%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : PHI006^4 : TPTP v9.3.1. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n012.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 08:20:21 AM UTC 2026
% Result : ContradictoryAxioms 0.68s 0.33s
% Output : Refutation 0.68s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : PHI006^4 : TPTP v9.3.1. Released v6.4.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Tue Sep 29 13:19:18 UTC 2026
% 0.00/0.10 % CPUTime :
% 0.00/0.10 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.12 Running first-order model finding
% 0.09/0.12 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
% 0.68/0.33 % (83649)Will run a generic schedule for satisfiability detection.
% 0.68/0.33 % (83655)% WARNING: option uhcvi not known.
% 0.68/0.33 % (83654)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1722044746_2999 on theBenchmark for (2999ds/0Mi)
% 0.68/0.33 % (83655)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1037018188:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.68/0.33 % (83656)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1339081405:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.68/0.33 % (83657)dis+10_1_sil=32000:sp=arity:random_seed=3158658241:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.68/0.33 % (83658)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3602934143:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.68/0.33 % (83659)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1046723541:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.68/0.33 % (83660)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=857475046:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.68/0.33 % (83655)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.68/0.33 % (83658)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.68/0.33 % (83655)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.68/0.33 % Exception at run slice level
% 0.68/0.33 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.68/0.33 % (83668)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2272723392:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.68/0.33 % Exception at run slice level
% 0.68/0.33 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.68/0.33 % (83670)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=356932220:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.68/0.33 % (83657)Instruction limit reached!
% 0.68/0.33 % (83657)------------------------------
% 0.68/0.33 % (83657)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.33 % (83657)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.33 % (83657)CaDiCaL version: 2.1.3
% 0.68/0.33 % (83657)Termination reason: Instruction limit
% 0.68/0.33 % (83657)Termination phase: Saturation
% 0.68/0.33 % (83657)Time elapsed: 0.026 s
% 0.68/0.33 % (83657)Peak memory usage: 12 MB
% 0.68/0.33 % (83657)Instructions burned: 103 (million)
% 0.68/0.33 % (83658)Instruction limit reached!
% 0.68/0.33 % (83658)------------------------------
% 0.68/0.33 % (83658)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.33 % (83658)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.33 % (83658)CaDiCaL version: 2.1.3
% 0.68/0.33 % (83658)Termination reason: Instruction limit
% 0.68/0.33 % (83658)Termination phase: Saturation
% 0.68/0.33 % (83658)Time elapsed: 0.029 s
% 0.68/0.33 % (83658)Peak memory usage: 12 MB
% 0.68/0.33 % (83658)Instructions burned: 116 (million)
% 0.68/0.33 % (83659)Instruction limit reached!
% 0.68/0.33 % (83659)------------------------------
% 0.68/0.33 % (83659)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.33 % (83659)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.33 % (83659)CaDiCaL version: 2.1.3
% 0.68/0.33 % (83659)Termination reason: Instruction limit
% 0.68/0.33 % (83659)Termination phase: Saturation
% 0.68/0.33 % (83659)Time elapsed: 0.033 s
% 0.68/0.33 % (83659)Peak memory usage: 12 MB
% 0.68/0.33 % (83659)Instructions burned: 132 (million)
% 0.68/0.33 % (83672)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=4117850321:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 0.68/0.33 % (83660)Instruction limit reached!
% 0.68/0.33 % (83660)------------------------------
% 0.68/0.33 % (83660)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.33 % (83660)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.33 % (83660)CaDiCaL version: 2.1.3
% 0.68/0.33 % (83660)Termination reason: Instruction limit
% 0.68/0.33 % (83660)Termination phase: Saturation
% 0.68/0.33 % (83660)Time elapsed: 0.037 s
% 0.68/0.33 % (83660)Peak memory usage: 12 MB
% 0.68/0.33 % (83660)Instructions burned: 160 (million)
% 0.68/0.33 % (83672)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.68/0.33 % (83672)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.68/0.33 % (83673)ott-21_1_sil=16000:fs=off:random_seed=1047802134:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 0.68/0.33 % (83674)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2746044919:i=477:bd=all_2999 on theBenchmark for (2999ds/477Mi)
% 0.68/0.33 % (83676)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=2782843373:fmbsr=1.3:i=865:ins=25_2999 on theBenchmark for (2999ds/865Mi)
% 0.68/0.33 % Exception at run slice level
% 0.68/0.33 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.68/0.33 % (83670)Instruction limit reached!
% 0.68/0.33 % (83670)------------------------------
% 0.68/0.33 % (83670)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.33 % (83670)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.33 % (83670)CaDiCaL version: 2.1.3
% 0.68/0.33 % (83670)Termination reason: Instruction limit
% 0.68/0.33 % (83670)Termination phase: Saturation
% 0.68/0.33 % (83670)Time elapsed: 0.034 s
% 0.68/0.33 % (83670)Peak memory usage: 12 MB
% 0.68/0.33 % (83670)Instructions burned: 132 (million)
% 0.68/0.33 % (83680)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=3653271055:i=1179_2999 on theBenchmark for (2999ds/1179Mi)
% 0.68/0.33 % (83681)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=2659518946:i=889:ins=1_2999 on theBenchmark for (2999ds/889Mi)
% 0.68/0.33 % Exception at run slice level
% 0.68/0.33 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.68/0.33 % (83684)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=3259925751:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2999 on theBenchmark for (2999ds/692Mi)
% 0.68/0.33 % (83684)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.68/0.33 % (83673)Instruction limit reached!
% 0.68/0.33 % (83673)------------------------------
% 0.68/0.33 % (83673)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.33 % (83673)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.33 % (83673)CaDiCaL version: 2.1.3
% 0.68/0.33 % (83673)Termination reason: Instruction limit
% 0.68/0.33 % (83673)Termination phase: Saturation
% 0.68/0.33 % (83673)Time elapsed: 0.043 s
% 0.68/0.33 % (83673)Peak memory usage: 12 MB
% 0.68/0.33 % (83673)Instructions burned: 181 (million)
% 0.68/0.33 % (83686)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=3073537197:i=879:kws=inv_precedence:fsr=off_2998 on theBenchmark for (2998ds/879Mi)
% 0.68/0.33 % (83686)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.68/0.33 % (83674)Instruction limit reached!
% 0.68/0.33 % (83674)------------------------------
% 0.68/0.33 % (83674)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.33 % (83674)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.33 % (83674)CaDiCaL version: 2.1.3
% 0.68/0.33 % (83674)Termination reason: Instruction limit
% 0.68/0.33 % (83674)Termination phase: Saturation
% 0.68/0.33 % (83674)Time elapsed: 0.116 s
% 0.68/0.33 % (83674)Peak memory usage: 13 MB
% 0.68/0.33 % (83674)Instructions burned: 481 (million)
% 0.68/0.33 % (83688)fmb+10_1_sil=64000:random_seed=24978717:i=22061:nm=2:gsp=on_2998 on theBenchmark for (2998ds/22061Mi)
% 0.68/0.33 % (83688)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.68/0.33 % Exception at run slice level
% 0.68/0.33 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.68/0.33 % (83672) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-83649-83672"...
% 0.68/0.33 % (83672)...printing done.
% 0.68/0.33 % (83672)Refutation found. Thanks to Tanya!
% 0.68/0.33 % SZS status ContradictoryAxioms for theBenchmark
% 0.68/0.33 % SZS output start Proof for theBenchmark
% 0.68/0.33 thf(type_def_5, type, mu: $tType).
% 0.68/0.33 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.68/0.33 thf(func_def_0, type, meq_ind: (mu > mu > $i > $o)).
% 0.68/0.33 thf(func_def_1, type, mtrue: ($i > $o)).
% 0.68/0.33 thf(func_def_2, type, mfalse: ($i > $o)).
% 0.68/0.33 thf(func_def_3, type, mnot: (($i > $o) > $i > $o)).
% 0.68/0.33 thf(func_def_5, type, mor: (($i > $o) > ($i > $o) > $i > $o)).
% 0.68/0.33 thf(func_def_6, type, mand: (($i > $o) > ($i > $o) > $i > $o)).
% 0.68/0.33 thf(func_def_7, type, mimplies: (($i > $o) > ($i > $o) > $i > $o)).
% 0.68/0.33 thf(func_def_8, type, mimplied: (($i > $o) > ($i > $o) > $i > $o)).
% 0.68/0.33 thf(func_def_9, type, mequiv: (($i > $o) > ($i > $o) > $i > $o)).
% 0.68/0.33 thf(func_def_10, type, mxor: (($i > $o) > ($i > $o) > $i > $o)).
% 0.68/0.33 thf(func_def_11, type, mforall_ind: ((mu > $i > $o) > $i > $o)).
% 0.68/0.33 thf(func_def_12, type, mforall_indset: (((mu > $i > $o) > $i > $o) > $i > $o)).
% 0.68/0.33 thf(func_def_13, type, mforall_prop: ((($i > $o) > $i > $o) > $i > $o)).
% 0.68/0.33 thf(func_def_14, type, mexists_ind: ((mu > $i > $o) > $i > $o)).
% 0.68/0.33 thf(func_def_15, type, mexists_indset: (((mu > $i > $o) > $i > $o) > $i > $o)).
% 0.68/0.33 thf(func_def_16, type, mexists_prop: ((($i > $o) > $i > $o) > $i > $o)).
% 0.68/0.33 thf(func_def_17, type, mbox: (($i > $o) > $i > $o)).
% 0.68/0.33 thf(func_def_18, type, mdia: (($i > $o) > $i > $o)).
% 0.68/0.33 thf(func_def_19, type, mvalid: (($i > $o) > $o)).
% 0.68/0.33 thf(func_def_20, type, minvalid: (($i > $o) > $o)).
% 0.68/0.33 thf(func_def_21, type, positive: ((mu > $i > $o) > $i > $o)).
% 0.68/0.33 thf(func_def_22, type, god: (mu > $i > $o)).
% 0.68/0.33 thf(func_def_23, type, essence: ((mu > $i > $o) > mu > $i > $o)).
% 0.68/0.33 thf(func_def_24, type, necessary_existence: (mu > $i > $o)).
% 0.68/0.33 thf(func_def_25, type, db2: !>[X0: $tType]:(X0)).
% 0.68/0.33 thf(func_def_26, type, db1: !>[X0: $tType]:(X0)).
% 0.68/0.33 thf(func_def_27, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.68/0.33 thf(func_def_28, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.68/0.33 thf(func_def_31, type, vNOT: ($o > $o)).
% 0.68/0.33 thf(func_def_32, type, db0: !>[X0: $tType]:(X0)).
% 0.68/0.33 thf(func_def_33, type, vOR: ($o > $o > $o)).
% 0.68/0.33 thf(func_def_34, type, vAND: ($o > $o > $o)).
% 0.68/0.33 thf(func_def_35, type, vIMP: ($o > $o > $o)).
% 0.68/0.33 thf(func_def_36, type, vIFF: ($o > $o > $o)).
% 0.68/0.33 thf(func_def_37, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.68/0.33 thf(func_def_38, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.68/0.33 thf(func_def_39, type, db3: !>[X0: $tType]:(X0)).
% 0.68/0.33 thf(func_def_40, type, db4: !>[X0: $tType]:(X0)).
% 0.68/0.33 thf(func_def_41, type, db5: !>[X0: $tType]:(X0)).
% 0.68/0.33 thf(func_def_42, type, sK0: ((mu > $i > $o) > (mu > $i > $o) > $i)).
% 0.68/0.33 thf(func_def_43, type, sK1: ((mu > $i > $o) > (mu > $i > $o) > mu)).
% 0.68/0.33 thf(func_def_44, type, sK2: ((mu > $i > $o) > (mu > $i > $o) > mu)).
% 0.68/0.33 thf(func_def_45, type, sK3: ((mu > $i > $o) > (mu > $i > $o) > mu)).
% 0.68/0.33 thf(func_def_46, type, sK4: ((mu > $i > $o) > (mu > $i > $o) > mu)).
% 0.68/0.33 thf(func_def_47, type, sK5: ((mu > $i > $o) > (mu > $i > $o) > mu)).
% 0.68/0.33 thf(func_def_48, type, sK6: ((mu > $i > $o) > (mu > $i > $o) > mu)).
% 0.68/0.33 thf(func_def_49, type, sK7: ((mu > $i > $o) > (mu > $i > $o) > mu)).
% 0.68/0.33 thf(func_def_51, type, sK9: ((mu > $i > $o) > mu)).
% 0.68/0.33 thf(func_def_52, type, sK10: ((mu > $i > $o) > mu)).
% 0.68/0.33 thf(func_def_53, type, sK11: ((mu > $i > $o) > $i)).
% 0.68/0.33 thf(func_def_54, type, sK12: ((mu > $i > $o) > mu)).
% 0.68/0.33 thf(func_def_55, type, sK13: ((mu > $i > $o) > $i)).
% 0.68/0.33 thf(func_def_56, type, sK14: ((mu > $i > $o) > mu)).
% 0.68/0.33 thf(func_def_57, type, sK15: ((mu > $i > $o) > $i)).
% 0.68/0.33 thf(func_def_58, type, sK16: ((mu > $i > $o) > mu > $i > $o)).
% 0.68/0.33 thf(func_def_59, type, sK17: ((mu > $i > $o) > $i > mu)).
% 0.68/0.33 thf(func_def_60, type, sK18: ((mu > $i > $o) > $i)).
% 0.68/0.33 thf(func_def_61, type, sK19: ((mu > $i > $o) > $i > mu)).
% 0.68/0.33 thf(func_def_62, type, sK20: ((mu > $i > $o) > mu)).
% 0.68/0.33 thf(func_def_63, type, sK21: ((mu > $i > $o) > mu > $i > $o)).
% 0.68/0.33 thf(func_def_64, type, sK22: ((mu > $i > $o) > $i > mu)).
% 0.68/0.33 thf(func_def_65, type, sK23: ((mu > $i > $o) > $i)).
% 0.68/0.33 thf(func_def_66, type, sK24: ((mu > $i > $o) > $i > mu)).
% 0.68/0.33 thf(func_def_67, type, sK25: ((mu > $i > $o) > mu)).
% 0.68/0.33 thf(func_def_68, type, sK26: ((mu > $i > $o) > mu)).
% 0.68/0.33 thf(func_def_69, type, sK27: ((mu > $i > $o) > $i)).
% 0.68/0.33 thf(func_def_70, type, sK28: ((mu > $i > $o) > mu)).
% 0.68/0.33 thf(func_def_71, type, sK29: ((mu > $i > $o) > $i)).
% 0.68/0.33 thf(func_def_72, type, sK30: ((mu > $i > $o) > mu)).
% 0.68/0.33 thf(func_def_73, type, sK31: ((mu > $i > $o) > $i)).
% 0.68/0.33 thf(func_def_74, type, sK32: ((mu > $i > $o) > mu)).
% 0.68/0.33 thf(func_def_75, type, sK33: ((mu > $i > $o) > $i)).
% 0.68/0.33 thf(func_def_76, type, sK34: ((mu > $i > $o) > mu)).
% 0.68/0.33 thf(func_def_77, type, sK35: ((mu > $i > $o) > $i)).
% 0.68/0.33 thf(func_def_78, type, sK36: ((mu > $i > $o) > mu)).
% 0.68/0.33 thf(func_def_79, type, sK37: ((mu > $i > $o) > $i)).
% 0.68/0.33 thf(func_def_80, type, sK38: ((mu > $i > $o) > mu)).
% 0.68/0.33 thf(func_def_81, type, sK39: ((mu > $i > $o) > $i)).
% 0.68/0.33 thf(func_def_82, type, sK40: ((mu > $i > $o) > mu)).
% 0.68/0.33 thf(func_def_83, type, sK41: ((mu > $i > $o) > mu)).
% 0.68/0.33 thf(f4,axiom,(
% 0.68/0.33 (mnot = (^[X0 : ($i > $o), X1 : $i] : (~(X0 @ X1))))),
% 0.68/0.33 file('/export/starexec/sandbox/benchmark/Axioms/LCL017^0.ax',mnot)).
% 0.68/0.33 thf(f6,axiom,(
% 0.68/0.33 (mand = (^[X0 : ($i > $o), X1 : ($i > $o), X2 : $i] : ((X1 @ X2) & (X0 @ X2))))),
% 0.68/0.33 file('/export/starexec/sandbox/benchmark/Axioms/LCL017^0.ax',mand)).
% 0.68/0.33 thf(f7,axiom,(
% 0.68/0.33 (mimplies = (^[X0 : ($i > $o), X1 : ($i > $o), X2 : $i] : ((X0 @ X2) => (X1 @ X2))))),
% 0.68/0.33 file('/export/starexec/sandbox/benchmark/Axioms/LCL017^0.ax',mimplies)).
% 0.68/0.33 thf(f11,axiom,(
% 0.68/0.33 (mforall_ind = (^[X0 : (mu > $i > $o), X1 : $i] : (! [X2 : mu] : (X0 @ X2 @ X1))))),
% 0.68/0.33 file('/export/starexec/sandbox/benchmark/Axioms/LCL017^0.ax',mforall_ind)).
% 0.68/0.33 thf(f12,axiom,(
% 0.68/0.33 (mforall_indset = (^[X0 : ((mu > $i > $o) > $i > $o), X1 : $i] : (! [X2 : (mu > $i > $o)] : (X0 @ X2 @ X1))))),
% 0.68/0.33 file('/export/starexec/sandbox/benchmark/Axioms/LCL017^0.ax',mforall_indset)).
% 0.68/0.33 thf(f14,axiom,(
% 0.68/0.33 (mexists_ind = (^[X0 : (mu > $i > $o), X1 : $i] : (? [X2 : mu] : (X0 @ X2 @ X1))))),
% 0.68/0.33 file('/export/starexec/sandbox/benchmark/Axioms/LCL017^0.ax',mexists_ind)).
% 0.68/0.33 thf(f17,axiom,(
% 0.68/0.33 (mbox = (^[X0 : ($i > $o), X1 : $i] : (! [X2 : $i] : (X0 @ X2))))),
% 0.68/0.33 file('/export/starexec/sandbox/benchmark/Axioms/LCL017^0.ax',mbox)).
% 0.68/0.33 thf(f19,axiom,(
% 0.68/0.33 (mvalid = (^[X0 : ($i > $o)] : (! [X1 : $i] : (X0 @ X1))))),
% 0.68/0.33 file('/export/starexec/sandbox/benchmark/Axioms/LCL017^0.ax',mvalid)).
% 0.68/0.33 thf(f21,axiom,(
% 0.68/0.33 (mvalid @ (mforall_indset @ (^[X0 : (mu > $i > $o)] : ((mimplies @ (positive @ (^[X1 : mu] : ((mnot @ (X0 @ X1))))) @ (mnot @ (positive @ X0)))))))),
% 0.68/0.33 file('/export/starexec/sandbox/benchmark/theBenchmark.p',axA1a)).
% 0.68/0.33 thf(f22,axiom,(
% 0.68/0.33 (mvalid @ (mforall_indset @ (^[X0 : (mu > $i > $o)] : ((mimplies @ (mnot @ (positive @ X0)) @ (positive @ (^[X1 : mu] : ((mnot @ (X0 @ X1))))))))))),
% 0.68/0.33 file('/export/starexec/sandbox/benchmark/theBenchmark.p',axA1b)).
% 0.68/0.33 thf(f23,axiom,(
% 0.68/0.33 (mvalid @ (mforall_indset @ (^[X0 : (mu > $i > $o)] : ((mforall_indset @ (^[X1 : (mu > $i > $o)] : ((mimplies @ (mand @ (positive @ X0) @ (mbox @ (mforall_ind @ (^[X2 : mu] : ((mimplies @ (X0 @ X2) @ (X1 @ X2))))))) @ (positive @ X1)))))))))),
% 0.68/0.33 file('/export/starexec/sandbox/benchmark/theBenchmark.p',axA2)).
% 0.68/0.33 thf(f26,axiom,(
% 0.68/0.33 (mvalid @ (mforall_indset @ (^[X0 : (mu > $i > $o)] : ((mimplies @ (positive @ X0) @ (mbox @ (positive @ X0)))))))),
% 0.68/0.33 file('/export/starexec/sandbox/benchmark/theBenchmark.p',axA4)).
% 0.68/0.33 thf(f27,axiom,(
% 0.68/0.33 (essence = (^[X0 : (mu > $i > $o), X1 : mu] : ((mforall_indset @ (^[X2 : (mu > $i > $o)] : ((mimplies @ (X2 @ X1) @ (mbox @ (mforall_ind @ (^[X3 : mu] : ((mimplies @ (X0 @ X3) @ (X2 @ X3)))))))))))))),
% 0.68/0.33 file('/export/starexec/sandbox/benchmark/theBenchmark.p',defD2)).
% 0.68/0.33 thf(f28,axiom,(
% 0.68/0.33 (necessary_existence = (^[X0 : mu] : ((mforall_indset @ (^[X1 : (mu > $i > $o)] : ((mimplies @ (essence @ X1 @ X0) @ (mbox @ (mexists_ind @ (^[X2 : mu] : ((X1 @ X2))))))))))))),
% 0.68/0.33 file('/export/starexec/sandbox/benchmark/theBenchmark.p',defD3)).
% 0.68/0.33 thf(f29,axiom,(
% 0.68/0.33 (mvalid @ (positive @ necessary_existence))),
% 0.68/0.33 file('/export/starexec/sandbox/benchmark/theBenchmark.p',axA5)).
% 0.68/0.33 thf(f35,plain,(
% 0.68/0.33 (mnot = (^[X0 : ($i > $o), X1 : $i] : (~(X0 @ X1))))),
% 0.68/0.33 inference(rectify,[],[f4])).
% 0.68/0.33 thf(f36,plain,(
% 0.68/0.33 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.68/0.33 inference(fool_elimination,[],[f35])).
% 0.68/0.33 thf(f39,plain,(
% 0.68/0.33 (mand = (^[X0 : ($i > $o), X1 : ($i > $o), X2 : $i] : ((X1 @ X2) & (X0 @ X2))))),
% 0.68/0.33 inference(rectify,[],[f6])).
% 0.68/0.33 thf(f40,plain,(
% 0.68/0.33 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (Y1 @ Y2))))))))),
% 0.68/0.33 inference(fool_elimination,[],[f39])).
% 0.68/0.33 thf(f41,plain,(
% 0.68/0.33 (mimplies = (^[X0 : ($i > $o), X1 : ($i > $o), X2 : $i] : ((X0 @ X2) => (X1 @ X2))))),
% 0.68/0.33 inference(rectify,[],[f7])).
% 0.68/0.33 thf(f42,plain,(
% 0.68/0.33 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 0.68/0.33 inference(fool_elimination,[],[f41])).
% 0.68/0.33 thf(f49,plain,(
% 0.68/0.33 (mforall_ind = (^[X0 : (mu > $i > $o), X1 : $i] : (! [X2 : mu] : (X0 @ X2 @ X1))))),
% 0.68/0.33 inference(rectify,[],[f11])).
% 0.68/0.33 thf(f50,plain,(
% 0.68/0.33 (mforall_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: (Y0 @ Y2 @ Y1)))))))),
% 0.68/0.33 inference(fool_elimination,[],[f49])).
% 0.68/0.33 thf(f51,plain,(
% 0.68/0.33 (mforall_indset = (^[X0 : ((mu > $i > $o) > $i > $o), X1 : $i] : (! [X2 : (mu > $i > $o)] : (X0 @ X2 @ X1))))),
% 0.68/0.33 inference(rectify,[],[f12])).
% 0.68/0.33 thf(f52,plain,(
% 0.68/0.33 (mforall_indset = (^[Y0 : (mu > $i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: (Y0 @ Y2 @ Y1)))))))),
% 0.68/0.33 inference(fool_elimination,[],[f51])).
% 0.68/0.33 thf(f55,plain,(
% 0.68/0.33 (mexists_ind = (^[X0 : (mu > $i > $o), X1 : $i] : (? [X2 : mu] : (X0 @ X2 @ X1))))),
% 0.68/0.33 inference(rectify,[],[f14])).
% 0.68/0.33 thf(f56,plain,(
% 0.68/0.33 (mexists_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (?? @ mu @ (^[Y2 : mu]: (Y0 @ Y2 @ Y1)))))))),
% 0.68/0.33 inference(fool_elimination,[],[f55])).
% 0.68/0.33 thf(f61,plain,(
% 0.68/0.33 (mbox = (^[X0 : ($i > $o), X1 : $i] : (! [X2 : $i] : (X0 @ X2))))),
% 0.68/0.33 inference(rectify,[],[f17])).
% 0.68/0.33 thf(f62,plain,(
% 0.68/0.33 (mbox = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (Y0 @ Y2)))))))),
% 0.68/0.33 inference(fool_elimination,[],[f61])).
% 0.68/0.33 thf(f65,plain,(
% 0.68/0.33 (mvalid = (^[X0 : ($i > $o)] : (! [X1 : $i] : (X0 @ X1))))),
% 0.68/0.33 inference(rectify,[],[f19])).
% 0.68/0.33 thf(f66,plain,(
% 0.68/0.33 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.68/0.33 inference(fool_elimination,[],[f65])).
% 0.68/0.33 thf(f69,plain,(
% 0.68/0.33 (mvalid @ (mforall_indset @ (^[X0 : (mu > $i > $o)] : ((mimplies @ (positive @ (^[X1 : mu] : ((mnot @ (X0 @ X1))))) @ (mnot @ (positive @ X0)))))))),
% 0.68/0.33 inference(rectify,[],[f21])).
% 0.68/0.33 thf(f70,plain,(
% 0.68/0.33 ($true = ((mvalid @ (mforall_indset @ (^[Y0 : mu > $i > $o]: (mimplies @ (positive @ (^[Y1 : mu]: (mnot @ (Y0 @ Y1)))) @ (mnot @ (positive @ Y0))))))))),
% 0.68/0.33 inference(fool_elimination,[],[f69])).
% 0.68/0.33 thf(f71,plain,(
% 0.68/0.33 (mvalid @ (mforall_indset @ (^[X0 : (mu > $i > $o)] : ((mimplies @ (mnot @ (positive @ X0)) @ (positive @ (^[X1 : mu] : ((mnot @ (X0 @ X1))))))))))),
% 0.68/0.33 inference(rectify,[],[f22])).
% 0.68/0.33 thf(f72,plain,(
% 0.68/0.33 ($true = ((mvalid @ (mforall_indset @ (^[Y0 : mu > $i > $o]: (mimplies @ (mnot @ (positive @ Y0)) @ (positive @ (^[Y1 : mu]: (mnot @ (Y0 @ Y1))))))))))),
% 0.68/0.33 inference(fool_elimination,[],[f71])).
% 0.68/0.33 thf(f73,plain,(
% 0.68/0.33 (mvalid @ (mforall_indset @ (^[X0 : (mu > $i > $o)] : ((mforall_indset @ (^[X1 : (mu > $i > $o)] : ((mimplies @ (mand @ (positive @ X0) @ (mbox @ (mforall_ind @ (^[X2 : mu] : ((mimplies @ (X0 @ X2) @ (X1 @ X2))))))) @ (positive @ X1)))))))))),
% 0.68/0.33 inference(rectify,[],[f23])).
% 0.68/0.33 thf(f74,plain,(
% 0.68/0.33 ($true = ((mvalid @ (mforall_indset @ (^[Y0 : mu > $i > $o]: (mforall_indset @ (^[Y1 : mu > $i > $o]: (mimplies @ (mand @ (positive @ Y0) @ (mbox @ (mforall_ind @ (^[Y2 : mu]: (mimplies @ (Y0 @ Y2) @ (Y1 @ Y2)))))) @ (positive @ Y1)))))))))),
% 0.68/0.33 inference(fool_elimination,[],[f73])).
% 0.68/0.33 thf(f79,plain,(
% 0.68/0.33 (mvalid @ (mforall_indset @ (^[X0 : (mu > $i > $o)] : ((mimplies @ (positive @ X0) @ (mbox @ (positive @ X0)))))))),
% 0.68/0.33 inference(rectify,[],[f26])).
% 0.68/0.33 thf(f80,plain,(
% 0.68/0.33 ($true = ((mvalid @ (mforall_indset @ (^[Y0 : mu > $i > $o]: (mimplies @ (positive @ Y0) @ (mbox @ (positive @ Y0))))))))),
% 0.68/0.33 inference(fool_elimination,[],[f79])).
% 0.68/0.33 thf(f81,plain,(
% 0.68/0.33 (essence = (^[X0 : (mu > $i > $o), X1 : mu] : ((mforall_indset @ (^[X2 : (mu > $i > $o)] : ((mimplies @ (X2 @ X1) @ (mbox @ (mforall_ind @ (^[X3 : mu] : ((mimplies @ (X0 @ X3) @ (X2 @ X3)))))))))))))),
% 0.68/0.33 inference(rectify,[],[f27])).
% 0.68/0.33 thf(f82,plain,(
% 0.68/0.33 (essence = (^[Y0 : mu > $i > $o]: ((^[Y1 : mu]: (mforall_indset @ (^[Y2 : mu > $i > $o]: (mimplies @ (Y2 @ Y1) @ (mbox @ (mforall_ind @ (^[Y3 : mu]: (mimplies @ (Y0 @ Y3) @ (Y2 @ Y3))))))))))))),
% 0.68/0.33 inference(fool_elimination,[],[f81])).
% 0.68/0.33 thf(f83,plain,(
% 0.68/0.33 (necessary_existence = (^[X0 : mu] : ((mforall_indset @ (^[X1 : (mu > $i > $o)] : ((mimplies @ (essence @ X1 @ X0) @ (mbox @ (mexists_ind @ (^[X2 : mu] : ((X1 @ X2))))))))))))),
% 0.68/0.33 inference(rectify,[],[f28])).
% 0.68/0.33 thf(f84,plain,(
% 0.68/0.33 (necessary_existence = (^[Y0 : mu]: (mforall_indset @ (^[Y1 : mu > $i > $o]: (mimplies @ (essence @ Y1 @ Y0) @ (mbox @ (mexists_ind @ (^[Y2 : mu]: (Y1 @ Y2)))))))))),
% 0.68/0.33 inference(fool_elimination,[],[f83])).
% 0.68/0.33 thf(f85,plain,(
% 0.68/0.33 (mvalid @ (positive @ necessary_existence))),
% 0.68/0.33 inference(rectify,[],[f29])).
% 0.68/0.33 thf(f86,plain,(
% 0.68/0.33 (((mvalid @ (positive @ necessary_existence))) = $true)),
% 0.68/0.33 inference(fool_elimination,[],[f85])).
% 0.68/0.33 thf(f91,plain,(
% 0.68/0.33 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.68/0.33 inference(cnf_transformation,[],[f36])).
% 0.68/0.33 thf(f93,plain,(
% 0.68/0.33 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (Y1 @ Y2))))))))),
% 0.68/0.33 inference(cnf_transformation,[],[f40])).
% 0.68/0.33 thf(f94,plain,(
% 0.68/0.33 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 0.68/0.33 inference(cnf_transformation,[],[f42])).
% 0.68/0.33 thf(f98,plain,(
% 0.68/0.33 (mforall_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: (Y0 @ Y2 @ Y1)))))))),
% 0.68/0.33 inference(cnf_transformation,[],[f50])).
% 0.68/0.33 thf(f99,plain,(
% 0.68/0.33 (mforall_indset = (^[Y0 : (mu > $i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: (Y0 @ Y2 @ Y1)))))))),
% 0.68/0.33 inference(cnf_transformation,[],[f52])).
% 0.68/0.33 thf(f101,plain,(
% 0.68/0.33 (mexists_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (?? @ mu @ (^[Y2 : mu]: (Y0 @ Y2 @ Y1)))))))),
% 0.68/0.33 inference(cnf_transformation,[],[f56])).
% 0.68/0.33 thf(f104,plain,(
% 0.68/0.33 (mbox = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (Y0 @ Y2)))))))),
% 0.68/0.33 inference(cnf_transformation,[],[f62])).
% 0.68/0.33 thf(f106,plain,(
% 0.68/0.33 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.68/0.33 inference(cnf_transformation,[],[f66])).
% 0.68/0.33 thf(f108,plain,(
% 0.68/0.33 ($true = ((mvalid @ (mforall_indset @ (^[Y0 : mu > $i > $o]: (mimplies @ (positive @ (^[Y1 : mu]: (mnot @ (Y0 @ Y1)))) @ (mnot @ (positive @ Y0))))))))),
% 0.68/0.33 inference(cnf_transformation,[],[f70])).
% 0.68/0.33 thf(f109,plain,(
% 0.68/0.33 ($true = ((mvalid @ (mforall_indset @ (^[Y0 : mu > $i > $o]: (mimplies @ (mnot @ (positive @ Y0)) @ (positive @ (^[Y1 : mu]: (mnot @ (Y0 @ Y1))))))))))),
% 0.68/0.33 inference(cnf_transformation,[],[f72])).
% 0.68/0.33 thf(f110,plain,(
% 0.68/0.33 ($true = ((mvalid @ (mforall_indset @ (^[Y0 : mu > $i > $o]: (mforall_indset @ (^[Y1 : mu > $i > $o]: (mimplies @ (mand @ (positive @ Y0) @ (mbox @ (mforall_ind @ (^[Y2 : mu]: (mimplies @ (Y0 @ Y2) @ (Y1 @ Y2)))))) @ (positive @ Y1)))))))))),
% 0.68/0.33 inference(cnf_transformation,[],[f74])).
% 0.68/0.33 thf(f113,plain,(
% 0.68/0.33 ($true = ((mvalid @ (mforall_indset @ (^[Y0 : mu > $i > $o]: (mimplies @ (positive @ Y0) @ (mbox @ (positive @ Y0))))))))),
% 0.68/0.33 inference(cnf_transformation,[],[f80])).
% 0.68/0.33 thf(f114,plain,(
% 0.68/0.33 (essence = (^[Y0 : mu > $i > $o]: ((^[Y1 : mu]: (mforall_indset @ (^[Y2 : mu > $i > $o]: (mimplies @ (Y2 @ Y1) @ (mbox @ (mforall_ind @ (^[Y3 : mu]: (mimplies @ (Y0 @ Y3) @ (Y2 @ Y3))))))))))))),
% 0.68/0.33 inference(cnf_transformation,[],[f82])).
% 0.68/0.33 thf(f115,plain,(
% 0.68/0.33 (necessary_existence = (^[Y0 : mu]: (mforall_indset @ (^[Y1 : mu > $i > $o]: (mimplies @ (essence @ Y1 @ Y0) @ (mbox @ (mexists_ind @ (^[Y2 : mu]: (Y1 @ Y2)))))))))),
% 0.68/0.33 inference(cnf_transformation,[],[f84])).
% 0.68/0.33 thf(f116,plain,(
% 0.68/0.33 (((mvalid @ (positive @ necessary_existence))) = $true)),
% 0.68/0.33 inference(cnf_transformation,[],[f86])).
% 0.68/0.33 thf(f117,definition,(
% 0.68/0.33 ($true != $false)),
% 0.68/0.33 introduced(theory,[fool_distinctness_axiom])).
% 0.68/0.33 thf(f120,plain,(
% 0.68/0.33 (essence = (^[Y0 : mu > $i > $o]: ((^[Y1 : mu]: ((^[Y2 : (mu > $i > $o) > $i > $o]: ((^[Y3 : $i]: (!! @ (mu > $i > $o) @ (^[Y4 : mu > $i > $o]: (Y2 @ Y4 @ Y3)))))) @ (^[Y2 : mu > $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: ((Y3 @ Y5) => (Y4 @ Y5))))))) @ (Y2 @ Y1) @ ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (Y3 @ Y5)))))) @ ((^[Y3 : mu > $i > $o]: ((^[Y4 : $i]: (!! @ mu @ (^[Y5 : mu]: (Y3 @ Y5 @ Y4)))))) @ (^[Y3 : mu]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) => (Y5 @ Y6))))))) @ (Y0 @ Y3) @ (Y2 @ Y3))))))))))))),
% 0.68/0.33 inference(definition_unfolding,[],[f114,f99,f94,f104,f98,f94])).
% 0.68/0.33 thf(f121,plain,(
% 0.68/0.33 (necessary_existence = (^[Y0 : mu]: ((^[Y1 : (mu > $i > $o) > $i > $o]: ((^[Y2 : $i]: (!! @ (mu > $i > $o) @ (^[Y3 : mu > $i > $o]: (Y1 @ Y3 @ Y2)))))) @ (^[Y1 : mu > $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) => (Y3 @ Y4))))))) @ ((^[Y2 : mu > $i > $o]: ((^[Y3 : mu]: ((^[Y4 : (mu > $i > $o) > $i > $o]: ((^[Y5 : $i]: (!! @ (mu > $i > $o) @ (^[Y6 : mu > $i > $o]: (Y4 @ Y6 @ Y5)))))) @ (^[Y4 : mu > $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i]: ((Y5 @ Y7) => (Y6 @ Y7))))))) @ (Y4 @ Y3) @ ((^[Y5 : $i > $o]: ((^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (Y5 @ Y7)))))) @ ((^[Y5 : mu > $i > $o]: ((^[Y6 : $i]: (!! @ mu @ (^[Y7 : mu]: (Y5 @ Y7 @ Y6)))))) @ (^[Y5 : mu]: ((^[Y6 : $i > $o]: ((^[Y7 : $i > $o]: ((^[Y8 : $i]: ((Y6 @ Y8) => (Y7 @ Y8))))))) @ (Y2 @ Y5) @ (Y4 @ Y5))))))))))) @ Y1 @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (Y2 @ Y4)))))) @ ((^[Y2 : mu > $i > $o]: ((^[Y3 : $i]: (?? @ mu @ (^[Y4 : mu]: (Y2 @ Y4 @ Y3)))))) @ (^[Y2 : mu]: (Y1 @ Y2)))))))))),
% 0.68/0.33 inference(definition_unfolding,[],[f115,f99,f94,f120,f104,f101])).
% 0.68/0.33 thf(f122,plain,(
% 0.68/0.33 ($true = (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : (mu > $i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: (Y0 @ Y2 @ Y1)))))) @ (^[Y0 : mu > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: ((Y1 @ Y3) => (Y2 @ Y3))))))) @ (positive @ (^[Y1 : mu]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ (Y0 @ Y1)))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ (positive @ Y0))))))))),
% 0.68/0.33 inference(definition_unfolding,[],[f108,f106,f99,f94,f91,f91])).
% 0.68/0.33 thf(f123,plain,(
% 0.68/0.33 ($true = (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : (mu > $i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: (Y0 @ Y2 @ Y1)))))) @ (^[Y0 : mu > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: ((Y1 @ Y3) => (Y2 @ Y3))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ (positive @ Y0)) @ (positive @ (^[Y1 : mu]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ (Y0 @ Y1))))))))))),
% 0.68/0.33 inference(definition_unfolding,[],[f109,f106,f99,f94,f91,f91])).
% 0.68/0.33 thf(f124,plain,(
% 0.68/0.33 ($true = (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : (mu > $i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: (Y0 @ Y2 @ Y1)))))) @ (^[Y0 : mu > $i > $o]: ((^[Y1 : (mu > $i > $o) > $i > $o]: ((^[Y2 : $i]: (!! @ (mu > $i > $o) @ (^[Y3 : mu > $i > $o]: (Y1 @ Y3 @ Y2)))))) @ (^[Y1 : mu > $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) => (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) & (Y3 @ Y4))))))) @ (positive @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (Y2 @ Y4)))))) @ ((^[Y2 : mu > $i > $o]: ((^[Y3 : $i]: (!! @ mu @ (^[Y4 : mu]: (Y2 @ Y4 @ Y3)))))) @ (^[Y2 : mu]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: ((Y3 @ Y5) => (Y4 @ Y5))))))) @ (Y0 @ Y2) @ (Y1 @ Y2)))))) @ (positive @ Y1)))))))))),
% 0.68/0.33 inference(definition_unfolding,[],[f110,f106,f99,f99,f94,f93,f104,f98,f94])).
% 0.68/0.33 thf(f126,plain,(
% 0.68/0.33 ($true = (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : (mu > $i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: (Y0 @ Y2 @ Y1)))))) @ (^[Y0 : mu > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: ((Y1 @ Y3) => (Y2 @ Y3))))))) @ (positive @ Y0) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (Y1 @ Y3)))))) @ (positive @ Y0))))))))),
% 0.68/0.33 inference(definition_unfolding,[],[f113,f106,f99,f94,f104])).
% 0.68/0.33 thf(f127,plain,(
% 0.68/0.33 ($true = (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ (positive @ (^[Y0 : mu]: ((^[Y1 : (mu > $i > $o) > $i > $o]: ((^[Y2 : $i]: (!! @ (mu > $i > $o) @ (^[Y3 : mu > $i > $o]: (Y1 @ Y3 @ Y2)))))) @ (^[Y1 : mu > $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) => (Y3 @ Y4))))))) @ ((^[Y2 : mu > $i > $o]: ((^[Y3 : mu]: ((^[Y4 : (mu > $i > $o) > $i > $o]: ((^[Y5 : $i]: (!! @ (mu > $i > $o) @ (^[Y6 : mu > $i > $o]: (Y4 @ Y6 @ Y5)))))) @ (^[Y4 : mu > $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i]: ((Y5 @ Y7) => (Y6 @ Y7))))))) @ (Y4 @ Y3) @ ((^[Y5 : $i > $o]: ((^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (Y5 @ Y7)))))) @ ((^[Y5 : mu > $i > $o]: ((^[Y6 : $i]: (!! @ mu @ (^[Y7 : mu]: (Y5 @ Y7 @ Y6)))))) @ (^[Y5 : mu]: ((^[Y6 : $i > $o]: ((^[Y7 : $i > $o]: ((^[Y8 : $i]: ((Y6 @ Y8) => (Y7 @ Y8))))))) @ (Y2 @ Y5) @ (Y4 @ Y5))))))))))) @ Y1 @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (Y2 @ Y4)))))) @ ((^[Y2 : mu > $i > $o]: ((^[Y3 : $i]: (?? @ mu @ (^[Y4 : mu]: (Y2 @ Y4 @ Y3)))))) @ (^[Y2 : mu]: (Y1 @ Y2))))))))))))),
% 0.68/0.33 inference(definition_unfolding,[],[f116,f106,f121])).
% 0.68/0.33 thf(f128,plain,(
% 0.68/0.33 ($true = ((!! @ $i @ (positive @ (^[Y0 : mu]: ((^[Y1 : $i]: (!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: ((!! @ (mu > $i > $o) @ (^[Y3 : mu > $i > $o]: ((Y3 @ Y0 @ Y1) => (!! @ $i @ (^[Y4 : $i]: (!! @ mu @ (^[Y5 : mu]: ((Y2 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4))))))))) => (!! @ $i @ (^[Y3 : $i]: (?? @ mu @ (^[Y4 : mu]: (Y2 @ Y4 @ Y3)))))))))))))))),
% 0.68/0.33 inference(beta-eta_normalization,[],[f127])).
% 0.68/0.33 thf(f129,plain,(
% 0.68/0.33 ( ! [X1 : $i] : (($true = ((positive @ (^[Y0 : mu]: ((^[Y1 : $i]: (!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: ((!! @ (mu > $i > $o) @ (^[Y3 : mu > $i > $o]: ((Y3 @ Y0 @ Y1) => (!! @ $i @ (^[Y4 : $i]: (!! @ mu @ (^[Y5 : mu]: ((Y2 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4))))))))) => (!! @ $i @ (^[Y3 : $i]: (?? @ mu @ (^[Y4 : mu]: (Y2 @ Y4 @ Y3))))))))))) @ X1)))) )),
% 0.68/0.33 inference(pi_proxy_clausification,[],[f128])).
% 0.68/0.33 thf(f130,plain,(
% 0.68/0.33 ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ (mu > $i > $o) @ (^[Y1 : mu > $i > $o]: ((positive @ Y1 @ Y0) => (!! @ $i @ (positive @ Y1)))))))))),
% 0.68/0.33 inference(beta-eta_normalization,[],[f126])).
% 0.68/0.33 thf(f131,plain,(
% 0.68/0.33 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ (mu > $i > $o) @ (^[Y1 : mu > $i > $o]: ((positive @ Y1 @ Y0) => (!! @ $i @ (positive @ Y1)))))) @ X1)))) )),
% 0.68/0.33 inference(pi_proxy_clausification,[],[f130])).
% 0.68/0.33 thf(f132,plain,(
% 0.68/0.33 ( ! [X1 : $i] : (($true = ((!! @ (mu > $i > $o) @ (^[Y0 : mu > $i > $o]: ((positive @ Y0 @ X1) => (!! @ $i @ (positive @ Y0)))))))) )),
% 0.68/0.33 inference(beta-eta_normalization,[],[f131])).
% 0.68/0.33 thf(f133,plain,(
% 0.68/0.33 ( ! [X2 : (mu > $i > $o),X1 : $i] : (($true = (((^[Y0 : mu > $i > $o]: ((positive @ Y0 @ X1) => (!! @ $i @ (positive @ Y0)))) @ X2)))) )),
% 0.68/0.33 inference(pi_proxy_clausification,[],[f132])).
% 0.68/0.33 thf(f134,plain,(
% 0.68/0.33 ( ! [X2 : (mu > $i > $o),X1 : $i] : (($true = (((positive @ X2 @ X1) => (!! @ $i @ (positive @ X2)))))) )),
% 0.68/0.33 inference(beta-eta_normalization,[],[f133])).
% 0.68/0.33 thf(f135,plain,(
% 0.68/0.33 ( ! [X2 : (mu > $i > $o),X1 : $i] : (($false = ((positive @ X2 @ X1))) | ($true = ((!! @ $i @ (positive @ X2))))) )),
% 0.68/0.33 inference(imp_proxy_clausification,[],[f134])).
% 0.68/0.33 thf(f136,plain,(
% 0.68/0.33 ( ! [X2 : (mu > $i > $o),X3 : $i,X1 : $i] : (($false = ((positive @ X2 @ X1))) | ($true = ((positive @ X2 @ X3)))) )),
% 0.68/0.33 inference(pi_proxy_clausification,[],[f135])).
% 0.68/0.33 thf(f139,plain,(
% 0.68/0.33 ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ (mu > $i > $o) @ (^[Y1 : mu > $i > $o]: (!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: (((positive @ Y1 @ Y0) & (!! @ $i @ (^[Y3 : $i]: (!! @ mu @ (^[Y4 : mu]: ((Y1 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (positive @ Y2 @ Y0))))))))))),
% 0.68/0.33 inference(beta-eta_normalization,[],[f124])).
% 0.68/0.33 thf(f140,plain,(
% 0.68/0.33 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ (mu > $i > $o) @ (^[Y1 : mu > $i > $o]: (!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: (((positive @ Y1 @ Y0) & (!! @ $i @ (^[Y3 : $i]: (!! @ mu @ (^[Y4 : mu]: ((Y1 @ Y4 @ Y3) => (Y2 @ Y4 @ Y3))))))) => (positive @ Y2 @ Y0))))))) @ X1)))) )),
% 0.68/0.33 inference(pi_proxy_clausification,[],[f139])).
% 0.68/0.33 thf(f141,plain,(
% 0.68/0.33 ( ! [X1 : $i] : (($true = ((!! @ (mu > $i > $o) @ (^[Y0 : mu > $i > $o]: (!! @ (mu > $i > $o) @ (^[Y1 : mu > $i > $o]: (((positive @ Y0 @ X1) & (!! @ $i @ (^[Y2 : $i]: (!! @ mu @ (^[Y3 : mu]: ((Y0 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))) => (positive @ Y1 @ X1))))))))) )),
% 0.68/0.33 inference(beta-eta_normalization,[],[f140])).
% 0.68/0.33 thf(f142,plain,(
% 0.68/0.33 ( ! [X2 : (mu > $i > $o),X1 : $i] : (($true = (((^[Y0 : mu > $i > $o]: (!! @ (mu > $i > $o) @ (^[Y1 : mu > $i > $o]: (((positive @ Y0 @ X1) & (!! @ $i @ (^[Y2 : $i]: (!! @ mu @ (^[Y3 : mu]: ((Y0 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))) => (positive @ Y1 @ X1))))) @ X2)))) )),
% 0.68/0.33 inference(pi_proxy_clausification,[],[f141])).
% 0.68/0.33 thf(f143,plain,(
% 0.68/0.33 ( ! [X2 : (mu > $i > $o),X1 : $i] : (($true = ((!! @ (mu > $i > $o) @ (^[Y0 : mu > $i > $o]: (((positive @ X2 @ X1) & (!! @ $i @ (^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: ((X2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (positive @ Y0 @ X1))))))) )),
% 0.68/0.33 inference(beta-eta_normalization,[],[f142])).
% 0.68/0.33 thf(f144,plain,(
% 0.68/0.33 ( ! [X2 : (mu > $i > $o),X3 : (mu > $i > $o),X1 : $i] : (($true = (((^[Y0 : mu > $i > $o]: (((positive @ X2 @ X1) & (!! @ $i @ (^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: ((X2 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) => (positive @ Y0 @ X1))) @ X3)))) )),
% 0.68/0.33 inference(pi_proxy_clausification,[],[f143])).
% 0.68/0.33 thf(f145,plain,(
% 0.68/0.33 ( ! [X2 : (mu > $i > $o),X3 : (mu > $i > $o),X1 : $i] : (($true = ((((positive @ X2 @ X1) & (!! @ $i @ (^[Y0 : $i]: (!! @ mu @ (^[Y1 : mu]: ((X2 @ Y1 @ Y0) => (X3 @ Y1 @ Y0))))))) => (positive @ X3 @ X1))))) )),
% 0.68/0.33 inference(beta-eta_normalization,[],[f144])).
% 0.68/0.33 thf(f146,plain,(
% 0.68/0.33 ( ! [X2 : (mu > $i > $o),X3 : (mu > $i > $o),X1 : $i] : (($false = (((positive @ X2 @ X1) & (!! @ $i @ (^[Y0 : $i]: (!! @ mu @ (^[Y1 : mu]: ((X2 @ Y1 @ Y0) => (X3 @ Y1 @ Y0))))))))) | ($true = ((positive @ X3 @ X1)))) )),
% 0.68/0.33 inference(imp_proxy_clausification,[],[f145])).
% 0.68/0.33 thf(f147,plain,(
% 0.68/0.33 ( ! [X2 : (mu > $i > $o),X3 : (mu > $i > $o),X1 : $i] : (($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ mu @ (^[Y1 : mu]: ((X2 @ Y1 @ Y0) => (X3 @ Y1 @ Y0)))))))) | ($true = ((positive @ X3 @ X1))) | ($false = ((positive @ X2 @ X1)))) )),
% 0.68/0.33 inference(and_proxy_clausification,[],[f146])).
% 0.68/0.33 thf(f148,plain,(
% 0.68/0.33 ( ! [X2 : (mu > $i > $o),X3 : (mu > $i > $o),X1 : $i] : (($false = (((^[Y0 : $i]: (!! @ mu @ (^[Y1 : mu]: ((X2 @ Y1 @ Y0) => (X3 @ Y1 @ Y0))))) @ (sK0 @ X3 @ X2)))) | ($true = ((positive @ X3 @ X1))) | ($false = ((positive @ X2 @ X1)))) )),
% 0.68/0.33 inference(sigma_proxy_clausification,[],[f147])).
% 0.68/0.33 thf(f149,plain,(
% 0.68/0.33 ( ! [X2 : (mu > $i > $o),X3 : (mu > $i > $o),X1 : $i] : (($false = ((!! @ mu @ (^[Y0 : mu]: ((X2 @ Y0 @ (sK0 @ X3 @ X2)) => (X3 @ Y0 @ (sK0 @ X3 @ X2))))))) | ($true = ((positive @ X3 @ X1))) | ($false = ((positive @ X2 @ X1)))) )),
% 0.68/0.33 inference(beta-eta_normalization,[],[f148])).
% 0.68/0.33 thf(f150,plain,(
% 0.68/0.33 ( ! [X2 : (mu > $i > $o),X3 : (mu > $i > $o),X1 : $i] : (($false = (((^[Y0 : mu]: ((X2 @ Y0 @ (sK0 @ X3 @ X2)) => (X3 @ Y0 @ (sK0 @ X3 @ X2)))) @ (sK1 @ X3 @ X2)))) | ($true = ((positive @ X3 @ X1))) | ($false = ((positive @ X2 @ X1)))) )),
% 0.68/0.33 inference(sigma_proxy_clausification,[],[f149])).
% 0.68/0.33 thf(f151,plain,(
% 0.68/0.33 ( ! [X2 : (mu > $i > $o),X3 : (mu > $i > $o),X1 : $i] : (($false = (((X2 @ (sK1 @ X3 @ X2) @ (sK0 @ X3 @ X2)) => (X3 @ (sK1 @ X3 @ X2) @ (sK0 @ X3 @ X2))))) | ($true = ((positive @ X3 @ X1))) | ($false = ((positive @ X2 @ X1)))) )),
% 0.68/0.33 inference(beta-eta_normalization,[],[f150])).
% 0.68/0.33 thf(f152,plain,(
% 0.68/0.33 ( ! [X2 : (mu > $i > $o),X3 : (mu > $i > $o),X1 : $i] : (($false = ((X3 @ (sK1 @ X3 @ X2) @ (sK0 @ X3 @ X2)))) | ($true = ((positive @ X3 @ X1))) | ($false = ((positive @ X2 @ X1)))) )),
% 0.68/0.33 inference(imp_proxy_clausification,[],[f151])).
% 0.68/0.33 thf(f154,plain,(
% 0.68/0.33 ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ (mu > $i > $o) @ (^[Y1 : mu > $i > $o]: ((~ (positive @ Y1 @ Y0)) => (positive @ (^[Y2 : mu]: ((^[Y3 : $i]: (~ (Y1 @ Y2 @ Y3))))) @ Y0))))))))),
% 0.68/0.33 inference(beta-eta_normalization,[],[f123])).
% 0.68/0.33 thf(f155,plain,(
% 0.68/0.33 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ (mu > $i > $o) @ (^[Y1 : mu > $i > $o]: ((~ (positive @ Y1 @ Y0)) => (positive @ (^[Y2 : mu]: ((^[Y3 : $i]: (~ (Y1 @ Y2 @ Y3))))) @ Y0))))) @ X1)))) )),
% 0.68/0.33 inference(pi_proxy_clausification,[],[f154])).
% 0.68/0.33 thf(f156,plain,(
% 0.68/0.33 ( ! [X1 : $i] : (($true = ((!! @ (mu > $i > $o) @ (^[Y0 : mu > $i > $o]: ((~ (positive @ Y0 @ X1)) => (positive @ (^[Y1 : mu]: ((^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2))))) @ X1))))))) )),
% 0.68/0.33 inference(beta-eta_normalization,[],[f155])).
% 0.68/0.33 thf(f157,plain,(
% 0.68/0.33 ( ! [X2 : (mu > $i > $o),X1 : $i] : (($true = (((^[Y0 : mu > $i > $o]: ((~ (positive @ Y0 @ X1)) => (positive @ (^[Y1 : mu]: ((^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2))))) @ X1))) @ X2)))) )),
% 0.68/0.33 inference(pi_proxy_clausification,[],[f156])).
% 0.68/0.33 thf(f158,plain,(
% 0.68/0.33 ( ! [X2 : (mu > $i > $o),X1 : $i] : (($true = (((~ (positive @ X2 @ X1)) => (positive @ (^[Y0 : mu]: ((^[Y1 : $i]: (~ (X2 @ Y0 @ Y1))))) @ X1))))) )),
% 0.68/0.33 inference(beta-eta_normalization,[],[f157])).
% 0.68/0.33 thf(f159,plain,(
% 0.68/0.33 ( ! [X2 : (mu > $i > $o),X1 : $i] : (($false = ((~ (positive @ X2 @ X1)))) | ($true = ((positive @ (^[Y0 : mu]: ((^[Y1 : $i]: (~ (X2 @ Y0 @ Y1))))) @ X1)))) )),
% 0.68/0.33 inference(imp_proxy_clausification,[],[f158])).
% 0.68/0.33 thf(f160,plain,(
% 0.68/0.33 ( ! [X2 : (mu > $i > $o),X1 : $i] : (($true = ((positive @ (^[Y0 : mu]: ((^[Y1 : $i]: (~ (X2 @ Y0 @ Y1))))) @ X1))) | ($true = ((positive @ X2 @ X1)))) )),
% 0.68/0.33 inference(not_proxy_clausification,[],[f159])).
% 0.68/0.33 thf(f161,plain,(
% 0.68/0.33 ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ (mu > $i > $o) @ (^[Y1 : mu > $i > $o]: ((positive @ (^[Y2 : mu]: ((^[Y3 : $i]: (~ (Y1 @ Y2 @ Y3))))) @ Y0) => (~ (positive @ Y1 @ Y0)))))))))),
% 0.68/0.33 inference(beta-eta_normalization,[],[f122])).
% 0.68/0.33 thf(f162,plain,(
% 0.68/0.33 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ (mu > $i > $o) @ (^[Y1 : mu > $i > $o]: ((positive @ (^[Y2 : mu]: ((^[Y3 : $i]: (~ (Y1 @ Y2 @ Y3))))) @ Y0) => (~ (positive @ Y1 @ Y0)))))) @ X1)))) )),
% 0.68/0.33 inference(pi_proxy_clausification,[],[f161])).
% 0.68/0.33 thf(f163,plain,(
% 0.68/0.33 ( ! [X1 : $i] : (($true = ((!! @ (mu > $i > $o) @ (^[Y0 : mu > $i > $o]: ((positive @ (^[Y1 : mu]: ((^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2))))) @ X1) => (~ (positive @ Y0 @ X1)))))))) )),
% 0.68/0.33 inference(beta-eta_normalization,[],[f162])).
% 0.68/0.33 thf(f164,plain,(
% 0.68/0.33 ( ! [X2 : (mu > $i > $o),X1 : $i] : (($true = (((^[Y0 : mu > $i > $o]: ((positive @ (^[Y1 : mu]: ((^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2))))) @ X1) => (~ (positive @ Y0 @ X1)))) @ X2)))) )),
% 0.68/0.33 inference(pi_proxy_clausification,[],[f163])).
% 0.68/0.33 thf(f165,plain,(
% 0.68/0.33 ( ! [X2 : (mu > $i > $o),X1 : $i] : (($true = (((positive @ (^[Y0 : mu]: ((^[Y1 : $i]: (~ (X2 @ Y0 @ Y1))))) @ X1) => (~ (positive @ X2 @ X1)))))) )),
% 0.68/0.33 inference(beta-eta_normalization,[],[f164])).
% 0.68/0.33 thf(f166,plain,(
% 0.68/0.33 ( ! [X2 : (mu > $i > $o),X1 : $i] : (($false = ((positive @ (^[Y0 : mu]: ((^[Y1 : $i]: (~ (X2 @ Y0 @ Y1))))) @ X1))) | ($true = ((~ (positive @ X2 @ X1))))) )),
% 0.68/0.33 inference(imp_proxy_clausification,[],[f165])).
% 0.68/0.33 thf(f167,plain,(
% 0.68/0.33 ( ! [X2 : (mu > $i > $o),X1 : $i] : (($false = ((positive @ (^[Y0 : mu]: ((^[Y1 : $i]: (~ (X2 @ Y0 @ Y1))))) @ X1))) | ($false = ((positive @ X2 @ X1)))) )),
% 0.68/0.33 inference(not_proxy_clausification,[],[f166])).
% 0.68/0.33 thf(f184,plain,(
% 0.68/0.33 ( ! [X2 : $i,X0 : (mu > $i > $o),X1 : $i] : (($true = $false) | ($true = ((positive @ (^[Y0 : mu]: ((^[Y1 : $i]: (~ (X0 @ Y0 @ Y1))))) @ X2))) | ($true = ((positive @ X0 @ X1)))) )),
% 0.68/0.33 inference(constrained_superposition,[],[f136,f160])).
% 0.68/0.33 thf(f185,plain,(
% 0.68/0.33 ( ! [X2 : $i,X0 : (mu > $i > $o),X1 : $i] : (($true = ((positive @ (^[Y0 : mu]: ((^[Y1 : $i]: (~ (X0 @ Y0 @ Y1))))) @ X2))) | ($true = ((positive @ X0 @ X1)))) )),
% 0.68/0.33 inference(trivial_inequality_removal,[],[f184])).
% 0.68/0.33 thf(f190,plain,(
% 0.68/0.33 ( ! [X2 : $i,X0 : (mu > $i > $o),X1 : $i] : (($true = $false) | ($false = ((positive @ (^[Y0 : mu]: ((^[Y1 : $i]: (~ (X0 @ Y0 @ Y1))))) @ X2))) | ($false = ((positive @ X0 @ X1)))) )),
% 0.68/0.33 inference(constrained_superposition,[],[f136,f167])).
% 0.68/0.33 thf(f191,plain,(
% 0.68/0.33 ( ! [X2 : (mu > $i > $o),X0 : (mu > $i > $o),X1 : $i] : (($true = $false) | ($true = ((positive @ X0 @ X1))) | ($false = ((positive @ X2 @ X1))) | (X0 != X2)) )),
% 0.68/0.33 inference(constrained_superposition,[],[f160,f167])).
% 0.68/0.33 thf(f192,plain,(
% 0.68/0.33 ( ! [X2 : (mu > $i > $o),X0 : (mu > $i > $o),X1 : $i] : (($true = ((positive @ X0 @ X1))) | ($false = ((positive @ X2 @ X1))) | (X0 != X2)) )),
% 0.68/0.33 inference(trivial_inequality_removal,[],[f191])).
% 0.68/0.33 thf(f193,plain,(
% 0.68/0.33 ( ! [X2 : $i,X0 : (mu > $i > $o),X1 : $i] : (($false = ((positive @ (^[Y0 : mu]: ((^[Y1 : $i]: (~ (X0 @ Y0 @ Y1))))) @ X2))) | ($false = ((positive @ X0 @ X1)))) )),
% 0.68/0.33 inference(trivial_inequality_removal,[],[f190])).
% 0.68/0.33 thf(f1350,plain,(
% 0.68/0.33 ( ! [X0 : (mu > $i > $o),X1 : $i] : (($false != $false) | ($true = ((positive @ (^[Y0 : mu]: ((^[Y1 : $i]: ($true)))) @ X1))) | ($false = ((positive @ X0 @ X1)))) )),
% 0.68/0.33 inference(constrained_superposition,[],[f117,f152])).
% 0.68/0.33 thf(f1487,plain,(
% 0.68/0.33 ( ! [X0 : (mu > $i > $o),X1 : $i] : (($true = ((positive @ (^[Y0 : mu]: ((^[Y1 : $i]: ($true)))) @ X1))) | ($false = ((positive @ X0 @ X1)))) )),
% 0.68/0.33 inference(trivial_inequality_removal,[],[f1350])).
% 0.68/0.33 thf(f1575,plain,(
% 0.68/0.33 ( ! [X2 : $i,X0 : $i,X1 : (mu > $i > $o)] : (($true = $false) | ($false = ((positive @ X1 @ X0))) | ($false = ((positive @ (^[Y0 : mu]: ((^[Y1 : $i]: (~ ((^[Y2 : mu]: ((^[Y3 : $i]: ($true)))) @ Y0 @ Y1))))) @ X2)))) )),
% 0.68/0.33 inference(constrained_superposition,[],[f1487,f193])).
% 0.68/0.33 thf(f1706,plain,(
% 0.68/0.33 ( ! [X2 : $i,X0 : $i,X1 : (mu > $i > $o)] : (($false = ((positive @ X1 @ X0))) | ($false = ((positive @ (^[Y0 : mu]: ((^[Y1 : $i]: (~ ((^[Y2 : mu]: ((^[Y3 : $i]: ($true)))) @ Y0 @ Y1))))) @ X2)))) )),
% 0.68/0.33 inference(trivial_inequality_removal,[],[f1575])).
% 0.68/0.33 thf(f1707,plain,(
% 0.68/0.33 ( ! [X2 : $i,X0 : $i,X1 : (mu > $i > $o)] : (($false = ((positive @ X1 @ X0))) | ($false = ((positive @ (^[Y0 : mu]: ((^[Y1 : $i]: (~ $true)))) @ X2)))) )),
% 0.68/0.33 inference(beta-eta_normalization,[],[f1706])).
% 0.68/0.33 thf(f1708,plain,(
% 0.68/0.33 ( ! [X2 : $i,X0 : $i,X1 : (mu > $i > $o)] : (($false = ((positive @ X1 @ X0))) | ($false = ((positive @ (^[Y0 : mu]: ((^[Y1 : $i]: ($false)))) @ X2)))) )),
% 0.68/0.33 inference(boolean_simplification,[],[f1707])).
% 0.68/0.33 thf(f1760,definition,(
% 0.68/0.33 spl8_15 <=> ! [X2 : $i,X0 : (mu > $i > $o)] : ($false = ((positive @ X0 @ X2)))),
% 0.68/0.33 introduced(definition,[new_symbols(definition,[spl8_15])],[avatar_definition])).
% 0.68/0.33 thf(f1761,plain,(
% 0.68/0.33 ( ! [X2 : $i,X0 : (mu > $i > $o)] : (($false = ((positive @ X0 @ X2)))) ) | ~spl8_15),
% 0.68/0.33 inference(avatar_component_clause,[],[f1760])).
% 0.68/0.33 thf(f1788,definition,(
% 0.68/0.33 spl8_22 <=> ! [X1 : $i] : ($false = ((positive @ (^[Y0 : mu]: ((^[Y1 : $i]: ($false)))) @ X1)))),
% 0.68/0.33 introduced(definition,[new_symbols(definition,[spl8_22])],[avatar_definition])).
% 0.68/0.33 thf(f1789,plain,(
% 0.68/0.33 ( ! [X1 : $i] : (($false = ((positive @ (^[Y0 : mu]: ((^[Y1 : $i]: ($false)))) @ X1)))) ) | ~spl8_22),
% 0.68/0.33 inference(avatar_component_clause,[],[f1788])).
% 0.68/0.33 thf(f1810,plain,(
% 0.68/0.33 spl8_22 | spl8_15),
% 0.68/0.33 inference(avatar_split_clause,[],[f1708,f1760,f1788])).
% 0.68/0.33 thf(f1813,plain,(
% 0.68/0.33 ( ! [X2 : $i,X0 : (mu > $i > $o)] : (($true = $false) | ($true = ((positive @ (^[Y0 : mu]: ((^[Y1 : $i]: (~ (X0 @ Y0 @ Y1))))) @ X2)))) ) | ~spl8_15),
% 0.68/0.33 inference(constrained_superposition,[],[f1761,f185])).
% 0.68/0.33 thf(f1852,plain,(
% 0.68/0.33 ( ! [X2 : $i,X0 : (mu > $i > $o)] : (($true = ((positive @ (^[Y0 : mu]: ((^[Y1 : $i]: (~ (X0 @ Y0 @ Y1))))) @ X2)))) ) | ~spl8_15),
% 0.68/0.33 inference(trivial_inequality_removal,[],[f1813])).
% 0.68/0.33 thf(f1901,plain,(
% 0.68/0.33 ($true = $false) | ~spl8_15),
% 0.68/0.33 inference(forward_demodulation,[],[f1852,f1761])).
% 0.68/0.33 thf(f1902,plain,(
% 0.68/0.33 $false | ~spl8_15),
% 0.68/0.33 inference(trivial_inequality_removal,[],[f1901])).
% 0.68/0.33 thf(f1903,plain,(
% 0.68/0.33 ~spl8_15),
% 0.68/0.33 inference(avatar_contradiction_clause,[],[f1902])).
% 0.68/0.33 thf(f2046,plain,(
% 0.68/0.33 ( ! [X0 : $i,X1 : (mu > $i > $o)] : (($true = $false) | ($false = ((positive @ X1 @ X0))) | ((^[Y0 : mu]: ((^[Y1 : $i]: ($false)))) != X1)) ) | ~spl8_22),
% 0.68/0.33 inference(constrained_superposition,[],[f1789,f192])).
% 0.68/0.33 thf(f2073,plain,(
% 0.68/0.33 ( ! [X0 : $i,X1 : (mu > $i > $o)] : (((^[Y0 : mu]: ((^[Y1 : $i]: ($false)))) != X1) | ($false = ((positive @ X1 @ X0)))) ) | ~spl8_22),
% 0.68/0.33 inference(trivial_inequality_removal,[],[f2046])).
% 0.68/0.33 thf(f2093,plain,(
% 0.68/0.33 ( ! [X0 : $i,X1 : (mu > $i > $o)] : (((((^[Y0 : mu]: ((^[Y1 : $i]: ($false)))) @ (sK12 @ X1))) != ((X1 @ (sK12 @ X1)))) | ($false = ((positive @ X1 @ X0)))) ) | ~spl8_22),
% 0.68/0.33 inference(negative_extensionality,[],[f2073])).
% 0.68/0.33 thf(f2095,plain,(
% 0.68/0.33 ( ! [X0 : $i,X1 : (mu > $i > $o)] : (((^[Y0 : $i]: ($false)) != ((X1 @ (sK12 @ X1)))) | ($false = ((positive @ X1 @ X0)))) ) | ~spl8_22),
% 0.68/0.33 inference(beta-eta_normalization,[],[f2093])).
% 0.68/0.33 thf(f2096,plain,(
% 0.68/0.33 ( ! [X0 : $i,X1 : (mu > $i > $o)] : (((((^[Y0 : $i]: ($false)) @ (sK13 @ X1))) != ((X1 @ (sK12 @ X1) @ (sK13 @ X1)))) | ($false = ((positive @ X1 @ X0)))) ) | ~spl8_22),
% 0.68/0.33 inference(negative_extensionality,[],[f2095])).
% 0.68/0.33 thf(f2098,plain,(
% 0.68/0.33 ( ! [X0 : $i,X1 : (mu > $i > $o)] : (($true = (((^[Y0 : $i]: ($false)) @ (sK13 @ X1)))) | ($false = ((positive @ X1 @ X0))) | ($true = ((X1 @ (sK12 @ X1) @ (sK13 @ X1))))) ) | ~spl8_22),
% 0.68/0.33 inference(xor_proxy_clausification,[],[f2096])).
% 0.68/0.33 thf(f2101,plain,(
% 0.68/0.33 ( ! [X0 : $i,X1 : (mu > $i > $o)] : (($true = $false) | ($false = ((positive @ X1 @ X0))) | ($true = ((X1 @ (sK12 @ X1) @ (sK13 @ X1))))) ) | ~spl8_22),
% 0.68/0.33 inference(beta-eta_normalization,[],[f2098])).
% 0.68/0.33 thf(f2102,plain,(
% 0.68/0.33 ( ! [X0 : $i,X1 : (mu > $i > $o)] : (($false = ((positive @ X1 @ X0))) | ($true = ((X1 @ (sK12 @ X1) @ (sK13 @ X1))))) ) | ~spl8_22),
% 0.68/0.33 inference(trivial_inequality_removal,[],[f2101])).
% 0.68/0.33 thf(f2496,plain,(
% 0.68/0.33 ($true = $false) | ($true = (((^[Y0 : mu]: ((^[Y1 : $i]: (!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: ((!! @ (mu > $i > $o) @ (^[Y3 : mu > $i > $o]: ((Y3 @ Y0 @ Y1) => (!! @ $i @ (^[Y4 : $i]: (!! @ mu @ (^[Y5 : mu]: ((Y2 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4))))))))) => (!! @ $i @ (^[Y3 : $i]: (?? @ mu @ (^[Y4 : mu]: (Y2 @ Y4 @ Y3))))))))))) @ (sK12 @ (^[Y0 : mu]: ((^[Y1 : $i]: (!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: ((!! @ (mu > $i > $o) @ (^[Y3 : mu > $i > $o]: ((Y3 @ Y0 @ Y1) => (!! @ $i @ (^[Y4 : $i]: (!! @ mu @ (^[Y5 : mu]: ((Y2 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4))))))))) => (!! @ $i @ (^[Y3 : $i]: (?? @ mu @ (^[Y4 : mu]: (Y2 @ Y4 @ Y3)))))))))))) @ (sK13 @ (^[Y0 : mu]: ((^[Y1 : $i]: (!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: ((!! @ (mu > $i > $o) @ (^[Y3 : mu > $i > $o]: ((Y3 @ Y0 @ Y1) => (!! @ $i @ (^[Y4 : $i]: (!! @ mu @ (^[Y5 : mu]: ((Y2 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4))))))))) => (!! @ $i @ (^[Y3 : $i]: (?? @ mu @ (^[Y4 : mu]: (Y2 @ Y4 @ Y3))))))))))))))) | ~spl8_22),
% 0.68/0.33 inference(constrained_superposition,[],[f129,f2102])).
% 0.68/0.33 thf(f2531,plain,(
% 0.68/0.33 ($true = (((^[Y0 : mu]: ((^[Y1 : $i]: (!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: ((!! @ (mu > $i > $o) @ (^[Y3 : mu > $i > $o]: ((Y3 @ Y0 @ Y1) => (!! @ $i @ (^[Y4 : $i]: (!! @ mu @ (^[Y5 : mu]: ((Y2 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4))))))))) => (!! @ $i @ (^[Y3 : $i]: (?? @ mu @ (^[Y4 : mu]: (Y2 @ Y4 @ Y3))))))))))) @ (sK12 @ (^[Y0 : mu]: ((^[Y1 : $i]: (!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: ((!! @ (mu > $i > $o) @ (^[Y3 : mu > $i > $o]: ((Y3 @ Y0 @ Y1) => (!! @ $i @ (^[Y4 : $i]: (!! @ mu @ (^[Y5 : mu]: ((Y2 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4))))))))) => (!! @ $i @ (^[Y3 : $i]: (?? @ mu @ (^[Y4 : mu]: (Y2 @ Y4 @ Y3)))))))))))) @ (sK13 @ (^[Y0 : mu]: ((^[Y1 : $i]: (!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: ((!! @ (mu > $i > $o) @ (^[Y3 : mu > $i > $o]: ((Y3 @ Y0 @ Y1) => (!! @ $i @ (^[Y4 : $i]: (!! @ mu @ (^[Y5 : mu]: ((Y2 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4))))))))) => (!! @ $i @ (^[Y3 : $i]: (?? @ mu @ (^[Y4 : mu]: (Y2 @ Y4 @ Y3))))))))))))))) | ~spl8_22),
% 0.68/0.33 inference(trivial_inequality_removal,[],[f2496])).
% 0.68/0.33 thf(f2532,plain,(
% 0.68/0.33 ($true = ((!! @ (mu > $i > $o) @ (^[Y0 : mu > $i > $o]: ((!! @ (mu > $i > $o) @ (^[Y1 : mu > $i > $o]: ((Y1 @ (sK12 @ (^[Y2 : mu]: ((^[Y3 : $i]: (!! @ (mu > $i > $o) @ (^[Y4 : mu > $i > $o]: ((!! @ (mu > $i > $o) @ (^[Y5 : mu > $i > $o]: ((Y5 @ Y2 @ Y3) => (!! @ $i @ (^[Y6 : $i]: (!! @ mu @ (^[Y7 : mu]: ((Y4 @ Y7 @ Y6) => (Y5 @ Y7 @ Y6))))))))) => (!! @ $i @ (^[Y5 : $i]: (?? @ mu @ (^[Y6 : mu]: (Y4 @ Y6 @ Y5)))))))))))) @ (sK13 @ (^[Y2 : mu]: ((^[Y3 : $i]: (!! @ (mu > $i > $o) @ (^[Y4 : mu > $i > $o]: ((!! @ (mu > $i > $o) @ (^[Y5 : mu > $i > $o]: ((Y5 @ Y2 @ Y3) => (!! @ $i @ (^[Y6 : $i]: (!! @ mu @ (^[Y7 : mu]: ((Y4 @ Y7 @ Y6) => (Y5 @ Y7 @ Y6))))))))) => (!! @ $i @ (^[Y5 : $i]: (?? @ mu @ (^[Y6 : mu]: (Y4 @ Y6 @ Y5))))))))))))) => (!! @ $i @ (^[Y2 : $i]: (!! @ mu @ (^[Y3 : mu]: ((Y0 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))))) => (!! @ $i @ (^[Y1 : $i]: (?? @ mu @ (^[Y2 : mu]: (Y0 @ Y2 @ Y1)))))))))) | ~spl8_22),
% 0.68/0.33 inference(beta-eta_normalization,[],[f2531])).
% 0.68/0.33 thf(f2533,plain,(
% 0.68/0.33 ( ! [X1 : (mu > $i > $o)] : (($true = (((^[Y0 : mu > $i > $o]: ((!! @ (mu > $i > $o) @ (^[Y1 : mu > $i > $o]: ((Y1 @ (sK12 @ (^[Y2 : mu]: ((^[Y3 : $i]: (!! @ (mu > $i > $o) @ (^[Y4 : mu > $i > $o]: ((!! @ (mu > $i > $o) @ (^[Y5 : mu > $i > $o]: ((Y5 @ Y2 @ Y3) => (!! @ $i @ (^[Y6 : $i]: (!! @ mu @ (^[Y7 : mu]: ((Y4 @ Y7 @ Y6) => (Y5 @ Y7 @ Y6))))))))) => (!! @ $i @ (^[Y5 : $i]: (?? @ mu @ (^[Y6 : mu]: (Y4 @ Y6 @ Y5)))))))))))) @ (sK13 @ (^[Y2 : mu]: ((^[Y3 : $i]: (!! @ (mu > $i > $o) @ (^[Y4 : mu > $i > $o]: ((!! @ (mu > $i > $o) @ (^[Y5 : mu > $i > $o]: ((Y5 @ Y2 @ Y3) => (!! @ $i @ (^[Y6 : $i]: (!! @ mu @ (^[Y7 : mu]: ((Y4 @ Y7 @ Y6) => (Y5 @ Y7 @ Y6))))))))) => (!! @ $i @ (^[Y5 : $i]: (?? @ mu @ (^[Y6 : mu]: (Y4 @ Y6 @ Y5))))))))))))) => (!! @ $i @ (^[Y2 : $i]: (!! @ mu @ (^[Y3 : mu]: ((Y0 @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))))) => (!! @ $i @ (^[Y1 : $i]: (?? @ mu @ (^[Y2 : mu]: (Y0 @ Y2 @ Y1))))))) @ X1)))) ) | ~spl8_22),
% 0.68/0.33 inference(pi_proxy_clausification,[],[f2532])).
% 0.68/0.33 thf(f2534,plain,(
% 0.68/0.33 ( ! [X1 : (mu > $i > $o)] : (($true = (((!! @ (mu > $i > $o) @ (^[Y0 : mu > $i > $o]: ((Y0 @ (sK12 @ (^[Y1 : mu]: ((^[Y2 : $i]: (!! @ (mu > $i > $o) @ (^[Y3 : mu > $i > $o]: ((!! @ (mu > $i > $o) @ (^[Y4 : mu > $i > $o]: ((Y4 @ Y1 @ Y2) => (!! @ $i @ (^[Y5 : $i]: (!! @ mu @ (^[Y6 : mu]: ((Y3 @ Y6 @ Y5) => (Y4 @ Y6 @ Y5))))))))) => (!! @ $i @ (^[Y4 : $i]: (?? @ mu @ (^[Y5 : mu]: (Y3 @ Y5 @ Y4)))))))))))) @ (sK13 @ (^[Y1 : mu]: ((^[Y2 : $i]: (!! @ (mu > $i > $o) @ (^[Y3 : mu > $i > $o]: ((!! @ (mu > $i > $o) @ (^[Y4 : mu > $i > $o]: ((Y4 @ Y1 @ Y2) => (!! @ $i @ (^[Y5 : $i]: (!! @ mu @ (^[Y6 : mu]: ((Y3 @ Y6 @ Y5) => (Y4 @ Y6 @ Y5))))))))) => (!! @ $i @ (^[Y4 : $i]: (?? @ mu @ (^[Y5 : mu]: (Y3 @ Y5 @ Y4))))))))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: ((X1 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))))) => (!! @ $i @ (^[Y0 : $i]: (?? @ mu @ (^[Y1 : mu]: (X1 @ Y1 @ Y0))))))))) ) | ~spl8_22),
% 0.68/0.33 inference(beta-eta_normalization,[],[f2533])).
% 0.68/0.33 thf(f2535,plain,(
% 0.68/0.33 ( ! [X1 : (mu > $i > $o)] : (($false = ((!! @ (mu > $i > $o) @ (^[Y0 : mu > $i > $o]: ((Y0 @ (sK12 @ (^[Y1 : mu]: ((^[Y2 : $i]: (!! @ (mu > $i > $o) @ (^[Y3 : mu > $i > $o]: ((!! @ (mu > $i > $o) @ (^[Y4 : mu > $i > $o]: ((Y4 @ Y1 @ Y2) => (!! @ $i @ (^[Y5 : $i]: (!! @ mu @ (^[Y6 : mu]: ((Y3 @ Y6 @ Y5) => (Y4 @ Y6 @ Y5))))))))) => (!! @ $i @ (^[Y4 : $i]: (?? @ mu @ (^[Y5 : mu]: (Y3 @ Y5 @ Y4)))))))))))) @ (sK13 @ (^[Y1 : mu]: ((^[Y2 : $i]: (!! @ (mu > $i > $o) @ (^[Y3 : mu > $i > $o]: ((!! @ (mu > $i > $o) @ (^[Y4 : mu > $i > $o]: ((Y4 @ Y1 @ Y2) => (!! @ $i @ (^[Y5 : $i]: (!! @ mu @ (^[Y6 : mu]: ((Y3 @ Y6 @ Y5) => (Y4 @ Y6 @ Y5))))))))) => (!! @ $i @ (^[Y4 : $i]: (?? @ mu @ (^[Y5 : mu]: (Y3 @ Y5 @ Y4))))))))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: ((X1 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))))))) | ($true = ((!! @ $i @ (^[Y0 : $i]: (?? @ mu @ (^[Y1 : mu]: (X1 @ Y1 @ Y0)))))))) ) | ~spl8_22),
% 0.68/0.33 inference(imp_proxy_clausification,[],[f2534])).
% 0.68/0.33 thf(f2536,plain,(
% 0.68/0.33 ( ! [X1 : (mu > $i > $o)] : (($false = (((^[Y0 : mu > $i > $o]: ((Y0 @ (sK12 @ (^[Y1 : mu]: ((^[Y2 : $i]: (!! @ (mu > $i > $o) @ (^[Y3 : mu > $i > $o]: ((!! @ (mu > $i > $o) @ (^[Y4 : mu > $i > $o]: ((Y4 @ Y1 @ Y2) => (!! @ $i @ (^[Y5 : $i]: (!! @ mu @ (^[Y6 : mu]: ((Y3 @ Y6 @ Y5) => (Y4 @ Y6 @ Y5))))))))) => (!! @ $i @ (^[Y4 : $i]: (?? @ mu @ (^[Y5 : mu]: (Y3 @ Y5 @ Y4)))))))))))) @ (sK13 @ (^[Y1 : mu]: ((^[Y2 : $i]: (!! @ (mu > $i > $o) @ (^[Y3 : mu > $i > $o]: ((!! @ (mu > $i > $o) @ (^[Y4 : mu > $i > $o]: ((Y4 @ Y1 @ Y2) => (!! @ $i @ (^[Y5 : $i]: (!! @ mu @ (^[Y6 : mu]: ((Y3 @ Y6 @ Y5) => (Y4 @ Y6 @ Y5))))))))) => (!! @ $i @ (^[Y4 : $i]: (?? @ mu @ (^[Y5 : mu]: (Y3 @ Y5 @ Y4))))))))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: ((X1 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1)))))))) @ (sK16 @ X1)))) | ($true = ((!! @ $i @ (^[Y0 : $i]: (?? @ mu @ (^[Y1 : mu]: (X1 @ Y1 @ Y0)))))))) ) | ~spl8_22),
% 0.68/0.33 inference(sigma_proxy_clausification,[],[f2535])).
% 0.68/0.33 thf(f2537,plain,(
% 0.68/0.33 ( ! [X2 : $i,X1 : (mu > $i > $o)] : (($false = (((^[Y0 : mu > $i > $o]: ((Y0 @ (sK12 @ (^[Y1 : mu]: ((^[Y2 : $i]: (!! @ (mu > $i > $o) @ (^[Y3 : mu > $i > $o]: ((!! @ (mu > $i > $o) @ (^[Y4 : mu > $i > $o]: ((Y4 @ Y1 @ Y2) => (!! @ $i @ (^[Y5 : $i]: (!! @ mu @ (^[Y6 : mu]: ((Y3 @ Y6 @ Y5) => (Y4 @ Y6 @ Y5))))))))) => (!! @ $i @ (^[Y4 : $i]: (?? @ mu @ (^[Y5 : mu]: (Y3 @ Y5 @ Y4)))))))))))) @ (sK13 @ (^[Y1 : mu]: ((^[Y2 : $i]: (!! @ (mu > $i > $o) @ (^[Y3 : mu > $i > $o]: ((!! @ (mu > $i > $o) @ (^[Y4 : mu > $i > $o]: ((Y4 @ Y1 @ Y2) => (!! @ $i @ (^[Y5 : $i]: (!! @ mu @ (^[Y6 : mu]: ((Y3 @ Y6 @ Y5) => (Y4 @ Y6 @ Y5))))))))) => (!! @ $i @ (^[Y4 : $i]: (?? @ mu @ (^[Y5 : mu]: (Y3 @ Y5 @ Y4))))))))))))) => (!! @ $i @ (^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: ((X1 @ Y2 @ Y1) => (Y0 @ Y2 @ Y1)))))))) @ (sK16 @ X1)))) | ($true = (((^[Y0 : $i]: (?? @ mu @ (^[Y1 : mu]: (X1 @ Y1 @ Y0)))) @ X2)))) ) | ~spl8_22),
% 0.68/0.33 inference(pi_proxy_clausification,[],[f2536])).
% 0.68/0.33 thf(f2538,plain,(
% 0.68/0.33 ( ! [X2 : $i,X1 : (mu > $i > $o)] : (($false = (((sK16 @ X1 @ (sK12 @ (^[Y0 : mu]: ((^[Y1 : $i]: (!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: ((!! @ (mu > $i > $o) @ (^[Y3 : mu > $i > $o]: ((Y3 @ Y0 @ Y1) => (!! @ $i @ (^[Y4 : $i]: (!! @ mu @ (^[Y5 : mu]: ((Y2 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4))))))))) => (!! @ $i @ (^[Y3 : $i]: (?? @ mu @ (^[Y4 : mu]: (Y2 @ Y4 @ Y3)))))))))))) @ (sK13 @ (^[Y0 : mu]: ((^[Y1 : $i]: (!! @ (mu > $i > $o) @ (^[Y2 : mu > $i > $o]: ((!! @ (mu > $i > $o) @ (^[Y3 : mu > $i > $o]: ((Y3 @ Y0 @ Y1) => (!! @ $i @ (^[Y4 : $i]: (!! @ mu @ (^[Y5 : mu]: ((Y2 @ Y5 @ Y4) => (Y3 @ Y5 @ Y4))))))))) => (!! @ $i @ (^[Y3 : $i]: (?? @ mu @ (^[Y4 : mu]: (Y2 @ Y4 @ Y3))))))))))))) => (!! @ $i @ (^[Y0 : $i]: (!! @ mu @ (^[Y1 : mu]: ((X1 @ Y1 @ Y0) => (sK16 @ X1 @ Y1 @ Y0))))))))) | ($true = ((?? @ mu @ (^[Y0 : mu]: (X1 @ Y0 @ X2)))))) ) | ~spl8_22),
% 0.68/0.33 inference(beta-eta_normalization,[],[f2537])).
% 0.68/0.33 thf(f2539,plain,(
% 0.68/0.33 ( ! [X2 : $i,X1 : (mu > $i > $o)] : (($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ mu @ (^[Y1 : mu]: ((X1 @ Y1 @ Y0) => (sK16 @ X1 @ Y1 @ Y0)))))))) | ($true = ((?? @ mu @ (^[Y0 : mu]: (X1 @ Y0 @ X2)))))) ) | ~spl8_22),
% 0.68/0.33 inference(imp_proxy_clausification,[],[f2538])).
% 0.68/0.33 thf(f2543,plain,(
% 0.68/0.33 ( ! [X2 : $i,X1 : (mu > $i > $o)] : (($false = (((^[Y0 : $i]: (!! @ mu @ (^[Y1 : mu]: ((X1 @ Y1 @ Y0) => (sK16 @ X1 @ Y1 @ Y0))))) @ (sK18 @ X1)))) | ($true = ((?? @ mu @ (^[Y0 : mu]: (X1 @ Y0 @ X2)))))) ) | ~spl8_22),
% 0.68/0.33 inference(sigma_proxy_clausification,[],[f2539])).
% 0.68/0.33 thf(f2544,plain,(
% 0.68/0.33 ( ! [X2 : $i,X1 : (mu > $i > $o)] : (($false = (((^[Y0 : $i]: (!! @ mu @ (^[Y1 : mu]: ((X1 @ Y1 @ Y0) => (sK16 @ X1 @ Y1 @ Y0))))) @ (sK18 @ X1)))) | ($true = (((^[Y0 : mu]: (X1 @ Y0 @ X2)) @ (sK19 @ X1 @ X2))))) ) | ~spl8_22),
% 0.68/0.33 inference(sigma_proxy_clausification,[],[f2543])).
% 0.68/0.33 thf(f2545,plain,(
% 0.68/0.33 ( ! [X2 : $i,X1 : (mu > $i > $o)] : (($false = ((!! @ mu @ (^[Y0 : mu]: ((X1 @ Y0 @ (sK18 @ X1)) => (sK16 @ X1 @ Y0 @ (sK18 @ X1))))))) | ($true = ((X1 @ (sK19 @ X1 @ X2) @ X2)))) ) | ~spl8_22),
% 0.68/0.33 inference(beta-eta_normalization,[],[f2544])).
% 0.68/0.33 thf(f2546,plain,(
% 0.68/0.33 ( ! [X2 : $i,X1 : (mu > $i > $o)] : (($false = (((^[Y0 : mu]: ((X1 @ Y0 @ (sK18 @ X1)) => (sK16 @ X1 @ Y0 @ (sK18 @ X1)))) @ (sK20 @ X1)))) | ($true = ((X1 @ (sK19 @ X1 @ X2) @ X2)))) ) | ~spl8_22),
% 0.68/0.33 inference(sigma_proxy_clausification,[],[f2545])).
% 0.68/0.33 thf(f2547,plain,(
% 0.68/0.33 ( ! [X2 : $i,X1 : (mu > $i > $o)] : (($false = (((X1 @ (sK20 @ X1) @ (sK18 @ X1)) => (sK16 @ X1 @ (sK20 @ X1) @ (sK18 @ X1))))) | ($true = ((X1 @ (sK19 @ X1 @ X2) @ X2)))) ) | ~spl8_22),
% 0.68/0.33 inference(beta-eta_normalization,[],[f2546])).
% 0.68/0.33 thf(f2549,plain,(
% 0.68/0.33 ( ! [X2 : $i,X1 : (mu > $i > $o)] : (($true = ((X1 @ (sK20 @ X1) @ (sK18 @ X1)))) | ($true = ((X1 @ (sK19 @ X1 @ X2) @ X2)))) ) | ~spl8_22),
% 0.68/0.33 inference(imp_proxy_clausification,[],[f2547])).
% 0.68/0.33 thf(f4401,plain,(
% 0.68/0.33 ( ! [X2 : $i,X0 : (mu > $i > $i),X1 : $i] : (($true = $false) | ($true = (((^[Y0 : mu]: ((^[Y1 : $i]: (positive @ ((^[Y2 : mu]: ((^[Y3 : $i]: ((^[Y4 : mu]: ((^[Y5 : $i]: ($false)))))))) @ Y0 @ Y1) @ (X0 @ Y0 @ Y1))))) @ (sK19 @ (^[Y0 : mu]: ((^[Y1 : $i]: (positive @ ((^[Y2 : mu]: ((^[Y3 : $i]: ((^[Y4 : mu]: ((^[Y5 : $i]: ($false)))))))) @ Y0 @ Y1) @ (X0 @ Y0 @ Y1))))) @ X2) @ X2))) | (((X0 @ (sK20 @ (^[Y0 : mu]: ((^[Y1 : $i]: (positive @ (^[Y2 : mu]: ((^[Y3 : $i]: ($false)))) @ (X0 @ Y0 @ Y1)))))) @ (sK18 @ (^[Y0 : mu]: ((^[Y1 : $i]: (positive @ (^[Y2 : mu]: ((^[Y3 : $i]: ($false)))) @ (X0 @ Y0 @ Y1)))))))) != X1)) ) | ~spl8_22),
% 0.68/0.33 inference(constrained_superposition,[],[f2549,f1789])).
% 0.68/0.33 thf(f4643,plain,(
% 0.68/0.33 ( ! [X2 : $i,X0 : (mu > $i > $i),X1 : $i] : (($true = (((^[Y0 : mu]: ((^[Y1 : $i]: (positive @ ((^[Y2 : mu]: ((^[Y3 : $i]: ((^[Y4 : mu]: ((^[Y5 : $i]: ($false)))))))) @ Y0 @ Y1) @ (X0 @ Y0 @ Y1))))) @ (sK19 @ (^[Y0 : mu]: ((^[Y1 : $i]: (positive @ ((^[Y2 : mu]: ((^[Y3 : $i]: ((^[Y4 : mu]: ((^[Y5 : $i]: ($false)))))))) @ Y0 @ Y1) @ (X0 @ Y0 @ Y1))))) @ X2) @ X2))) | (((X0 @ (sK20 @ (^[Y0 : mu]: ((^[Y1 : $i]: (positive @ (^[Y2 : mu]: ((^[Y3 : $i]: ($false)))) @ (X0 @ Y0 @ Y1)))))) @ (sK18 @ (^[Y0 : mu]: ((^[Y1 : $i]: (positive @ (^[Y2 : mu]: ((^[Y3 : $i]: ($false)))) @ (X0 @ Y0 @ Y1)))))))) != X1)) ) | ~spl8_22),
% 0.68/0.33 inference(trivial_inequality_removal,[],[f4401])).
% 0.68/0.33 thf(f4644,plain,(
% 0.68/0.33 ( ! [X2 : $i,X0 : (mu > $i > $i),X1 : $i] : (($true = ((positive @ (^[Y0 : mu]: ((^[Y1 : $i]: ($false)))) @ (X0 @ (sK19 @ (^[Y0 : mu]: ((^[Y1 : $i]: (positive @ (^[Y2 : mu]: ((^[Y3 : $i]: ($false)))) @ (X0 @ Y0 @ Y1))))) @ X2) @ X2)))) | (((X0 @ (sK20 @ (^[Y0 : mu]: ((^[Y1 : $i]: (positive @ (^[Y2 : mu]: ((^[Y3 : $i]: ($false)))) @ (X0 @ Y0 @ Y1)))))) @ (sK18 @ (^[Y0 : mu]: ((^[Y1 : $i]: (positive @ (^[Y2 : mu]: ((^[Y3 : $i]: ($false)))) @ (X0 @ Y0 @ Y1)))))))) != X1)) ) | ~spl8_22),
% 0.68/0.33 inference(beta-eta_normalization,[],[f4643])).
% 0.68/0.33 thf(f4715,plain,(
% 0.68/0.33 ( ! [X0 : (mu > $i > $i),X1 : $i] : (($true = $false) | (((X0 @ (sK20 @ (^[Y0 : mu]: ((^[Y1 : $i]: (positive @ (^[Y2 : mu]: ((^[Y3 : $i]: ($false)))) @ (X0 @ Y0 @ Y1)))))) @ (sK18 @ (^[Y0 : mu]: ((^[Y1 : $i]: (positive @ (^[Y2 : mu]: ((^[Y3 : $i]: ($false)))) @ (X0 @ Y0 @ Y1)))))))) != X1)) ) | ~spl8_22),
% 0.68/0.33 inference(forward_demodulation,[],[f4644,f1789])).
% 0.68/0.33 thf(f4716,plain,(
% 0.68/0.33 ( ! [X0 : (mu > $i > $i),X1 : $i] : ((((X0 @ (sK20 @ (^[Y0 : mu]: ((^[Y1 : $i]: (positive @ (^[Y2 : mu]: ((^[Y3 : $i]: ($false)))) @ (X0 @ Y0 @ Y1)))))) @ (sK18 @ (^[Y0 : mu]: ((^[Y1 : $i]: (positive @ (^[Y2 : mu]: ((^[Y3 : $i]: ($false)))) @ (X0 @ Y0 @ Y1)))))))) != X1)) ) | ~spl8_22),
% 0.68/0.33 inference(trivial_inequality_removal,[],[f4715])).
% 0.68/0.33 thf(f4717,plain,(
% 0.68/0.33 $false | ~spl8_22),
% 0.68/0.33 inference(flex-flex_simplification,[],[f4716])).
% 0.68/0.33 thf(f4718,plain,(
% 0.68/0.33 ~spl8_22),
% 0.68/0.33 inference(avatar_contradiction_clause,[],[f4717])).
% 0.68/0.33 cnf(s41, plain, spl8_15 | spl8_22, inference(sat_conversion,[],[f1810])).
% 0.68/0.33 cnf(s60, plain, ~spl8_15, inference(sat_conversion,[],[f1903])).
% 0.68/0.33 cnf(s66, plain, ~spl8_22, inference(sat_conversion,[],[f4718])).
% 0.68/0.33 cnf(s68, plain, $false, inference(rat,[],[s41,s66,s60])).
% 0.68/0.33 thf(f4719,plain,(
% 0.68/0.33 $false),
% 0.68/0.33 inference(avatar_sat_refutation,[],[s68])).
% 0.68/0.33 % SZS output end Proof for theBenchmark
% 0.68/0.33 % (83672)------------------------------
% 0.68/0.33 % (83672)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.33 % (83672)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.33 % (83672)CaDiCaL version: 2.1.3
% 0.68/0.33 % (83672)Termination reason: Refutation
% 0.68/0.33 % (83672)Time elapsed: 0.144 s
% 0.68/0.33 % (83672)Peak memory usage: 14 MB
% 0.68/0.33 % (83672)Instructions burned: 611 (million)
% 0.68/0.33 % (83649)Success in time 0.205 s
% 0.68/0.33 % Vampire exiting
%------------------------------------------------------------------------------