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
0.08/0.34	% Computer   : n022.cluster.edu
0.08/0.34	% Model      : x86_64 x86_64
0.08/0.34	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.08/0.34	% Memory     : 8046.5625MB
0.08/0.34	% OS         : Linux 6.8.0-71-generic
0.08/0.34	% CPULimit   : 1440
0.08/0.34	% WCLimit    : 180
0.08/0.34	% DateTime   : Mon Jul 27 12:07:13 UTC 2026
0.08/0.35	% CPUTime    : 
0.08/0.40	This is a THF_ problem
0.08/0.40	Running higher-order theorem proving
0.17/0.45	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.jN269shynw/E---3.1_857315.p -m 16384 -t 180
0.17/0.52	% (857403)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_857315 for (1799ds/275Mi)
0.17/0.53	% (857403)Refutation not found, incomplete strategy
0.17/0.53	% (857403)------------------------------
0.17/0.53	% (857403)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.17/0.53	% (857403)Termination reason: Refutation not found, incomplete strategy
0.17/0.53	
0.17/0.53	
0.17/0.53	% (857403)Memory used [KB]: 5628
0.17/0.53	% (857403)Time elapsed: 0.036 s
0.17/0.53	% (857403)Instructions burned: 14 (million)
0.17/0.53	% (857403)------------------------------
0.17/0.53	% (857403)------------------------------
0.17/0.53	% (857400)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_857315 for (1799ds/27Mi)
0.17/0.53	% (857398)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on E---3.1_857315 for (1799ds/183Mi)
0.17/0.55	% (857400)Instruction limit reached!
0.17/0.55	% (857400)------------------------------
0.17/0.55	% (857400)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.17/0.55	% (857400)Termination reason: Unknown
0.17/0.55	% (857400)Termination phase: Saturation
0.17/0.55	
0.17/0.55	% (857400)Memory used [KB]: 5756
0.17/0.55	% (857400)Time elapsed: 0.027 s
0.17/0.55	% (857400)Instructions burned: 27 (million)
0.17/0.55	% (857400)------------------------------
0.17/0.55	% (857400)------------------------------
0.17/0.57	% (857406)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on E---3.1_857315 for (1799ds/37Mi)
0.17/0.57	% (857399)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_857315 for (1799ds/4Mi)
0.17/0.58	% (857401)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on E---3.1_857315 for (1799ds/2Mi)
0.17/0.58	% (857404)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on E---3.1_857315 for (1799ds/18Mi)
0.17/0.58	% (857402)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_857315 for (1799ds/2Mi)
0.17/0.58	% (857399)Instruction limit reached!
0.17/0.58	% (857399)------------------------------
0.17/0.58	% (857399)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.17/0.58	% (857399)Termination reason: Unknown
0.17/0.58	% (857399)Termination phase: shuffling
0.17/0.58	
0.17/0.58	% (857399)Memory used [KB]: 1151
0.17/0.58	% (857399)Time elapsed: 0.008 s
0.17/0.58	% (857399)Instructions burned: 4 (million)
0.17/0.58	% (857399)------------------------------
0.17/0.58	% (857399)------------------------------
0.17/0.58	% (857402)Instruction limit reached!
0.17/0.58	% (857402)------------------------------
0.17/0.58	% (857402)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.17/0.58	% (857402)Termination reason: Unknown
0.17/0.58	% (857402)Termination phase: shuffling
0.17/0.58	
0.17/0.58	% (857402)Memory used [KB]: 1023
0.17/0.58	% (857402)Time elapsed: 0.005 s
0.17/0.58	% (857402)Instructions burned: 2 (million)
0.17/0.58	% (857402)------------------------------
0.17/0.58	% (857402)------------------------------
0.17/0.59	% (857401)Instruction limit reached!
0.17/0.59	% (857401)------------------------------
0.17/0.59	% (857401)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.17/0.59	% (857401)Termination reason: Unknown
0.17/0.59	% (857401)Termination phase: shuffling
0.17/0.59	
0.17/0.59	% (857401)Memory used [KB]: 1023
0.17/0.59	% (857401)Time elapsed: 0.006 s
0.17/0.59	% (857401)Instructions burned: 3 (million)
0.17/0.59	% (857401)------------------------------
0.17/0.59	% (857401)------------------------------
0.17/0.60	% (857406)Instruction limit reached!
0.17/0.60	% (857406)------------------------------
0.17/0.60	% (857406)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.17/0.60	% (857406)Termination reason: Unknown
0.17/0.60	% (857406)Termination phase: Saturation
0.17/0.60	
0.17/0.60	% (857406)Memory used [KB]: 5884
0.17/0.60	% (857406)Time elapsed: 0.021 s
0.17/0.60	% (857406)Instructions burned: 38 (million)
0.17/0.60	% (857406)------------------------------
0.17/0.60	% (857406)------------------------------
0.17/0.60	% (857404)Instruction limit reached!
0.17/0.60	% (857404)------------------------------
0.17/0.60	% (857404)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.17/0.60	% (857404)Termination reason: Unknown
0.17/0.60	% (857404)Termination phase: Property scanning
0.17/0.60	
0.17/0.60	% (857404)Memory used [KB]: 1151
0.17/0.60	% (857404)Time elapsed: 0.019 s
0.17/0.60	% (857404)Instructions burned: 18 (million)
0.17/0.60	% (857404)------------------------------
0.17/0.60	% (857404)------------------------------
0.17/0.61	% (857405)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_857315 for (1799ds/3Mi)
0.17/0.62	% (857405)Instruction limit reached!
0.17/0.62	% (857405)------------------------------
0.17/0.62	% (857405)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.17/0.62	% (857405)Termination reason: Unknown
0.17/0.62	% (857405)Termination phase: shuffling
0.17/0.62	
0.17/0.62	% (857405)Memory used [KB]: 1023
0.17/0.62	% (857405)Time elapsed: 0.006 s
0.17/0.62	% (857405)Instructions burned: 3 (million)
0.17/0.62	% (857405)------------------------------
0.17/0.62	% (857405)------------------------------
0.17/0.62	% (857398)First to succeed.
0.51/0.63	% (857398)Refutation found. Thanks to Tanya!
0.51/0.63	% SZS status Theorem for E---3.1_857315
0.51/0.63	% SZS output start Proof for E---3.1_857315
0.51/0.63	thf(type_def_5, type, mu: $tType).
0.51/0.63	thf(func_def_0, type, mu: $tType).
0.51/0.63	thf(func_def_1, type, meq_ind: mu > mu > $i > $o).
0.51/0.63	thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
0.51/0.63	thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
0.51/0.63	thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
0.51/0.63	thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o).
0.51/0.63	thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
0.51/0.63	thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
0.51/0.63	thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
0.51/0.63	thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
0.51/0.63	thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o).
0.51/0.63	thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
0.51/0.63	thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o).
0.51/0.63	thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
0.51/0.63	thf(func_def_15, type, mtrue: $i > $o).
0.51/0.63	thf(func_def_16, type, mfalse: $i > $o).
0.51/0.63	thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
0.51/0.63	thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
0.51/0.63	thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o).
0.51/0.63	thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o).
0.51/0.63	thf(func_def_21, type, mserial: ($i > $i > $o) > $o).
0.51/0.63	thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o).
0.51/0.63	thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o).
0.51/0.63	thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o).
0.51/0.63	thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o).
0.51/0.63	thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o).
0.51/0.63	thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o).
0.51/0.63	thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o).
0.51/0.63	thf(func_def_29, type, mvalid: ($i > $o) > $o).
0.51/0.63	thf(func_def_30, type, minvalid: ($i > $o) > $o).
0.51/0.63	thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
0.51/0.63	thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
0.51/0.63	thf(func_def_33, type, a1: $i > $i > $o).
0.51/0.63	thf(func_def_34, type, a2: $i > $i > $o).
0.51/0.63	thf(func_def_35, type, a3: $i > $i > $o).
0.51/0.63	thf(func_def_36, type, jan: mu).
0.51/0.63	thf(func_def_37, type, piotr: mu).
0.51/0.63	thf(func_def_38, type, cola: mu).
0.51/0.63	thf(func_def_39, type, pepsi: mu).
0.51/0.63	thf(func_def_40, type, beer: mu).
0.51/0.63	thf(func_def_41, type, likes: mu > mu > $i > $o).
0.51/0.63	thf(func_def_42, type, very_much_likes: mu > mu > $i > $o).
0.51/0.63	thf(func_def_43, type, possibly_likes: mu > mu > $i > $o).
0.51/0.63	thf(func_def_44, type, subrel: ($i > $i > $o) > ($i > $i > $o) > $o).
0.51/0.63	thf(func_def_45, type, cond4s: ($i > $i > $o) > ($i > $i > $o) > $o).
0.51/0.63	thf(func_def_63, type, sK2: mu > mu > $i > $i).
0.51/0.63	thf(func_def_64, type, sK3: mu > mu > $i > $i).
0.51/0.63	thf(func_def_65, type, sK4: mu > $i > mu > $i).
0.51/0.63	thf(func_def_66, type, sK5: $i > $i).
0.51/0.63	thf(func_def_67, type, sK6: $i > $i).
0.51/0.63	thf(func_def_68, type, sK7: $i > $i).
0.51/0.63	thf(func_def_69, type, sK8: $i > $i).
0.51/0.63	thf(func_def_70, type, sK9: $i > $i).
0.51/0.63	thf(f849,plain,(
0.51/0.63	  $false),
0.51/0.63	  inference(trivial_inequality_removal,[status(thm)],[f840])).
0.51/0.63	thf(f840,plain,(
0.51/0.63	  ($true = $false)),
0.51/0.63	  inference(superposition,[status(thm)],[f831,f706])).
0.51/0.63	thf(f706,plain,(
0.51/0.63	  ( ! [X1 : $i] : (($true = (a1 @ X1 @ (sK9 @ X1)))) )),
0.51/0.63	  inference(not_proxy_clausification,[status(thm)],[f705])).
0.51/0.63	thf(f705,plain,(
0.51/0.63	  ( ! [X1 : $i] : (($false = (~ (a1 @ X1 @ (sK9 @ X1))))) )),
0.51/0.63	  inference(binary_proxy_clausification,[status(thm)],[f703])).
0.51/0.63	thf(f703,plain,(
0.51/0.63	  ( ! [X1 : $i] : (($false = ((~ (a1 @ X1 @ (sK9 @ X1))) | (~ (likes @ piotr @ beer @ (sK9 @ X1)))))) )),
0.51/0.63	  inference(beta_eta_normalization,[status(thm)],[f702])).
0.51/0.63	thf(f702,plain,(
0.51/0.63	  ( ! [X1 : $i] : ((((^[Y0 : $i]: ((~ (a1 @ X1 @ Y0)) | (~ (likes @ piotr @ beer @ Y0)))) @ (sK9 @ X1)) = $false)) )),
0.51/0.63	  inference(sigma_clausification,[status(thm)],[f701])).
0.51/0.63	thf(f701,plain,(
0.51/0.63	  ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((~ (a1 @ X1 @ Y0)) | (~ (likes @ piotr @ beer @ Y0))))) = $false)) )),
0.51/0.63	  inference(not_proxy_clausification,[status(thm)],[f700])).
0.51/0.63	thf(f700,plain,(
0.51/0.63	  ( ! [X1 : $i] : (($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (a1 @ X1 @ Y0)) | (~ (likes @ piotr @ beer @ Y0)))))))) )),
0.51/0.63	  inference(beta_eta_normalization,[status(thm)],[f699])).
0.51/0.63	thf(f699,plain,(
0.51/0.63	  ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (~ (!! @ $i @ (^[Y1 : $i]: ((~ (a1 @ Y0 @ Y1)) | (~ (likes @ piotr @ beer @ Y1))))))) @ X1))) )),
0.51/0.63	  inference(pi_clausification,[status(thm)],[f698])).
0.51/0.63	thf(f698,plain,(
0.51/0.63	  ((!! @ $i @ (^[Y0 : $i]: (~ (!! @ $i @ (^[Y1 : $i]: ((~ (a1 @ Y0 @ Y1)) | (~ (likes @ piotr @ beer @ Y1)))))))) = $true)),
0.51/0.63	  inference(beta_eta_normalization,[status(thm)],[f316])).
0.51/0.63	thf(f316,plain,(
0.51/0.63	  ($true = ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y2 @ Y4 @ Y5)) | (Y3 @ Y5))))))))) @ Y0 @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))) @ a1 @ (likes @ piotr @ beer))))),
0.51/0.63	  inference(definition_unfolding,[status(thm)],[f245,f272,f300])).
0.51/0.63	thf(f300,plain,(
0.51/0.63	  (mdia = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y2 @ Y4 @ Y5)) | (Y3 @ Y5))))))))) @ Y0 @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))))),
0.51/0.63	  inference(definition_unfolding,[status(thm)],[f231,f275,f230,f275])).
0.51/0.63	thf(f230,plain,(
0.51/0.63	  (mbox = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y3))))))))))),
0.51/0.63	  inference(cnf_transformation,[status(thm)],[f89])).
0.51/0.63	thf(f89,plain,(
0.51/0.63	  (mbox = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y3))))))))))),
0.51/0.63	  inference(fool_elimination,[status(thm)],[f88])).
0.51/0.63	thf(f88,plain,(
0.51/0.63	  ((^[X0 : $i > $i > $o, X1 : $i > $o, X2 : $i] : (! [X3 : $i] : ((X1 @ X3) | ~(X0 @ X2 @ X3)))) = mbox)),
0.51/0.63	  inference(rectify,[status(thm)],[f16])).
0.51/0.63	thf(f16,axiom,(
0.51/0.63	  ((^[X6 : $i > $i > $o, X3 : $i > $o, X2 : $i] : (! [X7 : $i] : ((X3 @ X7) | ~(X6 @ X2 @ X7)))) = mbox)),
0.51/0.63	  file('/export/starexec/sandbox2/tmp/tmp.jN269shynw/E---3.1_857315.p',mbox)).
0.51/0.63	thf(f275,plain,(
0.51/0.63	  (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
0.51/0.63	  inference(cnf_transformation,[status(thm)],[f124])).
0.51/0.63	thf(f124,plain,(
0.51/0.63	  (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
0.51/0.63	  inference(fool_elimination,[status(thm)],[f123])).
0.51/0.63	thf(f123,plain,(
0.51/0.63	  (mnot = (^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))))),
0.51/0.63	  inference(rectify,[status(thm)],[f3])).
0.51/0.63	thf(f3,axiom,(
0.51/0.63	  (mnot = (^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))))),
0.51/0.63	  file('/export/starexec/sandbox2/tmp/tmp.jN269shynw/E---3.1_857315.p',mnot)).
0.51/0.63	thf(f231,plain,(
0.51/0.63	  (mdia = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mbox @ Y0 @ (mnot @ Y1)))))))),
0.51/0.63	  inference(cnf_transformation,[status(thm)],[f99])).
0.51/0.63	thf(f99,plain,(
0.51/0.63	  (mdia = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mbox @ Y0 @ (mnot @ Y1)))))))),
0.51/0.63	  inference(fool_elimination,[status(thm)],[f98])).
0.51/0.63	thf(f98,plain,(
0.51/0.63	  ((^[X0 : $i > $i > $o, X1 : $i > $o] : (mnot @ (mbox @ X0 @ (mnot @ X1)))) = mdia)),
0.51/0.63	  inference(rectify,[status(thm)],[f17])).
0.51/0.63	thf(f17,axiom,(
0.51/0.63	  ((^[X6 : $i > $i > $o, X3 : $i > $o] : (mnot @ (mbox @ X6 @ (mnot @ X3)))) = mdia)),
0.51/0.63	  file('/export/starexec/sandbox2/tmp/tmp.jN269shynw/E---3.1_857315.p',mdia)).
0.51/0.63	thf(f272,plain,(
0.51/0.63	  (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
0.51/0.63	  inference(cnf_transformation,[status(thm)],[f144])).
0.51/0.63	thf(f144,plain,(
0.51/0.63	  (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
0.51/0.63	  inference(fool_elimination,[status(thm)],[f143])).
0.51/0.63	thf(f143,plain,(
0.51/0.63	  ((^[X0 : $i > $o] : (! [X1 : $i] : (X0 @ X1))) = mvalid)),
0.51/0.63	  inference(rectify,[status(thm)],[f28])).
0.51/0.63	thf(f28,axiom,(
0.51/0.63	  ((^[X3 : $i > $o] : (! [X2 : $i] : (X3 @ X2))) = mvalid)),
0.51/0.63	  file('/export/starexec/sandbox2/tmp/tmp.jN269shynw/E---3.1_857315.p',mvalid)).
0.51/0.63	thf(f245,plain,(
0.51/0.63	  ((mvalid @ (mdia @ a1 @ (likes @ piotr @ beer))) = $true)),
0.51/0.63	  inference(cnf_transformation,[status(thm)],[f182])).
0.51/0.63	thf(f182,plain,(
0.51/0.63	  ((mvalid @ (mdia @ a1 @ (likes @ piotr @ beer))) = $true)),
0.51/0.63	  inference(fool_elimination,[status(thm)],[f181])).
0.51/0.63	thf(f181,plain,(
0.51/0.63	  (mvalid @ (mdia @ a1 @ (likes @ piotr @ beer)))),
0.51/0.63	  inference(rectify,[status(thm)],[f52])).
0.51/0.63	thf(f52,axiom,(
0.51/0.63	  (mvalid @ (mdia @ a1 @ (likes @ piotr @ beer)))),
0.51/0.63	  file('/export/starexec/sandbox2/tmp/tmp.jN269shynw/E---3.1_857315.p',axiom_a3_3)).
0.51/0.63	thf(f831,plain,(
0.51/0.63	  ( ! [X0 : $i] : (((a1 @ sK1 @ X0) = $false)) )),
0.51/0.63	  inference(trivial_inequality_removal,[status(thm)],[f822])).
0.51/0.63	thf(f822,plain,(
0.51/0.63	  ( ! [X0 : $i] : (($true = $false) | ((a1 @ sK1 @ X0) = $false)) )),
0.51/0.63	  inference(superposition,[status(thm)],[f678,f769])).
0.51/0.63	thf(f769,plain,(
0.51/0.63	  ( ! [X0 : $i,X1 : $i] : (((a2 @ X1 @ X0) = $false) | ((a1 @ sK1 @ X1) = $false)) )),
0.51/0.63	  inference(trivial_inequality_removal,[status(thm)],[f755])).
0.51/0.63	thf(f755,plain,(
0.51/0.63	  ( ! [X0 : $i,X1 : $i] : (((a1 @ sK1 @ X1) = $false) | ((a2 @ X1 @ X0) = $false) | ($true = $false)) )),
0.51/0.63	  inference(superposition,[status(thm)],[f750,f403])).
0.51/0.63	thf(f403,plain,(
0.51/0.63	  ( ! [X2 : $i,X1 : $i] : (($true = (a2 @ X2 @ X1)) | ($false = (a2 @ X1 @ X2))) )),
0.51/0.63	  inference(binary_proxy_clausification,[status(thm)],[f402])).
0.51/0.63	thf(f402,plain,(
0.51/0.63	  ( ! [X2 : $i,X1 : $i] : ((((a2 @ X1 @ X2) => (a2 @ X2 @ X1)) = $true)) )),
0.51/0.63	  inference(beta_eta_normalization,[status(thm)],[f401])).
0.51/0.63	thf(f401,plain,(
0.51/0.63	  ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((a2 @ X1 @ Y0) => (a2 @ Y0 @ X1))) @ X2) = $true)) )),
0.51/0.63	  inference(pi_clausification,[status(thm)],[f400])).
0.51/0.63	thf(f400,plain,(
0.51/0.63	  ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((a2 @ X1 @ Y0) => (a2 @ Y0 @ X1)))) = $true)) )),
0.51/0.63	  inference(beta_eta_normalization,[status(thm)],[f399])).
0.51/0.63	thf(f399,plain,(
0.51/0.63	  ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((a2 @ Y0 @ Y1) => (a2 @ Y1 @ Y0))))) @ X1))) )),
0.51/0.63	  inference(pi_clausification,[status(thm)],[f398])).
0.51/0.63	thf(f398,plain,(
0.51/0.63	  ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((a2 @ Y0 @ Y1) => (a2 @ Y1 @ Y0)))))))),
0.51/0.63	  inference(beta_eta_normalization,[status(thm)],[f312])).
0.51/0.63	thf(f312,plain,(
0.51/0.63	  ($true = ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1))))))) @ a2))),
0.51/0.63	  inference(definition_unfolding,[status(thm)],[f239,f242])).
0.51/0.63	thf(f242,plain,(
0.51/0.63	  (msymmetric = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1))))))))),
0.51/0.63	  inference(cnf_transformation,[status(thm)],[f130])).
0.51/0.63	thf(f130,plain,(
0.51/0.63	  (msymmetric = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1))))))))),
0.51/0.63	  inference(fool_elimination,[status(thm)],[f129])).
0.51/0.63	thf(f129,plain,(
0.51/0.63	  (msymmetric = (^[X0 : $i > $i > $o] : (! [X1 : $i,X2 : $i] : ((X0 @ X2 @ X1) => (X0 @ X1 @ X2)))))),
0.51/0.63	  inference(rectify,[status(thm)],[f19])).
0.51/0.63	thf(f19,axiom,(
0.51/0.63	  (msymmetric = (^[X6 : $i > $i > $o] : (! [X9 : $i,X8 : $i] : ((X6 @ X8 @ X9) => (X6 @ X9 @ X8)))))),
0.51/0.63	  file('/export/starexec/sandbox2/tmp/tmp.jN269shynw/E---3.1_857315.p',msymmetric)).
0.51/0.63	thf(f239,plain,(
0.51/0.63	  ((msymmetric @ a2) = $true)),
0.51/0.63	  inference(cnf_transformation,[status(thm)],[f122])).
0.51/0.63	thf(f122,plain,(
0.51/0.63	  ((msymmetric @ a2) = $true)),
0.51/0.63	  inference(fool_elimination,[status(thm)],[f121])).
0.51/0.63	thf(f121,plain,(
0.51/0.63	  (msymmetric @ a2)),
0.51/0.63	  inference(rectify,[status(thm)],[f57])).
0.51/0.63	thf(f57,axiom,(
0.51/0.63	  (msymmetric @ a2)),
0.51/0.63	  file('/export/starexec/sandbox2/tmp/tmp.jN269shynw/E---3.1_857315.p',axioms_B_a2)).
0.51/0.63	thf(f750,plain,(
0.51/0.63	  ( ! [X0 : $i,X1 : $i] : (((a2 @ X1 @ X0) = $false) | ((a1 @ sK1 @ X0) = $false)) )),
0.51/0.63	  inference(trivial_inequality_removal,[status(thm)],[f743])).
0.51/0.63	thf(f743,plain,(
0.51/0.63	  ( ! [X0 : $i,X1 : $i] : (($true = $false) | ((a1 @ sK1 @ X0) = $false) | ((a2 @ X1 @ X0) = $false)) )),
0.51/0.63	  inference(superposition,[status(thm)],[f742,f483])).
0.51/0.63	thf(f483,plain,(
0.51/0.63	  ( ! [X2 : $i,X1 : $i] : (((likes @ jan @ pepsi @ X2) = $true) | ($false = (a2 @ X1 @ X2))) )),
0.51/0.63	  inference(not_proxy_clausification,[status(thm)],[f482])).
0.51/0.63	thf(f482,plain,(
0.51/0.63	  ( ! [X2 : $i,X1 : $i] : (((likes @ jan @ pepsi @ X2) = $true) | ($true = (~ (a2 @ X1 @ X2)))) )),
0.51/0.63	  inference(binary_proxy_clausification,[status(thm)],[f481])).
0.51/0.63	thf(f481,plain,(
0.51/0.63	  ( ! [X2 : $i,X1 : $i] : (($true = ((~ (a2 @ X1 @ X2)) | (likes @ jan @ pepsi @ X2)))) )),
0.51/0.63	  inference(beta_eta_normalization,[status(thm)],[f480])).
0.51/0.63	thf(f480,plain,(
0.51/0.63	  ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((~ (a2 @ X1 @ Y0)) | (likes @ jan @ pepsi @ Y0))) @ X2) = $true)) )),
0.51/0.63	  inference(pi_clausification,[status(thm)],[f479])).
0.51/0.63	thf(f479,plain,(
0.51/0.63	  ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((~ (a2 @ X1 @ Y0)) | (likes @ jan @ pepsi @ Y0)))))) )),
0.51/0.63	  inference(beta_eta_normalization,[status(thm)],[f478])).
0.51/0.63	thf(f478,plain,(
0.51/0.63	  ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (a2 @ Y0 @ Y1)) | (likes @ jan @ pepsi @ Y1))))) @ X1))) )),
0.51/0.63	  inference(pi_clausification,[status(thm)],[f477])).
0.51/0.63	thf(f477,plain,(
0.51/0.63	  ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (a2 @ Y0 @ Y1)) | (likes @ jan @ pepsi @ Y1)))))))),
0.51/0.63	  inference(beta_eta_normalization,[status(thm)],[f301])).
0.51/0.63	thf(f301,plain,(
0.51/0.63	  (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y3))))))))) @ a2 @ (likes @ jan @ pepsi))) = $true)),
0.51/0.63	  inference(definition_unfolding,[status(thm)],[f219,f272,f230])).
0.51/0.63	thf(f219,plain,(
0.51/0.63	  ((mvalid @ (mbox @ a2 @ (likes @ jan @ pepsi))) = $true)),
0.51/0.63	  inference(cnf_transformation,[status(thm)],[f140])).
0.51/0.63	thf(f140,plain,(
0.51/0.63	  ((mvalid @ (mbox @ a2 @ (likes @ jan @ pepsi))) = $true)),
0.51/0.63	  inference(fool_elimination,[status(thm)],[f139])).
0.51/0.63	thf(f139,plain,(
0.51/0.63	  (mvalid @ (mbox @ a2 @ (likes @ jan @ pepsi)))),
0.51/0.63	  inference(rectify,[status(thm)],[f35])).
0.51/0.63	thf(f35,axiom,(
0.51/0.63	  (mvalid @ (mbox @ a2 @ (likes @ jan @ pepsi)))),
0.51/0.63	  file('/export/starexec/sandbox2/tmp/tmp.jN269shynw/E---3.1_857315.p',axiom_a2_1)).
0.51/0.63	thf(f742,plain,(
0.51/0.63	  ( ! [X0 : $i] : (((likes @ jan @ pepsi @ X0) = $false) | ((a1 @ sK1 @ X0) = $false)) )),
0.51/0.63	  inference(trivial_inequality_removal,[status(thm)],[f739])).
0.51/0.63	thf(f739,plain,(
0.51/0.63	  ( ! [X0 : $i] : (((likes @ jan @ pepsi @ X0) = $false) | ((a1 @ sK1 @ X0) = $false) | ($true = $false)) )),
0.51/0.63	  inference(superposition,[status(thm)],[f395,f397])).
0.51/0.63	thf(f397,plain,(
0.51/0.63	  ($false = (possibly_likes @ jan @ pepsi @ sK1))),
0.51/0.63	  inference(sigma_clausification,[status(thm)],[f396])).
0.51/0.63	thf(f396,plain,(
0.51/0.63	  ($true != (!! @ $i @ (possibly_likes @ jan @ pepsi)))),
0.51/0.63	  inference(beta_eta_normalization,[status(thm)],[f332])).
0.51/0.63	thf(f332,plain,(
0.51/0.63	  (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ (possibly_likes @ jan @ pepsi)) != $true)),
0.51/0.63	  inference(definition_unfolding,[status(thm)],[f273,f272])).
0.51/0.63	thf(f273,plain,(
0.51/0.63	  ((mvalid @ (possibly_likes @ jan @ pepsi)) != $true)),
0.51/0.63	  inference(cnf_transformation,[status(thm)],[f218])).
0.51/0.63	thf(f218,plain,(
0.51/0.63	  ((mvalid @ (possibly_likes @ jan @ pepsi)) != $true)),
0.51/0.63	  inference(flattening,[status(thm)],[f112])).
0.51/0.63	thf(f112,plain,(
0.51/0.63	  ~((mvalid @ (possibly_likes @ jan @ pepsi)) = $true)),
0.51/0.63	  inference(fool_elimination,[status(thm)],[f111])).
0.51/0.63	thf(f111,plain,(
0.51/0.63	  ~(mvalid @ (possibly_likes @ jan @ pepsi))),
0.51/0.63	  inference(rectify,[status(thm)],[f63])).
0.51/0.63	thf(f63,negated_conjecture,(
0.51/0.63	  ~(mvalid @ (possibly_likes @ jan @ pepsi))),
0.51/0.63	  inference(negated_conjecture,[status(cth)],[f62])).
0.51/0.63	thf(f62,conjecture,(
0.51/0.63	  (mvalid @ (possibly_likes @ jan @ pepsi))),
0.51/0.63	  file('/export/starexec/sandbox2/tmp/tmp.jN269shynw/E---3.1_857315.p',conj)).
0.51/0.63	thf(f395,plain,(
0.51/0.63	  ( ! [X2 : mu,X3 : mu,X1 : $i,X4 : $i] : (($true = (possibly_likes @ X2 @ X3 @ X1)) | ($false = (a1 @ X1 @ X4)) | ((likes @ X2 @ X3 @ X4) = $false)) )),
0.51/0.63	  inference(not_proxy_clausification,[status(thm)],[f394])).
0.51/0.63	thf(f394,plain,(
0.51/0.63	  ( ! [X2 : mu,X3 : mu,X1 : $i,X4 : $i] : (((~ (a1 @ X1 @ X4)) = $true) | ((likes @ X2 @ X3 @ X4) = $false) | ($true = (possibly_likes @ X2 @ X3 @ X1))) )),
0.51/0.63	  inference(not_proxy_clausification,[status(thm)],[f393])).
0.51/0.63	thf(f393,plain,(
0.51/0.63	  ( ! [X2 : mu,X3 : mu,X1 : $i,X4 : $i] : (($true = (~ (likes @ X2 @ X3 @ X4))) | ($true = (possibly_likes @ X2 @ X3 @ X1)) | ((~ (a1 @ X1 @ X4)) = $true)) )),
0.51/0.63	  inference(binary_proxy_clausification,[status(thm)],[f392])).
0.51/0.63	thf(f392,plain,(
0.51/0.63	  ( ! [X2 : mu,X3 : mu,X1 : $i,X4 : $i] : (($true = ((~ (a1 @ X1 @ X4)) | (~ (likes @ X2 @ X3 @ X4)))) | ($true = (possibly_likes @ X2 @ X3 @ X1))) )),
0.51/0.63	  inference(beta_eta_normalization,[status(thm)],[f391])).
0.51/0.63	thf(f391,plain,(
0.51/0.63	  ( ! [X2 : mu,X3 : mu,X1 : $i,X4 : $i] : (($true = (possibly_likes @ X2 @ X3 @ X1)) | ($true = ((^[Y0 : $i]: ((~ (a1 @ X1 @ Y0)) | (~ (likes @ X2 @ X3 @ Y0)))) @ X4))) )),
0.51/0.63	  inference(pi_clausification,[status(thm)],[f390])).
0.51/0.63	thf(f390,plain,(
0.51/0.63	  ( ! [X2 : mu,X3 : mu,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((~ (a1 @ X1 @ Y0)) | (~ (likes @ X2 @ X3 @ Y0)))))) | ($true = (possibly_likes @ X2 @ X3 @ X1))) )),
0.51/0.63	  inference(binary_proxy_clausification,[status(thm)],[f389])).
0.51/0.63	thf(f389,plain,(
0.51/0.63	  ( ! [X2 : mu,X3 : mu,X1 : $i] : (($true = ((possibly_likes @ X2 @ X3 @ X1) | (!! @ $i @ (^[Y0 : $i]: ((~ (a1 @ X1 @ Y0)) | (~ (likes @ X2 @ X3 @ Y0)))))))) )),
0.51/0.63	  inference(beta_eta_normalization,[status(thm)],[f388])).
0.51/0.63	thf(f388,plain,(
0.51/0.63	  ( ! [X2 : mu,X3 : mu,X1 : $i] : (($true = ((^[Y0 : mu]: ((possibly_likes @ X2 @ Y0 @ X1) | (!! @ $i @ (^[Y1 : $i]: ((~ (a1 @ X1 @ Y1)) | (~ (likes @ X2 @ Y0 @ Y1))))))) @ X3))) )),
0.51/0.63	  inference(pi_clausification,[status(thm)],[f387])).
0.51/0.63	thf(f387,plain,(
0.51/0.63	  ( ! [X2 : mu,X1 : $i] : (($true = (!! @ mu @ (^[Y0 : mu]: ((possibly_likes @ X2 @ Y0 @ X1) | (!! @ $i @ (^[Y1 : $i]: ((~ (a1 @ X1 @ Y1)) | (~ (likes @ X2 @ Y0 @ Y1)))))))))) )),
0.51/0.63	  inference(beta_eta_normalization,[status(thm)],[f386])).
0.51/0.63	thf(f386,plain,(
0.51/0.63	  ( ! [X2 : mu,X1 : $i] : (($true = ((^[Y0 : mu]: (!! @ mu @ (^[Y1 : mu]: ((possibly_likes @ Y0 @ Y1 @ X1) | (!! @ $i @ (^[Y2 : $i]: ((~ (a1 @ X1 @ Y2)) | (~ (likes @ Y0 @ Y1 @ Y2))))))))) @ X2))) )),
0.51/0.63	  inference(pi_clausification,[status(thm)],[f385])).
0.51/0.63	thf(f385,plain,(
0.51/0.63	  ( ! [X1 : $i] : (($true = (!! @ mu @ (^[Y0 : mu]: (!! @ mu @ (^[Y1 : mu]: ((possibly_likes @ Y0 @ Y1 @ X1) | (!! @ $i @ (^[Y2 : $i]: ((~ (a1 @ X1 @ Y2)) | (~ (likes @ Y0 @ Y1 @ Y2)))))))))))) )),
0.51/0.63	  inference(beta_eta_normalization,[status(thm)],[f384])).
0.51/0.63	thf(f384,plain,(
0.51/0.63	  ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ mu @ (^[Y1 : mu]: (!! @ mu @ (^[Y2 : mu]: ((possibly_likes @ Y1 @ Y2 @ Y0) | (!! @ $i @ (^[Y3 : $i]: ((~ (a1 @ Y0 @ Y3)) | (~ (likes @ Y1 @ Y2 @ Y3))))))))))) @ X1))) )),
0.51/0.63	  inference(pi_clausification,[status(thm)],[f383])).
0.51/0.63	thf(f383,plain,(
0.51/0.63	  ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ mu @ (^[Y1 : mu]: (!! @ mu @ (^[Y2 : mu]: ((possibly_likes @ Y1 @ Y2 @ Y0) | (!! @ $i @ (^[Y3 : $i]: ((~ (a1 @ Y0 @ Y3)) | (~ (likes @ Y1 @ Y2 @ Y3)))))))))))))),
0.51/0.63	  inference(boolean_simplification,[status(thm)],[f382])).
0.51/0.63	thf(f382,plain,(
0.51/0.63	  ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ mu @ (^[Y1 : mu]: (!! @ mu @ (^[Y2 : mu]: ((possibly_likes @ Y1 @ Y2 @ Y0) | (~ (~ (!! @ $i @ (^[Y3 : $i]: ((~ (a1 @ Y0 @ Y3)) | (~ (likes @ Y1 @ Y2 @ Y3)))))))))))))))),
0.51/0.63	  inference(beta_eta_normalization,[status(thm)],[f329])).
0.51/0.63	thf(f329,plain,(
0.51/0.63	  ($true = ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: (Y0 @ Y2 @ Y1)))))) @ (^[Y0 : mu]: ((^[Y1 : mu > $i > $o]: ((^[Y2 : $i]: (!! @ mu @ (^[Y3 : mu]: (Y1 @ Y3 @ Y2)))))) @ (^[Y1 : mu]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ ((^[Y4 : $i > $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y4 @ Y6 @ Y7)) | (Y5 @ Y7))))))))) @ Y2 @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y3)))))) @ a1 @ (likes @ Y0 @ Y1)) @ (possibly_likes @ Y0 @ Y1))))))))),
0.51/0.63	  inference(definition_unfolding,[status(thm)],[f264,f272,f244,f244,f293,f300])).
0.51/0.63	thf(f293,plain,(
0.51/0.63	  (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) | (Y2 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))))),
0.51/0.63	  inference(definition_unfolding,[status(thm)],[f290,f235,f275])).
0.51/0.63	thf(f235,plain,(
0.51/0.63	  (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
0.51/0.63	  inference(cnf_transformation,[status(thm)],[f170])).
0.51/0.63	thf(f170,plain,(
0.51/0.63	  (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
0.51/0.63	  inference(fool_elimination,[status(thm)],[f169])).
0.51/0.63	thf(f169,plain,(
0.51/0.63	  ((^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X0 @ X2) | (X1 @ X2))) = mor)),
0.51/0.63	  inference(rectify,[status(thm)],[f4])).
0.51/0.63	thf(f4,axiom,(
0.51/0.63	  ((^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X3 @ X2) | (X4 @ X2))) = mor)),
0.51/0.63	  file('/export/starexec/sandbox2/tmp/tmp.jN269shynw/E---3.1_857315.p',mor)).
0.51/0.63	thf(f290,plain,(
0.51/0.63	  (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
0.51/0.63	  inference(cnf_transformation,[status(thm)],[f172])).
0.51/0.63	thf(f172,plain,(
0.51/0.63	  (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
0.51/0.63	  inference(fool_elimination,[status(thm)],[f171])).
0.51/0.63	thf(f171,plain,(
0.51/0.63	  (mimplies = (^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)))),
0.51/0.63	  inference(rectify,[status(thm)],[f6])).
0.51/0.63	thf(f6,axiom,(
0.51/0.63	  (mimplies = (^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)))),
0.51/0.63	  file('/export/starexec/sandbox2/tmp/tmp.jN269shynw/E---3.1_857315.p',mimplies)).
0.51/0.63	thf(f244,plain,(
0.51/0.63	  (mforall_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: (Y0 @ Y2 @ Y1)))))))),
0.51/0.63	  inference(cnf_transformation,[status(thm)],[f194])).
0.51/0.63	thf(f194,plain,(
0.51/0.63	  (mforall_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: (Y0 @ Y2 @ Y1)))))))),
0.51/0.63	  inference(fool_elimination,[status(thm)],[f193])).
0.51/0.63	thf(f193,plain,(
0.51/0.63	  (mforall_ind = (^[X0 : mu > $i > $o, X1 : $i] : (! [X2 : mu] : (X0 @ X2 @ X1))))),
0.51/0.63	  inference(rectify,[status(thm)],[f10])).
0.51/0.63	thf(f10,axiom,(
0.51/0.63	  (mforall_ind = (^[X3 : mu > $i > $o, X2 : $i] : (! [X0 : mu] : (X3 @ X0 @ X2))))),
0.51/0.63	  file('/export/starexec/sandbox2/tmp/tmp.jN269shynw/E---3.1_857315.p',mforall_ind)).
0.51/0.63	thf(f264,plain,(
0.51/0.63	  ($true = (mvalid @ (mforall_ind @ (^[Y0 : mu]: (mforall_ind @ (^[Y1 : mu]: (mimplies @ (mdia @ a1 @ (likes @ Y0 @ Y1)) @ (possibly_likes @ Y0 @ Y1))))))))),
0.51/0.63	  inference(cnf_transformation,[status(thm)],[f132])).
0.51/0.63	thf(f132,plain,(
0.51/0.63	  ($true = (mvalid @ (mforall_ind @ (^[Y0 : mu]: (mforall_ind @ (^[Y1 : mu]: (mimplies @ (mdia @ a1 @ (likes @ Y0 @ Y1)) @ (possibly_likes @ Y0 @ Y1))))))))),
0.51/0.63	  inference(fool_elimination,[status(thm)],[f131])).
0.51/0.63	thf(f131,plain,(
0.51/0.63	  (mvalid @ (mforall_ind @ (^[X0 : mu] : (mforall_ind @ (^[X1 : mu] : (mimplies @ (mdia @ a1 @ (likes @ X0 @ X1)) @ (possibly_likes @ X0 @ X1)))))))),
0.51/0.63	  inference(rectify,[status(thm)],[f43])).
0.51/0.63	thf(f43,axiom,(
0.51/0.63	  (mvalid @ (mforall_ind @ (^[X0 : mu] : (mforall_ind @ (^[X1 : mu] : (mimplies @ (mdia @ a1 @ (likes @ X0 @ X1)) @ (possibly_likes @ X0 @ X1)))))))),
0.51/0.63	  file('/export/starexec/sandbox2/tmp/tmp.jN269shynw/E---3.1_857315.p',axiom_user_communication_3)).
0.51/0.63	thf(f678,plain,(
0.51/0.63	  ( ! [X1 : $i] : (($true = (a2 @ X1 @ (sK7 @ X1)))) )),
0.51/0.63	  inference(sigma_clausification,[status(thm)],[f677])).
0.51/0.63	thf(f677,plain,(
0.51/0.63	  ( ! [X1 : $i] : (($true = (?? @ $i @ (a2 @ X1)))) )),
0.51/0.63	  inference(beta_eta_normalization,[status(thm)],[f676])).
0.51/0.63	thf(f676,plain,(
0.51/0.63	  ( ! [X1 : $i] : ((((^[Y0 : $i]: (?? @ $i @ (a2 @ Y0))) @ X1) = $true)) )),
0.51/0.63	  inference(pi_clausification,[status(thm)],[f675])).
0.51/0.63	thf(f675,plain,(
0.51/0.63	  ($true = (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (a2 @ Y0)))))),
0.51/0.63	  inference(beta_eta_normalization,[status(thm)],[f339])).
0.51/0.63	thf(f339,plain,(
0.51/0.63	  (((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y1 @ Y2)))))) @ a2) = $true)),
0.51/0.63	  inference(definition_unfolding,[status(thm)],[f286,f255])).
0.51/0.63	thf(f255,plain,(
0.51/0.63	  (mserial = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y1 @ Y2)))))))),
0.51/0.63	  inference(cnf_transformation,[status(thm)],[f85])).
0.51/0.63	thf(f85,plain,(
0.51/0.63	  (mserial = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y1 @ Y2)))))))),
0.51/0.63	  inference(fool_elimination,[status(thm)],[f84])).
0.51/0.63	thf(f84,plain,(
0.51/0.63	  ((^[X0 : $i > $i > $o] : (! [X1 : $i] : ? [X2 : $i] : (X0 @ X1 @ X2))) = mserial)),
0.51/0.63	  inference(rectify,[status(thm)],[f20])).
0.51/0.63	thf(f20,axiom,(
0.51/0.63	  ((^[X6 : $i > $i > $o] : (! [X8 : $i] : ? [X9 : $i] : (X6 @ X8 @ X9))) = mserial)),
0.51/0.63	  file('/export/starexec/sandbox2/tmp/tmp.jN269shynw/E---3.1_857315.p',mserial)).
0.51/0.63	thf(f286,plain,(
0.51/0.63	  ((mserial @ a2) = $true)),
0.51/0.63	  inference(cnf_transformation,[status(thm)],[f174])).
0.51/0.63	thf(f174,plain,(
0.51/0.63	  ((mserial @ a2) = $true)),
0.51/0.63	  inference(fool_elimination,[status(thm)],[f173])).
0.51/0.63	thf(f173,plain,(
0.51/0.63	  (mserial @ a2)),
0.51/0.63	  inference(rectify,[status(thm)],[f61])).
0.51/0.63	thf(f61,axiom,(
0.51/0.63	  (mserial @ a2)),
0.51/0.63	  file('/export/starexec/sandbox2/tmp/tmp.jN269shynw/E---3.1_857315.p',axioms_D_a2)).
0.51/0.63	% SZS output end Proof for E---3.1_857315
0.51/0.63	% (857398)------------------------------
0.51/0.63	% (857398)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.51/0.63	% (857398)Termination reason: Refutation
0.51/0.63	
0.51/0.63	% (857398)Memory used [KB]: 6396
0.51/0.63	% (857398)Time elapsed: 0.120 s
0.51/0.63	% (857398)Instructions burned: 88 (million)
0.51/0.63	% (857398)------------------------------
0.51/0.63	% (857398)------------------------------
0.51/0.63	% (857397)Success in time 0.144 s
0.51/0.63	EOF