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
0.10/0.35	% Computer   : n015.cluster.edu
0.10/0.35	% Model      : x86_64 x86_64
0.10/0.35	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.10/0.35	% Memory     : 8046.5625MB
0.10/0.35	% OS         : Linux 6.8.0-71-generic
0.10/0.35	% CPULimit   : 1440
0.10/0.35	% WCLimit    : 180
0.10/0.35	% DateTime   : Mon Jul 27 11:54:34 UTC 2026
0.14/0.36	% CPUTime    : 
0.14/0.39	This is a THF_ problem
0.14/0.39	Running higher-order theorem proving
0.14/0.40	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.8dWzseZ5vn/E---3.1_972716.p -m 16384 -t 180
0.14/0.44	% (972761)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_972716 for (1799ds/4Mi)
0.14/0.44	% (972761)Instruction limit reached!
0.14/0.44	% (972761)------------------------------
0.14/0.44	% (972761)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.14/0.44	% (972761)Termination reason: Unknown
0.14/0.44	% (972761)Termination phase: Saturation
0.14/0.44	
0.14/0.44	% (972761)Memory used [KB]: 1023
0.14/0.44	% (972761)Time elapsed: 0.003 s
0.14/0.44	% (972761)Instructions burned: 4 (million)
0.14/0.44	% (972761)------------------------------
0.14/0.44	% (972761)------------------------------
0.14/0.44	% (972760)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on E---3.1_972716 for (1799ds/183Mi)
0.14/0.44	% (972762)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_972716 for (1799ds/27Mi)
0.14/0.44	% (972763)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on E---3.1_972716 for (1799ds/2Mi)
0.14/0.44	% (972764)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_972716 for (1799ds/2Mi)
0.14/0.45	% (972763)Instruction limit reached!
0.14/0.45	% (972763)------------------------------
0.14/0.45	% (972763)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.14/0.45	% (972763)Termination reason: Unknown
0.14/0.45	% (972763)Termination phase: Property scanning
0.14/0.45	
0.14/0.45	% (972763)Memory used [KB]: 1023
0.14/0.45	% (972763)Time elapsed: 0.004 s
0.14/0.45	% (972763)Instructions burned: 3 (million)
0.14/0.45	% (972763)------------------------------
0.14/0.45	% (972763)------------------------------
0.14/0.45	% (972764)Instruction limit reached!
0.14/0.45	% (972764)------------------------------
0.14/0.45	% (972764)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.14/0.45	% (972764)Termination reason: Unknown
0.14/0.45	% (972764)Termination phase: Property scanning
0.14/0.45	
0.14/0.45	% (972764)Memory used [KB]: 1023
0.14/0.45	% (972764)Time elapsed: 0.004 s
0.14/0.45	% (972764)Instructions burned: 3 (million)
0.14/0.45	% (972764)------------------------------
0.14/0.45	% (972764)------------------------------
0.14/0.45	% (972767)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_972716 for (1799ds/3Mi)
0.14/0.45	% (972767)Instruction limit reached!
0.14/0.45	% (972767)------------------------------
0.14/0.45	% (972767)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.14/0.45	% (972767)Termination reason: Unknown
0.14/0.45	% (972767)Termination phase: Property scanning
0.14/0.45	
0.14/0.45	% (972767)Memory used [KB]: 1023
0.14/0.45	% (972767)Time elapsed: 0.002 s
0.14/0.45	% (972767)Instructions burned: 3 (million)
0.14/0.45	% (972767)------------------------------
0.14/0.45	% (972767)------------------------------
0.25/0.46	% (972770)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on E---3.1_972716 for (1799ds/3Mi)
0.25/0.46	% (972762)First to succeed.
0.25/0.46	% (972770)Instruction limit reached!
0.25/0.46	% (972770)------------------------------
0.25/0.46	% (972770)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.25/0.46	% (972770)Termination reason: Unknown
0.25/0.46	% (972770)Termination phase: Property scanning
0.25/0.46	
0.25/0.46	% (972770)Memory used [KB]: 1023
0.25/0.46	% (972770)Time elapsed: 0.002 s
0.25/0.46	% (972770)Instructions burned: 3 (million)
0.25/0.46	% (972770)------------------------------
0.25/0.46	% (972770)------------------------------
0.25/0.46	% (972766)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on E---3.1_972716 for (1799ds/18Mi)
0.25/0.46	% (972765)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_972716 for (1799ds/275Mi)
0.25/0.46	% (972762)Refutation found. Thanks to Tanya!
0.25/0.46	% SZS status Theorem for E---3.1_972716
0.25/0.46	% SZS output start Proof for E---3.1_972716
0.25/0.46	thf(func_def_0, type, fun_image: ($i > $i) > ($i > $o) > $i > $o).
0.25/0.46	thf(func_def_2, type, fun_composition: ($i > $i) > ($i > $i) > $i > $i).
0.25/0.46	thf(func_def_3, type, fun_inv_image: ($i > $i) > ($i > $o) > $i > $o).
0.25/0.46	thf(func_def_4, type, fun_injective: ($i > $i) > $o).
0.25/0.46	thf(func_def_5, type, fun_surjective: ($i > $i) > $o).
0.25/0.46	thf(func_def_6, type, fun_bijective: ($i > $i) > $o).
0.25/0.46	thf(func_def_7, type, fun_decreasing: ($i > $i) > ($i > $i > $o) > $o).
0.25/0.46	thf(func_def_8, type, fun_increasing: ($i > $i) > ($i > $i > $o) > $o).
0.25/0.46	thf(func_def_9, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
0.25/0.46	thf(func_def_22, type, sK0: $i > $i).
0.25/0.46	thf(func_def_23, type, sK1: $i > $i).
0.25/0.46	thf(func_def_24, type, sK2: $i > $i).
0.25/0.46	thf(func_def_29, type, sK7: $i > $i).
0.25/0.46	thf(func_def_30, type, sK8: $i > $i).
0.25/0.46	thf(f160,plain,(
0.25/0.46	  $false),
0.25/0.46	  inference(avatar_sat_refutation,[status(thm)],[f94,f99,f116,f150])).
0.25/0.46	thf(f150,plain,(
0.25/0.46	  spl3_1 | ~spl3_3),
0.25/0.46	  inference(avatar_split_clause,[status(thm)],[f149,f96,f88])).
0.25/0.46	thf(f88,definition,(
0.25/0.46	  spl3_1 <=> (sK4 = sK6)),
0.25/0.46	  introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition])).
0.25/0.46	thf(f96,definition,(
0.25/0.46	  spl3_3 <=> ((sK2 @ sK6) = (sK2 @ sK4))),
0.25/0.46	  introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition])).
0.25/0.46	thf(f149,plain,(
0.25/0.46	  (sK4 = sK6) | ~spl3_3),
0.25/0.46	  inference(forward_demodulation,[status(thm)],[f144,f72])).
0.25/0.46	thf(f72,plain,(
0.25/0.46	  ( ! [X1 : $i] : (((sK1 @ (sK0 @ (sK2 @ (sK7 @ X1)))) = X1)) )),
0.25/0.46	  inference(equality_proxy_clausification,[status(thm)],[f71])).
0.25/0.46	thf(f71,plain,(
0.25/0.46	  ( ! [X1 : $i] : (($true = ((sK1 @ (sK0 @ (sK2 @ (sK7 @ X1)))) = X1))) )),
0.25/0.46	  inference(beta_eta_normalization,[status(thm)],[f70])).
0.25/0.46	thf(f70,plain,(
0.25/0.46	  ( ! [X1 : $i] : ((((^[Y0 : $i]: ((sK1 @ (sK0 @ (sK2 @ Y0))) = X1)) @ (sK7 @ X1)) = $true)) )),
0.25/0.46	  inference(sigma_clausification,[status(thm)],[f69])).
0.25/0.46	thf(f69,plain,(
0.25/0.46	  ( ! [X1 : $i] : (((?? @ $i @ (^[Y0 : $i]: ((sK1 @ (sK0 @ (sK2 @ Y0))) = X1))) = $true)) )),
0.25/0.46	  inference(beta_eta_normalization,[status(thm)],[f68])).
0.25/0.46	thf(f68,plain,(
0.25/0.46	  ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((sK1 @ (sK0 @ (sK2 @ Y1))) = Y0)))) @ X1))) )),
0.25/0.46	  inference(pi_clausification,[status(thm)],[f67])).
0.25/0.46	thf(f67,plain,(
0.25/0.46	  ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((sK1 @ (sK0 @ (sK2 @ Y1))) = Y0))))) = $true)),
0.25/0.46	  inference(beta_eta_normalization,[status(thm)],[f50])).
0.25/0.46	thf(f50,plain,(
0.25/0.46	  (((^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = Y1)))))) @ ((^[Y0 : $i > $i]: ((^[Y1 : $i > $i]: ((^[Y2 : $i]: (Y1 @ (Y0 @ Y2))))))) @ ((^[Y0 : $i > $i]: ((^[Y1 : $i > $i]: ((^[Y2 : $i]: (Y1 @ (Y0 @ Y2))))))) @ sK2 @ sK0) @ sK1)) = $true)),
0.25/0.46	  inference(definition_unfolding,[status(thm)],[f42,f37,f39,f39])).
0.25/0.46	thf(f39,plain,(
0.25/0.46	  (fun_composition = (^[Y0 : $i > $i]: ((^[Y1 : $i > $i]: ((^[Y2 : $i]: (Y1 @ (Y0 @ Y2))))))))),
0.25/0.46	  inference(cnf_transformation,[status(thm)],[f17])).
0.25/0.46	thf(f17,plain,(
0.25/0.46	  (fun_composition = (^[Y0 : $i > $i]: ((^[Y1 : $i > $i]: ((^[Y2 : $i]: (Y1 @ (Y0 @ Y2))))))))),
0.25/0.46	  inference(fool_elimination,[status(thm)],[f16])).
0.25/0.46	thf(f16,plain,(
0.25/0.46	  ((^[X0 : $i > $i, X1 : $i > $i, X2 : $i] : (X1 @ (X0 @ X2))) = fun_composition)),
0.25/0.46	  inference(rectify,[status(thm)],[f2])).
0.25/0.46	thf(f2,axiom,(
0.25/0.46	  ((^[X0 : $i > $i, X4 : $i > $i, X3 : $i] : (X4 @ (X0 @ X3))) = fun_composition)),
0.25/0.46	  file('/export/starexec/sandbox2/tmp/tmp.8dWzseZ5vn/E---3.1_972716.p',fun_composition)).
0.25/0.46	thf(f37,plain,(
0.25/0.46	  (fun_surjective = (^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = Y1)))))))),
0.25/0.46	  inference(cnf_transformation,[status(thm)],[f29])).
0.25/0.46	thf(f29,plain,(
0.25/0.46	  (fun_surjective = (^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = Y1)))))))),
0.25/0.46	  inference(fool_elimination,[status(thm)],[f28])).
0.25/0.46	thf(f28,plain,(
0.25/0.46	  ((^[X0 : $i > $i] : (! [X1 : $i] : ? [X2 : $i] : ((X0 @ X2) = X1))) = fun_surjective)),
0.25/0.46	  inference(rectify,[status(thm)],[f5])).
0.25/0.46	thf(f5,axiom,(
0.25/0.46	  ((^[X0 : $i > $i] : (! [X2 : $i] : ? [X3 : $i] : ((X0 @ X3) = X2))) = fun_surjective)),
0.25/0.46	  file('/export/starexec/sandbox2/tmp/tmp.8dWzseZ5vn/E---3.1_972716.p',fun_surjective)).
0.25/0.46	thf(f42,plain,(
0.25/0.46	  ($true = (fun_surjective @ (fun_composition @ (fun_composition @ sK2 @ sK0) @ sK1)))),
0.25/0.46	  inference(cnf_transformation,[status(thm)],[f33])).
0.25/0.46	thf(f33,plain,(
0.25/0.46	  ((fun_injective @ (fun_composition @ (fun_composition @ sK0 @ sK1) @ sK2)) = $true) & ((fun_surjective @ (fun_composition @ (fun_composition @ sK1 @ sK2) @ sK0)) = $true) & ((fun_bijective @ sK2) != $true) & ($true = (fun_surjective @ (fun_composition @ (fun_composition @ sK2 @ sK0) @ sK1)))),
0.25/0.46	  inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f31,f32])).
0.25/0.46	thf(f32,plain,(
0.25/0.46	  ? [X0 : $i > $i,X1 : $i > $i,X2 : $i > $i] : (((fun_injective @ (fun_composition @ (fun_composition @ X0 @ X1) @ X2)) = $true) & ($true = (fun_surjective @ (fun_composition @ (fun_composition @ X1 @ X2) @ X0))) & ((fun_bijective @ X2) != $true) & ((fun_surjective @ (fun_composition @ (fun_composition @ X2 @ X0) @ X1)) = $true)) => (((fun_injective @ (fun_composition @ (fun_composition @ sK0 @ sK1) @ sK2)) = $true) & ((fun_surjective @ (fun_composition @ (fun_composition @ sK1 @ sK2) @ sK0)) = $true) & ((fun_bijective @ sK2) != $true) & ($true = (fun_surjective @ (fun_composition @ (fun_composition @ sK2 @ sK0) @ sK1))))),
0.25/0.46	  introduced(definition,[],[choice_axiom])).
0.25/0.46	thf(f31,plain,(
0.25/0.46	  ? [X0 : $i > $i,X1 : $i > $i,X2 : $i > $i] : (((fun_injective @ (fun_composition @ (fun_composition @ X0 @ X1) @ X2)) = $true) & ($true = (fun_surjective @ (fun_composition @ (fun_composition @ X1 @ X2) @ X0))) & ((fun_bijective @ X2) != $true) & ((fun_surjective @ (fun_composition @ (fun_composition @ X2 @ X0) @ X1)) = $true))),
0.25/0.46	  inference(flattening,[status(thm)],[f30])).
0.25/0.46	thf(f30,plain,(
0.25/0.46	  ? [X0 : $i > $i,X1 : $i > $i,X2 : $i > $i] : (((fun_bijective @ X2) != $true) & (($true = (fun_surjective @ (fun_composition @ (fun_composition @ X1 @ X2) @ X0))) & ((fun_injective @ (fun_composition @ (fun_composition @ X0 @ X1) @ X2)) = $true) & ((fun_surjective @ (fun_composition @ (fun_composition @ X2 @ X0) @ X1)) = $true)))),
0.25/0.46	  inference(ennf_transformation,[status(thm)],[f21])).
0.25/0.46	thf(f21,plain,(
0.25/0.46	  ~! [X0 : $i > $i,X1 : $i > $i,X2 : $i > $i] : ((($true = (fun_surjective @ (fun_composition @ (fun_composition @ X1 @ X2) @ X0))) & ((fun_injective @ (fun_composition @ (fun_composition @ X0 @ X1) @ X2)) = $true) & ((fun_surjective @ (fun_composition @ (fun_composition @ X2 @ X0) @ X1)) = $true)) => ((fun_bijective @ X2) = $true))),
0.25/0.46	  inference(fool_elimination,[status(thm)],[f20])).
0.25/0.46	thf(f20,plain,(
0.25/0.46	  ~! [X0 : $i > $i,X1 : $i > $i,X2 : $i > $i] : (((fun_injective @ (fun_composition @ (fun_composition @ X0 @ X1) @ X2)) & (fun_surjective @ (fun_composition @ (fun_composition @ X2 @ X0) @ X1)) & (fun_surjective @ (fun_composition @ (fun_composition @ X1 @ X2) @ X0))) => (fun_bijective @ X2))),
0.25/0.46	  inference(rectify,[status(thm)],[f10])).
0.25/0.46	thf(f10,negated_conjecture,(
0.25/0.46	  ~! [X0 : $i > $i,X4 : $i > $i,X7 : $i > $i] : (((fun_injective @ (fun_composition @ (fun_composition @ X0 @ X4) @ X7)) & (fun_surjective @ (fun_composition @ (fun_composition @ X7 @ X0) @ X4)) & (fun_surjective @ (fun_composition @ (fun_composition @ X4 @ X7) @ X0))) => (fun_bijective @ X7))),
0.25/0.46	  inference(negated_conjecture,[status(cth)],[f9])).
0.25/0.46	thf(f9,conjecture,(
0.25/0.46	  ! [X0 : $i > $i,X4 : $i > $i,X7 : $i > $i] : (((fun_injective @ (fun_composition @ (fun_composition @ X0 @ X4) @ X7)) & (fun_surjective @ (fun_composition @ (fun_composition @ X7 @ X0) @ X4)) & (fun_surjective @ (fun_composition @ (fun_composition @ X4 @ X7) @ X0))) => (fun_bijective @ X7))),
0.25/0.46	  file('/export/starexec/sandbox2/tmp/tmp.8dWzseZ5vn/E---3.1_972716.p',thm)).
0.25/0.46	thf(f144,plain,(
0.25/0.46	  ((sK1 @ (sK0 @ (sK2 @ (sK7 @ sK4)))) = sK6) | ~spl3_3),
0.25/0.46	  inference(superposition,[status(thm)],[f72,f143])).
0.25/0.46	thf(f143,plain,(
0.25/0.46	  ((sK2 @ (sK7 @ sK6)) = (sK2 @ (sK7 @ sK4))) | ~spl3_3),
0.25/0.46	  inference(equality_resolution,[status(thm)],[f127])).
0.25/0.46	thf(f127,plain,(
0.25/0.46	  ( ! [X0 : $i] : (((sK2 @ sK4) != (sK2 @ X0)) | ((sK2 @ (sK7 @ sK6)) = (sK2 @ (sK7 @ X0)))) ) | ~spl3_3),
0.25/0.46	  inference(superposition,[status(thm)],[f106,f98])).
0.25/0.46	thf(f98,plain,(
0.25/0.46	  ((sK2 @ sK6) = (sK2 @ sK4)) | ~spl3_3),
0.25/0.46	  inference(avatar_component_clause,[status(thm)],[f96])).
0.25/0.46	thf(f106,plain,(
0.25/0.46	  ( ! [X0 : $i,X1 : $i] : (((sK2 @ X0) != (sK2 @ X1)) | ((sK2 @ (sK7 @ X1)) = (sK2 @ (sK7 @ X0)))) )),
0.25/0.46	  inference(superposition,[status(thm)],[f101,f72])).
0.25/0.46	thf(f101,plain,(
0.25/0.46	  ( ! [X0 : $i,X1 : $i] : (((sK2 @ (sK1 @ (sK0 @ X1))) != (sK2 @ X0)) | ((sK2 @ (sK7 @ X0)) = X1)) )),
0.25/0.46	  inference(superposition,[status(thm)],[f86,f72])).
0.25/0.46	thf(f86,plain,(
0.25/0.46	  ( ! [X2 : $i,X1 : $i] : (((sK2 @ (sK1 @ (sK0 @ X1))) != (sK2 @ (sK1 @ (sK0 @ X2)))) | (X1 = X2)) )),
0.25/0.46	  inference(equality_proxy_clausification,[status(thm)],[f85])).
0.25/0.46	thf(f85,plain,(
0.25/0.46	  ( ! [X2 : $i,X1 : $i] : ((X1 = X2) | ($false = ((sK2 @ (sK1 @ (sK0 @ X1))) = (sK2 @ (sK1 @ (sK0 @ X2)))))) )),
0.25/0.46	  inference(equality_proxy_clausification,[status(thm)],[f84])).
0.25/0.46	thf(f84,plain,(
0.25/0.46	  ( ! [X2 : $i,X1 : $i] : (((X2 = X1) = $true) | ($false = ((sK2 @ (sK1 @ (sK0 @ X1))) = (sK2 @ (sK1 @ (sK0 @ X2)))))) )),
0.25/0.46	  inference(binary_proxy_clausification,[status(thm)],[f83])).
0.25/0.46	thf(f83,plain,(
0.25/0.46	  ( ! [X2 : $i,X1 : $i] : (((((sK2 @ (sK1 @ (sK0 @ X1))) = (sK2 @ (sK1 @ (sK0 @ X2)))) => (X2 = X1)) = $true)) )),
0.25/0.46	  inference(beta_eta_normalization,[status(thm)],[f82])).
0.25/0.46	thf(f82,plain,(
0.25/0.46	  ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (((sK2 @ (sK1 @ (sK0 @ X1))) = (sK2 @ (sK1 @ (sK0 @ Y0)))) => (Y0 = X1))) @ X2) = $true)) )),
0.25/0.46	  inference(pi_clausification,[status(thm)],[f81])).
0.25/0.46	thf(f81,plain,(
0.25/0.46	  ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (((sK2 @ (sK1 @ (sK0 @ X1))) = (sK2 @ (sK1 @ (sK0 @ Y0)))) => (Y0 = X1)))))) )),
0.25/0.46	  inference(beta_eta_normalization,[status(thm)],[f80])).
0.25/0.46	thf(f80,plain,(
0.25/0.46	  ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((sK2 @ (sK1 @ (sK0 @ Y0))) = (sK2 @ (sK1 @ (sK0 @ Y1)))) => (Y1 = Y0))))) @ X1) = $true)) )),
0.25/0.46	  inference(pi_clausification,[status(thm)],[f79])).
0.25/0.46	thf(f79,plain,(
0.25/0.46	  ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((sK2 @ (sK1 @ (sK0 @ Y0))) = (sK2 @ (sK1 @ (sK0 @ Y1)))) => (Y1 = Y0)))))) = $true)),
0.25/0.46	  inference(beta_eta_normalization,[status(thm)],[f47])).
0.25/0.46	thf(f47,plain,(
0.25/0.46	  (((^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((Y0 @ Y1) = (Y0 @ Y2)) => (Y2 = Y1))))))) @ ((^[Y0 : $i > $i]: ((^[Y1 : $i > $i]: ((^[Y2 : $i]: (Y1 @ (Y0 @ Y2))))))) @ ((^[Y0 : $i > $i]: ((^[Y1 : $i > $i]: ((^[Y2 : $i]: (Y1 @ (Y0 @ Y2))))))) @ sK0 @ sK1) @ sK2)) = $true)),
0.25/0.46	  inference(definition_unfolding,[status(thm)],[f45,f38,f39,f39])).
0.25/0.46	thf(f38,plain,(
0.25/0.46	  (fun_injective = (^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((Y0 @ Y1) = (Y0 @ Y2)) => (Y2 = Y1))))))))),
0.25/0.46	  inference(cnf_transformation,[status(thm)],[f15])).
0.25/0.46	thf(f15,plain,(
0.25/0.46	  (fun_injective = (^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((Y0 @ Y1) = (Y0 @ Y2)) => (Y2 = Y1))))))))),
0.25/0.46	  inference(fool_elimination,[status(thm)],[f14])).
0.25/0.46	thf(f14,plain,(
0.25/0.46	  (fun_injective = (^[X0 : $i > $i] : (! [X1 : $i,X2 : $i] : (((X0 @ X2) = (X0 @ X1)) => (X1 = X2)))))),
0.25/0.46	  inference(rectify,[status(thm)],[f4])).
0.25/0.46	thf(f4,axiom,(
0.25/0.46	  (fun_injective = (^[X0 : $i > $i] : (! [X3 : $i,X2 : $i] : (((X0 @ X3) = (X0 @ X2)) => (X2 = X3)))))),
0.25/0.46	  file('/export/starexec/sandbox2/tmp/tmp.8dWzseZ5vn/E---3.1_972716.p',fun_injective)).
0.25/0.46	thf(f45,plain,(
0.25/0.46	  ((fun_injective @ (fun_composition @ (fun_composition @ sK0 @ sK1) @ sK2)) = $true)),
0.25/0.46	  inference(cnf_transformation,[status(thm)],[f33])).
0.25/0.46	thf(f116,plain,(
0.25/0.46	  ~spl3_2),
0.25/0.46	  inference(avatar_contradiction_clause,[status(thm)],[f115])).
0.25/0.46	thf(f115,plain,(
0.25/0.46	  $false | ~spl3_2),
0.25/0.46	  inference(equality_resolution,[status(thm)],[f110])).
0.25/0.46	thf(f110,plain,(
0.25/0.46	  ( ! [X0 : $i] : ((sK5 != X0)) ) | ~spl3_2),
0.25/0.46	  inference(superposition,[status(thm)],[f93,f107])).
0.25/0.46	thf(f107,plain,(
0.25/0.46	  ( ! [X0 : $i] : (((sK2 @ (sK7 @ (sK1 @ (sK0 @ X0)))) = X0)) )),
0.25/0.46	  inference(equality_resolution,[status(thm)],[f101])).
0.25/0.46	thf(f93,plain,(
0.25/0.46	  ( ! [X1 : $i] : ((sK5 != (sK2 @ X1))) ) | ~spl3_2),
0.25/0.46	  inference(avatar_component_clause,[status(thm)],[f92])).
0.25/0.46	thf(f92,definition,(
0.25/0.46	  spl3_2 <=> ! [X1 : $i] : (sK5 != (sK2 @ X1))),
0.25/0.46	  introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition])).
0.25/0.46	thf(f99,plain,(
0.25/0.46	  spl3_2 | spl3_3),
0.25/0.46	  inference(avatar_split_clause,[status(thm)],[f64,f96,f92])).
0.25/0.46	thf(f64,plain,(
0.25/0.46	  ( ! [X1 : $i] : ((sK5 != (sK2 @ X1)) | ((sK2 @ sK6) = (sK2 @ sK4))) )),
0.25/0.46	  inference(equality_proxy_clausification,[status(thm)],[f63])).
0.25/0.46	thf(f63,plain,(
0.25/0.46	  ( ! [X1 : $i] : ((sK5 != (sK2 @ X1)) | (((sK2 @ sK4) = (sK2 @ sK6)) = $true)) )),
0.25/0.46	  inference(equality_proxy_clausification,[status(thm)],[f62])).
0.25/0.46	thf(f62,plain,(
0.25/0.46	  ( ! [X1 : $i] : (($false = ((sK2 @ X1) = sK5)) | (((sK2 @ sK4) = (sK2 @ sK6)) = $true)) )),
0.25/0.46	  inference(binary_proxy_clausification,[status(thm)],[f60])).
0.25/0.46	thf(f60,plain,(
0.25/0.46	  ( ! [X1 : $i] : (($false = (((sK2 @ sK4) = (sK2 @ sK6)) => (sK6 = sK4))) | ($false = ((sK2 @ X1) = sK5))) )),
0.25/0.46	  inference(beta_eta_normalization,[status(thm)],[f59])).
0.25/0.46	thf(f59,plain,(
0.25/0.46	  ( ! [X1 : $i] : ((((^[Y0 : $i]: (((sK2 @ sK4) = (sK2 @ Y0)) => (Y0 = sK4))) @ sK6) = $false) | ($false = ((sK2 @ X1) = sK5))) )),
0.25/0.46	  inference(sigma_clausification,[status(thm)],[f58])).
0.25/0.46	thf(f58,plain,(
0.25/0.46	  ( ! [X1 : $i] : (($false = (!! @ $i @ (^[Y0 : $i]: (((sK2 @ sK4) = (sK2 @ Y0)) => (Y0 = sK4))))) | ($false = ((sK2 @ X1) = sK5))) )),
0.25/0.46	  inference(beta_eta_normalization,[status(thm)],[f57])).
0.25/0.46	thf(f57,plain,(
0.25/0.46	  ( ! [X1 : $i] : (($false = (!! @ $i @ (^[Y0 : $i]: (((sK2 @ sK4) = (sK2 @ Y0)) => (Y0 = sK4))))) | (((^[Y0 : $i]: ((sK2 @ Y0) = sK5)) @ X1) = $false)) )),
0.25/0.46	  inference(pi_clausification,[status(thm)],[f56])).
0.25/0.46	thf(f56,plain,(
0.25/0.46	  ((?? @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) = sK5))) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: (((sK2 @ sK4) = (sK2 @ Y0)) => (Y0 = sK4)))))),
0.25/0.46	  inference(beta_eta_normalization,[status(thm)],[f55])).
0.25/0.46	thf(f55,plain,(
0.25/0.46	  ($false = (!! @ $i @ (^[Y0 : $i]: (((sK2 @ sK4) = (sK2 @ Y0)) => (Y0 = sK4))))) | ($false = ((^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((sK2 @ Y1) = Y0)))) @ sK5))),
0.25/0.46	  inference(sigma_clausification,[status(thm)],[f54])).
0.25/0.46	thf(f54,plain,(
0.25/0.46	  ($false = (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((sK2 @ Y1) = Y0)))))) | ($false = (!! @ $i @ (^[Y0 : $i]: (((sK2 @ sK4) = (sK2 @ Y0)) => (Y0 = sK4)))))),
0.25/0.46	  inference(beta_eta_normalization,[status(thm)],[f53])).
0.25/0.46	thf(f53,plain,(
0.25/0.46	  (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((sK2 @ Y0) = (sK2 @ Y1)) => (Y1 = Y0))))) @ sK4) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((sK2 @ Y1) = Y0))))))),
0.25/0.46	  inference(sigma_clausification,[status(thm)],[f52])).
0.25/0.46	thf(f52,plain,(
0.25/0.46	  ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((sK2 @ Y0) = (sK2 @ Y1)) => (Y1 = Y0)))))) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((sK2 @ Y1) = Y0))))))),
0.25/0.46	  inference(binary_proxy_clausification,[status(thm)],[f51])).
0.25/0.46	thf(f51,plain,(
0.25/0.46	  (((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((sK2 @ Y1) = Y0))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((sK2 @ Y0) = (sK2 @ Y1)) => (Y1 = Y0))))))) != $true)),
0.25/0.46	  inference(beta_eta_normalization,[status(thm)],[f49])).
0.25/0.46	thf(f49,plain,(
0.25/0.46	  (((^[Y0 : $i > $i]: (((^[Y1 : $i > $i]: (!! @ $i @ (^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) = Y2)))))) @ Y0) & ((^[Y1 : $i > $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y1 @ Y2) = (Y1 @ Y3)) => (Y3 = Y2))))))) @ Y0))) @ sK2) != $true)),
0.25/0.46	  inference(definition_unfolding,[status(thm)],[f43,f46])).
0.25/0.46	thf(f46,plain,(
0.25/0.46	  (fun_bijective = (^[Y0 : $i > $i]: (((^[Y1 : $i > $i]: (!! @ $i @ (^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) = Y2)))))) @ Y0) & ((^[Y1 : $i > $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y1 @ Y2) = (Y1 @ Y3)) => (Y3 = Y2))))))) @ Y0))))),
0.25/0.46	  inference(definition_unfolding,[status(thm)],[f40,f37,f38])).
0.25/0.46	thf(f40,plain,(
0.25/0.46	  (fun_bijective = (^[Y0 : $i > $i]: ((fun_surjective @ Y0) & (fun_injective @ Y0))))),
0.25/0.46	  inference(cnf_transformation,[status(thm)],[f23])).
0.25/0.46	thf(f23,plain,(
0.25/0.46	  (fun_bijective = (^[Y0 : $i > $i]: ((fun_surjective @ Y0) & (fun_injective @ Y0))))),
0.25/0.46	  inference(fool_elimination,[status(thm)],[f22])).
0.25/0.46	thf(f22,plain,(
0.25/0.46	  (fun_bijective = (^[X0 : $i > $i] : ((fun_injective @ X0) & (fun_surjective @ X0))))),
0.25/0.46	  inference(rectify,[status(thm)],[f6])).
0.25/0.46	thf(f6,axiom,(
0.25/0.46	  (fun_bijective = (^[X0 : $i > $i] : ((fun_injective @ X0) & (fun_surjective @ X0))))),
0.25/0.46	  file('/export/starexec/sandbox2/tmp/tmp.8dWzseZ5vn/E---3.1_972716.p',fun_bijective)).
0.25/0.46	thf(f43,plain,(
0.25/0.46	  ((fun_bijective @ sK2) != $true)),
0.25/0.46	  inference(cnf_transformation,[status(thm)],[f33])).
0.25/0.46	thf(f94,plain,(
0.25/0.46	  ~spl3_1 | spl3_2),
0.25/0.46	  inference(avatar_split_clause,[status(thm)],[f66,f92,f88])).
0.25/0.46	thf(f66,plain,(
0.25/0.46	  ( ! [X1 : $i] : ((sK4 != sK6) | (sK5 != (sK2 @ X1))) )),
0.25/0.46	  inference(equality_proxy_clausification,[status(thm)],[f65])).
0.25/0.46	thf(f65,plain,(
0.25/0.46	  ( ! [X1 : $i] : (($false = (sK6 = sK4)) | (sK5 != (sK2 @ X1))) )),
0.25/0.46	  inference(equality_proxy_clausification,[status(thm)],[f61])).
0.25/0.46	thf(f61,plain,(
0.25/0.46	  ( ! [X1 : $i] : (($false = ((sK2 @ X1) = sK5)) | ($false = (sK6 = sK4))) )),
0.25/0.46	  inference(binary_proxy_clausification,[status(thm)],[f60])).
0.25/0.46	% SZS output end Proof for E---3.1_972716
0.25/0.46	% (972762)------------------------------
0.25/0.46	% (972762)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.25/0.46	% (972762)Termination reason: Refutation
0.25/0.46	
0.25/0.46	% (972762)Memory used [KB]: 5628
0.25/0.46	% (972762)Time elapsed: 0.019 s
0.25/0.46	% (972762)Instructions burned: 21 (million)
0.25/0.46	% (972762)------------------------------
0.25/0.46	% (972762)------------------------------
0.25/0.46	% (972759)Success in time 0.033 s
0.25/0.46	EOF