%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO858^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n009.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 08:50:28 AM UTC 2026
% Result : Theorem 5.11s 1.20s
% Output : Refutation 5.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO858^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n009.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % 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 17:19:15 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
% 5.46/1.11 % (101283)Will run a generic schedule for satisfiability detection.
% 5.46/1.11 % (101294)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3362178497:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 5.46/1.11 % (101293)% WARNING: option uhcvi not known.
% 5.46/1.11 % (101295)dis+10_1_sil=32000:sp=arity:random_seed=153902638:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 5.46/1.11 % (101292)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1585087901_2999 on theBenchmark for (2999ds/0Mi)
% 5.46/1.11 % (101293)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1173385850:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 5.46/1.11 % (101293)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.46/1.11 % (101297)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2966785776:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 5.46/1.11 % (101296)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1965919944:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 5.46/1.11 % (101298)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=150254080:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 5.46/1.11 % (101296)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.46/1.11 % (101295)Instruction limit reached!
% 5.46/1.11 % (101295)------------------------------
% 5.46/1.11 % (101295)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.46/1.11 % (101295)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.46/1.11 % (101295)CaDiCaL version: 2.1.3
% 5.46/1.11 % (101295)Termination reason: Instruction limit
% 5.46/1.11 % (101295)Termination phase: Property scanning
% 5.46/1.11 % (101295)Time elapsed: 0.043 s
% 5.46/1.11 % (101295)Peak memory usage: 11 MB
% 5.46/1.11 % (101295)Instructions burned: 105 (million)
% 5.46/1.11 % Exception at run slice level
% 5.46/1.11 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.46/1.11 % (101293)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 5.46/1.11 % (101306)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1476938824:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 5.46/1.11 % (101307)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2426687372:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 5.46/1.11 % (101296)Instruction limit reached!
% 5.46/1.11 % (101296)------------------------------
% 5.46/1.11 % (101296)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.46/1.11 % (101296)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.46/1.11 % (101296)CaDiCaL version: 2.1.3
% 5.46/1.11 % (101296)Termination reason: Instruction limit
% 5.46/1.11 % (101296)Termination phase: Saturation
% 5.46/1.11 % (101296)Time elapsed: 0.048 s
% 5.46/1.11 % (101296)Peak memory usage: 12 MB
% 5.46/1.11 % (101296)Instructions burned: 118 (million)
% 5.46/1.11 % (101297)Instruction limit reached!
% 5.46/1.11 % (101297)------------------------------
% 5.46/1.11 % (101297)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.46/1.11 % (101297)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.46/1.11 % (101297)CaDiCaL version: 2.1.3
% 5.46/1.11 % (101297)Termination reason: Instruction limit
% 5.46/1.11 % (101297)Termination phase: Saturation
% 5.46/1.11 % (101297)Time elapsed: 0.053 s
% 5.46/1.11 % (101297)Peak memory usage: 12 MB
% 5.46/1.11 % (101297)Instructions burned: 132 (million)
% 5.46/1.11 % (101310)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=1960610972:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 5.46/1.11 % (101298)Instruction limit reached!
% 5.46/1.11 % (101298)------------------------------
% 5.46/1.11 % (101298)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.46/1.11 % (101298)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.46/1.11 % (101298)CaDiCaL version: 2.1.3
% 5.46/1.11 % (101298)Termination reason: Instruction limit
% 5.46/1.11 % (101298)Termination phase: Saturation
% 5.46/1.11 % (101298)Time elapsed: 0.065 s
% 5.46/1.11 % (101298)Peak memory usage: 12 MB
% 5.46/1.11 % (101298)Instructions burned: 160 (million)
% 5.46/1.11 % (101311)ott-21_1_sil=16000:fs=off:random_seed=811832294:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 5.11/1.20 % (101310)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.11/1.20 % (101313)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2318744592:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 5.11/1.20 % Exception at run slice level
% 5.11/1.20 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.11/1.20 % (101307)Instruction limit reached!
% 5.11/1.20 % (101307)------------------------------
% 5.11/1.20 % (101307)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.11/1.20 % (101307)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.11/1.20 % (101307)CaDiCaL version: 2.1.3
% 5.11/1.20 % (101307)Termination reason: Instruction limit
% 5.11/1.20 % (101307)Termination phase: Saturation
% 5.11/1.20 % (101307)Time elapsed: 0.053 s
% 5.11/1.20 % (101307)Peak memory usage: 12 MB
% 5.11/1.20 % (101307)Instructions burned: 132 (million)
% 5.11/1.20 % (101316)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=3463228164:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 5.11/1.20 % (101310)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 5.11/1.20 % (101317)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=3719967184:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 5.11/1.20 % Exception at run slice level
% 5.11/1.20 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.11/1.20 % (101320)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=2829376593:i=889:ins=1_2997 on theBenchmark for (2997ds/889Mi)
% 5.11/1.20 % (101311)Instruction limit reached!
% 5.11/1.20 % (101311)------------------------------
% 5.11/1.20 % (101311)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.11/1.20 % (101311)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.11/1.20 % (101311)CaDiCaL version: 2.1.3
% 5.11/1.20 % (101311)Termination reason: Instruction limit
% 5.11/1.20 % (101311)Termination phase: Saturation
% 5.11/1.20 % (101311)Time elapsed: 0.128 s
% 5.11/1.20 % (101311)Peak memory usage: 12 MB
% 5.11/1.20 % (101311)Instructions burned: 180 (million)
% 5.11/1.20 % Exception at run slice level
% 5.11/1.20 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.11/1.20 % (101322)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=2356339694:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2997 on theBenchmark for (2997ds/692Mi)
% 5.11/1.20 % (101323)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=659628281:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 5.11/1.20 % (101323)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.11/1.20 % (101322)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.11/1.20 % (101313)Instruction limit reached!
% 5.11/1.20 % (101313)------------------------------
% 5.11/1.20 % (101313)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.11/1.20 % (101313)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.11/1.20 % (101313)CaDiCaL version: 2.1.3
% 5.11/1.20 % (101313)Termination reason: Instruction limit
% 5.11/1.20 % (101313)Termination phase: Saturation
% 5.11/1.20 % (101313)Time elapsed: 0.220 s
% 5.11/1.20 % (101313)Peak memory usage: 15 MB
% 5.11/1.20 % (101313)Instructions burned: 477 (million)
% 5.11/1.20 % (101326)fmb+10_1_sil=64000:random_seed=3570626148:i=22061:nm=2:gsp=on_2996 on theBenchmark for (2996ds/22061Mi)
% 5.11/1.20 % (101326)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 5.11/1.20 % (101310)Instruction limit reached!
% 5.11/1.20 % (101310)------------------------------
% 5.11/1.20 % (101310)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.11/1.20 % (101310)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.11/1.20 % (101310)CaDiCaL version: 2.1.3
% 5.11/1.20 % (101310)Termination reason: Instruction limit
% 5.11/1.20 % (101310)Termination phase: Saturation
% 5.11/1.20 % (101310)Time elapsed: 0.302 s
% 5.11/1.20 % (101310)Peak memory usage: 16 MB
% 5.11/1.20 % (101310)Instructions burned: 686 (million)
% 5.11/1.20 % Exception at run slice level
% 5.11/1.20 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.11/1.20 % (101328)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=2399959602:i=9515:nm=5_2995 on theBenchmark for (2995ds/9515Mi)
% 5.11/1.20 % (101329)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=811453836:fmbsr=1.7:i=920_2995 on theBenchmark for (2995ds/920Mi)
% 5.11/1.20 % Exception at run slice level
% 5.11/1.20 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.11/1.20 % Exception at run slice level
% 5.11/1.20 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.11/1.20 % (101332)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=641467224:i=5131_2995 on theBenchmark for (2995ds/5131Mi)
% 5.11/1.20 % (101333)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=798178657:i=1472:ins=7:fdi=8:gsp=on_2995 on theBenchmark for (2995ds/1472Mi)
% 5.11/1.20 % (101332)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.11/1.20 % (101333)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 5.11/1.20 % (101333)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 5.11/1.20 % (101322)Instruction limit reached!
% 5.11/1.20 % (101322)------------------------------
% 5.11/1.20 % (101322)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.11/1.20 % (101322)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.11/1.20 % (101322)CaDiCaL version: 2.1.3
% 5.11/1.20 % (101322)Termination reason: Instruction limit
% 5.11/1.20 % (101322)Termination phase: Saturation
% 5.11/1.20 % (101322)Time elapsed: 0.284 s
% 5.11/1.20 % (101322)Peak memory usage: 16 MB
% 5.11/1.20 % (101322)Instructions burned: 693 (million)
% 5.11/1.20 % (101336)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=1406336485:i=6324_2994 on theBenchmark for (2994ds/6324Mi)
% 5.11/1.20 % Exception at run slice level
% 5.11/1.20 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.11/1.20 % (101338)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=2615724607:fmbsr=2.30978:i=2174_2993 on theBenchmark for (2993ds/2174Mi)
% 5.11/1.20 % (101323)Instruction limit reached!
% 5.11/1.20 % (101323)------------------------------
% 5.11/1.20 % (101323)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.11/1.20 % (101323)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.11/1.20 % (101323)CaDiCaL version: 2.1.3
% 5.11/1.20 % (101323)Termination reason: Instruction limit
% 5.11/1.20 % (101323)Termination phase: Saturation
% 5.11/1.20 % (101323)Time elapsed: 0.372 s
% 5.11/1.20 % (101323)Peak memory usage: 15 MB
% 5.11/1.20 % (101323)Instructions burned: 879 (million)
% 5.11/1.20 % (101340)ott-2_1_sil=16000:newcnf=on:random_seed=2634391948:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2993 on theBenchmark for (2993ds/869Mi)
% 5.11/1.20 % (101340)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.11/1.20 % Exception at run slice level
% 5.11/1.20 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.11/1.20 % (101342)ott+10_1_sil=32000:tgt=ground:random_seed=2068232821:i=5114:av=off_2992 on theBenchmark for (2992ds/5114Mi)
% 5.11/1.20 % (101317)Instruction limit reached!
% 5.11/1.20 % (101317)------------------------------
% 5.11/1.20 % (101317)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.11/1.20 % (101317)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.11/1.20 % (101317)CaDiCaL version: 2.1.3
% 5.11/1.20 % (101317)Termination reason: Instruction limit
% 5.11/1.20 % (101317)Termination phase: Saturation
% 5.11/1.20 % (101317)Time elapsed: 0.613 s
% 5.11/1.20 % (101317)Peak memory usage: 17 MB
% 5.11/1.20 % (101317)Instructions burned: 1180 (million)
% 5.11/1.20 % (101344)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=2781191369:i=54282_2992 on theBenchmark for (2992ds/54282Mi)
% 5.11/1.20 % Exception at run slice level
% 5.11/1.20 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.11/1.20 % (101346)dis-11_1_sil=16000:sp=reverse_frequency:alpa=true:random_seed=3001129920:i=3512:aac=none_2991 on theBenchmark for (2991ds/3512Mi)
% 5.11/1.20 % (101346)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 5.11/1.20 % (101294) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-101283-101294"...
% 5.11/1.20 % (101294)...printing done.
% 5.11/1.20 % (101294)Refutation found. Thanks to Tanya!
% 5.11/1.20 % SZS status Theorem for theBenchmark
% 5.11/1.20 % SZS output start Proof for theBenchmark
% 5.11/1.20 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 5.11/1.20 thf(func_def_0, type, c_Eps_i: (($i > $o) > $i)).
% 5.11/1.20 thf(func_def_1, type, c_False: $o).
% 5.11/1.20 thf(func_def_2, type, c_True: $o).
% 5.11/1.20 thf(func_def_3, type, c_not: ($o > $o)).
% 5.11/1.20 thf(func_def_4, type, c_and: ($o > $o > $o)).
% 5.11/1.20 thf(func_def_5, type, c_or: ($o > $o > $o)).
% 5.11/1.20 thf(func_def_6, type, c_iff: ($o > $o > $o)).
% 5.11/1.20 thf(func_def_7, type, c_In: ($i > $i > $o)).
% 5.11/1.20 thf(func_def_8, type, c_Subq: ($i > $i > $o)).
% 5.11/1.20 thf(func_def_10, type, c_Union: ($i > $i)).
% 5.11/1.20 thf(func_def_11, type, c_Power: ($i > $i)).
% 5.11/1.20 thf(func_def_12, type, c_Repl: ($i > ($i > $i) > $i)).
% 5.11/1.20 thf(func_def_13, type, c_TransSet: ($i > $o)).
% 5.11/1.20 thf(func_def_14, type, c_atleast2: ($i > $o)).
% 5.11/1.20 thf(func_def_15, type, c_atleast3: ($i > $o)).
% 5.11/1.20 thf(func_def_16, type, c_atleast4: ($i > $o)).
% 5.11/1.20 thf(func_def_17, type, c_atleast5: ($i > $o)).
% 5.11/1.20 thf(func_def_18, type, c_atleast6: ($i > $o)).
% 5.11/1.20 thf(func_def_19, type, c_exactly2: ($i > $o)).
% 5.11/1.20 thf(func_def_20, type, c_exactly3: ($i > $o)).
% 5.11/1.20 thf(func_def_21, type, c_exactly4: ($i > $o)).
% 5.11/1.20 thf(func_def_22, type, c_exactly5: ($i > $o)).
% 5.11/1.20 thf(func_def_23, type, c_exu_i: (($i > $o) > $o)).
% 5.11/1.20 thf(func_def_24, type, c_reflexive_i: (($i > $i > $o) > $o)).
% 5.11/1.20 thf(func_def_25, type, c_irreflexive_i: (($i > $i > $o) > $o)).
% 5.11/1.20 thf(func_def_26, type, c_symmetric_i: (($i > $i > $o) > $o)).
% 5.11/1.20 thf(func_def_27, type, c_antisymmetric_i: (($i > $i > $o) > $o)).
% 5.11/1.20 thf(func_def_28, type, c_transitive_i: (($i > $i > $o) > $o)).
% 5.11/1.20 thf(func_def_29, type, c_eqreln_i: (($i > $i > $o) > $o)).
% 5.11/1.20 thf(func_def_30, type, c_per_i: (($i > $i > $o) > $o)).
% 5.11/1.20 thf(func_def_31, type, c_linear_i: (($i > $i > $o) > $o)).
% 5.11/1.20 thf(func_def_32, type, c_trichotomous_or_i: (($i > $i > $o) > $o)).
% 5.11/1.20 thf(func_def_33, type, c_partialorder_i: (($i > $i > $o) > $o)).
% 5.11/1.20 thf(func_def_34, type, c_totalorder_i: (($i > $i > $o) > $o)).
% 5.11/1.20 thf(func_def_35, type, c_strictpartialorder_i: (($i > $i > $o) > $o)).
% 5.11/1.20 thf(func_def_36, type, c_stricttotalorder_i: (($i > $i > $o) > $o)).
% 5.11/1.20 thf(func_def_37, type, c_If_i: ($o > $i > $i > $i)).
% 5.11/1.20 thf(func_def_38, type, c_exactly1of2: ($o > $o > $o)).
% 5.11/1.20 thf(func_def_39, type, c_exactly1of3: ($o > $o > $o > $o)).
% 5.11/1.20 thf(func_def_40, type, c_nIn: ($i > $i > $o)).
% 5.11/1.20 thf(func_def_41, type, c_nSubq: ($i > $i > $o)).
% 5.11/1.20 thf(func_def_42, type, c_UPair: ($i > $i > $i)).
% 5.11/1.20 thf(func_def_43, type, c_Sing: ($i > $i)).
% 5.11/1.20 thf(func_def_44, type, c_binunion: ($i > $i > $i)).
% 5.11/1.20 thf(func_def_45, type, c_SetAdjoin: ($i > $i > $i)).
% 5.11/1.20 thf(func_def_46, type, c_famunion: ($i > ($i > $i) > $i)).
% 5.11/1.20 thf(func_def_47, type, c_Sep: ($i > ($i > $o) > $i)).
% 5.11/1.20 thf(func_def_48, type, c_ReplSep: ($i > ($i > $o) > ($i > $i) > $i)).
% 5.11/1.20 thf(func_def_49, type, c_binintersect: ($i > $i > $i)).
% 5.11/1.20 thf(func_def_50, type, c_setminus: ($i > $i > $i)).
% 5.11/1.20 thf(func_def_51, type, c_inj: ($i > $i > ($i > $i) > $o)).
% 5.11/1.20 thf(func_def_52, type, c_bij: ($i > $i > ($i > $i) > $o)).
% 5.11/1.20 thf(func_def_53, type, c_atleastp: ($i > $i > $o)).
% 5.11/1.20 thf(func_def_54, type, c_equip: ($i > $i > $o)).
% 5.11/1.20 thf(func_def_55, type, c_In_rec_poly_G_i: (($i > ($i > $i) > $i) > $i > $i > $o)).
% 5.11/1.20 thf(func_def_56, type, c_In_rec_poly_i: (($i > ($i > $i) > $i) > $i > $i)).
% 5.11/1.20 thf(func_def_57, type, c_ordsucc: ($i > $i)).
% 5.11/1.20 thf(func_def_58, type, c_nat_p: ($i > $o)).
% 5.11/1.20 thf(func_def_59, type, c_nat_primrec: ($i > ($i > $i > $i) > $i > $i)).
% 5.11/1.20 thf(func_def_60, type, c_add_nat: ($i > $i > $i)).
% 5.11/1.20 thf(func_def_61, type, c_mul_nat: ($i > $i > $i)).
% 5.11/1.20 thf(func_def_62, type, c_ordinal: ($i > $o)).
% 5.11/1.20 thf(func_def_63, type, c_V_: ($i > $i)).
% 5.11/1.20 thf(func_def_64, type, c_Inj1: ($i > $i)).
% 5.11/1.20 thf(func_def_65, type, c_Inj0: ($i > $i)).
% 5.11/1.20 thf(func_def_66, type, c_Unj: ($i > $i)).
% 5.11/1.20 thf(func_def_67, type, c_combine_funcs: ($i > $i > ($i > $i) > ($i > $i) > $i > $i)).
% 5.11/1.20 thf(func_def_68, type, c_setsum: ($i > $i > $i)).
% 5.11/1.20 thf(func_def_69, type, c_proj0: ($i > $i)).
% 5.11/1.20 thf(func_def_70, type, c_proj1: ($i > $i)).
% 5.11/1.20 thf(func_def_71, type, c_binrep: ($i > $i > $i)).
% 5.11/1.20 thf(func_def_72, type, c_lam: ($i > ($i > $i) > $i)).
% 5.11/1.20 thf(func_def_73, type, c_setprod: ($i > $i > $i)).
% 5.11/1.20 thf(func_def_74, type, c_ap: ($i > $i > $i)).
% 5.11/1.20 thf(func_def_75, type, c_setsum_p: ($i > $o)).
% 5.11/1.20 thf(func_def_76, type, c_tuple_p: ($i > $i > $o)).
% 5.11/1.20 thf(func_def_77, type, c_Pi: ($i > ($i > $i) > $i)).
% 5.11/1.20 thf(func_def_78, type, c_setexp: ($i > $i > $i)).
% 5.11/1.20 thf(func_def_79, type, c_Sep2: ($i > ($i > $i) > ($i > $i > $o) > $i)).
% 5.11/1.20 thf(func_def_80, type, c_set_of_pairs: ($i > $o)).
% 5.11/1.20 thf(func_def_81, type, c_lam2: ($i > ($i > $i) > ($i > $i > $i) > $i)).
% 5.11/1.20 thf(func_def_82, type, c_PNoEq_: ($i > ($i > $o) > ($i > $o) > $o)).
% 5.11/1.20 thf(func_def_83, type, c_PNoLt_: ($i > ($i > $o) > ($i > $o) > $o)).
% 5.11/1.20 thf(func_def_84, type, c_PNoLt: ($i > ($i > $o) > $i > ($i > $o) > $o)).
% 5.11/1.20 thf(func_def_85, type, c_PNoLe: ($i > ($i > $o) > $i > ($i > $o) > $o)).
% 5.11/1.20 thf(func_def_86, type, c_PNo_downc: (($i > ($i > $o) > $o) > $i > ($i > $o) > $o)).
% 5.11/1.20 thf(func_def_87, type, c_PNo_upc: (($i > ($i > $o) > $o) > $i > ($i > $o) > $o)).
% 5.11/1.20 thf(func_def_88, type, c_SNoElts_: ($i > $i)).
% 5.11/1.20 thf(func_def_89, type, c_SNo_: ($i > $i > $o)).
% 5.11/1.20 thf(func_def_90, type, c_PSNo: ($i > ($i > $o) > $i)).
% 5.11/1.20 thf(func_def_91, type, c_SNo: ($i > $o)).
% 5.11/1.20 thf(func_def_92, type, c_SNoLev: ($i > $i)).
% 5.11/1.20 thf(func_def_93, type, c_SNoEq_: ($i > $i > $i > $o)).
% 5.11/1.20 thf(func_def_94, type, c_SNoLt: ($i > $i > $o)).
% 5.11/1.20 thf(func_def_95, type, c_SNoLe: ($i > $i > $o)).
% 5.11/1.20 thf(func_def_96, type, c_binop_on: ($i > ($i > $i > $i) > $o)).
% 5.11/1.20 thf(func_def_97, type, c_Loop: ($i > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > $i > $o)).
% 5.11/1.20 thf(func_def_98, type, c_Loop_with_defs: ($i > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > $i > ($i > $i > $i) > ($i > $i > $i > $i) > ($i > $i > $i) > ($i > $i > $i > $i) > ($i > $i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > $o)).
% 5.11/1.20 thf(func_def_99, type, c_Loop_with_defs_cex1: ($i > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > $i > ($i > $i > $i) > ($i > $i > $i > $i) > ($i > $i > $i) > ($i > $i > $i > $i) > ($i > $i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > $o)).
% 5.11/1.20 thf(func_def_100, type, c_Loop_with_defs_cex2: ($i > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > $i > ($i > $i > $i) > ($i > $i > $i > $i) > ($i > $i > $i) > ($i > $i > $i > $i) > ($i > $i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > $o)).
% 5.11/1.20 thf(func_def_101, type, c_combinator: ($i > $o)).
% 5.11/1.20 thf(func_def_102, type, c_combinator_equiv: ($i > $i > $o)).
% 5.11/1.20 thf(func_def_103, type, c_equip_mod: ($i > $i > $i > $o)).
% 5.11/1.20 thf(func_def_107, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 5.11/1.20 thf(func_def_108, type, db0: !>[X0: $tType]:(X0)).
% 5.11/1.20 thf(func_def_109, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 5.11/1.20 thf(func_def_110, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 5.11/1.20 thf(func_def_111, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 5.11/1.20 thf(func_def_112, type, vIMP: ($o > $o > $o)).
% 5.11/1.20 thf(func_def_113, type, db2: !>[X0: $tType]:(X0)).
% 5.11/1.20 thf(func_def_114, type, db1: !>[X0: $tType]:(X0)).
% 5.11/1.20 thf(func_def_115, type, db3: !>[X0: $tType]:(X0)).
% 5.11/1.20 thf(func_def_116, type, db4: !>[X0: $tType]:(X0)).
% 5.11/1.20 thf(func_def_117, type, db5: !>[X0: $tType]:(X0)).
% 5.11/1.20 thf(func_def_118, type, db6: !>[X0: $tType]:(X0)).
% 5.11/1.20 thf(func_def_119, type, db13: !>[X0: $tType]:(X0)).
% 5.11/1.20 thf(func_def_120, type, db12: !>[X0: $tType]:(X0)).
% 5.11/1.20 thf(func_def_121, type, db11: !>[X0: $tType]:(X0)).
% 5.11/1.20 thf(func_def_122, type, db10: !>[X0: $tType]:(X0)).
% 5.11/1.20 thf(func_def_123, type, db9: !>[X0: $tType]:(X0)).
% 5.11/1.20 thf(func_def_124, type, db14: !>[X0: $tType]:(X0)).
% 5.11/1.20 thf(func_def_125, type, db15: !>[X0: $tType]:(X0)).
% 5.11/1.20 thf(func_def_126, type, db16: !>[X0: $tType]:(X0)).
% 5.11/1.20 thf(func_def_127, type, db8: !>[X0: $tType]:(X0)).
% 5.11/1.20 thf(func_def_128, type, db7: !>[X0: $tType]:(X0)).
% 5.11/1.20 thf(func_def_129, type, db17: !>[X0: $tType]:(X0)).
% 5.11/1.20 thf(func_def_130, type, db18: !>[X0: $tType]:(X0)).
% 5.11/1.20 thf(func_def_131, type, sP0: (($i > $o) > $o)).
% 5.11/1.20 thf(func_def_132, type, sP1: (($i > $o) > $o)).
% 5.11/1.20 thf(func_def_133, type, sK2: (($i > $o) > $i)).
% 5.11/1.20 thf(func_def_134, type, sK3: (($i > $o) > $i > $i)).
% 5.11/1.20 thf(func_def_135, type, sK4: (($i > $o) > $i)).
% 5.11/1.20 thf(func_def_136, type, sK5: (($i > $o) > $i)).
% 5.11/1.20 thf(func_def_137, type, sK6: (($i > $o) > $i)).
% 5.11/1.20 thf(func_def_138, type, sK7: (($i > $o) > $i)).
% 5.11/1.20 thf(func_def_139, type, sK8: (($i > $o) > $i)).
% 5.11/1.20 thf(func_def_140, type, sK9: (($i > $i > $i > $i) > ($i > $i) > (($i > $i > $i) > $i) > $i)).
% 5.11/1.20 thf(func_def_141, type, sK10: (($i > $i) > $i > $i)).
% 5.11/1.20 thf(func_def_142, type, sK11: (((($i > $i > $i > $i) > $i) > $i > $i) > $i > $i)).
% 5.11/1.20 thf(func_def_143, type, sK12: (($i > $i) > ($i > $i) > $i)).
% 5.11/1.20 thf(func_def_144, type, vNOT: ($o > $o)).
% 5.11/1.20 thf(func_def_145, type, sK13: $o).
% 5.11/1.20 thf(func_def_146, type, sK14: $o).
% 5.11/1.20 thf(func_def_147, type, sK15: (($i > $i) > $i > $i > $i)).
% 5.11/1.20 thf(func_def_148, type, sK16: ($i > ($i > $i) > $i > $i > $o)).
% 5.11/1.20 thf(func_def_149, type, sK17: ($i > $i > $i)).
% 5.11/1.20 thf(func_def_150, type, sK18: ($i > $i > $i)).
% 5.11/1.20 thf(func_def_151, type, sK19: ($i > $i > $i > $o)).
% 5.11/1.20 thf(func_def_152, type, sK20: ($i > $i > $i)).
% 5.11/1.20 thf(func_def_153, type, sK21: ($i > $i > $i)).
% 5.11/1.20 thf(func_def_154, type, sK22: ($o > $o > $o)).
% 5.11/1.20 thf(func_def_155, type, sK23: ($o > $o > $o)).
% 5.11/1.20 thf(func_def_157, type, sK25: ($i > $i)).
% 5.11/1.20 thf(func_def_158, type, sK26: ((($i > $i > $i) > $i) > $i > $i > $i)).
% 5.11/1.20 thf(func_def_159, type, sK27: ((($i > $i > $i) > $i) > $i > $i > $i)).
% 5.11/1.20 thf(func_def_160, type, sK28: ((($i > $i > $i) > $i) > $i > $i > $i)).
% 5.11/1.20 thf(func_def_161, type, sK29: ((($i > $i > $i) > $i) > $i > $i > $i)).
% 5.11/1.20 thf(func_def_162, type, sK30: ((($i > $i > $i) > $i) > $i > $i > $i)).
% 5.11/1.20 thf(func_def_163, type, sK31: ((($i > $i > $i) > $i) > $i > $i > $i)).
% 5.11/1.20 thf(func_def_164, type, sK32: ((($i > $i > $i) > $i) > $i > $i > $i)).
% 5.11/1.20 thf(func_def_165, type, sK33: (($i > $o) > $i > $i)).
% 5.11/1.20 thf(func_def_166, type, sK34: (($i > $o) > $i > $i)).
% 5.11/1.20 thf(func_def_167, type, sK35: (($i > $i) > $i)).
% 5.11/1.20 thf(func_def_168, type, sK36: (($i > $i) > $i)).
% 5.11/1.20 thf(func_def_169, type, sK37: ($i > ($i > $o) > $i)).
% 5.11/1.20 thf(f1,axiom,(
% 5.11/1.20 ! [X0 : ($i > $o),X1 : $i] : ((X0 @ X1) => (X0 @ (c_Eps_i @ X0)))),
% 5.11/1.20 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1)).
% 5.11/1.20 thf(f5,axiom,(
% 5.11/1.20 (c_not @ ? [X0 : $i] : (c_In @ X0 @ c_Empty))),
% 5.11/1.20 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax5)).
% 5.11/1.20 thf(f6,axiom,(
% 5.11/1.20 ! [X0 : $i,X1 : $i] : (c_iff @ (c_In @ X1 @ (c_Union @ X0)) @ ? [X2 : $i] : (c_and @ (c_In @ X1 @ X2) @ (c_In @ X2 @ X0)))),
% 5.11/1.20 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax6)).
% 5.11/1.20 thf(f7,axiom,(
% 5.11/1.20 ! [X0 : $i,X1 : $i] : (c_iff @ (c_In @ X1 @ (c_Power @ X0)) @ (c_Subq @ X1 @ X0))),
% 5.11/1.20 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax7)).
% 5.11/1.20 thf(f13,axiom,(
% 5.11/1.20 (c_not = (^[X0 : $o] : (X0 => c_False)))),
% 5.11/1.20 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax13)).
% 5.11/1.20 thf(f14,axiom,(
% 5.11/1.20 (c_and = (^[X0 : $o, X1 : $o] : (! [X2 : $o] : ((X0 => (X1 => X2)) => X2))))),
% 5.11/1.20 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax14)).
% 5.11/1.20 thf(f15,axiom,(
% 5.11/1.20 (c_or = (^[X0 : $o, X1 : $o] : (! [X2 : $o] : ((X0 => X2) => ((X1 => X2) => X2)))))),
% 5.11/1.20 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax15)).
% 5.11/1.20 thf(f16,axiom,(
% 5.11/1.20 (c_iff = (^[X0 : $o, X1 : $o] : ((c_and @ X0 => X1 @ X1 => X0))))),
% 5.11/1.20 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax16)).
% 5.11/1.20 thf(f17,axiom,(
% 5.11/1.20 (c_Subq = (^[X0 : $i, X1 : $i] : (! [X2 : $i] : ((c_In @ X2 @ X0) => (c_In @ X2 @ X1)))))),
% 5.11/1.20 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax17)).
% 5.11/1.20 thf(f42,axiom,(
% 5.11/1.20 (c_If_i = (^[X0 : $o, X1 : $i, X2 : $i] : ((c_Eps_i @ (^[X3 : $i] : ((c_or @ (c_and @ X0 @ (X3 = X1)) @ (c_and @ (c_not @ X0) @ (X3 = X2)))))))))),
% 5.11/1.20 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax42)).
% 5.11/1.20 thf(f47,axiom,(
% 5.11/1.20 (c_UPair = (^[X0 : $i, X1 : $i] : ((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[X2 : $i] : ((c_If_i @ (c_In @ c_Empty @ X2) @ X0 @ X1)))))))),
% 5.11/1.20 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax47)).
% 5.11/1.20 thf(f48,axiom,(
% 5.11/1.20 (c_Sing = (^[X0 : $i] : ((c_UPair @ X0 @ X0))))),
% 5.11/1.20 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax48)).
% 5.11/1.20 thf(f49,axiom,(
% 5.11/1.20 (c_binunion = (^[X0 : $i, X1 : $i] : ((c_Union @ (c_UPair @ X0 @ X1)))))),
% 5.11/1.20 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax49)).
% 5.11/1.20 thf(f60,axiom,(
% 5.11/1.20 (c_In_rec_poly_G_i = (^[X0 : ($i > ($i > $i) > $i), X1 : $i, X2 : $i] : (! [X3 : ($i > $i > $o)] : (! [X4 : $i,X5 : ($i > $i)] : (! [X6 : $i] : ((c_In @ X6 @ X4) => (X3 @ X6 @ (X5 @ X6))) => (X3 @ X4 @ (X0 @ X4 @ X5))) => (X3 @ X1 @ X2)))))),
% 5.11/1.20 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax60)).
% 5.11/1.20 thf(f61,axiom,(
% 5.11/1.20 (c_In_rec_poly_i = (^[X0 : ($i > ($i > $i) > $i), X1 : $i] : ((c_Eps_i @ (^[X2 : $i] : ((c_In_rec_poly_G_i @ X0 @ X1 @ X2)))))))),
% 5.11/1.20 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax61)).
% 5.11/1.20 thf(f69,axiom,(
% 5.11/1.20 (c_Inj1 = ((c_In_rec_poly_i @ (^[X0 : $i, X1 : ($i > $i)] : ((c_binunion @ (c_Sing @ c_Empty) @ (c_Repl @ X0 @ (^[X2 : $i] : ((X1 @ X2))))))))))),
% 5.11/1.20 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax69)).
% 5.11/1.20 thf(f70,axiom,(
% 5.11/1.20 (c_Inj0 = (^[X0 : $i] : ((c_Repl @ X0 @ (^[X1 : $i] : ((c_Inj1 @ X1)))))))),
% 5.11/1.20 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax70)).
% 5.11/1.20 thf(f73,axiom,(
% 5.11/1.20 (c_setsum = (^[X0 : $i, X1 : $i] : ((c_binunion @ (c_Repl @ X0 @ (^[X2 : $i] : ((c_Inj0 @ X2)))) @ (c_Repl @ X1 @ (^[X2 : $i] : ((c_Inj1 @ X2))))))))),
% 5.11/1.20 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax73)).
% 5.11/1.20 thf(f109,conjecture,(
% 5.11/1.20 ! [X0 : (($i > $i > $i > $i) > ($i > $i) > (($i > $i > $i) > $i) > $i),X1 : (($i > $i) > $i > $i),X2 : (((($i > $i > $i > $i) > $i) > $i > $i) > $i > $i),X3 : (($i > $i) > ($i > $i) > $i)] : (! [X4 : ($i > (($i > $i) > $i) > $i),X5 : (($i > $i) > $i),X6 : ((($i > $i > $i) > ($i > $i) > $i) > $i),X7 : $i] : (((X3 @ (^[X8 : $i] : ((c_Inj1 @ c_Empty))) @ (^[X8 : $i] : ((c_setsum @ c_Empty @ c_Empty))))) = ((c_Inj1 @ c_Empty))) => (! [X4 : $i,X5 : $i,X6 : $i,X7 : $i] : (((X3 @ (^[X8 : $i] : (X6)) @ (^[X8 : $i] : (X7)))) = ((c_setsum @ (X2 @ (^[X8 : (($i > $i > $i > $i) > $i), X9 : $i] : (c_Empty)) @ (X0 @ (^[X8 : $i, X9 : $i, X10 : $i] : ((X3 @ (^[X11 : $i] : (X10)) @ (^[X11 : $i] : (c_Empty))))) @ (^[X8 : $i] : (c_Empty)) @ (^[X8 : ($i > $i > $i)] : (c_Empty)))) @ c_Empty))) => (! [X4 : ($i > $i),X5 : ($i > $i > $i),X6 : ($i > $i),X7 : $i] : (((X2 @ (^[X8 : (($i > $i > $i > $i) > $i), X9 : $i] : (X7)) @ c_Empty)) = X7) => (! [X4 : ($i > ($i > $i > $i) > $i),X5 : ($i > $i),X6 : (((($i > $i) > $i) > $i) > $i),X7 : ($i > $i)] : (((X2 @ (^[X8 : (($i > $i > $i > $i) > $i), X9 : $i] : ((X7 @ (X2 @ (^[X10 : (($i > $i > $i > $i) > $i), X11 : $i] : ((X0 @ (^[X12 : $i, X13 : $i, X14 : $i] : ((c_Inj1 @ c_Empty))) @ (^[X12 : $i] : ((c_Inj0 @ c_Empty))) @ (^[X12 : ($i > $i > $i)] : ((X3 @ (^[X13 : $i] : (c_Empty)) @ (^[X13 : $i] : (c_Empty)))))))) @ (c_Inj0 @ (X0 @ (^[X10 : $i, X11 : $i, X12 : $i] : (c_Empty)) @ (^[X10 : $i] : (c_Empty)) @ (^[X10 : ($i > $i > $i)] : (c_Empty)))))))) @ (X3 @ (^[X8 : $i] : ((c_setsum @ X8 @ c_Empty))) @ (^[X8 : $i] : (c_Empty))))) = ((c_setsum @ (X7 @ (X5 @ (X0 @ (^[X8 : $i, X9 : $i, X10 : $i] : ((c_Inj1 @ c_Empty))) @ (^[X8 : $i] : ((X0 @ (^[X9 : $i, X10 : $i, X11 : $i] : (c_Empty)) @ (^[X9 : $i] : (c_Empty)) @ (^[X9 : ($i > $i > $i)] : (c_Empty))))) @ (^[X8 : ($i > $i > $i)] : ((c_setsum @ c_Empty @ c_Empty)))))) @ (X1 @ (^[X8 : $i] : ((X7 @ c_Empty))) @ (X5 @ (X4 @ (X1 @ (^[X8 : $i] : (c_Empty)) @ c_Empty) @ (^[X8 : $i, X9 : $i] : (c_Empty)))))))) => (! [X4 : ((($i > $i) > $i > $i) > $i),X5 : $i,X6 : $i,X7 : $i] : (((X1 @ (^[X8 : $i] : ((c_Inj1 @ (X1 @ (^[X9 : $i] : ((c_Inj0 @ (X0 @ (^[X10 : $i, X11 : $i, X12 : $i] : (c_Empty)) @ (^[X10 : $i] : (c_Empty)) @ (^[X10 : ($i > $i > $i)] : (c_Empty)))))) @ (c_Inj1 @ X7))))) @ (c_Inj0 @ (X2 @ (^[X8 : (($i > $i > $i > $i) > $i), X9 : $i] : (X9)) @ X5)))) = ((c_Inj0 @ (X2 @ (^[X8 : (($i > $i > $i > $i) > $i), X9 : $i] : (X7)) @ (c_setsum @ c_Empty @ c_Empty))))) => (! [X4 : ((($i > $i) > $i) > $i),X5 : ($i > $i > ($i > $i) > $i),X6 : $i,X7 : (($i > $i) > ($i > $i) > $i)] : (((X1 @ (^[X8 : $i] : ((X7 @ (^[X9 : $i] : ((c_setsum @ X9 @ X8))) @ (^[X9 : $i] : (c_Empty))))) @ c_Empty)) = ((X7 @ (^[X8 : $i] : ((c_setsum @ (X2 @ (^[X9 : (($i > $i > $i > $i) > $i), X10 : $i] : (c_Empty)) @ (X3 @ (^[X9 : $i] : ((X2 @ (^[X10 : (($i > $i > $i > $i) > $i), X11 : $i] : (c_Empty)) @ c_Empty))) @ (^[X9 : $i] : ((X1 @ (^[X10 : $i] : (c_Empty)) @ c_Empty))))) @ (X2 @ (^[X9 : (($i > $i > $i > $i) > $i), X10 : $i] : (c_Empty)) @ (X2 @ (^[X9 : (($i > $i > $i > $i) > $i), X10 : $i] : ((c_setsum @ c_Empty @ c_Empty))) @ (X2 @ (^[X9 : (($i > $i > $i > $i) > $i), X10 : $i] : (c_Empty)) @ c_Empty)))))) @ (^[X8 : $i] : ((c_Inj1 @ (X1 @ (^[X9 : $i] : ((X7 @ (^[X10 : $i] : ((X1 @ (^[X11 : $i] : (c_Empty)) @ c_Empty))) @ (^[X10 : $i] : ((c_Inj1 @ c_Empty)))))) @ X6))))))) => (! [X4 : ($i > (($i > $i) > $i > $i) > $i),X5 : $i,X6 : $i,X7 : $i] : (((X0 @ (^[X8 : $i, X9 : $i, X10 : $i] : (X7)) @ (^[X8 : $i] : (X6)) @ (^[X8 : ($i > $i > $i)] : (c_Empty)))) = X6) => (! [X4 : $i,X5 : $i,X6 : ($i > ($i > $i) > $i),X7 : ($i > $i)] : (((X0 @ (^[X8 : $i, X9 : $i, X10 : $i] : ((X1 @ (^[X11 : $i] : ((X2 @ (^[X12 : (($i > $i > $i > $i) > $i), X13 : $i] : (X10)) @ (X2 @ (^[X12 : (($i > $i > $i > $i) > $i), X13 : $i] : ((c_setsum @ c_Empty @ c_Empty))) @ X11)))) @ (c_Inj1 @ c_Empty)))) @ (^[X8 : $i] : ((X7 @ c_Empty))) @ (^[X8 : ($i > $i > $i)] : (c_Empty)))) = ((X7 @ X4))) => c_False))))))))),
% 5.11/1.20 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj)).
% 5.11/1.20 thf(f110,negated_conjecture,(
% 5.11/1.20 ~ ! [X0 : (($i > $i > $i > $i) > ($i > $i) > (($i > $i > $i) > $i) > $i),X1 : (($i > $i) > $i > $i),X2 : (((($i > $i > $i > $i) > $i) > $i > $i) > $i > $i),X3 : (($i > $i) > ($i > $i) > $i)] : (! [X4 : ($i > (($i > $i) > $i) > $i),X5 : (($i > $i) > $i),X6 : ((($i > $i > $i) > ($i > $i) > $i) > $i),X7 : $i] : (((X3 @ (^[X8 : $i] : ((c_Inj1 @ c_Empty))) @ (^[X8 : $i] : ((c_setsum @ c_Empty @ c_Empty))))) = ((c_Inj1 @ c_Empty))) => (! [X4 : $i,X5 : $i,X6 : $i,X7 : $i] : (((X3 @ (^[X8 : $i] : (X6)) @ (^[X8 : $i] : (X7)))) = ((c_setsum @ (X2 @ (^[X8 : (($i > $i > $i > $i) > $i), X9 : $i] : (c_Empty)) @ (X0 @ (^[X8 : $i, X9 : $i, X10 : $i] : ((X3 @ (^[X11 : $i] : (X10)) @ (^[X11 : $i] : (c_Empty))))) @ (^[X8 : $i] : (c_Empty)) @ (^[X8 : ($i > $i > $i)] : (c_Empty)))) @ c_Empty))) => (! [X4 : ($i > $i),X5 : ($i > $i > $i),X6 : ($i > $i),X7 : $i] : (((X2 @ (^[X8 : (($i > $i > $i > $i) > $i), X9 : $i] : (X7)) @ c_Empty)) = X7) => (! [X4 : ($i > ($i > $i > $i) > $i),X5 : ($i > $i),X6 : (((($i > $i) > $i) > $i) > $i),X7 : ($i > $i)] : (((X2 @ (^[X8 : (($i > $i > $i > $i) > $i), X9 : $i] : ((X7 @ (X2 @ (^[X10 : (($i > $i > $i > $i) > $i), X11 : $i] : ((X0 @ (^[X12 : $i, X13 : $i, X14 : $i] : ((c_Inj1 @ c_Empty))) @ (^[X12 : $i] : ((c_Inj0 @ c_Empty))) @ (^[X12 : ($i > $i > $i)] : ((X3 @ (^[X13 : $i] : (c_Empty)) @ (^[X13 : $i] : (c_Empty)))))))) @ (c_Inj0 @ (X0 @ (^[X10 : $i, X11 : $i, X12 : $i] : (c_Empty)) @ (^[X10 : $i] : (c_Empty)) @ (^[X10 : ($i > $i > $i)] : (c_Empty)))))))) @ (X3 @ (^[X8 : $i] : ((c_setsum @ X8 @ c_Empty))) @ (^[X8 : $i] : (c_Empty))))) = ((c_setsum @ (X7 @ (X5 @ (X0 @ (^[X8 : $i, X9 : $i, X10 : $i] : ((c_Inj1 @ c_Empty))) @ (^[X8 : $i] : ((X0 @ (^[X9 : $i, X10 : $i, X11 : $i] : (c_Empty)) @ (^[X9 : $i] : (c_Empty)) @ (^[X9 : ($i > $i > $i)] : (c_Empty))))) @ (^[X8 : ($i > $i > $i)] : ((c_setsum @ c_Empty @ c_Empty)))))) @ (X1 @ (^[X8 : $i] : ((X7 @ c_Empty))) @ (X5 @ (X4 @ (X1 @ (^[X8 : $i] : (c_Empty)) @ c_Empty) @ (^[X8 : $i, X9 : $i] : (c_Empty)))))))) => (! [X4 : ((($i > $i) > $i > $i) > $i),X5 : $i,X6 : $i,X7 : $i] : (((X1 @ (^[X8 : $i] : ((c_Inj1 @ (X1 @ (^[X9 : $i] : ((c_Inj0 @ (X0 @ (^[X10 : $i, X11 : $i, X12 : $i] : (c_Empty)) @ (^[X10 : $i] : (c_Empty)) @ (^[X10 : ($i > $i > $i)] : (c_Empty)))))) @ (c_Inj1 @ X7))))) @ (c_Inj0 @ (X2 @ (^[X8 : (($i > $i > $i > $i) > $i), X9 : $i] : (X9)) @ X5)))) = ((c_Inj0 @ (X2 @ (^[X8 : (($i > $i > $i > $i) > $i), X9 : $i] : (X7)) @ (c_setsum @ c_Empty @ c_Empty))))) => (! [X4 : ((($i > $i) > $i) > $i),X5 : ($i > $i > ($i > $i) > $i),X6 : $i,X7 : (($i > $i) > ($i > $i) > $i)] : (((X1 @ (^[X8 : $i] : ((X7 @ (^[X9 : $i] : ((c_setsum @ X9 @ X8))) @ (^[X9 : $i] : (c_Empty))))) @ c_Empty)) = ((X7 @ (^[X8 : $i] : ((c_setsum @ (X2 @ (^[X9 : (($i > $i > $i > $i) > $i), X10 : $i] : (c_Empty)) @ (X3 @ (^[X9 : $i] : ((X2 @ (^[X10 : (($i > $i > $i > $i) > $i), X11 : $i] : (c_Empty)) @ c_Empty))) @ (^[X9 : $i] : ((X1 @ (^[X10 : $i] : (c_Empty)) @ c_Empty))))) @ (X2 @ (^[X9 : (($i > $i > $i > $i) > $i), X10 : $i] : (c_Empty)) @ (X2 @ (^[X9 : (($i > $i > $i > $i) > $i), X10 : $i] : ((c_setsum @ c_Empty @ c_Empty))) @ (X2 @ (^[X9 : (($i > $i > $i > $i) > $i), X10 : $i] : (c_Empty)) @ c_Empty)))))) @ (^[X8 : $i] : ((c_Inj1 @ (X1 @ (^[X9 : $i] : ((X7 @ (^[X10 : $i] : ((X1 @ (^[X11 : $i] : (c_Empty)) @ c_Empty))) @ (^[X10 : $i] : ((c_Inj1 @ c_Empty)))))) @ X6))))))) => (! [X4 : ($i > (($i > $i) > $i > $i) > $i),X5 : $i,X6 : $i,X7 : $i] : (((X0 @ (^[X8 : $i, X9 : $i, X10 : $i] : (X7)) @ (^[X8 : $i] : (X6)) @ (^[X8 : ($i > $i > $i)] : (c_Empty)))) = X6) => (! [X4 : $i,X5 : $i,X6 : ($i > ($i > $i) > $i),X7 : ($i > $i)] : (((X0 @ (^[X8 : $i, X9 : $i, X10 : $i] : ((X1 @ (^[X11 : $i] : ((X2 @ (^[X12 : (($i > $i > $i > $i) > $i), X13 : $i] : (X10)) @ (X2 @ (^[X12 : (($i > $i > $i > $i) > $i), X13 : $i] : ((c_setsum @ c_Empty @ c_Empty))) @ X11)))) @ (c_Inj1 @ c_Empty)))) @ (^[X8 : $i] : ((X7 @ c_Empty))) @ (^[X8 : ($i > $i > $i)] : (c_Empty)))) = ((X7 @ X4))) => c_False))))))))),
% 5.11/1.20 inference(negated_conjecture,[status(cth)],[f109])).
% 5.11/1.20 thf(f111,plain,(
% 5.11/1.20 ! [X0 : ($i > $o),X1 : $i] : ((X0 @ X1) => (X0 @ (c_Eps_i @ X0)))),
% 5.11/1.20 inference(rectify,[],[f1])).
% 5.11/1.20 thf(f112,plain,(
% 5.11/1.20 ! [X0 : ($i > $o),X1 : $i] : ((((X0 @ X1)) = $true) => (((X0 @ (c_Eps_i @ X0))) = $true))),
% 5.11/1.20 inference(fool_elimination,[],[f111])).
% 5.11/1.20 thf(f119,plain,(
% 5.11/1.20 (c_not @ ? [X0 : $i] : (c_In @ X0 @ c_Empty))),
% 5.11/1.20 inference(rectify,[],[f5])).
% 5.11/1.20 thf(f120,plain,(
% 5.11/1.20 ($true = ((c_not @ (?? @ $i @ (^[Y0 : $i]: (c_In @ Y0 @ c_Empty))))))),
% 5.11/1.20 inference(fool_elimination,[],[f119])).
% 5.11/1.20 thf(f121,plain,(
% 5.11/1.20 ! [X0 : $i,X1 : $i] : (c_iff @ (c_In @ X1 @ (c_Union @ X0)) @ ? [X2 : $i] : (c_and @ (c_In @ X1 @ X2) @ (c_In @ X2 @ X0)))),
% 5.11/1.20 inference(rectify,[],[f6])).
% 5.11/1.20 thf(f122,plain,(
% 5.11/1.20 ! [X0 : $i,X1 : $i] : ($true = ((c_iff @ (c_In @ X1 @ (c_Union @ X0)) @ (?? @ $i @ (^[Y0 : $i]: (c_and @ (c_In @ X1 @ Y0) @ (c_In @ Y0 @ X0)))))))),
% 5.11/1.20 inference(fool_elimination,[],[f121])).
% 5.11/1.20 thf(f123,plain,(
% 5.11/1.20 ! [X0 : $i,X1 : $i] : (c_iff @ (c_In @ X1 @ (c_Power @ X0)) @ (c_Subq @ X1 @ X0))),
% 5.11/1.20 inference(rectify,[],[f7])).
% 5.11/1.20 thf(f124,plain,(
% 5.11/1.20 ! [X0 : $i,X1 : $i] : (((c_iff @ (c_In @ X1 @ (c_Power @ X0)) @ (c_Subq @ X1 @ X0))) = $true)),
% 5.11/1.20 inference(fool_elimination,[],[f123])).
% 5.11/1.20 thf(f135,plain,(
% 5.11/1.20 (c_not = (^[X0 : $o] : (X0 => c_False)))),
% 5.11/1.20 inference(rectify,[],[f13])).
% 5.11/1.20 thf(f136,plain,(
% 5.11/1.20 (c_not = (^[Y0 : $o]: (Y0 => c_False)))),
% 5.11/1.20 inference(fool_elimination,[],[f135])).
% 5.11/1.20 thf(f137,plain,(
% 5.11/1.20 (c_and = (^[X0 : $o, X1 : $o] : (! [X2 : $o] : ((X0 => (X1 => X2)) => X2))))),
% 5.11/1.20 inference(rectify,[],[f14])).
% 5.11/1.20 thf(f138,plain,(
% 5.11/1.20 (c_and = (^[Y0 : $o]: ((^[Y1 : $o]: (!! @ $o @ (^[Y2 : $o]: ((Y0 => (Y1 => Y2)) => Y2)))))))),
% 5.11/1.20 inference(fool_elimination,[],[f137])).
% 5.11/1.20 thf(f139,plain,(
% 5.11/1.20 (c_or = (^[X0 : $o, X1 : $o] : (! [X2 : $o] : ((X0 => X2) => ((X1 => X2) => X2)))))),
% 5.11/1.20 inference(rectify,[],[f15])).
% 5.11/1.20 thf(f140,plain,(
% 5.11/1.20 (c_or = (^[Y0 : $o]: ((^[Y1 : $o]: (!! @ $o @ (^[Y2 : $o]: ((Y0 => Y2) => ((Y1 => Y2) => Y2))))))))),
% 5.11/1.20 inference(fool_elimination,[],[f139])).
% 5.11/1.20 thf(f141,plain,(
% 5.11/1.20 (c_iff = (^[X0 : $o, X1 : $o] : ((c_and @ X0 => X1 @ X1 => X0))))),
% 5.11/1.20 inference(rectify,[],[f16])).
% 5.11/1.20 thf(f142,plain,(
% 5.11/1.20 (c_iff = (^[Y0 : $o]: ((^[Y1 : $o]: (c_and @ (Y0 => Y1) @ (Y1 => Y0))))))),
% 5.11/1.20 inference(fool_elimination,[],[f141])).
% 5.11/1.20 thf(f143,plain,(
% 5.11/1.20 (c_Subq = (^[X0 : $i, X1 : $i] : (! [X2 : $i] : ((c_In @ X2 @ X0) => (c_In @ X2 @ X1)))))),
% 5.11/1.20 inference(rectify,[],[f17])).
% 5.11/1.20 thf(f144,plain,(
% 5.11/1.20 (c_Subq = (^[Y0 : $i]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ Y2 @ Y0) => (c_In @ Y2 @ Y1))))))))),
% 5.11/1.20 inference(fool_elimination,[],[f143])).
% 5.11/1.20 thf(f183,plain,(
% 5.11/1.20 (c_If_i = (^[X0 : $o, X1 : $i, X2 : $i] : ((c_Eps_i @ (^[X3 : $i] : ((c_or @ (c_and @ X0 @ (X3 = X1)) @ (c_and @ (c_not @ X0) @ (X3 = X2)))))))))),
% 5.11/1.20 inference(rectify,[],[f42])).
% 5.11/1.20 thf(f184,plain,(
% 5.11/1.20 (c_If_i = (^[Y0 : $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (c_Eps_i @ (^[Y3 : $i]: (c_or @ (c_and @ Y0 @ (Y1 = Y3)) @ (c_and @ (c_not @ Y0) @ (Y2 = Y3)))))))))))),
% 5.11/1.20 inference(fool_elimination,[],[f183])).
% 5.11/1.20 thf(f189,plain,(
% 5.11/1.20 (c_UPair = (^[X0 : $i, X1 : $i] : ((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[X2 : $i] : ((c_If_i @ (c_In @ c_Empty @ X2) @ X0 @ X1)))))))),
% 5.11/1.20 inference(rectify,[],[f47])).
% 5.11/1.20 thf(f190,plain,(
% 5.11/1.20 (c_UPair = (^[Y0 : $i]: ((^[Y1 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y2 : $i]: (c_If_i @ (c_In @ c_Empty @ Y2) @ Y0 @ Y1)))))))),
% 5.11/1.20 inference(fool_elimination,[],[f189])).
% 5.11/1.20 thf(f191,plain,(
% 5.11/1.20 (c_Sing = (^[Y0 : $i]: (c_UPair @ Y0 @ Y0)))),
% 5.11/1.20 inference(fool_elimination,[],[f48])).
% 5.11/1.20 thf(f192,plain,(
% 5.11/1.20 (c_binunion = (^[Y0 : $i]: ((^[Y1 : $i]: (c_Union @ (c_UPair @ Y0 @ Y1))))))),
% 5.11/1.20 inference(fool_elimination,[],[f49])).
% 5.11/1.20 thf(f212,plain,(
% 5.11/1.20 (c_In_rec_poly_G_i = (^[X0 : ($i > ($i > $i) > $i), X1 : $i, X2 : $i] : (! [X3 : ($i > $i > $o)] : (! [X4 : $i,X5 : ($i > $i)] : (! [X6 : $i] : ((c_In @ X6 @ X4) => (X3 @ X6 @ (X5 @ X6))) => (X3 @ X4 @ (X0 @ X4 @ X5))) => (X3 @ X1 @ X2)))))),
% 5.11/1.20 inference(rectify,[],[f60])).
% 5.11/1.20 thf(f213,plain,(
% 5.11/1.20 (c_In_rec_poly_G_i = (^[Y0 : $i > ($i > $i) > $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y4 : $i > $i]: (!! @ $i @ (^[Y5 : $i]: ((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y5) => (Y3 @ Y6 @ (Y4 @ Y6))))) => (Y3 @ Y5 @ (Y0 @ Y5 @ Y4))))))) => (Y3 @ Y1 @ Y2))))))))))),
% 5.11/1.20 inference(fool_elimination,[],[f212])).
% 5.11/1.20 thf(f214,plain,(
% 5.11/1.20 (c_In_rec_poly_i = (^[X0 : ($i > ($i > $i) > $i), X1 : $i] : ((c_Eps_i @ (^[X2 : $i] : ((c_In_rec_poly_G_i @ X0 @ X1 @ X2)))))))),
% 5.11/1.20 inference(rectify,[],[f61])).
% 5.11/1.20 thf(f215,plain,(
% 5.11/1.20 (c_In_rec_poly_i = (^[Y0 : $i > ($i > $i) > $i]: ((^[Y1 : $i]: (c_Eps_i @ (^[Y2 : $i]: (c_In_rec_poly_G_i @ Y0 @ Y1 @ Y2)))))))),
% 5.11/1.20 inference(fool_elimination,[],[f214])).
% 5.11/1.20 thf(f229,plain,(
% 5.11/1.20 (c_Inj1 = ((c_In_rec_poly_i @ (^[X0 : $i, X1 : ($i > $i)] : ((c_binunion @ (c_Sing @ c_Empty) @ (c_Repl @ X0 @ (^[X2 : $i] : ((X1 @ X2))))))))))),
% 5.11/1.20 inference(rectify,[],[f69])).
% 5.11/1.20 thf(f230,plain,(
% 5.11/1.20 (c_Inj1 = ((c_In_rec_poly_i @ (^[Y0 : $i]: ((^[Y1 : $i > $i]: (c_binunion @ (c_Sing @ c_Empty) @ (c_Repl @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))))),
% 5.11/1.20 inference(fool_elimination,[],[f229])).
% 5.11/1.20 thf(f231,plain,(
% 5.11/1.20 (c_Inj0 = (^[X0 : $i] : ((c_Repl @ X0 @ (^[X1 : $i] : ((c_Inj1 @ X1)))))))),
% 5.11/1.20 inference(rectify,[],[f70])).
% 5.11/1.20 thf(f232,plain,(
% 5.11/1.20 (c_Inj0 = (^[Y0 : $i]: (c_Repl @ Y0 @ (^[Y1 : $i]: (c_Inj1 @ Y1)))))),
% 5.11/1.20 inference(fool_elimination,[],[f231])).
% 5.11/1.20 thf(f237,plain,(
% 5.11/1.20 (c_setsum = (^[X0 : $i, X1 : $i] : ((c_binunion @ (c_Repl @ X0 @ (^[X2 : $i] : ((c_Inj0 @ X2)))) @ (c_Repl @ X1 @ (^[X3 : $i] : ((c_Inj1 @ X3))))))))),
% 5.11/1.20 inference(rectify,[],[f73])).
% 5.11/1.20 thf(f238,plain,(
% 5.11/1.20 (c_setsum = (^[Y0 : $i]: ((^[Y1 : $i]: (c_binunion @ (c_Repl @ Y0 @ (^[Y2 : $i]: (c_Inj0 @ Y2))) @ (c_Repl @ Y1 @ (^[Y2 : $i]: (c_Inj1 @ Y2))))))))),
% 5.11/1.20 inference(fool_elimination,[],[f237])).
% 5.11/1.20 thf(f306,plain,(
% 5.11/1.20 ~ ! [X0 : (($i > $i > $i > $i) > ($i > $i) > (($i > $i > $i) > $i) > $i),X1 : (($i > $i) > $i > $i),X2 : (((($i > $i > $i > $i) > $i) > $i > $i) > $i > $i),X3 : (($i > $i) > ($i > $i) > $i)] : ((((X3 @ (^[X8 : $i] : ((c_Inj1 @ c_Empty))) @ (^[X9 : $i] : ((c_setsum @ c_Empty @ c_Empty))))) = ((c_Inj1 @ c_Empty))) => (! [X12 : $i,X13 : $i] : (((X3 @ (^[X14 : $i] : (X12)) @ (^[X15 : $i] : (X13)))) = ((c_setsum @ (X2 @ (^[X16 : (($i > $i > $i > $i) > $i), X17 : $i] : (c_Empty)) @ (X0 @ (^[X18 : $i, X19 : $i, X20 : $i] : ((X3 @ (^[X21 : $i] : (X20)) @ (^[X22 : $i] : (c_Empty))))) @ (^[X23 : $i] : (c_Empty)) @ (^[X24 : ($i > $i > $i)] : (c_Empty)))) @ c_Empty))) => (! [X28 : $i] : (((X2 @ (^[X29 : (($i > $i > $i > $i) > $i), X30 : $i] : (X28)) @ c_Empty)) = X28) => (! [X31 : ($i > ($i > $i > $i) > $i),X32 : ($i > $i),X34 : ($i > $i)] : (((X2 @ (^[X35 : (($i > $i > $i > $i) > $i), X36 : $i] : ((X34 @ (X2 @ (^[X37 : (($i > $i > $i > $i) > $i), X38 : $i] : ((X0 @ (^[X39 : $i, X40 : $i, X41 : $i] : ((c_Inj1 @ c_Empty))) @ (^[X42 : $i] : ((c_Inj0 @ c_Empty))) @ (^[X43 : ($i > $i > $i)] : ((X3 @ (^[X44 : $i] : (c_Empty)) @ (^[X45 : $i] : (c_Empty)))))))) @ (c_Inj0 @ (X0 @ (^[X46 : $i, X47 : $i, X48 : $i] : (c_Empty)) @ (^[X49 : $i] : (c_Empty)) @ (^[X50 : ($i > $i > $i)] : (c_Empty)))))))) @ (X3 @ (^[X51 : $i] : ((c_setsum @ X51 @ c_Empty))) @ (^[X52 : $i] : (c_Empty))))) = ((c_setsum @ (X34 @ (X32 @ (X0 @ (^[X53 : $i, X54 : $i, X55 : $i] : ((c_Inj1 @ c_Empty))) @ (^[X56 : $i] : ((X0 @ (^[X57 : $i, X58 : $i, X59 : $i] : (c_Empty)) @ (^[X60 : $i] : (c_Empty)) @ (^[X61 : ($i > $i > $i)] : (c_Empty))))) @ (^[X62 : ($i > $i > $i)] : ((c_setsum @ c_Empty @ c_Empty)))))) @ (X1 @ (^[X63 : $i] : ((X34 @ c_Empty))) @ (X32 @ (X31 @ (X1 @ (^[X64 : $i] : (c_Empty)) @ c_Empty) @ (^[X65 : $i, X66 : $i] : (c_Empty)))))))) => (! [X68 : $i,X70 : $i] : (((X1 @ (^[X71 : $i] : ((c_Inj1 @ (X1 @ (^[X72 : $i] : ((c_Inj0 @ (X0 @ (^[X73 : $i, X74 : $i, X75 : $i] : (c_Empty)) @ (^[X76 : $i] : (c_Empty)) @ (^[X77 : ($i > $i > $i)] : (c_Empty)))))) @ (c_Inj1 @ X70))))) @ (c_Inj0 @ (X2 @ (^[X78 : (($i > $i > $i > $i) > $i), X79 : $i] : (X79)) @ X68)))) = ((c_Inj0 @ (X2 @ (^[X80 : (($i > $i > $i > $i) > $i), X81 : $i] : (X70)) @ (c_setsum @ c_Empty @ c_Empty))))) => (! [X84 : $i,X85 : (($i > $i) > ($i > $i) > $i)] : (((X1 @ (^[X86 : $i] : ((X85 @ (^[X87 : $i] : ((c_setsum @ X87 @ X86))) @ (^[X88 : $i] : (c_Empty))))) @ c_Empty)) = ((X85 @ (^[X89 : $i] : ((c_setsum @ (X2 @ (^[X90 : (($i > $i > $i > $i) > $i), X91 : $i] : (c_Empty)) @ (X3 @ (^[X92 : $i] : ((X2 @ (^[X93 : (($i > $i > $i > $i) > $i), X94 : $i] : (c_Empty)) @ c_Empty))) @ (^[X95 : $i] : ((X1 @ (^[X96 : $i] : (c_Empty)) @ c_Empty))))) @ (X2 @ (^[X97 : (($i > $i > $i > $i) > $i), X98 : $i] : (c_Empty)) @ (X2 @ (^[X99 : (($i > $i > $i > $i) > $i), X100 : $i] : ((c_setsum @ c_Empty @ c_Empty))) @ (X2 @ (^[X101 : (($i > $i > $i > $i) > $i), X102 : $i] : (c_Empty)) @ c_Empty)))))) @ (^[X103 : $i] : ((c_Inj1 @ (X1 @ (^[X104 : $i] : ((X85 @ (^[X105 : $i] : ((X1 @ (^[X106 : $i] : (c_Empty)) @ c_Empty))) @ (^[X107 : $i] : ((c_Inj1 @ c_Empty)))))) @ X84))))))) => (! [X110 : $i,X111 : $i] : (((X0 @ (^[X112 : $i, X113 : $i, X114 : $i] : (X111)) @ (^[X115 : $i] : (X110)) @ (^[X116 : ($i > $i > $i)] : (c_Empty)))) = X110) => (! [X117 : $i,X120 : ($i > $i)] : (((X0 @ (^[X121 : $i, X122 : $i, X123 : $i] : ((X1 @ (^[X124 : $i] : ((X2 @ (^[X125 : (($i > $i > $i > $i) > $i), X126 : $i] : (X123)) @ (X2 @ (^[X127 : (($i > $i > $i > $i) > $i), X128 : $i] : ((c_setsum @ c_Empty @ c_Empty))) @ X124)))) @ (c_Inj1 @ c_Empty)))) @ (^[X129 : $i] : ((X120 @ c_Empty))) @ (^[X130 : ($i > $i > $i)] : (c_Empty)))) = ((X120 @ X117))) => c_False))))))))),
% 5.11/1.20 inference(rectify,[],[f110])).
% 5.11/1.20 thf(f307,plain,(
% 5.11/1.20 ~ ! [X0 : (($i > $i > $i > $i) > ($i > $i) > (($i > $i > $i) > $i) > $i),X1 : (($i > $i) > $i > $i),X2 : (((($i > $i > $i > $i) > $i) > $i > $i) > $i > $i),X3 : (($i > $i) > ($i > $i) > $i)] : ((((c_Inj1 @ c_Empty)) = ((X3 @ (^[Y0 : $i]: (c_Inj1 @ c_Empty)) @ (^[Y0 : $i]: (c_setsum @ c_Empty @ c_Empty))))) => (! [X12 : $i,X13 : $i] : (((X3 @ (^[Y0 : $i]: (X12)) @ (^[Y0 : $i]: (X13)))) = ((c_setsum @ (X2 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (c_Empty)))) @ (X0 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (X3 @ (^[Y3 : $i]: (Y2)) @ (^[Y3 : $i]: (c_Empty)))))))) @ (^[Y0 : $i]: (c_Empty)) @ (^[Y0 : $i > $i > $i]: (c_Empty)))) @ c_Empty))) => (! [X28 : $i] : (((X2 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (X28)))) @ c_Empty)) = X28) => (! [X31 : ($i > ($i > $i > $i) > $i),X32 : ($i > $i),X34 : ($i > $i)] : (((X2 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (X34 @ (X2 @ (^[Y2 : ($i > $i > $i > $i) > $i]: ((^[Y3 : $i]: (X0 @ (^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (c_Inj1 @ c_Empty)))))) @ (^[Y4 : $i]: (c_Inj0 @ c_Empty)) @ (^[Y4 : $i > $i > $i]: (X3 @ (^[Y5 : $i]: (c_Empty)) @ (^[Y5 : $i]: (c_Empty)))))))) @ (c_Inj0 @ (X0 @ (^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (c_Empty)))))) @ (^[Y2 : $i]: (c_Empty)) @ (^[Y2 : $i > $i > $i]: (c_Empty))))))))) @ (X3 @ (^[Y0 : $i]: (c_setsum @ Y0 @ c_Empty)) @ (^[Y0 : $i]: (c_Empty))))) = ((c_setsum @ (X34 @ (X32 @ (X0 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (c_Inj1 @ c_Empty)))))) @ (^[Y0 : $i]: (X0 @ (^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: (c_Empty)))))) @ (^[Y1 : $i]: (c_Empty)) @ (^[Y1 : $i > $i > $i]: (c_Empty)))) @ (^[Y0 : $i > $i > $i]: (c_setsum @ c_Empty @ c_Empty))))) @ (X1 @ (^[Y0 : $i]: (X34 @ c_Empty)) @ (X32 @ (X31 @ (X1 @ (^[Y0 : $i]: (c_Empty)) @ c_Empty) @ (^[Y0 : $i]: ((^[Y1 : $i]: (c_Empty)))))))))) => (! [X68 : $i,X70 : $i] : (((X1 @ (^[Y0 : $i]: (c_Inj1 @ (X1 @ (^[Y1 : $i]: (c_Inj0 @ (X0 @ (^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (c_Empty)))))) @ (^[Y2 : $i]: (c_Empty)) @ (^[Y2 : $i > $i > $i]: (c_Empty))))) @ (c_Inj1 @ X70)))) @ (c_Inj0 @ (X2 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (Y1)))) @ X68)))) = ((c_Inj0 @ (X2 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (X70)))) @ (c_setsum @ c_Empty @ c_Empty))))) => (! [X84 : $i,X85 : (($i > $i) > ($i > $i) > $i)] : (((X1 @ (^[Y0 : $i]: (X85 @ (^[Y1 : $i]: (c_setsum @ Y1 @ Y0)) @ (^[Y1 : $i]: (c_Empty)))) @ c_Empty)) = ((X85 @ (^[Y0 : $i]: (c_setsum @ (X2 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_Empty)))) @ (X3 @ (^[Y1 : $i]: (X2 @ (^[Y2 : ($i > $i > $i > $i) > $i]: ((^[Y3 : $i]: (c_Empty)))) @ c_Empty)) @ (^[Y1 : $i]: (X1 @ (^[Y2 : $i]: (c_Empty)) @ c_Empty)))) @ (X2 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_Empty)))) @ (X2 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_setsum @ c_Empty @ c_Empty)))) @ (X2 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_Empty)))) @ c_Empty))))) @ (^[Y0 : $i]: (c_Inj1 @ (X1 @ (^[Y1 : $i]: (X85 @ (^[Y2 : $i]: (X1 @ (^[Y3 : $i]: (c_Empty)) @ c_Empty)) @ (^[Y2 : $i]: (c_Inj1 @ c_Empty)))) @ X84)))))) => (! [X110 : $i,X111 : $i] : (((X0 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (X111)))))) @ (^[Y0 : $i]: (X110)) @ (^[Y0 : $i > $i > $i]: (c_Empty)))) = X110) => (! [X117 : $i,X120 : ($i > $i)] : (((X120 @ X117)) = ((X0 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (X1 @ (^[Y3 : $i]: (X2 @ (^[Y4 : ($i > $i > $i > $i) > $i]: ((^[Y5 : $i]: (Y2)))) @ (X2 @ (^[Y4 : ($i > $i > $i > $i) > $i]: ((^[Y5 : $i]: (c_setsum @ c_Empty @ c_Empty)))) @ Y3))) @ (c_Inj1 @ c_Empty))))))) @ (^[Y0 : $i]: (X120 @ c_Empty)) @ (^[Y0 : $i > $i > $i]: (c_Empty))))) => (c_False = $true)))))))))),
% 5.11/1.20 inference(fool_elimination,[],[f306])).
% 5.11/1.20 thf(f309,plain,(
% 5.11/1.20 ~ ! [X0 : (($i > $i > $i > $i) > ($i > $i) > (($i > $i > $i) > $i) > $i),X1 : (($i > $i) > $i > $i),X2 : (((($i > $i > $i > $i) > $i) > $i > $i) > $i > $i),X3 : (($i > $i) > ($i > $i) > $i)] : ((((c_Inj1 @ c_Empty)) = ((X3 @ (^[Y0 : $i]: (c_Inj1 @ c_Empty)) @ (^[Y0 : $i]: (c_setsum @ c_Empty @ c_Empty))))) => (! [X4 : $i,X5 : $i] : (((c_setsum @ (X2 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (c_Empty)))) @ (X0 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (X3 @ (^[Y3 : $i]: (Y2)) @ (^[Y3 : $i]: (c_Empty)))))))) @ (^[Y0 : $i]: (c_Empty)) @ (^[Y0 : $i > $i > $i]: (c_Empty)))) @ c_Empty)) = ((X3 @ (^[Y0 : $i]: (X4)) @ (^[Y0 : $i]: (X5))))) => (! [X6 : $i] : (((X2 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (X6)))) @ c_Empty)) = X6) => (! [X7 : ($i > ($i > $i > $i) > $i),X8 : ($i > $i),X9 : ($i > $i)] : (((X2 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (X9 @ (X2 @ (^[Y2 : ($i > $i > $i > $i) > $i]: ((^[Y3 : $i]: (X0 @ (^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (c_Inj1 @ c_Empty)))))) @ (^[Y4 : $i]: (c_Inj0 @ c_Empty)) @ (^[Y4 : $i > $i > $i]: (X3 @ (^[Y5 : $i]: (c_Empty)) @ (^[Y5 : $i]: (c_Empty)))))))) @ (c_Inj0 @ (X0 @ (^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (c_Empty)))))) @ (^[Y2 : $i]: (c_Empty)) @ (^[Y2 : $i > $i > $i]: (c_Empty))))))))) @ (X3 @ (^[Y0 : $i]: (c_setsum @ Y0 @ c_Empty)) @ (^[Y0 : $i]: (c_Empty))))) = ((c_setsum @ (X9 @ (X8 @ (X0 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (c_Inj1 @ c_Empty)))))) @ (^[Y0 : $i]: (X0 @ (^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: (c_Empty)))))) @ (^[Y1 : $i]: (c_Empty)) @ (^[Y1 : $i > $i > $i]: (c_Empty)))) @ (^[Y0 : $i > $i > $i]: (c_setsum @ c_Empty @ c_Empty))))) @ (X1 @ (^[Y0 : $i]: (X9 @ c_Empty)) @ (X8 @ (X7 @ (X1 @ (^[Y0 : $i]: (c_Empty)) @ c_Empty) @ (^[Y0 : $i]: ((^[Y1 : $i]: (c_Empty)))))))))) => (! [X10 : $i,X11 : $i] : (((X1 @ (^[Y0 : $i]: (c_Inj1 @ (X1 @ (^[Y1 : $i]: (c_Inj0 @ (X0 @ (^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (c_Empty)))))) @ (^[Y2 : $i]: (c_Empty)) @ (^[Y2 : $i > $i > $i]: (c_Empty))))) @ (c_Inj1 @ X11)))) @ (c_Inj0 @ (X2 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (Y1)))) @ X10)))) = ((c_Inj0 @ (X2 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (X11)))) @ (c_setsum @ c_Empty @ c_Empty))))) => (! [X12 : $i,X13 : (($i > $i) > ($i > $i) > $i)] : (((X1 @ (^[Y0 : $i]: (X13 @ (^[Y1 : $i]: (c_setsum @ Y1 @ Y0)) @ (^[Y1 : $i]: (c_Empty)))) @ c_Empty)) = ((X13 @ (^[Y0 : $i]: (c_setsum @ (X2 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_Empty)))) @ (X3 @ (^[Y1 : $i]: (X2 @ (^[Y2 : ($i > $i > $i > $i) > $i]: ((^[Y3 : $i]: (c_Empty)))) @ c_Empty)) @ (^[Y1 : $i]: (X1 @ (^[Y2 : $i]: (c_Empty)) @ c_Empty)))) @ (X2 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_Empty)))) @ (X2 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_setsum @ c_Empty @ c_Empty)))) @ (X2 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_Empty)))) @ c_Empty))))) @ (^[Y0 : $i]: (c_Inj1 @ (X1 @ (^[Y1 : $i]: (X13 @ (^[Y2 : $i]: (X1 @ (^[Y3 : $i]: (c_Empty)) @ c_Empty)) @ (^[Y2 : $i]: (c_Inj1 @ c_Empty)))) @ X12)))))) => (! [X14 : $i,X15 : $i] : (((X0 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (X15)))))) @ (^[Y0 : $i]: (X14)) @ (^[Y0 : $i > $i > $i]: (c_Empty)))) = X14) => (! [X16 : $i,X17 : ($i > $i)] : (((X17 @ X16)) = ((X0 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (X1 @ (^[Y3 : $i]: (X2 @ (^[Y4 : ($i > $i > $i > $i) > $i]: ((^[Y5 : $i]: (Y2)))) @ (X2 @ (^[Y4 : ($i > $i > $i > $i) > $i]: ((^[Y5 : $i]: (c_setsum @ c_Empty @ c_Empty)))) @ Y3))) @ (c_Inj1 @ c_Empty))))))) @ (^[Y0 : $i]: (X17 @ c_Empty)) @ (^[Y0 : $i > $i > $i]: (c_Empty))))) => (c_False = $true)))))))))),
% 5.11/1.20 inference(rectify,[],[f307])).
% 5.11/1.20 thf(f310,plain,(
% 5.11/1.20 ! [X0 : ($i > $o),X1 : $i] : ((((X0 @ (c_Eps_i @ X0))) = $true) | (((X0 @ X1)) != $true))),
% 5.11/1.20 inference(ennf_transformation,[],[f112])).
% 5.11/1.20 thf(f318,plain,(
% 5.11/1.20 ? [X0 : (($i > $i > $i > $i) > ($i > $i) > (($i > $i > $i) > $i) > $i),X1 : (($i > $i) > $i > $i),X2 : (((($i > $i > $i > $i) > $i) > $i > $i) > $i > $i),X3 : (($i > $i) > ($i > $i) > $i)] : (((((((((c_False != $true) & ! [X16 : $i,X17 : ($i > $i)] : (((X17 @ X16)) = ((X0 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (X1 @ (^[Y3 : $i]: (X2 @ (^[Y4 : ($i > $i > $i > $i) > $i]: ((^[Y5 : $i]: (Y2)))) @ (X2 @ (^[Y4 : ($i > $i > $i > $i) > $i]: ((^[Y5 : $i]: (c_setsum @ c_Empty @ c_Empty)))) @ Y3))) @ (c_Inj1 @ c_Empty))))))) @ (^[Y0 : $i]: (X17 @ c_Empty)) @ (^[Y0 : $i > $i > $i]: (c_Empty)))))) & ! [X14 : $i,X15 : $i] : (((X0 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (X15)))))) @ (^[Y0 : $i]: (X14)) @ (^[Y0 : $i > $i > $i]: (c_Empty)))) = X14)) & ! [X12 : $i,X13 : (($i > $i) > ($i > $i) > $i)] : (((X1 @ (^[Y0 : $i]: (X13 @ (^[Y1 : $i]: (c_setsum @ Y1 @ Y0)) @ (^[Y1 : $i]: (c_Empty)))) @ c_Empty)) = ((X13 @ (^[Y0 : $i]: (c_setsum @ (X2 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_Empty)))) @ (X3 @ (^[Y1 : $i]: (X2 @ (^[Y2 : ($i > $i > $i > $i) > $i]: ((^[Y3 : $i]: (c_Empty)))) @ c_Empty)) @ (^[Y1 : $i]: (X1 @ (^[Y2 : $i]: (c_Empty)) @ c_Empty)))) @ (X2 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_Empty)))) @ (X2 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_setsum @ c_Empty @ c_Empty)))) @ (X2 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_Empty)))) @ c_Empty))))) @ (^[Y0 : $i]: (c_Inj1 @ (X1 @ (^[Y1 : $i]: (X13 @ (^[Y2 : $i]: (X1 @ (^[Y3 : $i]: (c_Empty)) @ c_Empty)) @ (^[Y2 : $i]: (c_Inj1 @ c_Empty)))) @ X12))))))) & ! [X10 : $i,X11 : $i] : (((X1 @ (^[Y0 : $i]: (c_Inj1 @ (X1 @ (^[Y1 : $i]: (c_Inj0 @ (X0 @ (^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (c_Empty)))))) @ (^[Y2 : $i]: (c_Empty)) @ (^[Y2 : $i > $i > $i]: (c_Empty))))) @ (c_Inj1 @ X11)))) @ (c_Inj0 @ (X2 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (Y1)))) @ X10)))) = ((c_Inj0 @ (X2 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (X11)))) @ (c_setsum @ c_Empty @ c_Empty)))))) & ! [X7 : ($i > ($i > $i > $i) > $i),X8 : ($i > $i),X9 : ($i > $i)] : (((X2 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (X9 @ (X2 @ (^[Y2 : ($i > $i > $i > $i) > $i]: ((^[Y3 : $i]: (X0 @ (^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (c_Inj1 @ c_Empty)))))) @ (^[Y4 : $i]: (c_Inj0 @ c_Empty)) @ (^[Y4 : $i > $i > $i]: (X3 @ (^[Y5 : $i]: (c_Empty)) @ (^[Y5 : $i]: (c_Empty)))))))) @ (c_Inj0 @ (X0 @ (^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (c_Empty)))))) @ (^[Y2 : $i]: (c_Empty)) @ (^[Y2 : $i > $i > $i]: (c_Empty))))))))) @ (X3 @ (^[Y0 : $i]: (c_setsum @ Y0 @ c_Empty)) @ (^[Y0 : $i]: (c_Empty))))) = ((c_setsum @ (X9 @ (X8 @ (X0 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (c_Inj1 @ c_Empty)))))) @ (^[Y0 : $i]: (X0 @ (^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: (c_Empty)))))) @ (^[Y1 : $i]: (c_Empty)) @ (^[Y1 : $i > $i > $i]: (c_Empty)))) @ (^[Y0 : $i > $i > $i]: (c_setsum @ c_Empty @ c_Empty))))) @ (X1 @ (^[Y0 : $i]: (X9 @ c_Empty)) @ (X8 @ (X7 @ (X1 @ (^[Y0 : $i]: (c_Empty)) @ c_Empty) @ (^[Y0 : $i]: ((^[Y1 : $i]: (c_Empty))))))))))) & ! [X6 : $i] : (((X2 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (X6)))) @ c_Empty)) = X6)) & ! [X4 : $i,X5 : $i] : (((c_setsum @ (X2 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (c_Empty)))) @ (X0 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (X3 @ (^[Y3 : $i]: (Y2)) @ (^[Y3 : $i]: (c_Empty)))))))) @ (^[Y0 : $i]: (c_Empty)) @ (^[Y0 : $i > $i > $i]: (c_Empty)))) @ c_Empty)) = ((X3 @ (^[Y0 : $i]: (X4)) @ (^[Y0 : $i]: (X5)))))) & (((c_Inj1 @ c_Empty)) = ((X3 @ (^[Y0 : $i]: (c_Inj1 @ c_Empty)) @ (^[Y0 : $i]: (c_setsum @ c_Empty @ c_Empty))))))),
% 5.11/1.20 inference(ennf_transformation,[],[f309])).
% 5.11/1.20 thf(f319,plain,(
% 5.11/1.20 ? [X0 : (($i > $i > $i > $i) > ($i > $i) > (($i > $i > $i) > $i) > $i),X1 : (($i > $i) > $i > $i),X2 : (((($i > $i > $i > $i) > $i) > $i > $i) > $i > $i),X3 : (($i > $i) > ($i > $i) > $i)] : ((c_False != $true) & ! [X16 : $i,X17 : ($i > $i)] : (((X17 @ X16)) = ((X0 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (X1 @ (^[Y3 : $i]: (X2 @ (^[Y4 : ($i > $i > $i > $i) > $i]: ((^[Y5 : $i]: (Y2)))) @ (X2 @ (^[Y4 : ($i > $i > $i > $i) > $i]: ((^[Y5 : $i]: (c_setsum @ c_Empty @ c_Empty)))) @ Y3))) @ (c_Inj1 @ c_Empty))))))) @ (^[Y0 : $i]: (X17 @ c_Empty)) @ (^[Y0 : $i > $i > $i]: (c_Empty))))) & ! [X14 : $i,X15 : $i] : (((X0 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (X15)))))) @ (^[Y0 : $i]: (X14)) @ (^[Y0 : $i > $i > $i]: (c_Empty)))) = X14) & ! [X12 : $i,X13 : (($i > $i) > ($i > $i) > $i)] : (((X1 @ (^[Y0 : $i]: (X13 @ (^[Y1 : $i]: (c_setsum @ Y1 @ Y0)) @ (^[Y1 : $i]: (c_Empty)))) @ c_Empty)) = ((X13 @ (^[Y0 : $i]: (c_setsum @ (X2 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_Empty)))) @ (X3 @ (^[Y1 : $i]: (X2 @ (^[Y2 : ($i > $i > $i > $i) > $i]: ((^[Y3 : $i]: (c_Empty)))) @ c_Empty)) @ (^[Y1 : $i]: (X1 @ (^[Y2 : $i]: (c_Empty)) @ c_Empty)))) @ (X2 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_Empty)))) @ (X2 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_setsum @ c_Empty @ c_Empty)))) @ (X2 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_Empty)))) @ c_Empty))))) @ (^[Y0 : $i]: (c_Inj1 @ (X1 @ (^[Y1 : $i]: (X13 @ (^[Y2 : $i]: (X1 @ (^[Y3 : $i]: (c_Empty)) @ c_Empty)) @ (^[Y2 : $i]: (c_Inj1 @ c_Empty)))) @ X12)))))) & ! [X10 : $i,X11 : $i] : (((X1 @ (^[Y0 : $i]: (c_Inj1 @ (X1 @ (^[Y1 : $i]: (c_Inj0 @ (X0 @ (^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (c_Empty)))))) @ (^[Y2 : $i]: (c_Empty)) @ (^[Y2 : $i > $i > $i]: (c_Empty))))) @ (c_Inj1 @ X11)))) @ (c_Inj0 @ (X2 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (Y1)))) @ X10)))) = ((c_Inj0 @ (X2 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (X11)))) @ (c_setsum @ c_Empty @ c_Empty))))) & ! [X7 : ($i > ($i > $i > $i) > $i),X8 : ($i > $i),X9 : ($i > $i)] : (((X2 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (X9 @ (X2 @ (^[Y2 : ($i > $i > $i > $i) > $i]: ((^[Y3 : $i]: (X0 @ (^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (c_Inj1 @ c_Empty)))))) @ (^[Y4 : $i]: (c_Inj0 @ c_Empty)) @ (^[Y4 : $i > $i > $i]: (X3 @ (^[Y5 : $i]: (c_Empty)) @ (^[Y5 : $i]: (c_Empty)))))))) @ (c_Inj0 @ (X0 @ (^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (c_Empty)))))) @ (^[Y2 : $i]: (c_Empty)) @ (^[Y2 : $i > $i > $i]: (c_Empty))))))))) @ (X3 @ (^[Y0 : $i]: (c_setsum @ Y0 @ c_Empty)) @ (^[Y0 : $i]: (c_Empty))))) = ((c_setsum @ (X9 @ (X8 @ (X0 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (c_Inj1 @ c_Empty)))))) @ (^[Y0 : $i]: (X0 @ (^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: (c_Empty)))))) @ (^[Y1 : $i]: (c_Empty)) @ (^[Y1 : $i > $i > $i]: (c_Empty)))) @ (^[Y0 : $i > $i > $i]: (c_setsum @ c_Empty @ c_Empty))))) @ (X1 @ (^[Y0 : $i]: (X9 @ c_Empty)) @ (X8 @ (X7 @ (X1 @ (^[Y0 : $i]: (c_Empty)) @ c_Empty) @ (^[Y0 : $i]: ((^[Y1 : $i]: (c_Empty)))))))))) & ! [X6 : $i] : (((X2 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (X6)))) @ c_Empty)) = X6) & ! [X4 : $i,X5 : $i] : (((c_setsum @ (X2 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (c_Empty)))) @ (X0 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (X3 @ (^[Y3 : $i]: (Y2)) @ (^[Y3 : $i]: (c_Empty)))))))) @ (^[Y0 : $i]: (c_Empty)) @ (^[Y0 : $i > $i > $i]: (c_Empty)))) @ c_Empty)) = ((X3 @ (^[Y0 : $i]: (X4)) @ (^[Y0 : $i]: (X5))))) & (((c_Inj1 @ c_Empty)) = ((X3 @ (^[Y0 : $i]: (c_Inj1 @ c_Empty)) @ (^[Y0 : $i]: (c_setsum @ c_Empty @ c_Empty))))))),
% 5.11/1.20 inference(flattening,[],[f318])).
% 5.11/1.20 thf(f332,plain,(
% 5.11/1.20 ? [X0 : (($i > $i > $i > $i) > ($i > $i) > (($i > $i > $i) > $i) > $i),X1 : (($i > $i) > $i > $i),X2 : (((($i > $i > $i > $i) > $i) > $i > $i) > $i > $i),X3 : (($i > $i) > ($i > $i) > $i)] : ((c_False != $true) & ! [X4 : $i,X5 : ($i > $i)] : (((X5 @ X4)) = ((X0 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (X1 @ (^[Y3 : $i]: (X2 @ (^[Y4 : ($i > $i > $i > $i) > $i]: ((^[Y5 : $i]: (Y2)))) @ (X2 @ (^[Y4 : ($i > $i > $i > $i) > $i]: ((^[Y5 : $i]: (c_setsum @ c_Empty @ c_Empty)))) @ Y3))) @ (c_Inj1 @ c_Empty))))))) @ (^[Y0 : $i]: (X5 @ c_Empty)) @ (^[Y0 : $i > $i > $i]: (c_Empty))))) & ! [X6 : $i,X7 : $i] : (((X0 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (X7)))))) @ (^[Y0 : $i]: (X6)) @ (^[Y0 : $i > $i > $i]: (c_Empty)))) = X6) & ! [X8 : $i,X9 : (($i > $i) > ($i > $i) > $i)] : (((X1 @ (^[Y0 : $i]: (X9 @ (^[Y1 : $i]: (c_setsum @ Y1 @ Y0)) @ (^[Y1 : $i]: (c_Empty)))) @ c_Empty)) = ((X9 @ (^[Y0 : $i]: (c_setsum @ (X2 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_Empty)))) @ (X3 @ (^[Y1 : $i]: (X2 @ (^[Y2 : ($i > $i > $i > $i) > $i]: ((^[Y3 : $i]: (c_Empty)))) @ c_Empty)) @ (^[Y1 : $i]: (X1 @ (^[Y2 : $i]: (c_Empty)) @ c_Empty)))) @ (X2 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_Empty)))) @ (X2 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_setsum @ c_Empty @ c_Empty)))) @ (X2 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_Empty)))) @ c_Empty))))) @ (^[Y0 : $i]: (c_Inj1 @ (X1 @ (^[Y1 : $i]: (X9 @ (^[Y2 : $i]: (X1 @ (^[Y3 : $i]: (c_Empty)) @ c_Empty)) @ (^[Y2 : $i]: (c_Inj1 @ c_Empty)))) @ X8)))))) & ! [X10 : $i,X11 : $i] : (((X1 @ (^[Y0 : $i]: (c_Inj1 @ (X1 @ (^[Y1 : $i]: (c_Inj0 @ (X0 @ (^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (c_Empty)))))) @ (^[Y2 : $i]: (c_Empty)) @ (^[Y2 : $i > $i > $i]: (c_Empty))))) @ (c_Inj1 @ X11)))) @ (c_Inj0 @ (X2 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (Y1)))) @ X10)))) = ((c_Inj0 @ (X2 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (X11)))) @ (c_setsum @ c_Empty @ c_Empty))))) & ! [X12 : ($i > ($i > $i > $i) > $i),X13 : ($i > $i),X14 : ($i > $i)] : (((X2 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (X14 @ (X2 @ (^[Y2 : ($i > $i > $i > $i) > $i]: ((^[Y3 : $i]: (X0 @ (^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (c_Inj1 @ c_Empty)))))) @ (^[Y4 : $i]: (c_Inj0 @ c_Empty)) @ (^[Y4 : $i > $i > $i]: (X3 @ (^[Y5 : $i]: (c_Empty)) @ (^[Y5 : $i]: (c_Empty)))))))) @ (c_Inj0 @ (X0 @ (^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (c_Empty)))))) @ (^[Y2 : $i]: (c_Empty)) @ (^[Y2 : $i > $i > $i]: (c_Empty))))))))) @ (X3 @ (^[Y0 : $i]: (c_setsum @ Y0 @ c_Empty)) @ (^[Y0 : $i]: (c_Empty))))) = ((c_setsum @ (X14 @ (X13 @ (X0 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (c_Inj1 @ c_Empty)))))) @ (^[Y0 : $i]: (X0 @ (^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: (c_Empty)))))) @ (^[Y1 : $i]: (c_Empty)) @ (^[Y1 : $i > $i > $i]: (c_Empty)))) @ (^[Y0 : $i > $i > $i]: (c_setsum @ c_Empty @ c_Empty))))) @ (X1 @ (^[Y0 : $i]: (X14 @ c_Empty)) @ (X13 @ (X12 @ (X1 @ (^[Y0 : $i]: (c_Empty)) @ c_Empty) @ (^[Y0 : $i]: ((^[Y1 : $i]: (c_Empty)))))))))) & ! [X15 : $i] : (((X2 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (X15)))) @ c_Empty)) = X15) & ! [X16 : $i,X17 : $i] : (((c_setsum @ (X2 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (c_Empty)))) @ (X0 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (X3 @ (^[Y3 : $i]: (Y2)) @ (^[Y3 : $i]: (c_Empty)))))))) @ (^[Y0 : $i]: (c_Empty)) @ (^[Y0 : $i > $i > $i]: (c_Empty)))) @ c_Empty)) = ((X3 @ (^[Y0 : $i]: (X16)) @ (^[Y0 : $i]: (X17))))) & (((c_Inj1 @ c_Empty)) = ((X3 @ (^[Y0 : $i]: (c_Inj1 @ c_Empty)) @ (^[Y0 : $i]: (c_setsum @ c_Empty @ c_Empty))))))),
% 5.11/1.20 inference(rectify,[],[f319])).
% 5.11/1.20 thf(f333,plain,(
% 5.11/1.20 (c_False != $true) & ! [X4 : $i,X5 : ($i > $i)] : (((X5 @ X4)) = ((sK9 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (sK10 @ (^[Y3 : $i]: (sK11 @ (^[Y4 : ($i > $i > $i > $i) > $i]: ((^[Y5 : $i]: (Y2)))) @ (sK11 @ (^[Y4 : ($i > $i > $i > $i) > $i]: ((^[Y5 : $i]: (c_setsum @ c_Empty @ c_Empty)))) @ Y3))) @ (c_Inj1 @ c_Empty))))))) @ (^[Y0 : $i]: (X5 @ c_Empty)) @ (^[Y0 : $i > $i > $i]: (c_Empty))))) & ! [X6 : $i,X7 : $i] : (((sK9 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (X7)))))) @ (^[Y0 : $i]: (X6)) @ (^[Y0 : $i > $i > $i]: (c_Empty)))) = X6) & ! [X8 : $i,X9 : (($i > $i) > ($i > $i) > $i)] : (((sK10 @ (^[Y0 : $i]: (X9 @ (^[Y1 : $i]: (c_setsum @ Y1 @ Y0)) @ (^[Y1 : $i]: (c_Empty)))) @ c_Empty)) = ((X9 @ (^[Y0 : $i]: (c_setsum @ (sK11 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_Empty)))) @ (sK12 @ (^[Y1 : $i]: (sK11 @ (^[Y2 : ($i > $i > $i > $i) > $i]: ((^[Y3 : $i]: (c_Empty)))) @ c_Empty)) @ (^[Y1 : $i]: (sK10 @ (^[Y2 : $i]: (c_Empty)) @ c_Empty)))) @ (sK11 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_Empty)))) @ (sK11 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_setsum @ c_Empty @ c_Empty)))) @ (sK11 @ (^[Y1 : ($i > $i > $i > $i) > $i]: ((^[Y2 : $i]: (c_Empty)))) @ c_Empty))))) @ (^[Y0 : $i]: (c_Inj1 @ (sK10 @ (^[Y1 : $i]: (X9 @ (^[Y2 : $i]: (sK10 @ (^[Y3 : $i]: (c_Empty)) @ c_Empty)) @ (^[Y2 : $i]: (c_Inj1 @ c_Empty)))) @ X8)))))) & ! [X10 : $i,X11 : $i] : (((sK10 @ (^[Y0 : $i]: (c_Inj1 @ (sK10 @ (^[Y1 : $i]: (c_Inj0 @ (sK9 @ (^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (c_Empty)))))) @ (^[Y2 : $i]: (c_Empty)) @ (^[Y2 : $i > $i > $i]: (c_Empty))))) @ (c_Inj1 @ X11)))) @ (c_Inj0 @ (sK11 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (Y1)))) @ X10)))) = ((c_Inj0 @ (sK11 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (X11)))) @ (c_setsum @ c_Empty @ c_Empty))))) & ! [X12 : ($i > ($i > $i > $i) > $i),X13 : ($i > $i),X14 : ($i > $i)] : (((sK11 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (X14 @ (sK11 @ (^[Y2 : ($i > $i > $i > $i) > $i]: ((^[Y3 : $i]: (sK9 @ (^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (c_Inj1 @ c_Empty)))))) @ (^[Y4 : $i]: (c_Inj0 @ c_Empty)) @ (^[Y4 : $i > $i > $i]: (sK12 @ (^[Y5 : $i]: (c_Empty)) @ (^[Y5 : $i]: (c_Empty)))))))) @ (c_Inj0 @ (sK9 @ (^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (c_Empty)))))) @ (^[Y2 : $i]: (c_Empty)) @ (^[Y2 : $i > $i > $i]: (c_Empty))))))))) @ (sK12 @ (^[Y0 : $i]: (c_setsum @ Y0 @ c_Empty)) @ (^[Y0 : $i]: (c_Empty))))) = ((c_setsum @ (X14 @ (X13 @ (sK9 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (c_Inj1 @ c_Empty)))))) @ (^[Y0 : $i]: (sK9 @ (^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: (c_Empty)))))) @ (^[Y1 : $i]: (c_Empty)) @ (^[Y1 : $i > $i > $i]: (c_Empty)))) @ (^[Y0 : $i > $i > $i]: (c_setsum @ c_Empty @ c_Empty))))) @ (sK10 @ (^[Y0 : $i]: (X14 @ c_Empty)) @ (X13 @ (X12 @ (sK10 @ (^[Y0 : $i]: (c_Empty)) @ c_Empty) @ (^[Y0 : $i]: ((^[Y1 : $i]: (c_Empty)))))))))) & ! [X15 : $i] : (((sK11 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (X15)))) @ c_Empty)) = X15) & ! [X16 : $i,X17 : $i] : (((c_setsum @ (sK11 @ (^[Y0 : ($i > $i > $i > $i) > $i]: ((^[Y1 : $i]: (c_Empty)))) @ (sK9 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (sK12 @ (^[Y3 : $i]: (Y2)) @ (^[Y3 : $i]: (c_Empty)))))))) @ (^[Y0 : $i]: (c_Empty)) @ (^[Y0 : $i > $i > $i]: (c_Empty)))) @ c_Empty)) = ((sK12 @ (^[Y0 : $i]: (X16)) @ (^[Y0 : $i]: (X17))))) & (((c_Inj1 @ c_Empty)) = ((sK12 @ (^[Y0 : $i]: (c_Inj1 @ c_Empty)) @ (^[Y0 : $i]: (c_setsum @ c_Empty @ c_Empty)))))),
% 5.11/1.20 inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10,sK11,sK12]),skolemize(X0,sK9),skolemize(X1,sK10),skolemize(X2,sK11),skolemize(X3,sK12)],[f332])).
% 5.11/1.20 thf(f334,plain,(
% 5.11/1.20 ( ! [X0 : ($i > $o),X1 : $i] : ((((X0 @ X1)) != $true) | (((X0 @ (c_Eps_i @ X0))) = $true)) )),
% 5.11/1.20 inference(cnf_transformation,[],[f310])).
% 5.11/1.20 thf(f338,plain,(
% 5.11/1.20 ($true = ((c_not @ (?? @ $i @ (^[Y0 : $i]: (c_In @ Y0 @ c_Empty))))))),
% 5.11/1.20 inference(cnf_transformation,[],[f120])).
% 5.11/1.20 thf(f339,plain,(
% 5.11/1.20 ( ! [X0 : $i,X1 : $i] : (($true = ((c_iff @ (c_In @ X1 @ (c_Union @ X0)) @ (?? @ $i @ (^[Y0 : $i]: (c_and @ (c_In @ X1 @ Y0) @ (c_In @ Y0 @ X0)))))))) )),
% 5.11/1.20 inference(cnf_transformation,[],[f122])).
% 5.11/1.20 thf(f340,plain,(
% 5.11/1.20 ( ! [X0 : $i,X1 : $i] : ((((c_iff @ (c_In @ X1 @ (c_Power @ X0)) @ (c_Subq @ X1 @ X0))) = $true)) )),
% 5.11/1.20 inference(cnf_transformation,[],[f124])).
% 5.11/1.20 thf(f356,plain,(
% 5.11/1.20 (c_not = (^[Y0 : $o]: (Y0 => c_False)))),
% 5.11/1.20 inference(cnf_transformation,[],[f136])).
% 5.11/1.20 thf(f357,plain,(
% 5.11/1.20 (c_and = (^[Y0 : $o]: ((^[Y1 : $o]: (!! @ $o @ (^[Y2 : $o]: ((Y0 => (Y1 => Y2)) => Y2)))))))),
% 5.11/1.20 inference(cnf_transformation,[],[f138])).
% 5.11/1.20 thf(f358,plain,(
% 5.11/1.20 (c_or = (^[Y0 : $o]: ((^[Y1 : $o]: (!! @ $o @ (^[Y2 : $o]: ((Y0 => Y2) => ((Y1 => Y2) => Y2))))))))),
% 5.11/1.20 inference(cnf_transformation,[],[f140])).
% 5.11/1.20 thf(f359,plain,(
% 5.11/1.20 (c_iff = (^[Y0 : $o]: ((^[Y1 : $o]: (c_and @ (Y0 => Y1) @ (Y1 => Y0))))))),
% 5.11/1.20 inference(cnf_transformation,[],[f142])).
% 5.11/1.20 thf(f360,plain,(
% 5.11/1.20 (c_Subq = (^[Y0 : $i]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ Y2 @ Y0) => (c_In @ Y2 @ Y1))))))))),
% 5.11/1.20 inference(cnf_transformation,[],[f144])).
% 5.11/1.20 thf(f385,plain,(
% 5.11/1.20 (c_If_i = (^[Y0 : $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (c_Eps_i @ (^[Y3 : $i]: (c_or @ (c_and @ Y0 @ (Y1 = Y3)) @ (c_and @ (c_not @ Y0) @ (Y2 = Y3)))))))))))),
% 5.11/1.20 inference(cnf_transformation,[],[f184])).
% 5.11/1.20 thf(f390,plain,(
% 5.11/1.20 (c_UPair = (^[Y0 : $i]: ((^[Y1 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y2 : $i]: (c_If_i @ (c_In @ c_Empty @ Y2) @ Y0 @ Y1)))))))),
% 5.11/1.20 inference(cnf_transformation,[],[f190])).
% 5.11/1.20 thf(f391,plain,(
% 5.11/1.20 (c_Sing = (^[Y0 : $i]: (c_UPair @ Y0 @ Y0)))),
% 5.11/1.20 inference(cnf_transformation,[],[f191])).
% 5.11/1.20 thf(f392,plain,(
% 5.11/1.20 (c_binunion = (^[Y0 : $i]: ((^[Y1 : $i]: (c_Union @ (c_UPair @ Y0 @ Y1))))))),
% 5.11/1.20 inference(cnf_transformation,[],[f192])).
% 5.11/1.20 thf(f403,plain,(
% 5.11/1.20 (c_In_rec_poly_G_i = (^[Y0 : $i > ($i > $i) > $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y4 : $i > $i]: (!! @ $i @ (^[Y5 : $i]: ((!! @ $i @ (^[Y6 : $i]: ((c_In @ Y6 @ Y5) => (Y3 @ Y6 @ (Y4 @ Y6))))) => (Y3 @ Y5 @ (Y0 @ Y5 @ Y4))))))) => (Y3 @ Y1 @ Y2))))))))))),
% 5.11/1.20 inference(cnf_transformation,[],[f213])).
% 5.11/1.20 thf(f404,plain,(
% 5.11/1.20 (c_In_rec_poly_i = (^[Y0 : $i > ($i > $i) > $i]: ((^[Y1 : $i]: (c_Eps_i @ (^[Y2 : $i]: (c_In_rec_poly_G_i @ Y0 @ Y1 @ Y2)))))))),
% 5.11/1.20 inference(cnf_transformation,[],[f215])).
% 5.11/1.20 thf(f412,plain,(
% 5.11/1.20 (c_Inj1 = ((c_In_rec_poly_i @ (^[Y0 : $i]: ((^[Y1 : $i > $i]: (c_binunion @ (c_Sing @ c_Empty) @ (c_Repl @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))))),
% 5.11/1.20 inference(cnf_transformation,[],[f230])).
% 5.11/1.20 thf(f413,plain,(
% 5.11/1.20 (c_Inj0 = (^[Y0 : $i]: (c_Repl @ Y0 @ (^[Y1 : $i]: (c_Inj1 @ Y1)))))),
% 5.11/1.20 inference(cnf_transformation,[],[f232])).
% 5.11/1.20 thf(f416,plain,(
% 5.11/1.20 (c_setsum = (^[Y0 : $i]: ((^[Y1 : $i]: (c_binunion @ (c_Repl @ Y0 @ (^[Y2 : $i]: (c_Inj0 @ Y2))) @ (c_Repl @ Y1 @ (^[Y2 : $i]: (c_Inj1 @ Y2))))))))),
% 5.11/1.20 inference(cnf_transformation,[],[f238])).
% 5.11/1.20 thf(f459,plain,(
% 5.11/1.20 ( ! [X4 : $i,X5 : ($i > $i)] : ((((X5 @ X4)) = ((sK9 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (sK10 @ (^[Y3 : $i]: (sK11 @ (^[Y4 : ($i > $i > $i > $i) > $i]: ((^[Y5 : $i]: (Y2)))) @ (sK11 @ (^[Y4 : ($i > $i > $i > $i) > $i]: ((^[Y5 : $i]: (c_setsum @ c_Empty @ c_Empty)))) @ Y3))) @ (c_Inj1 @ c_Empty))))))) @ (^[Y0 : $i]: (X5 @ c_Empty)) @ (^[Y0 : $i > $i > $i]: (c_Empty)))))) )),
% 5.11/1.20 inference(cnf_transformation,[],[f333])).
% 5.11/1.20 thf(f460,plain,(
% 5.11/1.20 (c_False != $true)),
% 5.11/1.20 inference(cnf_transformation,[],[f333])).
% 5.11/1.20 thf(f463,plain,(
% 5.11/1.20 (c_iff = (^[Y0 : $o]: ((^[Y1 : $o]: ((^[Y2 : $o]: ((^[Y3 : $o]: (!! @ $o @ (^[Y4 : $o]: ((Y2 => (Y3 => Y4)) => Y4)))))) @ (Y0 => Y1) @ (Y1 => Y0))))))),
% 5.11/1.20 inference(definition_unfolding,[],[f359,f357])).
% 5.11/1.20 thf(f484,plain,(
% 5.11/1.20 (c_If_i = (^[Y0 : $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (c_Eps_i @ (^[Y3 : $i]: ((^[Y4 : $o]: ((^[Y5 : $o]: (!! @ $o @ (^[Y6 : $o]: ((Y4 => Y6) => ((Y5 => Y6) => Y6))))))) @ ((^[Y4 : $o]: ((^[Y5 : $o]: (!! @ $o @ (^[Y6 : $o]: ((Y4 => (Y5 => Y6)) => Y6)))))) @ Y0 @ (Y1 = Y3)) @ ((^[Y4 : $o]: ((^[Y5 : $o]: (!! @ $o @ (^[Y6 : $o]: ((Y4 => (Y5 => Y6)) => Y6)))))) @ ((^[Y4 : $o]: (Y4 => c_False)) @ Y0) @ (Y2 = Y3)))))))))))),
% 5.11/1.20 inference(definition_unfolding,[],[f385,f358,f357,f357,f356])).
% 5.11/1.20 thf(f489,plain,(
% 5.11/1.20 (c_UPair = (^[Y0 : $i]: ((^[Y1 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y2 : $i]: ((^[Y3 : $o]: ((^[Y4 : $i]: ((^[Y5 : $i]: (c_Eps_i @ (^[Y6 : $i]: ((^[Y7 : $o]: ((^[Y8 : $o]: (!! @ $o @ (^[Y9 : $o]: ((Y7 => Y9) => ((Y8 => Y9) => Y9))))))) @ ((^[Y7 : $o]: ((^[Y8 : $o]: (!! @ $o @ (^[Y9 : $o]: ((Y7 => (Y8 => Y9)) => Y9)))))) @ Y3 @ (Y4 = Y6)) @ ((^[Y7 : $o]: ((^[Y8 : $o]: (!! @ $o @ (^[Y9 : $o]: ((Y7 => (Y8 => Y9)) => Y9)))))) @ ((^[Y7 : $o]: (Y7 => c_False)) @ Y3) @ (Y5 = Y6)))))))))) @ (c_In @ c_Empty @ Y2) @ Y0 @ Y1)))))))),
% 5.11/1.20 inference(definition_unfolding,[],[f390,f484])).
% 5.11/1.20 thf(f490,plain,(
% 5.11/1.20 (c_Sing = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y3 : $i]: ((^[Y4 : $o]: ((^[Y5 : $i]: ((^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: ((^[Y8 : $o]: ((^[Y9 : $o]: (!! @ $o @ (^[Y10 : $o]: ((Y8 => Y10) => ((Y9 => Y10) => Y10))))))) @ ((^[Y8 : $o]: ((^[Y9 : $o]: (!! @ $o @ (^[Y10 : $o]: ((Y8 => (Y9 => Y10)) => Y10)))))) @ Y4 @ (Y5 = Y7)) @ ((^[Y8 : $o]: ((^[Y9 : $o]: (!! @ $o @ (^[Y10 : $o]: ((Y8 => (Y9 => Y10)) => Y10)))))) @ ((^[Y8 : $o]: (Y8 => c_False)) @ Y4) @ (Y6 = Y7)))))))))) @ (c_In @ c_Empty @ Y3) @ Y1 @ Y2)))))) @ Y0 @ Y0)))),
% 5.11/1.20 inference(definition_unfolding,[],[f391,f489])).
% 5.11/1.20 thf(f491,plain,(
% 5.11/1.20 (c_binunion = (^[Y0 : $i]: ((^[Y1 : $i]: (c_Union @ ((^[Y2 : $i]: ((^[Y3 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y4 : $i]: ((^[Y5 : $o]: ((^[Y6 : $i]: ((^[Y7 : $i]: (c_Eps_i @ (^[Y8 : $i]: ((^[Y9 : $o]: ((^[Y10 : $o]: (!! @ $o @ (^[Y11 : $o]: ((Y9 => Y11) => ((Y10 => Y11) => Y11))))))) @ ((^[Y9 : $o]: ((^[Y10 : $o]: (!! @ $o @ (^[Y11 : $o]: ((Y9 => (Y10 => Y11)) => Y11)))))) @ Y5 @ (Y6 = Y8)) @ ((^[Y9 : $o]: ((^[Y10 : $o]: (!! @ $o @ (^[Y11 : $o]: ((Y9 => (Y10 => Y11)) => Y11)))))) @ ((^[Y9 : $o]: (Y9 => c_False)) @ Y5) @ (Y7 = Y8)))))))))) @ (c_In @ c_Empty @ Y4) @ Y2 @ Y3)))))) @ Y0 @ Y1))))))),
% 5.11/1.20 inference(definition_unfolding,[],[f392,f489])).
% 5.11/1.20 thf(f501,plain,(
% 5.11/1.20 (c_In_rec_poly_i = (^[Y0 : $i > ($i > $i) > $i]: ((^[Y1 : $i]: (c_Eps_i @ (^[Y2 : $i]: ((^[Y3 : $i > ($i > $i) > $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y7 : $i > $i]: (!! @ $i @ (^[Y8 : $i]: ((!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ Y8) => (Y6 @ Y9 @ (Y7 @ Y9))))) => (Y6 @ Y8 @ (Y3 @ Y8 @ Y7))))))) => (Y6 @ Y4 @ Y5))))))))) @ Y0 @ Y1 @ Y2)))))))),
% 5.11/1.20 inference(definition_unfolding,[],[f404,f403])).
% 5.11/1.20 thf(f509,plain,(
% 5.11/1.20 (c_Inj1 = (((^[Y0 : $i > ($i > $i) > $i]: ((^[Y1 : $i]: (c_Eps_i @ (^[Y2 : $i]: ((^[Y3 : $i > ($i > $i) > $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y7 : $i > $i]: (!! @ $i @ (^[Y8 : $i]: ((!! @ $i @ (^[Y9 : $i]: ((c_In @ Y9 @ Y8) => (Y6 @ Y9 @ (Y7 @ Y9))))) => (Y6 @ Y8 @ (Y3 @ Y8 @ Y7))))))) => (Y6 @ Y4 @ Y5))))))))) @ Y0 @ Y1 @ Y2)))))) @ (^[Y0 : $i]: ((^[Y1 : $i > $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: (c_Union @ ((^[Y4 : $i]: ((^[Y5 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y6 : $i]: ((^[Y7 : $o]: ((^[Y8 : $i]: ((^[Y9 : $i]: (c_Eps_i @ (^[Y10 : $i]: ((^[Y11 : $o]: ((^[Y12 : $o]: (!! @ $o @ (^[Y13 : $o]: ((Y11 => Y13) => ((Y12 => Y13) => Y13))))))) @ ((^[Y11 : $o]: ((^[Y12 : $o]: (!! @ $o @ (^[Y13 : $o]: ((Y11 => (Y12 => Y13)) => Y13)))))) @ Y7 @ (Y8 = Y10)) @ ((^[Y11 : $o]: ((^[Y12 : $o]: (!! @ $o @ (^[Y13 : $o]: ((Y11 => (Y12 => Y13)) => Y13)))))) @ ((^[Y11 : $o]: (Y11 => c_False)) @ Y7) @ (Y9 = Y10)))))))))) @ (c_In @ c_Empty @ Y6) @ Y4 @ Y5)))))) @ Y2 @ Y3))))) @ ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y5 : $i]: ((^[Y6 : $o]: ((^[Y7 : $i]: ((^[Y8 : $i]: (c_Eps_i @ (^[Y9 : $i]: ((^[Y10 : $o]: ((^[Y11 : $o]: (!! @ $o @ (^[Y12 : $o]: ((Y10 => Y12) => ((Y11 => Y12) => Y12))))))) @ ((^[Y10 : $o]: ((^[Y11 : $o]: (!! @ $o @ (^[Y12 : $o]: ((Y10 => (Y11 => Y12)) => Y12)))))) @ Y6 @ (Y7 = Y9)) @ ((^[Y10 : $o]: ((^[Y11 : $o]: (!! @ $o @ (^[Y12 : $o]: ((Y10 => (Y11 => Y12)) => Y12)))))) @ ((^[Y10 : $o]: (Y10 => c_False)) @ Y6) @ (Y8 = Y9)))))))))) @ (c_In @ c_Empty @ Y5) @ Y3 @ Y4)))))) @ Y2 @ Y2)) @ c_Empty) @ (c_Repl @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))))),
% 5.11/1.20 inference(definition_unfolding,[],[f412,f501,f491,f490])).
% 5.11/1.20 thf(f510,plain,(
% 5.11/1.20 (c_Inj0 = (^[Y0 : $i]: (c_Repl @ Y0 @ (^[Y1 : $i]: ((^[Y2 : $i > ($i > $i) > $i]: ((^[Y3 : $i]: (c_Eps_i @ (^[Y4 : $i]: ((^[Y5 : $i > ($i > $i) > $i]: ((^[Y6 : $i]: ((^[Y7 : $i]: (!! @ ($i > $i > $o) @ (^[Y8 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y9 : $i > $i]: (!! @ $i @ (^[Y10 : $i]: ((!! @ $i @ (^[Y11 : $i]: ((c_In @ Y11 @ Y10) => (Y8 @ Y11 @ (Y9 @ Y11))))) => (Y8 @ Y10 @ (Y5 @ Y10 @ Y9))))))) => (Y8 @ Y6 @ Y7))))))))) @ Y2 @ Y3 @ Y4)))))) @ (^[Y2 : $i]: ((^[Y3 : $i > $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (c_Union @ ((^[Y6 : $i]: ((^[Y7 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y8 : $i]: ((^[Y9 : $o]: ((^[Y10 : $i]: ((^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => Y15) => ((Y14 => Y15) => Y15))))))) @ ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => (Y14 => Y15)) => Y15)))))) @ Y9 @ (Y10 = Y12)) @ ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => (Y14 => Y15)) => Y15)))))) @ ((^[Y13 : $o]: (Y13 => c_False)) @ Y9) @ (Y11 = Y12)))))))))) @ (c_In @ c_Empty @ Y8) @ Y6 @ Y7)))))) @ Y4 @ Y5))))) @ ((^[Y4 : $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y7 : $i]: ((^[Y8 : $o]: ((^[Y9 : $i]: ((^[Y10 : $i]: (c_Eps_i @ (^[Y11 : $i]: ((^[Y12 : $o]: ((^[Y13 : $o]: (!! @ $o @ (^[Y14 : $o]: ((Y12 => Y14) => ((Y13 => Y14) => Y14))))))) @ ((^[Y12 : $o]: ((^[Y13 : $o]: (!! @ $o @ (^[Y14 : $o]: ((Y12 => (Y13 => Y14)) => Y14)))))) @ Y8 @ (Y9 = Y11)) @ ((^[Y12 : $o]: ((^[Y13 : $o]: (!! @ $o @ (^[Y14 : $o]: ((Y12 => (Y13 => Y14)) => Y14)))))) @ ((^[Y12 : $o]: (Y12 => c_False)) @ Y8) @ (Y10 = Y11)))))))))) @ (c_In @ c_Empty @ Y7) @ Y5 @ Y6)))))) @ Y4 @ Y4)) @ c_Empty) @ (c_Repl @ Y2 @ (^[Y4 : $i]: (Y3 @ Y4))))))) @ Y1)))))),
% 5.11/1.20 inference(definition_unfolding,[],[f413,f509])).
% 5.11/1.20 thf(f513,plain,(
% 5.11/1.20 (c_setsum = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: (c_Union @ ((^[Y4 : $i]: ((^[Y5 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y6 : $i]: ((^[Y7 : $o]: ((^[Y8 : $i]: ((^[Y9 : $i]: (c_Eps_i @ (^[Y10 : $i]: ((^[Y11 : $o]: ((^[Y12 : $o]: (!! @ $o @ (^[Y13 : $o]: ((Y11 => Y13) => ((Y12 => Y13) => Y13))))))) @ ((^[Y11 : $o]: ((^[Y12 : $o]: (!! @ $o @ (^[Y13 : $o]: ((Y11 => (Y12 => Y13)) => Y13)))))) @ Y7 @ (Y8 = Y10)) @ ((^[Y11 : $o]: ((^[Y12 : $o]: (!! @ $o @ (^[Y13 : $o]: ((Y11 => (Y12 => Y13)) => Y13)))))) @ ((^[Y11 : $o]: (Y11 => c_False)) @ Y7) @ (Y9 = Y10)))))))))) @ (c_In @ c_Empty @ Y6) @ Y4 @ Y5)))))) @ Y2 @ Y3))))) @ (c_Repl @ Y0 @ (^[Y2 : $i]: ((^[Y3 : $i]: (c_Repl @ Y3 @ (^[Y4 : $i]: ((^[Y5 : $i > ($i > $i) > $i]: ((^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: ((^[Y8 : $i > ($i > $i) > $i]: ((^[Y9 : $i]: ((^[Y10 : $i]: (!! @ ($i > $i > $o) @ (^[Y11 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y12 : $i > $i]: (!! @ $i @ (^[Y13 : $i]: ((!! @ $i @ (^[Y14 : $i]: ((c_In @ Y14 @ Y13) => (Y11 @ Y14 @ (Y12 @ Y14))))) => (Y11 @ Y13 @ (Y8 @ Y13 @ Y12))))))) => (Y11 @ Y9 @ Y10))))))))) @ Y5 @ Y6 @ Y7)))))) @ (^[Y5 : $i]: ((^[Y6 : $i > $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: (c_Union @ ((^[Y9 : $i]: ((^[Y10 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y11 : $i]: ((^[Y12 : $o]: ((^[Y13 : $i]: ((^[Y14 : $i]: (c_Eps_i @ (^[Y15 : $i]: ((^[Y16 : $o]: ((^[Y17 : $o]: (!! @ $o @ (^[Y18 : $o]: ((Y16 => Y18) => ((Y17 => Y18) => Y18))))))) @ ((^[Y16 : $o]: ((^[Y17 : $o]: (!! @ $o @ (^[Y18 : $o]: ((Y16 => (Y17 => Y18)) => Y18)))))) @ Y12 @ (Y13 = Y15)) @ ((^[Y16 : $o]: ((^[Y17 : $o]: (!! @ $o @ (^[Y18 : $o]: ((Y16 => (Y17 => Y18)) => Y18)))))) @ ((^[Y16 : $o]: (Y16 => c_False)) @ Y12) @ (Y14 = Y15)))))))))) @ (c_In @ c_Empty @ Y11) @ Y9 @ Y10)))))) @ Y7 @ Y8))))) @ ((^[Y7 : $i]: ((^[Y8 : $i]: ((^[Y9 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y10 : $i]: ((^[Y11 : $o]: ((^[Y12 : $i]: ((^[Y13 : $i]: (c_Eps_i @ (^[Y14 : $i]: ((^[Y15 : $o]: ((^[Y16 : $o]: (!! @ $o @ (^[Y17 : $o]: ((Y15 => Y17) => ((Y16 => Y17) => Y17))))))) @ ((^[Y15 : $o]: ((^[Y16 : $o]: (!! @ $o @ (^[Y17 : $o]: ((Y15 => (Y16 => Y17)) => Y17)))))) @ Y11 @ (Y12 = Y14)) @ ((^[Y15 : $o]: ((^[Y16 : $o]: (!! @ $o @ (^[Y17 : $o]: ((Y15 => (Y16 => Y17)) => Y17)))))) @ ((^[Y15 : $o]: (Y15 => c_False)) @ Y11) @ (Y13 = Y14)))))))))) @ (c_In @ c_Empty @ Y10) @ Y8 @ Y9)))))) @ Y7 @ Y7)) @ c_Empty) @ (c_Repl @ Y5 @ (^[Y7 : $i]: (Y6 @ Y7))))))) @ Y4)))) @ Y2))) @ (c_Repl @ Y1 @ (^[Y2 : $i]: ((^[Y3 : $i > ($i > $i) > $i]: ((^[Y4 : $i]: (c_Eps_i @ (^[Y5 : $i]: ((^[Y6 : $i > ($i > $i) > $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: (!! @ ($i > $i > $o) @ (^[Y9 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y10 : $i > $i]: (!! @ $i @ (^[Y11 : $i]: ((!! @ $i @ (^[Y12 : $i]: ((c_In @ Y12 @ Y11) => (Y9 @ Y12 @ (Y10 @ Y12))))) => (Y9 @ Y11 @ (Y6 @ Y11 @ Y10))))))) => (Y9 @ Y7 @ Y8))))))))) @ Y3 @ Y4 @ Y5)))))) @ (^[Y3 : $i]: ((^[Y4 : $i > $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (c_Union @ ((^[Y7 : $i]: ((^[Y8 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y9 : $i]: ((^[Y10 : $o]: ((^[Y11 : $i]: ((^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: ((^[Y14 : $o]: ((^[Y15 : $o]: (!! @ $o @ (^[Y16 : $o]: ((Y14 => Y16) => ((Y15 => Y16) => Y16))))))) @ ((^[Y14 : $o]: ((^[Y15 : $o]: (!! @ $o @ (^[Y16 : $o]: ((Y14 => (Y15 => Y16)) => Y16)))))) @ Y10 @ (Y11 = Y13)) @ ((^[Y14 : $o]: ((^[Y15 : $o]: (!! @ $o @ (^[Y16 : $o]: ((Y14 => (Y15 => Y16)) => Y16)))))) @ ((^[Y14 : $o]: (Y14 => c_False)) @ Y10) @ (Y12 = Y13)))))))))) @ (c_In @ c_Empty @ Y9) @ Y7 @ Y8)))))) @ Y5 @ Y6))))) @ ((^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y8 : $i]: ((^[Y9 : $o]: ((^[Y10 : $i]: ((^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => Y15) => ((Y14 => Y15) => Y15))))))) @ ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => (Y14 => Y15)) => Y15)))))) @ Y9 @ (Y10 = Y12)) @ ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => (Y14 => Y15)) => Y15)))))) @ ((^[Y13 : $o]: (Y13 => c_False)) @ Y9) @ (Y11 = Y12)))))))))) @ (c_In @ c_Empty @ Y8) @ Y6 @ Y7)))))) @ Y5 @ Y5)) @ c_Empty) @ (c_Repl @ Y3 @ (^[Y5 : $i]: (Y4 @ Y5))))))) @ Y2))))))))),
% 5.11/1.20 inference(definition_unfolding,[],[f416,f491,f510,f509])).
% 5.11/1.20 thf(f551,plain,(
% 5.11/1.20 ($true = (((^[Y0 : $o]: (Y0 => c_False)) @ (?? @ $i @ (^[Y0 : $i]: (c_In @ Y0 @ c_Empty))))))),
% 5.11/1.20 inference(definition_unfolding,[],[f338,f356])).
% 5.11/1.20 thf(f552,plain,(
% 5.11/1.20 ( ! [X0 : $i,X1 : $i] : (($true = (((^[Y0 : $o]: ((^[Y1 : $o]: ((^[Y2 : $o]: ((^[Y3 : $o]: (!! @ $o @ (^[Y4 : $o]: ((Y2 => (Y3 => Y4)) => Y4)))))) @ (Y0 => Y1) @ (Y1 => Y0))))) @ (c_In @ X1 @ (c_Union @ X0)) @ (?? @ $i @ (^[Y0 : $i]: ((^[Y1 : $o]: ((^[Y2 : $o]: (!! @ $o @ (^[Y3 : $o]: ((Y1 => (Y2 => Y3)) => Y3)))))) @ (c_In @ X1 @ Y0) @ (c_In @ Y0 @ X0)))))))) )),
% 5.11/1.20 inference(definition_unfolding,[],[f339,f463,f357])).
% 5.11/1.20 thf(f553,plain,(
% 5.11/1.20 ( ! [X0 : $i,X1 : $i] : (($true = (((^[Y0 : $o]: ((^[Y1 : $o]: ((^[Y2 : $o]: ((^[Y3 : $o]: (!! @ $o @ (^[Y4 : $o]: ((Y2 => (Y3 => Y4)) => Y4)))))) @ (Y0 => Y1) @ (Y1 => Y0))))) @ (c_In @ X1 @ (c_Power @ X0)) @ ((^[Y0 : $i]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((c_In @ Y2 @ Y0) => (c_In @ Y2 @ Y1))))))) @ X1 @ X0))))) )),
% 5.11/1.20 inference(definition_unfolding,[],[f340,f463,f360])).
% 5.11/1.20 thf(f555,plain,(
% 5.11/1.20 ( ! [X4 : $i,X5 : ($i > $i)] : ((((X5 @ X4)) = ((sK9 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (sK10 @ (^[Y3 : $i]: (sK11 @ (^[Y4 : ($i > $i > $i > $i) > $i]: ((^[Y5 : $i]: (Y2)))) @ (sK11 @ (^[Y4 : ($i > $i > $i > $i) > $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: ((^[Y9 : $i]: (c_Union @ ((^[Y10 : $i]: ((^[Y11 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y12 : $i]: ((^[Y13 : $o]: ((^[Y14 : $i]: ((^[Y15 : $i]: (c_Eps_i @ (^[Y16 : $i]: ((^[Y17 : $o]: ((^[Y18 : $o]: (!! @ $o @ (^[Y19 : $o]: ((Y17 => Y19) => ((Y18 => Y19) => Y19))))))) @ ((^[Y17 : $o]: ((^[Y18 : $o]: (!! @ $o @ (^[Y19 : $o]: ((Y17 => (Y18 => Y19)) => Y19)))))) @ Y13 @ (Y14 = Y16)) @ ((^[Y17 : $o]: ((^[Y18 : $o]: (!! @ $o @ (^[Y19 : $o]: ((Y17 => (Y18 => Y19)) => Y19)))))) @ ((^[Y17 : $o]: (Y17 => c_False)) @ Y13) @ (Y15 = Y16)))))))))) @ (c_In @ c_Empty @ Y12) @ Y10 @ Y11)))))) @ Y8 @ Y9))))) @ (c_Repl @ Y6 @ (^[Y8 : $i]: ((^[Y9 : $i]: (c_Repl @ Y9 @ (^[Y10 : $i]: ((^[Y11 : $i > ($i > $i) > $i]: ((^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: ((^[Y14 : $i > ($i > $i) > $i]: ((^[Y15 : $i]: ((^[Y16 : $i]: (!! 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@ $o @ (^[Y22 : $o]: ((Y20 => Y22) => ((Y21 => Y22) => Y22))))))) @ ((^[Y20 : $o]: ((^[Y21 : $o]: (!! @ $o @ (^[Y22 : $o]: ((Y20 => (Y21 => Y22)) => Y22)))))) @ Y16 @ (Y17 = Y19)) @ ((^[Y20 : $o]: ((^[Y21 : $o]: (!! @ $o @ (^[Y22 : $o]: ((Y20 => (Y21 => Y22)) => Y22)))))) @ ((^[Y20 : $o]: (Y20 => c_False)) @ Y16) @ (Y18 = Y19)))))))))) @ (c_In @ c_Empty @ Y15) @ Y13 @ Y14)))))) @ Y11 @ Y12))))) @ ((^[Y11 : $i]: ((^[Y12 : $i]: ((^[Y13 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y14 : $i]: ((^[Y15 : $o]: ((^[Y16 : $i]: ((^[Y17 : $i]: (c_Eps_i @ (^[Y18 : $i]: ((^[Y19 : $o]: ((^[Y20 : $o]: (!! @ $o @ (^[Y21 : $o]: ((Y19 => Y21) => ((Y20 => Y21) => Y21))))))) @ ((^[Y19 : $o]: ((^[Y20 : $o]: (!! @ $o @ (^[Y21 : $o]: ((Y19 => (Y20 => Y21)) => Y21)))))) @ Y15 @ (Y16 = Y18)) @ ((^[Y19 : $o]: ((^[Y20 : $o]: (!! @ $o @ (^[Y21 : $o]: ((Y19 => (Y20 => Y21)) => Y21)))))) @ ((^[Y19 : $o]: (Y19 => c_False)) @ Y15) @ (Y17 = Y18)))))))))) @ (c_In @ c_Empty @ Y14) @ Y12 @ Y13)))))) @ Y11 @ Y11)) @ c_Empty) @ (c_Repl @ Y9 @ (^[Y11 : $i]: (Y10 @ Y11))))))) @ Y8))))))) @ c_Empty @ c_Empty)))) @ Y3))) @ ((^[Y3 : $i > ($i > $i) > $i]: ((^[Y4 : $i]: (c_Eps_i @ (^[Y5 : $i]: ((^[Y6 : $i > ($i > $i) > $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: (!! @ ($i > $i > $o) @ (^[Y9 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y10 : $i > $i]: (!! @ $i @ (^[Y11 : $i]: ((!! @ $i @ (^[Y12 : $i]: ((c_In @ Y12 @ Y11) => (Y9 @ Y12 @ (Y10 @ Y12))))) => (Y9 @ Y11 @ (Y6 @ Y11 @ Y10))))))) => (Y9 @ Y7 @ Y8))))))))) @ Y3 @ Y4 @ Y5)))))) @ (^[Y3 : $i]: ((^[Y4 : $i > $i]: ((^[Y5 : $i]: ((^[Y6 : $i]: (c_Union @ ((^[Y7 : $i]: ((^[Y8 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y9 : $i]: ((^[Y10 : $o]: ((^[Y11 : $i]: ((^[Y12 : $i]: (c_Eps_i @ (^[Y13 : $i]: ((^[Y14 : $o]: ((^[Y15 : $o]: (!! @ $o @ (^[Y16 : $o]: ((Y14 => Y16) => ((Y15 => Y16) => Y16))))))) @ ((^[Y14 : $o]: ((^[Y15 : $o]: (!! @ $o @ (^[Y16 : $o]: ((Y14 => (Y15 => Y16)) => Y16)))))) @ Y10 @ (Y11 = Y13)) @ ((^[Y14 : $o]: ((^[Y15 : $o]: (!! @ $o @ (^[Y16 : $o]: ((Y14 => (Y15 => Y16)) => Y16)))))) @ ((^[Y14 : $o]: (Y14 => c_False)) @ Y10) @ (Y12 = Y13)))))))))) @ (c_In @ c_Empty @ Y9) @ Y7 @ Y8)))))) @ Y5 @ Y6))))) @ ((^[Y5 : $i]: ((^[Y6 : $i]: ((^[Y7 : $i]: (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y8 : $i]: ((^[Y9 : $o]: ((^[Y10 : $i]: ((^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => Y15) => ((Y14 => Y15) => Y15))))))) @ ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => (Y14 => Y15)) => Y15)))))) @ Y9 @ (Y10 = Y12)) @ ((^[Y13 : $o]: ((^[Y14 : $o]: (!! @ $o @ (^[Y15 : $o]: ((Y13 => (Y14 => Y15)) => Y15)))))) @ ((^[Y13 : $o]: (Y13 => c_False)) @ Y9) @ (Y11 = Y12)))))))))) @ (c_In @ c_Empty @ Y8) @ Y6 @ Y7)))))) @ Y5 @ Y5)) @ c_Empty) @ (c_Repl @ Y3 @ (^[Y5 : $i]: (Y4 @ Y5))))))) @ c_Empty))))))) @ (^[Y0 : $i]: (X5 @ c_Empty)) @ (^[Y0 : $i > $i > $i]: (c_Empty)))))) )),
% 5.11/1.20 inference(definition_unfolding,[],[f459,f513,f509])).
% 5.11/1.20 thf(f566,plain,(
% 5.11/1.20 ( ! [X4 : $i,X5 : ($i > $i)] : ((((X5 @ X4)) = ((sK9 @ (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (sK10 @ (^[Y3 : $i]: (sK11 @ (^[Y4 : ($i > $i > $i > $i) > $i]: ((^[Y5 : $i]: (Y2)))) @ (sK11 @ (^[Y4 : ($i > $i > $i > $i) > $i]: ((^[Y5 : $i]: (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y6 : $i]: (c_Eps_i @ (^[Y7 : $i]: (!! @ $o @ (^[Y8 : $o]: (((!! @ $o @ (^[Y9 : $o]: (((c_In @ c_Empty @ Y6) => (((c_Repl @ c_Empty @ (^[Y10 : $i]: (c_Repl @ Y10 @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ ($i > $i > $o) @ (^[Y13 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y14 : $i > $i]: (!! @ $i @ (^[Y15 : $i]: ((!! @ $i @ (^[Y16 : $i]: ((c_In @ Y16 @ Y15) => (Y13 @ Y16 @ (Y14 @ Y16))))) => (Y13 @ Y15 @ (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y16 : $i]: (c_Eps_i @ (^[Y17 : $i]: (!! @ $o @ (^[Y18 : $o]: (((!! @ $o @ (^[Y19 : $o]: (((c_In @ c_Empty @ Y16) => (((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y20 : $i]: (c_Eps_i @ (^[Y21 : $i]: (!! @ $o @ (^[Y22 : $o]: (((!! @ $o @ (^[Y23 : $o]: (((c_In @ c_Empty @ Y20) => ((c_Empty = Y21) => Y23)) => Y23))) => Y22) => (((!! @ $o @ (^[Y23 : $o]: ((((c_In @ c_Empty @ Y20) => c_False) => ((c_Empty = Y21) => Y23)) => Y23))) => Y22) => Y22)))))))) = Y17) => Y19)) => Y19))) => Y18) => (((!! @ $o @ (^[Y19 : $o]: ((((c_In @ c_Empty @ Y16) => c_False) => (((c_Repl @ Y15 @ Y14) = Y17) => Y19)) => Y19))) => Y18) => Y18))))))))))))))) => (Y13 @ Y11 @ Y12)))))))))) = Y7) => Y9)) => Y9))) => Y8) => (((!! @ $o @ (^[Y9 : $o]: ((((c_In @ c_Empty @ Y6) => c_False) => (((c_Repl @ c_Empty @ (^[Y10 : $i]: (c_Eps_i @ (^[Y11 : $i]: (!! @ ($i > $i > $o) @ (^[Y12 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y13 : $i > $i]: (!! @ $i @ (^[Y14 : $i]: ((!! @ $i @ (^[Y15 : $i]: ((c_In @ Y15 @ Y14) => (Y12 @ Y15 @ (Y13 @ Y15))))) => (Y12 @ Y14 @ (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y15 : $i]: (c_Eps_i @ (^[Y16 : $i]: (!! @ $o @ (^[Y17 : $o]: (((!! @ $o @ (^[Y18 : $o]: (((c_In @ c_Empty @ Y15) => (((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y19 : $i]: (c_Eps_i @ (^[Y20 : $i]: (!! @ $o @ (^[Y21 : $o]: (((!! @ $o @ (^[Y22 : $o]: (((c_In @ c_Empty @ Y19) => ((c_Empty = Y20) => Y22)) => Y22))) => Y21) => (((!! @ $o @ (^[Y22 : $o]: ((((c_In @ c_Empty @ Y19) => c_False) => ((c_Empty = Y20) => Y22)) => Y22))) => Y21) => Y21)))))))) = Y16) => Y18)) => Y18))) => Y17) => (((!! @ $o @ (^[Y18 : $o]: ((((c_In @ c_Empty @ Y15) => c_False) => (((c_Repl @ Y14 @ Y13) = Y16) => Y18)) => Y18))) => Y17) => Y17))))))))))))))) => (Y12 @ Y10 @ Y11)))))))) = Y7) => Y9)) => Y9))) => Y8) => Y8)))))))))))) @ Y3))) @ (c_Eps_i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: ((!! @ ($i > $i) @ (^[Y5 : $i > $i]: (!! @ $i @ (^[Y6 : $i]: ((!! @ $i @ (^[Y7 : $i]: ((c_In @ Y7 @ Y6) => (Y4 @ Y7 @ (Y5 @ Y7))))) => (Y4 @ Y6 @ (c_Union @ (c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y7 : $i]: (c_Eps_i @ (^[Y8 : $i]: (!! @ $o @ (^[Y9 : $o]: (((!! @ $o @ (^[Y10 : $o]: (((c_In @ c_Empty @ Y7) => (((c_Repl @ (c_Power @ (c_Power @ c_Empty)) @ (^[Y11 : $i]: (c_Eps_i @ (^[Y12 : $i]: (!! @ $o @ (^[Y13 : $o]: (((!! @ $o @ (^[Y14 : $o]: (((c_In @ c_Empty @ Y11) => ((c_Empty = Y12) => Y14)) => Y14))) => Y13) => (((!! @ $o @ (^[Y14 : $o]: ((((c_In @ c_Empty @ Y11) => c_False) => ((c_Empty = Y12) => Y14)) => Y14))) => Y13) => Y13)))))))) = Y8) => Y10)) => Y10))) => Y9) => (((!! @ $o @ (^[Y10 : $o]: ((((c_In @ c_Empty @ Y7) => c_False) => (((c_Repl @ Y6 @ Y5) = Y8) => Y10)) => Y10))) => Y9) => Y9))))))))))))))) => (Y4 @ c_Empty @ Y3)))))))))))) @ (^[Y0 : $i]: (X5 @ c_Empty)) @ (^[Y0 : $i > $i > $i]: (c_Empty)))))) )),
% 5.11/1.20 inference(beta-eta_normalization,[],[f555])).
% 5.11/1.20 thf(f612,plain,(
% 5.11/1.20 ( ! [X0 : $i,X1 : $i] : (($true = ((!! @ $o @ (^[Y0 : $o]: ((((c_In @ X1 @ (c_Power @ X0)) => (!! @ $i @ (^[Y1 : $i]: ((c_In @ Y1 @ X1) => (c_In @ Y1 @ X0))))) => (((!! @ $i @ (^[Y1 : $i]: ((c_In @ Y1 @ X1) => (c_In @ Y1 @ X0)))) => (c_In @ X1 @ (c_Power @ X0))) => Y0)) => Y0)))))) )),
% 5.11/1.20 inference(beta-eta_normalization,[],[f553])).
% 5.11/1.20 thf(f613,plain,(
% 5.11/1.20 ( ! [X2 : $o,X0 : $i,X1 : $i] : (($true = (((^[Y0 : $o]: ((((c_In @ X1 @ (c_Power @ X0)) => (!! @ $i @ (^[Y1 : $i]: ((c_In @ Y1 @ X1) => (c_In @ Y1 @ X0))))) => (((!! @ $i @ (^[Y1 : $i]: ((c_In @ Y1 @ X1) => (c_In @ Y1 @ X0)))) => (c_In @ X1 @ (c_Power @ X0))) => Y0)) => Y0)) @ X2)))) )),
% 5.11/1.20 inference(pi_proxy_clausification,[],[f612])).
% 5.11/1.20 thf(f614,plain,(
% 5.11/1.20 ( ! [X2 : $o,X0 : $i,X1 : $i] : (($true = (((((c_In @ X1 @ (c_Power @ X0)) => (!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ X1) => (c_In @ Y0 @ X0))))) => (((!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ X1) => (c_In @ Y0 @ X0)))) => (c_In @ X1 @ (c_Power @ X0))) => X2)) => X2)))) )),
% 5.11/1.20 inference(beta-eta_normalization,[],[f613])).
% 5.11/1.20 thf(f615,plain,(
% 5.11/1.20 ( ! [X2 : $o,X0 : $i,X1 : $i] : (($false = ((((c_In @ X1 @ (c_Power @ X0)) => (!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ X1) => (c_In @ Y0 @ X0))))) => (((!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ X1) => (c_In @ Y0 @ X0)))) => (c_In @ X1 @ (c_Power @ X0))) => X2)))) | ($true = X2)) )),
% 5.11/1.20 inference(imp_proxy_clausification,[],[f614])).
% 5.11/1.20 thf(f616,plain,(
% 5.11/1.20 ( ! [X2 : $o,X0 : $i,X1 : $i] : (($false = ((((!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ X1) => (c_In @ Y0 @ X0)))) => (c_In @ X1 @ (c_Power @ X0))) => X2))) | ($true = X2)) )),
% 5.11/1.20 inference(imp_proxy_clausification,[],[f615])).
% 5.11/1.20 thf(f623,plain,(
% 5.11/1.20 ( ! [X2 : $o,X0 : $i,X1 : $i] : (($true = (((!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ X1) => (c_In @ Y0 @ X0)))) => (c_In @ X1 @ (c_Power @ X0))))) | ($true = X2)) )),
% 5.11/1.20 inference(imp_proxy_clausification,[],[f616])).
% 5.11/1.20 thf(f624,plain,(
% 5.11/1.20 ( ! [X2 : $o,X0 : $i,X1 : $i] : (($false = ((!! @ $i @ (^[Y0 : $i]: ((c_In @ Y0 @ X1) => (c_In @ Y0 @ X0)))))) | ($true = X2) | (((c_In @ X1 @ (c_Power @ X0))) = $true)) )),
% 5.11/1.20 inference(imp_proxy_clausification,[],[f623])).
% 5.11/1.20 thf(f625,plain,(
% 5.11/1.20 ( ! [X2 : $o,X0 : $i,X1 : $i] : (($false = (((^[Y0 : $i]: ((c_In @ Y0 @ X1) => (c_In @ Y0 @ X0))) @ (sK17 @ X1 @ X0)))) | ($true = X2) | (((c_In @ X1 @ (c_Power @ X0))) = $true)) )),
% 5.11/1.20 inference(sigma_proxy_clausification,[],[f624])).
% 5.11/1.20 thf(f626,plain,(
% 5.11/1.20 ( ! [X2 : $o,X0 : $i,X1 : $i] : (($false = (((c_In @ (sK17 @ X1 @ X0) @ X1) => (c_In @ (sK17 @ X1 @ X0) @ X0)))) | ($true = X2) | (((c_In @ X1 @ (c_Power @ X0))) = $true)) )),
% 5.11/1.20 inference(beta-eta_normalization,[],[f625])).
% 5.11/1.20 thf(f628,plain,(
% 5.11/1.20 ( ! [X2 : $o,X0 : $i,X1 : $i] : (($true = ((c_In @ (sK17 @ X1 @ X0) @ X1))) | ($true = X2) | (((c_In @ X1 @ (c_Power @ X0))) = $true)) )),
% 5.11/1.20 inference(imp_proxy_clausification,[],[f626])).
% 5.11/1.20 thf(f629,plain,(
% 5.11/1.20 ( ! [X0 : $i,X1 : $i] : (($true = ((!! @ $o @ (^[Y0 : $o]: ((((c_In @ X1 @ (c_Union @ X0)) => (?? @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (((c_In @ X1 @ Y1) => ((c_In @ Y1 @ X0) => Y2)) => Y2)))))) => (((?? @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (((c_In @ X1 @ Y1) => ((c_In @ Y1 @ X0) => Y2)) => Y2))))) => (c_In @ X1 @ (c_Union @ X0))) => Y0)) => Y0)))))) )),
% 5.11/1.20 inference(beta-eta_normalization,[],[f552])).
% 5.11/1.20 thf(f630,plain,(
% 5.11/1.20 ( ! [X2 : $o,X0 : $i,X1 : $i] : (($true = (((^[Y0 : $o]: ((((c_In @ X1 @ (c_Union @ X0)) => (?? @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (((c_In @ X1 @ Y1) => ((c_In @ Y1 @ X0) => Y2)) => Y2)))))) => (((?? @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: (((c_In @ X1 @ Y1) => ((c_In @ Y1 @ X0) => Y2)) => Y2))))) => (c_In @ X1 @ (c_Union @ X0))) => Y0)) => Y0)) @ X2)))) )),
% 5.11/1.20 inference(pi_proxy_clausification,[],[f629])).
% 5.11/1.20 thf(f631,plain,(
% 5.11/1.20 ( ! [X2 : $o,X0 : $i,X1 : $i] : (($true = (((((c_In @ X1 @ (c_Union @ X0)) => (?? @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (((c_In @ X1 @ Y0) => ((c_In @ Y0 @ X0) => Y1)) => Y1)))))) => (((?? @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (((c_In @ X1 @ Y0) => ((c_In @ Y0 @ X0) => Y1)) => Y1))))) => (c_In @ X1 @ (c_Union @ X0))) => X2)) => X2)))) )),
% 5.11/1.20 inference(beta-eta_normalization,[],[f630])).
% 5.11/1.20 thf(f632,plain,(
% 5.11/1.20 ( ! [X2 : $o,X0 : $i,X1 : $i] : (($false = ((((c_In @ X1 @ (c_Union @ X0)) => (?? @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (((c_In @ X1 @ Y0) => ((c_In @ Y0 @ X0) => Y1)) => Y1)))))) => (((?? @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (((c_In @ X1 @ Y0) => ((c_In @ Y0 @ X0) => Y1)) => Y1))))) => (c_In @ X1 @ (c_Union @ X0))) => X2)))) | ($true = X2)) )),
% 5.11/1.20 inference(imp_proxy_clausification,[],[f631])).
% 5.11/1.20 thf(f633,plain,(
% 5.11/1.20 ( ! [X2 : $o,X0 : $i,X1 : $i] : (($false = ((((?? @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: (((c_In @ X1 @ Y0) => ((c_In @ Y0 @ X0) => Y1)) => Y1))))) => (c_In @ X1 @ (c_Union @ X0))) => X2))) | ($true = X2)) )),
% 5.11/1.20 inference(imp_proxy_clausification,[],[f632])).
% 5.11/1.20 thf(f645,plain,(
% 5.11/1.20 ( ! [X2 : $o] : (($false = X2) | ($true = X2)) )),
% 5.11/1.20 inference(imp_proxy_clausification,[],[f633])).
% 5.11/1.20 thf(f656,plain,(
% 5.11/1.20 ($true = (((?? @ $i @ (^[Y0 : $i]: (c_In @ Y0 @ c_Empty))) => c_False)))),
% 5.11/1.20 inference(beta-eta_normalization,[],[f551])).
% 5.11/1.20 thf(f657,plain,(
% 5.11/1.20 (((?? @ $i @ (^[Y0 : $i]: (c_In @ Y0 @ c_Empty)))) = $false) | (c_False = $true)),
% 5.11/1.20 inference(imp_proxy_clausification,[],[f656])).
% 5.11/1.20 thf(f658,plain,(
% 5.11/1.20 ( ! [X1 : $i] : (($false = (((^[Y0 : $i]: (c_In @ Y0 @ c_Empty)) @ X1))) | (c_False = $true)) )),
% 5.11/1.20 inference(pi_proxy_clausification,[],[f657])).
% 5.11/1.20 thf(f659,plain,(
% 5.11/1.20 ( ! [X1 : $i] : (($false = ((c_In @ X1 @ c_Empty))) | (c_False = $true)) )),
% 5.11/1.20 inference(beta-eta_normalization,[],[f658])).
% 5.11/1.20 thf(f714,plain,(
% 5.11/1.20 ( ! [X1 : $i] : (($false = ((c_In @ X1 @ c_Empty)))) )),
% 5.11/1.20 inference(global_subsumption,[],[f659,f460])).
% 5.11/1.20 thf(f721,plain,(
% 5.11/1.20 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 5.11/1.20 inference(global_subsumption,[],[f645])).
% 5.11/1.20 thf(f778,definition,(
% 5.11/1.20 spl24_5 <=> ! [X0 : $i,X1 : $i] : (X0 = X1)),
% 5.11/1.20 introduced(definition,[new_symbols(definition,[spl24_5])],[avatar_definition])).
% 5.11/1.20 thf(f779,plain,(
% 5.11/1.20 ( ! [X0 : $i,X1 : $i] : ((X0 = X1)) ) | ~spl24_5),
% 5.11/1.20 inference(avatar_component_clause,[],[f778])).
% 5.11/1.20 thf(f796,definition,(
% 5.11/1.20 spl24_7 <=> ! [X0 : $o] : ($true = X0)),
% 5.11/1.20 introduced(definition,[new_symbols(definition,[spl24_7])],[avatar_definition])).
% 5.11/1.20 thf(f797,plain,(
% 5.11/1.20 ( ! [X0 : $o] : (($true = X0)) ) | ~spl24_7),
% 5.11/1.20 inference(avatar_component_clause,[],[f796])).
% 5.11/1.20 thf(f805,plain,(
% 5.11/1.20 ($true != $true) | (c_False = $false)),
% 5.11/1.20 inference(constrained_superposition,[],[f460,f721])).
% 5.11/1.20 thf(f817,plain,(
% 5.11/1.20 (c_False = $false)),
% 5.11/1.20 inference(trivial_inequality_removal,[],[f805])).
% 5.11/1.20 thf(f833,plain,(
% 5.11/1.20 ($true = $false) | ~spl24_7),
% 5.11/1.20 inference(constrained_superposition,[],[f817,f797])).
% 5.11/1.20 thf(f850,plain,(
% 5.11/1.20 $false | ~spl24_7),
% 5.11/1.20 inference(trivial_inequality_removal,[],[f833])).
% 5.11/1.20 thf(f851,plain,(
% 5.11/1.21 ~spl24_7),
% 5.11/1.21 inference(avatar_contradiction_clause,[],[f850])).
% 5.11/1.21 thf(f901,plain,(
% 5.11/1.21 ( ! [X0 : $i,X1 : $i] : ((((c_In @ X1 @ X0)) = $false)) ) | ~spl24_5),
% 5.11/1.21 inference(constrained_superposition,[],[f714,f779])).
% 5.11/1.21 thf(f1009,plain,(
% 5.11/1.21 ( ! [X0 : ($i > $o),X1 : $i] : (($true != $true) | (((X0 @ (c_Eps_i @ X0))) = $true) | (((X0 @ X1)) = $false)) )),
% 5.11/1.21 inference(constrained_superposition,[],[f334,f721])).
% 5.11/1.21 thf(f1083,plain,(
% 5.11/1.21 ( ! [X0 : ($i > $o),X1 : $i] : ((((X0 @ (c_Eps_i @ X0))) = $true) | (((X0 @ X1)) = $false)) )),
% 5.11/1.21 inference(trivial_inequality_removal,[],[f1009])).
% 5.11/1.21 thf(f1154,plain,(
% 5.11/1.21 ( ! [X0 : $i] : ((((c_Eps_i @ (= @ X0))) = X0)) )),
% 5.11/1.21 inference(leibniz_equality_elimination,[],[f1083])).
% 5.11/1.21 thf(f2637,plain,(
% 5.11/1.21 ( ! [X2 : $o,X0 : $i,X1 : $i] : (($true = $false) | ($true = X2) | (((c_In @ X1 @ (c_Power @ X0))) = $true)) ) | ~spl24_5),
% 5.11/1.21 inference(forward_demodulation,[],[f628,f901])).
% 5.11/1.21 thf(f2638,plain,(
% 5.11/1.21 ( ! [X2 : $o,X0 : $i,X1 : $i] : (($true = X2) | (((c_In @ X1 @ (c_Power @ X0))) = $true)) ) | ~spl24_5),
% 5.11/1.21 inference(trivial_inequality_removal,[],[f2637])).
% 5.11/1.21 thf(f2639,plain,(
% 5.11/1.21 ( ! [X2 : $o] : (($true = $false) | ($true = X2)) ) | ~spl24_5),
% 5.11/1.21 inference(forward_demodulation,[],[f2638,f901])).
% 5.11/1.21 thf(f2640,plain,(
% 5.11/1.21 ( ! [X2 : $o] : (($true = X2)) ) | ~spl24_5),
% 5.11/1.21 inference(trivial_inequality_removal,[],[f2639])).
% 5.11/1.21 thf(f2641,plain,(
% 5.11/1.21 spl24_7 | ~spl24_5),
% 5.11/1.21 inference(avatar_split_clause,[],[f2640,f778,f796])).
% 5.11/1.21 thf(f4625,definition,(
% 5.11/1.21 spl24_35 <=> ! [X0 : $i] : (c_Empty = X0)),
% 5.11/1.21 introduced(definition,[new_symbols(definition,[spl24_35])],[avatar_definition])).
% 5.11/1.21 thf(f4626,plain,(
% 5.11/1.21 ( ! [X0 : $i] : ((c_Empty = X0)) ) | ~spl24_35),
% 5.11/1.21 inference(avatar_component_clause,[],[f4625])).
% 5.11/1.21 thf(f4643,plain,(
% 5.11/1.21 ( ! [X0 : $i,X1 : $i] : ((X0 = X1)) ) | ~spl24_35),
% 5.11/1.21 inference(constrained_superposition,[],[f4626,f4626])).
% 5.11/1.21 thf(f4681,plain,(
% 5.11/1.21 spl24_5 | ~spl24_35),
% 5.11/1.21 inference(avatar_split_clause,[],[f4643,f4625,f778])).
% 5.11/1.21 thf(f9016,plain,(
% 5.11/1.21 ( ! [X2 : ($i > $i),X3 : $i,X0 : ($i > $i),X1 : $i] : ((((X2 @ X3)) = ((X0 @ X1))) | ((^[Y0 : $i]: (X0 @ c_Empty)) != (^[Y0 : $i]: (X2 @ c_Empty)))) )),
% 5.11/1.21 inference(constrained_superposition,[],[f566,f566])).
% 5.11/1.21 thf(f9676,plain,(
% 5.11/1.21 ( ! [X2 : $i,X3 : ($i > $o),X0 : ($i > $i),X1 : $i] : ((((X0 @ X1)) = X2) | ((^[Y0 : $i]: (X0 @ c_Empty)) != (^[Y0 : $i]: ((^[Y1 : $i]: (Y1)) @ c_Empty))) | (((= @ X2)) != X3)) )),
% 5.11/1.21 inference(constrained_superposition,[],[f1154,f9016])).
% 5.11/1.21 thf(f9761,plain,(
% 5.11/1.21 ( ! [X2 : $i,X3 : ($i > $o),X0 : ($i > $i),X1 : $i] : (((^[Y0 : $i]: (c_Empty)) != (^[Y0 : $i]: (X0 @ c_Empty))) | (((X0 @ X1)) = X2) | (((= @ X2)) != X3)) )),
% 5.11/1.21 inference(beta-eta_normalization,[],[f9676])).
% 5.11/1.21 thf(f10282,plain,(
% 5.11/1.21 ( ! [X2 : ($i > $o),X0 : $i,X1 : $i] : (((((^[Y0 : $i]: (c_Empty)) @ X0)) = X1) | (((= @ X1)) != X2)) )),
% 5.11/1.21 inference(equality_resolution,[],[f9761])).
% 5.11/1.21 thf(f10283,plain,(
% 5.11/1.21 ( ! [X2 : ($i > $o),X1 : $i] : ((((= @ X1)) != X2) | (c_Empty = X1)) )),
% 5.11/1.21 inference(beta-eta_normalization,[],[f10282])).
% 5.11/1.21 thf(f10293,plain,(
% 5.11/1.21 ( ! [X0 : $i] : ((c_Empty = X0)) )),
% 5.11/1.21 inference(equality_resolution,[],[f10283])).
% 5.11/1.21 thf(f10300,plain,(
% 5.11/1.21 spl24_35),
% 5.11/1.21 inference(avatar_split_clause,[],[f10293,f4625])).
% 5.11/1.21 cnf(s116, plain, ~spl24_7, inference(sat_conversion,[],[f851])).
% 5.11/1.21 cnf(s274, plain, ~spl24_5 | spl24_7, inference(sat_conversion,[],[f2641])).
% 5.11/1.21 cnf(s521, plain, spl24_5 | ~spl24_35, inference(sat_conversion,[],[f4681])).
% 5.11/1.21 cnf(s2385, plain, spl24_35, inference(sat_conversion,[],[f10300])).
% 5.11/1.21 cnf(s2396, plain, spl24_5, inference(rat,[],[s521,s2385])).
% 5.11/1.21 cnf(s2399, plain, spl24_7, inference(rat,[],[s274,s2396])).
% 5.11/1.21 cnf(s2402, plain, $false, inference(rat,[],[s116,s2399])).
% 5.11/1.21 thf(f10301,plain,(
% 5.11/1.21 $false),
% 5.11/1.21 inference(avatar_sat_refutation,[],[s2402])).
% 5.11/1.21 % SZS output end Proof for theBenchmark
% 5.11/1.21 % (101294)------------------------------
% 5.11/1.21 % (101294)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.11/1.21 % (101294)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.11/1.21 % (101294)CaDiCaL version: 2.1.3
% 5.11/1.21 % (101294)Termination reason: Refutation
% 5.11/1.21 % (101294)Time elapsed: 0.927 s
% 5.11/1.21 % (101294)Peak memory usage: 20 MB
% 5.11/1.21 % (101294)Instructions burned: 4106 (million)
% 5.11/1.21 % (101283)Success in time 0.962 s
% 5.11/1.21 % Vampire exiting
%------------------------------------------------------------------------------