%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU596^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n003.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 08:32:36 AM UTC 2026
% Result : Theorem 6.77s 1.30s
% Output : Refutation 7.53s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU596^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n003.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 13:57:59 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 Running first-order model finding
% 0.08/0.22 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
% 6.77/1.29 % (2543096)Will run a generic schedule for satisfiability detection.
% 6.77/1.29 % (2543102)% WARNING: option uhcvi not known.
% 6.77/1.29 % (2543102)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3735412406:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 6.77/1.29 % (2543102)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.77/1.29 % (2543101)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2020963715_2999 on theBenchmark for (2999ds/0Mi)
% 6.77/1.29 % (2543103)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1671182359:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 6.77/1.29 % (2543105)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=94160976:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 6.77/1.29 % (2543104)dis+10_1_sil=32000:sp=arity:random_seed=2528711390:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 6.77/1.29 % (2543102)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 6.77/1.29 % (2543105)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.77/1.29 % Exception at run slice level
% 6.77/1.29 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.77/1.29 % (2543107)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3716845653:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 6.77/1.29 % (2543106)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2191054478:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 6.77/1.29 % (2543115)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=418589839:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 6.77/1.29 % (2543105)Instruction limit reached!
% 6.77/1.29 % (2543105)------------------------------
% 6.77/1.29 % (2543105)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.77/1.29 % (2543105)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.77/1.29 % (2543105)CaDiCaL version: 2.1.3
% 6.77/1.29 % (2543105)Termination reason: Instruction limit
% 6.77/1.29 % (2543105)Termination phase: Saturation
% 6.77/1.29 % (2543105)Time elapsed: 0.054 s
% 6.77/1.29 % (2543105)Peak memory usage: 13 MB
% 6.77/1.29 % (2543105)Instructions burned: 118 (million)
% 6.77/1.29 % Exception at run slice level
% 6.77/1.29 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.77/1.29 % (2543104)Instruction limit reached!
% 6.77/1.29 % (2543104)------------------------------
% 6.77/1.29 % (2543104)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.77/1.29 % (2543104)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.77/1.29 % (2543104)CaDiCaL version: 2.1.3
% 6.77/1.29 % (2543104)Termination reason: Instruction limit
% 6.77/1.29 % (2543104)Termination phase: Saturation
% 6.77/1.29 % (2543104)Time elapsed: 0.067 s
% 6.77/1.29 % (2543104)Peak memory usage: 13 MB
% 6.77/1.29 % (2543104)Instructions burned: 105 (million)
% 6.77/1.29 % (2543117)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=993905714:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 6.77/1.29 % (2543118)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=4227549645:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 6.77/1.29 % (2543106)Instruction limit reached!
% 6.77/1.29 % (2543106)------------------------------
% 6.77/1.29 % (2543106)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.77/1.29 % (2543106)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.77/1.29 % (2543106)CaDiCaL version: 2.1.3
% 6.77/1.29 % (2543106)Termination reason: Instruction limit
% 6.77/1.29 % (2543106)Termination phase: Saturation
% 6.77/1.29 % (2543106)Time elapsed: 0.061 s
% 6.77/1.29 % (2543106)Peak memory usage: 14 MB
% 6.77/1.29 % (2543106)Instructions burned: 131 (million)
% 6.77/1.29 % (2543118)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.77/1.29 % (2543119)ott-21_1_sil=16000:fs=off:random_seed=3876812192:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 6.77/1.29 % (2543118)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 6.77/1.29 % (2543122)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=1575311511:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 6.77/1.29 % (2543107)Instruction limit reached!
% 6.77/1.29 % (2543107)------------------------------
% 6.77/1.29 % (2543107)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.77/1.29 % (2543107)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.77/1.29 % (2543107)CaDiCaL version: 2.1.3
% 6.77/1.29 % (2543107)Termination reason: Instruction limit
% 6.77/1.29 % (2543107)Termination phase: Saturation
% 6.77/1.29 % (2543107)Time elapsed: 0.087 s
% 6.77/1.29 % (2543107)Peak memory usage: 13 MB
% 6.77/1.29 % (2543107)Instructions burned: 160 (million)
% 6.77/1.29 % (2543125)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=3080408252:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 6.77/1.29 % (2543117)Instruction limit reached!
% 6.77/1.29 % (2543117)------------------------------
% 6.77/1.29 % (2543117)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.77/1.29 % (2543117)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.77/1.30 % (2543117)CaDiCaL version: 2.1.3
% 6.77/1.30 % (2543117)Termination reason: Instruction limit
% 6.77/1.30 % (2543117)Termination phase: Saturation
% 6.77/1.30 % (2543117)Time elapsed: 0.074 s
% 6.77/1.30 % (2543117)Peak memory usage: 13 MB
% 6.77/1.30 % (2543117)Instructions burned: 131 (million)
% 6.77/1.30 % Exception at run slice level
% 6.77/1.30 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.77/1.30 % (2543127)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=4209061692:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 6.77/1.30 % (2543128)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=1094170877:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 6.77/1.30 % (2543119)Instruction limit reached!
% 6.77/1.30 % (2543119)------------------------------
% 6.77/1.30 % (2543119)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.77/1.30 % (2543119)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.77/1.30 % (2543119)CaDiCaL version: 2.1.3
% 6.77/1.30 % (2543119)Termination reason: Instruction limit
% 6.77/1.30 % (2543119)Termination phase: Saturation
% 6.77/1.30 % (2543119)Time elapsed: 0.101 s
% 6.77/1.30 % (2543119)Peak memory usage: 13 MB
% 6.77/1.30 % (2543119)Instructions burned: 182 (million)
% 6.77/1.30 % Exception at run slice level
% 6.77/1.30 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.77/1.30 % (2543132)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=2306040914:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 6.77/1.30 % (2543131)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=2900090316: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)
% 6.77/1.30 % (2543132)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.77/1.30 % (2543131)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.77/1.30 % (2543122)Instruction limit reached!
% 6.77/1.30 % (2543122)------------------------------
% 6.77/1.30 % (2543122)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.77/1.30 % (2543122)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.77/1.30 % (2543122)CaDiCaL version: 2.1.3
% 6.77/1.30 % (2543122)Termination reason: Instruction limit
% 6.77/1.30 % (2543122)Termination phase: Saturation
% 6.77/1.30 % (2543122)Time elapsed: 0.257 s
% 6.77/1.30 % (2543122)Peak memory usage: 13 MB
% 6.77/1.30 % (2543122)Instructions burned: 477 (million)
% 6.77/1.30 % (2543118)Instruction limit reached!
% 6.77/1.30 % (2543118)------------------------------
% 6.77/1.30 % (2543118)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.77/1.30 % (2543118)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.77/1.30 % (2543118)CaDiCaL version: 2.1.3
% 6.77/1.30 % (2543118)Termination reason: Instruction limit
% 6.77/1.30 % (2543118)Termination phase: Saturation
% 6.77/1.30 % (2543118)Time elapsed: 0.289 s
% 6.77/1.30 % (2543118)Peak memory usage: 14 MB
% 6.77/1.30 % (2543118)Instructions burned: 684 (million)
% 6.77/1.30 % (2543135)fmb+10_1_sil=64000:random_seed=1005517053:i=22061:nm=2:gsp=on_2996 on theBenchmark for (2996ds/22061Mi)
% 6.77/1.30 % (2543136)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=3709493322:i=9515:nm=5_2995 on theBenchmark for (2995ds/9515Mi)
% 6.77/1.30 % (2543135)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 6.77/1.30 % Exception at run slice level
% 6.77/1.30 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.77/1.30 % Exception at run slice level
% 6.77/1.30 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.77/1.30 % (2543139)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=1953807123:fmbsr=1.7:i=920_2995 on theBenchmark for (2995ds/920Mi)
% 6.77/1.30 % (2543140)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=2327670344:i=5131_2995 on theBenchmark for (2995ds/5131Mi)
% 6.77/1.30 % Exception at run slice level
% 6.77/1.30 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.77/1.30 % (2543140)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.77/1.30 % (2543143)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=3719308135:i=1472:ins=7:fdi=8:gsp=on_2995 on theBenchmark for (2995ds/1472Mi)
% 6.77/1.30 % (2543143)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 6.77/1.30 % (2543143)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 6.77/1.30 % (2543131)Instruction limit reached!
% 6.77/1.30 % (2543131)------------------------------
% 6.77/1.30 % (2543131)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.77/1.30 % (2543131)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.77/1.30 % (2543131)CaDiCaL version: 2.1.3
% 6.77/1.30 % (2543131)Termination reason: Instruction limit
% 6.77/1.30 % (2543131)Termination phase: Saturation
% 6.77/1.30 % (2543131)Time elapsed: 0.335 s
% 6.77/1.30 % (2543131)Peak memory usage: 15 MB
% 6.77/1.30 % (2543131)Instructions burned: 693 (million)
% 6.77/1.30 % (2543145)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=3375899730:i=6324_2994 on theBenchmark for (2994ds/6324Mi)
% 6.77/1.30 % Exception at run slice level
% 6.77/1.30 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.77/1.30 % (2543147)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=3326185539:fmbsr=2.30978:i=2174_2993 on theBenchmark for (2993ds/2174Mi)
% 6.77/1.30 % Exception at run slice level
% 6.77/1.30 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.77/1.30 % (2543132)Instruction limit reached!
% 6.77/1.30 % (2543132)------------------------------
% 6.77/1.30 % (2543132)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.77/1.30 % (2543132)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.77/1.30 % (2543132)CaDiCaL version: 2.1.3
% 6.77/1.30 % (2543132)Termination reason: Instruction limit
% 6.77/1.30 % (2543132)Termination phase: Saturation
% 6.77/1.30 % (2543132)Time elapsed: 0.435 s
% 6.77/1.30 % (2543132)Peak memory usage: 17 MB
% 6.77/1.30 % (2543132)Instructions burned: 880 (million)
% 6.77/1.30 % (2543150)ott+10_1_sil=32000:tgt=ground:random_seed=2810494022:i=5114:av=off_2993 on theBenchmark for (2993ds/5114Mi)
% 6.77/1.30 % (2543149)ott-2_1_sil=16000:newcnf=on:random_seed=3591489310:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2993 on theBenchmark for (2993ds/869Mi)
% 6.77/1.30 % (2543149)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.77/1.30 % (2543150) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2543096-2543150"...
% 6.77/1.30 % (2543127)Instruction limit reached!
% 6.77/1.30 % (2543127)------------------------------
% 6.77/1.30 % (2543127)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.77/1.30 % (2543127)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.77/1.30 % (2543127)CaDiCaL version: 2.1.3
% 6.77/1.30 % (2543127)Termination reason: Instruction limit
% 6.77/1.30 % (2543127)Termination phase: Saturation
% 6.77/1.30 % (2543127)Time elapsed: 0.850 s
% 6.77/1.30 % (2543127)Peak memory usage: 17 MB
% 6.77/1.30 % (2543127)Instructions burned: 1179 (million)
% 6.77/1.30 % (2543150)...printing done.
% 6.77/1.30 % (2543150)Refutation found. Thanks to Tanya!
% 6.77/1.30 % SZS status Theorem for theBenchmark
% 6.77/1.30 % SZS output start Proof for theBenchmark
% 6.77/1.30 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 6.77/1.30 thf(func_def_0, type, in: ($i > $i > $o)).
% 6.77/1.30 thf(func_def_1, type, exu: (($i > $o) > $o)).
% 6.77/1.30 thf(func_def_3, type, setextAx: $o).
% 6.77/1.30 thf(func_def_5, type, emptysetAx: $o).
% 6.77/1.30 thf(func_def_6, type, setadjoin: ($i > $i > $i)).
% 6.77/1.30 thf(func_def_7, type, setadjoinAx: $o).
% 6.77/1.30 thf(func_def_8, type, powerset: ($i > $i)).
% 6.77/1.30 thf(func_def_9, type, powersetAx: $o).
% 6.77/1.30 thf(func_def_10, type, setunion: ($i > $i)).
% 6.77/1.30 thf(func_def_11, type, setunionAx: $o).
% 6.77/1.30 thf(func_def_13, type, omega0Ax: $o).
% 6.77/1.30 thf(func_def_14, type, omegaSAx: $o).
% 6.77/1.30 thf(func_def_15, type, omegaIndAx: $o).
% 6.77/1.30 thf(func_def_16, type, replAx: $o).
% 6.77/1.30 thf(func_def_17, type, foundationAx: $o).
% 6.77/1.30 thf(func_def_18, type, wellorderingAx: $o).
% 6.77/1.30 thf(func_def_19, type, descr: (($i > $o) > $i)).
% 6.77/1.30 thf(func_def_20, type, descrp: $o).
% 6.77/1.30 thf(func_def_21, type, dsetconstr: ($i > ($i > $o) > $i)).
% 6.77/1.30 thf(func_def_22, type, dsetconstrI: $o).
% 6.77/1.30 thf(func_def_23, type, dsetconstrEL: $o).
% 6.77/1.30 thf(func_def_24, type, dsetconstrER: $o).
% 6.77/1.30 thf(func_def_25, type, exuE1: $o).
% 6.77/1.30 thf(func_def_26, type, prop2set: ($o > $i)).
% 6.77/1.30 thf(func_def_27, type, prop2setE: $o).
% 6.77/1.30 thf(func_def_28, type, emptysetE: $o).
% 6.77/1.30 thf(func_def_29, type, emptysetimpfalse: $o).
% 6.77/1.30 thf(func_def_30, type, notinemptyset: $o).
% 6.77/1.30 thf(func_def_31, type, exuE3e: $o).
% 6.77/1.30 thf(func_def_32, type, setext: $o).
% 6.77/1.30 thf(func_def_33, type, emptyI: $o).
% 6.77/1.30 thf(func_def_34, type, noeltsimpempty: $o).
% 6.77/1.30 thf(func_def_35, type, setbeta: $o).
% 6.77/1.30 thf(func_def_36, type, nonempty: ($i > $o)).
% 6.77/1.30 thf(func_def_37, type, nonemptyE1: $o).
% 6.77/1.30 thf(func_def_38, type, nonemptyI: $o).
% 6.77/1.30 thf(func_def_39, type, nonemptyI1: $o).
% 6.77/1.30 thf(func_def_40, type, setadjoinIL: $o).
% 6.77/1.30 thf(func_def_41, type, emptyinunitempty: $o).
% 6.77/1.30 thf(func_def_42, type, setadjoinIR: $o).
% 6.77/1.30 thf(func_def_43, type, setadjoinE: $o).
% 6.77/1.30 thf(func_def_44, type, setadjoinOr: $o).
% 6.77/1.30 thf(func_def_45, type, setoftrueEq: $o).
% 6.77/1.30 thf(func_def_46, type, powersetI: $o).
% 6.77/1.30 thf(func_def_47, type, emptyinPowerset: $o).
% 6.77/1.30 thf(func_def_48, type, emptyInPowerset: $o).
% 6.77/1.30 thf(func_def_49, type, powersetE: $o).
% 6.77/1.30 thf(func_def_50, type, setunionI: $o).
% 6.77/1.30 thf(func_def_51, type, setunionE: $o).
% 6.77/1.30 thf(func_def_52, type, subPowSU: $o).
% 6.77/1.30 thf(func_def_53, type, exuE2: $o).
% 6.77/1.30 thf(func_def_54, type, nonemptyImpWitness: $o).
% 6.77/1.30 thf(func_def_55, type, uniqinunit: $o).
% 6.77/1.30 thf(func_def_56, type, notinsingleton: $o).
% 6.77/1.30 thf(func_def_57, type, eqinunit: $o).
% 6.77/1.30 thf(func_def_58, type, singletonsswitch: $o).
% 6.77/1.30 thf(func_def_59, type, upairsetE: $o).
% 6.77/1.30 thf(func_def_60, type, upairsetIL: $o).
% 6.77/1.30 thf(func_def_61, type, upairsetIR: $o).
% 6.77/1.30 thf(func_def_62, type, emptyE1: $o).
% 6.77/1.30 thf(func_def_63, type, vacuousDall: $o).
% 6.77/1.30 thf(func_def_64, type, quantDeMorgan1: $o).
% 6.77/1.30 thf(func_def_65, type, quantDeMorgan2: $o).
% 6.77/1.30 thf(func_def_66, type, quantDeMorgan3: $o).
% 6.77/1.30 thf(func_def_67, type, quantDeMorgan4: $o).
% 6.77/1.30 thf(func_def_68, type, prop2setI: $o).
% 6.77/1.30 thf(func_def_69, type, set2prop: ($i > $o)).
% 6.77/1.30 thf(func_def_70, type, prop2set2propI: $o).
% 6.77/1.30 thf(func_def_71, type, notdexE: $o).
% 6.77/1.30 thf(func_def_72, type, notdallE: $o).
% 6.77/1.30 thf(func_def_73, type, exuI1: $o).
% 6.77/1.30 thf(func_def_74, type, exuI3: $o).
% 6.77/1.30 thf(func_def_75, type, exuI2: $o).
% 6.77/1.30 thf(func_def_76, type, inCongP: $o).
% 6.77/1.30 thf(func_def_77, type, in__Cong: $o).
% 6.77/1.30 thf(func_def_78, type, exuE3u: $o).
% 6.77/1.30 thf(func_def_79, type, exu__Cong: $o).
% 6.77/1.30 thf(func_def_80, type, emptyset__Cong: $o).
% 6.77/1.30 thf(func_def_81, type, setadjoin__Cong: $o).
% 6.77/1.30 thf(func_def_82, type, powerset__Cong: $o).
% 6.77/1.30 thf(func_def_83, type, setunion__Cong: $o).
% 6.77/1.30 thf(func_def_84, type, omega__Cong: $o).
% 6.77/1.30 thf(func_def_85, type, exuEu: $o).
% 6.77/1.30 thf(func_def_86, type, descr__Cong: $o).
% 6.77/1.30 thf(func_def_87, type, dsetconstr__Cong: $o).
% 6.77/1.30 thf(func_def_88, type, subset: ($i > $i > $o)).
% 6.77/1.30 thf(func_def_89, type, disjoint: ($i > $i > $o)).
% 6.77/1.30 thf(func_def_90, type, setsmeet: ($i > $i > $o)).
% 6.77/1.30 thf(func_def_91, type, subsetI1: $o).
% 6.77/1.30 thf(func_def_92, type, eqimpsubset2: $o).
% 6.77/1.30 thf(func_def_93, type, eqimpsubset1: $o).
% 6.77/1.30 thf(func_def_94, type, subsetI2: $o).
% 6.77/1.30 thf(func_def_95, type, emptysetsubset: $o).
% 6.77/1.30 thf(func_def_96, type, subsetE: $o).
% 6.77/1.30 thf(func_def_97, type, subsetE2: $o).
% 6.77/1.30 thf(func_def_98, type, notsubsetI: $o).
% 6.77/1.30 thf(func_def_99, type, notequalI1: $o).
% 6.77/1.30 thf(func_def_100, type, notequalI2: $o).
% 6.77/1.30 thf(func_def_101, type, subsetRefl: $o).
% 6.77/1.30 thf(func_def_102, type, subsetTrans: $o).
% 6.77/1.30 thf(func_def_103, type, setadjoinSub: $o).
% 6.77/1.30 thf(func_def_104, type, setadjoinSub2: $o).
% 6.77/1.30 thf(func_def_105, type, subset2powerset: $o).
% 6.77/1.30 thf(func_def_106, type, setextsub: $o).
% 6.77/1.30 thf(func_def_107, type, subsetemptysetimpeq: $o).
% 6.77/1.30 thf(func_def_108, type, powersetI1: $o).
% 6.77/1.30 thf(func_def_109, type, powersetE1: $o).
% 6.77/1.30 thf(func_def_110, type, inPowerset: $o).
% 6.77/1.30 thf(func_def_111, type, powersetsubset: $o).
% 6.77/1.30 thf(func_def_112, type, sepInPowerset: $o).
% 6.77/1.30 thf(func_def_113, type, sepSubset: $o).
% 6.77/1.30 thf(func_def_114, type, binunion: ($i > $i > $i)).
% 6.77/1.30 thf(func_def_115, type, binunionIL: $o).
% 6.77/1.30 thf(func_def_116, type, upairset2IR: $o).
% 6.77/1.30 thf(func_def_117, type, binunionIR: $o).
% 6.77/1.30 thf(func_def_118, type, binunionEcases: $o).
% 6.77/1.30 thf(func_def_119, type, binunionE: $o).
% 6.77/1.30 thf(func_def_120, type, binunionLsub: $o).
% 6.77/1.30 thf(func_def_121, type, binunionRsub: $o).
% 6.77/1.30 thf(func_def_122, type, binintersect: ($i > $i > $i)).
% 6.77/1.30 thf(func_def_123, type, binintersectI: $o).
% 6.77/1.30 thf(func_def_124, type, binintersectSubset5: $o).
% 6.77/1.30 thf(func_def_125, type, binintersectEL: $o).
% 6.77/1.30 thf(func_def_126, type, binintersectLsub: $o).
% 6.77/1.30 thf(func_def_127, type, binintersectSubset2: $o).
% 6.77/1.30 thf(func_def_128, type, binintersectSubset3: $o).
% 6.77/1.30 thf(func_def_129, type, binintersectER: $o).
% 6.77/1.30 thf(func_def_130, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 6.77/1.30 thf(func_def_131, type, vAND: ($o > $o > $o)).
% 6.77/1.30 thf(func_def_132, type, db1: !>[X0: $tType]:(X0)).
% 6.77/1.30 thf(func_def_133, type, db0: !>[X0: $tType]:(X0)).
% 6.77/1.30 thf(func_def_134, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 6.77/1.30 thf(func_def_135, type, vIMP: ($o > $o > $o)).
% 6.77/1.30 thf(func_def_136, type, db2: !>[X0: $tType]:(X0)).
% 6.77/1.30 thf(func_def_137, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 6.77/1.30 thf(func_def_138, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 6.77/1.30 thf(func_def_139, type, vIFF: ($o > $o > $o)).
% 6.77/1.30 thf(func_def_140, type, vNOT: ($o > $o)).
% 6.77/1.30 thf(func_def_141, type, vOR: ($o > $o > $o)).
% 6.77/1.30 thf(func_def_142, type, db4: !>[X0: $tType]:(X0)).
% 6.77/1.30 thf(func_def_143, type, db3: !>[X0: $tType]:(X0)).
% 6.77/1.30 thf(func_def_146, type, db5: !>[X0: $tType]:(X0)).
% 6.77/1.30 thf(func_def_149, type, sF2: $o).
% 6.77/1.30 thf(func_def_150, type, sF3: $o).
% 6.77/1.30 thf(func_def_151, type, sF4: $o).
% 6.77/1.30 thf(func_def_152, type, sF5: $o).
% 6.77/1.30 thf(func_def_153, type, sF6: $o).
% 6.77/1.30 thf(func_def_154, type, sF7: $o).
% 6.77/1.30 thf(func_def_155, type, sF8: $o).
% 6.77/1.30 thf(func_def_156, type, sF9: $o).
% 6.77/1.30 thf(func_def_157, type, sF10: $o).
% 6.77/1.30 thf(func_def_158, type, sF11: $o).
% 6.77/1.30 thf(func_def_159, type, sF12: $o).
% 6.77/1.30 thf(func_def_160, type, sF13: $o).
% 6.77/1.30 thf(func_def_161, type, sF14: $o).
% 6.77/1.30 thf(func_def_162, type, sF15: $o).
% 6.77/1.30 thf(func_def_163, type, sF16: $o).
% 6.77/1.30 thf(func_def_164, type, sF17: $o).
% 6.77/1.30 thf(func_def_165, type, sF18: $o).
% 6.77/1.30 thf(func_def_166, type, sF19: $o).
% 6.77/1.30 thf(func_def_167, type, sF20: $o).
% 6.77/1.30 thf(func_def_168, type, sF21: $o).
% 6.77/1.30 thf(func_def_169, type, sF22: $o).
% 6.77/1.30 thf(func_def_170, type, sF23: $o).
% 6.77/1.30 thf(func_def_171, type, sF24: $o).
% 6.77/1.30 thf(func_def_172, type, sF25: $o).
% 6.77/1.30 thf(func_def_173, type, sF26: $o).
% 6.77/1.30 thf(func_def_174, type, sF27: $o).
% 6.77/1.30 thf(func_def_175, type, sF28: $o).
% 6.77/1.30 thf(func_def_176, type, sF29: $o).
% 6.77/1.30 thf(func_def_178, type, sF31: $o).
% 6.77/1.30 thf(func_def_179, type, sF32: $o).
% 6.77/1.30 thf(func_def_180, type, sF33: $o).
% 6.77/1.30 thf(func_def_181, type, sF34: $o).
% 6.77/1.30 thf(func_def_182, type, sF35: $o).
% 6.77/1.30 thf(func_def_183, type, sF36: $o).
% 6.77/1.30 thf(func_def_184, type, sF37: $o).
% 6.77/1.30 thf(func_def_185, type, sF38: $o).
% 6.77/1.30 thf(func_def_186, type, sF39: $o).
% 6.77/1.30 thf(func_def_187, type, sF40: $o).
% 6.77/1.30 thf(func_def_188, type, sF41: $o).
% 6.77/1.30 thf(func_def_189, type, sF42: $o).
% 6.77/1.30 thf(func_def_190, type, sF43: $o).
% 6.77/1.30 thf(func_def_191, type, sF44: $o).
% 6.77/1.30 thf(func_def_192, type, sF45: $o).
% 6.77/1.30 thf(func_def_193, type, sF46: $o).
% 6.77/1.30 thf(func_def_194, type, sF47: $o).
% 6.77/1.30 thf(func_def_195, type, sF48: $o).
% 6.77/1.30 thf(func_def_196, type, sF49: $o).
% 6.77/1.30 thf(func_def_197, type, sF50: $o).
% 6.77/1.30 thf(func_def_198, type, sF51: $o).
% 6.77/1.30 thf(func_def_199, type, sF52: $o).
% 6.77/1.30 thf(func_def_200, type, sF53: $o).
% 6.77/1.30 thf(func_def_201, type, sF54: $o).
% 6.77/1.30 thf(func_def_202, type, sF55: $o).
% 6.77/1.30 thf(func_def_203, type, sF56: $o).
% 6.77/1.30 thf(func_def_204, type, sF57: $o).
% 6.77/1.30 thf(func_def_205, type, sF58: $o).
% 6.77/1.30 thf(func_def_206, type, sF59: $o).
% 6.77/1.30 thf(func_def_207, type, sF60: $o).
% 6.77/1.30 thf(func_def_208, type, sF61: $o).
% 6.77/1.30 thf(func_def_209, type, sF62: $o).
% 6.77/1.30 thf(func_def_210, type, sF63: $o).
% 6.77/1.30 thf(func_def_211, type, sF64: $o).
% 6.77/1.30 thf(func_def_212, type, sF65: $o).
% 6.77/1.30 thf(func_def_213, type, sF66: $o).
% 6.77/1.30 thf(func_def_214, type, sF67: $o).
% 6.77/1.30 thf(func_def_215, type, sF68: $o).
% 6.77/1.30 thf(func_def_216, type, sF69: $o).
% 6.77/1.30 thf(func_def_217, type, sF70: $o).
% 6.77/1.30 thf(func_def_218, type, sF71: $o).
% 6.77/1.30 thf(func_def_219, type, sF72: $o).
% 6.77/1.30 thf(func_def_220, type, sF73: $o).
% 6.77/1.30 thf(func_def_221, type, sF74: $o).
% 6.77/1.30 thf(func_def_222, type, sF75: $o).
% 6.77/1.30 thf(func_def_223, type, sF76: $o).
% 6.77/1.30 thf(func_def_224, type, sF77: $o).
% 6.77/1.30 thf(func_def_225, type, sF78: $o).
% 6.77/1.30 thf(func_def_226, type, sF79: $o).
% 6.77/1.30 thf(func_def_227, type, sF80: $o).
% 6.77/1.30 thf(func_def_228, type, sF81: $o).
% 6.77/1.30 thf(func_def_229, type, sF82: $o).
% 6.77/1.30 thf(func_def_230, type, sF83: $o).
% 6.77/1.30 thf(func_def_231, type, sF84: $o).
% 6.77/1.30 thf(func_def_232, type, sF85: $o).
% 6.77/1.30 thf(func_def_233, type, sF86: $o).
% 6.77/1.30 thf(func_def_234, type, sF87: $o).
% 6.77/1.30 thf(func_def_235, type, sF88: $o).
% 6.77/1.30 thf(func_def_236, type, sF89: $o).
% 6.77/1.30 thf(func_def_237, type, sF90: $o).
% 6.77/1.30 thf(func_def_238, type, sF91: $o).
% 6.77/1.30 thf(func_def_239, type, sF92: $o).
% 6.77/1.30 thf(func_def_240, type, sF93: $o).
% 6.77/1.30 thf(func_def_241, type, sF94: $o).
% 6.77/1.30 thf(func_def_242, type, sF95: $o).
% 6.77/1.30 thf(func_def_243, type, sF96: $o).
% 6.77/1.30 thf(func_def_244, type, sF97: $o).
% 6.77/1.30 thf(func_def_245, type, sF98: $o).
% 6.77/1.30 thf(func_def_246, type, sF99: $o).
% 6.77/1.30 thf(func_def_247, type, sF100: $o).
% 6.77/1.30 thf(func_def_248, type, sF101: $o).
% 6.77/1.30 thf(func_def_249, type, sF102: $o).
% 6.77/1.30 thf(func_def_250, type, sF103: $o).
% 6.77/1.30 thf(func_def_251, type, sF104: $o).
% 6.77/1.30 thf(func_def_252, type, sF105: $o).
% 6.77/1.30 thf(func_def_253, type, sF106: $o).
% 6.77/1.30 thf(func_def_254, type, sF107: $o).
% 6.77/1.30 thf(func_def_258, type, sK111: ($i > $i > $i)).
% 6.77/1.30 thf(func_def_266, type, sK119: ($i > $i > $i)).
% 6.77/1.30 thf(func_def_270, type, sK123: ($i > $i > $i)).
% 6.77/1.30 thf(func_def_274, type, sK127: ($i > $i)).
% 6.77/1.30 thf(func_def_276, type, sK129: ($i > $i > $o)).
% 6.77/1.30 thf(func_def_277, type, sK130: ($i > $i)).
% 6.77/1.30 thf(func_def_278, type, sK131: ($i > $i)).
% 6.77/1.30 thf(func_def_279, type, sK132: ($i > $i)).
% 6.77/1.30 thf(func_def_280, type, sK133: ($i > ($i > $i > $o) > $i)).
% 6.77/1.30 thf(func_def_281, type, sK134: ($i > ($i > $i > $o) > $i)).
% 6.77/1.30 thf(func_def_282, type, sK135: ($i > $i > ($i > $i > $o) > $i)).
% 6.77/1.30 thf(func_def_283, type, sK136: ($i > $i > ($i > $i > $o) > $i)).
% 6.77/1.30 thf(func_def_284, type, sK137: ($i > $i > ($i > $i > $o) > $i)).
% 6.77/1.30 thf(func_def_285, type, sK138: ($i > $i > ($i > $i > $o) > $i)).
% 6.77/1.30 thf(func_def_288, type, sK141: ($i > $i)).
% 6.77/1.30 thf(func_def_289, type, sK142: ($i > $i)).
% 6.77/1.30 thf(func_def_291, type, sK144: ($i > $i)).
% 6.77/1.30 thf(func_def_292, type, sK145: ($i > $i)).
% 6.77/1.30 thf(func_def_293, type, sK146: ($i > $i)).
% 6.77/1.30 thf(func_def_294, type, sK147: ($i > $i)).
% 6.77/1.30 thf(func_def_295, type, sK148: ($i > $i)).
% 6.77/1.30 thf(func_def_296, type, sK149: ($i > $i)).
% 6.77/1.30 thf(func_def_297, type, sK150: ($i > $i)).
% 6.77/1.30 thf(func_def_298, type, sK151: ($i > $i)).
% 6.77/1.30 thf(func_def_299, type, sK152: ($i > $i)).
% 6.77/1.30 thf(func_def_300, type, sK153: ($i > $i)).
% 6.77/1.30 thf(func_def_301, type, sK154: ($i > $i)).
% 6.77/1.30 thf(func_def_302, type, sK155: ($i > $i)).
% 6.77/1.30 thf(func_def_303, type, sK156: ($i > $i)).
% 6.77/1.30 thf(func_def_304, type, sK157: ($i > $i)).
% 6.77/1.30 thf(func_def_305, type, sK158: ($i > $i)).
% 6.77/1.30 thf(func_def_306, type, sK159: ($i > $i)).
% 6.77/1.30 thf(func_def_307, type, sK160: ($i > $i)).
% 6.77/1.30 thf(func_def_308, type, sK161: ($i > $i)).
% 6.77/1.30 thf(func_def_309, type, sK162: ($i > $i)).
% 6.77/1.30 thf(func_def_310, type, sK163: ($i > $i)).
% 6.77/1.30 thf(func_def_311, type, sK164: ($i > $i)).
% 6.77/1.30 thf(func_def_312, type, sK165: ($i > $i > $i > $i)).
% 6.77/1.30 thf(func_def_313, type, sK166: ($i > $i > $i)).
% 6.77/1.30 thf(func_def_314, type, sK167: ($i > $i > $i > $i)).
% 6.77/1.30 thf(func_def_315, type, sK168: ($i > $i > $i > $i)).
% 6.77/1.30 thf(func_def_316, type, sK169: ($i > $i > $i)).
% 6.77/1.30 thf(func_def_317, type, sK170: ($i > $i > $i > $i)).
% 6.77/1.30 thf(func_def_318, type, sK171: ($i > $i > $i > $i)).
% 6.77/1.30 thf(func_def_319, type, sK172: ($i > $i > $i)).
% 6.77/1.30 thf(func_def_320, type, sK173: ($i > $i > $i > $i)).
% 6.77/1.30 thf(func_def_321, type, sK174: ($i > $i > $i > $i)).
% 6.77/1.30 thf(func_def_322, type, sK175: ($i > $i > $i)).
% 6.77/1.30 thf(func_def_323, type, sK176: ($i > $i > $i > $i)).
% 6.77/1.30 thf(func_def_324, type, sK177: ($i > $i > $i > $i)).
% 6.77/1.30 thf(func_def_325, type, sK178: ($i > $i > $i)).
% 6.77/1.30 thf(func_def_326, type, sK179: ($i > $i > $i > $i)).
% 6.77/1.30 thf(func_def_327, type, sK180: ($i > $i > $i > $i)).
% 6.77/1.30 thf(func_def_328, type, sK181: ($i > $i > $i)).
% 6.77/1.30 thf(func_def_329, type, sK182: ($i > $i > $i > $i)).
% 6.77/1.30 thf(func_def_330, type, sK183: ($i > $i > $i > $i)).
% 6.77/1.30 thf(func_def_331, type, sK184: ($i > $i > $i)).
% 6.77/1.30 thf(func_def_332, type, sK185: ($i > $i > $i > $i)).
% 6.77/1.30 thf(func_def_333, type, sK186: ($i > $i > $i > $i)).
% 6.77/1.30 thf(func_def_334, type, sK187: ($i > $i > $i)).
% 6.77/1.30 thf(func_def_335, type, sK188: ($i > $i > $i > $i)).
% 6.77/1.30 thf(func_def_336, type, sK189: ($i > $i)).
% 6.77/1.30 thf(func_def_337, type, sK190: ($i > $i > $i > $i)).
% 6.77/1.30 thf(func_def_338, type, sK191: ($i > $i > $i)).
% 6.77/1.30 thf(func_def_339, type, sK192: ($i > $i > $i > $i)).
% 6.77/1.30 thf(func_def_340, type, sK193: ($i > $i > $i)).
% 6.77/1.30 thf(func_def_341, type, sK194: ($i > $i > $i > $i)).
% 6.77/1.30 thf(func_def_342, type, sK195: ($i > $i > $i > $i)).
% 6.77/1.30 thf(func_def_343, type, sK196: ($i > $i > $i)).
% 6.77/1.30 thf(func_def_344, type, sK197: ($i > $i > $i > $i)).
% 6.77/1.30 thf(func_def_345, type, sK198: ($i > $i > $i)).
% 6.77/1.30 thf(func_def_346, type, sK199: ($i > $i > $i > $i)).
% 6.77/1.30 thf(func_def_347, type, sK200: ($i > $i > $i > $i)).
% 6.77/1.30 thf(func_def_348, type, sK201: ($i > $i > $i)).
% 6.77/1.30 thf(func_def_349, type, sK202: ($i > $i > $i > $i)).
% 6.77/1.30 thf(func_def_350, type, sK203: ($i > $i > $i)).
% 6.77/1.30 thf(func_def_351, type, sK204: ($i > $i > $i > $i)).
% 6.77/1.30 thf(func_def_352, type, sK205: ($i > $i > $i > $i)).
% 6.77/1.30 thf(func_def_353, type, sK206: ($i > $i > $i)).
% 6.77/1.30 thf(func_def_354, type, sK207: ($i > $i > $i > $i)).
% 6.77/1.30 thf(func_def_355, type, sK208: ($i > $i > $i)).
% 6.77/1.30 thf(func_def_356, type, sK209: ($i > $i > $i > $i)).
% 6.77/1.30 thf(func_def_357, type, sK210: ($i > $i)).
% 6.77/1.30 thf(func_def_358, type, sK211: ($i > $i > $i > $i)).
% 6.77/1.30 thf(func_def_359, type, sK212: ($i > $i > $i)).
% 6.77/1.30 thf(func_def_360, type, sK213: ($i > $i > $i > $i)).
% 6.77/1.30 thf(func_def_361, type, sK214: ($i > $i > $i)).
% 6.77/1.30 thf(func_def_362, type, sK215: ($i > $i > $i > $i)).
% 6.77/1.30 thf(func_def_363, type, sK216: ($i > $i > $i > $i)).
% 6.77/1.30 thf(func_def_364, type, sK217: ($i > $i > $i)).
% 6.77/1.30 thf(func_def_365, type, sK218: ($i > $i > $i > $i)).
% 6.77/1.30 thf(func_def_366, type, sK219: ($i > $i > $i)).
% 6.77/1.30 thf(func_def_367, type, sK220: ($i > $i > $i > $i)).
% 6.77/1.30 thf(func_def_368, type, sK221: ($i > $i > $i > $i)).
% 6.77/1.30 thf(func_def_369, type, sK222: ($i > $i > $i)).
% 6.77/1.30 thf(func_def_370, type, sK223: ($i > $i > $i > $i)).
% 6.77/1.30 thf(func_def_371, type, sK224: ($i > $i > $i)).
% 6.77/1.30 thf(func_def_372, type, sK225: ($i > $i > $i > $i)).
% 6.77/1.30 thf(func_def_373, type, sK226: ($i > $i > $i > $i)).
% 6.77/1.30 thf(func_def_374, type, sK227: ($i > $i > $i)).
% 6.77/1.30 thf(func_def_375, type, sK228: ($i > $i > $i > $i)).
% 6.77/1.30 thf(func_def_376, type, sK229: ($i > $i > $i)).
% 6.77/1.30 thf(func_def_377, type, sK230: ($i > $i > $i > $i)).
% 6.77/1.30 thf(func_def_378, type, sK231: ($i > $i)).
% 6.77/1.30 thf(func_def_379, type, sK232: ($i > $i > $i > $i)).
% 6.77/1.30 thf(func_def_380, type, sK233: ($i > $i > $i)).
% 6.77/1.30 thf(func_def_381, type, sK234: ($i > $i > $i > $i)).
% 6.77/1.30 thf(func_def_382, type, sK235: ($i > $i > $i > $i)).
% 6.77/1.30 thf(func_def_383, type, sK236: ($i > $i > $i)).
% 6.77/1.30 thf(func_def_384, type, sK237: ($i > $i > $i > $i)).
% 7.53/1.30 thf(func_def_385, type, sK238: ($i > $i > $i > $i)).
% 7.53/1.30 thf(func_def_386, type, sK239: ($i > $i > $i)).
% 7.53/1.30 thf(func_def_387, type, sK240: ($i > $i > $i > $i)).
% 7.53/1.30 thf(func_def_388, type, sK241: ($i > $i > $i > $i)).
% 7.53/1.30 thf(func_def_389, type, sK242: ($i > $i > $i)).
% 7.53/1.30 thf(func_def_390, type, sK243: ($i > $i > $i > $i)).
% 7.53/1.30 thf(func_def_391, type, sK244: ($i > $i > $i > $i)).
% 7.53/1.30 thf(func_def_392, type, sK245: ($i > $i > $i)).
% 7.53/1.30 thf(func_def_393, type, sK246: ($i > $i > $i > $i)).
% 7.53/1.30 thf(func_def_394, type, sK247: ($i > $i > $i > $i)).
% 7.53/1.30 thf(func_def_395, type, sK248: ($i > $i > $i)).
% 7.53/1.30 thf(func_def_396, type, sK249: ($i > $i > $i > $i)).
% 7.53/1.30 thf(func_def_397, type, sK250: ($i > $i > $i > $i)).
% 7.53/1.30 thf(func_def_398, type, sK251: ($i > $i > $i)).
% 7.53/1.30 thf(func_def_399, type, sK252: ($i > $i > $i > $i)).
% 7.53/1.30 thf(func_def_400, type, sK253: ($i > $i > $i > $i)).
% 7.53/1.30 thf(func_def_401, type, sK254: ($i > $i > $i)).
% 7.53/1.30 thf(func_def_402, type, sK255: ($i > $i > $i > $i)).
% 7.53/1.30 thf(func_def_403, type, sK256: ($i > $i > $i > $i)).
% 7.53/1.30 thf(func_def_404, type, sK257: ($i > $i > $i)).
% 7.53/1.30 thf(func_def_405, type, sK258: ($i > $i > $i > $i)).
% 7.53/1.30 thf(func_def_406, type, sK259: ($i > $i > $i > $i)).
% 7.53/1.30 thf(func_def_407, type, sK260: ($i > $i > $i)).
% 7.53/1.30 thf(func_def_408, type, sK261: ($i > $i > $i > $i)).
% 7.53/1.30 thf(func_def_409, type, sK262: ($i > $i > $i > $i)).
% 7.53/1.30 thf(func_def_410, type, sK263: ($i > $i > $i)).
% 7.53/1.30 thf(func_def_411, type, sK264: ($i > $i > $i > $i)).
% 7.53/1.30 thf(func_def_412, type, sK265: ($i > $i > $i > $i)).
% 7.53/1.30 thf(func_def_413, type, sK266: ($i > $i > $i)).
% 7.53/1.30 thf(func_def_414, type, sK267: ($i > $i > $i > $i)).
% 7.53/1.30 thf(func_def_415, type, sK268: ($i > $i > $i > $i)).
% 7.53/1.30 thf(func_def_416, type, sK269: ($i > $i > $i)).
% 7.53/1.30 thf(func_def_417, type, sK270: ($i > $i > $i > $i)).
% 7.53/1.30 thf(func_def_418, type, sK271: ($i > $i > $i > $i)).
% 7.53/1.30 thf(func_def_419, type, sK272: ($i > $i > $i)).
% 7.53/1.30 thf(func_def_420, type, sK273: ($i > $i > $i > $i)).
% 7.53/1.30 thf(func_def_421, type, sK274: ($i > $i > $i > $i)).
% 7.53/1.30 thf(func_def_422, type, sK275: ($i > $i > $i)).
% 7.53/1.30 thf(func_def_423, type, sK276: ($i > $i > $i > $i)).
% 7.53/1.30 thf(func_def_424, type, sK277: ($i > $i > $i > $i)).
% 7.53/1.30 thf(func_def_425, type, sK278: ($i > $i > $i)).
% 7.53/1.30 thf(func_def_426, type, sK279: ($i > $i > $i > $i)).
% 7.53/1.30 thf(func_def_427, type, sK280: ($i > $i)).
% 7.53/1.30 thf(func_def_428, type, sK281: ($i > $i > $i > $i)).
% 7.53/1.30 thf(func_def_429, type, sK282: ($i > $i > $i)).
% 7.53/1.30 thf(func_def_430, type, sK283: ($i > $i > $i > $i)).
% 7.53/1.30 thf(func_def_431, type, sK284: ($i > $i > $i)).
% 7.53/1.30 thf(func_def_432, type, sK285: ($i > $i > $i > $i)).
% 7.53/1.30 thf(func_def_433, type, sK286: ($i > $i > $i > $i)).
% 7.53/1.30 thf(func_def_434, type, sK287: ($i > $i > $i)).
% 7.53/1.30 thf(func_def_435, type, sK288: ($i > $i > $i > $i)).
% 7.53/1.30 thf(func_def_436, type, sK289: ($i > $i > $i)).
% 7.53/1.30 thf(func_def_437, type, sK290: ($i > $i > $i > $i)).
% 7.53/1.30 thf(func_def_438, type, sK291: ($i > $i > $i > $i)).
% 7.53/1.30 thf(func_def_439, type, sK292: ($i > $i > $i)).
% 7.53/1.30 thf(func_def_440, type, sK293: ($i > $i > $i > $i)).
% 7.53/1.30 thf(func_def_441, type, sK294: ($i > $i > $i)).
% 7.53/1.30 thf(func_def_442, type, sK295: ($i > $i > $i > $i)).
% 7.53/1.30 thf(func_def_443, type, sK296: ($i > $i > $i > $i)).
% 7.53/1.30 thf(func_def_444, type, sK297: ($i > $i > $i)).
% 7.53/1.30 thf(func_def_445, type, sK298: ($i > $i > $i > $i)).
% 7.53/1.30 thf(func_def_446, type, sK299: ($i > $i > $i)).
% 7.53/1.30 thf(func_def_447, type, sK300: ($i > $i > $i > $i)).
% 7.53/1.30 thf(func_def_448, type, sK301: ($i > $i > $i > $i)).
% 7.53/1.30 thf(func_def_449, type, sK302: ($i > $i > $i)).
% 7.53/1.30 thf(func_def_450, type, sK303: ($i > $i > $i > $i)).
% 7.53/1.30 thf(func_def_451, type, sK304: ($i > $i > $i)).
% 7.53/1.30 thf(func_def_452, type, sK305: ($i > $i > $i > $i)).
% 7.53/1.30 thf(func_def_453, type, sK306: ($i > $i > $i > $i)).
% 7.53/1.30 thf(func_def_454, type, sK307: ($i > $i > $i)).
% 7.53/1.30 thf(func_def_455, type, sK308: ($i > $i > $i > $i)).
% 7.53/1.30 thf(func_def_456, type, sK309: ($i > $i > $i)).
% 7.53/1.30 thf(func_def_457, type, sK310: ($i > $i > $i > $i)).
% 7.53/1.30 thf(func_def_458, type, sK311: ($i > $i > $i > $i)).
% 7.53/1.30 thf(func_def_459, type, sK312: ($i > $i > $i)).
% 7.53/1.30 thf(func_def_460, type, sK313: ($i > $i > $i > $i)).
% 7.53/1.30 thf(func_def_461, type, sK314: ($i > $i > $i)).
% 7.53/1.30 thf(func_def_462, type, sK315: ($i > $i > $i > $i)).
% 7.53/1.30 thf(func_def_463, type, sK316: ($i > $i > $i > $i)).
% 7.53/1.30 thf(func_def_464, type, sK317: ($i > $i > $i)).
% 7.53/1.30 thf(func_def_465, type, sK318: ($i > $i > $i > $i)).
% 7.53/1.30 thf(func_def_466, type, sK319: ($i > $i > $i)).
% 7.53/1.30 thf(func_def_467, type, sK320: ($i > $i > $i > $i)).
% 7.53/1.30 thf(func_def_468, type, sK321: ($i > $i)).
% 7.53/1.30 thf(func_def_469, type, sK322: ($i > $i > $i > $i)).
% 7.53/1.30 thf(func_def_470, type, sK323: ($i > $i > $i)).
% 7.53/1.30 thf(func_def_471, type, sK324: ($i > $i > $i > $i)).
% 7.53/1.30 thf(func_def_472, type, sK325: ($i > $i > $i)).
% 7.53/1.30 thf(func_def_473, type, sK326: ($i > $i > $i > $i)).
% 7.53/1.30 thf(func_def_474, type, sK327: ($i > $i > $i > $i)).
% 7.53/1.30 thf(func_def_475, type, sK328: ($i > $i > $i)).
% 7.53/1.30 thf(func_def_476, type, sK329: ($i > $i > $i > $i)).
% 7.53/1.30 thf(func_def_477, type, sK330: ($i > $i > $i)).
% 7.53/1.30 thf(func_def_478, type, sK331: ($i > $i > $i > $i)).
% 7.53/1.30 thf(func_def_479, type, sK332: ($i > $i > $i > $i)).
% 7.53/1.30 thf(func_def_480, type, sK333: ($i > $i > $i)).
% 7.53/1.30 thf(func_def_481, type, sK334: ($i > $i > $i > $i)).
% 7.53/1.30 thf(func_def_482, type, sK335: ($i > $i > $i)).
% 7.53/1.30 thf(func_def_483, type, sK336: ($i > $i > $i > $i)).
% 7.53/1.30 thf(func_def_484, type, sK337: ($i > $i > $i > $i)).
% 7.53/1.30 thf(func_def_485, type, sK338: ($i > $i > $i)).
% 7.53/1.30 thf(func_def_486, type, sK339: ($i > $i > $i > $i)).
% 7.53/1.30 thf(func_def_487, type, sK340: ($i > $i > $i)).
% 7.53/1.30 thf(func_def_488, type, sK341: ($i > $i > $i > $i)).
% 7.53/1.30 thf(func_def_489, type, sK342: ($i > $i > $i > $i)).
% 7.53/1.30 thf(func_def_490, type, sK343: ($i > $i > $i)).
% 7.53/1.30 thf(func_def_491, type, sK344: ($i > $i > $i > $i)).
% 7.53/1.30 thf(func_def_492, type, sK345: ($i > $i > $i)).
% 7.53/1.30 thf(func_def_493, type, sK346: ($i > $i > $i > $i)).
% 7.53/1.30 thf(func_def_494, type, sK347: ($i > $i > $i > $i)).
% 7.53/1.30 thf(func_def_495, type, sK348: ($i > $i > $i)).
% 7.53/1.30 thf(func_def_496, type, sK349: ($i > $i > $i > $i)).
% 7.53/1.30 thf(func_def_497, type, sK350: ($i > $i > $i)).
% 7.53/1.30 thf(func_def_498, type, sK351: ($i > $i > $i > $i)).
% 7.53/1.30 thf(func_def_499, type, sK352: ($i > $i > $i > $i)).
% 7.53/1.30 thf(func_def_500, type, sK353: ($i > $i > $i)).
% 7.53/1.30 thf(func_def_501, type, sK354: ($i > $i > $i > $i)).
% 7.53/1.30 thf(func_def_502, type, sK355: ($i > $i > $i)).
% 7.53/1.30 thf(func_def_503, type, sK356: ($i > $i > $i > $i)).
% 7.53/1.30 thf(func_def_504, type, sK357: ($i > $i > $i > $i)).
% 7.53/1.30 thf(func_def_505, type, sK358: ($i > $i > $i)).
% 7.53/1.30 thf(func_def_506, type, sK359: ($i > $i > $i > $i)).
% 7.53/1.30 thf(func_def_507, type, sK360: ($i > $i > $i)).
% 7.53/1.30 thf(func_def_508, type, sK361: ($i > $i > $i > $i)).
% 7.53/1.30 thf(func_def_509, type, sK362: ($i > $i)).
% 7.53/1.30 thf(func_def_510, type, sK363: ($i > $i > $i > $i)).
% 7.53/1.30 thf(func_def_511, type, sK364: ($i > $i > $i)).
% 7.53/1.30 thf(func_def_512, type, sK365: ($i > $i > $i)).
% 7.53/1.30 thf(func_def_513, type, sK366: ($i > $i > $i)).
% 7.53/1.30 thf(func_def_514, type, sK367: ($i > $o)).
% 7.53/1.30 thf(func_def_516, type, sK369: (($i > $o) > $i > $i)).
% 7.53/1.30 thf(func_def_518, type, sK371: ($i > $o)).
% 7.53/1.30 thf(func_def_521, type, sK374: ($i > $o)).
% 7.53/1.30 thf(func_def_524, type, sK377: ($i > $o)).
% 7.53/1.30 thf(func_def_526, type, sK379: ($i > $o)).
% 7.53/1.30 thf(func_def_528, type, sK381: ($i > $i)).
% 7.53/1.30 thf(func_def_529, type, sK382: (($i > $o) > $i)).
% 7.53/1.30 thf(func_def_530, type, sK383: (($i > $o) > $i > $i)).
% 7.53/1.30 thf(func_def_532, type, sK385: $o).
% 7.53/1.30 thf(func_def_533, type, sK386: $o).
% 7.53/1.30 thf(func_def_536, type, sK389: ($i > $o)).
% 7.53/1.30 thf(func_def_538, type, sK391: (($i > $o) > $i)).
% 7.53/1.30 thf(func_def_539, type, sK392: (($i > $o) > $i > $i)).
% 7.53/1.30 thf(func_def_542, type, sK395: ($i > $i > $i)).
% 7.53/1.30 thf(func_def_543, type, sK396: ($i > $i > $i)).
% 7.53/1.30 thf(func_def_545, type, sK398: ($i > $i)).
% 7.53/1.30 thf(func_def_547, type, sK400: ($i > $o)).
% 7.53/1.30 thf(func_def_550, type, sK403: ($i > $i)).
% 7.53/1.30 thf(func_def_552, type, sK405: ($i > $o)).
% 7.53/1.30 thf(func_def_564, type, sK417: $o).
% 7.53/1.30 thf(func_def_571, type, sK424: ($i > $i > $i)).
% 7.53/1.30 thf(func_def_581, type, sK434: $o).
% 7.53/1.30 thf(func_def_582, type, sK435: ($o > $i > $i > $i)).
% 7.53/1.30 thf(func_def_585, type, sK438: ($i > $o)).
% 7.53/1.30 thf(func_def_587, type, sK440: ($i > $i)).
% 7.53/1.30 thf(func_def_588, type, sK441: (($i > $o) > $i)).
% 7.53/1.30 thf(func_def_589, type, sK442: (($i > $o) > $i > $i)).
% 7.53/1.30 thf(func_def_591, type, sK444: ($i > $i)).
% 7.53/1.30 thf(func_def_607, type, sK460: ($i > $o)).
% 7.53/1.30 thf(func_def_611, type, sK464: ($i > $o)).
% 7.53/1.30 thf(func_def_612, type, sK465: ($i > $o)).
% 7.53/1.30 thf(func_def_615, type, sK468: (($i > $o) > $i > $i)).
% 7.53/1.30 thf(func_def_616, type, sK469: ($i > $o)).
% 7.53/1.30 thf(func_def_619, type, sK472: (($i > $o) > $i > $i)).
% 7.53/1.30 thf(func_def_620, type, sK473: ($i > $o)).
% 7.53/1.30 thf(func_def_623, type, sK476: (($i > $o) > $i > $i)).
% 7.53/1.30 thf(func_def_624, type, sK477: ($i > $o)).
% 7.53/1.30 thf(func_def_627, type, sK480: (($i > $o) > $i > $i)).
% 7.53/1.30 thf(func_def_628, type, sK481: $o).
% 7.53/1.30 thf(func_def_629, type, sK482: $o).
% 7.53/1.30 thf(func_def_630, type, sK483: ($i > $o)).
% 7.53/1.30 thf(func_def_632, type, sK485: ($i > $i)).
% 7.53/1.30 thf(func_def_633, type, sK486: (($i > $o) > $i)).
% 7.53/1.30 thf(func_def_634, type, sK487: (($i > $o) > $i > $i)).
% 7.53/1.30 thf(func_def_635, type, sK488: ($i > $o)).
% 7.53/1.30 thf(func_def_637, type, sK490: ($i > $i)).
% 7.53/1.30 thf(func_def_638, type, sK491: (($i > $o) > $i)).
% 7.53/1.30 thf(func_def_639, type, sK492: (($i > $o) > $i)).
% 7.53/1.30 thf(func_def_640, type, sK493: (($i > $o) > $i)).
% 7.53/1.30 thf(func_def_641, type, sK494: ($i > $o)).
% 7.53/1.30 thf(func_def_643, type, sK496: ($i > $i)).
% 7.53/1.30 thf(func_def_644, type, sK497: (($i > $o) > $i)).
% 7.53/1.30 thf(func_def_645, type, sK498: (($i > $o) > $i > $i)).
% 7.53/1.30 thf(func_def_654, type, sK507: ($i > $o)).
% 7.53/1.30 thf(func_def_658, type, sK511: (($i > $o) > $i > $i)).
% 7.53/1.30 thf(func_def_659, type, sK512: ($i > $o)).
% 7.53/1.30 thf(func_def_660, type, sK513: ($i > $o)).
% 7.53/1.30 thf(func_def_661, type, sK514: ($i > $i)).
% 7.53/1.30 thf(func_def_662, type, sK515: ($i > $i)).
% 7.53/1.30 thf(func_def_665, type, sK518: (($i > $o) > ($i > $o) > $i)).
% 7.53/1.30 thf(func_def_666, type, sK519: (($i > $o) > ($i > $o) > $i)).
% 7.53/1.30 thf(func_def_667, type, sK520: (($i > $o) > $i)).
% 7.53/1.30 thf(func_def_668, type, sK521: ($i > ($i > $o) > $i)).
% 7.53/1.30 thf(func_def_669, type, sK522: (($i > $o) > $i)).
% 7.53/1.30 thf(func_def_670, type, sK523: ($i > ($i > $o) > $i)).
% 7.53/1.30 thf(func_def_671, type, sK524: ($i > ($i > $o) > $i)).
% 7.53/1.30 thf(func_def_672, type, sK525: (($i > $o) > $i)).
% 7.53/1.30 thf(func_def_673, type, sK526: ($i > ($i > $o) > $i)).
% 7.53/1.30 thf(func_def_674, type, sK527: (($i > $o) > $i)).
% 7.53/1.30 thf(func_def_675, type, sK528: ($i > ($i > $o) > $i)).
% 7.53/1.30 thf(func_def_676, type, sK529: ($i > ($i > $o) > $i)).
% 7.53/1.30 thf(func_def_677, type, sK530: (($i > $o) > $i)).
% 7.53/1.30 thf(func_def_678, type, sK531: ($i > ($i > $o) > $i)).
% 7.53/1.30 thf(func_def_679, type, sK532: (($i > $o) > $i)).
% 7.53/1.30 thf(func_def_680, type, sK533: ($i > ($i > $o) > $i)).
% 7.53/1.30 thf(func_def_681, type, sK534: ($i > ($i > $o) > $i)).
% 7.53/1.30 thf(func_def_690, type, sK543: ($i > $o)).
% 7.53/1.30 thf(func_def_691, type, sK544: ($i > $o)).
% 7.53/1.30 thf(func_def_694, type, sK547: (($i > $o) > ($i > $o) > $i)).
% 7.53/1.30 thf(func_def_695, type, sK548: (($i > $o) > ($i > $o) > $i)).
% 7.53/1.30 thf(func_def_696, type, sK549: ($i > ($i > $o) > $i)).
% 7.53/1.30 thf(func_def_697, type, sK550: (($i > $o) > $i > $i)).
% 7.53/1.30 thf(func_def_700, type, sK553: ($i > $o)).
% 7.53/1.30 thf(func_def_701, type, sK554: ($i > $o)).
% 7.53/1.30 thf(func_def_702, type, sK555: (($i > $o) > ($i > $o) > $i > $i > $i)).
% 7.53/1.30 thf(func_def_703, type, sK556: ($i > $i > ($i > $o) > ($i > $o) > $i)).
% 7.53/1.30 thf(func_def_706, type, sK559: ($i > $i > $i)).
% 7.53/1.30 thf(func_def_747, type, sK600: ($i > $o)).
% 7.53/1.30 thf(func_def_749, type, sK602: ($i > $o)).
% 7.53/1.30 thf(func_def_757, type, sK610: $o).
% 7.53/1.30 thf(f27,axiom,(
% 7.53/1.30 (nonempty = (^[X0 : $i] : ((X0 != emptyset))))),
% 7.53/1.30 file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonempty)).
% 7.53/1.30 thf(f45,axiom,(
% 7.53/1.30 (nonemptyImpWitness = ! [X0 : $i] : ((nonempty @ X0) => ? [X1 : $i] : ($true & (in @ X1 @ X0))))),
% 7.53/1.30 file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyImpWitness)).
% 7.53/1.30 thf(f110,axiom,(
% 7.53/1.30 (binintersectEL = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (binintersect @ X0 @ X1)) => (in @ X2 @ X0)))),
% 7.53/1.30 file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectEL)).
% 7.53/1.30 thf(f114,axiom,(
% 7.53/1.30 (binintersectER = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (binintersect @ X0 @ X1)) => (in @ X2 @ X1)))),
% 7.53/1.30 file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectER)).
% 7.53/1.30 thf(f115,conjecture,(
% 7.53/1.30 setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => ! [X0 : $i,X1 : $i] : (~ ? [X2 : $i] : ((in @ X2 @ X1) & (in @ X2 @ X0)) => (((binintersect @ X0 @ X1)) = emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 7.53/1.30 file('/export/starexec/sandbox/benchmark/theBenchmark.p',disjointsetsI1)).
% 7.53/1.30 thf(f116,negated_conjecture,(
% 7.53/1.30 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => ! [X0 : $i,X1 : $i] : (~ ? [X2 : $i] : ((in @ X2 @ X1) & (in @ X2 @ X0)) => (((binintersect @ X0 @ X1)) = emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 7.53/1.30 inference(negated_conjecture,[status(cth)],[f115])).
% 7.53/1.30 thf(f167,plain,(
% 7.53/1.30 (nonempty = (^[Y0 : $i]: (~ (emptyset = Y0))))),
% 7.53/1.30 inference(fool_elimination,[],[f27])).
% 7.53/1.30 thf(f200,plain,(
% 7.53/1.30 (nonemptyImpWitness = ! [X0 : $i] : ((nonempty @ X0) => ? [X1 : $i] : ($true & (in @ X1 @ X0))))),
% 7.53/1.30 inference(rectify,[],[f45])).
% 7.53/1.30 thf(f201,plain,(
% 7.53/1.30 (nonemptyImpWitness = ((!! @ $i @ (^[Y0 : $i]: ((nonempty @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & $true))))))))),
% 7.53/1.30 inference(fool_elimination,[],[f200])).
% 7.53/1.30 thf(f325,plain,(
% 7.53/1.30 (binintersectEL = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (binintersect @ X0 @ X1)) => (in @ X2 @ X0)))),
% 7.53/1.30 inference(rectify,[],[f110])).
% 7.53/1.30 thf(f326,plain,(
% 7.53/1.30 (binintersectEL = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y2 @ Y1)) => (in @ Y0 @ Y2))))))))))),
% 7.53/1.30 inference(fool_elimination,[],[f325])).
% 7.53/1.30 thf(f333,plain,(
% 7.53/1.30 (binintersectER = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (binintersect @ X0 @ X1)) => (in @ X2 @ X1)))),
% 7.53/1.30 inference(rectify,[],[f114])).
% 7.53/1.30 thf(f334,plain,(
% 7.53/1.30 (binintersectER = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y2 @ Y1)) => (in @ Y0 @ Y1))))))))))),
% 7.53/1.30 inference(fool_elimination,[],[f333])).
% 7.53/1.30 thf(f335,plain,(
% 7.53/1.30 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => ! [X0 : $i,X1 : $i] : (~ ? [X2 : $i] : ((in @ X2 @ X1) & (in @ X2 @ X0)) => (((binintersect @ X0 @ X1)) = emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 7.53/1.30 inference(rectify,[],[f116])).
% 7.53/1.30 thf(f336,plain,(
% 7.53/1.30 ~((setextAx = $true) => ((emptysetAx = $true) => ((setadjoinAx = $true) => ((powersetAx = $true) => ((setunionAx = $true) => ((omega0Ax = $true) => ((omegaSAx = $true) => ((omegaIndAx = $true) => ((replAx = $true) => ((foundationAx = $true) => ((wellorderingAx = $true) => ((descrp = $true) => ((dsetconstrI = $true) => ((dsetconstrEL = $true) => ((dsetconstrER = $true) => ((exuE1 = $true) => ((prop2setE = $true) => ((emptysetE = $true) => ((emptysetimpfalse = $true) => ((notinemptyset = $true) => ((exuE3e = $true) => ((setext = $true) => ((emptyI = $true) => ((noeltsimpempty = $true) => ((setbeta = $true) => ((nonemptyE1 = $true) => ((nonemptyI = $true) => ((nonemptyI1 = $true) => ((setadjoinIL = $true) => ((emptyinunitempty = $true) => ((setadjoinIR = $true) => ((setadjoinE = $true) => ((setadjoinOr = $true) => ((setoftrueEq = $true) => ((powersetI = $true) => ((emptyinPowerset = $true) => ((emptyInPowerset = $true) => ((powersetE = $true) => ((setunionI = $true) => ((setunionE = $true) => ((subPowSU = $true) => ((exuE2 = $true) => ((nonemptyImpWitness = $true) => ((uniqinunit = $true) => ((notinsingleton = $true) => ((eqinunit = $true) => ((singletonsswitch = $true) => ((upairsetE = $true) => ((upairsetIL = $true) => ((upairsetIR = $true) => ((emptyE1 = $true) => ((vacuousDall = $true) => ((quantDeMorgan1 = $true) => ((quantDeMorgan2 = $true) => ((quantDeMorgan3 = $true) => ((quantDeMorgan4 = $true) => ((prop2setI = $true) => ((prop2set2propI = $true) => ((notdexE = $true) => ((notdallE = $true) => ((exuI1 = $true) => ((exuI3 = $true) => ((exuI2 = $true) => ((inCongP = $true) => ((in__Cong = $true) => ((exuE3u = $true) => ((exu__Cong = $true) => ((emptyset__Cong = $true) => ((setadjoin__Cong = $true) => ((powerset__Cong = $true) => ((setunion__Cong = $true) => ((omega__Cong = $true) => ((exuEu = $true) => ((descr__Cong = $true) => ((dsetconstr__Cong = $true) => ((subsetI1 = $true) => ((eqimpsubset2 = $true) => ((eqimpsubset1 = $true) => ((subsetI2 = $true) => ((emptysetsubset = $true) => ((subsetE = $true) => ((subsetE2 = $true) => ((notsubsetI = $true) => ((notequalI1 = $true) => ((notequalI2 = $true) => ((subsetRefl = $true) => ((subsetTrans = $true) => ((setadjoinSub = $true) => ((setadjoinSub2 = $true) => ((subset2powerset = $true) => ((setextsub = $true) => ((subsetemptysetimpeq = $true) => ((powersetI1 = $true) => ((powersetE1 = $true) => ((inPowerset = $true) => ((powersetsubset = $true) => ((sepInPowerset = $true) => ((sepSubset = $true) => ((binunionIL = $true) => ((upairset2IR = $true) => ((binunionIR = $true) => ((binunionEcases = $true) => ((binunionE = $true) => ((binunionLsub = $true) => ((binunionRsub = $true) => ((binintersectI = $true) => ((binintersectSubset5 = $true) => ((binintersectEL = $true) => ((binintersectLsub = $true) => ((binintersectSubset2 = $true) => ((binintersectSubset3 = $true) => ((binintersectER = $true) => ! [X0 : $i,X1 : $i] : (~ ? [X2 : $i] : ((((in @ X2 @ X1)) = $true) & (((in @ X2 @ X0)) = $true)) => (emptyset = ((binintersect @ X0 @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 7.53/1.30 inference(fool_elimination,[],[f335])).
% 7.53/1.30 thf(f337,plain,(
% 7.53/1.30 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i] : ((emptyset != ((binintersect @ X0 @ X1))) & ! [X2 : $i] : ((((in @ X2 @ X1)) != $true) | (((in @ X2 @ X0)) != $true))) & (binintersectER = $true)) & (binintersectSubset3 = $true)) & (binintersectSubset2 = $true)) & (binintersectLsub = $true)) & (binintersectEL = $true)) & (binintersectSubset5 = $true)) & (binintersectI = $true)) & (binunionRsub = $true)) & (binunionLsub = $true)) & (binunionE = $true)) & (binunionEcases = $true)) & (binunionIR = $true)) & (upairset2IR = $true)) & (binunionIL = $true)) & (sepSubset = $true)) & (sepInPowerset = $true)) & (powersetsubset = $true)) & (inPowerset = $true)) & (powersetE1 = $true)) & (powersetI1 = $true)) & (subsetemptysetimpeq = $true)) & (setextsub = $true)) & (subset2powerset = $true)) & (setadjoinSub2 = $true)) & (setadjoinSub = $true)) & (subsetTrans = $true)) & (subsetRefl = $true)) & (notequalI2 = $true)) & (notequalI1 = $true)) & (notsubsetI = $true)) & (subsetE2 = $true)) & (subsetE = $true)) & (emptysetsubset = $true)) & (subsetI2 = $true)) & (eqimpsubset1 = $true)) & (eqimpsubset2 = $true)) & (subsetI1 = $true)) & (dsetconstr__Cong = $true)) & (descr__Cong = $true)) & (exuEu = $true)) & (omega__Cong = $true)) & (setunion__Cong = $true)) & (powerset__Cong = $true)) & (setadjoin__Cong = $true)) & (emptyset__Cong = $true)) & (exu__Cong = $true)) & (exuE3u = $true)) & (in__Cong = $true)) & (inCongP = $true)) & (exuI2 = $true)) & (exuI3 = $true)) & (exuI1 = $true)) & (notdallE = $true)) & (notdexE = $true)) & (prop2set2propI = $true)) & (prop2setI = $true)) & (quantDeMorgan4 = $true)) & (quantDeMorgan3 = $true)) & (quantDeMorgan2 = $true)) & (quantDeMorgan1 = $true)) & (vacuousDall = $true)) & (emptyE1 = $true)) & (upairsetIR = $true)) & (upairsetIL = $true)) & (upairsetE = $true)) & (singletonsswitch = $true)) & (eqinunit = $true)) & (notinsingleton = $true)) & (uniqinunit = $true)) & (nonemptyImpWitness = $true)) & (exuE2 = $true)) & (subPowSU = $true)) & (setunionE = $true)) & (setunionI = $true)) & (powersetE = $true)) & (emptyInPowerset = $true)) & (emptyinPowerset = $true)) & (powersetI = $true)) & (setoftrueEq = $true)) & (setadjoinOr = $true)) & (setadjoinE = $true)) & (setadjoinIR = $true)) & (emptyinunitempty = $true)) & (setadjoinIL = $true)) & (nonemptyI1 = $true)) & (nonemptyI = $true)) & (nonemptyE1 = $true)) & (setbeta = $true)) & (noeltsimpempty = $true)) & (emptyI = $true)) & (setext = $true)) & (exuE3e = $true)) & (notinemptyset = $true)) & (emptysetimpfalse = $true)) & (emptysetE = $true)) & (prop2setE = $true)) & (exuE1 = $true)) & (dsetconstrER = $true)) & (dsetconstrEL = $true)) & (dsetconstrI = $true)) & (descrp = $true)) & (wellorderingAx = $true)) & (foundationAx = $true)) & (replAx = $true)) & (omegaIndAx = $true)) & (omegaSAx = $true)) & (omega0Ax = $true)) & (setunionAx = $true)) & (powersetAx = $true)) & (setadjoinAx = $true)) & (emptysetAx = $true)) & (setextAx = $true)),
% 7.53/1.30 inference(ennf_transformation,[],[f336])).
% 7.53/1.30 thf(f338,plain,(
% 7.53/1.30 ? [X0 : $i,X1 : $i] : ((emptyset != ((binintersect @ X0 @ X1))) & ! [X2 : $i] : ((((in @ X2 @ X1)) != $true) | (((in @ X2 @ X0)) != $true))) & (binintersectER = $true) & (binintersectSubset3 = $true) & (binintersectSubset2 = $true) & (binintersectLsub = $true) & (binintersectEL = $true) & (binintersectSubset5 = $true) & (binintersectI = $true) & (binunionRsub = $true) & (binunionLsub = $true) & (binunionE = $true) & (binunionEcases = $true) & (binunionIR = $true) & (upairset2IR = $true) & (binunionIL = $true) & (sepSubset = $true) & (sepInPowerset = $true) & (powersetsubset = $true) & (inPowerset = $true) & (powersetE1 = $true) & (powersetI1 = $true) & (subsetemptysetimpeq = $true) & (setextsub = $true) & (subset2powerset = $true) & (setadjoinSub2 = $true) & (setadjoinSub = $true) & (subsetTrans = $true) & (subsetRefl = $true) & (notequalI2 = $true) & (notequalI1 = $true) & (notsubsetI = $true) & (subsetE2 = $true) & (subsetE = $true) & (emptysetsubset = $true) & (subsetI2 = $true) & (eqimpsubset1 = $true) & (eqimpsubset2 = $true) & (subsetI1 = $true) & (dsetconstr__Cong = $true) & (descr__Cong = $true) & (exuEu = $true) & (omega__Cong = $true) & (setunion__Cong = $true) & (powerset__Cong = $true) & (setadjoin__Cong = $true) & (emptyset__Cong = $true) & (exu__Cong = $true) & (exuE3u = $true) & (in__Cong = $true) & (inCongP = $true) & (exuI2 = $true) & (exuI3 = $true) & (exuI1 = $true) & (notdallE = $true) & (notdexE = $true) & (prop2set2propI = $true) & (prop2setI = $true) & (quantDeMorgan4 = $true) & (quantDeMorgan3 = $true) & (quantDeMorgan2 = $true) & (quantDeMorgan1 = $true) & (vacuousDall = $true) & (emptyE1 = $true) & (upairsetIR = $true) & (upairsetIL = $true) & (upairsetE = $true) & (singletonsswitch = $true) & (eqinunit = $true) & (notinsingleton = $true) & (uniqinunit = $true) & (nonemptyImpWitness = $true) & (exuE2 = $true) & (subPowSU = $true) & (setunionE = $true) & (setunionI = $true) & (powersetE = $true) & (emptyInPowerset = $true) & (emptyinPowerset = $true) & (powersetI = $true) & (setoftrueEq = $true) & (setadjoinOr = $true) & (setadjoinE = $true) & (setadjoinIR = $true) & (emptyinunitempty = $true) & (setadjoinIL = $true) & (nonemptyI1 = $true) & (nonemptyI = $true) & (nonemptyE1 = $true) & (setbeta = $true) & (noeltsimpempty = $true) & (emptyI = $true) & (setext = $true) & (exuE3e = $true) & (notinemptyset = $true) & (emptysetimpfalse = $true) & (emptysetE = $true) & (prop2setE = $true) & (exuE1 = $true) & (dsetconstrER = $true) & (dsetconstrEL = $true) & (dsetconstrI = $true) & (descrp = $true) & (wellorderingAx = $true) & (foundationAx = $true) & (replAx = $true) & (omegaIndAx = $true) & (omegaSAx = $true) & (omega0Ax = $true) & (setunionAx = $true) & (powersetAx = $true) & (setadjoinAx = $true) & (emptysetAx = $true) & (setextAx = $true)),
% 7.53/1.30 inference(flattening,[],[f337])).
% 7.53/1.30 thf(f339,plain,(
% 7.53/1.30 ((emptyset != ((binintersect @ sK0 @ sK1))) & ! [X2 : $i] : (($true != ((in @ X2 @ sK1))) | ($true != ((in @ X2 @ sK0))))) & (binintersectER = $true) & (binintersectSubset3 = $true) & (binintersectSubset2 = $true) & (binintersectLsub = $true) & (binintersectEL = $true) & (binintersectSubset5 = $true) & (binintersectI = $true) & (binunionRsub = $true) & (binunionLsub = $true) & (binunionE = $true) & (binunionEcases = $true) & (binunionIR = $true) & (upairset2IR = $true) & (binunionIL = $true) & (sepSubset = $true) & (sepInPowerset = $true) & (powersetsubset = $true) & (inPowerset = $true) & (powersetE1 = $true) & (powersetI1 = $true) & (subsetemptysetimpeq = $true) & (setextsub = $true) & (subset2powerset = $true) & (setadjoinSub2 = $true) & (setadjoinSub = $true) & (subsetTrans = $true) & (subsetRefl = $true) & (notequalI2 = $true) & (notequalI1 = $true) & (notsubsetI = $true) & (subsetE2 = $true) & (subsetE = $true) & (emptysetsubset = $true) & (subsetI2 = $true) & (eqimpsubset1 = $true) & (eqimpsubset2 = $true) & (subsetI1 = $true) & (dsetconstr__Cong = $true) & (descr__Cong = $true) & (exuEu = $true) & (omega__Cong = $true) & (setunion__Cong = $true) & (powerset__Cong = $true) & (setadjoin__Cong = $true) & (emptyset__Cong = $true) & (exu__Cong = $true) & (exuE3u = $true) & (in__Cong = $true) & (inCongP = $true) & (exuI2 = $true) & (exuI3 = $true) & (exuI1 = $true) & (notdallE = $true) & (notdexE = $true) & (prop2set2propI = $true) & (prop2setI = $true) & (quantDeMorgan4 = $true) & (quantDeMorgan3 = $true) & (quantDeMorgan2 = $true) & (quantDeMorgan1 = $true) & (vacuousDall = $true) & (emptyE1 = $true) & (upairsetIR = $true) & (upairsetIL = $true) & (upairsetE = $true) & (singletonsswitch = $true) & (eqinunit = $true) & (notinsingleton = $true) & (uniqinunit = $true) & (nonemptyImpWitness = $true) & (exuE2 = $true) & (subPowSU = $true) & (setunionE = $true) & (setunionI = $true) & (powersetE = $true) & (emptyInPowerset = $true) & (emptyinPowerset = $true) & (powersetI = $true) & (setoftrueEq = $true) & (setadjoinOr = $true) & (setadjoinE = $true) & (setadjoinIR = $true) & (emptyinunitempty = $true) & (setadjoinIL = $true) & (nonemptyI1 = $true) & (nonemptyI = $true) & (nonemptyE1 = $true) & (setbeta = $true) & (noeltsimpempty = $true) & (emptyI = $true) & (setext = $true) & (exuE3e = $true) & (notinemptyset = $true) & (emptysetimpfalse = $true) & (emptysetE = $true) & (prop2setE = $true) & (exuE1 = $true) & (dsetconstrER = $true) & (dsetconstrEL = $true) & (dsetconstrI = $true) & (descrp = $true) & (wellorderingAx = $true) & (foundationAx = $true) & (replAx = $true) & (omegaIndAx = $true) & (omegaSAx = $true) & (omega0Ax = $true) & (setunionAx = $true) & (powersetAx = $true) & (setadjoinAx = $true) & (emptysetAx = $true) & (setextAx = $true)),
% 7.53/1.30 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f338])).
% 7.53/1.30 thf(f366,plain,(
% 7.53/1.30 (nonempty = (^[Y0 : $i]: (~ (emptyset = Y0))))),
% 7.53/1.30 inference(cnf_transformation,[],[f167])).
% 7.53/1.30 thf(f384,plain,(
% 7.53/1.30 (nonemptyImpWitness = ((!! @ $i @ (^[Y0 : $i]: ((nonempty @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & $true))))))))),
% 7.53/1.30 inference(cnf_transformation,[],[f201])).
% 7.53/1.30 thf(f449,plain,(
% 7.53/1.30 (binintersectEL = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y2 @ Y1)) => (in @ Y0 @ Y2))))))))))),
% 7.53/1.30 inference(cnf_transformation,[],[f326])).
% 7.53/1.30 thf(f453,plain,(
% 7.53/1.30 (binintersectER = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y2 @ Y1)) => (in @ Y0 @ Y1))))))))))),
% 7.53/1.30 inference(cnf_transformation,[],[f334])).
% 7.53/1.30 thf(f496,plain,(
% 7.53/1.30 (nonemptyImpWitness = $true)),
% 7.53/1.30 inference(cnf_transformation,[],[f339])).
% 7.53/1.30 thf(f561,plain,(
% 7.53/1.30 (binintersectEL = $true)),
% 7.53/1.30 inference(cnf_transformation,[],[f339])).
% 7.53/1.30 thf(f565,plain,(
% 7.53/1.30 (binintersectER = $true)),
% 7.53/1.30 inference(cnf_transformation,[],[f339])).
% 7.53/1.30 thf(f566,plain,(
% 7.53/1.30 ( ! [X2 : $i] : (($true != ((in @ X2 @ sK1))) | ($true != ((in @ X2 @ sK0)))) )),
% 7.53/1.30 inference(cnf_transformation,[],[f339])).
% 7.53/1.30 thf(f567,plain,(
% 7.53/1.30 (emptyset != ((binintersect @ sK0 @ sK1)))),
% 7.53/1.30 inference(cnf_transformation,[],[f339])).
% 7.53/1.30 thf(f569,definition,(
% 7.53/1.30 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 7.53/1.30 introduced(theory,[fool_exhaustiveness_axiom])).
% 7.53/1.30 thf(f612,plain,(
% 7.53/1.30 ($true = ((!! @ $i @ (^[Y0 : $i]: (((^[Y1 : $i]: (~ (emptyset = Y1))) @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & $true))))))))),
% 7.53/1.30 inference(definition_unfolding,[],[f384,f496,f366])).
% 7.53/1.30 thf(f677,plain,(
% 7.53/1.30 ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y2 @ Y1)) => (in @ Y0 @ Y2))))))))))),
% 7.53/1.30 inference(definition_unfolding,[],[f449,f561])).
% 7.53/1.30 thf(f681,plain,(
% 7.53/1.30 ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y2 @ Y1)) => (in @ Y0 @ Y1))))))))))),
% 7.53/1.30 inference(definition_unfolding,[],[f453,f565])).
% 7.53/1.30 thf(f806,definition,(
% 7.53/1.30 (sF43 = ((!! @ $i @ (^[Y0 : $i]: (((^[Y1 : $i]: (~ (emptyset = Y1))) @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & $true))))))))),
% 7.53/1.30 introduced(definition,[new_symbols(definition,[sF43])],[function_definition])).
% 7.53/1.30 thf(f807,plain,(
% 7.53/1.30 (((!! @ $i @ (^[Y0 : $i]: (((^[Y1 : $i]: (~ (emptyset = Y1))) @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & $true))))))) = sF43)),
% 7.53/1.30 inference(reorient_equations,[],[f806])).
% 7.53/1.30 thf(f808,plain,(
% 7.53/1.30 ($true = sF43)),
% 7.53/1.30 inference(definition_folding,[],[f612,f807])).
% 7.53/1.30 thf(f991,definition,(
% 7.53/1.30 (sF103 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y2 @ Y1)) => (in @ Y0 @ Y2))))))))))),
% 7.53/1.30 introduced(definition,[new_symbols(definition,[sF103])],[function_definition])).
% 7.53/1.30 thf(f992,plain,(
% 7.53/1.30 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y2 @ Y1)) => (in @ Y0 @ Y2))))))))) = sF103)),
% 7.53/1.30 inference(reorient_equations,[],[f991])).
% 7.53/1.30 thf(f993,plain,(
% 7.53/1.30 ($true = sF103)),
% 7.53/1.30 inference(definition_folding,[],[f677,f992])).
% 7.53/1.30 thf(f1003,definition,(
% 7.53/1.30 (sF107 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y2 @ Y1)) => (in @ Y0 @ Y1))))))))))),
% 7.53/1.30 introduced(definition,[new_symbols(definition,[sF107])],[function_definition])).
% 7.53/1.30 thf(f1004,plain,(
% 7.53/1.30 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y2 @ Y1)) => (in @ Y0 @ Y1))))))))) = sF107)),
% 7.53/1.30 inference(reorient_equations,[],[f1003])).
% 7.53/1.30 thf(f1005,plain,(
% 7.53/1.30 ($true = sF107)),
% 7.53/1.30 inference(definition_folding,[],[f681,f1004])).
% 7.53/1.30 thf(f1006,definition,(
% 7.53/1.30 (sF108 = ((binintersect @ sK0 @ sK1)))),
% 7.53/1.30 introduced(definition,[new_symbols(definition,[sF108])],[function_definition])).
% 7.53/1.30 thf(f1007,plain,(
% 7.53/1.30 (((binintersect @ sK0 @ sK1)) = sF108)),
% 7.53/1.30 inference(reorient_equations,[],[f1006])).
% 7.53/1.30 thf(f1008,plain,(
% 7.53/1.30 (emptyset != sF108)),
% 7.53/1.30 inference(definition_folding,[],[f567,f1007])).
% 7.53/1.30 thf(f4856,plain,(
% 7.53/1.30 ($true = ((!! @ $i @ (^[Y0 : $i]: (((^[Y1 : $i]: (~ (emptyset = Y1))) @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & $true)))))))) | ($false = sF43)),
% 7.53/1.30 inference(iff_proxy_clausification,[],[f807])).
% 7.53/1.30 thf(f4868,plain,(
% 7.53/1.30 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: (((^[Y1 : $i]: (~ (emptyset = Y1))) @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & $true))))) @ X1))) | ($false = sF43)) )),
% 7.53/1.30 inference(pi_proxy_clausification,[],[f4856])).
% 7.53/1.30 thf(f4869,plain,(
% 7.53/1.30 ( ! [X1 : $i] : (($true = (((~ (emptyset = X1)) => (?? @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) & $true)))))) | ($false = sF43)) )),
% 7.53/1.30 inference(beta-eta_normalization,[],[f4868])).
% 7.53/1.30 thf(f4870,plain,(
% 7.53/1.30 ( ! [X1 : $i] : (($false = ((~ (emptyset = X1)))) | ($false = sF43) | ($true = ((?? @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) & $true)))))) )),
% 7.53/1.30 inference(imp_proxy_clausification,[],[f4869])).
% 7.53/1.30 thf(f4871,plain,(
% 7.53/1.30 ( ! [X1 : $i] : (($true = ((emptyset = X1))) | ($false = sF43) | ($true = ((?? @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) & $true)))))) )),
% 7.53/1.30 inference(not_proxy_clausification,[],[f4870])).
% 7.53/1.30 thf(f4872,plain,(
% 7.53/1.30 ( ! [X1 : $i] : ((emptyset = X1) | ($false = sF43) | ($true = ((?? @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) & $true)))))) )),
% 7.53/1.30 inference(equality_proxy_clausification,[],[f4871])).
% 7.53/1.30 thf(f4873,plain,(
% 7.53/1.30 ( ! [X1 : $i] : ((emptyset = X1) | ($false = sF43) | ($true = (((^[Y0 : $i]: ((in @ Y0 @ X1) & $true)) @ (sK444 @ X1))))) )),
% 7.53/1.30 inference(sigma_proxy_clausification,[],[f4872])).
% 7.53/1.30 thf(f4874,plain,(
% 7.53/1.30 ( ! [X1 : $i] : ((emptyset = X1) | ($false = sF43) | ($true = (((in @ (sK444 @ X1) @ X1) & $true)))) )),
% 7.53/1.30 inference(beta-eta_normalization,[],[f4873])).
% 7.53/1.30 thf(f4876,plain,(
% 7.53/1.30 ( ! [X1 : $i] : ((emptyset = X1) | ($false = sF43) | ($true = ((in @ (sK444 @ X1) @ X1)))) )),
% 7.53/1.30 inference(and_proxy_clausification,[],[f4874])).
% 7.53/1.30 thf(f6319,plain,(
% 7.53/1.30 ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y2 @ Y1)) => (in @ Y0 @ Y2)))))))))) | ($false = sF103)),
% 7.53/1.30 inference(iff_proxy_clausification,[],[f992])).
% 7.53/1.30 thf(f6329,plain,(
% 7.53/1.30 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y2 @ Y1)) => (in @ Y0 @ Y2))))))) @ X1))) | ($false = sF103)) )),
% 7.53/1.30 inference(pi_proxy_clausification,[],[f6319])).
% 7.53/1.30 thf(f6330,plain,(
% 7.53/1.30 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ X1 @ (binintersect @ Y1 @ Y0)) => (in @ X1 @ Y1)))))))) | ($false = sF103)) )),
% 7.53/1.30 inference(beta-eta_normalization,[],[f6329])).
% 7.53/1.30 thf(f6331,plain,(
% 7.53/1.30 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ X1 @ (binintersect @ Y1 @ Y0)) => (in @ X1 @ Y1))))) @ X2))) | ($false = sF103)) )),
% 7.53/1.30 inference(pi_proxy_clausification,[],[f6330])).
% 7.53/1.30 thf(f6332,plain,(
% 7.53/1.30 ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ X1 @ (binintersect @ Y0 @ X2)) => (in @ X1 @ Y0)))))) | ($false = sF103)) )),
% 7.53/1.30 inference(beta-eta_normalization,[],[f6331])).
% 7.53/1.30 thf(f6333,plain,(
% 7.53/1.30 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((in @ X1 @ (binintersect @ Y0 @ X2)) => (in @ X1 @ Y0))) @ X3))) | ($false = sF103)) )),
% 7.53/1.30 inference(pi_proxy_clausification,[],[f6332])).
% 7.53/1.30 thf(f6334,plain,(
% 7.53/1.30 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((in @ X1 @ (binintersect @ X3 @ X2)) => (in @ X1 @ X3)))) | ($false = sF103)) )),
% 7.53/1.30 inference(beta-eta_normalization,[],[f6333])).
% 7.53/1.30 thf(f6335,plain,(
% 7.53/1.30 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((in @ X1 @ (binintersect @ X3 @ X2)))) | ($false = sF103) | (((in @ X1 @ X3)) = $true)) )),
% 7.53/1.30 inference(imp_proxy_clausification,[],[f6334])).
% 7.53/1.30 thf(f6376,plain,(
% 7.53/1.30 ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y2 @ Y1)) => (in @ Y0 @ Y1)))))))))) | ($false = sF107)),
% 7.53/1.30 inference(iff_proxy_clausification,[],[f1004])).
% 7.53/1.30 thf(f6386,plain,(
% 7.53/1.30 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (binintersect @ Y2 @ Y1)) => (in @ Y0 @ Y1))))))) @ X1))) | ($false = sF107)) )),
% 7.53/1.30 inference(pi_proxy_clausification,[],[f6376])).
% 7.53/1.30 thf(f6387,plain,(
% 7.53/1.30 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ X1 @ (binintersect @ Y1 @ Y0)) => (in @ X1 @ Y0)))))))) | ($false = sF107)) )),
% 7.53/1.30 inference(beta-eta_normalization,[],[f6386])).
% 7.53/1.30 thf(f6388,plain,(
% 7.53/1.30 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ X1 @ (binintersect @ Y1 @ Y0)) => (in @ X1 @ Y0))))) @ X2))) | ($false = sF107)) )),
% 7.53/1.30 inference(pi_proxy_clausification,[],[f6387])).
% 7.53/1.30 thf(f6389,plain,(
% 7.53/1.30 ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ X1 @ (binintersect @ Y0 @ X2)) => (in @ X1 @ X2)))))) | ($false = sF107)) )),
% 7.53/1.30 inference(beta-eta_normalization,[],[f6388])).
% 7.53/1.30 thf(f6390,plain,(
% 7.53/1.30 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((in @ X1 @ (binintersect @ Y0 @ X2)) => (in @ X1 @ X2))) @ X3))) | ($false = sF107)) )),
% 7.53/1.30 inference(pi_proxy_clausification,[],[f6389])).
% 7.53/1.30 thf(f6391,plain,(
% 7.53/1.30 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((in @ X1 @ (binintersect @ X3 @ X2)) => (in @ X1 @ X2)))) | ($false = sF107)) )),
% 7.53/1.30 inference(beta-eta_normalization,[],[f6390])).
% 7.53/1.30 thf(f6392,plain,(
% 7.53/1.30 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((in @ X1 @ (binintersect @ X3 @ X2)))) | ($false = sF107) | (((in @ X1 @ X2)) = $true)) )),
% 7.53/1.30 inference(imp_proxy_clausification,[],[f6391])).
% 7.53/1.30 thf(f6559,plain,(
% 7.53/1.30 ( ! [X1 : $i] : (($false = $true) | (emptyset = X1) | ($true = ((in @ (sK444 @ X1) @ X1)))) )),
% 7.53/1.30 inference(forward_demodulation,[],[f4876,f808])).
% 7.53/1.30 thf(f6560,plain,(
% 7.53/1.30 ( ! [X1 : $i] : (($true = ((in @ (sK444 @ X1) @ X1))) | (emptyset = X1)) )),
% 7.53/1.30 inference(trivial_inequality_removal,[],[f6559])).
% 7.53/1.30 thf(f6787,plain,(
% 7.53/1.30 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = $true) | ($false = ((in @ X1 @ (binintersect @ X3 @ X2)))) | (((in @ X1 @ X3)) = $true)) )),
% 7.53/1.30 inference(forward_demodulation,[],[f6335,f993])).
% 7.53/1.30 thf(f6788,plain,(
% 7.53/1.30 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((in @ X1 @ (binintersect @ X3 @ X2)))) | (((in @ X1 @ X3)) = $true)) )),
% 7.53/1.30 inference(trivial_inequality_removal,[],[f6787])).
% 7.53/1.30 thf(f6795,plain,(
% 7.53/1.30 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = $true) | ($false = ((in @ X1 @ (binintersect @ X3 @ X2)))) | (((in @ X1 @ X2)) = $true)) )),
% 7.53/1.30 inference(forward_demodulation,[],[f6392,f1005])).
% 7.53/1.30 thf(f6796,plain,(
% 7.53/1.30 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((in @ X1 @ (binintersect @ X3 @ X2)))) | (((in @ X1 @ X2)) = $true)) )),
% 7.53/1.30 inference(trivial_inequality_removal,[],[f6795])).
% 7.53/1.30 thf(f6799,plain,(
% 7.53/1.30 ( ! [X0 : $i] : (($true != $true) | ($true != ((in @ X0 @ sK0))) | ($false = ((in @ X0 @ sK1)))) )),
% 7.53/1.30 inference(constrained_superposition,[],[f566,f569])).
% 7.53/1.30 thf(f6803,plain,(
% 7.53/1.30 ( ! [X0 : $i] : (($true != ((in @ X0 @ sK0))) | ($false = ((in @ X0 @ sK1)))) )),
% 7.53/1.30 inference(trivial_inequality_removal,[],[f6799])).
% 7.53/1.30 thf(f7432,plain,(
% 7.53/1.30 ( ! [X0 : $i] : (($false = ((in @ X0 @ sF108))) | ($true = ((in @ X0 @ sK0)))) )),
% 7.53/1.30 inference(constrained_superposition,[],[f6788,f1007])).
% 7.53/1.30 thf(f7460,plain,(
% 7.53/1.30 ( ! [X0 : $i] : (($false = ((in @ X0 @ sF108))) | ($true = ((in @ X0 @ sK1)))) )),
% 7.53/1.30 inference(constrained_superposition,[],[f6796,f1007])).
% 7.53/1.30 thf(f9044,plain,(
% 7.53/1.30 ($false = $true) | (emptyset = sF108) | ($true = ((in @ (sK444 @ sF108) @ sK0)))),
% 7.53/1.30 inference(constrained_superposition,[],[f6560,f7432])).
% 7.53/1.30 thf(f9049,plain,(
% 7.53/1.30 (emptyset = sF108) | ($true = ((in @ (sK444 @ sF108) @ sK0)))),
% 7.53/1.30 inference(trivial_inequality_removal,[],[f9044])).
% 7.53/1.30 thf(f9065,plain,(
% 7.53/1.30 ($true = ((in @ (sK444 @ sF108) @ sK0)))),
% 7.53/1.30 inference(forward_subsumption_resolution,[],[f9049,f1008])).
% 7.53/1.30 thf(f9080,plain,(
% 7.53/1.30 ($true != $true) | ($false = ((in @ (sK444 @ sF108) @ sK1)))),
% 7.53/1.30 inference(constrained_superposition,[],[f6803,f9065])).
% 7.53/1.30 thf(f9081,plain,(
% 7.53/1.30 ($false = ((in @ (sK444 @ sF108) @ sK1)))),
% 7.53/1.30 inference(trivial_inequality_removal,[],[f9080])).
% 7.53/1.30 thf(f9105,plain,(
% 7.53/1.30 ($false = $true) | (emptyset = sF108) | ($true = ((in @ (sK444 @ sF108) @ sK1)))),
% 7.53/1.30 inference(constrained_superposition,[],[f6560,f7460])).
% 7.53/1.30 thf(f9110,plain,(
% 7.53/1.30 (emptyset = sF108) | ($true = ((in @ (sK444 @ sF108) @ sK1)))),
% 7.53/1.30 inference(trivial_inequality_removal,[],[f9105])).
% 7.53/1.30 thf(f9126,plain,(
% 7.53/1.30 ($true = ((in @ (sK444 @ sF108) @ sK1)))),
% 7.53/1.30 inference(forward_subsumption_resolution,[],[f9110,f1008])).
% 7.53/1.30 thf(f9132,plain,(
% 7.53/1.30 ($false = $true)),
% 7.53/1.30 inference(forward_demodulation,[],[f9126,f9081])).
% 7.53/1.30 thf(f9133,plain,(
% 7.53/1.30 $false),
% 7.53/1.30 inference(trivial_inequality_removal,[],[f9132])).
% 7.53/1.30 % SZS output end Proof for theBenchmark
% 7.53/1.30 % (2543150)------------------------------
% 7.53/1.30 % (2543150)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.53/1.30 % (2543150)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.53/1.30 % (2543150)CaDiCaL version: 2.1.3
% 7.53/1.30 % (2543150)Termination reason: Refutation
% 7.53/1.30 % (2543150)Time elapsed: 0.343 s
% 7.53/1.30 % (2543150)Peak memory usage: 15 MB
% 7.53/1.30 % (2543150)Instructions burned: 512 (million)
% 7.53/1.30 % (2543096)Success in time 1.062 s
% 7.53/1.30 % Vampire exiting
%------------------------------------------------------------------------------