0.12/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.12/0.12	% Command    : run_vampire %s %d THM
0.12/0.33	% Computer : n005.cluster.edu
0.12/0.33	% Model    : x86_64 x86_64
0.12/0.33	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.12/0.33	% Memory   : 8042.1875MB
0.12/0.33	% OS       : Linux 3.10.0-693.el7.x86_64
0.12/0.33	% CPULimit   : 1440
0.12/0.33	% WCLimit    : 180
0.12/0.33	% DateTime   : Thu Jul  4 08:22:54 EDT 2024
0.12/0.33	% CPUTime    : 
0.18/0.35	This is a THF_ problem
0.18/0.35	Running higher-order theorem proving
0.18/0.36	Running /export/starexec/sandbox/solver/bin/vampire_ho --cores 7 --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox/tmp/tmp.1AG3BdALeJ/E---3.1_3609.p -m 16384 -t 180
0.18/0.38	% (3717)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on E---3.1_3609 for (1799ds/183Mi)
0.18/0.38	% (3719)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_3609 for (1799ds/27Mi)
0.18/0.38	% (3720)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on E---3.1_3609 for (1799ds/2Mi)
0.18/0.38	% (3722)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_3609 for (1799ds/275Mi)
0.18/0.38	% (3718)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_3609 for (1799ds/4Mi)
0.18/0.38	% (3721)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_3609 for (1799ds/2Mi)
0.18/0.38	% (3723)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on E---3.1_3609 for (1799ds/18Mi)
0.18/0.38	% (3720)Instruction limit reached!
0.18/0.38	% (3720)------------------------------
0.18/0.38	% (3720)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
0.18/0.38	% (3720)Termination reason: Unknown
0.18/0.38	% (3721)Instruction limit reached!
0.18/0.38	% (3721)------------------------------
0.18/0.38	% (3721)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
0.18/0.38	% (3721)Termination reason: Unknown
0.18/0.38	% (3721)Termination phase: Property scanning
0.18/0.38	
0.18/0.38	% (3721)Memory used [KB]: 1023
0.18/0.38	% (3721)Time elapsed: 0.004 s
0.18/0.38	% (3721)Instructions burned: 3 (million)
0.18/0.38	% (3721)------------------------------
0.18/0.38	% (3721)------------------------------
0.18/0.38	% (3720)Termination phase: Preprocessing 3
0.18/0.38	
0.18/0.38	% (3720)Memory used [KB]: 1023
0.18/0.38	% (3720)Time elapsed: 0.004 s
0.18/0.38	% (3720)Instructions burned: 3 (million)
0.18/0.38	% (3720)------------------------------
0.18/0.38	% (3720)------------------------------
0.18/0.38	% (3718)Instruction limit reached!
0.18/0.38	% (3718)------------------------------
0.18/0.38	% (3718)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
0.18/0.38	% (3718)Termination reason: Unknown
0.18/0.38	% (3718)Termination phase: Saturation
0.18/0.38	
0.18/0.38	% (3718)Memory used [KB]: 1023
0.18/0.38	% (3718)Time elapsed: 0.005 s
0.18/0.38	% (3718)Instructions burned: 4 (million)
0.18/0.38	% (3718)------------------------------
0.18/0.38	% (3718)------------------------------
0.18/0.39	% (3719)First to succeed.
0.18/0.40	% (3723)Instruction limit reached!
0.18/0.40	% (3723)------------------------------
0.18/0.40	% (3723)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
0.18/0.40	% (3723)Termination reason: Unknown
0.18/0.40	% (3723)Termination phase: Saturation
0.18/0.40	
0.18/0.40	% (3723)Memory used [KB]: 5628
0.18/0.40	% (3723)Time elapsed: 0.015 s
0.18/0.40	% (3723)Instructions burned: 19 (million)
0.18/0.40	% (3723)------------------------------
0.18/0.40	% (3723)------------------------------
0.18/0.40	% (3717)Also succeeded, but the first one will report.
0.18/0.40	% (3719)Refutation found. Thanks to Tanya!
0.18/0.40	% SZS status Theorem for E---3.1_3609
0.18/0.40	% SZS output start Proof for E---3.1_3609
0.18/0.40	thf(func_def_0, type, in: $i > $i > $o).
0.18/0.40	thf(func_def_1, type, dsetconstr: $i > ($i > $o) > $i).
0.18/0.40	thf(func_def_5, type, kpair: $i > $i > $i).
0.18/0.40	thf(func_def_6, type, cartprod: $i > $i > $i).
0.18/0.40	thf(func_def_8, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
0.18/0.40	thf(func_def_9, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
0.18/0.40	thf(func_def_24, type, sK1: $i > $i > $o).
0.18/0.40	thf(func_def_29, type, sK6: $i > $i > $i).
0.18/0.40	thf(func_def_30, type, sK7: $i > $i > $i).
0.18/0.40	thf(func_def_31, type, sK8: $i > $i > $i).
0.18/0.40	thf(func_def_32, type, ph9: !>[X0: $tType]:(X0)).
0.18/0.40	thf(f123,plain,(
0.18/0.40	  $false),
0.18/0.40	  inference(avatar_sat_refutation,[],[f97,f111,f122])).
0.18/0.40	thf(f122,plain,(
0.18/0.40	  ~spl5_1),
0.18/0.40	  inference(avatar_contradiction_clause,[],[f121])).
0.18/0.40	thf(f121,plain,(
0.18/0.40	  $false | ~spl5_1),
0.18/0.40	  inference(trivial_inequality_removal,[],[f120])).
0.18/0.40	thf(f120,plain,(
0.18/0.40	  ($true = $false) | ~spl5_1),
0.18/0.40	  inference(backward_demodulation,[],[f27,f117])).
0.18/0.40	thf(f117,plain,(
0.18/0.40	  ($false = (in @ sK4 @ sK3)) | ~spl5_1),
0.18/0.40	  inference(trivial_inequality_removal,[],[f116])).
0.18/0.40	thf(f116,plain,(
0.18/0.40	  ($false = (in @ sK4 @ sK3)) | ($true = $false) | ~spl5_1),
0.18/0.40	  inference(forward_demodulation,[],[f115,f29])).
0.18/0.40	thf(f29,plain,(
0.18/0.40	  ($true = (in @ sK2 @ sK0))),
0.18/0.40	  inference(cnf_transformation,[],[f22])).
0.18/0.40	thf(f22,plain,(
0.18/0.40	  (dsetconstrI = $true) & (cartprodpairin = $true) & (($true = (in @ sK2 @ sK0)) & (($true = (sK1 @ sK2 @ sK4)) & ($true = (in @ sK4 @ sK3)) & ($true != (in @ (kpair @ sK2 @ sK4) @ (dpsetconstr @ sK0 @ sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK1 @ Y0 @ Y1))))))))) & (setext = $true)),
0.18/0.40	  inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f19,f21,f20])).
0.18/0.40	thf(f20,plain,(
0.18/0.40	  ? [X0,X1 : $i > $i > $o,X2,X3] : (((in @ X2 @ X0) = $true) & ? [X4] : (($true = (X1 @ X2 @ X4)) & ($true = (in @ X4 @ X3)) & ($true != (in @ (kpair @ X2 @ X4) @ (dpsetconstr @ X0 @ X3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X1 @ Y0 @ Y1))))))))) => (($true = (in @ sK2 @ sK0)) & ? [X4] : (($true = (sK1 @ sK2 @ X4)) & ($true = (in @ X4 @ sK3)) & ($true != (in @ (kpair @ sK2 @ X4) @ (dpsetconstr @ sK0 @ sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK1 @ Y0 @ Y1)))))))))),
0.18/0.40	  introduced(choice_axiom,[])).
0.18/0.40	thf(f21,plain,(
0.18/0.40	  ? [X4] : (($true = (sK1 @ sK2 @ X4)) & ($true = (in @ X4 @ sK3)) & ($true != (in @ (kpair @ sK2 @ X4) @ (dpsetconstr @ sK0 @ sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK1 @ Y0 @ Y1)))))))) => (($true = (sK1 @ sK2 @ sK4)) & ($true = (in @ sK4 @ sK3)) & ($true != (in @ (kpair @ sK2 @ sK4) @ (dpsetconstr @ sK0 @ sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK1 @ Y0 @ Y1))))))))),
0.18/0.40	  introduced(choice_axiom,[])).
0.18/0.40	thf(f19,plain,(
0.18/0.40	  (dsetconstrI = $true) & (cartprodpairin = $true) & ? [X0,X1 : $i > $i > $o,X2,X3] : (((in @ X2 @ X0) = $true) & ? [X4] : (($true = (X1 @ X2 @ X4)) & ($true = (in @ X4 @ X3)) & ($true != (in @ (kpair @ X2 @ X4) @ (dpsetconstr @ X0 @ X3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X1 @ Y0 @ Y1))))))))) & (setext = $true)),
0.18/0.40	  inference(flattening,[],[f18])).
0.18/0.40	thf(f18,plain,(
0.18/0.40	  ((? [X0,X1 : $i > $i > $o,X2,X3] : (? [X4] : ((($true != (in @ (kpair @ X2 @ X4) @ (dpsetconstr @ X0 @ X3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X1 @ Y0 @ Y1))))))) & ($true = (X1 @ X2 @ X4))) & ($true = (in @ X4 @ X3))) & ((in @ X2 @ X0) = $true)) & (cartprodpairin = $true)) & (setext = $true)) & (dsetconstrI = $true)),
0.18/0.40	  inference(ennf_transformation,[],[f13])).
0.18/0.40	thf(f13,plain,(
0.18/0.40	  ~((dsetconstrI = $true) => ((setext = $true) => ((cartprodpairin = $true) => ! [X0,X1 : $i > $i > $o,X2,X3] : (((in @ X2 @ X0) = $true) => ! [X4] : (($true = (in @ X4 @ X3)) => (($true = (X1 @ X2 @ X4)) => ($true = (in @ (kpair @ X2 @ X4) @ (dpsetconstr @ X0 @ X3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X1 @ Y0 @ Y1)))))))))))))),
0.18/0.40	  inference(fool_elimination,[],[f12])).
0.18/0.40	thf(f12,plain,(
0.18/0.40	  ~(dsetconstrI => (setext => (cartprodpairin => ! [X0,X1 : $i > $i > $o,X2,X3] : ((in @ X2 @ X0) => ! [X4] : ((in @ X4 @ X3) => ((X1 @ X2 @ X4) => (in @ (kpair @ X2 @ X4) @ (dpsetconstr @ X0 @ X3 @ (^[X5 : $i, X6 : $i] : (X1 @ X5 @ X6))))))))))),
0.18/0.40	  inference(rectify,[],[f6])).
0.18/0.40	thf(f6,negated_conjecture,(
0.18/0.40	  ~(dsetconstrI => (setext => (cartprodpairin => ! [X0,X1 : $i > $i > $o,X2,X4] : ((in @ X2 @ X0) => ! [X3] : ((in @ X3 @ X4) => ((X1 @ X2 @ X3) => (in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X0 @ X4 @ (^[X6 : $i, X5 : $i] : (X1 @ X6 @ X5))))))))))),
0.18/0.40	  inference(negated_conjecture,[],[f5])).
0.18/0.40	thf(f5,conjecture,(
0.18/0.40	  dsetconstrI => (setext => (cartprodpairin => ! [X0,X1 : $i > $i > $o,X2,X4] : ((in @ X2 @ X0) => ! [X3] : ((in @ X3 @ X4) => ((X1 @ X2 @ X3) => (in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X0 @ X4 @ (^[X6 : $i, X5 : $i] : (X1 @ X6 @ X5)))))))))),
0.18/0.40	  file('/export/starexec/sandbox/tmp/tmp.1AG3BdALeJ/E---3.1_3609.p',dpsetconstrI)).
0.18/0.40	thf(f115,plain,(
0.18/0.40	  ($false = (in @ sK4 @ sK3)) | ((in @ sK2 @ sK0) = $false) | ~spl5_1),
0.18/0.40	  inference(trivial_inequality_removal,[],[f113])).
0.18/0.40	thf(f113,plain,(
0.18/0.40	  ($true = $false) | ((in @ sK2 @ sK0) = $false) | ($false = (in @ sK4 @ sK3)) | ~spl5_1),
0.18/0.40	  inference(superposition,[],[f68,f93])).
0.18/0.40	thf(f93,plain,(
0.18/0.40	  ($false = (in @ (kpair @ sK2 @ sK4) @ (cartprod @ sK0 @ sK3))) | ~spl5_1),
0.18/0.40	  inference(avatar_component_clause,[],[f91])).
0.18/0.40	thf(f91,plain,(
0.18/0.40	  spl5_1 <=> ($false = (in @ (kpair @ sK2 @ sK4) @ (cartprod @ sK0 @ sK3)))),
0.18/0.40	  introduced(avatar_definition,[new_symbols(naming,[spl5_1])])).
0.18/0.40	thf(f68,plain,(
0.18/0.40	  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (in @ (kpair @ X3 @ X4) @ (cartprod @ X2 @ X1))) | ((in @ X4 @ X1) = $false) | ((in @ X3 @ X2) = $false)) )),
0.18/0.40	  inference(binary_proxy_clausification,[],[f67])).
0.18/0.40	thf(f67,plain,(
0.18/0.40	  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((in @ X3 @ X2) = $false) | ($true = ((in @ X4 @ X1) => (in @ (kpair @ X3 @ X4) @ (cartprod @ X2 @ X1))))) )),
0.18/0.40	  inference(beta_eta_normalization,[],[f66])).
0.18/0.40	thf(f66,plain,(
0.18/0.40	  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((^[Y0 : $i]: ((in @ Y0 @ X1) => (in @ (kpair @ X3 @ Y0) @ (cartprod @ X2 @ X1)))) @ X4)) | ((in @ X3 @ X2) = $false)) )),
0.18/0.40	  inference(pi_clausification,[],[f65])).
0.18/0.40	thf(f65,plain,(
0.18/0.40	  ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (in @ (kpair @ X3 @ Y0) @ (cartprod @ X2 @ X1)))))) | ((in @ X3 @ X2) = $false)) )),
0.18/0.40	  inference(binary_proxy_clausification,[],[f64])).
0.18/0.40	thf(f64,plain,(
0.18/0.40	  ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((in @ X3 @ X2) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (in @ (kpair @ X3 @ Y0) @ (cartprod @ X2 @ X1)))))))) )),
0.18/0.40	  inference(beta_eta_normalization,[],[f63])).
0.18/0.40	thf(f63,plain,(
0.18/0.40	  ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((in @ Y0 @ X2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (in @ (kpair @ Y0 @ Y1) @ (cartprod @ X2 @ X1))))))) @ X3))) )),
0.18/0.40	  inference(pi_clausification,[],[f62])).
0.18/0.40	thf(f62,plain,(
0.18/0.40	  ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (in @ (kpair @ Y0 @ Y1) @ (cartprod @ X2 @ X1)))))))))) )),
0.18/0.40	  inference(beta_eta_normalization,[],[f61])).
0.18/0.40	thf(f61,plain,(
0.18/0.40	  ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => (in @ (kpair @ Y1 @ Y2) @ (cartprod @ Y0 @ X1))))))))) @ X2))) )),
0.18/0.40	  inference(pi_clausification,[],[f60])).
0.18/0.40	thf(f60,plain,(
0.18/0.40	  ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => (in @ (kpair @ Y1 @ Y2) @ (cartprod @ Y0 @ X1)))))))))))) )),
0.18/0.40	  inference(beta_eta_normalization,[],[f59])).
0.18/0.40	thf(f59,plain,(
0.18/0.40	  ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (kpair @ Y2 @ Y3) @ (cartprod @ Y1 @ Y0))))))))))) @ X1))) )),
0.18/0.40	  inference(pi_clausification,[],[f37])).
0.18/0.40	thf(f37,plain,(
0.18/0.40	  ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (kpair @ Y2 @ Y3) @ (cartprod @ Y1 @ Y0)))))))))))))),
0.18/0.40	  inference(definition_unfolding,[],[f32,f30])).
0.18/0.40	thf(f30,plain,(
0.18/0.40	  (cartprodpairin = $true)),
0.18/0.40	  inference(cnf_transformation,[],[f22])).
0.18/0.40	thf(f32,plain,(
0.18/0.40	  (cartprodpairin = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (kpair @ Y2 @ Y3) @ (cartprod @ Y1 @ Y0)))))))))))))),
0.18/0.40	  inference(cnf_transformation,[],[f9])).
0.18/0.40	thf(f9,plain,(
0.18/0.40	  (cartprodpairin = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (in @ (kpair @ Y2 @ Y3) @ (cartprod @ Y1 @ Y0)))))))))))))),
0.18/0.40	  inference(fool_elimination,[],[f8])).
0.18/0.40	thf(f8,plain,(
0.18/0.40	  (cartprodpairin = ! [X0,X1,X2] : ((in @ X0 @ X1) => ! [X3] : ((in @ X3 @ X2) => (in @ (kpair @ X0 @ X3) @ (cartprod @ X1 @ X2)))))),
0.18/0.40	  inference(rectify,[],[f3])).
0.18/0.40	thf(f3,axiom,(
0.18/0.40	  (cartprodpairin = ! [X2,X0,X4] : ((in @ X2 @ X0) => ! [X3] : ((in @ X3 @ X4) => (in @ (kpair @ X2 @ X3) @ (cartprod @ X0 @ X4)))))),
0.18/0.40	  file('/export/starexec/sandbox/tmp/tmp.1AG3BdALeJ/E---3.1_3609.p',cartprodpairin)).
0.18/0.40	thf(f27,plain,(
0.18/0.40	  ($true = (in @ sK4 @ sK3))),
0.18/0.40	  inference(cnf_transformation,[],[f22])).
0.18/0.40	thf(f111,plain,(
0.18/0.40	  ~spl5_2),
0.18/0.40	  inference(avatar_contradiction_clause,[],[f110])).
0.18/0.40	thf(f110,plain,(
0.18/0.40	  $false | ~spl5_2),
0.18/0.40	  inference(trivial_inequality_removal,[],[f109])).
0.18/0.40	thf(f109,plain,(
0.18/0.40	  ($true = $false) | ~spl5_2),
0.18/0.40	  inference(backward_demodulation,[],[f28,f108])).
0.18/0.40	thf(f108,plain,(
0.18/0.40	  ((sK1 @ sK2 @ sK4) = $false) | ~spl5_2),
0.18/0.40	  inference(trivial_inequality_removal,[],[f107])).
0.18/0.40	thf(f107,plain,(
0.18/0.40	  ($true = $false) | ((sK1 @ sK2 @ sK4) = $false) | ~spl5_2),
0.18/0.40	  inference(forward_demodulation,[],[f106,f29])).
0.18/0.40	thf(f106,plain,(
0.18/0.40	  ((sK1 @ sK2 @ sK4) = $false) | ((in @ sK2 @ sK0) = $false) | ~spl5_2),
0.18/0.40	  inference(trivial_inequality_removal,[],[f105])).
0.18/0.40	thf(f105,plain,(
0.18/0.40	  ((in @ sK2 @ sK0) = $false) | ($true = $false) | ((sK1 @ sK2 @ sK4) = $false) | ~spl5_2),
0.18/0.40	  inference(forward_demodulation,[],[f104,f27])).
0.18/0.40	thf(f104,plain,(
0.18/0.40	  ($false = (in @ sK4 @ sK3)) | ((sK1 @ sK2 @ sK4) = $false) | ((in @ sK2 @ sK0) = $false) | ~spl5_2),
0.18/0.40	  inference(equality_resolution,[],[f96])).
0.18/0.40	thf(f96,plain,(
0.18/0.40	  ( ! [X2 : $i,X1 : $i] : (((kpair @ sK2 @ sK4) != (kpair @ X1 @ X2)) | ((sK1 @ X1 @ X2) = $false) | ((in @ X1 @ sK0) = $false) | ((in @ X2 @ sK3) = $false)) ) | ~spl5_2),
0.18/0.40	  inference(avatar_component_clause,[],[f95])).
0.18/0.40	thf(f95,plain,(
0.18/0.40	  spl5_2 <=> ! [X2,X1] : (((in @ X2 @ sK3) = $false) | ((sK1 @ X1 @ X2) = $false) | ((in @ X1 @ sK0) = $false) | ((kpair @ sK2 @ sK4) != (kpair @ X1 @ X2)))),
0.18/0.40	  introduced(avatar_definition,[new_symbols(naming,[spl5_2])])).
0.18/0.40	thf(f28,plain,(
0.18/0.40	  ($true = (sK1 @ sK2 @ sK4))),
0.18/0.40	  inference(cnf_transformation,[],[f22])).
0.18/0.40	thf(f97,plain,(
0.18/0.40	  spl5_1 | spl5_2),
0.18/0.40	  inference(avatar_split_clause,[],[f89,f95,f91])).
0.18/0.40	thf(f89,plain,(
0.18/0.40	  ( ! [X2 : $i,X1 : $i] : (((in @ X2 @ sK3) = $false) | ((in @ X1 @ sK0) = $false) | ((kpair @ sK2 @ sK4) != (kpair @ X1 @ X2)) | ((sK1 @ X1 @ X2) = $false) | ($false = (in @ (kpair @ sK2 @ sK4) @ (cartprod @ sK0 @ sK3)))) )),
0.18/0.40	  inference(equality_proxy_clausification,[],[f88])).
0.18/0.40	thf(f88,plain,(
0.18/0.40	  ( ! [X2 : $i,X1 : $i] : ((((kpair @ X1 @ X2) = (kpair @ sK2 @ sK4)) = $false) | ((sK1 @ X1 @ X2) = $false) | ((in @ X1 @ sK0) = $false) | ((in @ X2 @ sK3) = $false) | ($false = (in @ (kpair @ sK2 @ sK4) @ (cartprod @ sK0 @ sK3)))) )),
0.18/0.40	  inference(binary_proxy_clausification,[],[f87])).
0.18/0.40	thf(f87,plain,(
0.18/0.40	  ( ! [X2 : $i,X1 : $i] : (($false = (in @ (kpair @ sK2 @ sK4) @ (cartprod @ sK0 @ sK3))) | ((((kpair @ X1 @ X2) = (kpair @ sK2 @ sK4)) & (sK1 @ X1 @ X2)) = $false) | ((in @ X2 @ sK3) = $false) | ((in @ X1 @ sK0) = $false)) )),
0.18/0.40	  inference(binary_proxy_clausification,[],[f86])).
0.18/0.40	thf(f86,plain,(
0.18/0.40	  ( ! [X2 : $i,X1 : $i] : (($false = ((((kpair @ X1 @ X2) = (kpair @ sK2 @ sK4)) & (sK1 @ X1 @ X2)) & (in @ X2 @ sK3))) | ((in @ X1 @ sK0) = $false) | ($false = (in @ (kpair @ sK2 @ sK4) @ (cartprod @ sK0 @ sK3)))) )),
0.18/0.40	  inference(beta_eta_normalization,[],[f85])).
0.18/0.40	thf(f85,plain,(
0.18/0.40	  ( ! [X2 : $i,X1 : $i] : (((in @ X1 @ sK0) = $false) | ($false = (in @ (kpair @ sK2 @ sK4) @ (cartprod @ sK0 @ sK3))) | (((^[Y0 : $i]: ((((kpair @ X1 @ Y0) = (kpair @ sK2 @ sK4)) & (sK1 @ X1 @ Y0)) & (in @ Y0 @ sK3))) @ X2) = $false)) )),
0.18/0.40	  inference(pi_clausification,[],[f84])).
0.18/0.40	thf(f84,plain,(
0.18/0.40	  ( ! [X1 : $i] : (($false = (?? @ $i @ (^[Y0 : $i]: ((((kpair @ X1 @ Y0) = (kpair @ sK2 @ sK4)) & (sK1 @ X1 @ Y0)) & (in @ Y0 @ sK3))))) | ($false = (in @ (kpair @ sK2 @ sK4) @ (cartprod @ sK0 @ sK3))) | ((in @ X1 @ sK0) = $false)) )),
0.18/0.40	  inference(binary_proxy_clausification,[],[f83])).
0.18/0.40	thf(f83,plain,(
0.18/0.40	  ( ! [X1 : $i] : ((((?? @ $i @ (^[Y0 : $i]: ((((kpair @ X1 @ Y0) = (kpair @ sK2 @ sK4)) & (sK1 @ X1 @ Y0)) & (in @ Y0 @ sK3)))) & (in @ X1 @ sK0)) = $false) | ($false = (in @ (kpair @ sK2 @ sK4) @ (cartprod @ sK0 @ sK3)))) )),
0.18/0.40	  inference(beta_eta_normalization,[],[f82])).
0.18/0.40	thf(f82,plain,(
0.18/0.40	  ( ! [X1 : $i] : ((((^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: ((((kpair @ Y0 @ Y1) = (kpair @ sK2 @ sK4)) & (sK1 @ Y0 @ Y1)) & (in @ Y1 @ sK3)))) & (in @ Y0 @ sK0))) @ X1) = $false) | ($false = (in @ (kpair @ sK2 @ sK4) @ (cartprod @ sK0 @ sK3)))) )),
0.18/0.40	  inference(pi_clausification,[],[f81])).
0.18/0.40	thf(f81,plain,(
0.18/0.40	  ((?? @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: ((((kpair @ Y0 @ Y1) = (kpair @ sK2 @ sK4)) & (sK1 @ Y0 @ Y1)) & (in @ Y1 @ sK3)))) & (in @ Y0 @ sK0)))) = $false) | ($false = (in @ (kpair @ sK2 @ sK4) @ (cartprod @ sK0 @ sK3)))),
0.18/0.40	  inference(beta_eta_normalization,[],[f80])).
0.18/0.40	thf(f80,plain,(
0.18/0.40	  ($false = (in @ (kpair @ sK2 @ sK4) @ (cartprod @ sK0 @ sK3))) | (((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((((kpair @ Y1 @ Y2) = Y0) & (sK1 @ Y1 @ Y2)) & (in @ Y2 @ sK3)))) & (in @ Y1 @ sK0))))) @ (kpair @ sK2 @ sK4)) = $false)),
0.18/0.40	  inference(trivial_inequality_removal,[],[f79])).
0.18/0.40	thf(f79,plain,(
0.18/0.40	  (((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((((kpair @ Y1 @ Y2) = Y0) & (sK1 @ Y1 @ Y2)) & (in @ Y2 @ sK3)))) & (in @ Y1 @ sK0))))) @ (kpair @ sK2 @ sK4)) = $false) | ($false = (in @ (kpair @ sK2 @ sK4) @ (cartprod @ sK0 @ sK3))) | ($true != $true)),
0.18/0.40	  inference(superposition,[],[f78,f77])).
0.18/0.40	thf(f77,plain,(
0.18/0.40	  ( ! [X2 : $i,X3 : $i,X1 : $i > $o] : (((in @ X3 @ (dsetconstr @ X2 @ X1)) = $true) | ((X1 @ X3) = $false) | ((in @ X3 @ X2) = $false)) )),
0.18/0.40	  inference(binary_proxy_clausification,[],[f76])).
0.18/0.40	thf(f76,plain,(
0.18/0.40	  ( ! [X2 : $i,X3 : $i,X1 : $i > $o] : (($true = ((X1 @ X3) => (in @ X3 @ (dsetconstr @ X2 @ X1)))) | ((in @ X3 @ X2) = $false)) )),
0.18/0.40	  inference(binary_proxy_clausification,[],[f75])).
0.18/0.40	thf(f75,plain,(
0.18/0.40	  ( ! [X2 : $i,X3 : $i,X1 : $i > $o] : (($true = ((in @ X3 @ X2) => ((X1 @ X3) => (in @ X3 @ (dsetconstr @ X2 @ X1)))))) )),
0.18/0.40	  inference(beta_eta_normalization,[],[f74])).
0.18/0.40	thf(f74,plain,(
0.18/0.40	  ( ! [X2 : $i,X3 : $i,X1 : $i > $o] : (($true = ((^[Y0 : $i]: ((in @ Y0 @ X2) => ((X1 @ Y0) => (in @ Y0 @ (dsetconstr @ X2 @ X1))))) @ X3))) )),
0.18/0.40	  inference(pi_clausification,[],[f73])).
0.18/0.40	thf(f73,plain,(
0.18/0.40	  ( ! [X2 : $i,X1 : $i > $o] : (($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => ((X1 @ Y0) => (in @ Y0 @ (dsetconstr @ X2 @ X1)))))))) )),
0.18/0.40	  inference(beta_eta_normalization,[],[f72])).
0.18/0.40	thf(f72,plain,(
0.18/0.40	  ( ! [X2 : $i,X1 : $i > $o] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => ((X1 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ X1))))))) @ X2))) )),
0.18/0.40	  inference(pi_clausification,[],[f71])).
0.18/0.40	thf(f71,plain,(
0.18/0.40	  ( ! [X1 : $i > $o] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => ((X1 @ Y1) => (in @ Y1 @ (dsetconstr @ Y0 @ X1)))))))))) )),
0.18/0.40	  inference(beta_eta_normalization,[],[f70])).
0.18/0.40	thf(f70,plain,(
0.18/0.40	  ( ! [X1 : $i > $o] : (($true = ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => (in @ Y2 @ (dsetconstr @ Y1 @ Y0))))))))) @ X1))) )),
0.18/0.40	  inference(pi_clausification,[],[f69])).
0.18/0.40	thf(f69,plain,(
0.18/0.40	  ($true = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => (in @ Y2 @ (dsetconstr @ Y1 @ Y0)))))))))))),
0.18/0.40	  inference(beta_eta_normalization,[],[f34])).
0.18/0.40	thf(f34,plain,(
0.18/0.40	  ($true = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => (in @ Y2 @ (dsetconstr @ Y1 @ (^[Y3 : $i]: (Y0 @ Y3)))))))))))))),
0.18/0.40	  inference(definition_unfolding,[],[f31,f23])).
0.18/0.40	thf(f23,plain,(
0.18/0.40	  (dsetconstrI = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => (in @ Y2 @ (dsetconstr @ Y1 @ (^[Y3 : $i]: (Y0 @ Y3)))))))))))))),
0.18/0.40	  inference(cnf_transformation,[],[f17])).
0.18/0.40	thf(f17,plain,(
0.18/0.40	  (dsetconstrI = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((Y0 @ Y2) => (in @ Y2 @ (dsetconstr @ Y1 @ (^[Y3 : $i]: (Y0 @ Y3)))))))))))))),
0.18/0.40	  inference(fool_elimination,[],[f16])).
0.18/0.40	thf(f16,plain,(
0.18/0.40	  (dsetconstrI = ! [X0,X1,X2 : $i > $o] : ((in @ X0 @ X1) => ((X2 @ X0) => (in @ X0 @ (dsetconstr @ X1 @ (^[X3 : $i] : (X2 @ X3)))))))),
0.18/0.40	  inference(rectify,[],[f1])).
0.18/0.40	thf(f1,axiom,(
0.18/0.40	  (dsetconstrI = ! [X2,X0,X1 : $i > $o] : ((in @ X2 @ X0) => ((X1 @ X2) => (in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))))))),
0.18/0.40	  file('/export/starexec/sandbox/tmp/tmp.1AG3BdALeJ/E---3.1_3609.p',dsetconstrI)).
0.18/0.40	thf(f31,plain,(
0.18/0.40	  (dsetconstrI = $true)),
0.18/0.40	  inference(cnf_transformation,[],[f22])).
0.18/0.40	thf(f78,plain,(
0.18/0.40	  ($true != (in @ (kpair @ sK2 @ sK4) @ (dsetconstr @ (cartprod @ sK0 @ sK3) @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((?? @ $i @ (^[Y2 : $i]: ((((kpair @ Y1 @ Y2) = Y0) & (sK1 @ Y1 @ Y2)) & (in @ Y2 @ sK3)))) & (in @ Y1 @ sK0))))))))),
0.18/0.40	  inference(beta_eta_normalization,[],[f35])).
0.18/0.40	thf(f35,plain,(
0.18/0.40	  ($true != (in @ (kpair @ sK2 @ sK4) @ ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i > $i > $o]: (dsetconstr @ (cartprod @ Y0 @ Y1) @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((?? @ $i @ (^[Y5 : $i]: ((((kpair @ Y4 @ Y5) = Y3) & (Y2 @ Y4 @ Y5)) & (in @ Y5 @ Y1)))) & (in @ Y4 @ Y0))))))))))) @ sK0 @ sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK1 @ Y0 @ Y1)))))))),
0.18/0.40	  inference(definition_unfolding,[],[f26,f33])).
0.18/0.40	thf(f33,plain,(
0.18/0.40	  (dpsetconstr = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i > $i > $o]: (dsetconstr @ (cartprod @ Y0 @ Y1) @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((?? @ $i @ (^[Y5 : $i]: ((((kpair @ Y4 @ Y5) = Y3) & (Y2 @ Y4 @ Y5)) & (in @ Y5 @ Y1)))) & (in @ Y4 @ Y0))))))))))))),
0.18/0.40	  inference(cnf_transformation,[],[f11])).
0.18/0.40	thf(f11,plain,(
0.18/0.40	  (dpsetconstr = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i > $i > $o]: (dsetconstr @ (cartprod @ Y0 @ Y1) @ (^[Y3 : $i]: (?? @ $i @ (^[Y4 : $i]: ((?? @ $i @ (^[Y5 : $i]: ((((kpair @ Y4 @ Y5) = Y3) & (Y2 @ Y4 @ Y5)) & (in @ Y5 @ Y1)))) & (in @ Y4 @ Y0))))))))))))),
0.18/0.40	  inference(fool_elimination,[],[f10])).
0.18/0.40	thf(f10,plain,(
0.18/0.40	  (dpsetconstr = (^[X0 : $i, X1 : $i, X2 : $i > $i > $o] : (dsetconstr @ (cartprod @ X0 @ X1) @ (^[X3 : $i] : (? [X4] : ((in @ X4 @ X0) & ? [X5] : ((in @ X5 @ X1) & (X2 @ X4 @ X5) & ((kpair @ X4 @ X5) = X3))))))))),
0.18/0.40	  inference(rectify,[],[f4])).
0.18/0.40	thf(f4,axiom,(
0.18/0.40	  (dpsetconstr = (^[X0 : $i, X4 : $i, X1 : $i > $i > $o] : (dsetconstr @ (cartprod @ X0 @ X4) @ (^[X5 : $i] : (? [X2] : ((in @ X2 @ X0) & ? [X3] : ((in @ X3 @ X4) & (X1 @ X2 @ X3) & ((kpair @ X2 @ X3) = X5))))))))),
0.18/0.40	  file('/export/starexec/sandbox/tmp/tmp.1AG3BdALeJ/E---3.1_3609.p',dpsetconstr)).
0.18/0.40	thf(f26,plain,(
0.18/0.40	  ($true != (in @ (kpair @ sK2 @ sK4) @ (dpsetconstr @ sK0 @ sK3 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK1 @ Y0 @ Y1)))))))),
0.18/0.40	  inference(cnf_transformation,[],[f22])).
0.18/0.40	% SZS output end Proof for E---3.1_3609
0.18/0.40	% (3719)------------------------------
0.18/0.40	% (3719)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
0.18/0.40	% (3719)Termination reason: Refutation
0.18/0.40	
0.18/0.40	% (3719)Memory used [KB]: 5628
0.18/0.40	% (3719)Time elapsed: 0.016 s
0.18/0.40	% (3719)Instructions burned: 14 (million)
0.18/0.40	% (3719)------------------------------
0.18/0.40	% (3719)------------------------------
0.18/0.40	% (3716)Success in time 0.018 s
0.18/0.40	EOF