%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU718^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n002.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 08:33:06 AM UTC 2026
% Result : Theorem 8.51s 2.02s
% Output : Refutation 8.51s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU718^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 % Computer : n002.cluster.edu
% 0.09/0.23 % Model : x86_64 x86_64
% 0.09/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.23 % Memory : 8046.5625MB
% 0.09/0.23 % OS : Linux 6.8.0-71-generic
% 0.09/0.23 % CPULimit : 300
% 0.09/0.23 % WCLimit : 300
% 0.09/0.23 % DateTime : Tue Sep 29 14:17:37 UTC 2026
% 0.09/0.24 % CPUTime :
% 0.09/0.24 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.26/0.29 Running first-order model finding
% 0.26/0.29 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.42/1.66 % (1354195)Will run a generic schedule for satisfiability detection.
% 7.42/1.66 % (1354205)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4072387659:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 7.42/1.66 % (1354201)% WARNING: option uhcvi not known.
% 7.42/1.66 % (1354202)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1925696014:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 7.42/1.66 % (1354206)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=20810665:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 7.42/1.66 % (1354201)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3374992001:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 7.42/1.66 % (1354200)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=516776577_2999 on theBenchmark for (2999ds/0Mi)
% 7.42/1.66 % (1354203)dis+10_1_sil=32000:sp=arity:random_seed=1342900177:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 7.42/1.66 % (1354204)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1515689589:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 7.42/1.66 % (1354205)Instruction limit reached!
% 7.42/1.66 % (1354205)------------------------------
% 7.42/1.66 % (1354205)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.42/1.66 % (1354205)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.42/1.66 % (1354205)CaDiCaL version: 2.1.3
% 7.42/1.66 % (1354205)Termination reason: Instruction limit
% 7.42/1.66 % (1354205)Termination phase: Saturation
% 7.42/1.66 % (1354205)Time elapsed: 0.055 s
% 7.42/1.66 % (1354205)Peak memory usage: 13 MB
% 7.42/1.66 % (1354205)Instructions burned: 132 (million)
% 7.42/1.66 % (1354201)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 7.42/1.66 % (1354204)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 7.42/1.66 % (1354214)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=195331969:i=714:nm=2_2998 on theBenchmark for (2998ds/714Mi)
% 7.42/1.66 % (1354203)Instruction limit reached!
% 7.42/1.66 % (1354203)------------------------------
% 7.42/1.66 % (1354203)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.42/1.66 % (1354203)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.42/1.66 % (1354203)CaDiCaL version: 2.1.3
% 7.42/1.66 % (1354203)Termination reason: Instruction limit
% 7.42/1.66 % (1354203)Termination phase: Property scanning
% 7.42/1.66 % (1354203)Time elapsed: 0.082 s
% 7.42/1.66 % (1354203)Peak memory usage: 11 MB
% 7.42/1.66 % (1354203)Instructions burned: 104 (million)
% 7.42/1.66 % Exception at run slice level
% 7.42/1.66 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.42/1.66 % (1354201)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 7.42/1.66 % (1354204)Instruction limit reached!
% 7.42/1.66 % (1354204)------------------------------
% 7.42/1.66 % (1354204)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.42/1.66 % (1354204)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.42/1.66 % (1354204)CaDiCaL version: 2.1.3
% 7.42/1.66 % (1354204)Termination reason: Instruction limit
% 7.42/1.66 % (1354204)Termination phase: Saturation
% 7.42/1.66 % (1354204)Time elapsed: 0.092 s
% 7.42/1.66 % (1354204)Peak memory usage: 12 MB
% 7.42/1.66 % (1354204)Instructions burned: 116 (million)
% 7.42/1.66 % Exception at run slice level
% 7.42/1.66 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 7.42/1.66 % (1354216)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2888575797:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 7.42/1.66 % (1354217)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=2457227969:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 7.42/1.66 % (1354218)ott-21_1_sil=16000:fs=off:random_seed=752849146:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 7.42/1.66 % (1354206)Instruction limit reached!
% 7.42/1.66 % (1354206)------------------------------
% 7.42/1.66 % (1354206)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 7.42/1.66 % (1354206)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.51/1.98 % (1354206)CaDiCaL version: 2.1.3
% 8.51/1.98 % (1354206)Termination reason: Instruction limit
% 8.51/1.98 % (1354206)Termination phase: Saturation
% 8.51/1.98 % (1354206)Time elapsed: 0.129 s
% 8.51/1.98 % (1354206)Peak memory usage: 13 MB
% 8.51/1.98 % (1354206)Instructions burned: 159 (million)
% 8.51/1.98 % (1354219)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=1335739628:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 8.51/1.98 % (1354223)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=2073970608:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 8.51/1.98 % (1354217)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 8.51/1.98 % (1354217)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 8.51/1.98 % Exception at run slice level
% 8.51/1.98 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 8.51/1.98 % (1354216)Instruction limit reached!
% 8.51/1.98 % (1354216)------------------------------
% 8.51/1.98 % (1354216)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.51/2.02 % (1354216)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.51/2.02 % (1354216)CaDiCaL version: 2.1.3
% 8.51/2.02 % (1354216)Termination reason: Instruction limit
% 8.51/2.02 % (1354216)Termination phase: Saturation
% 8.51/2.02 % (1354216)Time elapsed: 0.104 s
% 8.51/2.02 % (1354216)Peak memory usage: 13 MB
% 8.51/2.02 % (1354216)Instructions burned: 131 (million)
% 8.51/2.02 % (1354226)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=32820962:i=1179_2997 on theBenchmark for (2997ds/1179Mi)
% 8.51/2.02 % (1354227)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=1932828381:i=889:ins=1_2997 on theBenchmark for (2997ds/889Mi)
% 8.51/2.02 % (1354218)Instruction limit reached!
% 8.51/2.02 % (1354218)------------------------------
% 8.51/2.02 % (1354218)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.51/2.02 % (1354218)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.51/2.02 % (1354218)CaDiCaL version: 2.1.3
% 8.51/2.02 % (1354218)Termination reason: Instruction limit
% 8.51/2.02 % (1354218)Termination phase: Saturation
% 8.51/2.02 % (1354218)Time elapsed: 0.143 s
% 8.51/2.02 % (1354218)Peak memory usage: 13 MB
% 8.51/2.02 % (1354218)Instructions burned: 181 (million)
% 8.51/2.02 % (1354230)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=2816795305:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2996 on theBenchmark for (2996ds/692Mi)
% 8.51/2.02 % Exception at run slice level
% 8.51/2.02 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 8.51/2.02 % (1354219)Instruction limit reached!
% 8.51/2.02 % (1354219)------------------------------
% 8.51/2.02 % (1354219)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.51/2.02 % (1354219)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.51/2.02 % (1354219)CaDiCaL version: 2.1.3
% 8.51/2.02 % (1354219)Termination reason: Instruction limit
% 8.51/2.02 % (1354219)Termination phase: Saturation
% 8.51/2.02 % (1354219)Time elapsed: 0.224 s
% 8.51/2.02 % (1354219)Peak memory usage: 15 MB
% 8.51/2.02 % (1354219)Instructions burned: 477 (million)
% 8.51/2.02 % (1354230)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 8.51/2.02 % (1354232)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=3672063877:i=879:kws=inv_precedence:fsr=off_2995 on theBenchmark for (2995ds/879Mi)
% 8.51/2.02 % (1354233)fmb+10_1_sil=64000:random_seed=2048328783:i=22061:nm=2:gsp=on_2995 on theBenchmark for (2995ds/22061Mi)
% 8.51/2.02 % (1354232)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 8.51/2.02 % (1354233)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 8.51/2.02 % Exception at run slice level
% 8.51/2.02 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 8.51/2.02 % (1354236)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=721398289:i=9515:nm=5_2995 on theBenchmark for (2995ds/9515Mi)
% 8.51/2.02 % Exception at run slice level
% 8.51/2.02 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 8.51/2.02 % (1354238)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=3499711876:fmbsr=1.7:i=920_2993 on theBenchmark for (2993ds/920Mi)
% 8.51/2.02 % (1354217)Instruction limit reached!
% 8.51/2.02 % (1354217)------------------------------
% 8.51/2.02 % (1354217)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.51/2.02 % (1354217)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.51/2.02 % (1354217)CaDiCaL version: 2.1.3
% 8.51/2.02 % (1354217)Termination reason: Instruction limit
% 8.51/2.02 % (1354217)Termination phase: Saturation
% 8.51/2.02 % (1354217)Time elapsed: 0.526 s
% 8.51/2.02 % (1354217)Peak memory usage: 16 MB
% 8.51/2.02 % (1354217)Instructions burned: 685 (million)
% 8.51/2.02 % Exception at run slice level
% 8.51/2.02 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 8.51/2.02 % (1354240)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=2782373178:i=5131_2992 on theBenchmark for (2992ds/5131Mi)
% 8.51/2.02 % (1354241)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=3130879572:i=1472:ins=7:fdi=8:gsp=on_2992 on theBenchmark for (2992ds/1472Mi)
% 8.51/2.02 % (1354240)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 8.51/2.02 % (1354241)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 8.51/2.02 % (1354241)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 8.51/2.02 % (1354232)Instruction limit reached!
% 8.51/2.02 % (1354232)------------------------------
% 8.51/2.02 % (1354232)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.51/2.02 % (1354232)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.51/2.02 % (1354232)CaDiCaL version: 2.1.3
% 8.51/2.02 % (1354232)Termination reason: Instruction limit
% 8.51/2.02 % (1354232)Termination phase: Saturation
% 8.51/2.02 % (1354232)Time elapsed: 0.429 s
% 8.51/2.02 % (1354232)Peak memory usage: 18 MB
% 8.51/2.02 % (1354232)Instructions burned: 881 (million)
% 8.51/2.02 % (1354244)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=1225253644:i=6324_2991 on theBenchmark for (2991ds/6324Mi)
% 8.51/2.02 % (1354230)Instruction limit reached!
% 8.51/2.02 % (1354230)------------------------------
% 8.51/2.02 % (1354230)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.51/2.02 % (1354230)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.51/2.02 % (1354230)CaDiCaL version: 2.1.3
% 8.51/2.02 % (1354230)Termination reason: Instruction limit
% 8.51/2.02 % (1354230)Termination phase: Saturation
% 8.51/2.02 % (1354230)Time elapsed: 0.546 s
% 8.51/2.02 % (1354230)Peak memory usage: 17 MB
% 8.51/2.02 % (1354230)Instructions burned: 693 (million)
% 8.51/2.02 % (1354246)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=2028330976:fmbsr=2.30978:i=2174_2990 on theBenchmark for (2990ds/2174Mi)
% 8.51/2.02 % Exception at run slice level
% 8.51/2.02 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 8.51/2.02 % (1354248)ott-2_1_sil=16000:newcnf=on:random_seed=1239607303:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2990 on theBenchmark for (2990ds/869Mi)
% 8.51/2.02 % (1354248)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 8.51/2.02 % Exception at run slice level
% 8.51/2.02 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 8.51/2.02 % (1354250)ott+10_1_sil=32000:tgt=ground:random_seed=1359155136:i=5114:av=off_2989 on theBenchmark for (2989ds/5114Mi)
% 8.51/2.02 % (1354226)Instruction limit reached!
% 8.51/2.02 % (1354226)------------------------------
% 8.51/2.02 % (1354226)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.51/2.02 % (1354226)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.51/2.02 % (1354226)CaDiCaL version: 2.1.3
% 8.51/2.02 % (1354226)Termination reason: Instruction limit
% 8.51/2.02 % (1354226)Termination phase: Saturation
% 8.51/2.02 % (1354226)Time elapsed: 0.965 s
% 8.51/2.02 % (1354226)Peak memory usage: 20 MB
% 8.51/2.02 % (1354226)Instructions burned: 1180 (million)
% 8.51/2.02 % (1354252)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=2217396680:i=54282_2987 on theBenchmark for (2987ds/54282Mi)
% 8.51/2.02 % Exception at run slice level
% 8.51/2.02 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 8.51/2.02 % (1354248)Instruction limit reached!
% 8.51/2.02 % (1354248)------------------------------
% 8.51/2.02 % (1354248)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.51/2.02 % (1354248)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.51/2.02 % (1354248)CaDiCaL version: 2.1.3
% 8.51/2.02 % (1354248)Termination reason: Instruction limit
% 8.51/2.02 % (1354248)Termination phase: Saturation
% 8.51/2.02 % (1354248)Time elapsed: 0.391 s
% 8.51/2.02 % (1354248)Peak memory usage: 17 MB
% 8.51/2.02 % (1354248)Instructions burned: 869 (million)
% 8.51/2.02 % (1354254)dis-11_1_sil=16000:sp=reverse_frequency:alpa=true:random_seed=1995268202:i=3512:aac=none_2986 on theBenchmark for (2986ds/3512Mi)
% 8.51/2.02 % (1354255)dis+21_1_sil=32000:sas=cadical:random_seed=1877789202:i=3773:amm=off_2986 on theBenchmark for (2986ds/3773Mi)
% 8.51/2.02 % (1354254)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 8.51/2.02 % (1354201) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1354195-1354201"...
% 8.51/2.02 % (1354201)...printing done.
% 8.51/2.02 % (1354201)Refutation found. Thanks to Tanya!
% 8.51/2.02 % SZS status Theorem for theBenchmark
% 8.51/2.02 % SZS output start Proof for theBenchmark
% 8.51/2.02 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 8.51/2.02 thf(func_def_0, type, in: ($i > $i > $o)).
% 8.51/2.02 thf(func_def_1, type, exu: (($i > $o) > $o)).
% 8.51/2.02 thf(func_def_3, type, setextAx: $o).
% 8.51/2.02 thf(func_def_5, type, emptysetAx: $o).
% 8.51/2.02 thf(func_def_6, type, setadjoin: ($i > $i > $i)).
% 8.51/2.02 thf(func_def_7, type, setadjoinAx: $o).
% 8.51/2.02 thf(func_def_8, type, powerset: ($i > $i)).
% 8.51/2.02 thf(func_def_9, type, powersetAx: $o).
% 8.51/2.02 thf(func_def_10, type, setunion: ($i > $i)).
% 8.51/2.02 thf(func_def_11, type, setunionAx: $o).
% 8.51/2.02 thf(func_def_13, type, omega0Ax: $o).
% 8.51/2.02 thf(func_def_14, type, omegaSAx: $o).
% 8.51/2.02 thf(func_def_15, type, omegaIndAx: $o).
% 8.51/2.02 thf(func_def_16, type, replAx: $o).
% 8.51/2.02 thf(func_def_17, type, foundationAx: $o).
% 8.51/2.02 thf(func_def_18, type, wellorderingAx: $o).
% 8.51/2.02 thf(func_def_19, type, descr: (($i > $o) > $i)).
% 8.51/2.02 thf(func_def_20, type, descrp: $o).
% 8.51/2.02 thf(func_def_21, type, dsetconstr: ($i > ($i > $o) > $i)).
% 8.51/2.02 thf(func_def_22, type, dsetconstrI: $o).
% 8.51/2.02 thf(func_def_23, type, dsetconstrEL: $o).
% 8.51/2.02 thf(func_def_24, type, dsetconstrER: $o).
% 8.51/2.02 thf(func_def_25, type, exuE1: $o).
% 8.51/2.02 thf(func_def_26, type, prop2set: ($o > $i)).
% 8.51/2.02 thf(func_def_27, type, prop2setE: $o).
% 8.51/2.02 thf(func_def_28, type, emptysetE: $o).
% 8.51/2.02 thf(func_def_29, type, emptysetimpfalse: $o).
% 8.51/2.02 thf(func_def_30, type, notinemptyset: $o).
% 8.51/2.02 thf(func_def_31, type, exuE3e: $o).
% 8.51/2.02 thf(func_def_32, type, setext: $o).
% 8.51/2.02 thf(func_def_33, type, emptyI: $o).
% 8.51/2.02 thf(func_def_34, type, noeltsimpempty: $o).
% 8.51/2.02 thf(func_def_35, type, setbeta: $o).
% 8.51/2.02 thf(func_def_36, type, nonempty: ($i > $o)).
% 8.51/2.02 thf(func_def_37, type, nonemptyE1: $o).
% 8.51/2.02 thf(func_def_38, type, nonemptyI: $o).
% 8.51/2.02 thf(func_def_39, type, nonemptyI1: $o).
% 8.51/2.02 thf(func_def_40, type, setadjoinIL: $o).
% 8.51/2.02 thf(func_def_41, type, emptyinunitempty: $o).
% 8.51/2.02 thf(func_def_42, type, setadjoinIR: $o).
% 8.51/2.02 thf(func_def_43, type, setadjoinE: $o).
% 8.51/2.02 thf(func_def_44, type, setadjoinOr: $o).
% 8.51/2.02 thf(func_def_45, type, setoftrueEq: $o).
% 8.51/2.02 thf(func_def_46, type, powersetI: $o).
% 8.51/2.02 thf(func_def_47, type, emptyinPowerset: $o).
% 8.51/2.02 thf(func_def_48, type, emptyInPowerset: $o).
% 8.51/2.02 thf(func_def_49, type, powersetE: $o).
% 8.51/2.02 thf(func_def_50, type, setunionI: $o).
% 8.51/2.02 thf(func_def_51, type, setunionE: $o).
% 8.51/2.02 thf(func_def_52, type, subPowSU: $o).
% 8.51/2.02 thf(func_def_53, type, exuE2: $o).
% 8.51/2.02 thf(func_def_54, type, nonemptyImpWitness: $o).
% 8.51/2.02 thf(func_def_55, type, uniqinunit: $o).
% 8.51/2.02 thf(func_def_56, type, notinsingleton: $o).
% 8.51/2.02 thf(func_def_57, type, eqinunit: $o).
% 8.51/2.02 thf(func_def_58, type, singletonsswitch: $o).
% 8.51/2.02 thf(func_def_59, type, upairsetE: $o).
% 8.51/2.02 thf(func_def_60, type, upairsetIL: $o).
% 8.51/2.02 thf(func_def_61, type, upairsetIR: $o).
% 8.51/2.02 thf(func_def_62, type, emptyE1: $o).
% 8.51/2.02 thf(func_def_63, type, vacuousDall: $o).
% 8.51/2.02 thf(func_def_64, type, quantDeMorgan1: $o).
% 8.51/2.02 thf(func_def_65, type, quantDeMorgan2: $o).
% 8.51/2.02 thf(func_def_66, type, quantDeMorgan3: $o).
% 8.51/2.02 thf(func_def_67, type, quantDeMorgan4: $o).
% 8.51/2.02 thf(func_def_68, type, prop2setI: $o).
% 8.51/2.02 thf(func_def_69, type, set2prop: ($i > $o)).
% 8.51/2.02 thf(func_def_70, type, prop2set2propI: $o).
% 8.51/2.02 thf(func_def_71, type, notdexE: $o).
% 8.51/2.02 thf(func_def_72, type, notdallE: $o).
% 8.51/2.02 thf(func_def_73, type, exuI1: $o).
% 8.51/2.02 thf(func_def_74, type, exuI3: $o).
% 8.51/2.02 thf(func_def_75, type, exuI2: $o).
% 8.51/2.02 thf(func_def_76, type, inCongP: $o).
% 8.51/2.02 thf(func_def_77, type, in__Cong: $o).
% 8.51/2.02 thf(func_def_78, type, exuE3u: $o).
% 8.51/2.02 thf(func_def_79, type, exu__Cong: $o).
% 8.51/2.02 thf(func_def_80, type, emptyset__Cong: $o).
% 8.51/2.02 thf(func_def_81, type, setadjoin__Cong: $o).
% 8.51/2.02 thf(func_def_82, type, powerset__Cong: $o).
% 8.51/2.02 thf(func_def_83, type, setunion__Cong: $o).
% 8.51/2.02 thf(func_def_84, type, omega__Cong: $o).
% 8.51/2.02 thf(func_def_85, type, exuEu: $o).
% 8.51/2.02 thf(func_def_86, type, descr__Cong: $o).
% 8.51/2.02 thf(func_def_87, type, dsetconstr__Cong: $o).
% 8.51/2.02 thf(func_def_88, type, subset: ($i > $i > $o)).
% 8.51/2.02 thf(func_def_89, type, disjoint: ($i > $i > $o)).
% 8.51/2.02 thf(func_def_90, type, setsmeet: ($i > $i > $o)).
% 8.51/2.02 thf(func_def_91, type, subsetI1: $o).
% 8.51/2.02 thf(func_def_92, type, eqimpsubset2: $o).
% 8.51/2.02 thf(func_def_93, type, eqimpsubset1: $o).
% 8.51/2.02 thf(func_def_94, type, subsetI2: $o).
% 8.51/2.02 thf(func_def_95, type, emptysetsubset: $o).
% 8.51/2.02 thf(func_def_96, type, subsetE: $o).
% 8.51/2.02 thf(func_def_97, type, subsetE2: $o).
% 8.51/2.02 thf(func_def_98, type, notsubsetI: $o).
% 8.51/2.02 thf(func_def_99, type, notequalI1: $o).
% 8.51/2.02 thf(func_def_100, type, notequalI2: $o).
% 8.51/2.02 thf(func_def_101, type, subsetRefl: $o).
% 8.51/2.02 thf(func_def_102, type, subsetTrans: $o).
% 8.51/2.02 thf(func_def_103, type, setadjoinSub: $o).
% 8.51/2.02 thf(func_def_104, type, setadjoinSub2: $o).
% 8.51/2.02 thf(func_def_105, type, subset2powerset: $o).
% 8.51/2.02 thf(func_def_106, type, setextsub: $o).
% 8.51/2.02 thf(func_def_107, type, subsetemptysetimpeq: $o).
% 8.51/2.02 thf(func_def_108, type, powersetI1: $o).
% 8.51/2.02 thf(func_def_109, type, powersetE1: $o).
% 8.51/2.02 thf(func_def_110, type, inPowerset: $o).
% 8.51/2.02 thf(func_def_111, type, powersetsubset: $o).
% 8.51/2.02 thf(func_def_112, type, sepInPowerset: $o).
% 8.51/2.02 thf(func_def_113, type, sepSubset: $o).
% 8.51/2.02 thf(func_def_114, type, binunion: ($i > $i > $i)).
% 8.51/2.02 thf(func_def_115, type, binunionIL: $o).
% 8.51/2.02 thf(func_def_116, type, upairset2IR: $o).
% 8.51/2.02 thf(func_def_117, type, binunionIR: $o).
% 8.51/2.02 thf(func_def_118, type, binunionEcases: $o).
% 8.51/2.02 thf(func_def_119, type, binunionE: $o).
% 8.51/2.03 thf(func_def_120, type, binunionLsub: $o).
% 8.51/2.03 thf(func_def_121, type, binunionRsub: $o).
% 8.51/2.03 thf(func_def_122, type, binintersect: ($i > $i > $i)).
% 8.51/2.03 thf(func_def_123, type, binintersectI: $o).
% 8.51/2.03 thf(func_def_124, type, binintersectSubset5: $o).
% 8.51/2.03 thf(func_def_125, type, binintersectEL: $o).
% 8.51/2.03 thf(func_def_126, type, binintersectLsub: $o).
% 8.51/2.03 thf(func_def_127, type, binintersectSubset2: $o).
% 8.51/2.03 thf(func_def_128, type, binintersectSubset3: $o).
% 8.51/2.03 thf(func_def_129, type, binintersectER: $o).
% 8.51/2.03 thf(func_def_130, type, disjointsetsI1: $o).
% 8.51/2.03 thf(func_def_131, type, binintersectRsub: $o).
% 8.51/2.03 thf(func_def_132, type, binintersectSubset4: $o).
% 8.51/2.03 thf(func_def_133, type, binintersectSubset1: $o).
% 8.51/2.03 thf(func_def_134, type, bs114d: $o).
% 8.51/2.03 thf(func_def_135, type, regular: ($i > $o)).
% 8.51/2.03 thf(func_def_136, type, setminus: ($i > $i > $i)).
% 8.51/2.03 thf(func_def_137, type, setminusI: $o).
% 8.51/2.03 thf(func_def_138, type, setminusEL: $o).
% 8.51/2.03 thf(func_def_139, type, setminusER: $o).
% 8.51/2.03 thf(func_def_140, type, setminusSubset2: $o).
% 8.51/2.03 thf(func_def_141, type, setminusERneg: $o).
% 8.51/2.03 thf(func_def_142, type, setminusELneg: $o).
% 8.51/2.03 thf(func_def_143, type, setminusILneg: $o).
% 8.51/2.03 thf(func_def_144, type, setminusIRneg: $o).
% 8.51/2.03 thf(func_def_145, type, setminusLsub: $o).
% 8.51/2.03 thf(func_def_146, type, setminusSubset1: $o).
% 8.51/2.03 thf(func_def_147, type, symdiff: ($i > $i > $i)).
% 8.51/2.03 thf(func_def_148, type, symdiffE: $o).
% 8.51/2.03 thf(func_def_149, type, symdiffI1: $o).
% 8.51/2.03 thf(func_def_150, type, symdiffI2: $o).
% 8.51/2.03 thf(func_def_151, type, symdiffIneg1: $o).
% 8.51/2.03 thf(func_def_152, type, symdiffIneg2: $o).
% 8.51/2.03 thf(func_def_153, type, iskpair: ($i > $o)).
% 8.51/2.03 thf(func_def_154, type, secondinupair: $o).
% 8.51/2.03 thf(func_def_155, type, setukpairIL: $o).
% 8.51/2.03 thf(func_def_156, type, setukpairIR: $o).
% 8.51/2.03 thf(func_def_157, type, kpairiskpair: $o).
% 8.51/2.03 thf(func_def_158, type, kpair: ($i > $i > $i)).
% 8.51/2.03 thf(func_def_159, type, kpairp: $o).
% 8.51/2.03 thf(func_def_160, type, cartprod: ($i > $i > $i)).
% 8.51/2.03 thf(func_def_161, type, singletonsubset: $o).
% 8.51/2.03 thf(func_def_162, type, singletoninpowerset: $o).
% 8.51/2.03 thf(func_def_163, type, singletoninpowunion: $o).
% 8.51/2.03 thf(func_def_164, type, upairset2E: $o).
% 8.51/2.03 thf(func_def_165, type, upairsubunion: $o).
% 8.51/2.03 thf(func_def_166, type, upairinpowunion: $o).
% 8.51/2.03 thf(func_def_167, type, ubforcartprodlem1: $o).
% 8.51/2.03 thf(func_def_168, type, ubforcartprodlem2: $o).
% 8.51/2.03 thf(func_def_169, type, ubforcartprodlem3: $o).
% 8.51/2.03 thf(func_def_170, type, cartprodpairin: $o).
% 8.51/2.03 thf(func_def_171, type, cartprodmempair1: $o).
% 8.51/2.03 thf(func_def_172, type, cartprodmempair: $o).
% 8.51/2.03 thf(func_def_173, type, setunionE2: $o).
% 8.51/2.03 thf(func_def_174, type, setunionsingleton1: $o).
% 8.51/2.03 thf(func_def_175, type, setunionsingleton2: $o).
% 8.51/2.03 thf(func_def_176, type, setunionsingleton: $o).
% 8.51/2.03 thf(func_def_177, type, singleton: ($i > $o)).
% 8.51/2.03 thf(func_def_178, type, singletonprop: $o).
% 8.51/2.03 thf(func_def_179, type, ex1: ($i > ($i > $o) > $o)).
% 8.51/2.03 thf(func_def_180, type, ex1E1: $o).
% 8.51/2.03 thf(func_def_181, type, ex1I: $o).
% 8.51/2.03 thf(func_def_182, type, ex1I2: $o).
% 8.51/2.03 thf(func_def_183, type, singletonsuniq: $o).
% 8.51/2.03 thf(func_def_184, type, atmost1p: ($i > $o)).
% 8.51/2.03 thf(func_def_185, type, atleast2p: ($i > $o)).
% 8.51/2.03 thf(func_def_186, type, atmost2p: ($i > $o)).
% 8.51/2.03 thf(func_def_187, type, upairsetp: ($i > $o)).
% 8.51/2.03 thf(func_def_188, type, setukpairinjL1: $o).
% 8.51/2.03 thf(func_def_189, type, kfstsingleton: $o).
% 8.51/2.03 thf(func_def_190, type, theprop: $o).
% 8.51/2.03 thf(func_def_191, type, kfst: ($i > $i)).
% 8.51/2.03 thf(func_def_192, type, kfstpairEq: $o).
% 8.51/2.03 thf(func_def_193, type, cartprodfstin: $o).
% 8.51/2.03 thf(func_def_194, type, setukpairinjL2: $o).
% 8.51/2.03 thf(func_def_195, type, setukpairinjL: $o).
% 8.51/2.03 thf(func_def_196, type, setukpairinjR11: $o).
% 8.51/2.03 thf(func_def_197, type, setukpairinjR12: $o).
% 8.51/2.03 thf(func_def_198, type, setukpairinjR1: $o).
% 8.51/2.03 thf(func_def_199, type, upairequniteq: $o).
% 8.51/2.03 thf(func_def_200, type, setukpairinjR2: $o).
% 8.51/2.03 thf(func_def_201, type, setukpairinjR: $o).
% 8.51/2.03 thf(func_def_202, type, ksndsingleton: $o).
% 8.51/2.03 thf(func_def_203, type, ksnd: ($i > $i)).
% 8.51/2.03 thf(func_def_204, type, ksndpairEq: $o).
% 8.51/2.03 thf(func_def_205, type, kpairsurjEq: $o).
% 8.51/2.03 thf(func_def_206, type, cartprodsndin: $o).
% 8.51/2.03 thf(func_def_207, type, cartprodpairmemEL: $o).
% 8.51/2.03 thf(func_def_208, type, cartprodpairmemER: $o).
% 8.51/2.03 thf(func_def_209, type, cartprodmempaircEq: $o).
% 8.51/2.03 thf(func_def_210, type, cartprodfstpairEq: $o).
% 8.51/2.03 thf(func_def_211, type, cartprodsndpairEq: $o).
% 8.51/2.03 thf(func_def_212, type, cartprodpairsurjEq: $o).
% 8.51/2.03 thf(func_def_213, type, breln: ($i > $i > $i > $o)).
% 8.51/2.03 thf(func_def_214, type, dpsetconstr: ($i > $i > ($i > $i > $o) > $i)).
% 8.51/2.03 thf(func_def_215, type, dpsetconstrI: $o).
% 8.51/2.03 thf(func_def_216, type, dpsetconstrSub: $o).
% 8.51/2.03 thf(func_def_217, type, setOfPairsIsBReln: $o).
% 8.51/2.03 thf(func_def_218, type, dpsetconstrERa: $o).
% 8.51/2.03 thf(func_def_219, type, dpsetconstrEL1: $o).
% 8.51/2.03 thf(func_def_220, type, dpsetconstrEL2: $o).
% 8.51/2.03 thf(func_def_221, type, dpsetconstrER: $o).
% 8.51/2.03 thf(func_def_222, type, func: ($i > $i > $i > $o)).
% 8.51/2.03 thf(func_def_223, type, funcSet: ($i > $i > $i)).
% 8.51/2.03 thf(func_def_224, type, funcImageSingleton: $o).
% 8.51/2.03 thf(func_def_225, type, apProp: $o).
% 8.51/2.03 thf(func_def_226, type, ap: ($i > $i > $i > $i > $i)).
% 8.51/2.03 thf(func_def_227, type, app: $o).
% 8.51/2.03 thf(func_def_228, type, infuncsetfunc: $o).
% 8.51/2.03 thf(func_def_229, type, ap2p: $o).
% 8.51/2.03 thf(func_def_230, type, funcinfuncset: $o).
% 8.51/2.03 thf(func_def_231, type, lamProp: $o).
% 8.51/2.03 thf(func_def_232, type, lam: ($i > $i > ($i > $i) > $i)).
% 8.51/2.03 thf(func_def_233, type, lamp: $o).
% 8.51/2.03 thf(func_def_234, type, lam2p: $o).
% 8.51/2.03 thf(func_def_235, type, brelnall1: $o).
% 8.51/2.03 thf(func_def_236, type, brelnall2: $o).
% 8.51/2.03 thf(func_def_237, type, ex1E2: $o).
% 8.51/2.03 thf(func_def_238, type, funcGraphProp1: $o).
% 8.51/2.03 thf(func_def_239, type, funcGraphProp3: $o).
% 8.51/2.03 thf(func_def_240, type, funcGraphProp2: $o).
% 8.51/2.03 thf(func_def_241, type, funcextLem: $o).
% 8.51/2.03 thf(func_def_242, type, funcGraphProp4: $o).
% 8.51/2.03 thf(func_def_243, type, subbreln: $o).
% 8.51/2.03 thf(func_def_244, type, eqbreln: $o).
% 8.51/2.03 thf(func_def_245, type, funcext: $o).
% 8.51/2.03 thf(func_def_246, type, funcext2: $o).
% 8.51/2.03 thf(func_def_247, type, ap2apEq1: $o).
% 8.51/2.03 thf(func_def_248, type, ap2apEq2: $o).
% 8.51/2.03 thf(func_def_249, type, beta1: $o).
% 8.51/2.03 thf(func_def_250, type, eta1: $o).
% 8.51/2.03 thf(func_def_251, type, lam2lamEq: $o).
% 8.51/2.03 thf(func_def_252, type, beta2: $o).
% 8.51/2.03 thf(func_def_253, type, eta2: $o).
% 8.51/2.03 thf(func_def_254, type, iffalseProp1: $o).
% 8.51/2.03 thf(func_def_255, type, iffalseProp2: $o).
% 8.51/2.03 thf(func_def_256, type, iftrueProp1: $o).
% 8.51/2.03 thf(func_def_257, type, iftrueProp2: $o).
% 8.51/2.03 thf(func_def_258, type, ifSingleton: $o).
% 8.51/2.03 thf(func_def_259, type, if: ($i > $o > $i > $i > $i)).
% 8.51/2.03 thf(func_def_260, type, ifp: $o).
% 8.51/2.03 thf(func_def_261, type, theeq: $o).
% 8.51/2.03 thf(func_def_262, type, iftrue: $o).
% 8.51/2.03 thf(func_def_263, type, iffalse: $o).
% 8.51/2.03 thf(func_def_264, type, iftrueorfalse: $o).
% 8.51/2.03 thf(func_def_265, type, binintersectT_lem: $o).
% 8.51/2.03 thf(func_def_266, type, binunionT_lem: $o).
% 8.51/2.03 thf(func_def_267, type, powersetT_lem: $o).
% 8.51/2.03 thf(func_def_268, type, setminusT_lem: $o).
% 8.51/2.03 thf(func_def_269, type, complementT_lem: $o).
% 8.51/2.03 thf(func_def_270, type, setextT: $o).
% 8.51/2.03 thf(func_def_271, type, subsetTI: $o).
% 8.51/2.03 thf(func_def_272, type, powersetTI1: $o).
% 8.51/2.03 thf(func_def_273, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 8.51/2.03 thf(func_def_274, type, vAND: ($o > $o > $o)).
% 8.51/2.03 thf(func_def_275, type, db1: !>[X0: $tType]:(X0)).
% 8.51/2.03 thf(func_def_276, type, db0: !>[X0: $tType]:(X0)).
% 8.51/2.03 thf(func_def_277, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 8.51/2.03 thf(func_def_278, type, vIMP: ($o > $o > $o)).
% 8.51/2.03 thf(func_def_279, type, db2: !>[X0: $tType]:(X0)).
% 8.51/2.03 thf(func_def_280, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 8.51/2.03 thf(func_def_281, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 8.51/2.03 thf(func_def_282, type, vIFF: ($o > $o > $o)).
% 8.51/2.03 thf(func_def_283, type, vNOT: ($o > $o)).
% 8.51/2.03 thf(func_def_284, type, vOR: ($o > $o > $o)).
% 8.51/2.03 thf(func_def_285, type, db4: !>[X0: $tType]:(X0)).
% 8.51/2.03 thf(func_def_286, type, db3: !>[X0: $tType]:(X0)).
% 8.51/2.03 thf(func_def_289, type, db5: !>[X0: $tType]:(X0)).
% 8.51/2.03 thf(func_def_294, type, sK4: ($i > $i > $i > $i)).
% 8.51/2.03 thf(func_def_295, type, sK5: ($i > $i > $i > $i)).
% 8.51/2.03 thf(func_def_296, type, sK6: ($i > $i > $i > $i)).
% 8.51/2.03 thf(func_def_297, type, sK7: ($i > $i > $i > $i)).
% 8.51/2.03 thf(func_def_298, type, sK8: ($i > ($i > $i) > $i > $i)).
% 8.51/2.03 thf(func_def_299, type, sK9: ($i > ($i > $i) > $i > $i)).
% 8.51/2.03 thf(func_def_300, type, sK10: ($i > ($i > $i) > $i > $i)).
% 8.51/2.03 thf(func_def_301, type, sK11: ($i > $i > $i > $i > $i)).
% 8.51/2.03 thf(func_def_302, type, sK12: ($i > $i > $i > $i > $i)).
% 8.51/2.03 thf(func_def_303, type, sK13: ($i > $i > $i > $i > $i)).
% 8.51/2.03 thf(func_def_304, type, sK14: ($i > $i > $i > $i > $i)).
% 8.51/2.03 thf(func_def_305, type, sK15: ($i > $i > $i > $i > $i)).
% 8.51/2.03 thf(func_def_306, type, sK16: ($i > $i > $i > $i > $i)).
% 8.51/2.03 thf(func_def_307, type, sK17: ($i > $i > $i > $i > $i)).
% 8.51/2.03 thf(func_def_308, type, sK18: ($i > $i > $i > $i > $i)).
% 8.51/2.03 thf(func_def_309, type, sK19: ($i > $i > $i > $i > $i)).
% 8.51/2.03 thf(func_def_310, type, sK20: ($i > $i > $i > $i > $i)).
% 8.51/2.03 thf(func_def_311, type, sK21: ($i > $i > $i > ($i > $o) > $i)).
% 8.51/2.03 thf(func_def_312, type, sK22: ($i > $i > $i > ($i > $o) > $i)).
% 8.51/2.03 thf(func_def_313, type, sK23: ($i > $i > $i > ($i > $o) > $i)).
% 8.51/2.03 thf(func_def_314, type, sK24: ($i > $i > $i > ($i > $o) > $i)).
% 8.51/2.03 thf(func_def_315, type, sK25: (($i > $i) > $i > $i > $i)).
% 8.51/2.03 thf(func_def_316, type, sK26: (($i > $i) > $i > $i > $i)).
% 8.51/2.03 thf(func_def_317, type, sK27: (($i > $i) > $i > $i > $i)).
% 8.51/2.03 thf(func_def_318, type, sK28: (($i > $o) > $i > $i)).
% 8.51/2.03 thf(func_def_319, type, sK29: (($i > $o) > $i > $i)).
% 8.51/2.03 thf(func_def_320, type, sK30: ($i > ($i > $o) > $i > $i)).
% 8.51/2.03 thf(func_def_321, type, sK31: (($i > $o) > $i > $i)).
% 8.51/2.03 thf(func_def_322, type, sK32: (($i > $o) > $i > $i)).
% 8.51/2.03 thf(func_def_323, type, sK33: (($i > $o) > $i > $i)).
% 8.51/2.03 thf(func_def_324, type, sK34: ($i > $i > $i)).
% 8.51/2.03 thf(func_def_325, type, sK35: ($i > $i > $i > $i)).
% 8.51/2.03 thf(func_def_326, type, sK36: ($i > $i > $i > $i)).
% 8.51/2.03 thf(func_def_327, type, sK37: ($i > $i > $i)).
% 8.51/2.03 thf(func_def_328, type, sK38: ($i > $i > $i)).
% 8.51/2.03 thf(func_def_329, type, sK39: ($i > $i > $i)).
% 8.51/2.03 thf(func_def_330, type, sK40: ($i > $i > ($i > $o) > ($i > $o) > $i)).
% 8.51/2.03 thf(func_def_331, type, sK41: ($i > ($i > $o) > ($i > $o) > $i > $i)).
% 8.51/2.03 thf(func_def_332, type, sK42: (($i > $o) > ($i > $o) > $i)).
% 8.51/2.03 thf(func_def_333, type, sK43: (($i > $o) > ($i > $o) > $i)).
% 8.51/2.03 thf(func_def_334, type, sK44: (($i > $o) > $i > $i)).
% 8.51/2.03 thf(func_def_335, type, sK45: (($i > $o) > $i > $i)).
% 8.51/2.03 thf(func_def_336, type, sK46: (($i > $o) > $i > $i)).
% 8.51/2.03 thf(func_def_337, type, sK47: (($i > $o) > ($i > $o) > $i)).
% 8.51/2.03 thf(func_def_338, type, sK48: (($i > $o) > ($i > $o) > $i)).
% 8.51/2.03 thf(func_def_339, type, sK49: (($i > $o) > $i)).
% 8.51/2.03 thf(func_def_340, type, sK50: (($i > $o) > $i > $i)).
% 8.51/2.03 thf(func_def_341, type, sK51: (($i > $o) > $i)).
% 8.51/2.03 thf(func_def_342, type, sK52: (($i > $o) > $i > $i)).
% 8.51/2.03 thf(func_def_343, type, sK53: (($i > $o) > $i > $i)).
% 8.51/2.03 thf(func_def_344, type, sK54: (($i > $o) > $i)).
% 8.51/2.03 thf(func_def_345, type, sK55: (($i > $o) > $i > $i)).
% 8.51/2.03 thf(func_def_346, type, sK56: (($i > $o) > $i)).
% 8.51/2.03 thf(func_def_347, type, sK57: (($i > $o) > $i > $i)).
% 8.51/2.03 thf(func_def_348, type, sK58: (($i > $o) > $i > $i)).
% 8.51/2.03 thf(func_def_349, type, sK59: (($i > $o) > $i)).
% 8.51/2.03 thf(func_def_350, type, sK60: (($i > $o) > $i > $i)).
% 8.51/2.03 thf(func_def_351, type, sK61: (($i > $o) > $i)).
% 8.51/2.03 thf(func_def_352, type, sK62: (($i > $o) > $i > $i)).
% 8.51/2.03 thf(func_def_353, type, sK63: (($i > $o) > $i > $i)).
% 8.51/2.03 thf(func_def_354, type, sK64: (($i > $o) > $i > $i)).
% 8.51/2.03 thf(func_def_355, type, sK65: (($i > $o) > $i)).
% 8.51/2.03 thf(func_def_356, type, sK66: (($i > $o) > $i > $i)).
% 8.51/2.03 thf(func_def_357, type, sK67: (($i > $o) > $i)).
% 8.51/2.03 thf(func_def_358, type, sK68: (($i > $o) > $i)).
% 8.51/2.03 thf(func_def_359, type, sK69: (($i > $o) > $i)).
% 8.51/2.03 thf(func_def_360, type, sK70: (($i > $o) > $i)).
% 8.51/2.03 thf(func_def_361, type, sK71: (($i > $o) > $i > $i)).
% 8.51/2.03 thf(func_def_362, type, sK72: (($i > $o) > $i > $i)).
% 8.51/2.03 thf(func_def_363, type, sK73: (($i > $o) > $i > $i)).
% 8.51/2.03 thf(func_def_364, type, sK74: (($i > $o) > $i > $i)).
% 8.51/2.03 thf(func_def_365, type, sK75: (($i > $o) > $i > $i)).
% 8.51/2.03 thf(func_def_366, type, sK76: (($i > $o) > $i > $i)).
% 8.51/2.03 thf(func_def_367, type, sK77: (($i > $o) > $i > $i)).
% 8.51/2.03 thf(func_def_368, type, sK78: ($i > $i)).
% 8.51/2.03 thf(func_def_369, type, sK79: (($i > $o) > $i)).
% 8.51/2.03 thf(func_def_370, type, sK80: (($i > $o) > $i > $i)).
% 8.51/2.03 thf(func_def_371, type, sK81: ($i > $o > $i > $i)).
% 8.51/2.03 thf(func_def_372, type, sK82: ($i > $i > $i)).
% 8.51/2.03 thf(func_def_373, type, sK83: ($i > $i)).
% 8.51/2.03 thf(func_def_374, type, sK84: ($i > $i)).
% 8.51/2.03 thf(func_def_375, type, sK85: ($i > $i)).
% 8.51/2.03 thf(func_def_376, type, sK86: ($i > $i > $i)).
% 8.51/2.03 thf(func_def_377, type, sK87: ($i > $i > $i)).
% 8.51/2.03 thf(func_def_378, type, sK88: (($i > $o) > $i)).
% 8.51/2.03 thf(func_def_379, type, sK89: (($i > $o) > $i > $i)).
% 8.51/2.03 thf(func_def_380, type, sK90: (($i > $o) > $i)).
% 8.51/2.03 thf(func_def_381, type, sK91: (($i > $o) > $i > $i)).
% 8.51/2.03 thf(func_def_382, type, sK92: (($i > $o) > $i > $i)).
% 8.51/2.03 thf(func_def_383, type, sK93: ($i > $i)).
% 8.51/2.03 thf(func_def_384, type, sK94: ($i > $i > $i > $i)).
% 8.51/2.03 thf(func_def_385, type, sK95: ($i > $i > $i)).
% 8.51/2.03 thf(func_def_386, type, sK96: ($i > $i > $i)).
% 8.51/2.03 thf(func_def_387, type, sK97: ($i > $i > $i)).
% 8.51/2.03 thf(func_def_388, type, sK98: ($i > $i)).
% 8.51/2.03 thf(func_def_389, type, sK99: ($i > ($i > $i > $o) > $i)).
% 8.51/2.03 thf(func_def_390, type, sK100: ($i > ($i > $i > $o) > $i)).
% 8.51/2.03 thf(func_def_391, type, sK101: ($i > $i > ($i > $i > $o) > $i)).
% 8.51/2.03 thf(func_def_392, type, sK102: ($i > ($i > $i > $o) > $i > $i)).
% 8.51/2.03 thf(func_def_393, type, sK103: ($i > $i > ($i > $i > $o) > $i)).
% 8.51/2.03 thf(func_def_394, type, sK104: ($i > $i > ($i > $i > $o) > $i)).
% 8.51/2.03 thf(func_def_395, type, sK105: ($i > $i)).
% 8.51/2.03 thf(func_def_396, type, sK106: ($i > $i > $i)).
% 8.51/2.03 thf(func_def_397, type, sK107: ($i > $i > $i)).
% 8.51/2.03 thf(func_def_398, type, sK108: ($i > $i > $i)).
% 8.51/2.03 thf(f40,axiom,(
% 8.51/2.03 (powersetE = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (powerset @ X0)) => ((in @ X2 @ X1) => (in @ X2 @ X0))))),
% 8.51/2.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetE)).
% 8.51/2.03 thf(f239,conjecture,(
% 8.51/2.03 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 => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X1 @ (powerset @ X2)) => ((in @ X3 @ X1) => (in @ X3 @ X2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.51/2.03 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetTE1)).
% 8.51/2.03 thf(f240,negated_conjecture,(
% 8.51/2.03 ~(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 => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X1 @ (powerset @ X2)) => ((in @ X3 @ X1) => (in @ X3 @ X2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.51/2.03 inference(negated_conjecture,[status(cth)],[f239])).
% 8.51/2.03 thf(f314,plain,(
% 8.51/2.03 (powersetE = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (powerset @ X0)) => ((in @ X2 @ X1) => (in @ X2 @ X0))))),
% 8.51/2.03 inference(rectify,[],[f40])).
% 8.51/2.03 thf(f315,plain,(
% 8.51/2.03 (powersetE = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (powerset @ Y2)) => ((in @ Y0 @ Y1) => (in @ Y0 @ Y2)))))))))))),
% 8.51/2.03 inference(fool_elimination,[],[f314])).
% 8.51/2.03 thf(f693,plain,(
% 8.51/2.03 ~(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 => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X1 @ (powerset @ X2)) => ((in @ X3 @ X1) => (in @ X3 @ X2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.51/2.03 inference(rectify,[],[f240])).
% 8.51/2.03 thf(f694,plain,(
% 8.51/2.03 ~((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) => ((disjointsetsI1 = $true) => ((binintersectRsub = $true) => ((binintersectSubset4 = $true) => ((binintersectSubset1 = $true) => ((bs114d = $true) => ((setminusI = $true) => ((setminusEL = $true) => ((setminusER = $true) => ((setminusSubset2 = $true) => ((setminusERneg = $true) => ((setminusELneg = $true) => ((setminusILneg = $true) => ((setminusIRneg = $true) => ((setminusLsub = $true) => ((setminusSubset1 = $true) => ((symdiffE = $true) => ((symdiffI1 = $true) => ((symdiffI2 = $true) => ((symdiffIneg1 = $true) => ((symdiffIneg2 = $true) => ((secondinupair = $true) => ((setukpairIL = $true) => ((setukpairIR = $true) => ((kpairiskpair = $true) => ((kpairp = $true) => ((singletonsubset = $true) => ((singletoninpowerset = $true) => ((singletoninpowunion = $true) => ((upairset2E = $true) => ((upairsubunion = $true) => ((upairinpowunion = $true) => ((ubforcartprodlem1 = $true) => ((ubforcartprodlem2 = $true) => ((ubforcartprodlem3 = $true) => ((cartprodpairin = $true) => ((cartprodmempair1 = $true) => ((cartprodmempair = $true) => ((setunionE2 = $true) => ((setunionsingleton1 = $true) => ((setunionsingleton2 = $true) => ((setunionsingleton = $true) => ((singletonprop = $true) => ((ex1E1 = $true) => ((ex1I = $true) => ((ex1I2 = $true) => ((singletonsuniq = $true) => ((setukpairinjL1 = $true) => ((kfstsingleton = $true) => ((theprop = $true) => ((kfstpairEq = $true) => ((cartprodfstin = $true) => ((setukpairinjL2 = $true) => ((setukpairinjL = $true) => ((setukpairinjR11 = $true) => ((setukpairinjR12 = $true) => ((setukpairinjR1 = $true) => ((upairequniteq = $true) => ((setukpairinjR2 = $true) => ((setukpairinjR = $true) => ((ksndsingleton = $true) => ((ksndpairEq = $true) => ((kpairsurjEq = $true) => ((cartprodsndin = $true) => ((cartprodpairmemEL = $true) => ((cartprodpairmemER = $true) => ((cartprodmempaircEq = $true) => ((cartprodfstpairEq = $true) => ((cartprodsndpairEq = $true) => ((cartprodpairsurjEq = $true) => ((dpsetconstrI = $true) => ((dpsetconstrSub = $true) => ((setOfPairsIsBReln = $true) => ((dpsetconstrERa = $true) => ((dpsetconstrEL1 = $true) => ((dpsetconstrEL2 = $true) => ((dpsetconstrER = $true) => ((funcImageSingleton = $true) => ((apProp = $true) => ((app = $true) => ((infuncsetfunc = $true) => ((ap2p = $true) => ((funcinfuncset = $true) => ((lamProp = $true) => ((lamp = $true) => ((lam2p = $true) => ((brelnall1 = $true) => ((brelnall2 = $true) => ((ex1E2 = $true) => ((funcGraphProp1 = $true) => ((funcGraphProp3 = $true) => ((funcGraphProp2 = $true) => ((funcextLem = $true) => ((funcGraphProp4 = $true) => ((subbreln = $true) => ((eqbreln = $true) => ((funcext = $true) => ((funcext2 = $true) => ((ap2apEq1 = $true) => ((ap2apEq2 = $true) => ((beta1 = $true) => ((eta1 = $true) => ((lam2lamEq = $true) => ((beta2 = $true) => ((eta2 = $true) => ((iffalseProp1 = $true) => ((iffalseProp2 = $true) => ((iftrueProp1 = $true) => ((iftrueProp2 = $true) => ((ifSingleton = $true) => ((ifp = $true) => ((theeq = $true) => ((iftrue = $true) => ((iffalse = $true) => ((iftrueorfalse = $true) => ((binintersectT_lem = $true) => ((binunionT_lem = $true) => ((powersetT_lem = $true) => ((setminusT_lem = $true) => ((complementT_lem = $true) => ((setextT = $true) => ((subsetTI = $true) => ((powersetTI1 = $true) => ! [X0 : $i,X1 : $i] : ((((in @ X1 @ (powerset @ X0))) = $true) => ! [X2 : $i] : ((((in @ X2 @ (powerset @ X0))) = $true) => ! [X3 : $i] : ((((in @ X3 @ X0)) = $true) => ((((in @ X1 @ (powerset @ X2))) = $true) => ((((in @ X3 @ X1)) = $true) => (((in @ X3 @ X2)) = $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 8.51/2.03 inference(fool_elimination,[],[f693])).
% 8.51/2.03 thf(f695,plain,(
% 8.51/2.03 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i] : (? [X2 : $i] : (? [X3 : $i] : ((((((in @ X3 @ X2)) != $true) & (((in @ X3 @ X1)) = $true)) & (((in @ X1 @ (powerset @ X2))) = $true)) & (((in @ X3 @ X0)) = $true)) & (((in @ X2 @ (powerset @ X0))) = $true)) & (((in @ X1 @ (powerset @ X0))) = $true)) & (powersetTI1 = $true)) & (subsetTI = $true)) & (setextT = $true)) & (complementT_lem = $true)) & (setminusT_lem = $true)) & (powersetT_lem = $true)) & (binunionT_lem = $true)) & (binintersectT_lem = $true)) & (iftrueorfalse = $true)) & (iffalse = $true)) & (iftrue = $true)) & (theeq = $true)) & (ifp = $true)) & (ifSingleton = $true)) & (iftrueProp2 = $true)) & (iftrueProp1 = $true)) & (iffalseProp2 = $true)) & (iffalseProp1 = $true)) & (eta2 = $true)) & (beta2 = $true)) & (lam2lamEq = $true)) & (eta1 = $true)) & (beta1 = $true)) & (ap2apEq2 = $true)) & (ap2apEq1 = $true)) & (funcext2 = $true)) & (funcext = $true)) & (eqbreln = $true)) & (subbreln = $true)) & (funcGraphProp4 = $true)) & (funcextLem = $true)) & (funcGraphProp2 = $true)) & (funcGraphProp3 = $true)) & (funcGraphProp1 = $true)) & (ex1E2 = $true)) & (brelnall2 = $true)) & (brelnall1 = $true)) & (lam2p = $true)) & (lamp = $true)) & (lamProp = $true)) & (funcinfuncset = $true)) & (ap2p = $true)) & (infuncsetfunc = $true)) & (app = $true)) & (apProp = $true)) & (funcImageSingleton = $true)) & (dpsetconstrER = $true)) & (dpsetconstrEL2 = $true)) & (dpsetconstrEL1 = $true)) & (dpsetconstrERa = $true)) & (setOfPairsIsBReln = $true)) & (dpsetconstrSub = $true)) & (dpsetconstrI = $true)) & (cartprodpairsurjEq = $true)) & (cartprodsndpairEq = $true)) & (cartprodfstpairEq = $true)) & (cartprodmempaircEq = $true)) & (cartprodpairmemER = $true)) & (cartprodpairmemEL = $true)) & (cartprodsndin = $true)) & (kpairsurjEq = $true)) & (ksndpairEq = $true)) & (ksndsingleton = $true)) & (setukpairinjR = $true)) & (setukpairinjR2 = $true)) & (upairequniteq = $true)) & (setukpairinjR1 = $true)) & (setukpairinjR12 = $true)) & (setukpairinjR11 = $true)) & (setukpairinjL = $true)) & (setukpairinjL2 = $true)) & (cartprodfstin = $true)) & (kfstpairEq = $true)) & (theprop = $true)) & (kfstsingleton = $true)) & (setukpairinjL1 = $true)) & (singletonsuniq = $true)) & (ex1I2 = $true)) & (ex1I = $true)) & (ex1E1 = $true)) & (singletonprop = $true)) & (setunionsingleton = $true)) & (setunionsingleton2 = $true)) & (setunionsingleton1 = $true)) & (setunionE2 = $true)) & (cartprodmempair = $true)) & (cartprodmempair1 = $true)) & (cartprodpairin = $true)) & (ubforcartprodlem3 = $true)) & (ubforcartprodlem2 = $true)) & (ubforcartprodlem1 = $true)) & (upairinpowunion = $true)) & (upairsubunion = $true)) & (upairset2E = $true)) & (singletoninpowunion = $true)) & (singletoninpowerset = $true)) & (singletonsubset = $true)) & (kpairp = $true)) & (kpairiskpair = $true)) & (setukpairIR = $true)) & (setukpairIL = $true)) & (secondinupair = $true)) & (symdiffIneg2 = $true)) & (symdiffIneg1 = $true)) & (symdiffI2 = $true)) & (symdiffI1 = $true)) & (symdiffE = $true)) & (setminusSubset1 = $true)) & (setminusLsub = $true)) & (setminusIRneg = $true)) & (setminusILneg = $true)) & (setminusELneg = $true)) & (setminusERneg = $true)) & (setminusSubset2 = $true)) & (setminusER = $true)) & (setminusEL = $true)) & (setminusI = $true)) & (bs114d = $true)) & (binintersectSubset1 = $true)) & (binintersectSubset4 = $true)) & (binintersectRsub = $true)) & (disjointsetsI1 = $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)),
% 8.51/2.03 inference(ennf_transformation,[],[f694])).
% 8.51/2.03 thf(f696,plain,(
% 8.51/2.03 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (? [X3 : $i] : ((((in @ X3 @ X2)) != $true) & (((in @ X3 @ X1)) = $true) & (((in @ X1 @ (powerset @ X2))) = $true) & (((in @ X3 @ X0)) = $true)) & (((in @ X2 @ (powerset @ X0))) = $true)) & (((in @ X1 @ (powerset @ X0))) = $true)) & (powersetTI1 = $true) & (subsetTI = $true) & (setextT = $true) & (complementT_lem = $true) & (setminusT_lem = $true) & (powersetT_lem = $true) & (binunionT_lem = $true) & (binintersectT_lem = $true) & (iftrueorfalse = $true) & (iffalse = $true) & (iftrue = $true) & (theeq = $true) & (ifp = $true) & (ifSingleton = $true) & (iftrueProp2 = $true) & (iftrueProp1 = $true) & (iffalseProp2 = $true) & (iffalseProp1 = $true) & (eta2 = $true) & (beta2 = $true) & (lam2lamEq = $true) & (eta1 = $true) & (beta1 = $true) & (ap2apEq2 = $true) & (ap2apEq1 = $true) & (funcext2 = $true) & (funcext = $true) & (eqbreln = $true) & (subbreln = $true) & (funcGraphProp4 = $true) & (funcextLem = $true) & (funcGraphProp2 = $true) & (funcGraphProp3 = $true) & (funcGraphProp1 = $true) & (ex1E2 = $true) & (brelnall2 = $true) & (brelnall1 = $true) & (lam2p = $true) & (lamp = $true) & (lamProp = $true) & (funcinfuncset = $true) & (ap2p = $true) & (infuncsetfunc = $true) & (app = $true) & (apProp = $true) & (funcImageSingleton = $true) & (dpsetconstrER = $true) & (dpsetconstrEL2 = $true) & (dpsetconstrEL1 = $true) & (dpsetconstrERa = $true) & (setOfPairsIsBReln = $true) & (dpsetconstrSub = $true) & (dpsetconstrI = $true) & (cartprodpairsurjEq = $true) & (cartprodsndpairEq = $true) & (cartprodfstpairEq = $true) & (cartprodmempaircEq = $true) & (cartprodpairmemER = $true) & (cartprodpairmemEL = $true) & (cartprodsndin = $true) & (kpairsurjEq = $true) & (ksndpairEq = $true) & (ksndsingleton = $true) & (setukpairinjR = $true) & (setukpairinjR2 = $true) & (upairequniteq = $true) & (setukpairinjR1 = $true) & (setukpairinjR12 = $true) & (setukpairinjR11 = $true) & (setukpairinjL = $true) & (setukpairinjL2 = $true) & (cartprodfstin = $true) & (kfstpairEq = $true) & (theprop = $true) & (kfstsingleton = $true) & (setukpairinjL1 = $true) & (singletonsuniq = $true) & (ex1I2 = $true) & (ex1I = $true) & (ex1E1 = $true) & (singletonprop = $true) & (setunionsingleton = $true) & (setunionsingleton2 = $true) & (setunionsingleton1 = $true) & (setunionE2 = $true) & (cartprodmempair = $true) & (cartprodmempair1 = $true) & (cartprodpairin = $true) & (ubforcartprodlem3 = $true) & (ubforcartprodlem2 = $true) & (ubforcartprodlem1 = $true) & (upairinpowunion = $true) & (upairsubunion = $true) & (upairset2E = $true) & (singletoninpowunion = $true) & (singletoninpowerset = $true) & (singletonsubset = $true) & (kpairp = $true) & (kpairiskpair = $true) & (setukpairIR = $true) & (setukpairIL = $true) & (secondinupair = $true) & (symdiffIneg2 = $true) & (symdiffIneg1 = $true) & (symdiffI2 = $true) & (symdiffI1 = $true) & (symdiffE = $true) & (setminusSubset1 = $true) & (setminusLsub = $true) & (setminusIRneg = $true) & (setminusILneg = $true) & (setminusELneg = $true) & (setminusERneg = $true) & (setminusSubset2 = $true) & (setminusER = $true) & (setminusEL = $true) & (setminusI = $true) & (bs114d = $true) & (binintersectSubset1 = $true) & (binintersectSubset4 = $true) & (binintersectRsub = $true) & (disjointsetsI1 = $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 = $true)),
% 8.51/2.03 inference(flattening,[],[f695])).
% 8.51/2.03 thf(f697,plain,(
% 8.51/2.03 (((($true != ((in @ sK3 @ sK2))) & ($true = ((in @ sK3 @ sK1))) & ($true = ((in @ sK1 @ (powerset @ sK2)))) & ($true = ((in @ sK3 @ sK0)))) & ($true = ((in @ sK2 @ (powerset @ sK0))))) & ($true = ((in @ sK1 @ (powerset @ sK0))))) & (powersetTI1 = $true) & (subsetTI = $true) & (setextT = $true) & (complementT_lem = $true) & (setminusT_lem = $true) & (powersetT_lem = $true) & (binunionT_lem = $true) & (binintersectT_lem = $true) & (iftrueorfalse = $true) & (iffalse = $true) & (iftrue = $true) & (theeq = $true) & (ifp = $true) & (ifSingleton = $true) & (iftrueProp2 = $true) & (iftrueProp1 = $true) & (iffalseProp2 = $true) & (iffalseProp1 = $true) & (eta2 = $true) & (beta2 = $true) & (lam2lamEq = $true) & (eta1 = $true) & (beta1 = $true) & (ap2apEq2 = $true) & (ap2apEq1 = $true) & (funcext2 = $true) & (funcext = $true) & (eqbreln = $true) & (subbreln = $true) & (funcGraphProp4 = $true) & (funcextLem = $true) & (funcGraphProp2 = $true) & (funcGraphProp3 = $true) & (funcGraphProp1 = $true) & (ex1E2 = $true) & (brelnall2 = $true) & (brelnall1 = $true) & (lam2p = $true) & (lamp = $true) & (lamProp = $true) & (funcinfuncset = $true) & (ap2p = $true) & (infuncsetfunc = $true) & (app = $true) & (apProp = $true) & (funcImageSingleton = $true) & (dpsetconstrER = $true) & (dpsetconstrEL2 = $true) & (dpsetconstrEL1 = $true) & (dpsetconstrERa = $true) & (setOfPairsIsBReln = $true) & (dpsetconstrSub = $true) & (dpsetconstrI = $true) & (cartprodpairsurjEq = $true) & (cartprodsndpairEq = $true) & (cartprodfstpairEq = $true) & (cartprodmempaircEq = $true) & (cartprodpairmemER = $true) & (cartprodpairmemEL = $true) & (cartprodsndin = $true) & (kpairsurjEq = $true) & (ksndpairEq = $true) & (ksndsingleton = $true) & (setukpairinjR = $true) & (setukpairinjR2 = $true) & (upairequniteq = $true) & (setukpairinjR1 = $true) & (setukpairinjR12 = $true) & (setukpairinjR11 = $true) & (setukpairinjL = $true) & (setukpairinjL2 = $true) & (cartprodfstin = $true) & (kfstpairEq = $true) & (theprop = $true) & (kfstsingleton = $true) & (setukpairinjL1 = $true) & (singletonsuniq = $true) & (ex1I2 = $true) & (ex1I = $true) & (ex1E1 = $true) & (singletonprop = $true) & (setunionsingleton = $true) & (setunionsingleton2 = $true) & (setunionsingleton1 = $true) & (setunionE2 = $true) & (cartprodmempair = $true) & (cartprodmempair1 = $true) & (cartprodpairin = $true) & (ubforcartprodlem3 = $true) & (ubforcartprodlem2 = $true) & (ubforcartprodlem1 = $true) & (upairinpowunion = $true) & (upairsubunion = $true) & (upairset2E = $true) & (singletoninpowunion = $true) & (singletoninpowerset = $true) & (singletonsubset = $true) & (kpairp = $true) & (kpairiskpair = $true) & (setukpairIR = $true) & (setukpairIL = $true) & (secondinupair = $true) & (symdiffIneg2 = $true) & (symdiffIneg1 = $true) & (symdiffI2 = $true) & (symdiffI1 = $true) & (symdiffE = $true) & (setminusSubset1 = $true) & (setminusLsub = $true) & (setminusIRneg = $true) & (setminusILneg = $true) & (setminusELneg = $true) & (setminusERneg = $true) & (setminusSubset2 = $true) & (setminusER = $true) & (setminusEL = $true) & (setminusI = $true) & (bs114d = $true) & (binintersectSubset1 = $true) & (binintersectSubset4 = $true) & (binintersectRsub = $true) & (disjointsetsI1 = $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)),
% 8.51/2.03 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f696])).
% 8.51/2.03 thf(f737,plain,(
% 8.51/2.03 (powersetE = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (powerset @ Y2)) => ((in @ Y0 @ Y1) => (in @ Y0 @ Y2)))))))))))),
% 8.51/2.03 inference(cnf_transformation,[],[f315])).
% 8.51/2.03 thf(f973,plain,(
% 8.51/2.03 (powersetE = $true)),
% 8.51/2.03 inference(cnf_transformation,[],[f697])).
% 8.51/2.03 thf(f1173,plain,(
% 8.51/2.03 ($true = ((in @ sK1 @ (powerset @ sK2))))),
% 8.51/2.03 inference(cnf_transformation,[],[f697])).
% 8.51/2.03 thf(f1174,plain,(
% 8.51/2.03 ($true = ((in @ sK3 @ sK1)))),
% 8.51/2.03 inference(cnf_transformation,[],[f697])).
% 8.51/2.03 thf(f1175,plain,(
% 8.51/2.03 ($true != ((in @ sK3 @ sK2)))),
% 8.51/2.03 inference(cnf_transformation,[],[f697])).
% 8.51/2.03 thf(f1177,definition,(
% 8.51/2.03 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 8.51/2.03 introduced(theory,[fool_exhaustiveness_axiom])).
% 8.51/2.03 thf(f1215,plain,(
% 8.51/2.03 ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (powerset @ Y2)) => ((in @ Y0 @ Y1) => (in @ Y0 @ Y2)))))))))))),
% 8.51/2.03 inference(definition_unfolding,[],[f737,f973])).
% 8.51/2.03 thf(f3529,plain,(
% 8.51/2.03 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (powerset @ Y2)) => ((in @ Y0 @ Y1) => (in @ Y0 @ Y2)))))))) @ X1)))) )),
% 8.51/2.03 inference(pi_proxy_clausification,[],[f1215])).
% 8.51/2.03 thf(f3530,plain,(
% 8.51/2.03 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => ((in @ X1 @ Y0) => (in @ X1 @ Y1)))))))))) )),
% 8.51/2.03 inference(beta-eta_normalization,[],[f3529])).
% 8.51/2.03 thf(f3531,plain,(
% 8.51/2.03 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => ((in @ X1 @ Y0) => (in @ X1 @ Y1)))))) @ X2)))) )),
% 8.51/2.03 inference(pi_proxy_clausification,[],[f3530])).
% 8.51/2.03 thf(f3532,plain,(
% 8.51/2.03 ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ X2 @ (powerset @ Y0)) => ((in @ X1 @ X2) => (in @ X1 @ Y0)))))))) )),
% 8.51/2.03 inference(beta-eta_normalization,[],[f3531])).
% 8.51/2.03 thf(f3533,plain,(
% 8.51/2.03 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((in @ X2 @ (powerset @ Y0)) => ((in @ X1 @ X2) => (in @ X1 @ Y0)))) @ X3)))) )),
% 8.51/2.03 inference(pi_proxy_clausification,[],[f3532])).
% 8.51/2.03 thf(f3534,plain,(
% 8.51/2.03 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((in @ X2 @ (powerset @ X3)) => ((in @ X1 @ X2) => (in @ X1 @ X3)))))) )),
% 8.51/2.03 inference(beta-eta_normalization,[],[f3533])).
% 8.51/2.03 thf(f3535,plain,(
% 8.51/2.03 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((in @ X2 @ (powerset @ X3)))) | ($true = (((in @ X1 @ X2) => (in @ X1 @ X3))))) )),
% 8.51/2.03 inference(imp_proxy_clausification,[],[f3534])).
% 8.51/2.03 thf(f3536,plain,(
% 8.51/2.03 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((in @ X2 @ (powerset @ X3)))) | (((in @ X1 @ X2)) = $false) | (((in @ X1 @ X3)) = $true)) )),
% 8.51/2.03 inference(imp_proxy_clausification,[],[f3535])).
% 8.51/2.03 thf(f3980,definition,(
% 8.51/2.03 spl109_4 <=> ! [X4 : $o] : (($false = X4) | ($true = X4))),
% 8.51/2.03 introduced(definition,[new_symbols(definition,[spl109_4])],[avatar_definition])).
% 8.51/2.03 thf(f3981,plain,(
% 8.51/2.03 ( ! [X4 : $o] : (($true = X4) | ($false = X4)) ) | ~spl109_4),
% 8.51/2.03 inference(avatar_component_clause,[],[f3980])).
% 8.51/2.03 thf(f4052,plain,(
% 8.51/2.03 spl109_4),
% 8.51/2.03 inference(avatar_split_clause,[],[f1177,f3980])).
% 8.51/2.03 thf(f4054,plain,(
% 8.51/2.03 ($true != $true) | ($false = ((in @ sK3 @ sK2))) | ~spl109_4),
% 8.51/2.03 inference(constrained_superposition,[],[f1175,f3981])).
% 8.51/2.03 thf(f4056,plain,(
% 8.51/2.03 ($false = ((in @ sK3 @ sK2))) | ~spl109_4),
% 8.51/2.03 inference(trivial_inequality_removal,[],[f4054])).
% 8.51/2.03 thf(f6077,plain,(
% 8.51/2.03 ( ! [X0 : $i] : (($false = $true) | ($false = ((in @ X0 @ sK1))) | ($true = ((in @ X0 @ sK2)))) )),
% 8.51/2.03 inference(constrained_superposition,[],[f1173,f3536])).
% 8.51/2.03 thf(f6167,plain,(
% 8.51/2.03 ( ! [X0 : $i] : (($true = ((in @ X0 @ sK2))) | ($false = ((in @ X0 @ sK1)))) )),
% 8.51/2.03 inference(trivial_inequality_removal,[],[f6077])).
% 8.51/2.03 thf(f14958,plain,(
% 8.51/2.03 ($false = $true) | ($false = ((in @ sK3 @ sK1))) | ~spl109_4),
% 8.51/2.03 inference(constrained_superposition,[],[f4056,f6167])).
% 8.51/2.03 thf(f14959,plain,(
% 8.51/2.03 ($false = ((in @ sK3 @ sK1))) | ~spl109_4),
% 8.51/2.03 inference(trivial_inequality_removal,[],[f14958])).
% 8.51/2.03 thf(f18170,plain,(
% 8.51/2.03 ($false = $true) | ~spl109_4),
% 8.51/2.03 inference(constrained_superposition,[],[f14959,f1174])).
% 8.51/2.03 thf(f18178,plain,(
% 8.51/2.03 $false | ~spl109_4),
% 8.51/2.03 inference(trivial_inequality_removal,[],[f18170])).
% 8.51/2.03 thf(f18179,plain,(
% 8.51/2.03 ~spl109_4),
% 8.51/2.03 inference(avatar_contradiction_clause,[],[f18178])).
% 8.51/2.03 cnf(s22, plain, spl109_4, inference(sat_conversion,[],[f4052])).
% 8.51/2.03 cnf(s237, plain, ~spl109_4, inference(sat_conversion,[],[f18179])).
% 8.51/2.03 cnf(s262, plain, $false, inference(rat,[],[s22,s237])).
% 8.51/2.03 thf(f18183,plain,(
% 8.51/2.03 $false),
% 8.51/2.03 inference(avatar_sat_refutation,[],[s262])).
% 8.51/2.03 % SZS output end Proof for theBenchmark
% 8.51/2.03 % (1354201)------------------------------
% 8.51/2.03 % (1354201)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.51/2.03 % (1354201)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.51/2.03 % (1354201)CaDiCaL version: 2.1.3
% 8.51/2.03 % (1354201)Termination reason: Refutation
% 8.51/2.03 % (1354201)Time elapsed: 1.592 s
% 8.51/2.03 % (1354201)Peak memory usage: 20 MB
% 8.51/2.03 % (1354201)Instructions burned: 1877 (million)
% 8.51/2.03 % (1354195)Success in time 1.721 s
% 8.51/2.03 % Vampire exiting
%------------------------------------------------------------------------------