0.00/0.03	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.00/0.03	% Command    : run_vampire %s %d THM
0.09/0.35	% Computer   : n023.cluster.edu
0.09/0.35	% Model      : x86_64 x86_64
0.09/0.35	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.09/0.35	% Memory     : 8046.5625MB
0.09/0.35	% OS         : Linux 6.8.0-71-generic
0.09/0.35	% CPULimit   : 1440
0.09/0.35	% WCLimit    : 180
0.09/0.35	% DateTime   : Mon Jul 27 11:03:51 UTC 2026
0.09/0.35	% CPUTime    : 
0.15/0.40	This is a THF_ problem
0.15/0.40	Running higher-order theorem proving
0.15/0.42	Running /export/starexec/sandbox2/solver/bin/vampire-hol --cores 7 --input_syntax tptp --proof tptp --output_axiom_names on --print_def_sorts on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox2/tmp/tmp.0LIdL31CqO/E---3.1_811584.p -m 16384 -t 180
0.15/0.45	% (811660)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_811584 for (1799ds/4Mi)
0.15/0.45	% (811660)Instruction limit reached!
0.15/0.45	% (811660)------------------------------
0.15/0.45	% (811660)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.15/0.45	% (811660)Termination reason: Unknown
0.15/0.45	% (811660)Termination phase: Saturation
0.15/0.45	
0.15/0.45	% (811660)Memory used [KB]: 5500
0.15/0.45	% (811660)Time elapsed: 0.004 s
0.15/0.45	% (811660)Instructions burned: 5 (million)
0.15/0.45	% (811660)------------------------------
0.15/0.45	% (811660)------------------------------
0.15/0.46	% (811661)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_811584 for (1799ds/27Mi)
0.15/0.46	% (811665)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on E---3.1_811584 for (1799ds/18Mi)
0.15/0.46	% (811659)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on E---3.1_811584 for (1799ds/183Mi)
0.15/0.46	% (811662)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on E---3.1_811584 for (1799ds/2Mi)
0.15/0.46	% (811663)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_811584 for (1799ds/2Mi)
0.15/0.47	% (811663)Instruction limit reached!
0.15/0.47	% (811663)------------------------------
0.15/0.47	% (811663)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.15/0.47	% (811663)Termination reason: Unknown
0.15/0.47	% (811663)Termination phase: shuffling
0.15/0.47	
0.15/0.47	% (811663)Memory used [KB]: 1023
0.15/0.47	% (811663)Time elapsed: 0.003 s
0.15/0.47	% (811663)Instructions burned: 2 (million)
0.15/0.47	% (811663)------------------------------
0.15/0.47	% (811663)------------------------------
0.15/0.47	% (811664)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_811584 for (1799ds/275Mi)
0.15/0.47	% (811662)Instruction limit reached!
0.15/0.47	% (811662)------------------------------
0.15/0.47	% (811662)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.15/0.47	% (811662)Termination reason: Unknown
0.15/0.47	% (811662)Termination phase: Property scanning
0.15/0.47	
0.15/0.47	% (811662)Memory used [KB]: 1023
0.15/0.47	% (811662)Time elapsed: 0.005 s
0.15/0.47	% (811662)Instructions burned: 2 (million)
0.15/0.47	% (811662)------------------------------
0.15/0.47	% (811662)------------------------------
0.15/0.47	% (811666)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on E---3.1_811584 for (1799ds/3Mi)
0.15/0.47	% (811666)Instruction limit reached!
0.15/0.47	% (811666)------------------------------
0.15/0.47	% (811666)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.15/0.47	% (811666)Termination reason: Unknown
0.15/0.47	% (811666)Termination phase: Property scanning
0.15/0.47	
0.15/0.47	% (811666)Memory used [KB]: 1023
0.15/0.47	% (811664)Refutation not found, incomplete strategy
0.15/0.47	% (811664)------------------------------
0.15/0.47	% (811664)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.15/0.47	% (811666)Time elapsed: 0.002 s
0.15/0.47	% (811666)Instructions burned: 3 (million)
0.15/0.47	% (811666)------------------------------
0.15/0.47	% (811666)------------------------------
0.15/0.47	% (811664)Termination reason: Refutation not found, incomplete strategy
0.15/0.47	
0.15/0.47	
0.15/0.47	% (811664)Memory used [KB]: 5500
0.15/0.47	% (811664)Time elapsed: 0.007 s
0.15/0.47	% (811664)Instructions burned: 5 (million)
0.15/0.47	% (811664)------------------------------
0.15/0.47	% (811664)------------------------------
0.15/0.47	% (811661)First to succeed.
0.15/0.48	% (811665)Instruction limit reached!
0.15/0.48	% (811665)------------------------------
0.15/0.48	% (811665)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.15/0.48	% (811665)Termination reason: Unknown
0.15/0.48	% (811665)Termination phase: Saturation
0.15/0.48	
0.15/0.48	% (811665)Memory used [KB]: 5628
0.15/0.48	% (811665)Time elapsed: 0.018 s
0.15/0.48	% (811665)Instructions burned: 18 (million)
0.15/0.48	% (811665)------------------------------
0.15/0.48	% (811665)------------------------------
0.15/0.48	% (811659)Also succeeded, but the first one will report.
0.15/0.48	% (811661)Refutation found. Thanks to Tanya!
0.15/0.48	% SZS status Theorem for E---3.1_811584
0.15/0.48	% SZS output start Proof for E---3.1_811584
0.15/0.48	thf(func_def_0, type, in: $i > $i > $o).
0.15/0.48	thf(func_def_2, type, setadjoin: $i > $i > $i).
0.15/0.48	thf(func_def_3, type, powerset: $i > $i).
0.15/0.48	thf(func_def_4, type, dsetconstr: $i > ($i > $o) > $i).
0.15/0.48	thf(func_def_7, type, binunion: $i > $i > $i).
0.15/0.48	thf(func_def_8, type, kpair: $i > $i > $i).
0.15/0.48	thf(func_def_9, type, cartprod: $i > $i > $i).
0.15/0.48	thf(func_def_11, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
0.15/0.48	thf(func_def_30, type, ph5: !>[X0: $tType]:(X0)).
0.15/0.48	thf(f93,plain,(
0.15/0.48	  $false),
0.15/0.48	  inference(avatar_sat_refutation,[status(thm)],[f75,f81,f92])).
0.15/0.48	thf(f92,plain,(
0.15/0.48	  ~spl4_1),
0.15/0.48	  inference(avatar_contradiction_clause,[status(thm)],[f91])).
0.15/0.48	thf(f91,plain,(
0.15/0.48	  $false | ~spl4_1),
0.15/0.48	  inference(trivial_inequality_removal,[status(thm)],[f90])).
0.15/0.48	thf(f90,plain,(
0.15/0.48	  ($false = $true) | ~spl4_1),
0.15/0.48	  inference(backward_demodulation,[status(thm)],[f28,f87])).
0.15/0.48	thf(f87,plain,(
0.15/0.48	  ($false = (in @ sK3 @ sK0)) | ~spl4_1),
0.15/0.48	  inference(trivial_inequality_removal,[status(thm)],[f86])).
0.15/0.48	thf(f86,plain,(
0.15/0.48	  ($false = $true) | ($false = (in @ sK3 @ sK0)) | ~spl4_1),
0.15/0.48	  inference(forward_demodulation,[status(thm)],[f85,f26])).
0.15/0.48	thf(f26,plain,(
0.15/0.48	  ((in @ sK1 @ sK2) = $true)),
0.15/0.48	  inference(cnf_transformation,[status(thm)],[f22])).
0.15/0.48	thf(f22,plain,(
0.15/0.48	  ((((in @ sK3 @ sK0) = $true) & ((in @ (kpair @ sK1 @ sK3) @ (cartprod @ sK2 @ sK0)) != $true)) & ((in @ sK1 @ sK2) = $true)) & (dsetconstrI = $true) & (ubforcartprodlem3 = $true)),
0.15/0.48	  inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f19,f21,f20])).
0.15/0.48	thf(f20,plain,(
0.15/0.48	  ? [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : $i] : (((in @ X3 @ X0) = $true) & ((in @ (kpair @ X1 @ X3) @ (cartprod @ X2 @ X0)) != $true)) & ((in @ X1 @ X2) = $true)) => (? [X3 : $i] : (((in @ X3 @ sK0) = $true) & ($true != (in @ (kpair @ sK1 @ X3) @ (cartprod @ sK2 @ sK0)))) & ((in @ sK1 @ sK2) = $true))),
0.15/0.48	  introduced(definition,[],[choice_axiom])).
0.15/0.48	thf(f21,plain,(
0.15/0.48	  ? [X3 : $i] : (((in @ X3 @ sK0) = $true) & ($true != (in @ (kpair @ sK1 @ X3) @ (cartprod @ sK2 @ sK0)))) => (((in @ sK3 @ sK0) = $true) & ((in @ (kpair @ sK1 @ sK3) @ (cartprod @ sK2 @ sK0)) != $true))),
0.15/0.48	  introduced(definition,[],[choice_axiom])).
0.15/0.48	thf(f19,plain,(
0.15/0.48	  ? [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : $i] : (((in @ X3 @ X0) = $true) & ((in @ (kpair @ X1 @ X3) @ (cartprod @ X2 @ X0)) != $true)) & ((in @ X1 @ X2) = $true)) & (dsetconstrI = $true) & (ubforcartprodlem3 = $true)),
0.15/0.48	  inference(flattening,[status(thm)],[f18])).
0.15/0.48	thf(f18,plain,(
0.15/0.48	  (? [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : $i] : (((in @ X3 @ X0) = $true) & ((in @ (kpair @ X1 @ X3) @ (cartprod @ X2 @ X0)) != $true)) & ((in @ X1 @ X2) = $true)) & (ubforcartprodlem3 = $true)) & (dsetconstrI = $true)),
0.15/0.48	  inference(ennf_transformation,[status(thm)],[f17])).
0.15/0.48	thf(f17,plain,(
0.15/0.48	  ~((dsetconstrI = $true) => ((ubforcartprodlem3 = $true) => ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ X2) = $true) => ! [X3 : $i] : (((in @ X3 @ X0) = $true) => ((in @ (kpair @ X1 @ X3) @ (cartprod @ X2 @ X0)) = $true)))))),
0.15/0.48	  inference(fool_elimination,[status(thm)],[f16])).
0.15/0.48	thf(f16,plain,(
0.15/0.48	  ~(dsetconstrI => (ubforcartprodlem3 => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ X2) => ! [X3 : $i] : ((in @ X3 @ X0) => (in @ (kpair @ X1 @ X3) @ (cartprod @ X2 @ X0))))))),
0.15/0.48	  inference(rectify,[status(thm)],[f6])).
0.15/0.48	thf(f6,negated_conjecture,(
0.15/0.48	  ~(dsetconstrI => (ubforcartprodlem3 => ! [X4 : $i,X2 : $i,X0 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X4) => (in @ (kpair @ X2 @ X3) @ (cartprod @ X0 @ X4))))))),
0.15/0.48	  inference(negated_conjecture,[status(cth)],[f5])).
0.15/0.48	thf(f5,conjecture,(
0.15/0.48	  dsetconstrI => (ubforcartprodlem3 => ! [X4 : $i,X2 : $i,X0 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X4) => (in @ (kpair @ X2 @ X3) @ (cartprod @ X0 @ X4)))))),
0.15/0.48	  file('/export/starexec/sandbox2/tmp/tmp.0LIdL31CqO/E---3.1_811584.p',cartprodpairin)).
0.15/0.48	thf(f85,plain,(
0.15/0.48	  ($false = (in @ sK3 @ sK0)) | ((in @ sK1 @ sK2) = $false) | ~spl4_1),
0.15/0.48	  inference(trivial_inequality_removal,[status(thm)],[f82])).
0.15/0.48	thf(f82,plain,(
0.15/0.48	  ((in @ sK1 @ sK2) = $false) | ($false = $true) | ($false = (in @ sK3 @ sK0)) | ~spl4_1),
0.15/0.48	  inference(superposition,[status(thm)],[f71,f47])).
0.15/0.48	thf(f47,plain,(
0.15/0.48	  ( ! [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) | ((in @ X1 @ X2) = $false) | ($false = (in @ X4 @ X3))) )),
0.15/0.48	  inference(binary_proxy_clausification,[status(thm)],[f46])).
0.15/0.48	thf(f46,plain,(
0.15/0.48	  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((in @ X4 @ X3) => (in @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X4 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X2 @ X3)))))) | ((in @ X1 @ X2) = $false)) )),
0.15/0.48	  inference(beta_eta_normalization,[status(thm)],[f45])).
0.15/0.48	thf(f45,plain,(
0.15/0.48	  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((in @ X1 @ X2) = $false) | ($true = ((^[Y0 : $i]: ((in @ Y0 @ X3) => (in @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X2 @ X3)))))) @ X4))) )),
0.15/0.48	  inference(pi_clausification,[status(thm)],[f44])).
0.15/0.48	thf(f44,plain,(
0.15/0.48	  ( ! [X2 : $i,X3 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X3) => (in @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X2 @ X3))))))) = $true) | ((in @ X1 @ X2) = $false)) )),
0.15/0.48	  inference(binary_proxy_clausification,[status(thm)],[f43])).
0.15/0.48	thf(f43,plain,(
0.15/0.48	  ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((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)))))))) = $true)) )),
0.15/0.48	  inference(beta_eta_normalization,[status(thm)],[f42])).
0.15/0.48	thf(f42,plain,(
0.15/0.48	  ( ! [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)) )),
0.15/0.48	  inference(pi_clausification,[status(thm)],[f41])).
0.15/0.48	thf(f41,plain,(
0.15/0.48	  ( ! [X2 : $i,X1 : $i] : (((!! @ $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)))))))))) = $true)) )),
0.15/0.48	  inference(beta_eta_normalization,[status(thm)],[f40])).
0.15/0.48	thf(f40,plain,(
0.15/0.48	  ( ! [X2 : $i,X1 : $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))))))))))) @ X2) = $true)) )),
0.15/0.48	  inference(pi_clausification,[status(thm)],[f39])).
0.15/0.48	thf(f39,plain,(
0.15/0.48	  ( ! [X1 : $i] : (((!! @ $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)))))))))))) = $true)) )),
0.15/0.48	  inference(beta_eta_normalization,[status(thm)],[f38])).
0.15/0.48	thf(f38,plain,(
0.15/0.48	  ( ! [X1 : $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))))))))))))) @ X1) = $true)) )),
0.15/0.48	  inference(pi_clausification,[status(thm)],[f37])).
0.15/0.48	thf(f37,plain,(
0.15/0.48	  ((!! @ $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)))))))))))))) = $true)),
0.15/0.48	  inference(beta_eta_normalization,[status(thm)],[f35])).
0.15/0.48	thf(f35,plain,(
0.15/0.48	  ((!! @ $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)))))))))))))) = $true)),
0.15/0.48	  inference(definition_unfolding,[status(thm)],[f24,f33])).
0.15/0.48	thf(f33,plain,(
0.15/0.48	  (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)))))))))))))))),
0.15/0.48	  inference(definition_unfolding,[status(thm)],[f23,f29])).
0.15/0.48	thf(f29,plain,(
0.15/0.48	  (kpair = (^[Y0 : $i]: ((^[Y1 : $i]: (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))))),
0.15/0.48	  inference(cnf_transformation,[status(thm)],[f11])).
0.15/0.48	thf(f11,plain,(
0.15/0.48	  (kpair = (^[Y0 : $i]: ((^[Y1 : $i]: (setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset))))))),
0.15/0.48	  inference(fool_elimination,[status(thm)],[f10])).
0.15/0.48	thf(f10,plain,(
0.15/0.48	  (kpair = (^[X0 : $i, X1 : $i] : (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))))),
0.15/0.48	  inference(rectify,[status(thm)],[f2])).
0.15/0.48	thf(f2,axiom,(
0.15/0.48	  (kpair = (^[X2 : $i, X3 : $i] : (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))),
0.15/0.48	  file('/export/starexec/sandbox2/tmp/tmp.0LIdL31CqO/E---3.1_811584.p',kpair)).
0.15/0.48	thf(f23,plain,(
0.15/0.48	  (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)))))))))))))))),
0.15/0.48	  inference(cnf_transformation,[status(thm)],[f15])).
0.15/0.48	thf(f15,plain,(
0.15/0.48	  (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)))))))))))))))),
0.15/0.48	  inference(fool_elimination,[status(thm)],[f14])).
0.15/0.48	thf(f14,plain,(
0.15/0.48	  (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X1) => ! [X3 : $i] : ((in @ X3 @ X0) => (in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X1 @ X0)))))) = ubforcartprodlem3)),
0.15/0.48	  inference(rectify,[status(thm)],[f4])).
0.15/0.48	thf(f4,axiom,(
0.15/0.48	  (! [X4 : $i,X0 : $i,X2 : $i] : ((in @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X4) => (in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X0 @ X4)))))) = ubforcartprodlem3)),
0.15/0.48	  file('/export/starexec/sandbox2/tmp/tmp.0LIdL31CqO/E---3.1_811584.p',ubforcartprodlem3)).
0.15/0.48	thf(f24,plain,(
0.15/0.48	  (ubforcartprodlem3 = $true)),
0.15/0.48	  inference(cnf_transformation,[status(thm)],[f22])).
0.15/0.48	thf(f71,plain,(
0.15/0.48	  ($false = (in @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ sK2 @ sK0))))) | ~spl4_1),
0.15/0.48	  inference(avatar_component_clause,[status(thm)],[f69])).
0.15/0.48	thf(f69,definition,(
0.15/0.48	  spl4_1 <=> ($false = (in @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ sK2 @ sK0)))))),
0.15/0.48	  introduced(definition,[new_symbols(naming,[spl4_1])],[avatar_definition])).
0.15/0.48	thf(f28,plain,(
0.15/0.48	  ((in @ sK3 @ sK0) = $true)),
0.15/0.48	  inference(cnf_transformation,[status(thm)],[f22])).
0.15/0.48	thf(f81,plain,(
0.15/0.48	  ~spl4_2),
0.15/0.48	  inference(avatar_contradiction_clause,[status(thm)],[f80])).
0.15/0.48	thf(f80,plain,(
0.15/0.48	  $false | ~spl4_2),
0.15/0.48	  inference(trivial_inequality_removal,[status(thm)],[f79])).
0.15/0.48	thf(f79,plain,(
0.15/0.48	  ($false = $true) | ~spl4_2),
0.15/0.48	  inference(backward_demodulation,[status(thm)],[f28,f78])).
0.15/0.48	thf(f78,plain,(
0.15/0.48	  ($false = (in @ sK3 @ sK0)) | ~spl4_2),
0.15/0.48	  inference(trivial_inequality_removal,[status(thm)],[f77])).
0.15/0.48	thf(f77,plain,(
0.15/0.48	  ($false = (in @ sK3 @ sK0)) | ($false = $true) | ~spl4_2),
0.15/0.48	  inference(forward_demodulation,[status(thm)],[f76,f26])).
0.15/0.48	thf(f76,plain,(
0.15/0.48	  ((in @ sK1 @ sK2) = $false) | ($false = (in @ sK3 @ sK0)) | ~spl4_2),
0.15/0.48	  inference(equality_resolution,[status(thm)],[f74])).
0.15/0.48	thf(f74,plain,(
0.15/0.48	  ( ! [X2 : $i,X1 : $i] : (((setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) != (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset))) | ($false = (in @ X1 @ sK2)) | ($false = (in @ X2 @ sK0))) ) | ~spl4_2),
0.15/0.48	  inference(avatar_component_clause,[status(thm)],[f73])).
0.15/0.48	thf(f73,definition,(
0.15/0.48	  spl4_2 <=> ! [X2 : $i,X1 : $i] : (($false = (in @ X2 @ sK0)) | ($false = (in @ X1 @ sK2)) | ((setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) != (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset))))),
0.15/0.48	  introduced(definition,[new_symbols(naming,[spl4_2])],[avatar_definition])).
0.15/0.48	thf(f75,plain,(
0.15/0.48	  spl4_1 | spl4_2),
0.15/0.48	  inference(avatar_split_clause,[status(thm)],[f67,f73,f69])).
0.15/0.48	thf(f67,plain,(
0.15/0.48	  ( ! [X2 : $i,X1 : $i] : (($false = (in @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ sK2 @ sK0))))) | ($false = (in @ X2 @ sK0)) | ($false = (in @ X1 @ sK2)) | ((setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) != (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)))) )),
0.15/0.48	  inference(equality_proxy_clausification,[status(thm)],[f66])).
0.15/0.48	thf(f66,plain,(
0.15/0.48	  ( ! [X2 : $i,X1 : $i] : (($false = (in @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ sK2 @ sK0))))) | ($false = (in @ X1 @ sK2)) | ($false = (in @ X2 @ sK0)) | ($false = ((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK3 @ emptyset)) @ emptyset))))) )),
0.15/0.48	  inference(binary_proxy_clausification,[status(thm)],[f65])).
0.15/0.48	thf(f65,plain,(
0.15/0.48	  ( ! [X2 : $i,X1 : $i] : (($false = (in @ X1 @ sK2)) | ((((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)) = $false) | ($false = (in @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ sK2 @ sK0)))))) )),
0.15/0.48	  inference(beta_eta_normalization,[status(thm)],[f64])).
0.15/0.48	thf(f64,plain,(
0.15/0.48	  ( ! [X2 : $i,X1 : $i] : (($false = (in @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ sK2 @ sK0))))) | ($false = ((^[Y0 : $i]: (((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK3 @ emptyset)) @ emptyset))) & (in @ Y0 @ sK0))) @ X2)) | ($false = (in @ X1 @ sK2))) )),
0.15/0.48	  inference(pi_clausification,[status(thm)],[f63])).
0.15/0.48	thf(f63,plain,(
0.15/0.48	  ( ! [X1 : $i] : (($false = (?? @ $i @ (^[Y0 : $i]: (((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ Y0 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK3 @ emptyset)) @ emptyset))) & (in @ Y0 @ sK0))))) | ($false = (in @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ sK2 @ sK0))))) | ($false = (in @ X1 @ sK2))) )),
0.15/0.48	  inference(binary_proxy_clausification,[status(thm)],[f62])).
0.15/0.48	thf(f62,plain,(
0.15/0.48	  ( ! [X1 : $i] : (($false = (in @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ sK2 @ sK0))))) | (((?? @ $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)) )),
0.15/0.48	  inference(beta_eta_normalization,[status(thm)],[f61])).
0.15/0.48	thf(f61,plain,(
0.15/0.48	  ( ! [X1 : $i] : (($false = (in @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ sK2 @ sK0))))) | ($false = ((^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (((setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK3 @ emptyset)) @ emptyset))) & (in @ Y1 @ sK0)))) & (in @ Y0 @ sK2))) @ X1))) )),
0.15/0.48	  inference(pi_clausification,[status(thm)],[f60])).
0.15/0.48	thf(f60,plain,(
0.15/0.48	  ($false = (?? @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (((setadjoin @ (setadjoin @ Y0 @ emptyset) @ (setadjoin @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK3 @ emptyset)) @ emptyset))) & (in @ Y1 @ sK0)))) & (in @ Y0 @ sK2))))) | ($false = (in @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ sK2 @ sK0)))))),
0.15/0.48	  inference(beta_eta_normalization,[status(thm)],[f59])).
0.15/0.48	thf(f59,plain,(
0.15/0.48	  ($false = ((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: (((setadjoin @ (setadjoin @ Y1 @ emptyset) @ (setadjoin @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset)) @ emptyset)) = Y0) & (in @ Y2 @ sK0)))) & (in @ Y1 @ sK2))))) @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)))) | ($false = (in @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ sK2 @ sK0)))))),
0.15/0.48	  inference(trivial_inequality_removal,[status(thm)],[f58])).
0.15/0.48	thf(f58,plain,(
0.15/0.48	  ($false = (in @ (setadjoin @ (setadjoin @ sK1 @ emptyset) @ (setadjoin @ (setadjoin @ sK1 @ (setadjoin @ sK3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ sK2 @ sK0))))) | ($true != $true) | ($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))))),
0.15/0.48	  inference(superposition,[status(thm)],[f48,f57])).
0.15/0.48	thf(f57,plain,(
0.15/0.48	  ( ! [X2 : $i,X3 : $i > $o,X1 : $i] : (($true = (in @ X1 @ (dsetconstr @ X2 @ X3))) | ($false = (X3 @ X1)) | ((in @ X1 @ X2) = $false)) )),
0.15/0.48	  inference(binary_proxy_clausification,[status(thm)],[f56])).
0.15/0.48	thf(f56,plain,(
0.15/0.48	  ( ! [X2 : $i,X3 : $i > $o,X1 : $i] : (((in @ X1 @ X2) = $false) | ($true = ((X3 @ X1) => (in @ X1 @ (dsetconstr @ X2 @ X3))))) )),
0.15/0.48	  inference(binary_proxy_clausification,[status(thm)],[f55])).
0.15/0.48	thf(f55,plain,(
0.15/0.48	  ( ! [X2 : $i,X3 : $i > $o,X1 : $i] : (($true = ((in @ X1 @ X2) => ((X3 @ X1) => (in @ X1 @ (dsetconstr @ X2 @ X3)))))) )),
0.15/0.48	  inference(beta_eta_normalization,[status(thm)],[f54])).
0.15/0.48	thf(f54,plain,(
0.15/0.48	  ( ! [X2 : $i,X3 : $i > $o,X1 : $i] : ((((^[Y0 : $i > $o]: ((in @ X1 @ X2) => ((Y0 @ X1) => (in @ X1 @ (dsetconstr @ X2 @ Y0))))) @ X3) = $true)) )),
0.15/0.48	  inference(pi_clausification,[status(thm)],[f53])).
0.15/0.48	thf(f53,plain,(
0.15/0.48	  ( ! [X2 : $i,X1 : $i] : (($true = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((in @ X1 @ X2) => ((Y0 @ X1) => (in @ X1 @ (dsetconstr @ X2 @ Y0)))))))) )),
0.15/0.48	  inference(beta_eta_normalization,[status(thm)],[f52])).
0.15/0.48	thf(f52,plain,(
0.15/0.48	  ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ X1 @ Y0) => ((Y1 @ X1) => (in @ X1 @ (dsetconstr @ Y0 @ Y1))))))) @ X2))) )),
0.15/0.48	  inference(pi_clausification,[status(thm)],[f51])).
0.15/0.48	thf(f51,plain,(
0.15/0.48	  ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ X1 @ Y0) => ((Y1 @ X1) => (in @ X1 @ (dsetconstr @ Y0 @ Y1)))))))))) )),
0.15/0.48	  inference(beta_eta_normalization,[status(thm)],[f50])).
0.15/0.48	thf(f50,plain,(
0.15/0.48	  ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2))))))))) @ X1) = $true)) )),
0.15/0.48	  inference(pi_clausification,[status(thm)],[f49])).
0.15/0.48	thf(f49,plain,(
0.15/0.48	  ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ Y2)))))))))))),
0.15/0.48	  inference(beta_eta_normalization,[status(thm)],[f36])).
0.15/0.48	thf(f36,plain,(
0.15/0.48	  ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ (^[Y3 : $i]: (Y2 @ Y3)))))))))))) = $true)),
0.15/0.48	  inference(definition_unfolding,[status(thm)],[f30,f25])).
0.15/0.48	thf(f25,plain,(
0.15/0.48	  (dsetconstrI = $true)),
0.15/0.48	  inference(cnf_transformation,[status(thm)],[f22])).
0.15/0.48	thf(f30,plain,(
0.15/0.48	  (dsetconstrI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ (^[Y3 : $i]: (Y2 @ Y3)))))))))))))),
0.15/0.48	  inference(cnf_transformation,[status(thm)],[f9])).
0.15/0.48	thf(f9,plain,(
0.15/0.48	  (dsetconstrI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y0 @ Y1) => ((Y2 @ Y0) => (in @ Y0 @ (dsetconstr @ Y1 @ (^[Y3 : $i]: (Y2 @ Y3)))))))))))))),
0.15/0.48	  inference(fool_elimination,[status(thm)],[f8])).
0.15/0.48	thf(f8,plain,(
0.15/0.48	  (! [X0 : $i > $o,X1 : $i,X2 : $i] : ((in @ X2 @ X1) => ((X0 @ X2) => (in @ X2 @ (dsetconstr @ X1 @ (^[X3 : $i] : (X0 @ X3)))))) = dsetconstrI)),
0.15/0.48	  inference(rectify,[status(thm)],[f1])).
0.15/0.48	thf(f1,axiom,(
0.15/0.48	  (! [X1 : $i > $o,X0 : $i,X2 : $i] : ((in @ X2 @ X0) => ((X1 @ X2) => (in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))))) = dsetconstrI)),
0.15/0.48	  file('/export/starexec/sandbox2/tmp/tmp.0LIdL31CqO/E---3.1_811584.p',dsetconstrI)).
0.15/0.48	thf(f48,plain,(
0.15/0.48	  ($true != (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))))))))),
0.15/0.48	  inference(beta_eta_normalization,[status(thm)],[f34])).
0.15/0.48	thf(f34,plain,(
0.15/0.48	  ((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)),
0.15/0.48	  inference(definition_unfolding,[status(thm)],[f27,f29,f32])).
0.15/0.48	thf(f32,plain,(
0.15/0.48	  (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))))))))))),
0.15/0.48	  inference(definition_unfolding,[status(thm)],[f31,f29])).
0.15/0.48	thf(f31,plain,(
0.15/0.48	  (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))))))))))),
0.15/0.48	  inference(cnf_transformation,[status(thm)],[f13])).
0.15/0.48	thf(f13,plain,(
0.15/0.48	  (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))))))))))),
0.15/0.48	  inference(fool_elimination,[status(thm)],[f12])).
0.15/0.48	thf(f12,plain,(
0.15/0.48	  ((^[X0 : $i, X1 : $i] : (dsetconstr @ (powerset @ (powerset @ (binunion @ X0 @ X1))) @ (^[X2 : $i] : (? [X3 : $i] : ((in @ X3 @ X0) & ? [X4 : $i] : ((in @ X4 @ X1) & ((kpair @ X3 @ X4) = X2))))))) = cartprod)),
0.15/0.48	  inference(rectify,[status(thm)],[f3])).
0.15/0.48	thf(f3,axiom,(
0.15/0.48	  ((^[X0 : $i, X4 : $i] : (dsetconstr @ (powerset @ (powerset @ (binunion @ X0 @ X4))) @ (^[X2 : $i] : (? [X3 : $i] : ((in @ X3 @ X0) & ? [X5 : $i] : ((in @ X5 @ X4) & ((kpair @ X3 @ X5) = X2))))))) = cartprod)),
0.15/0.48	  file('/export/starexec/sandbox2/tmp/tmp.0LIdL31CqO/E---3.1_811584.p',cartprod)).
0.15/0.48	thf(f27,plain,(
0.15/0.48	  ((in @ (kpair @ sK1 @ sK3) @ (cartprod @ sK2 @ sK0)) != $true)),
0.15/0.48	  inference(cnf_transformation,[status(thm)],[f22])).
0.15/0.48	% SZS output end Proof for E---3.1_811584
0.15/0.48	% (811661)------------------------------
0.15/0.48	% (811661)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.15/0.48	% (811661)Termination reason: Refutation
0.15/0.48	
0.15/0.48	% (811661)Memory used [KB]: 5628
0.15/0.48	% (811661)Time elapsed: 0.022 s
0.15/0.48	% (811661)Instructions burned: 14 (million)
0.15/0.48	% (811661)------------------------------
0.15/0.48	% (811661)------------------------------
0.15/0.48	% (811658)Success in time 0.041 s
0.15/0.49	EOF