.13/0.37
% 0.13/0.37 % (28161)Memory used [KB]: 5628
% 0.13/0.37 % (28161)Time elapsed: 0.015 s
% 0.13/0.37 % (28161)Instructions burned: 13 (million)
% 0.13/0.37 % (28161)------------------------------
% 0.13/0.37 % (28161)------------------------------
% 0.13/0.37 % (28160)Success in time 0.016 s
% 0.13/0.37 % Vampire---4.8 exiting
%------------------------------------------------------------------------------