0.04/0.13	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.04/0.13	% Command    : run_vampire %s %d THM
0.13/0.34	% Computer : n007.cluster.edu
0.13/0.34	% Model    : x86_64 x86_64
0.13/0.34	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.13/0.34	% Memory   : 8042.1875MB
0.13/0.34	% OS       : Linux 3.10.0-693.el7.x86_64
0.13/0.34	% CPULimit   : 1440
0.13/0.34	% WCLimit    : 180
0.13/0.34	% DateTime   : Thu Jul  4 06:58:09 EDT 2024
0.13/0.34	% CPUTime    : 
0.13/0.36	This is a THF_ problem
0.13/0.36	Running higher-order theorem proving
0.13/0.37	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.WOZzNViGra/E---3.1_13273.p -m 16384 -t 180
0.23/0.39	% (13487)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on E---3.1_13273 for (1799ds/183Mi)
0.23/0.39	% (13490)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on E---3.1_13273 for (1799ds/2Mi)
0.23/0.39	% (13488)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_13273 for (1799ds/4Mi)
0.23/0.39	% (13489)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_13273 for (1799ds/27Mi)
0.23/0.39	% (13490)Instruction limit reached!
0.23/0.39	% (13490)------------------------------
0.23/0.39	% (13490)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
0.23/0.39	% (13490)Termination reason: Unknown
0.23/0.39	% (13490)Termination phase: shuffling
0.23/0.39	
0.23/0.39	% (13490)Memory used [KB]: 1023
0.23/0.39	% (13490)Time elapsed: 0.004 s
0.23/0.39	% (13490)Instructions burned: 2 (million)
0.23/0.39	% (13490)------------------------------
0.23/0.39	% (13490)------------------------------
0.23/0.39	% (13488)Instruction limit reached!
0.23/0.39	% (13488)------------------------------
0.23/0.39	% (13488)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
0.23/0.39	% (13488)Termination reason: Unknown
0.23/0.39	% (13488)Termination phase: Saturation
0.23/0.39	
0.23/0.39	% (13488)Memory used [KB]: 5500
0.23/0.39	% (13488)Time elapsed: 0.005 s
0.23/0.39	% (13488)Instructions burned: 4 (million)
0.23/0.40	% (13488)------------------------------
0.23/0.40	% (13488)------------------------------
0.23/0.40	% (13489)First to succeed.
0.23/0.40	% (13491)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_13273 for (1799ds/2Mi)
0.23/0.40	% (13492)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_13273 for (1799ds/275Mi)
0.23/0.40	% (13493)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on E---3.1_13273 for (1799ds/18Mi)
0.23/0.40	% (13487)Also succeeded, but the first one will report.
0.23/0.40	% (13491)Instruction limit reached!
0.23/0.40	% (13491)------------------------------
0.23/0.40	% (13491)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
0.23/0.40	% (13491)Termination reason: Unknown
0.23/0.40	% (13489)Refutation found. Thanks to Tanya!
0.23/0.40	% SZS status Theorem for E---3.1_13273
0.23/0.40	% SZS output start Proof for E---3.1_13273
0.23/0.40	thf(func_def_0, type, in: $i > $i > $o).
0.23/0.40	thf(func_def_1, type, subset: $i > $i > $o).
0.23/0.40	thf(func_def_2, type, kpair: $i > $i > $i).
0.23/0.40	thf(func_def_3, type, cartprod: $i > $i > $i).
0.23/0.40	thf(func_def_4, type, breln: $i > $i > $i > $o).
0.23/0.40	thf(func_def_6, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
0.23/0.40	thf(func_def_8, type, breln1: $i > $i > $o).
0.23/0.40	thf(func_def_9, type, breln1compset: $i > $i > $i > $i).
0.23/0.40	thf(func_def_10, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
0.23/0.40	thf(func_def_32, type, ph7: !>[X0: $tType]:(X0)).
0.23/0.40	thf(f80,plain,(
0.23/0.40	  $false),
0.23/0.40	  inference(trivial_inequality_removal,[],[f79])).
0.23/0.40	thf(f79,plain,(
0.23/0.40	  ($true = $false)),
0.23/0.40	  inference(backward_demodulation,[],[f32,f76])).
0.23/0.40	thf(f76,plain,(
0.23/0.40	  ($false = (in @ (kpair @ sK5 @ sK4) @ sK2))),
0.23/0.40	  inference(trivial_inequality_removal,[],[f75])).
0.23/0.40	thf(f75,plain,(
0.23/0.40	  ($true = $false) | ($false = (in @ (kpair @ sK5 @ sK4) @ sK2))),
0.23/0.40	  inference(forward_demodulation,[],[f74,f30])).
0.23/0.40	thf(f30,plain,(
0.23/0.40	  ($true = (in @ sK5 @ sK0))),
0.23/0.40	  inference(cnf_transformation,[],[f24])).
0.23/0.40	thf(f24,plain,(
0.23/0.40	  (dpsetconstrI = $true) & (((((($true = (in @ (kpair @ sK5 @ sK4) @ sK2)) & ($true = (in @ (kpair @ sK3 @ sK5) @ sK1)) & ($true = (in @ sK5 @ sK0)) & ($true != (in @ (kpair @ sK3 @ sK4) @ (breln1compset @ sK0 @ sK1 @ sK2)))) & ($true = (in @ sK4 @ sK0))) & ($true = (in @ sK3 @ sK0))) & ((breln1 @ sK0 @ sK2) = $true)) & ($true = (breln1 @ sK0 @ sK1)))),
0.23/0.40	  inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f18,f23,f22,f21,f20,f19])).
0.23/0.40	thf(f19,plain,(
0.23/0.40	  ? [X0,X1] : (? [X2] : (? [X3] : (? [X4] : (? [X5] : (($true = (in @ (kpair @ X5 @ X4) @ X2)) & ($true = (in @ (kpair @ X3 @ X5) @ X1)) & ((in @ X5 @ X0) = $true) & ($true != (in @ (kpair @ X3 @ X4) @ (breln1compset @ X0 @ X1 @ X2)))) & ((in @ X4 @ X0) = $true)) & ($true = (in @ X3 @ X0))) & ($true = (breln1 @ X0 @ X2))) & ($true = (breln1 @ X0 @ X1))) => (? [X2] : (? [X3] : (? [X4] : (? [X5] : (($true = (in @ (kpair @ X5 @ X4) @ X2)) & ((in @ (kpair @ X3 @ X5) @ sK1) = $true) & ((in @ X5 @ sK0) = $true) & ($true != (in @ (kpair @ X3 @ X4) @ (breln1compset @ sK0 @ sK1 @ X2)))) & ($true = (in @ X4 @ sK0))) & ($true = (in @ X3 @ sK0))) & ($true = (breln1 @ sK0 @ X2))) & ($true = (breln1 @ sK0 @ sK1)))),
0.23/0.40	  introduced(choice_axiom,[])).
0.23/0.40	thf(f20,plain,(
0.23/0.40	  ? [X2] : (? [X3] : (? [X4] : (? [X5] : (($true = (in @ (kpair @ X5 @ X4) @ X2)) & ((in @ (kpair @ X3 @ X5) @ sK1) = $true) & ((in @ X5 @ sK0) = $true) & ($true != (in @ (kpair @ X3 @ X4) @ (breln1compset @ sK0 @ sK1 @ X2)))) & ($true = (in @ X4 @ sK0))) & ($true = (in @ X3 @ sK0))) & ($true = (breln1 @ sK0 @ X2))) => (? [X3] : (? [X4] : (? [X5] : (($true = (in @ (kpair @ X5 @ X4) @ sK2)) & ((in @ (kpair @ X3 @ X5) @ sK1) = $true) & ((in @ X5 @ sK0) = $true) & ($true != (in @ (kpair @ X3 @ X4) @ (breln1compset @ sK0 @ sK1 @ sK2)))) & ($true = (in @ X4 @ sK0))) & ($true = (in @ X3 @ sK0))) & ((breln1 @ sK0 @ sK2) = $true))),
0.23/0.40	  introduced(choice_axiom,[])).
0.23/0.40	thf(f21,plain,(
0.23/0.40	  ? [X3] : (? [X4] : (? [X5] : (($true = (in @ (kpair @ X5 @ X4) @ sK2)) & ((in @ (kpair @ X3 @ X5) @ sK1) = $true) & ((in @ X5 @ sK0) = $true) & ($true != (in @ (kpair @ X3 @ X4) @ (breln1compset @ sK0 @ sK1 @ sK2)))) & ($true = (in @ X4 @ sK0))) & ($true = (in @ X3 @ sK0))) => (? [X4] : (? [X5] : (($true = (in @ (kpair @ X5 @ X4) @ sK2)) & ($true = (in @ (kpair @ sK3 @ X5) @ sK1)) & ((in @ X5 @ sK0) = $true) & ($true != (in @ (kpair @ sK3 @ X4) @ (breln1compset @ sK0 @ sK1 @ sK2)))) & ($true = (in @ X4 @ sK0))) & ($true = (in @ sK3 @ sK0)))),
0.23/0.40	  introduced(choice_axiom,[])).
0.23/0.40	thf(f22,plain,(
0.23/0.40	  ? [X4] : (? [X5] : (($true = (in @ (kpair @ X5 @ X4) @ sK2)) & ($true = (in @ (kpair @ sK3 @ X5) @ sK1)) & ((in @ X5 @ sK0) = $true) & ($true != (in @ (kpair @ sK3 @ X4) @ (breln1compset @ sK0 @ sK1 @ sK2)))) & ($true = (in @ X4 @ sK0))) => (? [X5] : (($true = (in @ (kpair @ X5 @ sK4) @ sK2)) & ($true = (in @ (kpair @ sK3 @ X5) @ sK1)) & ((in @ X5 @ sK0) = $true) & ($true != (in @ (kpair @ sK3 @ sK4) @ (breln1compset @ sK0 @ sK1 @ sK2)))) & ($true = (in @ sK4 @ sK0)))),
0.23/0.40	  introduced(choice_axiom,[])).
0.23/0.40	thf(f23,plain,(
0.23/0.40	  ? [X5] : (($true = (in @ (kpair @ X5 @ sK4) @ sK2)) & ($true = (in @ (kpair @ sK3 @ X5) @ sK1)) & ((in @ X5 @ sK0) = $true) & ($true != (in @ (kpair @ sK3 @ sK4) @ (breln1compset @ sK0 @ sK1 @ sK2)))) => (($true = (in @ (kpair @ sK5 @ sK4) @ sK2)) & ($true = (in @ (kpair @ sK3 @ sK5) @ sK1)) & ($true = (in @ sK5 @ sK0)) & ($true != (in @ (kpair @ sK3 @ sK4) @ (breln1compset @ sK0 @ sK1 @ sK2))))),
0.23/0.40	  introduced(choice_axiom,[])).
0.23/0.40	thf(f18,plain,(
0.23/0.40	  (dpsetconstrI = $true) & ? [X0,X1] : (? [X2] : (? [X3] : (? [X4] : (? [X5] : (($true = (in @ (kpair @ X5 @ X4) @ X2)) & ($true = (in @ (kpair @ X3 @ X5) @ X1)) & ((in @ X5 @ X0) = $true) & ($true != (in @ (kpair @ X3 @ X4) @ (breln1compset @ X0 @ X1 @ X2)))) & ((in @ X4 @ X0) = $true)) & ($true = (in @ X3 @ X0))) & ($true = (breln1 @ X0 @ X2))) & ($true = (breln1 @ X0 @ X1)))),
0.23/0.40	  inference(flattening,[],[f17])).
0.23/0.40	thf(f17,plain,(
0.23/0.40	  ? [X0,X1] : (? [X2] : (? [X3] : (? [X4] : (? [X5] : (((($true != (in @ (kpair @ X3 @ X4) @ (breln1compset @ X0 @ X1 @ X2))) & ($true = (in @ (kpair @ X5 @ X4) @ X2))) & ($true = (in @ (kpair @ X3 @ X5) @ X1))) & ((in @ X5 @ X0) = $true)) & ((in @ X4 @ X0) = $true)) & ($true = (in @ X3 @ X0))) & ($true = (breln1 @ X0 @ X2))) & ($true = (breln1 @ X0 @ X1))) & (dpsetconstrI = $true)),
0.23/0.40	  inference(ennf_transformation,[],[f13])).
0.23/0.40	thf(f13,plain,(
0.23/0.40	  ~((dpsetconstrI = $true) => ! [X0,X1] : (($true = (breln1 @ X0 @ X1)) => ! [X2] : (($true = (breln1 @ X0 @ X2)) => ! [X3] : (($true = (in @ X3 @ X0)) => ! [X4] : (((in @ X4 @ X0) = $true) => ! [X5] : (((in @ X5 @ X0) = $true) => (($true = (in @ (kpair @ X3 @ X5) @ X1)) => (($true = (in @ (kpair @ X5 @ X4) @ X2)) => ($true = (in @ (kpair @ X3 @ X4) @ (breln1compset @ X0 @ X1 @ X2)))))))))))),
0.23/0.40	  inference(fool_elimination,[],[f12])).
0.23/0.40	thf(f12,plain,(
0.23/0.40	  ~(dpsetconstrI => ! [X0,X1] : ((breln1 @ X0 @ X1) => ! [X2] : ((breln1 @ X0 @ X2) => ! [X3] : ((in @ X3 @ X0) => ! [X4] : ((in @ X4 @ X0) => ! [X5] : ((in @ X5 @ X0) => ((in @ (kpair @ X3 @ X5) @ X1) => ((in @ (kpair @ X5 @ X4) @ X2) => (in @ (kpair @ X3 @ X4) @ (breln1compset @ X0 @ X1 @ X2))))))))))),
0.23/0.40	  inference(rectify,[],[f6])).
0.23/0.40	thf(f6,negated_conjecture,(
0.23/0.40	  ~(dpsetconstrI => ! [X0,X8] : ((breln1 @ X0 @ X8) => ! [X9] : ((breln1 @ X0 @ X9) => ! [X4] : ((in @ X4 @ X0) => ! [X5] : ((in @ X5 @ X0) => ! [X6] : ((in @ X6 @ X0) => ((in @ (kpair @ X4 @ X6) @ X8) => ((in @ (kpair @ X6 @ X5) @ X9) => (in @ (kpair @ X4 @ X5) @ (breln1compset @ X0 @ X8 @ X9))))))))))),
0.23/0.40	  inference(negated_conjecture,[],[f5])).
0.23/0.40	thf(f5,conjecture,(
0.23/0.40	  dpsetconstrI => ! [X0,X8] : ((breln1 @ X0 @ X8) => ! [X9] : ((breln1 @ X0 @ X9) => ! [X4] : ((in @ X4 @ X0) => ! [X5] : ((in @ X5 @ X0) => ! [X6] : ((in @ X6 @ X0) => ((in @ (kpair @ X4 @ X6) @ X8) => ((in @ (kpair @ X6 @ X5) @ X9) => (in @ (kpair @ X4 @ X5) @ (breln1compset @ X0 @ X8 @ X9)))))))))),
0.23/0.40	  file('/export/starexec/sandbox2/tmp/tmp.WOZzNViGra/E---3.1_13273.p',breln1compI)).
0.23/0.40	thf(f74,plain,(
0.23/0.40	  ((in @ sK5 @ sK0) = $false) | ($false = (in @ (kpair @ sK5 @ sK4) @ sK2))),
0.23/0.40	  inference(trivial_inequality_removal,[],[f72])).
0.23/0.40	thf(f72,plain,(
0.23/0.40	  ($false = (in @ (kpair @ sK5 @ sK4) @ sK2)) | ($true = $false) | ((in @ sK5 @ sK0) = $false)),
0.23/0.40	  inference(superposition,[],[f31,f70])).
0.23/0.40	thf(f70,plain,(
0.23/0.40	  ( ! [X1 : $i] : (((in @ (kpair @ sK3 @ X1) @ sK1) = $false) | ((in @ (kpair @ X1 @ sK4) @ sK2) = $false) | ((in @ X1 @ sK0) = $false)) )),
0.23/0.40	  inference(trivial_inequality_removal,[],[f69])).
0.23/0.40	thf(f69,plain,(
0.23/0.40	  ( ! [X1 : $i] : (((in @ (kpair @ sK3 @ X1) @ sK1) = $false) | ((in @ (kpair @ X1 @ sK4) @ sK2) = $false) | ($true = $false) | ((in @ X1 @ sK0) = $false)) )),
0.23/0.40	  inference(forward_demodulation,[],[f68,f28])).
0.23/0.40	thf(f28,plain,(
0.23/0.40	  ($true = (in @ sK4 @ sK0))),
0.23/0.40	  inference(cnf_transformation,[],[f24])).
0.23/0.40	thf(f68,plain,(
0.23/0.40	  ( ! [X1 : $i] : (((in @ X1 @ sK0) = $false) | ((in @ sK4 @ sK0) = $false) | ((in @ (kpair @ sK3 @ X1) @ sK1) = $false) | ((in @ (kpair @ X1 @ sK4) @ sK2) = $false)) )),
0.23/0.40	  inference(trivial_inequality_removal,[],[f67])).
0.23/0.40	thf(f67,plain,(
0.23/0.40	  ( ! [X1 : $i] : (($true = $false) | ((in @ sK4 @ sK0) = $false) | ((in @ (kpair @ X1 @ sK4) @ sK2) = $false) | ((in @ (kpair @ sK3 @ X1) @ sK1) = $false) | ((in @ X1 @ sK0) = $false)) )),
0.23/0.40	  inference(forward_demodulation,[],[f66,f27])).
0.23/0.40	thf(f27,plain,(
0.23/0.40	  ($true = (in @ sK3 @ sK0))),
0.23/0.40	  inference(cnf_transformation,[],[f24])).
0.23/0.40	thf(f66,plain,(
0.23/0.40	  ( ! [X1 : $i] : (((in @ sK3 @ sK0) = $false) | ((in @ X1 @ sK0) = $false) | ((in @ (kpair @ X1 @ sK4) @ sK2) = $false) | ((in @ (kpair @ sK3 @ X1) @ sK1) = $false) | ((in @ sK4 @ sK0) = $false)) )),
0.23/0.40	  inference(binary_proxy_clausification,[],[f65])).
0.23/0.40	thf(f65,plain,(
0.23/0.40	  ( ! [X1 : $i] : ((((in @ (kpair @ sK3 @ X1) @ sK1) & (in @ (kpair @ X1 @ sK4) @ sK2)) = $false) | ((in @ sK3 @ sK0) = $false) | ((in @ sK4 @ sK0) = $false) | ((in @ X1 @ sK0) = $false)) )),
0.23/0.40	  inference(binary_proxy_clausification,[],[f64])).
0.23/0.40	thf(f64,plain,(
0.23/0.40	  ( ! [X1 : $i] : (((((in @ (kpair @ sK3 @ X1) @ sK1) & (in @ (kpair @ X1 @ sK4) @ sK2)) & (in @ X1 @ sK0)) = $false) | ((in @ sK4 @ sK0) = $false) | ((in @ sK3 @ sK0) = $false)) )),
0.23/0.40	  inference(beta_eta_normalization,[],[f63])).
0.23/0.40	thf(f63,plain,(
0.23/0.40	  ( ! [X1 : $i] : (((in @ sK3 @ sK0) = $false) | ((in @ sK4 @ sK0) = $false) | (((^[Y0 : $i]: (((in @ (kpair @ sK3 @ Y0) @ sK1) & (in @ (kpair @ Y0 @ sK4) @ sK2)) & (in @ Y0 @ sK0))) @ X1) = $false)) )),
0.23/0.40	  inference(pi_clausification,[],[f62])).
0.23/0.40	thf(f62,plain,(
0.23/0.40	  ((?? @ $i @ (^[Y0 : $i]: (((in @ (kpair @ sK3 @ Y0) @ sK1) & (in @ (kpair @ Y0 @ sK4) @ sK2)) & (in @ Y0 @ sK0)))) = $false) | ((in @ sK3 @ sK0) = $false) | ((in @ sK4 @ sK0) = $false)),
0.23/0.40	  inference(beta_eta_normalization,[],[f61])).
0.23/0.40	thf(f61,plain,(
0.23/0.40	  (((^[Y0 : $i]: ((^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (((in @ (kpair @ Y0 @ Y2) @ sK1) & (in @ (kpair @ Y2 @ Y1) @ sK2)) & (in @ Y2 @ sK0))))))) @ sK3 @ sK4) = $false) | ((in @ sK3 @ sK0) = $false) | ((in @ sK4 @ sK0) = $false)),
0.23/0.40	  inference(trivial_inequality_removal,[],[f60])).
0.23/0.40	thf(f60,plain,(
0.23/0.40	  ($true != $true) | ((in @ sK4 @ sK0) = $false) | ((in @ sK3 @ sK0) = $false) | (((^[Y0 : $i]: ((^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (((in @ (kpair @ Y0 @ Y2) @ sK1) & (in @ (kpair @ Y2 @ Y1) @ sK2)) & (in @ Y2 @ sK0))))))) @ sK3 @ sK4) = $false)),
0.23/0.40	  inference(superposition,[],[f43,f59])).
0.23/0.40	thf(f59,plain,(
0.23/0.40	  ( ! [X2 : $i,X3 : $i,X1 : $i > $i > $o,X4 : $i,X5 : $i] : (($true = (in @ (kpair @ X3 @ X5) @ (dpsetconstr @ X2 @ X4 @ X1))) | ($false = (in @ X5 @ X4)) | ((X1 @ X3 @ X5) = $false) | ((in @ X3 @ X2) = $false)) )),
0.23/0.40	  inference(binary_proxy_clausification,[],[f58])).
0.23/0.40	thf(f58,plain,(
0.23/0.40	  ( ! [X2 : $i,X3 : $i,X1 : $i > $i > $o,X4 : $i,X5 : $i] : (((in @ X3 @ X2) = $false) | ($false = (in @ X5 @ X4)) | ($true = ((X1 @ X3 @ X5) => (in @ (kpair @ X3 @ X5) @ (dpsetconstr @ X2 @ X4 @ X1))))) )),
0.23/0.40	  inference(binary_proxy_clausification,[],[f57])).
0.23/0.40	thf(f57,plain,(
0.23/0.40	  ( ! [X2 : $i,X3 : $i,X1 : $i > $i > $o,X4 : $i,X5 : $i] : (($true = ((in @ X5 @ X4) => ((X1 @ X3 @ X5) => (in @ (kpair @ X3 @ X5) @ (dpsetconstr @ X2 @ X4 @ X1))))) | ((in @ X3 @ X2) = $false)) )),
0.23/0.40	  inference(beta_eta_normalization,[],[f56])).
0.23/0.40	thf(f56,plain,(
0.23/0.40	  ( ! [X2 : $i,X3 : $i,X1 : $i > $i > $o,X4 : $i,X5 : $i] : (($true = ((^[Y0 : $i]: ((in @ Y0 @ X4) => ((X1 @ X3 @ Y0) => (in @ (kpair @ X3 @ Y0) @ (dpsetconstr @ X2 @ X4 @ X1))))) @ X5)) | ((in @ X3 @ X2) = $false)) )),
0.23/0.40	  inference(pi_clausification,[],[f55])).
0.23/0.40	thf(f55,plain,(
0.23/0.40	  ( ! [X2 : $i,X3 : $i,X1 : $i > $i > $o,X4 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X4) => ((X1 @ X3 @ Y0) => (in @ (kpair @ X3 @ Y0) @ (dpsetconstr @ X2 @ X4 @ X1))))))) | ((in @ X3 @ X2) = $false)) )),
0.23/0.40	  inference(binary_proxy_clausification,[],[f54])).
0.23/0.40	thf(f54,plain,(
0.23/0.40	  ( ! [X2 : $i,X3 : $i,X1 : $i > $i > $o,X4 : $i] : (($true = ((in @ X3 @ X2) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X4) => ((X1 @ X3 @ Y0) => (in @ (kpair @ X3 @ Y0) @ (dpsetconstr @ X2 @ X4 @ X1))))))))) )),
0.23/0.40	  inference(beta_eta_normalization,[],[f53])).
0.23/0.40	thf(f53,plain,(
0.23/0.40	  ( ! [X2 : $i,X3 : $i,X1 : $i > $i > $o,X4 : $i] : (($true = ((^[Y0 : $i]: ((in @ X3 @ X2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => ((X1 @ X3 @ Y1) => (in @ (kpair @ X3 @ Y1) @ (dpsetconstr @ X2 @ Y0 @ X1)))))))) @ X4))) )),
0.23/0.40	  inference(pi_clausification,[],[f52])).
0.23/0.40	thf(f52,plain,(
0.23/0.40	  ( ! [X2 : $i,X3 : $i,X1 : $i > $i > $o] : (($true = (!! @ $i @ (^[Y0 : $i]: ((in @ X3 @ X2) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => ((X1 @ X3 @ Y1) => (in @ (kpair @ X3 @ Y1) @ (dpsetconstr @ X2 @ Y0 @ X1))))))))))) )),
0.23/0.40	  inference(beta_eta_normalization,[],[f51])).
0.23/0.40	thf(f51,plain,(
0.23/0.40	  ( ! [X2 : $i,X3 : $i,X1 : $i > $i > $o] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ X2) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((X1 @ Y0 @ Y2) => (in @ (kpair @ Y0 @ Y2) @ (dpsetconstr @ X2 @ Y1 @ X1)))))))))) @ X3) = $true)) )),
0.23/0.40	  inference(pi_clausification,[],[f50])).
0.23/0.40	thf(f50,plain,(
0.23/0.40	  ( ! [X2 : $i,X1 : $i > $i > $o] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ X2) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((X1 @ Y0 @ Y2) => (in @ (kpair @ Y0 @ Y2) @ (dpsetconstr @ X2 @ Y1 @ X1))))))))))))) )),
0.23/0.40	  inference(beta_eta_normalization,[],[f49])).
0.23/0.40	thf(f49,plain,(
0.23/0.40	  ( ! [X2 : $i,X1 : $i > $i > $o] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((X1 @ Y1 @ Y3) => (in @ (kpair @ Y1 @ Y3) @ (dpsetconstr @ Y0 @ Y2 @ X1)))))))))))) @ X2))) )),
0.23/0.40	  inference(pi_clausification,[],[f48])).
0.23/0.40	thf(f48,plain,(
0.23/0.40	  ( ! [X1 : $i > $i > $o] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => ((X1 @ Y1 @ Y3) => (in @ (kpair @ Y1 @ Y3) @ (dpsetconstr @ Y0 @ Y2 @ X1))))))))))))) = $true)) )),
0.23/0.40	  inference(beta_eta_normalization,[],[f47])).
0.23/0.40	thf(f47,plain,(
0.23/0.40	  ( ! [X1 : $i > $i > $o] : (($true = ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => ((Y0 @ Y2 @ Y4) => (in @ (kpair @ Y2 @ Y4) @ (dpsetconstr @ Y1 @ Y3 @ Y0)))))))))))))) @ X1))) )),
0.23/0.40	  inference(pi_clausification,[],[f46])).
0.23/0.40	thf(f46,plain,(
0.23/0.40	  ($true = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => ((Y0 @ Y2 @ Y4) => (in @ (kpair @ Y2 @ Y4) @ (dpsetconstr @ Y1 @ Y3 @ Y0))))))))))))))))),
0.23/0.40	  inference(beta_eta_normalization,[],[f42])).
0.23/0.40	thf(f42,plain,(
0.23/0.40	  ($true = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => ((Y0 @ Y2 @ Y4) => (in @ (kpair @ Y2 @ Y4) @ (dpsetconstr @ Y1 @ Y3 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y0 @ Y5 @ Y6))))))))))))))))))))),
0.23/0.40	  inference(definition_unfolding,[],[f35,f33])).
0.23/0.40	thf(f33,plain,(
0.23/0.40	  (dpsetconstrI = $true)),
0.23/0.40	  inference(cnf_transformation,[],[f24])).
0.23/0.40	thf(f35,plain,(
0.23/0.40	  (dpsetconstrI = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => ((Y0 @ Y2 @ Y4) => (in @ (kpair @ Y2 @ Y4) @ (dpsetconstr @ Y1 @ Y3 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y0 @ Y5 @ Y6))))))))))))))))))))),
0.23/0.41	  inference(cnf_transformation,[],[f15])).
0.23/0.41	thf(f15,plain,(
0.23/0.41	  (dpsetconstrI = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y2 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y3) => ((Y0 @ Y2 @ Y4) => (in @ (kpair @ Y2 @ Y4) @ (dpsetconstr @ Y1 @ Y3 @ (^[Y5 : $i]: ((^[Y6 : $i]: (Y0 @ Y5 @ Y6))))))))))))))))))))),
0.23/0.41	  inference(fool_elimination,[],[f14])).
0.23/0.41	thf(f14,plain,(
0.23/0.41	  (! [X0,X1,X2,X3 : $i > $i > $o] : ((in @ X1 @ X2) => ! [X4] : ((in @ X4 @ X0) => ((X3 @ X1 @ X4) => (in @ (kpair @ X1 @ X4) @ (dpsetconstr @ X2 @ X0 @ (^[X5 : $i, X6 : $i] : (X3 @ X5 @ X6))))))) = dpsetconstrI)),
0.23/0.41	  inference(rectify,[],[f2])).
0.23/0.41	thf(f2,axiom,(
0.23/0.41	  (! [X1,X4,X0,X3 : $i > $i > $o] : ((in @ X4 @ X0) => ! [X5] : ((in @ X5 @ X1) => ((X3 @ X4 @ X5) => (in @ (kpair @ X4 @ X5) @ (dpsetconstr @ X0 @ X1 @ (^[X6 : $i, X7 : $i] : (X3 @ X6 @ X7))))))) = dpsetconstrI)),
0.23/0.41	  file('/export/starexec/sandbox2/tmp/tmp.WOZzNViGra/E---3.1_13273.p',dpsetconstrI)).
0.23/0.41	thf(f43,plain,(
0.23/0.41	  ($true != (in @ (kpair @ sK3 @ sK4) @ (dpsetconstr @ sK0 @ sK0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (((in @ (kpair @ Y0 @ Y2) @ sK1) & (in @ (kpair @ Y2 @ Y1) @ sK2)) & (in @ Y2 @ sK0))))))))))),
0.23/0.41	  inference(beta_eta_normalization,[],[f39])).
0.23/0.41	thf(f39,plain,(
0.23/0.41	  ($true != (in @ (kpair @ sK3 @ sK4) @ ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (dpsetconstr @ Y0 @ Y0 @ (^[Y3 : $i]: ((^[Y4 : $i]: (?? @ $i @ (^[Y5 : $i]: (((in @ (kpair @ Y3 @ Y5) @ Y1) & (in @ (kpair @ Y5 @ Y4) @ Y2)) & (in @ Y5 @ Y0))))))))))))) @ sK0 @ sK1 @ sK2)))),
0.23/0.41	  inference(definition_unfolding,[],[f29,f37])).
0.23/0.41	thf(f37,plain,(
0.23/0.41	  (breln1compset = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (dpsetconstr @ Y0 @ Y0 @ (^[Y3 : $i]: ((^[Y4 : $i]: (?? @ $i @ (^[Y5 : $i]: (((in @ (kpair @ Y3 @ Y5) @ Y1) & (in @ (kpair @ Y5 @ Y4) @ Y2)) & (in @ Y5 @ Y0))))))))))))))),
0.23/0.41	  inference(cnf_transformation,[],[f9])).
0.23/0.41	thf(f9,plain,(
0.23/0.41	  (breln1compset = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (dpsetconstr @ Y0 @ Y0 @ (^[Y3 : $i]: ((^[Y4 : $i]: (?? @ $i @ (^[Y5 : $i]: (((in @ (kpair @ Y3 @ Y5) @ Y1) & (in @ (kpair @ Y5 @ Y4) @ Y2)) & (in @ Y5 @ Y0))))))))))))))),
0.23/0.41	  inference(fool_elimination,[],[f8])).
0.23/0.41	thf(f8,plain,(
0.23/0.41	  (breln1compset = (^[X0 : $i, X1 : $i, X2 : $i] : (dpsetconstr @ X0 @ X0 @ (^[X3 : $i, X4 : $i] : (? [X5] : ((in @ X5 @ X0) & (in @ (kpair @ X5 @ X4) @ X2) & (in @ (kpair @ X3 @ X5) @ X1)))))))),
0.23/0.41	  inference(rectify,[],[f4])).
0.23/0.41	thf(f4,axiom,(
0.23/0.41	  (breln1compset = (^[X0 : $i, X8 : $i, X9 : $i] : (dpsetconstr @ X0 @ X0 @ (^[X4 : $i, X5 : $i] : (? [X6] : ((in @ X6 @ X0) & (in @ (kpair @ X6 @ X5) @ X9) & (in @ (kpair @ X4 @ X6) @ X8)))))))),
0.23/0.41	  file('/export/starexec/sandbox2/tmp/tmp.WOZzNViGra/E---3.1_13273.p',breln1compset)).
0.23/0.41	thf(f29,plain,(
0.23/0.41	  ($true != (in @ (kpair @ sK3 @ sK4) @ (breln1compset @ sK0 @ sK1 @ sK2)))),
0.23/0.41	  inference(cnf_transformation,[],[f24])).
0.23/0.41	thf(f31,plain,(
0.23/0.41	  ($true = (in @ (kpair @ sK3 @ sK5) @ sK1))),
0.23/0.41	  inference(cnf_transformation,[],[f24])).
0.23/0.41	thf(f32,plain,(
0.23/0.41	  ($true = (in @ (kpair @ sK5 @ sK4) @ sK2))),
0.23/0.41	  inference(cnf_transformation,[],[f24])).
0.23/0.41	% SZS output end Proof for E---3.1_13273
0.23/0.41	% (13489)------------------------------
0.23/0.41	% (13489)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
0.23/0.41	% (13489)Termination reason: Refutation
0.23/0.41	
0.23/0.41	% (13489)Memory used [KB]: 5628
0.23/0.41	% (13489)Time elapsed: 0.012 s
0.23/0.41	% (13489)Instructions burned: 9 (million)
0.23/0.41	% (13489)------------------------------
0.23/0.41	% (13489)------------------------------
0.23/0.41	% (13486)Success in time 0.017 s
0.23/0.41	EOF