Vampire-SAT---5.0.1.THM-Ref.s

%------------------------------------------------------------------------------
% File     : Vampire-SAT---5.0.1
% Problem  : SEV292^5 : TPTP v9.3.1. Bugfixed v6.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT

% Computer : n007.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 08:39:16 AM UTC 2026

% Result   : Theorem 0.96s 0.59s
% Output   : Refutation 0.96s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SEV292^5 : TPTP v9.3.1. Bugfixed v6.2.0.
% 0.00/0.06  % Command  : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20  % Computer : n007.cluster.edu
% 0.09/0.20  % Model    : x86_64 x86_64
% 0.09/0.20  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20  % Memory   : 8046.5625MB
% 0.09/0.20  % OS       : Linux 6.8.0-71-generic
% 0.09/0.20  % CPULimit : 300
% 0.09/0.20  % WCLimit  : 300
% 0.09/0.20  % DateTime : Tue Sep 29 15:29:41 UTC 2026
% 0.09/0.20  % CPUTime  : 
% 0.09/0.20  Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23  Running first-order model finding
% 0.09/0.23  Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.96/0.59  % (3508642)Will run a generic schedule for satisfiability detection.
% 0.96/0.59  % (3508648)% WARNING: option uhcvi not known.
% 0.96/0.59  % (3508648)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1028343107:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.96/0.59  % (3508648)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.96/0.59  % (3508648)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.96/0.59  % (3508647)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1662194953_2999 on theBenchmark for (2999ds/0Mi)
% 0.96/0.59  % (3508649)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1372089103:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.96/0.59  % (3508650)dis+10_1_sil=32000:sp=arity:random_seed=1724383454:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.96/0.59  % (3508651)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1521352982:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.96/0.59  % Exception at run slice level
% 0.96/0.59  User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.96/0.59  % (3508651)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.96/0.59  % (3508653)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=336142201:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.96/0.59  % (3508652)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1234493887:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.96/0.59  % (3508659)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3354997139:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.96/0.59  % Exception at run slice level
% 0.96/0.59  User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.96/0.59  % (3508663)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2204170889:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.96/0.59  % (3508650)Instruction limit reached! 
% 0.96/0.59  % (3508650)------------------------------
% 0.96/0.59  % (3508650)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.96/0.59  % (3508650)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.96/0.59  % (3508650)CaDiCaL version: 2.1.3
% 0.96/0.59  % (3508650)Termination reason: Instruction limit
% 0.96/0.59  % (3508650)Termination phase: Saturation
% 0.96/0.59  % (3508650)Time elapsed: 0.048 s
% 0.96/0.59  % (3508650)Peak memory usage: 12 MB
% 0.96/0.59  % (3508650)Instructions burned: 105 (million)
% 0.96/0.59  % (3508651)Instruction limit reached! 
% 0.96/0.59  % (3508651)------------------------------
% 0.96/0.59  % (3508651)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.96/0.59  % (3508651)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.96/0.59  % (3508651)CaDiCaL version: 2.1.3
% 0.96/0.59  % (3508651)Termination reason: Instruction limit
% 0.96/0.59  % (3508651)Termination phase: Saturation
% 0.96/0.59  % (3508651)Time elapsed: 0.065 s
% 0.96/0.59  % (3508651)Peak memory usage: 12 MB
% 0.96/0.59  % (3508651)Instructions burned: 116 (million)
% 0.96/0.59  % (3508665)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=3915062557:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 0.96/0.59  % (3508665)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.96/0.59  % (3508665)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.96/0.59  % (3508653)Instruction limit reached! 
% 0.96/0.59  % (3508653)------------------------------
% 0.96/0.59  % (3508653)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.96/0.59  % (3508653)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.96/0.59  % (3508653)CaDiCaL version: 2.1.3
% 0.96/0.59  % (3508653)Termination reason: Instruction limit
% 0.96/0.59  % (3508653)Termination phase: Saturation
% 0.96/0.59  % (3508653)Time elapsed: 0.074 s
% 0.96/0.59  % (3508653)Peak memory usage: 13 MB
% 0.96/0.59  % (3508653)Instructions burned: 160 (million)
% 0.96/0.59  % (3508666)ott-21_1_sil=16000:fs=off:random_seed=3938842127:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 0.96/0.59  % (3508668)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2741555742:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 0.96/0.59  % (3508663)Instruction limit reached! 
% 0.96/0.59  % (3508663)------------------------------
% 0.96/0.59  % (3508663)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.96/0.59  % (3508663)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.96/0.59  % (3508663)CaDiCaL version: 2.1.3
% 0.96/0.59  % (3508663)Termination reason: Instruction limit
% 0.96/0.59  % (3508663)Termination phase: Saturation
% 0.96/0.59  % (3508663)Time elapsed: 0.063 s
% 0.96/0.59  % (3508663)Peak memory usage: 12 MB
% 0.96/0.59  % (3508663)Instructions burned: 133 (million)
% 0.96/0.59  % (3508652)Instruction limit reached! 
% 0.96/0.59  % (3508652)------------------------------
% 0.96/0.59  % (3508652)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.96/0.59  % (3508652)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.96/0.59  % (3508652)CaDiCaL version: 2.1.3
% 0.96/0.59  % (3508652)Termination reason: Instruction limit
% 0.96/0.59  % (3508652)Termination phase: Saturation
% 0.96/0.59  % (3508652)Time elapsed: 0.107 s
% 0.96/0.59  % (3508652)Peak memory usage: 12 MB
% 0.96/0.59  % (3508652)Instructions burned: 131 (million)
% 0.96/0.59  % (3508671)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=500877077:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 0.96/0.59  % Exception at run slice level
% 0.96/0.59  User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.96/0.59  % (3508672)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=222081111:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 0.96/0.59  % (3508674)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=4259603985:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 0.96/0.59  % Exception at run slice level
% 0.96/0.59  User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.96/0.59  % (3508677)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=880494701:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2998 on theBenchmark for (2998ds/692Mi)
% 0.96/0.59  % (3508666)Instruction limit reached! 
% 0.96/0.59  % (3508666)------------------------------
% 0.96/0.59  % (3508666)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.96/0.59  % (3508677)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.96/0.59  % (3508666)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.96/0.59  % (3508666)CaDiCaL version: 2.1.3
% 0.96/0.59  % (3508666)Termination reason: Instruction limit
% 0.96/0.59  % (3508666)Termination phase: Saturation
% 0.96/0.59  % (3508666)Time elapsed: 0.082 s
% 0.96/0.59  % (3508666)Peak memory usage: 13 MB
% 0.96/0.59  % (3508666)Instructions burned: 182 (million)
% 0.96/0.59  % (3508679)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=3128024060:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 0.96/0.59  % (3508679)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.96/0.59  % (3508677) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3508642-3508677"...
% 0.96/0.59  % (3508677)...printing done.
% 0.96/0.59  % (3508677)Refutation found. Thanks to Tanya!
% 0.96/0.59  % SZS status Theorem for theBenchmark
% 0.96/0.59  % SZS output start Proof for theBenchmark
% 0.96/0.59  thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.96/0.59  thf(func_def_0, type, cP: ((($i > $o) > $o) > $o)).
% 0.96/0.59  thf(func_def_1, type, cONE: (($i > $o) > $o)).
% 0.96/0.59  thf(func_def_2, type, cSUCC: ((($i > $o) > $o) > ($i > $o) > $o)).
% 0.96/0.59  thf(func_def_3, type, cZERO: (($i > $o) > $o)).
% 0.96/0.59  thf(func_def_4, type, c_less__eq_: ((($i > $o) > $o) > (($i > $o) > $o) > $o)).
% 0.96/0.59  thf(func_def_6, type, vNOT: ($o > $o)).
% 0.96/0.59  thf(func_def_7, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.96/0.59  thf(func_def_8, type, db1: !>[X0: $tType]:(X0)).
% 0.96/0.59  thf(func_def_9, type, db0: !>[X0: $tType]:(X0)).
% 0.96/0.59  thf(func_def_10, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.96/0.59  thf(func_def_11, type, vAND: ($o > $o > $o)).
% 0.96/0.59  thf(func_def_12, type, db2: !>[X0: $tType]:(X0)).
% 0.96/0.59  thf(func_def_13, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.96/0.59  thf(func_def_14, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.96/0.59  thf(func_def_15, type, vIMP: ($o > $o > $o)).
% 0.96/0.59  thf(func_def_18, type, db3: !>[X0: $tType]:(X0)).
% 0.96/0.59  thf(func_def_19, type, db4: !>[X0: $tType]:(X0)).
% 0.96/0.59  thf(func_def_20, type, db5: !>[X0: $tType]:(X0)).
% 0.96/0.59  thf(func_def_21, type, sK0: ((($i > $o) > $o) > (($i > $o) > $o) > $o)).
% 0.96/0.59  thf(func_def_22, type, sK1: ((($i > $o) > $o) > (($i > $o) > $o) > $o)).
% 0.96/0.59  thf(func_def_24, type, sK3: ((($i > $o) > $i > $o) > $i > $o)).
% 0.96/0.59  thf(func_def_25, type, sK4: ((($i > $o) > $i > $o) > $i > $o)).
% 0.96/0.59  thf(func_def_26, type, sK5: ((($i > $o) > $i > $o) > $i > $o)).
% 0.96/0.59  thf(func_def_27, type, sK6: ((($i > $o) > $i > $o) > $i)).
% 0.96/0.59  thf(func_def_28, type, sK7: ((($i > $o) > $i > $o) > $i)).
% 0.96/0.59  thf(func_def_29, type, sK8: ((($i > $o) > $i > $o) > $i)).
% 0.96/0.59  thf(func_def_30, type, sK9: ((($i > $o) > $i > $o) > $i)).
% 0.96/0.59  thf(func_def_31, type, sK10: ((($i > $o) > $i > $i > $o) > $i > $o)).
% 0.96/0.59  thf(func_def_32, type, db6: !>[X0: $tType]:(X0)).
% 0.96/0.59  thf(func_def_33, type, sK11: ((($i > $o) > $i > $i > $o) > $i)).
% 0.96/0.59  thf(func_def_34, type, sK12: ((($i > $o) > $i > $i > $o) > $i)).
% 0.96/0.59  thf(func_def_35, type, sK13: ((($i > $o) > $i > $i > $o) > $i)).
% 0.96/0.59  thf(func_def_36, type, sK14: ((($i > $o) > $i > $i > $o) > $i)).
% 0.96/0.59  thf(func_def_37, type, sK15: ((($i > $o) > $i > $i > $o) > $i)).
% 0.96/0.59  thf(func_def_38, type, sK16: ((($i > $o) > $i > $i > $o) > $i)).
% 0.96/0.59  thf(func_def_39, type, sK17: ((($i > $o) > $i > $i > $o) > $i > $o)).
% 0.96/0.59  thf(func_def_40, type, sK18: ((($i > $o) > $i > $i > $o) > $i)).
% 0.96/0.59  thf(func_def_41, type, sK19: ((($i > $o) > $i > $i > $o) > $i)).
% 0.96/0.59  thf(func_def_42, type, sK20: ((($i > $o) > $i > $i > $o) > $i)).
% 0.96/0.59  thf(func_def_43, type, sK21: ((($i > $o) > $i > $o) > $i)).
% 0.96/0.59  thf(func_def_44, type, sK22: ((($i > $o) > $i > $o) > $i > $o)).
% 0.96/0.59  thf(func_def_45, type, sK23: ((($i > $o) > $i > $i > $i) > $i > $o)).
% 0.96/0.59  thf(func_def_46, type, sK24: ((($i > $o) > $i > $i > $i) > $i)).
% 0.96/0.59  thf(func_def_47, type, sK25: ((($i > $o) > $i > $i > $o) > $i > $o)).
% 0.96/0.59  thf(func_def_48, type, sK26: ((($i > $o) > $i > $i > $i) > $i)).
% 0.96/0.59  thf(func_def_49, type, sK27: ((($i > $o) > $i > $i > $i) > $i)).
% 0.96/0.59  thf(func_def_50, type, db7: !>[X0: $tType]:(X0)).
% 0.96/0.59  thf(func_def_51, type, sK28: ((($i > $o) > $i > $i > $o) > $i)).
% 0.96/0.59  thf(func_def_52, type, sK29: ((($i > $o) > $i > $i > $o) > $i)).
% 0.96/0.59  thf(func_def_53, type, sK30: ((($i > $o) > $i > $i > $i) > $i > $o)).
% 0.96/0.59  thf(func_def_54, type, sK31: ((($i > $o) > $i > $i > $i) > $i > $o)).
% 0.96/0.59  thf(func_def_55, type, sK32: ((($i > $o) > $i > $i > $i) > $i > $o)).
% 0.96/0.59  thf(f1,axiom,(
% 0.96/0.59    (cZERO = (^[X0 : ($i > $o)] : (~ ? [X1 : $i] : (X0 @ X1))))),
% 0.96/0.59    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cZERO_def)).
% 0.96/0.59  thf(f2,axiom,(
% 0.96/0.59    (cSUCC = (^[X0 : (($i > $o) > $o), X1 : ($i > $o)] : (? [X2 : $i] : ((X0 @ (^[X3 : $i] : ((X1 @ X3) & (X3 != X2)))) & (X1 @ X2)))))),
% 0.96/0.59    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cSUCC_def)).
% 0.96/0.59  thf(f3,axiom,(
% 0.96/0.59    (cONE = ((cSUCC @ cZERO)))),
% 0.96/0.59    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cONE_def)).
% 0.96/0.59  thf(f4,axiom,(
% 0.96/0.59    (c_less__eq_ = (^[X0 : (($i > $o) > $o), X1 : (($i > $o) > $o)] : (! [X2 : ((($i > $o) > $o) > $o)] : ((! [X3 : (($i > $o) > $o)] : ((X2 @ X3) => (X2 @ (cSUCC @ X3))) & (X2 @ X0)) => (X2 @ X1)))))),
% 0.96/0.59    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_less__eq__def)).
% 0.96/0.59  thf(f5,conjecture,(
% 0.96/0.59    (cP @ cONE) => ? [X0 : (($i > $o) > $o)] : ((cP @ X0) & (c_less__eq_ @ X0 @ (cSUCC @ cONE)) & (c_less__eq_ @ cZERO @ X0))),
% 0.96/0.59    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cBLEDSOE7A)).
% 0.96/0.59  thf(f6,negated_conjecture,(
% 0.96/0.59    ~((cP @ cONE) => ? [X0 : (($i > $o) > $o)] : ((cP @ X0) & (c_less__eq_ @ X0 @ (cSUCC @ cONE)) & (c_less__eq_ @ cZERO @ X0)))),
% 0.96/0.59    inference(negated_conjecture,[status(cth)],[f5])).
% 0.96/0.59  thf(f7,plain,(
% 0.96/0.59    (cZERO = (^[X0 : ($i > $o)] : (~ ? [X1 : $i] : (X0 @ X1))))),
% 0.96/0.59    inference(rectify,[],[f1])).
% 0.96/0.59  thf(f8,plain,(
% 0.96/0.59    (cZERO = (^[Y0 : $i > $o]: (~ (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))))),
% 0.96/0.59    inference(fool_elimination,[],[f7])).
% 0.96/0.59  thf(f9,plain,(
% 0.96/0.59    (cSUCC = (^[X0 : (($i > $o) > $o), X1 : ($i > $o)] : (? [X2 : $i] : ((X0 @ (^[X3 : $i] : ((X1 @ X3) & (X3 != X2)))) & (X1 @ X2)))))),
% 0.96/0.59    inference(rectify,[],[f2])).
% 0.96/0.59  thf(f10,plain,(
% 0.96/0.59    (cSUCC = (^[Y0 : ($i > $o) > $o]: ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))))))))))),
% 0.96/0.59    inference(fool_elimination,[],[f9])).
% 0.96/0.59  thf(f11,plain,(
% 0.96/0.59    (c_less__eq_ = (^[X0 : (($i > $o) > $o), X1 : (($i > $o) > $o)] : (! [X2 : ((($i > $o) > $o) > $o)] : ((! [X3 : (($i > $o) > $o)] : ((X2 @ X3) => (X2 @ (cSUCC @ X3))) & (X2 @ X0)) => (X2 @ X1)))))),
% 0.96/0.59    inference(rectify,[],[f4])).
% 0.96/0.59  thf(f12,plain,(
% 0.96/0.59    (c_less__eq_ = (^[Y0 : ($i > $o) > $o]: ((^[Y1 : ($i > $o) > $o]: (!! @ ((($i > $o) > $o) > $o) @ (^[Y2 : (($i > $o) > $o) > $o]: (((Y2 @ Y0) & (!! @ (($i > $o) > $o) @ (^[Y3 : ($i > $o) > $o]: ((Y2 @ Y3) => (Y2 @ (cSUCC @ Y3)))))) => (Y2 @ Y1))))))))),
% 0.96/0.59    inference(fool_elimination,[],[f11])).
% 0.96/0.59  thf(f13,plain,(
% 0.96/0.59    ~((cP @ cONE) => ? [X0 : (($i > $o) > $o)] : ((cP @ X0) & (c_less__eq_ @ X0 @ (cSUCC @ cONE)) & (c_less__eq_ @ cZERO @ X0)))),
% 0.96/0.59    inference(rectify,[],[f6])).
% 0.96/0.59  thf(f14,plain,(
% 0.96/0.59    ~((((cP @ cONE)) = $true) => ? [X0 : (($i > $o) > $o)] : ((((cP @ X0)) = $true) & (((c_less__eq_ @ X0 @ (cSUCC @ cONE))) = $true) & (((c_less__eq_ @ cZERO @ X0)) = $true)))),
% 0.96/0.59    inference(fool_elimination,[],[f13])).
% 0.96/0.59  thf(f15,plain,(
% 0.96/0.59    ! [X0 : (($i > $o) > $o)] : ((((cP @ X0)) != $true) | (((c_less__eq_ @ X0 @ (cSUCC @ cONE))) != $true) | (((c_less__eq_ @ cZERO @ X0)) != $true)) & (((cP @ cONE)) = $true)),
% 0.96/0.59    inference(ennf_transformation,[],[f14])).
% 0.96/0.59  thf(f16,plain,(
% 0.96/0.59    (cZERO = (^[Y0 : $i > $o]: (~ (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))))),
% 0.96/0.59    inference(cnf_transformation,[],[f8])).
% 0.96/0.59  thf(f17,plain,(
% 0.96/0.59    (cSUCC = (^[Y0 : ($i > $o) > $o]: ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))))))))))),
% 0.96/0.59    inference(cnf_transformation,[],[f10])).
% 0.96/0.59  thf(f18,plain,(
% 0.96/0.59    (cONE = ((cSUCC @ cZERO)))),
% 0.96/0.59    inference(cnf_transformation,[],[f3])).
% 0.96/0.59  thf(f19,plain,(
% 0.96/0.59    (c_less__eq_ = (^[Y0 : ($i > $o) > $o]: ((^[Y1 : ($i > $o) > $o]: (!! @ ((($i > $o) > $o) > $o) @ (^[Y2 : (($i > $o) > $o) > $o]: (((Y2 @ Y0) & (!! @ (($i > $o) > $o) @ (^[Y3 : ($i > $o) > $o]: ((Y2 @ Y3) => (Y2 @ (cSUCC @ Y3)))))) => (Y2 @ Y1))))))))),
% 0.96/0.59    inference(cnf_transformation,[],[f12])).
% 0.96/0.59  thf(f20,plain,(
% 0.96/0.59    (((cP @ cONE)) = $true)),
% 0.96/0.59    inference(cnf_transformation,[],[f15])).
% 0.96/0.59  thf(f21,plain,(
% 0.96/0.59    ( ! [X0 : (($i > $o) > $o)] : ((((cP @ X0)) != $true) | (((c_less__eq_ @ X0 @ (cSUCC @ cONE))) != $true) | (((c_less__eq_ @ cZERO @ X0)) != $true)) )),
% 0.96/0.59    inference(cnf_transformation,[],[f15])).
% 0.96/0.59  thf(f23,definition,(
% 0.96/0.59    ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.96/0.59    introduced(theory,[fool_exhaustiveness_axiom])).
% 0.96/0.59  thf(f24,plain,(
% 0.96/0.59    (cONE = (((^[Y0 : ($i > $o) > $o]: ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))))))))) @ (^[Y0 : $i > $o]: (~ (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))))))),
% 0.96/0.59    inference(definition_unfolding,[],[f18,f17,f16])).
% 0.96/0.59  thf(f25,plain,(
% 0.96/0.59    (c_less__eq_ = (^[Y0 : ($i > $o) > $o]: ((^[Y1 : ($i > $o) > $o]: (!! @ ((($i > $o) > $o) > $o) @ (^[Y2 : (($i > $o) > $o) > $o]: (((Y2 @ Y0) & (!! @ (($i > $o) > $o) @ (^[Y3 : ($i > $o) > $o]: ((Y2 @ Y3) => (Y2 @ ((^[Y4 : ($i > $o) > $o]: ((^[Y5 : $i > $o]: (?? @ $i @ (^[Y6 : $i]: ((Y5 @ Y6) & (Y4 @ (^[Y7 : $i]: ((~ (Y6 = Y7)) & (Y5 @ Y7)))))))))) @ Y3)))))) => (Y2 @ Y1))))))))),
% 0.96/0.59    inference(definition_unfolding,[],[f19,f17])).
% 0.96/0.59  thf(f26,plain,(
% 0.96/0.59    ( ! [X0 : (($i > $o) > $o)] : ((((cP @ X0)) != $true) | ($true != (((^[Y0 : ($i > $o) > $o]: ((^[Y1 : ($i > $o) > $o]: (!! @ ((($i > $o) > $o) > $o) @ (^[Y2 : (($i > $o) > $o) > $o]: (((Y2 @ Y0) & (!! @ (($i > $o) > $o) @ (^[Y3 : ($i > $o) > $o]: ((Y2 @ Y3) => (Y2 @ ((^[Y4 : ($i > $o) > $o]: ((^[Y5 : $i > $o]: (?? @ $i @ (^[Y6 : $i]: ((Y5 @ Y6) & (Y4 @ (^[Y7 : $i]: ((~ (Y6 = Y7)) & (Y5 @ Y7)))))))))) @ Y3)))))) => (Y2 @ Y1))))))) @ X0 @ ((^[Y0 : ($i > $o) > $o]: ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))))))))) @ ((^[Y0 : ($i > $o) > $o]: ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))))))))) @ (^[Y0 : $i > $o]: (~ (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))))))) | ($true != (((^[Y0 : ($i > $o) > $o]: ((^[Y1 : ($i > $o) > $o]: (!! @ ((($i > $o) > $o) > $o) @ (^[Y2 : (($i > $o) > $o) > $o]: (((Y2 @ Y0) & (!! @ (($i > $o) > $o) @ (^[Y3 : ($i > $o) > $o]: ((Y2 @ Y3) => (Y2 @ ((^[Y4 : ($i > $o) > $o]: ((^[Y5 : $i > $o]: (?? @ $i @ (^[Y6 : $i]: ((Y5 @ Y6) & (Y4 @ (^[Y7 : $i]: ((~ (Y6 = Y7)) & (Y5 @ Y7)))))))))) @ Y3)))))) => (Y2 @ Y1))))))) @ (^[Y0 : $i > $o]: (~ (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) @ X0)))) )),
% 0.96/0.59    inference(definition_unfolding,[],[f21,f25,f17,f24,f25,f16])).
% 0.96/0.59  thf(f27,plain,(
% 0.96/0.59    ($true = ((cP @ ((^[Y0 : ($i > $o) > $o]: ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))))))))) @ (^[Y0 : $i > $o]: (~ (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))))))),
% 0.96/0.59    inference(definition_unfolding,[],[f20,f24])).
% 0.96/0.59  thf(f28,plain,(
% 0.96/0.59    ($true = ((cP @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))))))),
% 0.96/0.59    inference(beta-eta_normalization,[],[f27])).
% 0.96/0.59  thf(f29,plain,(
% 0.96/0.59    ( ! [X0 : (($i > $o) > $o)] : ((((cP @ X0)) != $true) | ($true != ((!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((Y0 @ X0) & (!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4))))))))))))) => (Y0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (?? @ $i @ (^[Y3 : $i]: (((~ (Y2 = Y3)) & (Y1 @ Y3)) & (~ (?? @ $i @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & ((~ (Y2 = Y4)) & (Y1 @ Y4))))))))))))))))))) | ($true != ((!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1)))) & (!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4))))))))))))) => (Y0 @ X0))))))) )),
% 0.96/0.59    inference(beta-eta_normalization,[],[f26])).
% 0.96/0.59  thf(f30,plain,(
% 0.96/0.59    ( ! [X0 : (($i > $o) > $o)] : ((((cP @ X0)) != $true) | ($false = (((^[Y0 : (($i > $o) > $o) > $o]: (((Y0 @ X0) & (!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4))))))))))))) => (Y0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (?? @ $i @ (^[Y3 : $i]: (((~ (Y2 = Y3)) & (Y1 @ Y3)) & (~ (?? @ $i @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & ((~ (Y2 = Y4)) & (Y1 @ Y4)))))))))))))))) @ (sK0 @ X0)))) | ($true != ((!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1)))) & (!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4))))))))))))) => (Y0 @ X0))))))) )),
% 0.96/0.59    inference(sigma_proxy_clausification,[],[f29])).
% 0.96/0.59  thf(f31,plain,(
% 0.96/0.59    ( ! [X0 : (($i > $o) > $o)] : ((((cP @ X0)) != $true) | ($false = (((^[Y0 : (($i > $o) > $o) > $o]: (((Y0 @ X0) & (!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4))))))))))))) => (Y0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (?? @ $i @ (^[Y3 : $i]: (((~ (Y2 = Y3)) & (Y1 @ Y3)) & (~ (?? @ $i @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & ((~ (Y2 = Y4)) & (Y1 @ Y4)))))))))))))))) @ (sK0 @ X0)))) | ($false = (((^[Y0 : (($i > $o) > $o) > $o]: (((Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1)))) & (!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4))))))))))))) => (Y0 @ X0))) @ (sK1 @ X0))))) )),
% 0.96/0.59    inference(sigma_proxy_clausification,[],[f30])).
% 0.96/0.59  thf(f32,plain,(
% 0.96/0.59    ( ! [X0 : (($i > $o) > $o)] : ((((cP @ X0)) != $true) | ($false = ((((sK0 @ X0 @ X0) & (!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((sK0 @ X0 @ Y0) => (sK0 @ X0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3))))))))))))) => (sK0 @ X0 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (?? @ $i @ (^[Y2 : $i]: (((~ (Y1 = Y2)) & (Y0 @ Y2)) & (~ (?? @ $i @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & ((~ (Y1 = Y3)) & (Y0 @ Y3))))))))))))))))) | ($false = ((((sK1 @ X0 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))) & (!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((sK1 @ X0 @ Y0) => (sK1 @ X0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3))))))))))))) => (sK1 @ X0 @ X0))))) )),
% 0.96/0.59    inference(beta-eta_normalization,[],[f31])).
% 0.96/0.59  thf(f33,plain,(
% 0.96/0.59    ( ! [X0 : (($i > $o) > $o)] : ((((cP @ X0)) != $true) | ($false = ((sK0 @ X0 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (?? @ $i @ (^[Y2 : $i]: (((~ (Y1 = Y2)) & (Y0 @ Y2)) & (~ (?? @ $i @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & ((~ (Y1 = Y3)) & (Y0 @ Y3)))))))))))))))) | ($false = ((((sK1 @ X0 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))) & (!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((sK1 @ X0 @ Y0) => (sK1 @ X0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3))))))))))))) => (sK1 @ X0 @ X0))))) )),
% 0.96/0.59    inference(imp_proxy_clausification,[],[f32])).
% 0.96/0.59  thf(f34,plain,(
% 0.96/0.59    ( ! [X0 : (($i > $o) > $o)] : ((((cP @ X0)) != $true) | ($true = (((sK0 @ X0 @ X0) & (!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((sK0 @ X0 @ Y0) => (sK0 @ X0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3))))))))))))))) | ($false = ((((sK1 @ X0 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))) & (!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((sK1 @ X0 @ Y0) => (sK1 @ X0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3))))))))))))) => (sK1 @ X0 @ X0))))) )),
% 0.96/0.59    inference(imp_proxy_clausification,[],[f32])).
% 0.96/0.59  thf(f35,plain,(
% 0.96/0.59    ( ! [X0 : (($i > $o) > $o)] : ((((cP @ X0)) != $true) | ($true = ((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((sK0 @ X0 @ Y0) => (sK0 @ X0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))))))))))))) | ($false = ((((sK1 @ X0 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))) & (!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((sK1 @ X0 @ Y0) => (sK1 @ X0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3))))))))))))) => (sK1 @ X0 @ X0))))) )),
% 0.96/0.59    inference(and_proxy_clausification,[],[f34])).
% 0.96/0.59  thf(f36,plain,(
% 0.96/0.59    ( ! [X0 : (($i > $o) > $o)] : ((((cP @ X0)) != $true) | ($true = ((sK0 @ X0 @ X0))) | ($false = ((((sK1 @ X0 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))) & (!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((sK1 @ X0 @ Y0) => (sK1 @ X0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3))))))))))))) => (sK1 @ X0 @ X0))))) )),
% 0.96/0.59    inference(and_proxy_clausification,[],[f34])).
% 0.96/0.59  thf(f37,plain,(
% 0.96/0.59    ( ! [X0 : (($i > $o) > $o)] : ((((cP @ X0)) != $true) | ($true = ((sK0 @ X0 @ X0))) | ($false = ((sK1 @ X0 @ X0)))) )),
% 0.96/0.59    inference(imp_proxy_clausification,[],[f36])).
% 0.96/0.59  thf(f38,plain,(
% 0.96/0.59    ( ! [X0 : (($i > $o) > $o)] : ((((cP @ X0)) != $true) | ($true = ((sK0 @ X0 @ X0))) | ($true = (((sK1 @ X0 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))) & (!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((sK1 @ X0 @ Y0) => (sK1 @ X0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))))))))))))))) )),
% 0.96/0.59    inference(imp_proxy_clausification,[],[f36])).
% 0.96/0.59  thf(f39,plain,(
% 0.96/0.59    ( ! [X0 : (($i > $o) > $o)] : ((((cP @ X0)) != $true) | ($true = ((sK0 @ X0 @ X0))) | ($true = ((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((sK1 @ X0 @ Y0) => (sK1 @ X0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3))))))))))))))) )),
% 0.96/0.59    inference(and_proxy_clausification,[],[f38])).
% 0.96/0.59  thf(f40,plain,(
% 0.96/0.59    ( ! [X0 : (($i > $o) > $o)] : ((((cP @ X0)) != $true) | ($true = ((sK0 @ X0 @ X0))) | ($true = ((sK1 @ X0 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0))))))) )),
% 0.96/0.59    inference(and_proxy_clausification,[],[f38])).
% 0.96/0.59  thf(f41,plain,(
% 0.96/0.59    ( ! [X0 : (($i > $o) > $o),X1 : (($i > $o) > $o)] : ((((cP @ X0)) != $true) | ($true = ((sK0 @ X0 @ X0))) | ($true = (((^[Y0 : ($i > $o) > $o]: ((sK1 @ X0 @ Y0) => (sK1 @ X0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3))))))))))) @ X1)))) )),
% 0.96/0.59    inference(pi_proxy_clausification,[],[f39])).
% 0.96/0.59  thf(f42,plain,(
% 0.96/0.59    ( ! [X0 : (($i > $o) > $o),X1 : (($i > $o) > $o)] : ((((cP @ X0)) != $true) | ($true = ((sK0 @ X0 @ X0))) | ($true = (((sK1 @ X0 @ X1) => (sK1 @ X0 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (X1 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))))))) )),
% 0.96/0.59    inference(beta-eta_normalization,[],[f41])).
% 0.96/0.59  thf(f43,plain,(
% 0.96/0.59    ( ! [X0 : (($i > $o) > $o),X1 : (($i > $o) > $o)] : ((((cP @ X0)) != $true) | ($true = ((sK0 @ X0 @ X0))) | ($false = ((sK1 @ X0 @ X1))) | ($true = ((sK1 @ X0 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (X1 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))))))))))) )),
% 0.96/0.59    inference(imp_proxy_clausification,[],[f42])).
% 0.96/0.59  thf(f44,plain,(
% 0.96/0.59    ( ! [X0 : (($i > $o) > $o),X1 : (($i > $o) > $o)] : ((((cP @ X0)) != $true) | ($true = (((^[Y0 : ($i > $o) > $o]: ((sK0 @ X0 @ Y0) => (sK0 @ X0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3))))))))))) @ X1))) | ($false = ((((sK1 @ X0 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))) & (!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((sK1 @ X0 @ Y0) => (sK1 @ X0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3))))))))))))) => (sK1 @ X0 @ X0))))) )),
% 0.96/0.59    inference(pi_proxy_clausification,[],[f35])).
% 0.96/0.59  thf(f45,plain,(
% 0.96/0.59    ( ! [X0 : (($i > $o) > $o),X1 : (($i > $o) > $o)] : ((((cP @ X0)) != $true) | ($true = (((^[Y0 : ($i > $o) > $o]: ((sK0 @ X0 @ Y0) => (sK0 @ X0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3))))))))))) @ X1))) | ($false = ((sK1 @ X0 @ X0)))) )),
% 0.96/0.59    inference(imp_proxy_clausification,[],[f44])).
% 0.96/0.59  thf(f46,plain,(
% 0.96/0.59    ( ! [X0 : (($i > $o) > $o),X1 : (($i > $o) > $o)] : ((((cP @ X0)) != $true) | ($true = (((^[Y0 : ($i > $o) > $o]: ((sK0 @ X0 @ Y0) => (sK0 @ X0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3))))))))))) @ X1))) | ($true = (((sK1 @ X0 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))) & (!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((sK1 @ X0 @ Y0) => (sK1 @ X0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))))))))))))))) )),
% 0.96/0.59    inference(imp_proxy_clausification,[],[f44])).
% 0.96/0.59  thf(f47,plain,(
% 0.96/0.59    ( ! [X0 : (($i > $o) > $o),X1 : (($i > $o) > $o)] : ((((cP @ X0)) != $true) | ($true = (((^[Y0 : ($i > $o) > $o]: ((sK0 @ X0 @ Y0) => (sK0 @ X0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3))))))))))) @ X1))) | ($true = ((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((sK1 @ X0 @ Y0) => (sK1 @ X0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3))))))))))))))) )),
% 0.96/0.59    inference(and_proxy_clausification,[],[f46])).
% 0.96/0.59  thf(f48,plain,(
% 0.96/0.59    ( ! [X0 : (($i > $o) > $o),X1 : (($i > $o) > $o)] : ((((cP @ X0)) != $true) | ($true = (((^[Y0 : ($i > $o) > $o]: ((sK0 @ X0 @ Y0) => (sK0 @ X0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3))))))))))) @ X1))) | ($true = ((sK1 @ X0 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0))))))) )),
% 0.96/0.59    inference(and_proxy_clausification,[],[f46])).
% 0.96/0.59  thf(f49,plain,(
% 0.96/0.59    ( ! [X0 : (($i > $o) > $o),X1 : (($i > $o) > $o)] : ((((cP @ X0)) != $true) | ($true = (((sK0 @ X0 @ X1) => (sK0 @ X0 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (X1 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))))))))))) | ($true = ((sK1 @ X0 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0))))))) )),
% 0.96/0.59    inference(beta-eta_normalization,[],[f48])).
% 0.96/0.59  thf(f50,plain,(
% 0.96/0.59    ( ! [X0 : (($i > $o) > $o),X1 : (($i > $o) > $o)] : ((((cP @ X0)) != $true) | ($false = ((sK0 @ X0 @ X1))) | ($true = ((sK1 @ X0 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))))) | ($true = ((sK0 @ X0 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (X1 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))))))))))) )),
% 0.96/0.59    inference(imp_proxy_clausification,[],[f49])).
% 0.96/0.59  thf(f51,plain,(
% 0.96/0.59    ( ! [X2 : (($i > $o) > $o),X0 : (($i > $o) > $o),X1 : (($i > $o) > $o)] : ((((cP @ X0)) != $true) | ($true = (((^[Y0 : ($i > $o) > $o]: ((sK0 @ X0 @ Y0) => (sK0 @ X0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3))))))))))) @ X1))) | ($true = (((^[Y0 : ($i > $o) > $o]: ((sK1 @ X0 @ Y0) => (sK1 @ X0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3))))))))))) @ X2)))) )),
% 0.96/0.59    inference(pi_proxy_clausification,[],[f47])).
% 0.96/0.59  thf(f52,plain,(
% 0.96/0.59    ( ! [X2 : (($i > $o) > $o),X0 : (($i > $o) > $o),X1 : (($i > $o) > $o)] : ((((cP @ X0)) != $true) | ($true = (((sK0 @ X0 @ X1) => (sK0 @ X0 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (X1 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))))))))))) | ($true = (((sK1 @ X0 @ X2) => (sK1 @ X0 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (X2 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))))))) )),
% 0.96/0.59    inference(beta-eta_normalization,[],[f51])).
% 0.96/0.59  thf(f53,plain,(
% 0.96/0.59    ( ! [X2 : (($i > $o) > $o),X0 : (($i > $o) > $o),X1 : (($i > $o) > $o)] : ((((cP @ X0)) != $true) | ($false = ((sK0 @ X0 @ X1))) | ($true = (((sK1 @ X0 @ X2) => (sK1 @ X0 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (X2 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))))))))))) | ($true = ((sK0 @ X0 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (X1 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))))))))))) )),
% 0.96/0.59    inference(imp_proxy_clausification,[],[f52])).
% 0.96/0.59  thf(f54,plain,(
% 0.96/0.59    ( ! [X2 : (($i > $o) > $o),X0 : (($i > $o) > $o),X1 : (($i > $o) > $o)] : ((((cP @ X0)) != $true) | ($false = ((sK0 @ X0 @ X1))) | ($false = ((sK1 @ X0 @ X2))) | ($true = ((sK0 @ X0 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (X1 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))))) | ($true = ((sK1 @ X0 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (X2 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))))))))))) )),
% 0.96/0.59    inference(imp_proxy_clausification,[],[f53])).
% 0.96/0.59  thf(f55,plain,(
% 0.96/0.59    ( ! [X0 : (($i > $o) > $o),X1 : (($i > $o) > $o)] : ((((cP @ X0)) != $true) | ($true = (((sK0 @ X0 @ X1) => (sK0 @ X0 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (X1 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))))))))))) | ($false = ((sK1 @ X0 @ X0)))) )),
% 0.96/0.59    inference(beta-eta_normalization,[],[f45])).
% 0.96/0.59  thf(f56,plain,(
% 0.96/0.59    ( ! [X0 : (($i > $o) > $o),X1 : (($i > $o) > $o)] : ((((cP @ X0)) != $true) | ($false = ((sK0 @ X0 @ X1))) | ($false = ((sK1 @ X0 @ X0))) | ($true = ((sK0 @ X0 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (X1 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))))))))))) )),
% 0.96/0.59    inference(imp_proxy_clausification,[],[f55])).
% 0.96/0.59  thf(f57,plain,(
% 0.96/0.59    ( ! [X0 : (($i > $o) > $o)] : ((((cP @ X0)) != $true) | ($false = ((sK0 @ X0 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (?? @ $i @ (^[Y2 : $i]: (((~ (Y1 = Y2)) & (Y0 @ Y2)) & (~ (?? @ $i @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & ((~ (Y1 = Y3)) & (Y0 @ Y3)))))))))))))))) | ($false = ((sK1 @ X0 @ X0)))) )),
% 0.96/0.59    inference(imp_proxy_clausification,[],[f33])).
% 0.96/0.59  thf(f58,plain,(
% 0.96/0.59    ( ! [X0 : (($i > $o) > $o)] : ((((cP @ X0)) != $true) | ($false = ((sK0 @ X0 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (?? @ $i @ (^[Y2 : $i]: (((~ (Y1 = Y2)) & (Y0 @ Y2)) & (~ (?? @ $i @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & ((~ (Y1 = Y3)) & (Y0 @ Y3)))))))))))))))) | ($true = (((sK1 @ X0 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))) & (!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((sK1 @ X0 @ Y0) => (sK1 @ X0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))))))))))))))) )),
% 0.96/0.59    inference(imp_proxy_clausification,[],[f33])).
% 0.96/0.59  thf(f59,plain,(
% 0.96/0.59    ( ! [X0 : (($i > $o) > $o)] : ((((cP @ X0)) != $true) | ($false = ((sK0 @ X0 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (?? @ $i @ (^[Y2 : $i]: (((~ (Y1 = Y2)) & (Y0 @ Y2)) & (~ (?? @ $i @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & ((~ (Y1 = Y3)) & (Y0 @ Y3)))))))))))))))) | ($true = ((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((sK1 @ X0 @ Y0) => (sK1 @ X0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3))))))))))))))) )),
% 0.96/0.59    inference(and_proxy_clausification,[],[f58])).
% 0.96/0.59  thf(f60,plain,(
% 0.96/0.59    ( ! [X0 : (($i > $o) > $o)] : ((((cP @ X0)) != $true) | ($false = ((sK0 @ X0 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (?? @ $i @ (^[Y2 : $i]: (((~ (Y1 = Y2)) & (Y0 @ Y2)) & (~ (?? @ $i @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & ((~ (Y1 = Y3)) & (Y0 @ Y3)))))))))))))))) | ($true = ((sK1 @ X0 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0))))))) )),
% 0.96/0.59    inference(and_proxy_clausification,[],[f58])).
% 0.96/0.59  thf(f61,plain,(
% 0.96/0.59    ( ! [X0 : (($i > $o) > $o),X1 : (($i > $o) > $o)] : ((((cP @ X0)) != $true) | ($false = ((sK0 @ X0 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (?? @ $i @ (^[Y2 : $i]: (((~ (Y1 = Y2)) & (Y0 @ Y2)) & (~ (?? @ $i @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & ((~ (Y1 = Y3)) & (Y0 @ Y3)))))))))))))))) | ($true = (((^[Y0 : ($i > $o) > $o]: ((sK1 @ X0 @ Y0) => (sK1 @ X0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3))))))))))) @ X1)))) )),
% 0.96/0.59    inference(pi_proxy_clausification,[],[f59])).
% 0.96/0.59  thf(f62,plain,(
% 0.96/0.59    ( ! [X0 : (($i > $o) > $o),X1 : (($i > $o) > $o)] : ((((cP @ X0)) != $true) | ($false = ((sK0 @ X0 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (?? @ $i @ (^[Y2 : $i]: (((~ (Y1 = Y2)) & (Y0 @ Y2)) & (~ (?? @ $i @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & ((~ (Y1 = Y3)) & (Y0 @ Y3)))))))))))))))) | ($true = (((sK1 @ X0 @ X1) => (sK1 @ X0 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (X1 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))))))) )),
% 0.96/0.59    inference(beta-eta_normalization,[],[f61])).
% 0.96/0.59  thf(f63,plain,(
% 0.96/0.59    ( ! [X0 : (($i > $o) > $o),X1 : (($i > $o) > $o)] : ((((cP @ X0)) != $true) | ($false = ((sK0 @ X0 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (?? @ $i @ (^[Y2 : $i]: (((~ (Y1 = Y2)) & (Y0 @ Y2)) & (~ (?? @ $i @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & ((~ (Y1 = Y3)) & (Y0 @ Y3)))))))))))))))) | ($false = ((sK1 @ X0 @ X1))) | ($true = ((sK1 @ X0 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (X1 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))))))))))) )),
% 0.96/0.59    inference(imp_proxy_clausification,[],[f62])).
% 0.96/0.59  thf(f73,plain,(
% 0.96/0.59    ($true != $true) | ($true = ((sK0 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))))))))))) | ($false = ((sK1 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))))))),
% 0.96/0.59    inference(constrained_superposition,[],[f37,f28])).
% 0.96/0.59  thf(f74,plain,(
% 0.96/0.59    ($true = ((sK0 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))))))))))) | ($false = ((sK1 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))))))),
% 0.96/0.59    inference(trivial_inequality_removal,[],[f73])).
% 0.96/0.59  thf(f76,definition,(
% 0.96/0.59    spl2_1 <=> ($false = ((sK1 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))))))),
% 0.96/0.59    introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition])).
% 0.96/0.59  thf(f77,plain,(
% 0.96/0.59    ($false != ((sK1 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))))))))))) | spl2_1),
% 0.96/0.59    inference(avatar_component_clause,[],[f76])).
% 0.96/0.59  thf(f78,plain,(
% 0.96/0.59    ($false = ((sK1 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))))))))))) | ~spl2_1),
% 0.96/0.59    inference(avatar_component_clause,[],[f76])).
% 0.96/0.59  thf(f80,definition,(
% 0.96/0.59    spl2_2 <=> ($true = ((sK0 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))))))),
% 0.96/0.59    introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition])).
% 0.96/0.59  thf(f82,plain,(
% 0.96/0.59    ($true = ((sK0 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))))))))))) | ~spl2_2),
% 0.96/0.59    inference(avatar_component_clause,[],[f80])).
% 0.96/0.59  thf(f83,plain,(
% 0.96/0.59    spl2_1 | spl2_2),
% 0.96/0.59    inference(avatar_split_clause,[],[f74,f80,f76])).
% 0.96/0.59  thf(f85,plain,(
% 0.96/0.59    ($true != $true) | ($true = ((sK0 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))))))))))) | ($true = ((sK1 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0))))))),
% 0.96/0.59    inference(constrained_superposition,[],[f40,f28])).
% 0.96/0.59  thf(f86,plain,(
% 0.96/0.59    ($true = ((sK0 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))))))))))) | ($true = ((sK1 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0))))))),
% 0.96/0.59    inference(trivial_inequality_removal,[],[f85])).
% 0.96/0.59  thf(f89,definition,(
% 0.96/0.59    spl2_3 <=> ($true = ((sK1 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0))))))),
% 0.96/0.59    introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition])).
% 0.96/0.59  thf(f91,plain,(
% 0.96/0.59    ($true = ((sK1 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))))) | ~spl2_3),
% 0.96/0.59    inference(avatar_component_clause,[],[f89])).
% 0.96/0.59  thf(f92,plain,(
% 0.96/0.59    spl2_3 | spl2_2),
% 0.96/0.59    inference(avatar_split_clause,[],[f86,f80,f89])).
% 0.96/0.59  thf(f94,plain,(
% 0.96/0.59    ($true != $true) | ($false = ((sK0 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (?? @ $i @ (^[Y2 : $i]: (((~ (Y1 = Y2)) & (Y0 @ Y2)) & (~ (?? @ $i @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & ((~ (Y1 = Y3)) & (Y0 @ Y3)))))))))))))))) | ($false = ((sK1 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))))))),
% 0.96/0.59    inference(constrained_superposition,[],[f57,f28])).
% 0.96/0.59  thf(f95,plain,(
% 0.96/0.59    ($false = ((sK0 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (?? @ $i @ (^[Y2 : $i]: (((~ (Y1 = Y2)) & (Y0 @ Y2)) & (~ (?? @ $i @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & ((~ (Y1 = Y3)) & (Y0 @ Y3)))))))))))))))) | ($false = ((sK1 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))))))),
% 0.96/0.59    inference(trivial_inequality_removal,[],[f94])).
% 0.96/0.59  thf(f98,plain,(
% 0.96/0.59    ($true != $true) | ($false = ((sK0 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (?? @ $i @ (^[Y2 : $i]: (((~ (Y1 = Y2)) & (Y0 @ Y2)) & (~ (?? @ $i @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & ((~ (Y1 = Y3)) & (Y0 @ Y3)))))))))))))))) | ($true = ((sK1 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0))))))),
% 0.96/0.59    inference(constrained_superposition,[],[f60,f28])).
% 0.96/0.59  thf(f99,plain,(
% 0.96/0.59    ($false = ((sK0 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (?? @ $i @ (^[Y2 : $i]: (((~ (Y1 = Y2)) & (Y0 @ Y2)) & (~ (?? @ $i @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & ((~ (Y1 = Y3)) & (Y0 @ Y3)))))))))))))))) | ($true = ((sK1 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0))))))),
% 0.96/0.59    inference(trivial_inequality_removal,[],[f98])).
% 0.96/0.59  thf(f102,definition,(
% 0.96/0.59    spl2_4 <=> ($false = ((sK0 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (?? @ $i @ (^[Y2 : $i]: (((~ (Y1 = Y2)) & (Y0 @ Y2)) & (~ (?? @ $i @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & ((~ (Y1 = Y3)) & (Y0 @ Y3))))))))))))))))),
% 0.96/0.59    introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition])).
% 0.96/0.59  thf(f103,plain,(
% 0.96/0.59    ($false != ((sK0 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (?? @ $i @ (^[Y2 : $i]: (((~ (Y1 = Y2)) & (Y0 @ Y2)) & (~ (?? @ $i @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & ((~ (Y1 = Y3)) & (Y0 @ Y3)))))))))))))))) | spl2_4),
% 0.96/0.59    inference(avatar_component_clause,[],[f102])).
% 0.96/0.59  thf(f104,plain,(
% 0.96/0.59    ($false = ((sK0 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (?? @ $i @ (^[Y2 : $i]: (((~ (Y1 = Y2)) & (Y0 @ Y2)) & (~ (?? @ $i @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & ((~ (Y1 = Y3)) & (Y0 @ Y3)))))))))))))))) | ~spl2_4),
% 0.96/0.59    inference(avatar_component_clause,[],[f102])).
% 0.96/0.59  thf(f105,plain,(
% 0.96/0.59    spl2_3 | spl2_4),
% 0.96/0.59    inference(avatar_split_clause,[],[f99,f102,f89])).
% 0.96/0.59  thf(f133,plain,(
% 0.96/0.59    ( ! [X0 : (($i > $o) > $o)] : (($true != $true) | ($false = ((sK0 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ X0))) | ($false = ((sK1 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))))))))))) | ($true = ((sK0 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (X0 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))))))))))) )),
% 0.96/0.59    inference(constrained_superposition,[],[f56,f28])).
% 0.96/0.59  thf(f135,plain,(
% 0.96/0.59    ( ! [X0 : (($i > $o) > $o)] : (($false = ((sK0 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ X0))) | ($false = ((sK1 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))))))))))) | ($true = ((sK0 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (X0 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))))))))))) )),
% 0.96/0.59    inference(trivial_inequality_removal,[],[f133])).
% 0.96/0.59  thf(f137,plain,(
% 0.96/0.59    ( ! [X0 : (($i > $o) > $o),X1 : (($i > $o) > $o)] : (($true != $true) | ($true = ((sK0 @ X0 @ X0))) | ($false = ((sK1 @ X0 @ X1))) | ($true = ((sK1 @ X0 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (X1 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))))) | (((cP @ X0)) = $false)) )),
% 0.96/0.59    inference(constrained_superposition,[],[f43,f23])).
% 0.96/0.59  thf(f141,plain,(
% 0.96/0.59    ( ! [X0 : (($i > $o) > $o),X1 : (($i > $o) > $o)] : (($true = ((sK0 @ X0 @ X0))) | ($true = ((sK1 @ X0 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (X1 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))))) | ($false = ((sK1 @ X0 @ X1))) | (((cP @ X0)) = $false)) )),
% 0.96/0.59    inference(trivial_inequality_removal,[],[f137])).
% 0.96/0.59  thf(f163,plain,(
% 0.96/0.59    ( ! [X0 : (($i > $o) > $o)] : (($true != $true) | ($false = ((sK0 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ X0))) | ($true = ((sK1 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))))) | ($true = ((sK0 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (X0 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))))))))))) )),
% 0.96/0.59    inference(constrained_superposition,[],[f50,f28])).
% 0.96/0.59  thf(f165,plain,(
% 0.96/0.59    ( ! [X0 : (($i > $o) > $o)] : (($false = ((sK0 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ X0))) | ($true = ((sK1 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))))) | ($true = ((sK0 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (X0 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))))))))))) )),
% 0.96/0.59    inference(trivial_inequality_removal,[],[f163])).
% 0.96/0.59  thf(f248,plain,(
% 0.96/0.59    ( ! [X0 : (($i > $o) > $o),X1 : (($i > $o) > $o)] : (($true != $true) | ($false = ((sK0 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ X0))) | ($false = ((sK1 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ X1))) | ($true = ((sK0 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (X0 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))))) | ($true = ((sK1 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (X1 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))))))))))) )),
% 0.96/0.59    inference(constrained_superposition,[],[f54,f28])).
% 0.96/0.59  thf(f251,plain,(
% 0.96/0.59    ( ! [X0 : (($i > $o) > $o),X1 : (($i > $o) > $o)] : (($false = ((sK0 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ X0))) | ($false = ((sK1 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ X1))) | ($true = ((sK0 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (X0 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))))) | ($true = ((sK1 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (X1 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))))))))))) )),
% 0.96/0.59    inference(trivial_inequality_removal,[],[f248])).
% 0.96/0.59  thf(f254,definition,(
% 0.96/0.59    spl2_10 <=> ! [X1 : (($i > $o) > $o)] : (($false = ((sK1 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ X1))) | ($true = ((sK1 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (X1 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))))))),
% 0.96/0.59    introduced(definition,[new_symbols(definition,[spl2_10])],[avatar_definition])).
% 0.96/0.59  thf(f255,plain,(
% 0.96/0.59    ( ! [X1 : (($i > $o) > $o)] : (($true = ((sK1 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (X1 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))))) | ($false = ((sK1 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ X1)))) ) | ~spl2_10),
% 0.96/0.59    inference(avatar_component_clause,[],[f254])).
% 0.96/0.59  thf(f257,definition,(
% 0.96/0.59    spl2_11 <=> ! [X0 : (($i > $o) > $o)] : (($false = ((sK0 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ X0))) | ($true = ((sK0 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (X0 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))))))),
% 0.96/0.59    introduced(definition,[new_symbols(definition,[spl2_11])],[avatar_definition])).
% 0.96/0.59  thf(f258,plain,(
% 0.96/0.59    ( ! [X0 : (($i > $o) > $o)] : (($true = ((sK0 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (X0 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))))) | ($false = ((sK0 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ X0)))) ) | ~spl2_11),
% 0.96/0.59    inference(avatar_component_clause,[],[f257])).
% 0.96/0.59  thf(f259,plain,(
% 0.96/0.59    spl2_10 | spl2_11),
% 0.96/0.59    inference(avatar_split_clause,[],[f251,f257,f254])).
% 0.96/0.59  thf(f264,plain,(
% 0.96/0.59    ( ! [X0 : (($i > $o) > $i > $o)] : (($true = $false) | ($false = ((sK1 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ (^[Y0 : $i > $o]: (~ ((^[Y1 : $i > $o]: (?? @ $i @ (X0 @ Y1))) @ Y0)))))) | ((^[Y0 : $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))) != (^[Y0 : $i > $o]: ((^[Y1 : $i]: (X0 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) ) | (~spl2_1 | ~spl2_10)),
% 0.96/0.59    inference(constrained_superposition,[],[f78,f255])).
% 0.96/0.59  thf(f274,plain,(
% 0.96/0.59    ( ! [X0 : (($i > $o) > $i > $o)] : (($false = ((sK1 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ (^[Y0 : $i > $o]: (~ ((^[Y1 : $i > $o]: (?? @ $i @ (X0 @ Y1))) @ Y0)))))) | ((^[Y0 : $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))) != (^[Y0 : $i > $o]: ((^[Y1 : $i]: (X0 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) ) | (~spl2_1 | ~spl2_10)),
% 0.96/0.59    inference(trivial_inequality_removal,[],[f264])).
% 0.96/0.59  thf(f275,plain,(
% 0.96/0.59    ( ! [X0 : (($i > $o) > $i > $o)] : (((^[Y0 : $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))) != (^[Y0 : $i > $o]: ((^[Y1 : $i]: (X0 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))))))) | ($false = ((sK1 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ (^[Y0 : $i > $o]: (~ (?? @ $i @ (X0 @ Y0)))))))) ) | (~spl2_1 | ~spl2_10)),
% 0.96/0.59    inference(beta-eta_normalization,[],[f274])).
% 0.96/0.59  thf(f285,plain,(
% 0.96/0.59    ($false = ((sK1 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ (^[Y0 : $i > $o]: (~ (?? @ $i @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (Y1 @ ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (Y4)))) @ Y1 @ Y2))))) @ Y0))))))) | (~spl2_1 | ~spl2_10)),
% 0.96/0.59    inference(equality_resolution,[],[f275])).
% 0.96/0.59  thf(f286,plain,(
% 0.96/0.59    ($false = ((sK1 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))))) | (~spl2_1 | ~spl2_10)),
% 0.96/0.59    inference(beta-eta_normalization,[],[f285])).
% 0.96/0.59  thf(f289,plain,(
% 0.96/0.59    ($true = $false) | (~spl2_1 | ~spl2_3 | ~spl2_10)),
% 0.96/0.59    inference(constrained_superposition,[],[f286,f91])).
% 0.96/0.59  thf(f293,plain,(
% 0.96/0.59    $false | (~spl2_1 | ~spl2_3 | ~spl2_10)),
% 0.96/0.59    inference(trivial_inequality_removal,[],[f289])).
% 0.96/0.59  thf(f294,plain,(
% 0.96/0.59    ~spl2_1 | ~spl2_3 | ~spl2_10),
% 0.96/0.59    inference(avatar_contradiction_clause,[],[f293])).
% 0.96/0.59  thf(f349,plain,(
% 0.96/0.59    ( ! [X0 : (($i > $o) > $o)] : (($true != $true) | ($false = ((sK0 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (?? @ $i @ (^[Y2 : $i]: (((~ (Y1 = Y2)) & (Y0 @ Y2)) & (~ (?? @ $i @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & ((~ (Y1 = Y3)) & (Y0 @ Y3)))))))))))))))) | ($false = ((sK1 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ X0))) | ($true = ((sK1 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (X0 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))))))))))) )),
% 0.96/0.59    inference(constrained_superposition,[],[f63,f28])).
% 0.96/0.59  thf(f352,plain,(
% 0.96/0.59    ( ! [X0 : (($i > $o) > $o)] : (($false = ((sK0 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (?? @ $i @ (^[Y2 : $i]: (((~ (Y1 = Y2)) & (Y0 @ Y2)) & (~ (?? @ $i @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & ((~ (Y1 = Y3)) & (Y0 @ Y3)))))))))))))))) | ($false = ((sK1 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ X0))) | ($true = ((sK1 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (X0 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))))))))))) )),
% 0.96/0.59    inference(trivial_inequality_removal,[],[f349])).
% 0.96/0.59  thf(f354,plain,(
% 0.96/0.59    spl2_10 | spl2_4),
% 0.96/0.59    inference(avatar_split_clause,[],[f352,f102,f254])).
% 0.96/0.59  thf(f360,plain,(
% 0.96/0.59    ( ! [X0 : (($i > $o) > $i > $o),X1 : (($i > $o) > $i > $o)] : (($true = $false) | ($false = ((sK0 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ (^[Y0 : $i > $o]: (?? @ $i @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((X0 @ Y1 @ Y2) & (X1 @ Y1 @ Y2))))) @ Y0)))))) | ((^[Y0 : $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))) != (^[Y0 : $i > $o]: ((^[Y1 : $i]: (X0 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))))))) | ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (X1 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))) != (^[Y0 : $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (~ (?? @ $i @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & ((~ (Y1 = Y3)) & (Y0 @ Y3))))))))))))) ) | (~spl2_4 | ~spl2_11)),
% 0.96/0.59    inference(constrained_superposition,[],[f258,f104])).
% 0.96/0.59  thf(f370,plain,(
% 0.96/0.59    ( ! [X0 : (($i > $o) > $i > $o),X1 : (($i > $o) > $i > $o)] : (($false = ((sK0 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ (^[Y0 : $i > $o]: (?? @ $i @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((X0 @ Y1 @ Y2) & (X1 @ Y1 @ Y2))))) @ Y0)))))) | ((^[Y0 : $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))) != (^[Y0 : $i > $o]: ((^[Y1 : $i]: (X0 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))))))) | ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (X1 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))) != (^[Y0 : $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (~ (?? @ $i @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & ((~ (Y1 = Y3)) & (Y0 @ Y3))))))))))))) ) | (~spl2_4 | ~spl2_11)),
% 0.96/0.59    inference(trivial_inequality_removal,[],[f360])).
% 0.96/0.59  thf(f371,plain,(
% 0.96/0.59    ( ! [X0 : (($i > $o) > $i > $o),X1 : (($i > $o) > $i > $o)] : (((^[Y0 : $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))) != (^[Y0 : $i > $o]: ((^[Y1 : $i]: (X0 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))))))) | ($false = ((sK0 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((X0 @ Y0 @ Y1) & (X1 @ Y0 @ Y1)))))))) | ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (X1 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))) != (^[Y0 : $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (~ (?? @ $i @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & ((~ (Y1 = Y3)) & (Y0 @ Y3))))))))))))) ) | (~spl2_4 | ~spl2_11)),
% 0.96/0.59    inference(beta-eta_normalization,[],[f370])).
% 0.96/0.59  thf(f384,plain,(
% 0.96/0.59    ( ! [X0 : (($i > $o) > $i > $o)] : (($false = ((sK0 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: (((^[Y2 : $i > $o]: ((^[Y3 : $i]: (Y2 @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (Y5)))) @ Y2 @ Y3))))) @ Y0 @ Y1) & (X0 @ Y0 @ Y1)))))))) | ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (X0 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))) != (^[Y0 : $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (~ (?? @ $i @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & ((~ (Y1 = Y3)) & (Y0 @ Y3))))))))))))) ) | (~spl2_4 | ~spl2_11)),
% 0.96/0.59    inference(equality_resolution,[],[f371])).
% 0.96/0.59  thf(f385,plain,(
% 0.96/0.59    ( ! [X0 : (($i > $o) > $i > $o)] : (((^[Y0 : $i > $o]: ((^[Y1 : $i]: (X0 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))) != (^[Y0 : $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (~ (?? @ $i @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & ((~ (Y1 = Y3)) & (Y0 @ Y3)))))))))))) | ($false = ((sK0 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (X0 @ Y0 @ Y1))))))))) ) | (~spl2_4 | ~spl2_11)),
% 0.96/0.59    inference(beta-eta_normalization,[],[f384])).
% 0.96/0.59  thf(f388,plain,(
% 0.96/0.59    ( ! [X0 : (($i > $o) > $i > $i > $o)] : (($false = ((sK0 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (?? @ $i @ (X0 @ Y4 @ Y5))))) @ Y2 @ Y3))))) @ Y0 @ Y1)))))))) | ((^[Y0 : $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((~ (Y2 = Y3)) & ((~ (Y1 = Y3)) & (Y0 @ Y3)))))))))) != (^[Y0 : $i > $o]: ((^[Y1 : $i]: (X0 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) ) | (~spl2_4 | ~spl2_11)),
% 0.96/0.59    inference(equality_resolution,[],[f385])).
% 0.96/0.59  thf(f389,plain,(
% 0.96/0.59    ( ! [X0 : (($i > $o) > $i > $i > $o)] : (((^[Y0 : $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((~ (Y2 = Y3)) & ((~ (Y1 = Y3)) & (Y0 @ Y3)))))))))) != (^[Y0 : $i > $o]: ((^[Y1 : $i]: (X0 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))))))) | ($false = ((sK0 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (X0 @ Y0 @ Y1))))))))))) ) | (~spl2_4 | ~spl2_11)),
% 0.96/0.59    inference(beta-eta_normalization,[],[f388])).
% 0.96/0.59  thf(f429,plain,(
% 0.96/0.59    ( ! [X0 : (($i > $o) > $i > $i > $o),X1 : (($i > $o) > $i > $i > $i)] : (($false = ((sK0 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((X0 @ Y2 @ Y3 @ Y4) & ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((^[Y7 : $i]: (Y5 @ (X1 @ Y5 @ Y6 @ Y7))))))) @ Y2 @ Y3 @ Y4))))))) @ Y0 @ Y1)))))))))) | ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (X0 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))) != (^[Y0 : $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: (~ (Y2 = Y3)))))))))) | ((^[Y0 : $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: (Y3)))))))) != (^[Y0 : $i > $o]: ((^[Y1 : $i]: (X1 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))))))) | ((^[Y0 : $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: (Y3)))))))) != (^[Y0 : $i > $o]: ((^[Y1 : $i]: (X1 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) ) | (~spl2_4 | ~spl2_11)),
% 0.96/0.59    inference(equality_resolution,[],[f389])).
% 0.96/0.59  thf(f432,plain,(
% 0.96/0.59    ( ! [X0 : (($i > $o) > $i > $i > $o),X1 : (($i > $o) > $i > $i > $i)] : (($false = ((sK0 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((X0 @ Y2 @ Y3 @ Y4) & ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((^[Y7 : $i]: (Y5 @ (X1 @ Y5 @ Y6 @ Y7))))))) @ Y2 @ Y3 @ Y4))))))) @ Y0 @ Y1)))))))))) | ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (X0 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))) != (^[Y0 : $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: (~ (Y2 = Y3)))))))))) | ((^[Y0 : $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: (Y3)))))))) != (^[Y0 : $i > $o]: ((^[Y1 : $i]: (X1 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) ) | (~spl2_4 | ~spl2_11)),
% 0.96/0.59    inference(duplicate_literal_removal,[],[f429])).
% 0.96/0.59  thf(f433,plain,(
% 0.96/0.59    ( ! [X0 : (($i > $o) > $i > $i > $o),X1 : (($i > $o) > $i > $i > $i)] : (((^[Y0 : $i > $o]: ((^[Y1 : $i]: (X0 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))) != (^[Y0 : $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: (~ (Y2 = Y3)))))))))) | ($false = ((sK0 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((X0 @ Y0 @ Y1 @ Y2) & (Y0 @ (X1 @ Y0 @ Y1 @ Y2))))))))))))) | ((^[Y0 : $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: (Y3)))))))) != (^[Y0 : $i > $o]: ((^[Y1 : $i]: (X1 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) ) | (~spl2_4 | ~spl2_11)),
% 0.96/0.59    inference(beta-eta_normalization,[],[f432])).
% 0.96/0.59  thf(f586,plain,(
% 0.96/0.59    ( ! [X2 : (($i > $o) > $i > $i > $i),X0 : (($i > $o) > $i > $i > $i),X1 : (($i > $o) > $i > $i > $i)] : (($false = ((sK0 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: (((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((^[Y5 : $i]: (~ ((^[Y6 : $i > $o]: ((^[Y7 : $i]: ((^[Y8 : $i]: ((X0 @ Y6 @ Y7 @ Y8) = (X1 @ Y6 @ Y7 @ Y8))))))) @ Y3 @ Y4 @ Y5))))))) @ Y0 @ Y1 @ Y2) & (Y0 @ (X2 @ Y0 @ Y1 @ Y2))))))))))))) | ((^[Y0 : $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: (Y3)))))))) != (^[Y0 : $i > $o]: ((^[Y1 : $i]: (X2 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))))))) | ((^[Y0 : $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: (Y3)))))))) != (^[Y0 : $i > $o]: ((^[Y1 : $i]: (X1 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))))))) | ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (X0 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))) != (^[Y0 : $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))))))))) ) | (~spl2_4 | ~spl2_11)),
% 0.96/0.59    inference(equality_resolution,[],[f433])).
% 0.96/0.59  thf(f587,plain,(
% 0.96/0.59    ( ! [X2 : (($i > $o) > $i > $i > $i),X0 : (($i > $o) > $i > $i > $i),X1 : (($i > $o) > $i > $i > $i)] : (((^[Y0 : $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: (Y3)))))))) != (^[Y0 : $i > $o]: ((^[Y1 : $i]: (X2 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))))))) | ($false = ((sK0 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ ((X0 @ Y0 @ Y1 @ Y2) = (X1 @ Y0 @ Y1 @ Y2))) & (Y0 @ (X2 @ Y0 @ Y1 @ Y2))))))))))))) | ((^[Y0 : $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: (Y3)))))))) != (^[Y0 : $i > $o]: ((^[Y1 : $i]: (X1 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))))))) | ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (X0 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))) != (^[Y0 : $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))))))))) ) | (~spl2_4 | ~spl2_11)),
% 0.96/0.59    inference(beta-eta_normalization,[],[f586])).
% 0.96/0.59  thf(f720,plain,(
% 0.96/0.59    ( ! [X0 : (($i > $o) > $i > $i > $i),X1 : (($i > $o) > $i > $i > $i)] : (($false = ((sK0 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ ((X0 @ Y0 @ Y1 @ Y2) = (X1 @ Y0 @ Y1 @ Y2))) & (Y0 @ ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((^[Y5 : $i]: (Y5)))))) @ Y0 @ Y1 @ Y2))))))))))))) | ((^[Y0 : $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: (Y3)))))))) != (^[Y0 : $i > $o]: ((^[Y1 : $i]: (X1 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))))))) | ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (X0 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))) != (^[Y0 : $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))))))))) ) | (~spl2_4 | ~spl2_11)),
% 0.96/0.59    inference(equality_resolution,[],[f587])).
% 0.96/0.59  thf(f721,plain,(
% 0.96/0.59    ( ! [X0 : (($i > $o) > $i > $i > $i),X1 : (($i > $o) > $i > $i > $i)] : (((^[Y0 : $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: (Y3)))))))) != (^[Y0 : $i > $o]: ((^[Y1 : $i]: (X1 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))))))) | ($false = ((sK0 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ ((X0 @ Y0 @ Y1 @ Y2) = (X1 @ Y0 @ Y1 @ Y2))) & (Y0 @ Y2)))))))))))) | ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (X0 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))) != (^[Y0 : $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))))))))) ) | (~spl2_4 | ~spl2_11)),
% 0.96/0.59    inference(beta-eta_normalization,[],[f720])).
% 0.96/0.59  thf(f724,plain,(
% 0.96/0.59    ( ! [X0 : (($i > $o) > $i > $i > $i)] : (($false = ((sK0 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ ((X0 @ Y0 @ Y1 @ Y2) = ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((^[Y5 : $i]: (Y5)))))) @ Y0 @ Y1 @ Y2))) & (Y0 @ Y2)))))))))))) | ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (X0 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))) != (^[Y0 : $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2)))))))))) ) | (~spl2_4 | ~spl2_11)),
% 0.96/0.59    inference(equality_resolution,[],[f721])).
% 0.96/0.59  thf(f725,plain,(
% 0.96/0.59    ( ! [X0 : (($i > $o) > $i > $i > $i)] : (((^[Y0 : $i > $o]: ((^[Y1 : $i]: (X0 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))) != (^[Y0 : $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: (Y2))))))))) | ($false = ((sK0 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ ((X0 @ Y0 @ Y1 @ Y2) = Y2)) & (Y0 @ Y2))))))))))))) ) | (~spl2_4 | ~spl2_11)),
% 0.96/0.59    inference(beta-eta_normalization,[],[f724])).
% 0.96/0.59  thf(f728,plain,(
% 0.96/0.59    ($false = ((sK0 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((^[Y5 : $i]: (Y4)))))) @ Y0 @ Y1 @ Y2) = Y2)) & (Y0 @ Y2)))))))))))) | (~spl2_4 | ~spl2_11)),
% 0.96/0.59    inference(equality_resolution,[],[f725])).
% 0.96/0.59  thf(f729,plain,(
% 0.96/0.59    ($false = ((sK0 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))))))))))) | (~spl2_4 | ~spl2_11)),
% 0.96/0.59    inference(beta-eta_normalization,[],[f728])).
% 0.96/0.59  thf(f732,plain,(
% 0.96/0.59    ($true = $false) | (~spl2_2 | ~spl2_4 | ~spl2_11)),
% 0.96/0.59    inference(constrained_superposition,[],[f729,f82])).
% 0.96/0.59  thf(f746,plain,(
% 0.96/0.59    ( ! [X0 : (($i > $o) > $o)] : (($true = $false) | ($true = ((sK1 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (X0 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))))) | ($false = ((sK1 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ X0))) | ($false = ((cP @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))))))) ) | (~spl2_4 | ~spl2_11)),
% 0.96/0.59    inference(constrained_superposition,[],[f141,f729])).
% 0.96/0.59  thf(f749,plain,(
% 0.96/0.59    ( ! [X0 : (($i > $o) > $o)] : (($true = ((sK1 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (X0 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))))) | ($false = ((sK1 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ X0))) | ($false = ((cP @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))))))) ) | (~spl2_4 | ~spl2_11)),
% 0.96/0.59    inference(trivial_inequality_removal,[],[f746])).
% 0.96/0.59  thf(f776,plain,(
% 0.96/0.59    $false | (~spl2_2 | ~spl2_4 | ~spl2_11)),
% 0.96/0.59    inference(trivial_inequality_removal,[],[f732])).
% 0.96/0.59  thf(f777,plain,(
% 0.96/0.59    ~spl2_2 | ~spl2_4 | ~spl2_11),
% 0.96/0.59    inference(avatar_contradiction_clause,[],[f776])).
% 0.96/0.59  thf(f779,plain,(
% 0.96/0.59    ( ! [X0 : (($i > $o) > $o)] : (($true = $false) | ($true = ((sK1 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (X0 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))))) | ($false = ((sK1 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ X0)))) ) | (~spl2_4 | ~spl2_11)),
% 0.96/0.59    inference(forward_demodulation,[],[f749,f28])).
% 0.96/0.59  thf(f780,plain,(
% 0.96/0.59    ( ! [X0 : (($i > $o) > $o)] : (($true = ((sK1 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (X0 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))))) | ($false = ((sK1 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ X0)))) ) | (~spl2_4 | ~spl2_11)),
% 0.96/0.59    inference(trivial_inequality_removal,[],[f779])).
% 0.96/0.59  thf(f785,plain,(
% 0.96/0.59    spl2_10 | ~spl2_4 | ~spl2_11),
% 0.96/0.59    inference(avatar_split_clause,[],[f780,f257,f102,f254])).
% 0.96/0.59  thf(f788,plain,(
% 0.96/0.59    spl2_3 | spl2_11),
% 0.96/0.59    inference(avatar_split_clause,[],[f165,f257,f89])).
% 0.96/0.59  thf(f789,plain,(
% 0.96/0.59    ( ! [X0 : (($i > $o) > $o)] : (($false = ((sK0 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ X0))) | ($true = ((sK0 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (X0 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))))))))))) ) | spl2_1),
% 0.96/0.59    inference(forward_subsumption_resolution,[],[f135,f77])).
% 0.96/0.59  thf(f790,plain,(
% 0.96/0.59    spl2_11 | spl2_1),
% 0.96/0.59    inference(avatar_split_clause,[],[f789,f76,f257])).
% 0.96/0.59  thf(f791,plain,(
% 0.96/0.59    ($false = ((sK1 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (~ (?? @ $i @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))))))))))) | spl2_4),
% 0.96/0.59    inference(forward_subsumption_resolution,[],[f95,f103])).
% 0.96/0.59  thf(f792,plain,(
% 0.96/0.59    $false | (spl2_1 | spl2_4)),
% 0.96/0.59    inference(forward_subsumption_resolution,[],[f791,f77])).
% 0.96/0.59  thf(f793,plain,(
% 0.96/0.59    spl2_1 | spl2_4),
% 0.96/0.59    inference(avatar_contradiction_clause,[],[f792])).
% 0.96/0.59  cnf(s1, plain, spl2_1 | spl2_2, inference(sat_conversion,[],[f83])).
% 0.96/0.59  cnf(s2, plain, spl2_2 | spl2_3, inference(sat_conversion,[],[f92])).
% 0.96/0.59  cnf(s3, plain, spl2_3 | spl2_4, inference(sat_conversion,[],[f105])).
% 0.96/0.59  cnf(s10, plain, spl2_10 | spl2_11, inference(sat_conversion,[],[f259])).
% 0.96/0.59  cnf(s12, plain, ~spl2_1 | ~spl2_3 | ~spl2_10, inference(sat_conversion,[],[f294])).
% 0.96/0.59  cnf(s13, plain, spl2_4 | spl2_10, inference(sat_conversion,[],[f354])).
% 0.96/0.59  cnf(s16, plain, ~spl2_2 | ~spl2_4 | ~spl2_11, inference(sat_conversion,[],[f777])).
% 0.96/0.59  cnf(s17, plain, ~spl2_4 | spl2_10 | ~spl2_11, inference(sat_conversion,[],[f785])).
% 0.96/0.59  cnf(s23, plain, spl2_3 | spl2_11, inference(sat_conversion,[],[f788])).
% 0.96/0.59  cnf(s24, plain, spl2_1 | spl2_11, inference(sat_conversion,[],[f790])).
% 0.96/0.59  cnf(s25, plain, spl2_1 | spl2_4, inference(sat_conversion,[],[f793])).
% 0.96/0.59  cnf(s26, plain, spl2_1, inference(rat,[],[s16,s1,s24,s25])).
% 0.96/0.59  cnf(s27, plain, spl2_3 | ~spl2_2, inference(rat,[],[s16,s3,s23])).
% 0.96/0.59  cnf(s28, plain, spl2_10, inference(rat,[],[s17,s10,s13])).
% 0.96/0.59  cnf(s29, plain, ~spl2_3, inference(rat,[],[s12,s26,s28])).
% 0.96/0.59  cnf(s32, plain, spl2_2, inference(rat,[],[s2,s29])).
% 0.96/0.59  cnf(s33, plain, $false, inference(rat,[],[s27,s32,s29])).
% 0.96/0.59  thf(f794,plain,(
% 0.96/0.59    $false),
% 0.96/0.59    inference(avatar_sat_refutation,[],[s33])).
% 0.96/0.59  % SZS output end Proof for theBenchmark
% 0.96/0.59  % (3508677)------------------------------
% 0.96/0.59  % (3508677)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.96/0.59  % (3508677)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.96/0.59  % (3508677)CaDiCaL version: 2.1.3
% 0.96/0.59  % (3508677)Termination reason: Refutation
% 0.96/0.59  % (3508677)Time elapsed: 0.133 s
% 0.96/0.59  % (3508677)Peak memory usage: 14 MB
% 0.96/0.59  % (3508677)Instructions burned: 291 (million)
% 0.96/0.59  % (3508642)Success in time 0.349 s
% 0.96/0.59  % Vampire exiting
%------------------------------------------------------------------------------