%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LCL959^24 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:15:29 AM UTC 2026
% Result : Theorem 0.08s 0.27s
% Output : Refutation 0.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL959^24 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.17 % Computer : n020.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Sep 29 10:57:04 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.21 Running first-order model finding
% 0.08/0.21 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.27 % (910507)Will run a generic schedule for satisfiability detection.
% 0.08/0.27 % (910513)% WARNING: option uhcvi not known.
% 0.08/0.27 % (910513)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2675527670:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.08/0.27 % (910513)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.08/0.27 % (910513)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.08/0.27 % (910515)dis+10_1_sil=32000:sp=arity:random_seed=780702839:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.08/0.27 % (910512)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2765325128_2999 on theBenchmark for (2999ds/0Mi)
% 0.08/0.27 % Exception at run slice level
% 0.08/0.27 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.08/0.27 % (910513) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-910507-910513"...
% 0.08/0.27 % (910517)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=163575299:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.08/0.27 % (910513)...printing done.
% 0.08/0.27 % (910513)Refutation found. Thanks to Tanya!
% 0.08/0.27 % SZS status Theorem for theBenchmark
% 0.08/0.27 % SZS output start Proof for theBenchmark
% 0.08/0.27 thf(type_def_5, type, mworld: $tType).
% 0.08/0.27 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.08/0.27 thf(func_def_0, type, mrel: (mworld > mworld > $o)).
% 0.08/0.27 thf(func_def_1, type, mactual: mworld).
% 0.08/0.27 thf(func_def_2, type, mlocal: ((mworld > $o) > $o)).
% 0.08/0.27 thf(func_def_4, type, mnot: ((mworld > $o) > mworld > $o)).
% 0.08/0.27 thf(func_def_5, type, mand: ((mworld > $o) > (mworld > $o) > mworld > $o)).
% 0.08/0.27 thf(func_def_6, type, mor: ((mworld > $o) > (mworld > $o) > mworld > $o)).
% 0.08/0.27 thf(func_def_7, type, mimplies: ((mworld > $o) > (mworld > $o) > mworld > $o)).
% 0.08/0.27 thf(func_def_8, type, mequiv: ((mworld > $o) > (mworld > $o) > mworld > $o)).
% 0.08/0.27 thf(func_def_9, type, mbox: ((mworld > $o) > mworld > $o)).
% 0.08/0.27 thf(func_def_10, type, mdia: ((mworld > $o) > mworld > $o)).
% 0.08/0.27 thf(func_def_11, type, eiw_di: ($i > mworld > $o)).
% 0.08/0.27 thf(func_def_12, type, mforall_di: (($i > mworld > $o) > mworld > $o)).
% 0.08/0.27 thf(func_def_13, type, mexists_di: (($i > mworld > $o) > mworld > $o)).
% 0.08/0.27 thf(func_def_14, type, f: ($i > mworld > $o)).
% 0.08/0.27 thf(func_def_15, type, db0: !>[X0: $tType]:(X0)).
% 0.08/0.27 thf(func_def_16, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.08/0.27 thf(func_def_17, type, vNOT: ($o > $o)).
% 0.08/0.27 thf(func_def_18, type, db1: !>[X0: $tType]:(X0)).
% 0.08/0.27 thf(func_def_19, type, vAND: ($o > $o > $o)).
% 0.08/0.27 thf(func_def_20, type, db2: !>[X0: $tType]:(X0)).
% 0.08/0.27 thf(func_def_21, type, vOR: ($o > $o > $o)).
% 0.08/0.27 thf(func_def_22, type, vIMP: ($o > $o > $o)).
% 0.08/0.27 thf(func_def_23, type, vIFF: ($o > $o > $o)).
% 0.08/0.27 thf(func_def_24, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.08/0.27 thf(func_def_25, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.08/0.27 thf(func_def_28, type, sK0: (mworld > $i)).
% 0.08/0.27 thf(func_def_29, type, db3: !>[X0: $tType]:(X0)).
% 0.08/0.27 thf(func_def_30, type, sK1: mworld).
% 0.08/0.27 thf(func_def_31, type, sK2: mworld).
% 0.08/0.27 thf(func_def_32, type, sK3: (mworld > mworld)).
% 0.08/0.27 thf(func_def_33, type, sK4: (mworld > $i)).
% 0.08/0.27 thf(func_def_34, type, sK5: (mworld > mworld)).
% 0.08/0.27 thf(func_def_35, type, sK6: ($i > mworld)).
% 0.08/0.27 thf(func_def_37, type, sK8: (mworld > mworld)).
% 0.08/0.27 thf(func_def_38, type, sK9: (mworld > mworld)).
% 0.08/0.27 thf(func_def_39, type, sK10: (mworld > $i)).
% 0.08/0.27 thf(func_def_40, type, sK11: (mworld > mworld)).
% 0.08/0.27 thf(func_def_41, type, sK12: (mworld > mworld)).
% 0.08/0.27 thf(func_def_42, type, sK13: (mworld > mworld)).
% 0.08/0.27 thf(func_def_43, type, sK14: (mworld > $i)).
% 0.08/0.27 thf(func_def_44, type, sK15: (mworld > mworld)).
% 0.08/0.27 thf(func_def_45, type, sK16: (mworld > mworld)).
% 0.08/0.27 thf(func_def_46, type, sK17: ($i > mworld)).
% 0.08/0.27 thf(func_def_47, type, sK18: ($i > mworld)).
% 0.08/0.27 thf(func_def_48, type, sK19: (mworld > mworld)).
% 0.08/0.27 thf(func_def_49, type, sK20: (mworld > mworld)).
% 0.08/0.27 thf(func_def_50, type, sK21: mworld).
% 0.08/0.27 thf(func_def_51, type, sK22: (mworld > mworld)).
% 0.08/0.27 thf(func_def_52, type, sK23: (mworld > $i)).
% 0.08/0.27 thf(func_def_53, type, sK24: (mworld > mworld)).
% 0.08/0.27 thf(func_def_54, type, sK25: (mworld > mworld)).
% 0.08/0.27 thf(func_def_55, type, sK26: (mworld > $i)).
% 0.08/0.27 thf(func_def_56, type, sK27: (mworld > mworld)).
% 0.08/0.27 thf(func_def_57, type, sK28: ($i > mworld)).
% 0.08/0.27 thf(func_def_58, type, sK29: ($i > mworld)).
% 0.08/0.27 thf(f1,axiom,(
% 0.08/0.27 (mlocal = (^[X0 : (mworld > $o)] : ((X0 @ mactual))))),
% 0.08/0.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mlocal_def)).
% 0.08/0.27 thf(f2,axiom,(
% 0.08/0.27 (mnot = (^[X0 : (mworld > $o), X1 : mworld] : (~(X0 @ X1))))),
% 0.08/0.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot_def)).
% 0.08/0.27 thf(f3,axiom,(
% 0.08/0.27 (mand = (^[X0 : (mworld > $o), X1 : (mworld > $o), X2 : mworld] : ((X1 @ X2) & (X0 @ X2))))),
% 0.08/0.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mand_def)).
% 0.08/0.27 thf(f5,axiom,(
% 0.08/0.27 (mimplies = (^[X0 : (mworld > $o), X1 : (mworld > $o), X2 : mworld] : ((X0 @ X2) => (X1 @ X2))))),
% 0.08/0.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies_def)).
% 0.08/0.27 thf(f7,axiom,(
% 0.08/0.27 (mbox = (^[X0 : (mworld > $o), X1 : mworld] : (! [X2 : mworld] : ((mrel @ X1 @ X2) => (X0 @ X2)))))),
% 0.08/0.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_def)).
% 0.08/0.27 thf(f9,axiom,(
% 0.08/0.27 ! [X0 : mworld,X1 : mworld] : (mrel @ X0 @ X1)),
% 0.08/0.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_universal)).
% 0.08/0.27 thf(f11,axiom,(
% 0.08/0.27 ! [X0 : mworld,X1 : mworld,X2 : $i] : (((mrel @ X1 @ X0) & (eiw_di @ X2 @ X0)) => (eiw_di @ X2 @ X1))),
% 0.08/0.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eiw_di_decr)).
% 0.08/0.27 thf(f12,axiom,(
% 0.08/0.27 (mforall_di = (^[X0 : ($i > mworld > $o), X1 : mworld] : (! [X2 : $i] : ((eiw_di @ X2 @ X1) => (X0 @ X2 @ X1)))))),
% 0.08/0.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mforall_di_def)).
% 0.08/0.27 thf(f13,axiom,(
% 0.08/0.27 (mexists_di = (^[X0 : ($i > mworld > $o), X1 : mworld] : (? [X2 : $i] : ((X0 @ X2 @ X1) & (eiw_di @ X2 @ X1)))))),
% 0.08/0.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mexists_di_def)).
% 0.08/0.27 thf(f14,conjecture,(
% 0.08/0.27 (mlocal @ (mand @ (mbox @ (mimplies @ (mbox @ (mnot @ (mbox @ (mforall_di @ (^[X0 : $i] : ((mbox @ (f @ X0)))))))) @ (mexists_di @ (^[X1 : $i] : ((mbox @ (mnot @ (mbox @ (f @ X1))))))))) @ (mbox @ (mimplies @ (mexists_di @ (^[X1 : $i] : ((mbox @ (mnot @ (mbox @ (f @ X1))))))) @ (mbox @ (mnot @ (mbox @ (mforall_di @ (^[X0 : $i] : ((mbox @ (f @ X0))))))))))))),
% 0.08/0.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kalish203)).
% 0.08/0.27 thf(f15,negated_conjecture,(
% 0.08/0.27 ~(mlocal @ (mand @ (mbox @ (mimplies @ (mbox @ (mnot @ (mbox @ (mforall_di @ (^[X0 : $i] : ((mbox @ (f @ X0)))))))) @ (mexists_di @ (^[X1 : $i] : ((mbox @ (mnot @ (mbox @ (f @ X1))))))))) @ (mbox @ (mimplies @ (mexists_di @ (^[X1 : $i] : ((mbox @ (mnot @ (mbox @ (f @ X1))))))) @ (mbox @ (mnot @ (mbox @ (mforall_di @ (^[X0 : $i] : ((mbox @ (f @ X0))))))))))))),
% 0.08/0.27 inference(negated_conjecture,[status(cth)],[f14])).
% 0.08/0.27 thf(f16,plain,(
% 0.08/0.27 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 0.08/0.27 inference(fool_elimination,[],[f1])).
% 0.08/0.27 thf(f17,plain,(
% 0.08/0.27 (mnot = (^[X0 : (mworld > $o), X1 : mworld] : (~(X0 @ X1))))),
% 0.08/0.27 inference(rectify,[],[f2])).
% 0.08/0.27 thf(f18,plain,(
% 0.08/0.27 (mnot = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))))),
% 0.08/0.27 inference(fool_elimination,[],[f17])).
% 0.08/0.27 thf(f19,plain,(
% 0.08/0.27 (mand = (^[X0 : (mworld > $o), X1 : (mworld > $o), X2 : mworld] : ((X1 @ X2) & (X0 @ X2))))),
% 0.08/0.27 inference(rectify,[],[f3])).
% 0.08/0.27 thf(f20,plain,(
% 0.08/0.27 (mand = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))))),
% 0.08/0.27 inference(fool_elimination,[],[f19])).
% 0.08/0.27 thf(f23,plain,(
% 0.08/0.27 (mimplies = (^[X0 : (mworld > $o), X1 : (mworld > $o), X2 : mworld] : ((X0 @ X2) => (X1 @ X2))))),
% 0.08/0.27 inference(rectify,[],[f5])).
% 0.08/0.27 thf(f24,plain,(
% 0.08/0.27 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 0.08/0.27 inference(fool_elimination,[],[f23])).
% 0.08/0.27 thf(f27,plain,(
% 0.08/0.27 (mbox = (^[X0 : (mworld > $o), X1 : mworld] : (! [X2 : mworld] : ((mrel @ X1 @ X2) => (X0 @ X2)))))),
% 0.08/0.27 inference(rectify,[],[f7])).
% 0.08/0.27 thf(f28,plain,(
% 0.08/0.27 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 0.08/0.27 inference(fool_elimination,[],[f27])).
% 0.08/0.27 thf(f31,plain,(
% 0.08/0.27 ! [X0 : mworld,X1 : mworld] : (mrel @ X0 @ X1)),
% 0.08/0.27 inference(rectify,[],[f9])).
% 0.08/0.27 thf(f32,plain,(
% 0.08/0.27 ! [X0 : mworld,X1 : mworld] : (((mrel @ X0 @ X1)) = $true)),
% 0.08/0.27 inference(fool_elimination,[],[f31])).
% 0.08/0.27 thf(f35,plain,(
% 0.08/0.27 ! [X0 : mworld,X1 : mworld,X2 : $i] : (((mrel @ X1 @ X0) & (eiw_di @ X2 @ X0)) => (eiw_di @ X2 @ X1))),
% 0.08/0.27 inference(rectify,[],[f11])).
% 0.08/0.27 thf(f36,plain,(
% 0.08/0.27 ! [X0 : mworld,X1 : mworld,X2 : $i] : (((((mrel @ X1 @ X0)) = $true) & (((eiw_di @ X2 @ X0)) = $true)) => (((eiw_di @ X2 @ X1)) = $true))),
% 0.08/0.27 inference(fool_elimination,[],[f35])).
% 0.08/0.27 thf(f37,plain,(
% 0.08/0.27 (mforall_di = (^[X0 : ($i > mworld > $o), X1 : mworld] : (! [X2 : $i] : ((eiw_di @ X2 @ X1) => (X0 @ X2 @ X1)))))),
% 0.08/0.27 inference(rectify,[],[f12])).
% 0.08/0.27 thf(f38,plain,(
% 0.08/0.27 (mforall_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))))),
% 0.08/0.27 inference(fool_elimination,[],[f37])).
% 0.08/0.27 thf(f39,plain,(
% 0.08/0.27 (mexists_di = (^[X0 : ($i > mworld > $o), X1 : mworld] : (? [X2 : $i] : ((X0 @ X2 @ X1) & (eiw_di @ X2 @ X1)))))),
% 0.08/0.27 inference(rectify,[],[f13])).
% 0.08/0.27 thf(f40,plain,(
% 0.08/0.27 (mexists_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (?? @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) & (Y0 @ Y2 @ Y1))))))))),
% 0.08/0.27 inference(fool_elimination,[],[f39])).
% 0.08/0.27 thf(f41,plain,(
% 0.08/0.27 ~(mlocal @ (mand @ (mbox @ (mimplies @ (mbox @ (mnot @ (mbox @ (mforall_di @ (^[X0 : $i] : ((mbox @ (f @ X0)))))))) @ (mexists_di @ (^[X1 : $i] : ((mbox @ (mnot @ (mbox @ (f @ X1))))))))) @ (mbox @ (mimplies @ (mexists_di @ (^[X2 : $i] : ((mbox @ (mnot @ (mbox @ (f @ X2))))))) @ (mbox @ (mnot @ (mbox @ (mforall_di @ (^[X3 : $i] : ((mbox @ (f @ X3))))))))))))),
% 0.08/0.27 inference(rectify,[],[f15])).
% 0.08/0.27 thf(f42,plain,(
% 0.08/0.27 ~ ($true = ((mlocal @ (mand @ (mbox @ (mimplies @ (mbox @ (mnot @ (mbox @ (mforall_di @ (^[Y0 : $i]: (mbox @ (f @ Y0))))))) @ (mexists_di @ (^[Y0 : $i]: (mbox @ (mnot @ (mbox @ (f @ Y0)))))))) @ (mbox @ (mimplies @ (mexists_di @ (^[Y0 : $i]: (mbox @ (mnot @ (mbox @ (f @ Y0)))))) @ (mbox @ (mnot @ (mbox @ (mforall_di @ (^[Y0 : $i]: (mbox @ (f @ Y0)))))))))))))),
% 0.08/0.27 inference(fool_elimination,[],[f41])).
% 0.08/0.27 thf(f43,plain,(
% 0.08/0.27 ($true != ((mlocal @ (mand @ (mbox @ (mimplies @ (mbox @ (mnot @ (mbox @ (mforall_di @ (^[Y0 : $i]: (mbox @ (f @ Y0))))))) @ (mexists_di @ (^[Y0 : $i]: (mbox @ (mnot @ (mbox @ (f @ Y0)))))))) @ (mbox @ (mimplies @ (mexists_di @ (^[Y0 : $i]: (mbox @ (mnot @ (mbox @ (f @ Y0)))))) @ (mbox @ (mnot @ (mbox @ (mforall_di @ (^[Y0 : $i]: (mbox @ (f @ Y0)))))))))))))),
% 0.08/0.27 inference(flattening,[],[f42])).
% 0.08/0.27 thf(f44,plain,(
% 0.08/0.27 ! [X0 : mworld,X1 : mworld,X2 : $i] : ((((eiw_di @ X2 @ X1)) = $true) | ((((mrel @ X1 @ X0)) != $true) | (((eiw_di @ X2 @ X0)) != $true)))),
% 0.08/0.27 inference(ennf_transformation,[],[f36])).
% 0.08/0.27 thf(f45,plain,(
% 0.08/0.27 ! [X0 : mworld,X1 : mworld,X2 : $i] : ((((eiw_di @ X2 @ X1)) = $true) | (((mrel @ X1 @ X0)) != $true) | (((eiw_di @ X2 @ X0)) != $true))),
% 0.08/0.27 inference(flattening,[],[f44])).
% 0.08/0.27 thf(f47,plain,(
% 0.08/0.27 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 0.08/0.27 inference(cnf_transformation,[],[f16])).
% 0.08/0.27 thf(f48,plain,(
% 0.08/0.27 (mnot = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))))),
% 0.08/0.27 inference(cnf_transformation,[],[f18])).
% 0.08/0.27 thf(f49,plain,(
% 0.08/0.27 (mand = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))))),
% 0.08/0.27 inference(cnf_transformation,[],[f20])).
% 0.08/0.27 thf(f51,plain,(
% 0.08/0.27 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 0.08/0.27 inference(cnf_transformation,[],[f24])).
% 0.08/0.27 thf(f53,plain,(
% 0.08/0.27 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 0.08/0.27 inference(cnf_transformation,[],[f28])).
% 0.08/0.27 thf(f55,plain,(
% 0.08/0.27 ( ! [X0 : mworld,X1 : mworld] : ((((mrel @ X0 @ X1)) = $true)) )),
% 0.08/0.27 inference(cnf_transformation,[],[f32])).
% 0.08/0.27 thf(f57,plain,(
% 0.08/0.27 ( ! [X2 : $i,X0 : mworld,X1 : mworld] : ((((eiw_di @ X2 @ X1)) = $true) | (((mrel @ X1 @ X0)) != $true) | (((eiw_di @ X2 @ X0)) != $true)) )),
% 0.08/0.27 inference(cnf_transformation,[],[f45])).
% 0.08/0.27 thf(f58,plain,(
% 0.08/0.27 (mforall_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))))),
% 0.08/0.27 inference(cnf_transformation,[],[f38])).
% 0.08/0.27 thf(f59,plain,(
% 0.08/0.27 (mexists_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (?? @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) & (Y0 @ Y2 @ Y1))))))))),
% 0.08/0.27 inference(cnf_transformation,[],[f40])).
% 0.08/0.27 thf(f60,plain,(
% 0.08/0.27 ($true != ((mlocal @ (mand @ (mbox @ (mimplies @ (mbox @ (mnot @ (mbox @ (mforall_di @ (^[Y0 : $i]: (mbox @ (f @ Y0))))))) @ (mexists_di @ (^[Y0 : $i]: (mbox @ (mnot @ (mbox @ (f @ Y0)))))))) @ (mbox @ (mimplies @ (mexists_di @ (^[Y0 : $i]: (mbox @ (mnot @ (mbox @ (f @ Y0)))))) @ (mbox @ (mnot @ (mbox @ (mforall_di @ (^[Y0 : $i]: (mbox @ (f @ Y0)))))))))))))),
% 0.08/0.27 inference(cnf_transformation,[],[f43])).
% 0.08/0.27 thf(f62,definition,(
% 0.08/0.27 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.08/0.27 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.08/0.27 thf(f63,plain,(
% 0.08/0.27 ($true != (((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) @ (^[Y0 : $i]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (Y1 @ Y3))))))) @ (f @ Y0))))))) @ ((^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (?? @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) & (Y0 @ Y2 @ Y1))))))) @ (^[Y0 : $i]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (Y1 @ Y3))))))) @ ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: (~ (Y1 @ Y2))))) @ ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (Y1 @ Y3))))))) @ (f @ Y0)))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))) @ ((^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (?? @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) & (Y0 @ Y2 @ Y1))))))) @ (^[Y0 : $i]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (Y1 @ Y3))))))) @ ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: (~ (Y1 @ Y2))))) @ ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (Y1 @ Y3))))))) @ (f @ Y0)))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) @ (^[Y0 : $i]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (Y1 @ Y3))))))) @ (f @ Y0)))))))))))))),
% 0.08/0.27 inference(definition_unfolding,[],[f60,f47,f49,f53,f51,f53,f48,f53,f58,f53,f59,f53,f48,f53,f53,f51,f59,f53,f48,f53,f53,f48,f53,f58,f53])).
% 0.08/0.27 thf(f64,plain,(
% 0.08/0.27 ($true != (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((eiw_di @ Y3 @ Y2) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y2 @ Y4) => (f @ Y3 @ Y4)))))))))))))) => (?? @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) & (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y0 @ Y2) => (~ (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (f @ Y1 @ Y3))))))))))))))) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => ((?? @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) & (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y0 @ Y2) => (~ (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (f @ Y1 @ Y3))))))))))) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((eiw_di @ Y3 @ Y2) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y2 @ Y4) => (f @ Y3 @ Y4)))))))))))))))))))))),
% 0.08/0.27 inference(beta-eta_normalization,[],[f63])).
% 0.08/0.27 thf(f65,plain,(
% 0.08/0.27 ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => ((?? @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) & (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y0 @ Y2) => (~ (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (f @ Y1 @ Y3))))))))))) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((eiw_di @ Y3 @ Y2) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y2 @ Y4) => (f @ Y3 @ Y4)))))))))))))))))))) | ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((eiw_di @ Y3 @ Y2) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y2 @ Y4) => (f @ Y3 @ Y4)))))))))))))) => (?? @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) & (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y0 @ Y2) => (~ (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (f @ Y1 @ Y3)))))))))))))))))),
% 0.08/0.27 inference(and_proxy_clausification,[],[f64])).
% 0.08/0.27 thf(f66,plain,(
% 0.08/0.27 ($false = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => ((?? @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) & (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y0 @ Y2) => (~ (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (f @ Y1 @ Y3))))))))))) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((eiw_di @ Y3 @ Y2) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y2 @ Y4) => (f @ Y3 @ Y4))))))))))))))))) @ sK1))) | ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((eiw_di @ Y3 @ Y2) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y2 @ Y4) => (f @ Y3 @ Y4)))))))))))))) => (?? @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) & (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y0 @ Y2) => (~ (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (f @ Y1 @ Y3)))))))))))))))))),
% 0.08/0.27 inference(sigma_proxy_clausification,[],[f65])).
% 0.08/0.27 thf(f67,plain,(
% 0.08/0.27 ($false = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => ((?? @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) & (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y0 @ Y2) => (~ (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (f @ Y1 @ Y3))))))))))) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((eiw_di @ Y3 @ Y2) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y2 @ Y4) => (f @ Y3 @ Y4))))))))))))))))) @ sK1))) | ($false = (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (~ (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (!! @ $i @ (^[Y3 : $i]: ((eiw_di @ Y3 @ Y2) => (!! @ mworld @ (^[Y4 : mworld]: ((mrel @ Y2 @ Y4) => (f @ Y3 @ Y4)))))))))))))) => (?? @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) & (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y0 @ Y2) => (~ (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (f @ Y1 @ Y3)))))))))))))) @ sK2)))),
% 0.08/0.27 inference(sigma_proxy_clausification,[],[f66])).
% 0.08/0.27 thf(f68,plain,(
% 0.08/0.27 ($false = (((mrel @ mactual @ sK1) => ((?? @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ sK1) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ sK1 @ Y1) => (~ (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (f @ Y0 @ Y2))))))))))) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK1 @ Y0) => (~ (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y1 @ Y3) => (f @ Y2 @ Y3)))))))))))))))))) | ($false = (((mrel @ mactual @ sK2) => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK2 @ Y0) => (~ (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y1 @ Y3) => (f @ Y2 @ Y3)))))))))))))) => (?? @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ sK2) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ sK2 @ Y1) => (~ (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (f @ Y0 @ Y2)))))))))))))))),
% 0.08/0.27 inference(beta-eta_normalization,[],[f67])).
% 0.08/0.27 thf(f69,plain,(
% 0.08/0.27 ($false = (((?? @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ sK1) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ sK1 @ Y1) => (~ (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (f @ Y0 @ Y2))))))))))) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK1 @ Y0) => (~ (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y1 @ Y3) => (f @ Y2 @ Y3))))))))))))))))) | ($false = (((mrel @ mactual @ sK2) => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK2 @ Y0) => (~ (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y1 @ Y3) => (f @ Y2 @ Y3)))))))))))))) => (?? @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ sK2) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ sK2 @ Y1) => (~ (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (f @ Y0 @ Y2)))))))))))))))),
% 0.08/0.27 inference(imp_proxy_clausification,[],[f68])).
% 0.08/0.27 thf(f102,plain,(
% 0.08/0.27 ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK1 @ Y0) => (~ (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y1 @ Y3) => (f @ Y2 @ Y3)))))))))))))))) | ($false = (((mrel @ mactual @ sK2) => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK2 @ Y0) => (~ (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y1 @ Y3) => (f @ Y2 @ Y3)))))))))))))) => (?? @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ sK2) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ sK2 @ Y1) => (~ (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (f @ Y0 @ Y2)))))))))))))))),
% 0.08/0.27 inference(imp_proxy_clausification,[],[f69])).
% 0.08/0.27 thf(f103,plain,(
% 0.08/0.27 ($true = ((?? @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ sK1) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ sK1 @ Y1) => (~ (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (f @ Y0 @ Y2))))))))))))) | ($false = (((mrel @ mactual @ sK2) => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK2 @ Y0) => (~ (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y1 @ Y3) => (f @ Y2 @ Y3)))))))))))))) => (?? @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ sK2) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ sK2 @ Y1) => (~ (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (f @ Y0 @ Y2)))))))))))))))),
% 0.08/0.27 inference(imp_proxy_clausification,[],[f69])).
% 0.08/0.27 thf(f104,plain,(
% 0.08/0.27 ($true = (((^[Y0 : $i]: ((eiw_di @ Y0 @ sK1) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ sK1 @ Y1) => (~ (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (f @ Y0 @ Y2)))))))))) @ sK7))) | ($false = (((mrel @ mactual @ sK2) => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK2 @ Y0) => (~ (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y1 @ Y3) => (f @ Y2 @ Y3)))))))))))))) => (?? @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ sK2) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ sK2 @ Y1) => (~ (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (f @ Y0 @ Y2)))))))))))))))),
% 0.08/0.27 inference(sigma_proxy_clausification,[],[f103])).
% 0.08/0.27 thf(f105,plain,(
% 0.08/0.27 ($true = (((^[Y0 : $i]: ((eiw_di @ Y0 @ sK1) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ sK1 @ Y1) => (~ (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (f @ Y0 @ Y2)))))))))) @ sK7))) | ($false = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK2 @ Y0) => (~ (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y1 @ Y3) => (f @ Y2 @ Y3)))))))))))))) => (?? @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ sK2) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ sK2 @ Y1) => (~ (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (f @ Y0 @ Y2))))))))))))))),
% 0.08/0.27 inference(imp_proxy_clausification,[],[f104])).
% 0.08/0.27 thf(f119,plain,(
% 0.08/0.27 ($true = (((^[Y0 : $i]: ((eiw_di @ Y0 @ sK1) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ sK1 @ Y1) => (~ (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (f @ Y0 @ Y2)))))))))) @ sK7))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK2 @ Y0) => (~ (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y1 @ Y3) => (f @ Y2 @ Y3))))))))))))))))),
% 0.08/0.27 inference(imp_proxy_clausification,[],[f105])).
% 0.08/0.27 thf(f120,plain,(
% 0.08/0.27 ( ! [X1 : mworld] : (($true = (((^[Y0 : $i]: ((eiw_di @ Y0 @ sK1) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ sK1 @ Y1) => (~ (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (f @ Y0 @ Y2)))))))))) @ sK7))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK2 @ Y0) => (~ (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y1 @ Y3) => (f @ Y2 @ Y3))))))))))))) @ X1)))) )),
% 0.08/0.27 inference(pi_proxy_clausification,[],[f119])).
% 0.08/0.27 thf(f121,plain,(
% 0.08/0.27 ( ! [X1 : mworld] : (($true = (((eiw_di @ sK7 @ sK1) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK1 @ Y0) => (~ (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (f @ sK7 @ Y1))))))))))) | ($true = (((mrel @ sK2 @ X1) => (~ (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y0 @ Y2) => (f @ Y1 @ Y2))))))))))))))) )),
% 0.08/0.27 inference(beta-eta_normalization,[],[f120])).
% 0.08/0.27 thf(f122,plain,(
% 0.08/0.27 ( ! [X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK1 @ Y0) => (~ (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (f @ sK7 @ Y1)))))))))) | ($true = (((mrel @ sK2 @ X1) => (~ (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y0 @ Y2) => (f @ Y1 @ Y2))))))))))))))) )),
% 0.08/0.27 inference(and_proxy_clausification,[],[f121])).
% 0.08/0.27 thf(f123,plain,(
% 0.08/0.27 ( ! [X1 : mworld] : (($true = ((eiw_di @ sK7 @ sK1))) | ($true = (((mrel @ sK2 @ X1) => (~ (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y0 @ Y2) => (f @ Y1 @ Y2))))))))))))))) )),
% 0.08/0.27 inference(and_proxy_clausification,[],[f121])).
% 0.08/0.27 thf(f124,plain,(
% 0.08/0.27 ( ! [X1 : mworld] : (($true = ((eiw_di @ sK7 @ sK1))) | ($false = ((mrel @ sK2 @ X1))) | ($true = ((~ (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y0 @ Y2) => (f @ Y1 @ Y2)))))))))))))) )),
% 0.08/0.27 inference(imp_proxy_clausification,[],[f123])).
% 0.08/0.27 thf(f125,plain,(
% 0.08/0.27 ( ! [X1 : mworld] : (($true = ((eiw_di @ sK7 @ sK1))) | ($false = ((mrel @ sK2 @ X1))) | ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y0 @ Y2) => (f @ Y1 @ Y2))))))))))))) )),
% 0.08/0.27 inference(not_proxy_clausification,[],[f124])).
% 0.08/0.27 thf(f126,plain,(
% 0.08/0.27 ( ! [X1 : mworld] : (($true = ((eiw_di @ sK7 @ sK1))) | ($false = ((mrel @ sK2 @ X1))) | ($false = (((^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y0 @ Y2) => (f @ Y1 @ Y2))))))))) @ (sK9 @ X1))))) )),
% 0.08/0.27 inference(sigma_proxy_clausification,[],[f125])).
% 0.08/0.27 thf(f127,plain,(
% 0.08/0.27 ( ! [X1 : mworld] : (($true = ((eiw_di @ sK7 @ sK1))) | ($false = ((mrel @ sK2 @ X1))) | ($false = (((mrel @ X1 @ (sK9 @ X1)) => (!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ (sK9 @ X1)) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ (sK9 @ X1) @ Y1) => (f @ Y0 @ Y1))))))))))) )),
% 0.08/0.27 inference(beta-eta_normalization,[],[f126])).
% 0.08/0.27 thf(f128,plain,(
% 0.08/0.27 ( ! [X1 : mworld] : (($true = ((eiw_di @ sK7 @ sK1))) | ($false = ((mrel @ sK2 @ X1))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ (sK9 @ X1)) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ (sK9 @ X1) @ Y1) => (f @ Y0 @ Y1)))))))))) )),
% 0.08/0.27 inference(imp_proxy_clausification,[],[f127])).
% 0.08/0.27 thf(f130,plain,(
% 0.08/0.27 ( ! [X1 : mworld] : (($true = ((eiw_di @ sK7 @ sK1))) | ($false = ((mrel @ sK2 @ X1))) | ($false = (((^[Y0 : $i]: ((eiw_di @ Y0 @ (sK9 @ X1)) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ (sK9 @ X1) @ Y1) => (f @ Y0 @ Y1)))))) @ (sK10 @ X1))))) )),
% 0.08/0.27 inference(sigma_proxy_clausification,[],[f128])).
% 0.08/0.27 thf(f131,plain,(
% 0.08/0.27 ( ! [X1 : mworld] : (($true = ((eiw_di @ sK7 @ sK1))) | ($false = ((mrel @ sK2 @ X1))) | ($false = (((eiw_di @ (sK10 @ X1) @ (sK9 @ X1)) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK9 @ X1) @ Y0) => (f @ (sK10 @ X1) @ Y0)))))))) )),
% 0.08/0.27 inference(beta-eta_normalization,[],[f130])).
% 0.08/0.27 thf(f132,plain,(
% 0.08/0.27 ( ! [X1 : mworld] : (($true = ((eiw_di @ sK7 @ sK1))) | ($false = ((mrel @ sK2 @ X1))) | ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK9 @ X1) @ Y0) => (f @ (sK10 @ X1) @ Y0))))))) )),
% 0.08/0.27 inference(imp_proxy_clausification,[],[f131])).
% 0.08/0.27 thf(f133,plain,(
% 0.08/0.27 ( ! [X1 : mworld] : (($true = ((eiw_di @ sK7 @ sK1))) | ($false = ((mrel @ sK2 @ X1))) | ($true = ((eiw_di @ (sK10 @ X1) @ (sK9 @ X1))))) )),
% 0.08/0.27 inference(imp_proxy_clausification,[],[f131])).
% 0.08/0.27 thf(f134,plain,(
% 0.08/0.27 ( ! [X1 : mworld] : (($true = ((eiw_di @ sK7 @ sK1))) | ($false = ((mrel @ sK2 @ X1))) | ($false = (((^[Y0 : mworld]: ((mrel @ (sK9 @ X1) @ Y0) => (f @ (sK10 @ X1) @ Y0))) @ (sK11 @ X1))))) )),
% 0.08/0.27 inference(sigma_proxy_clausification,[],[f132])).
% 0.08/0.27 thf(f135,plain,(
% 0.08/0.27 ( ! [X1 : mworld] : (($true = ((eiw_di @ sK7 @ sK1))) | ($false = ((mrel @ sK2 @ X1))) | ($false = (((mrel @ (sK9 @ X1) @ (sK11 @ X1)) => (f @ (sK10 @ X1) @ (sK11 @ X1)))))) )),
% 0.08/0.27 inference(beta-eta_normalization,[],[f134])).
% 0.08/0.27 thf(f136,plain,(
% 0.08/0.27 ( ! [X1 : mworld] : (($true = ((eiw_di @ sK7 @ sK1))) | ($false = ((mrel @ sK2 @ X1))) | ($false = ((f @ (sK10 @ X1) @ (sK11 @ X1))))) )),
% 0.08/0.27 inference(imp_proxy_clausification,[],[f135])).
% 0.08/0.27 thf(f138,plain,(
% 0.08/0.27 ( ! [X2 : mworld,X1 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ sK1 @ Y0) => (~ (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (f @ sK7 @ Y1))))))) @ X2))) | ($true = (((mrel @ sK2 @ X1) => (~ (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y0 @ Y2) => (f @ Y1 @ Y2))))))))))))))) )),
% 0.08/0.27 inference(pi_proxy_clausification,[],[f122])).
% 0.08/0.27 thf(f139,plain,(
% 0.08/0.27 ( ! [X2 : mworld,X1 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ sK1 @ Y0) => (~ (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (f @ sK7 @ Y1))))))) @ X2))) | ($false = ((mrel @ sK2 @ X1))) | ($true = ((~ (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y0 @ Y2) => (f @ Y1 @ Y2)))))))))))))) )),
% 0.08/0.27 inference(imp_proxy_clausification,[],[f138])).
% 0.08/0.27 thf(f140,plain,(
% 0.08/0.27 ( ! [X2 : mworld,X1 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ sK1 @ Y0) => (~ (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (f @ sK7 @ Y1))))))) @ X2))) | ($false = ((mrel @ sK2 @ X1))) | ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y0 @ Y2) => (f @ Y1 @ Y2))))))))))))) )),
% 0.08/0.27 inference(not_proxy_clausification,[],[f139])).
% 0.08/0.27 thf(f141,plain,(
% 0.08/0.27 ( ! [X2 : mworld,X1 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ sK1 @ Y0) => (~ (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (f @ sK7 @ Y1))))))) @ X2))) | ($false = ((mrel @ sK2 @ X1))) | ($false = (((^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y0 @ Y2) => (f @ Y1 @ Y2))))))))) @ (sK12 @ X1))))) )),
% 0.08/0.27 inference(sigma_proxy_clausification,[],[f140])).
% 0.08/0.27 thf(f142,plain,(
% 0.08/0.27 ( ! [X2 : mworld,X1 : mworld] : (($true = (((mrel @ sK1 @ X2) => (~ (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (f @ sK7 @ Y0)))))))) | ($false = ((mrel @ sK2 @ X1))) | ($false = (((mrel @ X1 @ (sK12 @ X1)) => (!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ (sK12 @ X1)) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ (sK12 @ X1) @ Y1) => (f @ Y0 @ Y1))))))))))) )),
% 0.08/0.27 inference(beta-eta_normalization,[],[f141])).
% 0.08/0.27 thf(f143,plain,(
% 0.08/0.27 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK1 @ X2))) | ($false = ((mrel @ sK2 @ X1))) | ($false = (((mrel @ X1 @ (sK12 @ X1)) => (!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ (sK12 @ X1)) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ (sK12 @ X1) @ Y1) => (f @ Y0 @ Y1)))))))))) | ($true = ((~ (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (f @ sK7 @ Y0)))))))) )),
% 0.08/0.27 inference(imp_proxy_clausification,[],[f142])).
% 0.08/0.27 thf(f144,plain,(
% 0.08/0.27 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK1 @ X2))) | ($false = ((mrel @ sK2 @ X1))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ (sK12 @ X1)) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ (sK12 @ X1) @ Y1) => (f @ Y0 @ Y1))))))))) | ($true = ((~ (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (f @ sK7 @ Y0)))))))) )),
% 0.08/0.27 inference(imp_proxy_clausification,[],[f143])).
% 0.08/0.27 thf(f151,plain,(
% 0.08/0.27 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK1 @ X2))) | ($false = ((mrel @ sK2 @ X1))) | ($false = (((^[Y0 : $i]: ((eiw_di @ Y0 @ (sK12 @ X1)) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ (sK12 @ X1) @ Y1) => (f @ Y0 @ Y1)))))) @ (sK14 @ X1)))) | ($true = ((~ (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (f @ sK7 @ Y0)))))))) )),
% 0.08/0.27 inference(sigma_proxy_clausification,[],[f144])).
% 0.08/0.27 thf(f152,plain,(
% 0.08/0.27 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK1 @ X2))) | ($false = ((mrel @ sK2 @ X1))) | ($false = (((^[Y0 : $i]: ((eiw_di @ Y0 @ (sK12 @ X1)) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ (sK12 @ X1) @ Y1) => (f @ Y0 @ Y1)))))) @ (sK14 @ X1)))) | ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (f @ sK7 @ Y0))))))) )),
% 0.08/0.27 inference(not_proxy_clausification,[],[f151])).
% 0.08/0.27 thf(f153,plain,(
% 0.08/0.27 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK1 @ X2))) | ($false = ((mrel @ sK2 @ X1))) | ($false = (((^[Y0 : $i]: ((eiw_di @ Y0 @ (sK12 @ X1)) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ (sK12 @ X1) @ Y1) => (f @ Y0 @ Y1)))))) @ (sK14 @ X1)))) | ($false = (((^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (f @ sK7 @ Y0))) @ (sK15 @ X2))))) )),
% 0.08/0.27 inference(sigma_proxy_clausification,[],[f152])).
% 0.08/0.27 thf(f154,plain,(
% 0.08/0.27 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK1 @ X2))) | ($false = ((mrel @ sK2 @ X1))) | ($false = (((eiw_di @ (sK14 @ X1) @ (sK12 @ X1)) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK12 @ X1) @ Y0) => (f @ (sK14 @ X1) @ Y0))))))) | ($false = (((mrel @ X2 @ (sK15 @ X2)) => (f @ sK7 @ (sK15 @ X2)))))) )),
% 0.08/0.27 inference(beta-eta_normalization,[],[f153])).
% 0.08/0.27 thf(f155,plain,(
% 0.08/0.27 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK1 @ X2))) | ($false = ((mrel @ sK2 @ X1))) | ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK12 @ X1) @ Y0) => (f @ (sK14 @ X1) @ Y0)))))) | ($false = (((mrel @ X2 @ (sK15 @ X2)) => (f @ sK7 @ (sK15 @ X2)))))) )),
% 0.08/0.27 inference(imp_proxy_clausification,[],[f154])).
% 0.08/0.27 thf(f156,plain,(
% 0.08/0.27 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK1 @ X2))) | ($false = ((mrel @ sK2 @ X1))) | ($true = ((eiw_di @ (sK14 @ X1) @ (sK12 @ X1)))) | ($false = (((mrel @ X2 @ (sK15 @ X2)) => (f @ sK7 @ (sK15 @ X2)))))) )),
% 0.08/0.27 inference(imp_proxy_clausification,[],[f154])).
% 0.08/0.27 thf(f157,plain,(
% 0.08/0.27 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK1 @ X2))) | ($false = ((mrel @ sK2 @ X1))) | ($true = ((eiw_di @ (sK14 @ X1) @ (sK12 @ X1)))) | ($false = ((f @ sK7 @ (sK15 @ X2))))) )),
% 0.08/0.27 inference(imp_proxy_clausification,[],[f156])).
% 0.08/0.27 thf(f159,plain,(
% 0.08/0.27 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK1 @ X2))) | ($false = ((mrel @ sK2 @ X1))) | ($false = (((^[Y0 : mworld]: ((mrel @ (sK12 @ X1) @ Y0) => (f @ (sK14 @ X1) @ Y0))) @ (sK16 @ X1)))) | ($false = (((mrel @ X2 @ (sK15 @ X2)) => (f @ sK7 @ (sK15 @ X2)))))) )),
% 0.08/0.27 inference(sigma_proxy_clausification,[],[f155])).
% 0.08/0.27 thf(f160,plain,(
% 0.08/0.27 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK1 @ X2))) | ($false = ((mrel @ sK2 @ X1))) | ($false = (((^[Y0 : mworld]: ((mrel @ (sK12 @ X1) @ Y0) => (f @ (sK14 @ X1) @ Y0))) @ (sK16 @ X1)))) | ($false = ((f @ sK7 @ (sK15 @ X2))))) )),
% 0.08/0.27 inference(imp_proxy_clausification,[],[f159])).
% 0.08/0.27 thf(f165,plain,(
% 0.08/0.27 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK1 @ X2))) | ($false = ((mrel @ sK2 @ X1))) | ($false = (((mrel @ (sK12 @ X1) @ (sK16 @ X1)) => (f @ (sK14 @ X1) @ (sK16 @ X1))))) | ($false = ((f @ sK7 @ (sK15 @ X2))))) )),
% 0.08/0.27 inference(beta-eta_normalization,[],[f160])).
% 0.08/0.27 thf(f166,plain,(
% 0.08/0.27 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK1 @ X2))) | ($false = ((mrel @ sK2 @ X1))) | ($false = ((f @ (sK14 @ X1) @ (sK16 @ X1)))) | ($false = ((f @ sK7 @ (sK15 @ X2))))) )),
% 0.08/0.27 inference(imp_proxy_clausification,[],[f165])).
% 0.08/0.27 thf(f201,plain,(
% 0.08/0.27 ($false = (((^[Y0 : mworld]: ((mrel @ sK1 @ Y0) => (~ (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y1 @ Y3) => (f @ Y2 @ Y3))))))))))))) @ sK21))) | ($false = (((mrel @ mactual @ sK2) => ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK2 @ Y0) => (~ (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y1 @ Y3) => (f @ Y2 @ Y3)))))))))))))) => (?? @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ sK2) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ sK2 @ Y1) => (~ (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (f @ Y0 @ Y2)))))))))))))))),
% 0.08/0.27 inference(sigma_proxy_clausification,[],[f102])).
% 0.08/0.27 thf(f202,plain,(
% 0.08/0.27 ($false = (((^[Y0 : mworld]: ((mrel @ sK1 @ Y0) => (~ (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y1 @ Y3) => (f @ Y2 @ Y3))))))))))))) @ sK21))) | ($false = (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK2 @ Y0) => (~ (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y1 @ Y3) => (f @ Y2 @ Y3)))))))))))))) => (?? @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ sK2) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ sK2 @ Y1) => (~ (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (f @ Y0 @ Y2))))))))))))))),
% 0.08/0.27 inference(imp_proxy_clausification,[],[f201])).
% 0.08/0.27 thf(f217,plain,(
% 0.08/0.27 ($false = (((^[Y0 : mworld]: ((mrel @ sK1 @ Y0) => (~ (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y1 @ Y3) => (f @ Y2 @ Y3))))))))))))) @ sK21))) | ($false = ((?? @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ sK2) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ sK2 @ Y1) => (~ (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (f @ Y0 @ Y2)))))))))))))),
% 0.08/0.27 inference(imp_proxy_clausification,[],[f202])).
% 0.08/0.27 thf(f218,plain,(
% 0.08/0.27 ($false = (((^[Y0 : mworld]: ((mrel @ sK1 @ Y0) => (~ (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y1 @ Y3) => (f @ Y2 @ Y3))))))))))))) @ sK21))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK2 @ Y0) => (~ (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y1 @ Y3) => (f @ Y2 @ Y3))))))))))))))))),
% 0.08/0.27 inference(imp_proxy_clausification,[],[f202])).
% 0.08/0.27 thf(f219,plain,(
% 0.08/0.27 ( ! [X1 : mworld] : (($false = (((^[Y0 : mworld]: ((mrel @ sK1 @ Y0) => (~ (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y1 @ Y3) => (f @ Y2 @ Y3))))))))))))) @ sK21))) | ($true = (((^[Y0 : mworld]: ((mrel @ sK2 @ Y0) => (~ (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y1 @ Y3) => (f @ Y2 @ Y3))))))))))))) @ X1)))) )),
% 0.08/0.27 inference(pi_proxy_clausification,[],[f218])).
% 0.08/0.27 thf(f220,plain,(
% 0.08/0.27 ( ! [X1 : mworld] : (($false = (((mrel @ sK1 @ sK21) => (~ (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK21 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y0 @ Y2) => (f @ Y1 @ Y2)))))))))))))) | ($true = (((mrel @ sK2 @ X1) => (~ (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y0 @ Y2) => (f @ Y1 @ Y2))))))))))))))) )),
% 0.08/0.27 inference(beta-eta_normalization,[],[f219])).
% 0.08/0.27 thf(f221,plain,(
% 0.08/0.27 ( ! [X1 : mworld] : (($false = ((~ (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK21 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y0 @ Y2) => (f @ Y1 @ Y2))))))))))))) | ($true = (((mrel @ sK2 @ X1) => (~ (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y0 @ Y2) => (f @ Y1 @ Y2))))))))))))))) )),
% 0.08/0.27 inference(imp_proxy_clausification,[],[f220])).
% 0.08/0.27 thf(f237,plain,(
% 0.08/0.27 ( ! [X1 : mworld] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK21 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y0 @ Y2) => (f @ Y1 @ Y2)))))))))))) | ($true = (((mrel @ sK2 @ X1) => (~ (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y0 @ Y2) => (f @ Y1 @ Y2))))))))))))))) )),
% 0.08/0.27 inference(not_proxy_clausification,[],[f221])).
% 0.08/0.27 thf(f238,plain,(
% 0.08/0.27 ( ! [X2 : mworld,X1 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ sK21 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y0 @ Y2) => (f @ Y1 @ Y2))))))))) @ X2))) | ($true = (((mrel @ sK2 @ X1) => (~ (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y0 @ Y2) => (f @ Y1 @ Y2))))))))))))))) )),
% 0.08/0.27 inference(pi_proxy_clausification,[],[f237])).
% 0.08/0.27 thf(f239,plain,(
% 0.08/0.27 ( ! [X2 : mworld,X1 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ sK21 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y0 @ Y2) => (f @ Y1 @ Y2))))))))) @ X2))) | ($false = ((mrel @ sK2 @ X1))) | ($true = ((~ (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y0 @ Y2) => (f @ Y1 @ Y2)))))))))))))) )),
% 0.08/0.27 inference(imp_proxy_clausification,[],[f238])).
% 0.08/0.27 thf(f240,plain,(
% 0.08/0.27 ( ! [X2 : mworld,X1 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ sK21 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y0 @ Y2) => (f @ Y1 @ Y2))))))))) @ X2))) | ($false = ((mrel @ sK2 @ X1))) | ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y0 @ Y2) => (f @ Y1 @ Y2))))))))))))) )),
% 0.08/0.27 inference(not_proxy_clausification,[],[f239])).
% 0.08/0.27 thf(f241,plain,(
% 0.08/0.27 ( ! [X2 : mworld,X1 : mworld] : (($true = (((^[Y0 : mworld]: ((mrel @ sK21 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y0 @ Y2) => (f @ Y1 @ Y2))))))))) @ X2))) | ($false = ((mrel @ sK2 @ X1))) | ($false = (((^[Y0 : mworld]: ((mrel @ X1 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y0 @ Y2) => (f @ Y1 @ Y2))))))))) @ (sK25 @ X1))))) )),
% 0.08/0.27 inference(sigma_proxy_clausification,[],[f240])).
% 0.08/0.27 thf(f242,plain,(
% 0.08/0.27 ( ! [X2 : mworld,X1 : mworld] : (($true = (((mrel @ sK21 @ X2) => (!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ X2) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ X2 @ Y1) => (f @ Y0 @ Y1)))))))))) | ($false = ((mrel @ sK2 @ X1))) | ($false = (((mrel @ X1 @ (sK25 @ X1)) => (!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ (sK25 @ X1)) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ (sK25 @ X1) @ Y1) => (f @ Y0 @ Y1))))))))))) )),
% 0.08/0.27 inference(beta-eta_normalization,[],[f241])).
% 0.08/0.27 thf(f243,plain,(
% 0.08/0.27 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK21 @ X2))) | ($false = ((mrel @ sK2 @ X1))) | ($false = (((mrel @ X1 @ (sK25 @ X1)) => (!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ (sK25 @ X1)) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ (sK25 @ X1) @ Y1) => (f @ Y0 @ Y1)))))))))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ X2) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ X2 @ Y1) => (f @ Y0 @ Y1)))))))))) )),
% 0.08/0.27 inference(imp_proxy_clausification,[],[f242])).
% 0.08/0.27 thf(f244,plain,(
% 0.08/0.27 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK21 @ X2))) | ($false = ((mrel @ sK2 @ X1))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ (sK25 @ X1)) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ (sK25 @ X1) @ Y1) => (f @ Y0 @ Y1))))))))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ X2) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ X2 @ Y1) => (f @ Y0 @ Y1)))))))))) )),
% 0.08/0.27 inference(imp_proxy_clausification,[],[f243])).
% 0.08/0.27 thf(f252,plain,(
% 0.08/0.27 ( ! [X2 : mworld,X1 : mworld] : (($false = ((mrel @ sK21 @ X2))) | ($false = ((mrel @ sK2 @ X1))) | ($false = (((^[Y0 : $i]: ((eiw_di @ Y0 @ (sK25 @ X1)) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ (sK25 @ X1) @ Y1) => (f @ Y0 @ Y1)))))) @ (sK26 @ X1)))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ X2) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ X2 @ Y1) => (f @ Y0 @ Y1)))))))))) )),
% 0.08/0.27 inference(sigma_proxy_clausification,[],[f244])).
% 0.08/0.27 thf(f253,plain,(
% 0.08/0.27 ( ! [X2 : mworld,X3 : $i,X1 : mworld] : (($false = ((mrel @ sK21 @ X2))) | ($false = ((mrel @ sK2 @ X1))) | ($false = (((^[Y0 : $i]: ((eiw_di @ Y0 @ (sK25 @ X1)) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ (sK25 @ X1) @ Y1) => (f @ Y0 @ Y1)))))) @ (sK26 @ X1)))) | ($true = (((^[Y0 : $i]: ((eiw_di @ Y0 @ X2) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ X2 @ Y1) => (f @ Y0 @ Y1)))))) @ X3)))) )),
% 0.08/0.27 inference(pi_proxy_clausification,[],[f252])).
% 0.08/0.27 thf(f254,plain,(
% 0.08/0.27 ( ! [X2 : mworld,X3 : $i,X1 : mworld] : (($false = ((mrel @ sK21 @ X2))) | ($false = ((mrel @ sK2 @ X1))) | ($false = (((eiw_di @ (sK26 @ X1) @ (sK25 @ X1)) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK25 @ X1) @ Y0) => (f @ (sK26 @ X1) @ Y0))))))) | ($true = (((eiw_di @ X3 @ X2) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (f @ X3 @ Y0)))))))) )),
% 0.08/0.27 inference(beta-eta_normalization,[],[f253])).
% 0.08/0.27 thf(f255,plain,(
% 0.08/0.27 ( ! [X2 : mworld,X3 : $i,X1 : mworld] : (($false = ((mrel @ sK21 @ X2))) | ($false = ((mrel @ sK2 @ X1))) | ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK25 @ X1) @ Y0) => (f @ (sK26 @ X1) @ Y0)))))) | ($true = (((eiw_di @ X3 @ X2) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (f @ X3 @ Y0)))))))) )),
% 0.08/0.27 inference(imp_proxy_clausification,[],[f254])).
% 0.08/0.27 thf(f256,plain,(
% 0.08/0.27 ( ! [X2 : mworld,X3 : $i,X1 : mworld] : (($false = ((mrel @ sK21 @ X2))) | ($false = ((mrel @ sK2 @ X1))) | ($true = ((eiw_di @ (sK26 @ X1) @ (sK25 @ X1)))) | ($true = (((eiw_di @ X3 @ X2) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (f @ X3 @ Y0)))))))) )),
% 0.08/0.27 inference(imp_proxy_clausification,[],[f254])).
% 0.08/0.27 thf(f257,plain,(
% 0.08/0.27 ( ! [X2 : mworld,X3 : $i,X1 : mworld] : (($false = ((mrel @ sK21 @ X2))) | ($false = ((mrel @ sK2 @ X1))) | ($true = ((eiw_di @ (sK26 @ X1) @ (sK25 @ X1)))) | ($false = ((eiw_di @ X3 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (f @ X3 @ Y0))))))) )),
% 0.08/0.27 inference(imp_proxy_clausification,[],[f256])).
% 0.08/0.27 thf(f258,plain,(
% 0.08/0.27 ( ! [X2 : mworld,X3 : $i,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK21 @ X2))) | ($false = ((mrel @ sK2 @ X1))) | ($true = ((eiw_di @ (sK26 @ X1) @ (sK25 @ X1)))) | ($false = ((eiw_di @ X3 @ X2))) | ($true = (((^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (f @ X3 @ Y0))) @ X4)))) )),
% 0.08/0.27 inference(pi_proxy_clausification,[],[f257])).
% 0.08/0.27 thf(f259,plain,(
% 0.08/0.27 ( ! [X2 : mworld,X3 : $i,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK21 @ X2))) | ($false = ((mrel @ sK2 @ X1))) | ($true = ((eiw_di @ (sK26 @ X1) @ (sK25 @ X1)))) | ($false = ((eiw_di @ X3 @ X2))) | ($true = (((mrel @ X2 @ X4) => (f @ X3 @ X4))))) )),
% 0.08/0.27 inference(beta-eta_normalization,[],[f258])).
% 0.08/0.27 thf(f260,plain,(
% 0.08/0.27 ( ! [X2 : mworld,X3 : $i,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK21 @ X2))) | ($false = ((mrel @ sK2 @ X1))) | ($true = ((eiw_di @ (sK26 @ X1) @ (sK25 @ X1)))) | ($false = ((eiw_di @ X3 @ X2))) | ($false = ((mrel @ X2 @ X4))) | ($true = ((f @ X3 @ X4)))) )),
% 0.08/0.27 inference(imp_proxy_clausification,[],[f259])).
% 0.08/0.27 thf(f261,plain,(
% 0.08/0.27 ( ! [X2 : mworld,X3 : $i,X1 : mworld] : (($false = ((mrel @ sK21 @ X2))) | ($false = ((mrel @ sK2 @ X1))) | ($false = (((^[Y0 : mworld]: ((mrel @ (sK25 @ X1) @ Y0) => (f @ (sK26 @ X1) @ Y0))) @ (sK27 @ X1)))) | ($true = (((eiw_di @ X3 @ X2) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (f @ X3 @ Y0)))))))) )),
% 0.08/0.27 inference(sigma_proxy_clausification,[],[f255])).
% 0.08/0.27 thf(f262,plain,(
% 0.08/0.27 ( ! [X2 : mworld,X3 : $i,X1 : mworld] : (($false = ((mrel @ sK21 @ X2))) | ($false = ((mrel @ sK2 @ X1))) | ($false = (((^[Y0 : mworld]: ((mrel @ (sK25 @ X1) @ Y0) => (f @ (sK26 @ X1) @ Y0))) @ (sK27 @ X1)))) | ($false = ((eiw_di @ X3 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (f @ X3 @ Y0))))))) )),
% 0.08/0.27 inference(imp_proxy_clausification,[],[f261])).
% 0.08/0.27 thf(f263,plain,(
% 0.08/0.27 ( ! [X2 : mworld,X3 : $i,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK21 @ X2))) | ($false = ((mrel @ sK2 @ X1))) | ($false = (((^[Y0 : mworld]: ((mrel @ (sK25 @ X1) @ Y0) => (f @ (sK26 @ X1) @ Y0))) @ (sK27 @ X1)))) | ($false = ((eiw_di @ X3 @ X2))) | ($true = (((^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (f @ X3 @ Y0))) @ X4)))) )),
% 0.08/0.27 inference(pi_proxy_clausification,[],[f262])).
% 0.08/0.27 thf(f264,plain,(
% 0.08/0.27 ( ! [X2 : mworld,X3 : $i,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK21 @ X2))) | ($false = ((mrel @ sK2 @ X1))) | ($false = (((mrel @ (sK25 @ X1) @ (sK27 @ X1)) => (f @ (sK26 @ X1) @ (sK27 @ X1))))) | ($false = ((eiw_di @ X3 @ X2))) | ($true = (((mrel @ X2 @ X4) => (f @ X3 @ X4))))) )),
% 0.08/0.27 inference(beta-eta_normalization,[],[f263])).
% 0.08/0.27 thf(f265,plain,(
% 0.08/0.27 ( ! [X2 : mworld,X3 : $i,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK21 @ X2))) | ($false = ((mrel @ sK2 @ X1))) | ($false = ((f @ (sK26 @ X1) @ (sK27 @ X1)))) | ($false = ((eiw_di @ X3 @ X2))) | ($true = (((mrel @ X2 @ X4) => (f @ X3 @ X4))))) )),
% 0.08/0.27 inference(imp_proxy_clausification,[],[f264])).
% 0.08/0.27 thf(f268,plain,(
% 0.08/0.27 ( ! [X2 : mworld,X3 : $i,X1 : mworld,X4 : mworld] : (($false = ((mrel @ sK21 @ X2))) | ($false = ((mrel @ sK2 @ X1))) | ($false = ((f @ (sK26 @ X1) @ (sK27 @ X1)))) | ($false = ((eiw_di @ X3 @ X2))) | ($false = ((mrel @ X2 @ X4))) | ($true = ((f @ X3 @ X4)))) )),
% 0.08/0.27 inference(imp_proxy_clausification,[],[f265])).
% 0.08/0.27 thf(f269,plain,(
% 0.08/0.27 ( ! [X1 : $i] : (($false = (((^[Y0 : mworld]: ((mrel @ sK1 @ Y0) => (~ (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) => (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y1 @ Y3) => (f @ Y2 @ Y3))))))))))))) @ sK21))) | ($false = (((^[Y0 : $i]: ((eiw_di @ Y0 @ sK2) & (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ sK2 @ Y1) => (~ (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (f @ Y0 @ Y2)))))))))) @ X1)))) )),
% 0.08/0.27 inference(pi_proxy_clausification,[],[f217])).
% 0.08/0.27 thf(f270,plain,(
% 0.08/0.27 ( ! [X1 : $i] : (($false = (((mrel @ sK1 @ sK21) => (~ (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK21 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y0 @ Y2) => (f @ Y1 @ Y2)))))))))))))) | ($false = (((eiw_di @ X1 @ sK2) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK2 @ Y0) => (~ (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (f @ X1 @ Y1)))))))))))) )),
% 0.08/0.27 inference(beta-eta_normalization,[],[f269])).
% 0.08/0.27 thf(f271,plain,(
% 0.08/0.27 ( ! [X1 : $i] : (($false = ((~ (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK21 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y0 @ Y2) => (f @ Y1 @ Y2))))))))))))) | ($false = (((eiw_di @ X1 @ sK2) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK2 @ Y0) => (~ (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (f @ X1 @ Y1)))))))))))) )),
% 0.08/0.27 inference(imp_proxy_clausification,[],[f270])).
% 0.08/0.27 thf(f282,plain,(
% 0.08/0.27 ( ! [X1 : $i] : (($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK21 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y0 @ Y2) => (f @ Y1 @ Y2)))))))))))) | ($false = (((eiw_di @ X1 @ sK2) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK2 @ Y0) => (~ (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (f @ X1 @ Y1)))))))))))) )),
% 0.08/0.27 inference(not_proxy_clausification,[],[f271])).
% 0.08/0.27 thf(f283,plain,(
% 0.08/0.27 ( ! [X2 : mworld,X1 : $i] : (($true = (((^[Y0 : mworld]: ((mrel @ sK21 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y0 @ Y2) => (f @ Y1 @ Y2))))))))) @ X2))) | ($false = (((eiw_di @ X1 @ sK2) & (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK2 @ Y0) => (~ (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (f @ X1 @ Y1)))))))))))) )),
% 0.08/0.27 inference(pi_proxy_clausification,[],[f282])).
% 0.08/0.27 thf(f284,plain,(
% 0.08/0.27 ( ! [X2 : mworld,X1 : $i] : (($true = (((^[Y0 : mworld]: ((mrel @ sK21 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y0 @ Y2) => (f @ Y1 @ Y2))))))))) @ X2))) | ($false = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK2 @ Y0) => (~ (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (f @ X1 @ Y1)))))))))) | ($false = ((eiw_di @ X1 @ sK2)))) )),
% 0.08/0.27 inference(and_proxy_clausification,[],[f283])).
% 0.08/0.27 thf(f285,plain,(
% 0.08/0.27 ( ! [X2 : mworld,X1 : $i] : (($true = (((^[Y0 : mworld]: ((mrel @ sK21 @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) => (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y0 @ Y2) => (f @ Y1 @ Y2))))))))) @ X2))) | ($false = (((^[Y0 : mworld]: ((mrel @ sK2 @ Y0) => (~ (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ Y0 @ Y1) => (f @ X1 @ Y1))))))) @ (sK29 @ X1)))) | ($false = ((eiw_di @ X1 @ sK2)))) )),
% 0.08/0.27 inference(sigma_proxy_clausification,[],[f284])).
% 0.08/0.27 thf(f286,plain,(
% 0.08/0.27 ( ! [X2 : mworld,X1 : $i] : (($true = (((mrel @ sK21 @ X2) => (!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ X2) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ X2 @ Y1) => (f @ Y0 @ Y1)))))))))) | ($false = (((mrel @ sK2 @ (sK29 @ X1)) => (~ (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK29 @ X1) @ Y0) => (f @ X1 @ Y0)))))))) | ($false = ((eiw_di @ X1 @ sK2)))) )),
% 0.08/0.27 inference(beta-eta_normalization,[],[f285])).
% 0.08/0.27 thf(f287,plain,(
% 0.08/0.27 ( ! [X2 : mworld,X1 : $i] : (($false = ((mrel @ sK21 @ X2))) | ($false = (((mrel @ sK2 @ (sK29 @ X1)) => (~ (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK29 @ X1) @ Y0) => (f @ X1 @ Y0)))))))) | ($false = ((eiw_di @ X1 @ sK2))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ X2) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ X2 @ Y1) => (f @ Y0 @ Y1)))))))))) )),
% 0.08/0.27 inference(imp_proxy_clausification,[],[f286])).
% 0.08/0.27 thf(f288,plain,(
% 0.08/0.27 ( ! [X2 : mworld,X1 : $i] : (($false = ((mrel @ sK21 @ X2))) | ($false = ((~ (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK29 @ X1) @ Y0) => (f @ X1 @ Y0))))))) | ($false = ((eiw_di @ X1 @ sK2))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ X2) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ X2 @ Y1) => (f @ Y0 @ Y1)))))))))) )),
% 0.08/0.27 inference(imp_proxy_clausification,[],[f287])).
% 0.08/0.27 thf(f296,plain,(
% 0.08/0.27 ( ! [X2 : mworld,X1 : $i] : (($false = ((mrel @ sK21 @ X2))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ (sK29 @ X1) @ Y0) => (f @ X1 @ Y0)))))) | ($false = ((eiw_di @ X1 @ sK2))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ X2) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ X2 @ Y1) => (f @ Y0 @ Y1)))))))))) )),
% 0.08/0.27 inference(not_proxy_clausification,[],[f288])).
% 0.08/0.27 thf(f297,plain,(
% 0.08/0.27 ( ! [X2 : mworld,X3 : mworld,X1 : $i] : (($false = ((mrel @ sK21 @ X2))) | ($true = (((^[Y0 : mworld]: ((mrel @ (sK29 @ X1) @ Y0) => (f @ X1 @ Y0))) @ X3))) | ($false = ((eiw_di @ X1 @ sK2))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ X2) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ X2 @ Y1) => (f @ Y0 @ Y1)))))))))) )),
% 0.08/0.27 inference(pi_proxy_clausification,[],[f296])).
% 0.08/0.27 thf(f298,plain,(
% 0.08/0.27 ( ! [X2 : mworld,X3 : mworld,X1 : $i,X4 : $i] : (($false = ((mrel @ sK21 @ X2))) | ($true = (((^[Y0 : mworld]: ((mrel @ (sK29 @ X1) @ Y0) => (f @ X1 @ Y0))) @ X3))) | ($false = ((eiw_di @ X1 @ sK2))) | ($true = (((^[Y0 : $i]: ((eiw_di @ Y0 @ X2) => (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ X2 @ Y1) => (f @ Y0 @ Y1)))))) @ X4)))) )),
% 0.08/0.27 inference(pi_proxy_clausification,[],[f297])).
% 0.08/0.27 thf(f299,plain,(
% 0.08/0.27 ( ! [X2 : mworld,X3 : mworld,X1 : $i,X4 : $i] : (($false = ((mrel @ sK21 @ X2))) | ($true = (((mrel @ (sK29 @ X1) @ X3) => (f @ X1 @ X3)))) | ($false = ((eiw_di @ X1 @ sK2))) | ($true = (((eiw_di @ X4 @ X2) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (f @ X4 @ Y0)))))))) )),
% 0.08/0.27 inference(beta-eta_normalization,[],[f298])).
% 0.08/0.27 thf(f300,plain,(
% 0.08/0.27 ( ! [X2 : mworld,X3 : mworld,X1 : $i,X4 : $i] : (($false = ((mrel @ sK21 @ X2))) | ($false = ((mrel @ (sK29 @ X1) @ X3))) | ($false = ((eiw_di @ X1 @ sK2))) | ($true = (((eiw_di @ X4 @ X2) => (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (f @ X4 @ Y0))))))) | ($true = ((f @ X1 @ X3)))) )),
% 0.08/0.27 inference(imp_proxy_clausification,[],[f299])).
% 0.08/0.27 thf(f301,plain,(
% 0.08/0.27 ( ! [X2 : mworld,X3 : mworld,X1 : $i,X4 : $i] : (($false = ((mrel @ sK21 @ X2))) | ($false = ((mrel @ (sK29 @ X1) @ X3))) | ($false = ((eiw_di @ X1 @ sK2))) | ($false = ((eiw_di @ X4 @ X2))) | ($true = ((f @ X1 @ X3))) | ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (f @ X4 @ Y0))))))) )),
% 0.08/0.27 inference(imp_proxy_clausification,[],[f300])).
% 0.08/0.27 thf(f302,plain,(
% 0.08/0.27 ( ! [X2 : mworld,X3 : mworld,X1 : $i,X4 : $i,X5 : mworld] : (($false = ((mrel @ sK21 @ X2))) | ($false = ((mrel @ (sK29 @ X1) @ X3))) | ($false = ((eiw_di @ X1 @ sK2))) | ($false = ((eiw_di @ X4 @ X2))) | ($true = ((f @ X1 @ X3))) | ($true = (((^[Y0 : mworld]: ((mrel @ X2 @ Y0) => (f @ X4 @ Y0))) @ X5)))) )),
% 0.08/0.27 inference(pi_proxy_clausification,[],[f301])).
% 0.08/0.27 thf(f303,plain,(
% 0.08/0.27 ( ! [X2 : mworld,X3 : mworld,X1 : $i,X4 : $i,X5 : mworld] : (($false = ((mrel @ sK21 @ X2))) | ($false = ((mrel @ (sK29 @ X1) @ X3))) | ($false = ((eiw_di @ X1 @ sK2))) | ($false = ((eiw_di @ X4 @ X2))) | ($true = ((f @ X1 @ X3))) | ($true = (((mrel @ X2 @ X5) => (f @ X4 @ X5))))) )),
% 0.08/0.27 inference(beta-eta_normalization,[],[f302])).
% 0.08/0.27 thf(f304,plain,(
% 0.08/0.27 ( ! [X2 : mworld,X3 : mworld,X1 : $i,X4 : $i,X5 : mworld] : (($false = ((mrel @ sK21 @ X2))) | ($false = ((mrel @ (sK29 @ X1) @ X3))) | ($false = ((eiw_di @ X1 @ sK2))) | ($false = ((eiw_di @ X4 @ X2))) | ($true = ((f @ X1 @ X3))) | ($false = ((mrel @ X2 @ X5))) | ($true = ((f @ X4 @ X5)))) )),
% 0.08/0.27 inference(imp_proxy_clausification,[],[f303])).
% 0.08/0.27 thf(f339,definition,(
% 0.08/0.27 spl30_9 <=> ($true = ((eiw_di @ sK7 @ sK1)))),
% 0.08/0.27 introduced(definition,[new_symbols(definition,[spl30_9])],[avatar_definition])).
% 0.08/0.27 thf(f341,plain,(
% 0.08/0.27 ($true = ((eiw_di @ sK7 @ sK1))) | ~spl30_9),
% 0.08/0.27 inference(avatar_component_clause,[],[f339])).
% 0.08/0.27 thf(f356,definition,(
% 0.08/0.27 spl30_13 <=> ! [X1 : mworld] : (($false = ((mrel @ sK2 @ X1))) | ($true = ((eiw_di @ (sK10 @ X1) @ (sK9 @ X1)))))),
% 0.08/0.27 introduced(definition,[new_symbols(definition,[spl30_13])],[avatar_definition])).
% 0.08/0.27 thf(f357,plain,(
% 0.08/0.27 ( ! [X1 : mworld] : (($false = ((mrel @ sK2 @ X1))) | ($true = ((eiw_di @ (sK10 @ X1) @ (sK9 @ X1))))) ) | ~spl30_13),
% 0.08/0.27 inference(avatar_component_clause,[],[f356])).
% 0.08/0.27 thf(f358,plain,(
% 0.08/0.27 spl30_13 | spl30_9),
% 0.08/0.27 inference(avatar_split_clause,[],[f133,f339,f356])).
% 0.08/0.27 thf(f364,definition,(
% 0.08/0.27 spl30_15 <=> ! [X1 : mworld] : (($false = ((mrel @ sK2 @ X1))) | ($false = ((f @ (sK10 @ X1) @ (sK11 @ X1)))))),
% 0.08/0.27 introduced(definition,[new_symbols(definition,[spl30_15])],[avatar_definition])).
% 0.08/0.27 thf(f365,plain,(
% 0.08/0.27 ( ! [X1 : mworld] : (($false = ((mrel @ sK2 @ X1))) | ($false = ((f @ (sK10 @ X1) @ (sK11 @ X1))))) ) | ~spl30_15),
% 0.08/0.27 inference(avatar_component_clause,[],[f364])).
% 0.08/0.27 thf(f366,plain,(
% 0.08/0.27 spl30_15 | spl30_9),
% 0.08/0.27 inference(avatar_split_clause,[],[f136,f339,f364])).
% 0.08/0.27 thf(f379,definition,(
% 0.08/0.27 spl30_19 <=> ! [X1 : mworld] : (($false = ((mrel @ sK2 @ X1))) | ($true = ((eiw_di @ (sK14 @ X1) @ (sK12 @ X1)))))),
% 0.08/0.27 introduced(definition,[new_symbols(definition,[spl30_19])],[avatar_definition])).
% 0.08/0.27 thf(f380,plain,(
% 0.08/0.27 ( ! [X1 : mworld] : (($false = ((mrel @ sK2 @ X1))) | ($true = ((eiw_di @ (sK14 @ X1) @ (sK12 @ X1))))) ) | ~spl30_19),
% 0.08/0.27 inference(avatar_component_clause,[],[f379])).
% 0.08/0.27 thf(f386,definition,(
% 0.08/0.27 spl30_21 <=> ! [X2 : mworld] : (($false = ((mrel @ sK1 @ X2))) | ($false = ((f @ sK7 @ (sK15 @ X2)))))),
% 0.08/0.27 introduced(definition,[new_symbols(definition,[spl30_21])],[avatar_definition])).
% 0.08/0.27 thf(f387,plain,(
% 0.08/0.27 ( ! [X2 : mworld] : (($false = ((mrel @ sK1 @ X2))) | ($false = ((f @ sK7 @ (sK15 @ X2))))) ) | ~spl30_21),
% 0.08/0.27 inference(avatar_component_clause,[],[f386])).
% 0.08/0.27 thf(f388,plain,(
% 0.08/0.27 spl30_19 | spl30_21),
% 0.08/0.27 inference(avatar_split_clause,[],[f157,f386,f379])).
% 0.08/0.27 thf(f394,definition,(
% 0.08/0.27 spl30_23 <=> ! [X1 : mworld] : (($false = ((mrel @ sK2 @ X1))) | ($false = ((f @ (sK14 @ X1) @ (sK16 @ X1)))))),
% 0.08/0.27 introduced(definition,[new_symbols(definition,[spl30_23])],[avatar_definition])).
% 0.08/0.27 thf(f395,plain,(
% 0.08/0.27 ( ! [X1 : mworld] : (($false = ((mrel @ sK2 @ X1))) | ($false = ((f @ (sK14 @ X1) @ (sK16 @ X1))))) ) | ~spl30_23),
% 0.08/0.27 inference(avatar_component_clause,[],[f394])).
% 0.08/0.27 thf(f398,plain,(
% 0.08/0.27 spl30_23 | spl30_21),
% 0.08/0.27 inference(avatar_split_clause,[],[f166,f386,f394])).
% 0.08/0.27 thf(f435,definition,(
% 0.08/0.27 spl30_33 <=> ! [X2 : $i,X1 : mworld,X3 : mworld] : (($false = ((mrel @ sK21 @ X1))) | ($true = ((f @ X2 @ X3))) | ($false = ((mrel @ X1 @ X3))) | (((eiw_di @ X2 @ X1)) = $false))),
% 0.08/0.27 introduced(definition,[new_symbols(definition,[spl30_33])],[avatar_definition])).
% 0.08/0.27 thf(f436,plain,(
% 0.08/0.27 ( ! [X2 : $i,X3 : mworld,X1 : mworld] : (($false = ((mrel @ sK21 @ X1))) | ($true = ((f @ X2 @ X3))) | ($false = ((mrel @ X1 @ X3))) | (((eiw_di @ X2 @ X1)) = $false)) ) | ~spl30_33),
% 0.08/0.27 inference(avatar_component_clause,[],[f435])).
% 0.08/0.27 thf(f459,definition,(
% 0.08/0.27 spl30_39 <=> ! [X1 : mworld] : (($false = ((mrel @ sK2 @ X1))) | ($true = ((eiw_di @ (sK26 @ X1) @ (sK25 @ X1)))))),
% 0.08/0.27 introduced(definition,[new_symbols(definition,[spl30_39])],[avatar_definition])).
% 0.08/0.27 thf(f460,plain,(
% 0.08/0.27 ( ! [X1 : mworld] : (($false = ((mrel @ sK2 @ X1))) | ($true = ((eiw_di @ (sK26 @ X1) @ (sK25 @ X1))))) ) | ~spl30_39),
% 0.08/0.27 inference(avatar_component_clause,[],[f459])).
% 0.08/0.27 thf(f461,plain,(
% 0.08/0.27 spl30_39 | spl30_33),
% 0.08/0.27 inference(avatar_split_clause,[],[f260,f435,f459])).
% 0.08/0.27 thf(f467,definition,(
% 0.08/0.27 spl30_41 <=> ! [X1 : mworld] : (($false = ((mrel @ sK2 @ X1))) | ($false = ((f @ (sK26 @ X1) @ (sK27 @ X1)))))),
% 0.08/0.27 introduced(definition,[new_symbols(definition,[spl30_41])],[avatar_definition])).
% 0.08/0.27 thf(f468,plain,(
% 0.08/0.27 ( ! [X1 : mworld] : (($false = ((mrel @ sK2 @ X1))) | ($false = ((f @ (sK26 @ X1) @ (sK27 @ X1))))) ) | ~spl30_41),
% 0.08/0.27 inference(avatar_component_clause,[],[f467])).
% 0.08/0.27 thf(f469,plain,(
% 0.08/0.27 spl30_41 | spl30_33),
% 0.08/0.27 inference(avatar_split_clause,[],[f268,f435,f467])).
% 0.08/0.27 thf(f483,definition,(
% 0.08/0.27 spl30_45 <=> ! [X1 : $i,X3 : mworld] : (($false = ((mrel @ (sK29 @ X1) @ X3))) | ($true = ((f @ X1 @ X3))) | ($false = ((eiw_di @ X1 @ sK2))))),
% 0.08/0.27 introduced(definition,[new_symbols(definition,[spl30_45])],[avatar_definition])).
% 0.08/0.27 thf(f484,plain,(
% 0.08/0.27 ( ! [X3 : mworld,X1 : $i] : (($false = ((mrel @ (sK29 @ X1) @ X3))) | ($true = ((f @ X1 @ X3))) | ($false = ((eiw_di @ X1 @ sK2)))) ) | ~spl30_45),
% 0.08/0.27 inference(avatar_component_clause,[],[f483])).
% 0.08/0.27 thf(f485,plain,(
% 0.08/0.27 spl30_45 | spl30_33),
% 0.08/0.27 inference(avatar_split_clause,[],[f304,f435,f483])).
% 0.08/0.27 thf(f493,plain,(
% 0.08/0.27 ( ! [X2 : $i,X0 : mworld,X1 : mworld] : ((((eiw_di @ X2 @ X0)) != $true) | (((eiw_di @ X2 @ X1)) = $true)) )),
% 0.08/0.27 inference(forward_subsumption_resolution,[],[f57,f55])).
% 0.08/0.27 thf(f494,plain,(
% 0.08/0.27 ( ! [X2 : mworld,X0 : $i,X1 : mworld] : (($true != $true) | ($true = ((eiw_di @ X0 @ X2))) | ($false = ((eiw_di @ X0 @ X1)))) )),
% 0.08/0.27 inference(constrained_superposition,[],[f493,f62])).
% 0.08/0.27 thf(f497,plain,(
% 0.08/0.27 ( ! [X2 : mworld,X0 : $i,X1 : mworld] : (($true = ((eiw_di @ X0 @ X2))) | ($false = ((eiw_di @ X0 @ X1)))) )),
% 0.08/0.27 inference(trivial_inequality_removal,[],[f494])).
% 0.08/0.27 thf(f498,plain,(
% 0.08/0.27 ( ! [X0 : mworld] : (($true != $true) | ($true = ((eiw_di @ sK7 @ X0)))) ) | ~spl30_9),
% 0.08/0.27 inference(constrained_superposition,[],[f493,f341])).
% 0.08/0.27 thf(f499,plain,(
% 0.08/0.27 ( ! [X0 : mworld] : (($true = ((eiw_di @ sK7 @ X0)))) ) | ~spl30_9),
% 0.08/0.27 inference(trivial_inequality_removal,[],[f498])).
% 0.08/0.27 thf(f539,plain,(
% 0.08/0.27 ( ! [X2 : $i,X0 : mworld,X1 : mworld] : (($true = $false) | ($false = ((mrel @ sK21 @ X0))) | ($true = ((f @ X2 @ X1))) | (((eiw_di @ X2 @ X0)) = $false)) ) | ~spl30_33),
% 0.08/0.27 inference(constrained_superposition,[],[f55,f436])).
% 0.08/0.27 thf(f542,plain,(
% 0.08/0.27 ( ! [X2 : mworld,X3 : mworld,X0 : $i,X1 : mworld] : (($true = $false) | ($false = ((eiw_di @ X0 @ X2))) | ($false = ((mrel @ sK21 @ X1))) | ($true = ((f @ X0 @ X3))) | ($false = ((mrel @ X1 @ X3)))) ) | ~spl30_33),
% 0.08/0.27 inference(constrained_superposition,[],[f497,f436])).
% 0.08/0.27 thf(f548,plain,(
% 0.08/0.27 ( ! [X2 : mworld,X3 : mworld,X0 : $i,X1 : mworld] : (($false = ((eiw_di @ X0 @ X2))) | ($false = ((mrel @ sK21 @ X1))) | ($true = ((f @ X0 @ X3))) | ($false = ((mrel @ X1 @ X3)))) ) | ~spl30_33),
% 0.08/0.27 inference(trivial_inequality_removal,[],[f542])).
% 0.08/0.27 thf(f551,plain,(
% 0.08/0.27 ( ! [X2 : $i,X0 : mworld,X1 : mworld] : (($false = ((mrel @ sK21 @ X0))) | ($true = ((f @ X2 @ X1))) | (((eiw_di @ X2 @ X0)) = $false)) ) | ~spl30_33),
% 0.08/0.27 inference(trivial_inequality_removal,[],[f539])).
% 0.08/0.27 thf(f578,plain,(
% 0.08/0.27 ( ! [X1 : mworld] : (($true = $false) | ($true = ((eiw_di @ (sK26 @ X1) @ (sK25 @ X1))))) ) | ~spl30_39),
% 0.08/0.27 inference(forward_demodulation,[],[f460,f55])).
% 0.08/0.27 thf(f579,plain,(
% 0.08/0.27 ( ! [X1 : mworld] : (($true = ((eiw_di @ (sK26 @ X1) @ (sK25 @ X1))))) ) | ~spl30_39),
% 0.08/0.27 inference(trivial_inequality_removal,[],[f578])).
% 0.08/0.27 thf(f580,plain,(
% 0.08/0.27 ( ! [X1 : mworld] : (($true = $false) | ($false = ((f @ (sK26 @ X1) @ (sK27 @ X1))))) ) | ~spl30_41),
% 0.08/0.27 inference(forward_demodulation,[],[f468,f55])).
% 0.08/0.27 thf(f581,plain,(
% 0.08/0.27 ( ! [X1 : mworld] : (($false = ((f @ (sK26 @ X1) @ (sK27 @ X1))))) ) | ~spl30_41),
% 0.08/0.27 inference(trivial_inequality_removal,[],[f580])).
% 0.08/0.27 thf(f588,plain,(
% 0.08/0.27 ( ! [X0 : $i,X1 : mworld] : (($true = $false) | ($true = ((f @ X0 @ X1))) | ($false = ((eiw_di @ X0 @ sK2)))) ) | ~spl30_45),
% 0.08/0.27 inference(constrained_superposition,[],[f55,f484])).
% 0.08/0.27 thf(f589,plain,(
% 0.08/0.27 ( ! [X0 : $i,X1 : mworld] : (($true = ((f @ X0 @ X1))) | ($false = ((eiw_di @ X0 @ sK2)))) ) | ~spl30_45),
% 0.08/0.27 inference(trivial_inequality_removal,[],[f588])).
% 0.08/0.27 thf(f594,plain,(
% 0.08/0.27 ( ! [X0 : mworld,X1 : mworld] : (($true != $true) | ($true = ((eiw_di @ (sK26 @ X0) @ X1)))) ) | ~spl30_39),
% 0.08/0.27 inference(constrained_superposition,[],[f493,f579])).
% 0.08/0.27 thf(f595,plain,(
% 0.08/0.27 ( ! [X0 : mworld,X1 : mworld] : (($true = ((eiw_di @ (sK26 @ X0) @ X1)))) ) | ~spl30_39),
% 0.08/0.27 inference(trivial_inequality_removal,[],[f594])).
% 0.08/0.27 thf(f623,plain,(
% 0.08/0.27 ( ! [X0 : mworld] : (($true = $false) | ($false = ((eiw_di @ (sK26 @ X0) @ sK2)))) ) | (~spl30_41 | ~spl30_45)),
% 0.08/0.27 inference(constrained_superposition,[],[f589,f581])).
% 0.08/0.27 thf(f624,plain,(
% 0.08/0.27 ( ! [X0 : mworld] : (($false = ((eiw_di @ (sK26 @ X0) @ sK2)))) ) | (~spl30_41 | ~spl30_45)),
% 0.08/0.27 inference(trivial_inequality_removal,[],[f623])).
% 0.08/0.27 thf(f627,plain,(
% 0.08/0.27 ( ! [X2 : mworld] : (($true = $false) | ($false = ((f @ sK7 @ (sK15 @ X2))))) ) | ~spl30_21),
% 0.08/0.27 inference(forward_demodulation,[],[f387,f55])).
% 0.08/0.27 thf(f628,plain,(
% 0.08/0.27 ( ! [X2 : mworld] : (($false = ((f @ sK7 @ (sK15 @ X2))))) ) | ~spl30_21),
% 0.08/0.27 inference(trivial_inequality_removal,[],[f627])).
% 0.08/0.27 thf(f648,plain,(
% 0.08/0.27 ( ! [X1 : mworld] : (($true = $false) | ($true = ((eiw_di @ (sK14 @ X1) @ (sK12 @ X1))))) ) | ~spl30_19),
% 0.08/0.27 inference(forward_demodulation,[],[f380,f55])).
% 0.08/0.27 thf(f649,plain,(
% 0.08/0.27 ( ! [X1 : mworld] : (($true = ((eiw_di @ (sK14 @ X1) @ (sK12 @ X1))))) ) | ~spl30_19),
% 0.08/0.27 inference(trivial_inequality_removal,[],[f648])).
% 0.08/0.27 thf(f650,plain,(
% 0.08/0.27 ( ! [X1 : mworld] : (($true = $false) | ($false = ((f @ (sK14 @ X1) @ (sK16 @ X1))))) ) | ~spl30_23),
% 0.08/0.27 inference(forward_demodulation,[],[f395,f55])).
% 0.08/0.27 thf(f651,plain,(
% 0.08/0.27 ( ! [X1 : mworld] : (($false = ((f @ (sK14 @ X1) @ (sK16 @ X1))))) ) | ~spl30_23),
% 0.08/0.27 inference(trivial_inequality_removal,[],[f650])).
% 0.08/0.27 thf(f653,plain,(
% 0.08/0.27 ($true = $false) | (~spl30_39 | ~spl30_41 | ~spl30_45)),
% 0.08/0.27 inference(constrained_superposition,[],[f624,f595])).
% 0.08/0.27 thf(f662,plain,(
% 0.08/0.27 $false | (~spl30_39 | ~spl30_41 | ~spl30_45)),
% 0.08/0.27 inference(trivial_inequality_removal,[],[f653])).
% 0.08/0.27 thf(f663,plain,(
% 0.08/0.27 ~spl30_39 | ~spl30_41 | ~spl30_45),
% 0.08/0.27 inference(avatar_contradiction_clause,[],[f662])).
% 0.08/0.27 thf(f791,plain,(
% 0.08/0.27 ( ! [X0 : mworld,X1 : mworld] : (($true = $false) | ($false = ((mrel @ sK21 @ (sK12 @ X0)))) | ($true = ((f @ (sK14 @ X0) @ X1)))) ) | (~spl30_19 | ~spl30_33)),
% 0.08/0.27 inference(constrained_superposition,[],[f649,f551])).
% 0.08/0.27 thf(f795,plain,(
% 0.08/0.27 ( ! [X0 : mworld,X1 : mworld] : (($false = ((mrel @ sK21 @ (sK12 @ X0)))) | ($true = ((f @ (sK14 @ X0) @ X1)))) ) | (~spl30_19 | ~spl30_33)),
% 0.08/0.27 inference(trivial_inequality_removal,[],[f791])).
% 0.08/0.27 thf(f813,definition,(
% 0.08/0.27 spl30_48 <=> ! [X1 : mworld] : ($false = ((mrel @ sK21 @ X1)))),
% 0.08/0.27 introduced(definition,[new_symbols(definition,[spl30_48])],[avatar_definition])).
% 0.08/0.27 thf(f814,plain,(
% 0.08/0.27 ( ! [X1 : mworld] : (($false = ((mrel @ sK21 @ X1)))) ) | ~spl30_48),
% 0.08/0.27 inference(avatar_component_clause,[],[f813])).
% 0.08/0.27 thf(f816,definition,(
% 0.08/0.27 spl30_49 <=> ! [X2 : mworld,X0 : $i,X3 : mworld] : (($false = ((eiw_di @ X0 @ X2))) | ($true = ((f @ X0 @ X3))))),
% 0.08/0.27 introduced(definition,[new_symbols(definition,[spl30_49])],[avatar_definition])).
% 0.08/0.27 thf(f817,plain,(
% 0.08/0.27 ( ! [X2 : mworld,X3 : mworld,X0 : $i] : (($false = ((eiw_di @ X0 @ X2))) | ($true = ((f @ X0 @ X3)))) ) | ~spl30_49),
% 0.08/0.27 inference(avatar_component_clause,[],[f816])).
% 0.08/0.27 thf(f819,plain,(
% 0.08/0.27 ( ! [X0 : mworld,X1 : mworld] : (($true = $false) | ($true = ((f @ (sK14 @ X0) @ X1)))) ) | (~spl30_19 | ~spl30_33)),
% 0.08/0.27 inference(forward_demodulation,[],[f795,f55])).
% 0.08/0.27 thf(f820,plain,(
% 0.08/0.27 ( ! [X0 : mworld,X1 : mworld] : (($true = ((f @ (sK14 @ X0) @ X1)))) ) | (~spl30_19 | ~spl30_33)),
% 0.08/0.27 inference(trivial_inequality_removal,[],[f819])).
% 0.08/0.27 thf(f895,definition,(
% 0.08/0.27 spl30_51 <=> ! [X2 : mworld,X0 : mworld] : ($true = ((f @ (sK14 @ X0) @ X2)))),
% 0.08/0.27 introduced(definition,[new_symbols(definition,[spl30_51])],[avatar_definition])).
% 0.08/0.27 thf(f896,plain,(
% 0.08/0.27 ( ! [X2 : mworld,X0 : mworld] : (($true = ((f @ (sK14 @ X0) @ X2)))) ) | ~spl30_51),
% 0.08/0.27 inference(avatar_component_clause,[],[f895])).
% 0.08/0.27 thf(f899,plain,(
% 0.08/0.27 spl30_51 | ~spl30_19 | ~spl30_33),
% 0.08/0.27 inference(avatar_split_clause,[],[f820,f435,f379,f895])).
% 0.08/0.27 thf(f914,plain,(
% 0.08/0.27 ($true = $false) | (~spl30_23 | ~spl30_51)),
% 0.08/0.27 inference(constrained_superposition,[],[f651,f896])).
% 0.08/0.27 thf(f930,plain,(
% 0.08/0.27 $false | (~spl30_23 | ~spl30_51)),
% 0.08/0.27 inference(trivial_inequality_removal,[],[f914])).
% 0.08/0.27 thf(f931,plain,(
% 0.08/0.27 ~spl30_23 | ~spl30_51),
% 0.08/0.27 inference(avatar_contradiction_clause,[],[f930])).
% 0.08/0.27 thf(f956,plain,(
% 0.08/0.27 ( ! [X2 : $i,X3 : mworld,X0 : mworld,X1 : mworld] : (($true = $false) | ($false = ((eiw_di @ X2 @ X3))) | ($false = ((mrel @ sK21 @ X0))) | ($true = ((f @ X2 @ X1)))) ) | ~spl30_33),
% 0.08/0.27 inference(constrained_superposition,[],[f548,f55])).
% 0.08/0.27 thf(f980,plain,(
% 0.08/0.27 ( ! [X2 : $i,X3 : mworld,X0 : mworld,X1 : mworld] : (($false = ((eiw_di @ X2 @ X3))) | ($false = ((mrel @ sK21 @ X0))) | ($true = ((f @ X2 @ X1)))) ) | ~spl30_33),
% 0.08/0.27 inference(trivial_inequality_removal,[],[f956])).
% 0.08/0.27 thf(f998,plain,(
% 0.08/0.27 spl30_48 | spl30_49 | ~spl30_33),
% 0.08/0.27 inference(avatar_split_clause,[],[f980,f435,f816,f813])).
% 0.08/0.27 thf(f1019,plain,(
% 0.08/0.27 ( ! [X1 : mworld] : (($true = $false) | ($false = ((mrel @ sK21 @ X1))) | ($false = ((eiw_di @ sK7 @ X1)))) ) | (~spl30_21 | ~spl30_33)),
% 0.08/0.27 inference(constrained_superposition,[],[f551,f628])).
% 0.08/0.27 thf(f1020,plain,(
% 0.08/0.27 ( ! [X1 : mworld] : (($false = ((mrel @ sK21 @ X1))) | ($false = ((eiw_di @ sK7 @ X1)))) ) | (~spl30_21 | ~spl30_33)),
% 0.08/0.27 inference(trivial_inequality_removal,[],[f1019])).
% 0.08/0.27 thf(f1023,plain,(
% 0.08/0.27 ( ! [X1 : mworld] : (($true = $false) | ($false = ((mrel @ sK21 @ X1)))) ) | (~spl30_9 | ~spl30_21 | ~spl30_33)),
% 0.08/0.27 inference(forward_demodulation,[],[f1020,f499])).
% 0.08/0.27 thf(f1024,plain,(
% 0.08/0.27 ( ! [X1 : mworld] : (($false = ((mrel @ sK21 @ X1)))) ) | (~spl30_9 | ~spl30_21 | ~spl30_33)),
% 0.08/0.27 inference(trivial_inequality_removal,[],[f1023])).
% 0.08/0.27 thf(f1027,plain,(
% 0.08/0.27 spl30_48 | ~spl30_9 | ~spl30_21 | ~spl30_33),
% 0.08/0.27 inference(avatar_split_clause,[],[f1024,f435,f386,f339,f813])).
% 0.08/0.27 thf(f1030,plain,(
% 0.08/0.27 ($true = $false) | ~spl30_48),
% 0.08/0.27 inference(constrained_superposition,[],[f814,f55])).
% 0.08/0.27 thf(f1034,plain,(
% 0.08/0.27 $false | ~spl30_48),
% 0.08/0.27 inference(trivial_inequality_removal,[],[f1030])).
% 0.08/0.27 thf(f1035,plain,(
% 0.08/0.27 ~spl30_48),
% 0.08/0.27 inference(avatar_contradiction_clause,[],[f1034])).
% 0.08/0.27 thf(f1038,plain,(
% 0.08/0.27 ( ! [X1 : mworld] : (($true = $false) | ($true = ((eiw_di @ (sK10 @ X1) @ (sK9 @ X1))))) ) | ~spl30_13),
% 0.08/0.27 inference(forward_demodulation,[],[f357,f55])).
% 0.08/0.27 thf(f1039,plain,(
% 0.08/0.27 ( ! [X1 : mworld] : (($true = ((eiw_di @ (sK10 @ X1) @ (sK9 @ X1))))) ) | ~spl30_13),
% 0.08/0.27 inference(trivial_inequality_removal,[],[f1038])).
% 0.08/0.27 thf(f1040,plain,(
% 0.08/0.27 ( ! [X1 : mworld] : (($true = $false) | ($false = ((f @ (sK10 @ X1) @ (sK11 @ X1))))) ) | ~spl30_15),
% 0.08/0.27 inference(forward_demodulation,[],[f365,f55])).
% 0.08/0.27 thf(f1041,plain,(
% 0.08/0.27 ( ! [X1 : mworld] : (($false = ((f @ (sK10 @ X1) @ (sK11 @ X1))))) ) | ~spl30_15),
% 0.08/0.27 inference(trivial_inequality_removal,[],[f1040])).
% 0.08/0.27 thf(f1108,plain,(
% 0.08/0.27 ( ! [X0 : mworld,X1 : mworld] : (($true = $false) | ($true = ((f @ (sK10 @ X0) @ X1)))) ) | (~spl30_13 | ~spl30_49)),
% 0.08/0.27 inference(constrained_superposition,[],[f817,f1039])).
% 0.08/0.27 thf(f1109,plain,(
% 0.08/0.27 ( ! [X0 : mworld,X1 : mworld] : (($true = ((f @ (sK10 @ X0) @ X1)))) ) | (~spl30_13 | ~spl30_49)),
% 0.08/0.27 inference(trivial_inequality_removal,[],[f1108])).
% 0.08/0.27 thf(f1157,plain,(
% 0.08/0.27 ($true = $false) | (~spl30_13 | ~spl30_15 | ~spl30_49)),
% 0.08/0.27 inference(constrained_superposition,[],[f1041,f1109])).
% 0.08/0.27 thf(f1181,plain,(
% 0.08/0.27 $false | (~spl30_13 | ~spl30_15 | ~spl30_49)),
% 0.08/0.27 inference(trivial_inequality_removal,[],[f1157])).
% 0.08/0.27 thf(f1182,plain,(
% 0.08/0.27 ~spl30_13 | ~spl30_15 | ~spl30_49),
% 0.08/0.27 inference(avatar_contradiction_clause,[],[f1181])).
% 0.08/0.27 cnf(s12, plain, spl30_9 | spl30_13, inference(sat_conversion,[],[f358])).
% 0.08/0.27 cnf(s14, plain, spl30_9 | spl30_15, inference(sat_conversion,[],[f366])).
% 0.08/0.27 cnf(s18, plain, spl30_19 | spl30_21, inference(sat_conversion,[],[f388])).
% 0.08/0.27 cnf(s22, plain, spl30_21 | spl30_23, inference(sat_conversion,[],[f398])).
% 0.08/0.27 cnf(s36, plain, spl30_33 | spl30_39, inference(sat_conversion,[],[f461])).
% 0.08/0.27 cnf(s38, plain, spl30_33 | spl30_41, inference(sat_conversion,[],[f469])).
% 0.08/0.27 cnf(s42, plain, spl30_33 | spl30_45, inference(sat_conversion,[],[f485])).
% 0.08/0.27 cnf(s50, plain, ~spl30_39 | ~spl30_41 | ~spl30_45, inference(sat_conversion,[],[f663])).
% 0.08/0.27 cnf(s69, plain, ~spl30_19 | ~spl30_33 | spl30_51, inference(sat_conversion,[],[f899])).
% 0.08/0.27 cnf(s74, plain, ~spl30_23 | ~spl30_51, inference(sat_conversion,[],[f931])).
% 0.08/0.27 cnf(s78, plain, ~spl30_33 | spl30_48 | spl30_49, inference(sat_conversion,[],[f998])).
% 0.08/0.27 cnf(s81, plain, ~spl30_9 | ~spl30_21 | ~spl30_33 | spl30_48, inference(sat_conversion,[],[f1027])).
% 0.08/0.27 cnf(s84, plain, ~spl30_48, inference(sat_conversion,[],[f1035])).
% 0.08/0.27 cnf(s87, plain, ~spl30_13 | ~spl30_15 | ~spl30_49, inference(sat_conversion,[],[f1182])).
% 0.08/0.27 cnf(s88, plain, ~spl30_9 | ~spl30_21 | ~spl30_33, inference(rat,[],[s81,s84])).
% 0.08/0.27 cnf(s89, plain, ~spl30_33 | spl30_49, inference(rat,[],[s78,s84])).
% 0.08/0.27 cnf(s107, plain, ~spl30_33 | ~spl30_9, inference(rat,[],[s69,s74,s18,s22,s88])).
% 0.08/0.27 cnf(s109, plain, spl30_33, inference(rat,[],[s50,s36,s38,s42])).
% 0.08/0.27 cnf(s110, plain, spl30_49, inference(rat,[],[s89,s109])).
% 0.08/0.27 cnf(s113, plain, ~spl30_9, inference(rat,[],[s107,s109])).
% 0.08/0.27 cnf(s116, plain, spl30_15, inference(rat,[],[s14,s113])).
% 0.08/0.27 cnf(s118, plain, spl30_13, inference(rat,[],[s12,s113])).
% 0.08/0.27 cnf(s120, plain, $false, inference(rat,[],[s87,s110,s116,s118])).
% 0.08/0.27 thf(f1196,plain,(
% 0.08/0.27 $false),
% 0.08/0.27 inference(avatar_sat_refutation,[],[s120])).
% 0.08/0.27 % SZS output end Proof for theBenchmark
% 0.08/0.27 % (910513)------------------------------
% 0.08/0.27 % (910513)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.27 % (910513)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.27 % (910513)CaDiCaL version: 2.1.3
% 0.08/0.27 % (910513)Termination reason: Refutation
% 0.08/0.27 % (910513)Time elapsed: 0.024 s
% 0.08/0.27 % (910513)Peak memory usage: 13 MB
% 0.08/0.27 % (910513)Instructions burned: 85 (million)
% 0.08/0.27 % (910507)Success in time 0.051 s
% 0.08/0.27 % Vampire exiting
%------------------------------------------------------------------------------