0.02/0.11	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.02/0.11	% Command    : run_vampire %s %d THM
0.10/0.31	% Computer : n006.cluster.edu
0.10/0.31	% Model    : x86_64 x86_64
0.10/0.31	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.10/0.31	% Memory   : 8042.1875MB
0.10/0.31	% OS       : Linux 3.10.0-693.el7.x86_64
0.10/0.31	% CPULimit   : 1440
0.10/0.31	% WCLimit    : 180
0.10/0.31	% DateTime   : Thu Jul  4 08:33:09 EDT 2024
0.10/0.31	% CPUTime    : 
0.10/0.33	This is a THF_ problem
0.10/0.33	Running higher-order theorem proving
0.10/0.34	Running /export/starexec/sandbox2/solver/bin/vampire_ho --cores 7 --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox2/tmp/tmp.pOnu9WtmKm/E---3.1_4694.p -m 16384 -t 180
0.18/0.35	% (4811)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on E---3.1_4694 for (1799ds/2Mi)
0.18/0.35	% (4806)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on E---3.1_4694 for (1799ds/183Mi)
0.18/0.35	% (4812)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on E---3.1_4694 for (1799ds/275Mi)
0.18/0.35	% (4807)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 E---3.1_4694 for (1799ds/4Mi)
0.18/0.35	% (4808)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 E---3.1_4694 for (1799ds/27Mi)
0.18/0.35	% (4813)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on E---3.1_4694 for (1799ds/18Mi)
0.18/0.35	% (4810)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on E---3.1_4694 for (1799ds/2Mi)
0.18/0.36	% (4810)Instruction limit reached!
0.18/0.36	% (4810)------------------------------
0.18/0.36	% (4810)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
0.18/0.36	% (4810)Termination reason: Unknown
0.18/0.36	% (4810)Termination phase: shuffling
0.18/0.36	% (4811)Instruction limit reached!
0.18/0.36	% (4811)------------------------------
0.18/0.36	% (4811)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
0.18/0.36	% (4811)Termination reason: Unknown
0.18/0.36	% (4811)Termination phase: Property scanning
0.18/0.36	
0.18/0.36	% (4811)Memory used [KB]: 1023
0.18/0.36	% (4811)Time elapsed: 0.003 s
0.18/0.36	% (4811)Instructions burned: 2 (million)
0.18/0.36	% (4811)------------------------------
0.18/0.36	% (4811)------------------------------
0.18/0.36	
0.18/0.36	% (4810)Memory used [KB]: 1023
0.18/0.36	% (4810)Time elapsed: 0.003 s
0.18/0.36	% (4810)Instructions burned: 2 (million)
0.18/0.36	% (4810)------------------------------
0.18/0.36	% (4810)------------------------------
0.18/0.36	% (4807)Instruction limit reached!
0.18/0.36	% (4807)------------------------------
0.18/0.36	% (4807)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
0.18/0.36	% (4807)Termination reason: Unknown
0.18/0.36	% (4807)Termination phase: Saturation
0.18/0.36	
0.18/0.36	% (4807)Memory used [KB]: 5500
0.18/0.36	% (4807)Time elapsed: 0.005 s
0.18/0.36	% (4807)Instructions burned: 5 (million)
0.18/0.36	% (4807)------------------------------
0.18/0.36	% (4807)------------------------------
0.18/0.36	% (4812)Refutation not found, incomplete strategy
0.18/0.36	% (4812)------------------------------
0.18/0.36	% (4812)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
0.18/0.36	% (4812)Termination reason: Refutation not found, incomplete strategy
0.18/0.36	
0.18/0.36	
0.18/0.36	% (4812)Memory used [KB]: 5500
0.18/0.36	% (4812)Time elapsed: 0.005 s
0.18/0.36	% (4812)Instructions burned: 5 (million)
0.18/0.36	% (4812)------------------------------
0.18/0.36	% (4812)------------------------------
0.18/0.36	% (4806)First to succeed.
0.18/0.36	% (4813)Instruction limit reached!
0.18/0.36	% (4813)------------------------------
0.18/0.36	% (4813)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
0.18/0.36	% (4813)Termination reason: Unknown
0.18/0.36	% (4813)Termination phase: Saturation
0.18/0.36	
0.18/0.36	% (4813)Memory used [KB]: 5628
0.18/0.36	% (4813)Time elapsed: 0.012 s
0.18/0.36	% (4813)Instructions burned: 18 (million)
0.18/0.36	% (4813)------------------------------
0.18/0.36	% (4813)------------------------------
0.18/0.36	% (4808)Also succeeded, but the first one will report.
0.18/0.37	% (4806)Refutation found. Thanks to Tanya!
0.18/0.37	% SZS status Theorem for E---3.1_4694
0.18/0.37	% SZS output start Proof for E---3.1_4694
0.18/0.37	thf(func_def_0, type, in: $i > $i > $o).
0.18/0.37	thf(func_def_2, type, setadjoin: $i > $i > $i).
0.18/0.37	thf(func_def_3, type, powerset: $i > $i).
0.18/0.37	thf(func_def_4, type, dsetconstr: $i > ($i > $o) > $i).
0.18/0.37	thf(func_def_7, type, binunion: $i > $i > $i).
0.18/0.37	thf(func_def_8, type, kpair: $i > $i > $i).
0.18/0.37	thf(func_def_9, type, cartprod: $i > $i > $i).
0.18/0.37	thf(func_def_30, type, ph5: !>[X0: $tType]:(X0)).
0.18/0.37	thf(f111,plain,(
0.18/0.37	  $false),
0.18/0.37	  inference(avatar_sat_refutation,[],[f77,f87,f93,f100,f110])).
0.18/0.37	thf(f110,plain,(
0.18/0.37	  ~spl4_1 | spl4_3 | spl4_4),
0.18/0.37	  inference(avatar_contradiction_clause,[],[f109])).
0.18/0.37	thf(f109,plain,(
0.18/0.37	  $false | (~spl4_1 | spl4_3 | spl4_4)),
0.18/0.37	  inference(subsumption_resolution,[],[f108,f81])).
0.18/0.37	thf(f81,plain,(
0.18/0.37	  ($false != (in @ sK2 @ sK0)) | spl4_3),
0.18/0.37	  inference(avatar_component_clause,[],[f80])).
0.18/0.37	thf(f80,plain,(
0.18/0.37	  spl4_3 <=> ($false = (in @ sK2 @ sK0))),
0.18/0.37	  introduced(avatar_definition,[new_symbols(naming,[spl4_3])])).
0.18/0.37	thf(f108,plain,(
0.18/0.37	  ($false = (in @ sK2 @ sK0)) | (~spl4_1 | spl4_4)),
0.18/0.37	  inference(subsumption_resolution,[],[f103,f85])).
0.18/0.37	thf(f85,plain,(
0.18/0.37	  ($false != (in @ sK3 @ sK1)) | spl4_4),
0.18/0.37	  inference(avatar_component_clause,[],[f84])).
0.18/0.37	thf(f84,plain,(
0.18/0.37	  spl4_4 <=> ($false = (in @ sK3 @ sK1))),
0.18/0.37	  introduced(avatar_definition,[new_symbols(naming,[spl4_4])])).
0.18/0.37	thf(f103,plain,(
0.18/0.37	  ($false = (in @ sK3 @ sK1)) | ($false = (in @ sK2 @ sK0)) | ~spl4_1),
0.18/0.37	  inference(trivial_inequality_removal,[],[f101])).
0.18/0.37	thf(f101,plain,(
0.18/0.37	  ($false = $true) | ($false = (in @ sK2 @ sK0)) | ($false = (in @ sK3 @ sK1)) | ~spl4_1),
0.18/0.37	  inference(superposition,[],[f73,f56])).
0.18/0.37	thf(f56,plain,(
0.18/0.37	  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((in @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X4 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X2 @ X3)))) = $true) | ($false = (in @ X1 @ X2)) | ((in @ X4 @ X3) = $false)) )),
0.18/0.37	  inference(binary_proxy_clausification,[],[f55])).
0.18/0.37	thf(f55,plain,(
0.18/0.37	  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = (in @ X1 @ X2)) | ($true = ((in @ X4 @ X3) => (in @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X4 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X2 @ X3))))))) )),
0.18/0.37	  inference(beta_eta_normalization,[],[f54])).
0.18/0.37	thf(f54,plain,(
0.18/0.37	  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : ((((^[Y0 : $i]: ((in @ Y0 @ X3) => (in @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X2 @ X3)))))) @ X4) = $true) | ($false = (in @ X1 @ X2))) )),
0.18/0.37	  inference(pi_clausification,[],[f53])).
0.18/0.37	thf(f53,plain,(
0.18/0.37	  ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X3) => (in @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X2 @ X3)))))))) | ($false = (in @ X1 @ X2))) )),
0.18/0.37	  inference(binary_proxy_clausification,[],[f52])).
0.18/0.37	thf(f52,plain,(
0.18/0.37	  ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((in @ X1 @ X2) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X3) => (in @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X2 @ X3)))))))))) )),
0.18/0.37	  inference(beta_eta_normalization,[],[f51])).
0.18/0.37	thf(f51,plain,(
0.18/0.37	  ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: ((in @ X1 @ X2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X2 @ Y0))))))))) @ X3) = $true)) )),
0.18/0.37	  inference(pi_clausification,[],[f50])).
0.18/0.37	thf(f50,plain,(
0.18/0.37	  ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((in @ X1 @ X2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X2 @ Y0)))))))))))) )),
0.18/0.37	  inference(beta_eta_normalization,[],[f49])).
0.18/0.37	thf(f49,plain,(
0.18/0.37	  ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ X1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y0 @ Y1))))))))))) @ X2))) )),
0.18/0.37	  inference(pi_clausification,[],[f48])).
0.18/0.37	thf(f48,plain,(
0.18/0.37	  ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ X1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y0 @ Y1)))))))))))))) )),
0.18/0.37	  inference(beta_eta_normalization,[],[f47])).
0.18/0.37	thf(f47,plain,(
0.18/0.37	  ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y1 @ Y2))))))))))))) @ X1))) )),
0.18/0.37	  inference(pi_clausification,[],[f46])).
0.18/0.37	thf(f46,plain,(
0.18/0.37	  ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ Y1 @ Y2)))))))))))))))),
0.18/0.37	  inference(beta_eta_normalization,[],[f34])).
0.18/0.37	thf(f34,plain,(
0.18/0.37	  ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ ((^[Y4 : $i]: ((^[Y5 : $i]: (setadjoin @ (setadjoin @ Y4 @ emptyset) @ (setadjoin @ (setadjoin @ Y4 @ (setadjoin @ Y5 @ emptyset)) @ emptyset))))) @ Y0 @ Y3) @ (powerset @ (powerset @ (binunion @ Y1 @ Y2)))))))))))))))),
0.18/0.37	  inference(definition_unfolding,[],[f28,f33])).
0.18/0.37	thf(f33,plain,(
0.18/0.37	  (ubforcartprodlem3 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ ((^[Y4 : $i]: ((^[Y5 : $i]: (setadjoin @ (setadjoin @ Y4 @ emptyset) @ (setadjoin @ (setadjoin @ Y4 @ (setadjoin @ Y5 @ emptyset)) @ emptyset))))) @ Y0 @ Y3) @ (powerset @ (powerset @ (binunion @ Y1 @ Y2)))))))))))))))),
0.18/0.37	  inference(definition_unfolding,[],[f24,f30])).
0.18/0.37	thf(f30,plain,(
0.18/0.37	  (kpair = (^[Y0 : $i]: ((^[Y1 : $i]: (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))))),
0.18/0.37	  inference(cnf_transformation,[],[f11])).
0.18/0.37	thf(f11,plain,(
0.18/0.37	  (kpair = (^[Y0 : $i]: ((^[Y1 : $i]: (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))))),
0.18/0.37	  inference(fool_elimination,[],[f10])).
0.18/0.37	thf(f10,plain,(
0.18/0.37	  ((^[X0 : $i, X1 : $i] : (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))) = kpair)),
0.18/0.37	  inference(rectify,[],[f2])).
0.18/0.37	thf(f2,axiom,(
0.18/0.37	  ((^[X2 : $i, X3 : $i] : (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))) = kpair)),
0.18/0.37	  file('/export/starexec/sandbox2/tmp/tmp.pOnu9WtmKm/E---3.1_4694.p',kpair)).
0.18/0.37	thf(f24,plain,(
0.18/0.37	  (ubforcartprodlem3 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (kpair @ Y0 @ Y3) @ (powerset @ (powerset @ (binunion @ Y1 @ Y2)))))))))))))))),
0.18/0.37	  inference(cnf_transformation,[],[f17])).
0.18/0.37	thf(f17,plain,(
0.18/0.37	  (ubforcartprodlem3 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (kpair @ Y0 @ Y3) @ (powerset @ (powerset @ (binunion @ Y1 @ Y2)))))))))))))))),
0.18/0.37	  inference(fool_elimination,[],[f16])).
0.18/0.37	thf(f16,plain,(
0.18/0.37	  (! [X0,X1,X2] : ((in @ X2 @ X1) => ! [X3] : ((in @ X3 @ X0) => (in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X1 @ X0)))))) = ubforcartprodlem3)),
0.18/0.37	  inference(rectify,[],[f4])).
0.18/0.37	thf(f4,axiom,(
0.18/0.37	  (! [X4,X0,X2] : ((in @ X2 @ X0) => ! [X3] : ((in @ X3 @ X4) => (in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X0 @ X4)))))) = ubforcartprodlem3)),
0.18/0.37	  file('/export/starexec/sandbox2/tmp/tmp.pOnu9WtmKm/E---3.1_4694.p',ubforcartprodlem3)).
0.18/0.37	thf(f28,plain,(
0.18/0.37	  (ubforcartprodlem3 = $true)),
0.18/0.37	  inference(cnf_transformation,[],[f22])).
0.18/0.37	thf(f22,plain,(
0.18/0.37	  (dsetconstrI = $true) & (ubforcartprodlem3 = $true) & ((((in @ sK3 @ sK1) = $true) & ((in @ (kpair @ sK2 @ sK3) @ (cartprod @ sK0 @ sK1)) != $true)) & ($true = (in @ sK2 @ sK0)))),
0.18/0.37	  inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f19,f21,f20])).
0.18/0.37	thf(f20,plain,(
0.18/0.37	  ? [X0,X1,X2] : (? [X3] : (($true = (in @ X3 @ X1)) & ((in @ (kpair @ X2 @ X3) @ (cartprod @ X0 @ X1)) != $true)) & ((in @ X2 @ X0) = $true)) => (? [X3] : (((in @ X3 @ sK1) = $true) & ((in @ (kpair @ sK2 @ X3) @ (cartprod @ sK0 @ sK1)) != $true)) & ($true = (in @ sK2 @ sK0)))),
0.18/0.37	  introduced(choice_axiom,[])).
0.18/0.37	thf(f21,plain,(
0.18/0.37	  ? [X3] : (((in @ X3 @ sK1) = $true) & ((in @ (kpair @ sK2 @ X3) @ (cartprod @ sK0 @ sK1)) != $true)) => (((in @ sK3 @ sK1) = $true) & ((in @ (kpair @ sK2 @ sK3) @ (cartprod @ sK0 @ sK1)) != $true))),
0.18/0.37	  introduced(choice_axiom,[])).
0.18/0.37	thf(f19,plain,(
0.18/0.37	  (dsetconstrI = $true) & (ubforcartprodlem3 = $true) & ? [X0,X1,X2] : (? [X3] : (($true = (in @ X3 @ X1)) & ((in @ (kpair @ X2 @ X3) @ (cartprod @ X0 @ X1)) != $true)) & ((in @ X2 @ X0) = $true))),
0.18/0.37	  inference(flattening,[],[f18])).
0.18/0.37	thf(f18,plain,(
0.18/0.37	  (? [X0,X1,X2] : (? [X3] : (($true = (in @ X3 @ X1)) & ((in @ (kpair @ X2 @ X3) @ (cartprod @ X0 @ X1)) != $true)) & ((in @ X2 @ X0) = $true)) & (ubforcartprodlem3 = $true)) & (dsetconstrI = $true)),
0.18/0.37	  inference(ennf_transformation,[],[f13])).
0.18/0.37	thf(f13,plain,(
0.18/0.37	  ~((dsetconstrI = $true) => ((ubforcartprodlem3 = $true) => ! [X0,X1,X2] : (((in @ X2 @ X0) = $true) => ! [X3] : (($true = (in @ X3 @ X1)) => ((in @ (kpair @ X2 @ X3) @ (cartprod @ X0 @ X1)) = $true)))))),
0.18/0.37	  inference(fool_elimination,[],[f12])).
0.18/0.37	thf(f12,plain,(
0.18/0.37	  ~(dsetconstrI => (ubforcartprodlem3 => ! [X0,X1,X2] : ((in @ X2 @ X0) => ! [X3] : ((in @ X3 @ X1) => (in @ (kpair @ X2 @ X3) @ (cartprod @ X0 @ X1))))))),
0.18/0.37	  inference(rectify,[],[f6])).
0.18/0.37	thf(f6,negated_conjecture,(
0.18/0.37	  ~(dsetconstrI => (ubforcartprodlem3 => ! [X0,X4,X2] : ((in @ X2 @ X0) => ! [X3] : ((in @ X3 @ X4) => (in @ (kpair @ X2 @ X3) @ (cartprod @ X0 @ X4))))))),
0.18/0.37	  inference(negated_conjecture,[],[f5])).
0.18/0.37	thf(f5,conjecture,(
0.18/0.37	  dsetconstrI => (ubforcartprodlem3 => ! [X0,X4,X2] : ((in @ X2 @ X0) => ! [X3] : ((in @ X3 @ X4) => (in @ (kpair @ X2 @ X3) @ (cartprod @ X0 @ X4)))))),
0.18/0.37	  file('/export/starexec/sandbox2/tmp/tmp.pOnu9WtmKm/E---3.1_4694.p',cartprodpairin)).
0.18/0.37	thf(f73,plain,(
0.18/0.37	  ($false = (in @ (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ sK0 @ sK1))))) | ~spl4_1),
0.18/0.37	  inference(avatar_component_clause,[],[f71])).
0.18/0.37	thf(f71,plain,(
0.18/0.37	  spl4_1 <=> ($false = (in @ (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ sK0 @ sK1)))))),
0.18/0.37	  introduced(avatar_definition,[new_symbols(naming,[spl4_1])])).
0.18/0.37	thf(f100,plain,(
0.18/0.37	  ~spl4_4),
0.18/0.37	  inference(avatar_contradiction_clause,[],[f99])).
0.18/0.37	thf(f99,plain,(
0.18/0.37	  $false | ~spl4_4),
0.18/0.37	  inference(trivial_inequality_removal,[],[f96])).
0.18/0.37	thf(f96,plain,(
0.18/0.37	  ($false = $true) | ~spl4_4),
0.18/0.37	  inference(superposition,[],[f27,f86])).
0.18/0.37	thf(f86,plain,(
0.18/0.37	  ($false = (in @ sK3 @ sK1)) | ~spl4_4),
0.18/0.37	  inference(avatar_component_clause,[],[f84])).
0.18/0.37	thf(f27,plain,(
0.18/0.37	  ((in @ sK3 @ sK1) = $true)),
0.18/0.37	  inference(cnf_transformation,[],[f22])).
0.18/0.37	thf(f93,plain,(
0.18/0.37	  ~spl4_3),
0.18/0.37	  inference(avatar_contradiction_clause,[],[f92])).
0.18/0.37	thf(f92,plain,(
0.18/0.37	  $false | ~spl4_3),
0.18/0.37	  inference(trivial_inequality_removal,[],[f88])).
0.18/0.37	thf(f88,plain,(
0.18/0.37	  ($false = $true) | ~spl4_3),
0.18/0.37	  inference(superposition,[],[f82,f25])).
0.18/0.37	thf(f25,plain,(
0.18/0.37	  ($true = (in @ sK2 @ sK0))),
0.18/0.37	  inference(cnf_transformation,[],[f22])).
0.18/0.37	thf(f82,plain,(
0.18/0.37	  ($false = (in @ sK2 @ sK0)) | ~spl4_3),
0.18/0.37	  inference(avatar_component_clause,[],[f80])).
0.18/0.37	thf(f87,plain,(
0.18/0.37	  spl4_3 | spl4_4 | ~spl4_2),
0.18/0.37	  inference(avatar_split_clause,[],[f78,f75,f84,f80])).
0.18/0.37	thf(f75,plain,(
0.18/0.37	  spl4_2 <=> ! [X2,X1] : (($false = (in @ X2 @ sK1)) | ((in @ X1 @ sK0) = $false) | ((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) != (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ emptyset))))),
0.18/0.37	  introduced(avatar_definition,[new_symbols(naming,[spl4_2])])).
0.18/0.37	thf(f78,plain,(
0.18/0.37	  ($false = (in @ sK3 @ sK1)) | ($false = (in @ sK2 @ sK0)) | ~spl4_2),
0.18/0.37	  inference(equality_resolution,[],[f76])).
0.18/0.37	thf(f76,plain,(
0.18/0.37	  ( ! [X2 : $i,X1 : $i] : (((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) != (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ emptyset))) | ($false = (in @ X2 @ sK1)) | ((in @ X1 @ sK0) = $false)) ) | ~spl4_2),
0.18/0.37	  inference(avatar_component_clause,[],[f75])).
0.18/0.37	thf(f77,plain,(
0.18/0.37	  spl4_1 | spl4_2),
0.18/0.37	  inference(avatar_split_clause,[],[f69,f75,f71])).
0.18/0.37	thf(f69,plain,(
0.18/0.37	  ( ! [X2 : $i,X1 : $i] : (($false = (in @ X2 @ sK1)) | ($false = (in @ (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ sK0 @ sK1))))) | ((in @ X1 @ sK0) = $false) | ((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) != (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)))) )),
0.18/0.37	  inference(equality_proxy_clausification,[],[f68])).
0.18/0.37	thf(f68,plain,(
0.18/0.37	  ( ! [X2 : $i,X1 : $i] : (((in @ X1 @ sK0) = $false) | ($false = ((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)))) | ($false = (in @ (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ sK0 @ sK1))))) | ($false = (in @ X2 @ sK1))) )),
0.18/0.37	  inference(binary_proxy_clausification,[],[f67])).
0.18/0.37	thf(f67,plain,(
0.18/0.37	  ( ! [X2 : $i,X1 : $i] : (($false = (((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ emptyset))) & (in @ X2 @ sK1))) | ($false = (in @ (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ sK0 @ sK1))))) | ((in @ X1 @ sK0) = $false)) )),
0.18/0.37	  inference(beta_eta_normalization,[],[f66])).
0.18/0.37	thf(f66,plain,(
0.18/0.37	  ( ! [X2 : $i,X1 : $i] : (($false = (in @ (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ sK0 @ sK1))))) | ($false = ((^[Y0 : $i]: (((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ emptyset))) & (in @ Y0 @ sK1))) @ X2)) | ((in @ X1 @ sK0) = $false)) )),
0.18/0.37	  inference(pi_clausification,[],[f65])).
0.18/0.37	thf(f65,plain,(
0.18/0.37	  ( ! [X1 : $i] : (((in @ X1 @ sK0) = $false) | ((?? @ $i @ (^[Y0 : $i]: (((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ emptyset))) & (in @ Y0 @ sK1)))) = $false) | ($false = (in @ (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ sK0 @ sK1)))))) )),
0.18/0.37	  inference(binary_proxy_clausification,[],[f64])).
0.18/0.37	thf(f64,plain,(
0.18/0.37	  ( ! [X1 : $i] : (($false = (in @ (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ sK0 @ sK1))))) | (((in @ X1 @ sK0) & (?? @ $i @ (^[Y0 : $i]: (((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ emptyset))) & (in @ Y0 @ sK1))))) = $false)) )),
0.18/0.37	  inference(beta_eta_normalization,[],[f63])).
0.18/0.37	thf(f63,plain,(
0.18/0.37	  ( ! [X1 : $i] : (($false = (in @ (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ sK0 @ sK1))))) | ($false = ((^[Y0 : $i]: ((in @ Y0 @ sK0) & (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ emptyset))) & (in @ Y1 @ sK1)))))) @ X1))) )),
0.18/0.37	  inference(pi_clausification,[],[f62])).
0.18/0.37	thf(f62,plain,(
0.18/0.37	  ($false = (in @ (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ sK0 @ sK1))))) | ($false = (?? @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK0) & (?? @ $i @ (^[Y1 : $i]: (((setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ emptyset))) & (in @ Y1 @ sK1))))))))),
0.18/0.37	  inference(beta_eta_normalization,[],[f61])).
0.18/0.37	thf(f61,plain,(
0.18/0.37	  ($false = ((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK0) & (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0) & (in @ Y2 @ sK1)))))))) @ (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)))) | ($false = (in @ (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ sK0 @ sK1)))))),
0.18/0.37	  inference(trivial_inequality_removal,[],[f60])).
0.18/0.37	thf(f60,plain,(
0.18/0.37	  ($true != $true) | ($false = (in @ (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ sK0 @ sK1))))) | ($false = ((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK0) & (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0) & (in @ Y2 @ sK1)))))))) @ (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ emptyset))))),
0.18/0.37	  inference(superposition,[],[f57,f45])).
0.18/0.37	thf(f45,plain,(
0.18/0.37	  ( ! [X2 : $i,X3 : $i,X1 : $i > $o] : (((in @ X2 @ (dsetconstr @ X3 @ X1)) = $true) | ($false = (in @ X2 @ X3)) | ((X1 @ X2) = $false)) )),
0.18/0.37	  inference(binary_proxy_clausification,[],[f44])).
0.18/0.37	thf(f44,plain,(
0.18/0.37	  ( ! [X2 : $i,X3 : $i,X1 : $i > $o] : (($false = (in @ X2 @ X3)) | (((X1 @ X2) => (in @ X2 @ (dsetconstr @ X3 @ X1))) = $true)) )),
0.18/0.37	  inference(binary_proxy_clausification,[],[f43])).
0.18/0.37	thf(f43,plain,(
0.18/0.37	  ( ! [X2 : $i,X3 : $i,X1 : $i > $o] : (($true = ((in @ X2 @ X3) => ((X1 @ X2) => (in @ X2 @ (dsetconstr @ X3 @ X1)))))) )),
0.18/0.37	  inference(beta_eta_normalization,[],[f42])).
0.18/0.37	thf(f42,plain,(
0.18/0.37	  ( ! [X2 : $i,X3 : $i,X1 : $i > $o] : (($true = ((^[Y0 : $i]: ((in @ X2 @ Y0) => ((X1 @ X2) => (in @ X2 @ (dsetconstr @ Y0 @ X1))))) @ X3))) )),
0.18/0.37	  inference(pi_clausification,[],[f41])).
0.18/0.37	thf(f41,plain,(
0.18/0.37	  ( ! [X2 : $i,X1 : $i > $o] : (($true = (!! @ $i @ (^[Y0 : $i]: ((in @ X2 @ Y0) => ((X1 @ X2) => (in @ X2 @ (dsetconstr @ Y0 @ X1)))))))) )),
0.18/0.37	  inference(beta_eta_normalization,[],[f40])).
0.18/0.37	thf(f40,plain,(
0.18/0.37	  ( ! [X2 : $i,X1 : $i > $o] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => ((X1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ X1))))))) @ X2) = $true)) )),
0.18/0.37	  inference(pi_clausification,[],[f39])).
0.18/0.37	thf(f39,plain,(
0.18/0.37	  ( ! [X1 : $i > $o] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => ((X1 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ X1)))))))))) )),
0.18/0.37	  inference(beta_eta_normalization,[],[f38])).
0.18/0.37	thf(f38,plain,(
0.18/0.37	  ( ! [X1 : $i > $o] : (($true = ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((Y0 @ Y1) => (in @ Y1 @ (dsetconstr @ Y2 @ Y0))))))))) @ X1))) )),
0.18/0.37	  inference(pi_clausification,[],[f37])).
0.18/0.37	thf(f37,plain,(
0.18/0.37	  ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((Y0 @ Y1) => (in @ Y1 @ (dsetconstr @ Y2 @ Y0)))))))))) = $true)),
0.18/0.37	  inference(beta_eta_normalization,[],[f36])).
0.18/0.37	thf(f36,plain,(
0.18/0.37	  ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((Y0 @ Y1) => (in @ Y1 @ (dsetconstr @ Y2 @ (^[Y3 : $i]: (Y0 @ Y3)))))))))))) = $true)),
0.18/0.37	  inference(definition_unfolding,[],[f31,f29])).
0.18/0.37	thf(f29,plain,(
0.18/0.37	  (dsetconstrI = $true)),
0.18/0.37	  inference(cnf_transformation,[],[f22])).
0.18/0.37	thf(f31,plain,(
0.18/0.37	  (dsetconstrI = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((Y0 @ Y1) => (in @ Y1 @ (dsetconstr @ Y2 @ (^[Y3 : $i]: (Y0 @ Y3)))))))))))))),
0.18/0.37	  inference(cnf_transformation,[],[f15])).
0.18/0.37	thf(f15,plain,(
0.18/0.37	  (dsetconstrI = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => ((Y0 @ Y1) => (in @ Y1 @ (dsetconstr @ Y2 @ (^[Y3 : $i]: (Y0 @ Y3)))))))))))))),
0.18/0.37	  inference(fool_elimination,[],[f14])).
0.18/0.37	thf(f14,plain,(
0.18/0.37	  (dsetconstrI = ! [X0,X1,X2 : $i > $o] : ((in @ X1 @ X0) => ((X2 @ X1) => (in @ X1 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X2 @ X3)))))))),
0.18/0.37	  inference(rectify,[],[f1])).
0.18/0.37	thf(f1,axiom,(
0.18/0.37	  (dsetconstrI = ! [X0,X2,X1 : $i > $o] : ((in @ X2 @ X0) => ((X1 @ X2) => (in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))))))),
0.18/0.37	  file('/export/starexec/sandbox2/tmp/tmp.pOnu9WtmKm/E---3.1_4694.p',dsetconstrI)).
0.18/0.37	thf(f57,plain,(
0.18/0.37	  ($true != (in @ (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (dsetconstr @ (powerset @ (powerset @ (binunion @ sK0 @ sK1))) @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK0) & (?? @ $i @ (^[Y2 : $i]: (((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0) & (in @ Y2 @ sK1)))))))))))),
0.18/0.37	  inference(beta_eta_normalization,[],[f35])).
0.18/0.37	thf(f35,plain,(
0.18/0.37	  ((in @ ((^[Y0 : $i]: ((^[Y1 : $i]: (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))) @ sK2 @ sK3) @ ((^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ (powerset @ (powerset @ (binunion @ Y0 @ Y1))) @ (^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) & (?? @ $i @ (^[Y4 : $i]: ((((^[Y5 : $i]: ((^[Y6 : $i]: (setadjoin @ (setadjoin @ Y5 @ emptyset) @ (setadjoin @ (setadjoin @ Y5 @ (setadjoin @ Y6 @ emptyset)) @ emptyset))))) @ Y3 @ Y4) = Y2) & (in @ Y4 @ Y1)))))))))))) @ sK0 @ sK1)) != $true)),
0.18/0.37	  inference(definition_unfolding,[],[f26,f30,f32])).
0.18/0.37	thf(f32,plain,(
0.18/0.37	  (cartprod = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ (powerset @ (powerset @ (binunion @ Y0 @ Y1))) @ (^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) & (?? @ $i @ (^[Y4 : $i]: ((((^[Y5 : $i]: ((^[Y6 : $i]: (setadjoin @ (setadjoin @ Y5 @ emptyset) @ (setadjoin @ (setadjoin @ Y5 @ (setadjoin @ Y6 @ emptyset)) @ emptyset))))) @ Y3 @ Y4) = Y2) & (in @ Y4 @ Y1)))))))))))))),
0.18/0.37	  inference(definition_unfolding,[],[f23,f30])).
0.18/0.37	thf(f23,plain,(
0.18/0.37	  (cartprod = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ (powerset @ (powerset @ (binunion @ Y0 @ Y1))) @ (^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) & (?? @ $i @ (^[Y4 : $i]: (((kpair @ Y3 @ Y4) = Y2) & (in @ Y4 @ Y1)))))))))))))),
0.18/0.37	  inference(cnf_transformation,[],[f9])).
0.18/0.37	thf(f9,plain,(
0.18/0.37	  (cartprod = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ (powerset @ (powerset @ (binunion @ Y0 @ Y1))) @ (^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) & (?? @ $i @ (^[Y4 : $i]: (((kpair @ Y3 @ Y4) = Y2) & (in @ Y4 @ Y1)))))))))))))),
0.18/0.37	  inference(fool_elimination,[],[f8])).
0.18/0.37	thf(f8,plain,(
0.18/0.37	  ((^[X0 : $i, X1 : $i] : (dsetconstr @ (powerset @ (powerset @ (binunion @ X0 @ X1))) @ (^[X2 : $i] : (? [X3] : (? [X4] : ((in @ X4 @ X1) & ((kpair @ X3 @ X4) = X2)) & (in @ X3 @ X0)))))) = cartprod)),
0.18/0.37	  inference(rectify,[],[f3])).
0.18/0.37	thf(f3,axiom,(
0.18/0.37	  ((^[X0 : $i, X4 : $i] : (dsetconstr @ (powerset @ (powerset @ (binunion @ X0 @ X4))) @ (^[X2 : $i] : (? [X3] : (? [X5] : ((in @ X5 @ X4) & ((kpair @ X3 @ X5) = X2)) & (in @ X3 @ X0)))))) = cartprod)),
0.18/0.37	  file('/export/starexec/sandbox2/tmp/tmp.pOnu9WtmKm/E---3.1_4694.p',cartprod)).
0.18/0.37	thf(f26,plain,(
0.18/0.37	  ((in @ (kpair @ sK2 @ sK3) @ (cartprod @ sK0 @ sK1)) != $true)),
0.18/0.37	  inference(cnf_transformation,[],[f22])).
0.18/0.37	% SZS output end Proof for E---3.1_4694
0.18/0.37	% (4806)------------------------------
0.18/0.37	% (4806)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
0.18/0.37	% (4806)Termination reason: Refutation
0.18/0.37	
0.18/0.37	% (4806)Memory used [KB]: 5628
0.18/0.37	% (4806)Time elapsed: 0.012 s
0.18/0.37	% (4806)Instructions burned: 10 (million)
0.18/0.37	% (4806)------------------------------
0.18/0.37	% (4806)------------------------------
0.18/0.37	% (4805)Success in time 0.023 s
0.18/0.37	EOF