0.07/0.13	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.07/0.13	% Command    : run_vampire %s %d THM
0.13/0.34	% Computer   : n026.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   : 1920
0.13/0.34	% WCLimit    : 240
0.13/0.34	% DateTime   : Wed Jul 30 02:14:34 EDT 2025
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-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.x7nx6qmTR1/E---3.1_30349.p -m 16384 -t 240
0.13/0.40	% (30544)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_30349 for (2399ds/27Mi)
0.13/0.40	% (30545)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on E---3.1_30349 for (2399ds/2Mi)
0.13/0.40	% (30546)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_30349 for (2399ds/2Mi)
0.13/0.40	% (30542)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on E---3.1_30349 for (2399ds/183Mi)
0.13/0.40	% (30547)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_30349 for (2399ds/275Mi)
0.13/0.40	% (30545)Instruction limit reached!
0.13/0.40	% (30545)------------------------------
0.13/0.40	% (30545)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.13/0.40	% (30545)Termination reason: Unknown
0.13/0.40	% (30545)Termination phase: Property scanning
0.13/0.40	% (30546)Instruction limit reached!
0.13/0.40	% (30546)------------------------------
0.13/0.40	% (30546)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.13/0.40	
0.13/0.40	% (30545)Memory used [KB]: 1023
0.13/0.40	% (30545)Time elapsed: 0.004 s
0.13/0.40	% (30545)Instructions burned: 3 (million)
0.13/0.40	% (30545)------------------------------
0.13/0.40	% (30545)------------------------------
0.13/0.40	% (30546)Termination reason: Unknown
0.13/0.40	% (30546)Termination phase: Property scanning
0.13/0.40	
0.13/0.40	% (30546)Memory used [KB]: 1023
0.13/0.40	% (30546)Time elapsed: 0.004 s
0.13/0.40	% (30546)Instructions burned: 3 (million)
0.13/0.40	% (30546)------------------------------
0.13/0.40	% (30546)------------------------------
0.13/0.40	% (30542)First to succeed.
0.13/0.40	% (30548)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on E---3.1_30349 for (2399ds/18Mi)
0.13/0.40	% (30544)Also succeeded, but the first one will report.
0.13/0.40	% (30547)Also succeeded, but the first one will report.
0.13/0.40	% (30542)Refutation found. Thanks to Tanya!
0.13/0.40	% SZS status Theorem for E---3.1_30349
0.13/0.40	% SZS output start Proof for E---3.1_30349
0.13/0.40	thf(func_def_0, type, in: $i > ($i > $o) > $o).
0.13/0.40	thf(func_def_2, type, is_a: $i > ($i > $o) > $o).
0.13/0.40	thf(func_def_3, type, emptyset: $i > $o).
0.13/0.40	thf(func_def_4, type, unord_pair: $i > $i > $i > $o).
0.13/0.40	thf(func_def_5, type, singleton: $i > $i > $o).
0.13/0.40	thf(func_def_6, type, union: ($i > $o) > ($i > $o) > $i > $o).
0.13/0.40	thf(func_def_7, type, excl_union: ($i > $o) > ($i > $o) > $i > $o).
0.13/0.40	thf(func_def_8, type, intersection: ($i > $o) > ($i > $o) > $i > $o).
0.13/0.40	thf(func_def_9, type, setminus: ($i > $o) > ($i > $o) > $i > $o).
0.13/0.40	thf(func_def_10, type, complement: ($i > $o) > $i > $o).
0.13/0.40	thf(func_def_11, type, disjoint: ($i > $o) > ($i > $o) > $o).
0.13/0.40	thf(func_def_12, type, subset: ($i > $o) > ($i > $o) > $o).
0.13/0.40	thf(func_def_13, type, meets: ($i > $o) > ($i > $o) > $o).
0.13/0.40	thf(func_def_14, type, misses: ($i > $o) > ($i > $o) > $o).
0.13/0.40	thf(func_def_15, type, fun_image: ($i > $i) > ($i > $o) > $i > $o).
0.13/0.40	thf(func_def_16, type, fun_composition: ($i > $i) > ($i > $i) > $i > $i).
0.13/0.40	thf(func_def_17, type, fun_inv_image: ($i > $i) > ($i > $o) > $i > $o).
0.13/0.40	thf(func_def_18, type, fun_injective: ($i > $i) > $o).
0.13/0.40	thf(func_def_19, type, fun_surjective: ($i > $i) > $o).
0.13/0.40	thf(func_def_20, type, fun_bijective: ($i > $i) > $o).
0.13/0.40	thf(func_def_21, type, fun_decreasing: ($i > $i) > ($i > $i > $o) > $o).
0.13/0.40	thf(func_def_22, type, fun_increasing: ($i > $i) > ($i > $i > $o) > $o).
0.13/0.40	thf(func_def_37, type, sK0: $i > $o).
0.13/0.40	thf(func_def_38, type, sK1: $i > $o).
0.13/0.40	thf(func_def_39, type, sK2: $i > $i).
0.13/0.40	thf(f142,plain,(
0.13/0.40	  $false),
0.13/0.40	  inference(avatar_sat_refutation,[status(thm)],[f125,f133,f141])).
0.13/0.40	thf(f141,plain,(
0.13/0.40	  ~spl3_1),
0.13/0.40	  inference(avatar_contradiction_clause,[status(thm)],[f140])).
0.13/0.40	thf(f140,plain,(
0.13/0.40	  $false | ~spl3_1),
0.13/0.40	  inference(subsumption_resolution,[status(thm)],[f136,f109])).
0.13/0.40	thf(f109,plain,(
0.13/0.40	  (sK4 = (sK2 @ sK5))),
0.13/0.40	  inference(equality_proxy_clausification,[status(thm)],[f105])).
0.13/0.40	thf(f105,plain,(
0.13/0.40	  (((sK2 @ sK5) = sK4) = $true)),
0.13/0.40	  inference(binary_proxy_clausification,[status(thm)],[f104])).
0.13/0.40	thf(f104,plain,(
0.13/0.40	  ($true = (((sK1 @ sK5) & (sK0 @ sK5)) & ((sK2 @ sK5) = sK4)))),
0.13/0.40	  inference(beta_eta_normalization,[status(thm)],[f103])).
0.13/0.40	thf(f103,plain,(
0.13/0.40	  ($true = ((^[Y0 : $i]: (((sK1 @ Y0) & (sK0 @ Y0)) & ((sK2 @ Y0) = sK4))) @ sK5))),
0.13/0.40	  inference(sigma_clausification,[status(thm)],[f102])).
0.13/0.40	thf(f102,plain,(
0.13/0.40	  ((?? @ $i @ (^[Y0 : $i]: (((sK1 @ Y0) & (sK0 @ Y0)) & ((sK2 @ Y0) = sK4)))) = $true)),
0.13/0.40	  inference(binary_proxy_clausification,[status(thm)],[f100])).
0.13/0.40	thf(f100,plain,(
0.13/0.40	  (((?? @ $i @ (^[Y0 : $i]: (((sK1 @ Y0) & (sK0 @ Y0)) & ((sK2 @ Y0) = sK4)))) => ((?? @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) & ((sK2 @ Y0) = sK4)))) & (?? @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) & ((sK2 @ Y0) = sK4)))))) = $false)),
0.13/0.40	  inference(beta_eta_normalization,[status(thm)],[f99])).
0.13/0.40	thf(f99,plain,(
0.13/0.40	  (((^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (((sK1 @ Y1) & (sK0 @ Y1)) & ((sK2 @ Y1) = Y0)))) => ((?? @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) & ((sK2 @ Y1) = Y0)))) & (?? @ $i @ (^[Y1 : $i]: ((sK0 @ Y1) & ((sK2 @ Y1) = Y0))))))) @ sK4) = $false)),
0.13/0.40	  inference(sigma_clausification,[status(thm)],[f98])).
0.13/0.40	thf(f98,plain,(
0.13/0.40	  ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (^[Y1 : $i]: (((sK1 @ Y1) & (sK0 @ Y1)) & ((sK2 @ Y1) = Y0)))) => ((?? @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) & ((sK2 @ Y1) = Y0)))) & (?? @ $i @ (^[Y1 : $i]: ((sK0 @ Y1) & ((sK2 @ Y1) = Y0)))))))) != $true)),
0.13/0.40	  inference(beta_eta_normalization,[status(thm)],[f97])).
0.13/0.40	thf(f97,plain,(
0.13/0.40	  (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 @ Y2))))))) @ ((^[Y0 : $i > $i]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) & ((Y0 @ Y3) = Y2))))))))) @ sK2 @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (Y1 @ Y2))))))) @ sK1 @ sK0)) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (Y1 @ Y2))))))) @ ((^[Y0 : $i > $i]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) & ((Y0 @ Y3) = Y2))))))))) @ sK2 @ sK1) @ ((^[Y0 : $i > $i]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) & ((Y0 @ Y3) = Y2))))))))) @ sK2 @ sK0))) != $true)),
0.13/0.40	  inference(definition_unfolding,[status(thm)],[f86,f90,f76,f83,f83,f76,f76])).
0.13/0.40	thf(f83,plain,(
0.13/0.40	  (intersection = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (Y1 @ Y2))))))))),
0.13/0.40	  inference(cnf_transformation,[status(thm)],[f62])).
0.13/0.40	thf(f62,plain,(
0.13/0.40	  (intersection = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (Y1 @ Y2))))))))),
0.13/0.40	  inference(fool_elimination,[status(thm)],[f61])).
0.13/0.40	thf(f61,plain,(
0.13/0.40	  ((^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X1 @ X2) & (X0 @ X2))) = intersection)),
0.13/0.40	  inference(rectify,[status(thm)],[f8])).
0.13/0.40	thf(f8,axiom,(
0.13/0.40	  ((^[X0 : $i > $o, X2 : $i > $o, X3 : $i] : ((X2 @ X3) & (X0 @ X3))) = intersection)),
0.13/0.40	  file('/export/starexec/sandbox2/tmp/tmp.x7nx6qmTR1/E---3.1_30349.p',intersection)).
0.13/0.40	thf(f76,plain,(
0.13/0.40	  (fun_image = (^[Y0 : $i > $i]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) & ((Y0 @ Y3) = Y2))))))))))),
0.13/0.40	  inference(cnf_transformation,[status(thm)],[f44])).
0.13/0.40	thf(f44,plain,(
0.13/0.40	  (fun_image = (^[Y0 : $i > $i]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) & ((Y0 @ Y3) = Y2))))))))))),
0.13/0.40	  inference(fool_elimination,[status(thm)],[f43])).
0.13/0.40	thf(f43,plain,(
0.13/0.40	  (fun_image = (^[X0 : $i > $i, X1 : $i > $o, X2 : $i] : (? [X3 : $i] : (((X0 @ X3) = X2) & (X1 @ X3)))))),
0.13/0.40	  inference(rectify,[status(thm)],[f15])).
0.13/0.40	thf(f15,axiom,(
0.13/0.40	  (fun_image = (^[X4 : $i > $i, X5 : $i > $o, X2 : $i] : (? [X0 : $i] : (((X4 @ X0) = X2) & (X5 @ X0)))))),
0.13/0.40	  file('/export/starexec/sandbox2/tmp/tmp.x7nx6qmTR1/E---3.1_30349.p',fun_image)).
0.13/0.40	thf(f90,plain,(
0.13/0.40	  (subset = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
0.13/0.40	  inference(cnf_transformation,[status(thm)],[f64])).
0.13/0.40	thf(f64,plain,(
0.13/0.40	  (subset = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
0.13/0.40	  inference(fool_elimination,[status(thm)],[f63])).
0.13/0.40	thf(f63,plain,(
0.13/0.40	  (subset = (^[X0 : $i > $o, X1 : $i > $o] : (! [X2 : $i] : ((X0 @ X2) => (X1 @ X2)))))),
0.13/0.40	  inference(rectify,[status(thm)],[f12])).
0.13/0.40	thf(f12,axiom,(
0.13/0.40	  (subset = (^[X0 : $i > $o, X2 : $i > $o] : (! [X3 : $i] : ((X0 @ X3) => (X2 @ X3)))))),
0.13/0.40	  file('/export/starexec/sandbox2/tmp/tmp.x7nx6qmTR1/E---3.1_30349.p',subset)).
0.13/0.40	thf(f86,plain,(
0.13/0.40	  ((subset @ (fun_image @ sK2 @ (intersection @ sK1 @ sK0)) @ (intersection @ (fun_image @ sK2 @ sK1) @ (fun_image @ sK2 @ sK0))) != $true)),
0.13/0.40	  inference(cnf_transformation,[status(thm)],[f71])).
0.13/0.40	thf(f71,plain,(
0.13/0.40	  ((subset @ (fun_image @ sK2 @ (intersection @ sK1 @ sK0)) @ (intersection @ (fun_image @ sK2 @ sK1) @ (fun_image @ sK2 @ sK0))) != $true)),
0.13/0.40	  inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f69,f70])).
0.13/0.40	thf(f70,plain,(
0.13/0.40	  ? [X0 : $i > $o,X1 : $i > $o,X2 : $i > $i] : ((subset @ (fun_image @ X2 @ (intersection @ X1 @ X0)) @ (intersection @ (fun_image @ X2 @ X1) @ (fun_image @ X2 @ X0))) != $true) => ((subset @ (fun_image @ sK2 @ (intersection @ sK1 @ sK0)) @ (intersection @ (fun_image @ sK2 @ sK1) @ (fun_image @ sK2 @ sK0))) != $true)),
0.13/0.40	  introduced(definition,[],[choice_axiom])).
0.13/0.40	thf(f69,plain,(
0.13/0.40	  ? [X0 : $i > $o,X1 : $i > $o,X2 : $i > $i] : ((subset @ (fun_image @ X2 @ (intersection @ X1 @ X0)) @ (intersection @ (fun_image @ X2 @ X1) @ (fun_image @ X2 @ X0))) != $true)),
0.13/0.40	  inference(ennf_transformation,[status(thm)],[f54])).
0.13/0.40	thf(f54,plain,(
0.13/0.40	  ~! [X0 : $i > $o,X1 : $i > $o,X2 : $i > $i] : ((subset @ (fun_image @ X2 @ (intersection @ X1 @ X0)) @ (intersection @ (fun_image @ X2 @ X1) @ (fun_image @ X2 @ X0))) = $true)),
0.13/0.40	  inference(fool_elimination,[status(thm)],[f53])).
0.13/0.40	thf(f53,plain,(
0.13/0.40	  ~! [X0 : $i > $o,X1 : $i > $o,X2 : $i > $i] : (subset @ (fun_image @ X2 @ (intersection @ X1 @ X0)) @ (intersection @ (fun_image @ X2 @ X1) @ (fun_image @ X2 @ X0)))),
0.13/0.40	  inference(rectify,[status(thm)],[f24])).
0.13/0.40	thf(f24,negated_conjecture,(
0.13/0.40	  ~! [X2 : $i > $o,X0 : $i > $o,X4 : $i > $i] : (subset @ (fun_image @ X4 @ (intersection @ X0 @ X2)) @ (intersection @ (fun_image @ X4 @ X0) @ (fun_image @ X4 @ X2)))),
0.13/0.40	  inference(negated_conjecture,[status(cth)],[f23])).
0.13/0.40	thf(f23,conjecture,(
0.13/0.40	  ! [X2 : $i > $o,X0 : $i > $o,X4 : $i > $i] : (subset @ (fun_image @ X4 @ (intersection @ X0 @ X2)) @ (intersection @ (fun_image @ X4 @ X0) @ (fun_image @ X4 @ X2)))),
0.13/0.40	  file('/export/starexec/sandbox2/tmp/tmp.x7nx6qmTR1/E---3.1_30349.p',thm)).
0.13/0.40	thf(f136,plain,(
0.13/0.40	  (sK4 != (sK2 @ sK5)) | ~spl3_1),
0.13/0.40	  inference(trivial_inequality_removal,[status(thm)],[f135])).
0.13/0.40	thf(f135,plain,(
0.13/0.40	  (sK4 != (sK2 @ sK5)) | ($false = $true) | ~spl3_1),
0.13/0.40	  inference(superposition,[status(thm)],[f107,f121])).
0.13/0.40	thf(f121,plain,(
0.13/0.40	  ( ! [X2 : $i] : (((sK0 @ X2) = $false) | (sK4 != (sK2 @ X2))) ) | ~spl3_1),
0.13/0.40	  inference(avatar_component_clause,[status(thm)],[f120])).
0.13/0.40	thf(f120,definition,(
0.13/0.40	  spl3_1 <=> ! [X2 : $i] : (((sK0 @ X2) = $false) | (sK4 != (sK2 @ X2)))),
0.13/0.40	  introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition])).
0.13/0.40	thf(f107,plain,(
0.13/0.40	  ((sK0 @ sK5) = $true)),
0.13/0.40	  inference(binary_proxy_clausification,[status(thm)],[f106])).
0.13/0.40	thf(f106,plain,(
0.13/0.40	  ($true = ((sK1 @ sK5) & (sK0 @ sK5)))),
0.13/0.40	  inference(binary_proxy_clausification,[status(thm)],[f104])).
0.13/0.40	thf(f133,plain,(
0.13/0.40	  ~spl3_2),
0.13/0.40	  inference(avatar_contradiction_clause,[status(thm)],[f132])).
0.13/0.40	thf(f132,plain,(
0.13/0.40	  $false | ~spl3_2),
0.13/0.40	  inference(subsumption_resolution,[status(thm)],[f128,f109])).
0.13/0.40	thf(f128,plain,(
0.13/0.40	  (sK4 != (sK2 @ sK5)) | ~spl3_2),
0.13/0.40	  inference(trivial_inequality_removal,[status(thm)],[f127])).
0.13/0.40	thf(f127,plain,(
0.13/0.40	  (sK4 != (sK2 @ sK5)) | ($false = $true) | ~spl3_2),
0.13/0.40	  inference(superposition,[status(thm)],[f124,f108])).
0.13/0.40	thf(f108,plain,(
0.13/0.40	  ((sK1 @ sK5) = $true)),
0.13/0.40	  inference(binary_proxy_clausification,[status(thm)],[f106])).
0.13/0.40	thf(f124,plain,(
0.13/0.40	  ( ! [X1 : $i] : (((sK1 @ X1) = $false) | ((sK2 @ X1) != sK4)) ) | ~spl3_2),
0.13/0.40	  inference(avatar_component_clause,[status(thm)],[f123])).
0.13/0.40	thf(f123,definition,(
0.13/0.40	  spl3_2 <=> ! [X1 : $i] : (((sK2 @ X1) != sK4) | ((sK1 @ X1) = $false))),
0.13/0.40	  introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition])).
0.13/0.40	thf(f125,plain,(
0.13/0.40	  spl3_1 | spl3_2),
0.13/0.40	  inference(avatar_split_clause,[status(thm)],[f118,f123,f120])).
0.13/0.40	thf(f118,plain,(
0.13/0.40	  ( ! [X2 : $i,X1 : $i] : (((sK2 @ X1) != sK4) | ((sK0 @ X2) = $false) | (sK4 != (sK2 @ X2)) | ((sK1 @ X1) = $false)) )),
0.13/0.40	  inference(equality_proxy_clausification,[status(thm)],[f117])).
0.13/0.40	thf(f117,plain,(
0.13/0.40	  ( ! [X2 : $i,X1 : $i] : (((sK0 @ X2) = $false) | ((sK1 @ X1) = $false) | ((sK2 @ X1) != sK4) | (((sK2 @ X2) = sK4) = $false)) )),
0.13/0.40	  inference(binary_proxy_clausification,[status(thm)],[f116])).
0.13/0.40	thf(f116,plain,(
0.13/0.40	  ( ! [X2 : $i,X1 : $i] : (((sK2 @ X1) != sK4) | ((sK1 @ X1) = $false) | (((sK0 @ X2) & ((sK2 @ X2) = sK4)) = $false)) )),
0.13/0.40	  inference(equality_proxy_clausification,[status(thm)],[f115])).
0.13/0.40	thf(f115,plain,(
0.13/0.40	  ( ! [X2 : $i,X1 : $i] : (((sK1 @ X1) = $false) | (((sK2 @ X1) = sK4) = $false) | (((sK0 @ X2) & ((sK2 @ X2) = sK4)) = $false)) )),
0.13/0.40	  inference(beta_eta_normalization,[status(thm)],[f114])).
0.13/0.40	thf(f114,plain,(
0.13/0.40	  ( ! [X2 : $i,X1 : $i] : (((sK1 @ X1) = $false) | (((^[Y0 : $i]: ((sK0 @ Y0) & ((sK2 @ Y0) = sK4))) @ X2) = $false) | (((sK2 @ X1) = sK4) = $false)) )),
0.13/0.40	  inference(pi_clausification,[status(thm)],[f113])).
0.13/0.40	thf(f113,plain,(
0.13/0.40	  ( ! [X1 : $i] : (($false = (?? @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) & ((sK2 @ Y0) = sK4))))) | ((sK1 @ X1) = $false) | (((sK2 @ X1) = sK4) = $false)) )),
0.13/0.40	  inference(binary_proxy_clausification,[status(thm)],[f112])).
0.13/0.40	thf(f112,plain,(
0.13/0.40	  ( ! [X1 : $i] : ((((sK1 @ X1) & ((sK2 @ X1) = sK4)) = $false) | ($false = (?? @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) & ((sK2 @ Y0) = sK4)))))) )),
0.13/0.40	  inference(beta_eta_normalization,[status(thm)],[f111])).
0.13/0.40	thf(f111,plain,(
0.13/0.40	  ( ! [X1 : $i] : ((((^[Y0 : $i]: ((sK1 @ Y0) & ((sK2 @ Y0) = sK4))) @ X1) = $false) | ($false = (?? @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) & ((sK2 @ Y0) = sK4)))))) )),
0.13/0.40	  inference(pi_clausification,[status(thm)],[f110])).
0.13/0.40	thf(f110,plain,(
0.13/0.40	  ($false = (?? @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) & ((sK2 @ Y0) = sK4))))) | ($false = (?? @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) & ((sK2 @ Y0) = sK4)))))),
0.13/0.40	  inference(binary_proxy_clausification,[status(thm)],[f101])).
0.13/0.40	thf(f101,plain,(
0.13/0.40	  (((?? @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) & ((sK2 @ Y0) = sK4)))) & (?? @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) & ((sK2 @ Y0) = sK4))))) = $false)),
0.13/0.40	  inference(binary_proxy_clausification,[status(thm)],[f100])).
0.13/0.40	% SZS output end Proof for E---3.1_30349
0.13/0.40	% (30542)------------------------------
0.13/0.40	% (30542)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.13/0.40	% (30542)Termination reason: Refutation
0.13/0.40	
0.13/0.40	% (30542)Memory used [KB]: 5628
0.13/0.40	% (30542)Time elapsed: 0.009 s
0.13/0.40	% (30542)Instructions burned: 7 (million)
0.13/0.40	% (30542)------------------------------
0.13/0.40	% (30542)------------------------------
0.13/0.40	% (30539)Success in time 0.016 s
0.29/0.41	EOF