%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU685^2 : 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 : n017.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 08:32:58 AM UTC 2026
% Result : Theorem 5.57s 1.07s
% Output : Refutation 5.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU685^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n017.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 14:04:07 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
% 3.80/0.94 % (391668)Will run a generic schedule for satisfiability detection.
% 3.80/0.94 % (391677)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1990512613:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 3.80/0.94 % (391677)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.80/0.94 % (391674)% WARNING: option uhcvi not known.
% 3.80/0.94 % (391673)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4091616593_2999 on theBenchmark for (2999ds/0Mi)
% 3.80/0.94 % (391674)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4093271209:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 3.80/0.94 % (391675)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4198690167:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 3.80/0.94 % (391676)dis+10_1_sil=32000:sp=arity:random_seed=1480537133:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 3.80/0.94 % (391678)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=650350678:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 3.80/0.94 % (391679)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2054613427:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 3.80/0.94 % (391674)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.80/0.94 % Exception at run slice level
% 3.80/0.94 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.80/0.94 % (391674)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.80/0.94 % (391687)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1411784842:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 3.80/0.94 % (391677)Instruction limit reached!
% 3.80/0.94 % (391677)------------------------------
% 3.80/0.94 % (391677)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.80/0.94 % (391677)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.80/0.94 % (391677)CaDiCaL version: 2.1.3
% 3.80/0.94 % (391677)Termination reason: Instruction limit
% 3.80/0.94 % (391677)Termination phase: Saturation
% 3.80/0.94 % (391677)Time elapsed: 0.030 s
% 3.80/0.94 % (391677)Peak memory usage: 12 MB
% 3.80/0.94 % (391677)Instructions burned: 118 (million)
% 3.80/0.94 % Exception at run slice level
% 3.80/0.94 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.80/0.94 % (391689)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2326285332:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 3.80/0.94 % (391690)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=2754865422:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 3.80/0.94 % (391690)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.80/0.94 % (391690)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.80/0.94 % (391676)Instruction limit reached!
% 3.80/0.94 % (391676)------------------------------
% 3.80/0.94 % (391676)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.80/0.94 % (391676)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.80/0.94 % (391676)CaDiCaL version: 2.1.3
% 3.80/0.94 % (391676)Termination reason: Instruction limit
% 3.80/0.94 % (391676)Termination phase: Saturation
% 3.80/0.94 % (391676)Time elapsed: 0.049 s
% 3.80/0.94 % (391676)Peak memory usage: 12 MB
% 3.80/0.94 % (391676)Instructions burned: 105 (million)
% 3.80/0.94 % (391678)Instruction limit reached!
% 3.80/0.94 % (391678)------------------------------
% 3.80/0.94 % (391678)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.80/0.94 % (391678)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.80/0.94 % (391678)CaDiCaL version: 2.1.3
% 3.80/0.94 % (391678)Termination reason: Instruction limit
% 3.80/0.94 % (391678)Termination phase: Saturation
% 3.80/0.94 % (391678)Time elapsed: 0.062 s
% 3.80/0.94 % (391678)Peak memory usage: 12 MB
% 3.80/0.94 % (391678)Instructions burned: 132 (million)
% 3.80/0.94 % (391689)Instruction limit reached!
% 3.80/0.94 % (391689)------------------------------
% 3.80/0.94 % (391689)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.80/0.94 % (391689)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.57/1.07 % (391689)CaDiCaL version: 2.1.3
% 5.57/1.07 % (391689)Termination reason: Instruction limit
% 5.57/1.07 % (391689)Termination phase: Saturation
% 5.57/1.07 % (391689)Time elapsed: 0.034 s
% 5.57/1.07 % (391689)Peak memory usage: 12 MB
% 5.57/1.07 % (391689)Instructions burned: 132 (million)
% 5.57/1.07 % (391693)ott-21_1_sil=16000:fs=off:random_seed=1496075591:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 5.57/1.07 % (391679)Instruction limit reached!
% 5.57/1.07 % (391679)------------------------------
% 5.57/1.07 % (391679)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.57/1.07 % (391679)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.57/1.07 % (391679)CaDiCaL version: 2.1.3
% 5.57/1.07 % (391679)Termination reason: Instruction limit
% 5.57/1.07 % (391679)Termination phase: Saturation
% 5.57/1.07 % (391679)Time elapsed: 0.076 s
% 5.57/1.07 % (391679)Peak memory usage: 12 MB
% 5.57/1.07 % (391679)Instructions burned: 161 (million)
% 5.57/1.07 % (391695)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=105209435:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 5.57/1.07 % Exception at run slice level
% 5.57/1.07 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.57/1.07 % (391694)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2938263066:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 5.57/1.07 % (391699)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=3036513435:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 5.57/1.07 % Exception at run slice level
% 5.57/1.07 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.57/1.07 % (391698)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=1784774064:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 5.57/1.07 % (391702)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=265552574:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2998 on theBenchmark for (2998ds/692Mi)
% 5.57/1.07 % (391702)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.57/1.07 % (391693)Instruction limit reached!
% 5.57/1.07 % (391693)------------------------------
% 5.57/1.07 % (391693)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.57/1.07 % (391693)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.57/1.07 % (391693)CaDiCaL version: 2.1.3
% 5.57/1.07 % (391693)Termination reason: Instruction limit
% 5.57/1.07 % (391693)Termination phase: Saturation
% 5.57/1.07 % (391693)Time elapsed: 0.082 s
% 5.57/1.07 % (391693)Peak memory usage: 12 MB
% 5.57/1.07 % (391693)Instructions burned: 181 (million)
% 5.57/1.07 % (391705)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=316725383:i=879:kws=inv_precedence:fsr=off_2998 on theBenchmark for (2998ds/879Mi)
% 5.57/1.07 % (391705)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.57/1.07 % (391702)Instruction limit reached!
% 5.57/1.07 % (391702)------------------------------
% 5.57/1.07 % (391702)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.57/1.07 % (391702)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.57/1.07 % (391702)CaDiCaL version: 2.1.3
% 5.57/1.07 % (391702)Termination reason: Instruction limit
% 5.57/1.07 % (391702)Termination phase: Saturation
% 5.57/1.07 % (391702)Time elapsed: 0.163 s
% 5.57/1.07 % (391702)Peak memory usage: 15 MB
% 5.57/1.07 % (391702)Instructions burned: 694 (million)
% 5.57/1.07 % (391707)fmb+10_1_sil=64000:random_seed=555528718:i=22061:nm=2:gsp=on_2996 on theBenchmark for (2996ds/22061Mi)
% 5.57/1.07 % (391707)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 5.57/1.07 % Exception at run slice level
% 5.57/1.07 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.57/1.07 % (391709)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=3294550601:i=9515:nm=5_2996 on theBenchmark for (2996ds/9515Mi)
% 5.57/1.07 % Exception at run slice level
% 5.57/1.07 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.57/1.07 % (391711)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=2648828880:fmbsr=1.7:i=920_2996 on theBenchmark for (2996ds/920Mi)
% 5.57/1.07 % Exception at run slice level
% 5.57/1.07 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.57/1.07 % (391713)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=3512764695:i=5131_2996 on theBenchmark for (2996ds/5131Mi)
% 5.57/1.07 % (391713)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.57/1.07 % (391694)Instruction limit reached!
% 5.57/1.07 % (391694)------------------------------
% 5.57/1.07 % (391694)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.57/1.07 % (391694)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.57/1.07 % (391694)CaDiCaL version: 2.1.3
% 5.57/1.07 % (391694)Termination reason: Instruction limit
% 5.57/1.07 % (391694)Termination phase: Saturation
% 5.57/1.07 % (391694)Time elapsed: 0.236 s
% 5.57/1.07 % (391694)Peak memory usage: 13 MB
% 5.57/1.07 % (391694)Instructions burned: 478 (million)
% 5.57/1.07 % (391715)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=3706609520:i=1472:ins=7:fdi=8:gsp=on_2996 on theBenchmark for (2996ds/1472Mi)
% 5.57/1.07 % (391715)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 5.57/1.07 % (391715)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 5.57/1.07 % (391690)Instruction limit reached!
% 5.57/1.07 % (391690)------------------------------
% 5.57/1.07 % (391690)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.57/1.07 % (391690)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.57/1.07 % (391690)CaDiCaL version: 2.1.3
% 5.57/1.07 % (391690)Termination reason: Instruction limit
% 5.57/1.07 % (391690)Termination phase: Saturation
% 5.57/1.07 % (391690)Time elapsed: 0.305 s
% 5.57/1.07 % (391690)Peak memory usage: 14 MB
% 5.57/1.07 % (391690)Instructions burned: 686 (million)
% 5.57/1.07 % (391717)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=1678405057:i=6324_2996 on theBenchmark for (2996ds/6324Mi)
% 5.57/1.07 % Exception at run slice level
% 5.57/1.07 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.57/1.07 % (391719)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=2560643047:fmbsr=2.30978:i=2174_2995 on theBenchmark for (2995ds/2174Mi)
% 5.57/1.07 % Exception at run slice level
% 5.57/1.07 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.57/1.07 % (391721)ott-2_1_sil=16000:newcnf=on:random_seed=2078302832:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2995 on theBenchmark for (2995ds/869Mi)
% 5.57/1.07 % (391721)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.57/1.07 % (391705)Instruction limit reached!
% 5.57/1.07 % (391705)------------------------------
% 5.57/1.07 % (391705)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.57/1.07 % (391705)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.57/1.07 % (391705)CaDiCaL version: 2.1.3
% 5.57/1.07 % (391705)Termination reason: Instruction limit
% 5.57/1.07 % (391705)Termination phase: Saturation
% 5.57/1.07 % (391705)Time elapsed: 0.431 s
% 5.57/1.07 % (391705)Peak memory usage: 14 MB
% 5.57/1.07 % (391705)Instructions burned: 880 (million)
% 5.57/1.07 % (391723)ott+10_1_sil=32000:tgt=ground:random_seed=2609107364:i=5114:av=off_2993 on theBenchmark for (2993ds/5114Mi)
% 5.57/1.07 % (391698)Instruction limit reached!
% 5.57/1.07 % (391698)------------------------------
% 5.57/1.07 % (391698)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.57/1.07 % (391698)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.57/1.07 % (391698)CaDiCaL version: 2.1.3
% 5.57/1.07 % (391698)Termination reason: Instruction limit
% 5.57/1.07 % (391698)Termination phase: Saturation
% 5.57/1.07 % (391698)Time elapsed: 0.533 s
% 5.57/1.07 % (391698)Peak memory usage: 16 MB
% 5.57/1.07 % (391698)Instructions burned: 1179 (million)
% 5.57/1.07 % (391725)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=3367538190:i=54282_2993 on theBenchmark for (2993ds/54282Mi)
% 5.57/1.07 % Exception at run slice level
% 5.57/1.07 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.57/1.07 % (391727)dis-11_1_sil=16000:sp=reverse_frequency:alpa=true:random_seed=1672885163:i=3512:aac=none_2993 on theBenchmark for (2993ds/3512Mi)
% 5.57/1.07 % (391727)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 5.57/1.07 % (391721) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-391668-391721"...
% 5.57/1.07 % (391721)...printing done.
% 5.57/1.07 % (391721)Refutation found. Thanks to Tanya!
% 5.57/1.07 % SZS status Theorem for theBenchmark
% 5.57/1.07 % SZS output start Proof for theBenchmark
% 5.57/1.07 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 5.57/1.07 thf(func_def_0, type, in: ($i > $i > $o)).
% 5.57/1.07 thf(func_def_2, type, setadjoin: ($i > $i > $i)).
% 5.57/1.07 thf(func_def_3, type, dsetconstr: ($i > ($i > $o) > $i)).
% 5.57/1.07 thf(func_def_4, type, subset: ($i > $i > $o)).
% 5.57/1.07 thf(func_def_5, type, kpair: ($i > $i > $i)).
% 5.57/1.07 thf(func_def_6, type, cartprod: ($i > $i > $i)).
% 5.57/1.07 thf(func_def_7, type, singleton: ($i > $o)).
% 5.57/1.07 thf(func_def_9, type, ex1: ($i > ($i > $o) > $o)).
% 5.57/1.07 thf(func_def_10, type, breln: ($i > $i > $i > $o)).
% 5.57/1.07 thf(func_def_11, type, func: ($i > $i > $i > $o)).
% 5.57/1.07 thf(func_def_12, type, funcSet: ($i > $i > $i)).
% 5.57/1.07 thf(func_def_13, type, ap: ($i > $i > $i > $i > $i)).
% 5.57/1.07 thf(func_def_14, type, infuncsetfunc: $o).
% 5.57/1.07 thf(func_def_15, type, funcGraphProp1: $o).
% 5.57/1.07 thf(func_def_16, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 5.57/1.07 thf(func_def_17, type, vAND: ($o > $o > $o)).
% 5.57/1.07 thf(func_def_18, type, db0: !>[X0: $tType]:(X0)).
% 5.57/1.07 thf(func_def_19, type, db1: !>[X0: $tType]:(X0)).
% 5.57/1.07 thf(func_def_20, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 5.57/1.07 thf(func_def_21, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 5.57/1.07 thf(func_def_22, type, db2: !>[X0: $tType]:(X0)).
% 5.57/1.07 thf(func_def_23, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 5.57/1.07 thf(func_def_24, type, vIMP: ($o > $o > $o)).
% 5.57/1.07 thf(func_def_25, type, db3: !>[X0: $tType]:(X0)).
% 5.57/1.07 thf(func_def_32, type, vNOT: ($o > $o)).
% 5.57/1.07 thf(func_def_33, type, sK4: ($i > $i > $i > $i)).
% 5.57/1.07 thf(func_def_34, type, sK5: ($i > $i > $i > $i)).
% 5.57/1.07 thf(func_def_36, type, sK7: ($i > $i)).
% 5.57/1.07 thf(func_def_38, type, sK9: ($i > $i)).
% 5.57/1.07 thf(func_def_39, type, sK10: ($i > $i)).
% 5.57/1.07 thf(func_def_40, type, sK11: ($i > $i)).
% 5.57/1.07 thf(func_def_41, type, sK12: ($i > $i)).
% 5.57/1.07 thf(f1,axiom,(
% 5.57/1.07 (singleton = (^[X0 : $i] : (? [X1 : $i] : ((X0 = ((setadjoin @ X1 @ emptyset))) & (in @ X1 @ X0)))))),
% 5.57/1.07 file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton)).
% 5.57/1.07 thf(f2,axiom,(
% 5.57/1.07 (ex1 = (^[X0 : $i, X1 : ($i > $o)] : ((singleton @ (dsetconstr @ X0 @ (^[X2 : $i] : ((X1 @ X2))))))))),
% 5.57/1.07 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1)).
% 5.57/1.07 thf(f3,axiom,(
% 5.57/1.07 (breln = (^[X0 : $i, X1 : $i, X2 : $i] : ((subset @ X2 @ (cartprod @ X0 @ X1)))))),
% 5.57/1.07 file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln)).
% 5.57/1.07 thf(f4,axiom,(
% 5.57/1.07 (func = (^[X0 : $i, X1 : $i, X2 : $i] : (! [X3 : $i] : ((in @ X3 @ X0) => (ex1 @ X1 @ (^[X4 : $i] : ((in @ (kpair @ X3 @ X4) @ X2))))) & (breln @ X0 @ X1 @ X2))))),
% 5.57/1.07 file('/export/starexec/sandbox/benchmark/theBenchmark.p',func)).
% 5.57/1.07 thf(f5,axiom,(
% 5.57/1.07 (infuncsetfunc = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (funcSet @ X0 @ X1)) => (func @ X0 @ X1 @ X2)))),
% 5.57/1.07 file('/export/starexec/sandbox/benchmark/theBenchmark.p',infuncsetfunc)).
% 5.57/1.07 thf(f6,axiom,(
% 5.57/1.07 (funcGraphProp1 = ! [X0 : $i,X1 : $i,X2 : $i] : ((func @ X0 @ X1 @ X2) => ! [X3 : $i] : ((in @ X3 @ X0) => (in @ (kpair @ X3 @ (ap @ X0 @ X1 @ X2 @ X3)) @ X2))))),
% 5.57/1.07 file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcGraphProp1)).
% 5.57/1.07 thf(f7,conjecture,(
% 5.57/1.07 infuncsetfunc => (funcGraphProp1 => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (funcSet @ X0 @ X1)) => ! [X3 : $i] : ((in @ X3 @ X0) => (in @ (kpair @ X3 @ (ap @ X0 @ X1 @ X2 @ X3)) @ X2))))),
% 5.57/1.07 file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcGraphProp3)).
% 5.57/1.07 thf(f8,negated_conjecture,(
% 5.57/1.07 ~(infuncsetfunc => (funcGraphProp1 => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (funcSet @ X0 @ X1)) => ! [X3 : $i] : ((in @ X3 @ X0) => (in @ (kpair @ X3 @ (ap @ X0 @ X1 @ X2 @ X3)) @ X2)))))),
% 5.57/1.07 inference(negated_conjecture,[status(cth)],[f7])).
% 5.57/1.07 thf(f9,plain,(
% 5.57/1.07 (singleton = (^[X0 : $i] : (? [X1 : $i] : ((X0 = ((setadjoin @ X1 @ emptyset))) & (in @ X1 @ X0)))))),
% 5.57/1.07 inference(rectify,[],[f1])).
% 5.57/1.07 thf(f10,plain,(
% 5.57/1.07 (singleton = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & ((setadjoin @ Y1 @ emptyset) = Y0))))))),
% 5.57/1.07 inference(fool_elimination,[],[f9])).
% 5.57/1.07 thf(f11,plain,(
% 5.57/1.07 (ex1 = (^[X0 : $i, X1 : ($i > $o)] : ((singleton @ (dsetconstr @ X0 @ (^[X2 : $i] : ((X1 @ X2))))))))),
% 5.57/1.07 inference(rectify,[],[f2])).
% 5.57/1.07 thf(f12,plain,(
% 5.57/1.07 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: (singleton @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 5.57/1.07 inference(fool_elimination,[],[f11])).
% 5.57/1.07 thf(f13,plain,(
% 5.57/1.07 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))),
% 5.57/1.07 inference(fool_elimination,[],[f3])).
% 5.57/1.07 thf(f14,plain,(
% 5.57/1.07 (func = (^[X0 : $i, X1 : $i, X2 : $i] : (! [X3 : $i] : ((in @ X3 @ X0) => (ex1 @ X1 @ (^[X4 : $i] : ((in @ (kpair @ X3 @ X4) @ X2))))) & (breln @ X0 @ X1 @ X2))))),
% 5.57/1.07 inference(rectify,[],[f4])).
% 5.57/1.07 thf(f15,plain,(
% 5.57/1.07 (func = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((breln @ Y0 @ Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (ex1 @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y2)))))))))))))),
% 5.57/1.07 inference(fool_elimination,[],[f14])).
% 5.57/1.07 thf(f16,plain,(
% 5.57/1.07 (infuncsetfunc = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (funcSet @ X0 @ X1)) => (func @ X0 @ X1 @ X2)))),
% 5.57/1.07 inference(rectify,[],[f5])).
% 5.57/1.07 thf(f17,plain,(
% 5.57/1.07 (infuncsetfunc = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (funcSet @ Y2 @ Y1)) => (func @ Y2 @ Y1 @ Y0))))))))))),
% 5.57/1.07 inference(fool_elimination,[],[f16])).
% 5.57/1.07 thf(f18,plain,(
% 5.57/1.07 (funcGraphProp1 = ! [X0 : $i,X1 : $i,X2 : $i] : ((func @ X0 @ X1 @ X2) => ! [X3 : $i] : ((in @ X3 @ X0) => (in @ (kpair @ X3 @ (ap @ X0 @ X1 @ X2 @ X3)) @ X2))))),
% 5.57/1.07 inference(rectify,[],[f6])).
% 5.57/1.07 thf(f19,plain,(
% 5.57/1.07 (funcGraphProp1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y2 @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (kpair @ Y3 @ (ap @ Y2 @ Y1 @ Y0 @ Y3)) @ Y0)))))))))))))),
% 5.57/1.07 inference(fool_elimination,[],[f18])).
% 5.57/1.07 thf(f20,plain,(
% 5.57/1.07 ~(infuncsetfunc => (funcGraphProp1 => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (funcSet @ X0 @ X1)) => ! [X3 : $i] : ((in @ X3 @ X0) => (in @ (kpair @ X3 @ (ap @ X0 @ X1 @ X2 @ X3)) @ X2)))))),
% 5.57/1.07 inference(rectify,[],[f8])).
% 5.57/1.07 thf(f21,plain,(
% 5.57/1.07 ~((infuncsetfunc = $true) => ((funcGraphProp1 = $true) => ! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X2 @ (funcSet @ X0 @ X1))) = $true) => ! [X3 : $i] : ((((in @ X3 @ X0)) = $true) => (((in @ (kpair @ X3 @ (ap @ X0 @ X1 @ X2 @ X3)) @ X2)) = $true)))))),
% 5.57/1.07 inference(fool_elimination,[],[f20])).
% 5.57/1.07 thf(f22,plain,(
% 5.57/1.07 (? [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : $i] : ((((in @ (kpair @ X3 @ (ap @ X0 @ X1 @ X2 @ X3)) @ X2)) != $true) & (((in @ X3 @ X0)) = $true)) & (((in @ X2 @ (funcSet @ X0 @ X1))) = $true)) & (funcGraphProp1 = $true)) & (infuncsetfunc = $true)),
% 5.57/1.07 inference(ennf_transformation,[],[f21])).
% 5.57/1.07 thf(f23,plain,(
% 5.57/1.07 ? [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : $i] : ((((in @ (kpair @ X3 @ (ap @ X0 @ X1 @ X2 @ X3)) @ X2)) != $true) & (((in @ X3 @ X0)) = $true)) & (((in @ X2 @ (funcSet @ X0 @ X1))) = $true)) & (funcGraphProp1 = $true) & (infuncsetfunc = $true)),
% 5.57/1.07 inference(flattening,[],[f22])).
% 5.57/1.07 thf(f24,plain,(
% 5.57/1.07 ((($true != ((in @ (kpair @ sK3 @ (ap @ sK0 @ sK1 @ sK2 @ sK3)) @ sK2))) & ($true = ((in @ sK3 @ sK0)))) & ($true = ((in @ sK2 @ (funcSet @ sK0 @ sK1))))) & (funcGraphProp1 = $true) & (infuncsetfunc = $true)),
% 5.57/1.07 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f23])).
% 5.57/1.07 thf(f25,plain,(
% 5.57/1.07 (singleton = (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) & ((setadjoin @ Y1 @ emptyset) = Y0))))))),
% 5.57/1.07 inference(cnf_transformation,[],[f10])).
% 5.57/1.07 thf(f26,plain,(
% 5.57/1.07 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: (singleton @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 5.57/1.07 inference(cnf_transformation,[],[f12])).
% 5.57/1.07 thf(f27,plain,(
% 5.57/1.07 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))),
% 5.57/1.07 inference(cnf_transformation,[],[f13])).
% 5.57/1.07 thf(f28,plain,(
% 5.57/1.07 (func = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((breln @ Y0 @ Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (ex1 @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y2)))))))))))))),
% 5.57/1.07 inference(cnf_transformation,[],[f15])).
% 5.57/1.07 thf(f29,plain,(
% 5.57/1.07 (infuncsetfunc = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (funcSet @ Y2 @ Y1)) => (func @ Y2 @ Y1 @ Y0))))))))))),
% 5.57/1.07 inference(cnf_transformation,[],[f17])).
% 5.57/1.07 thf(f30,plain,(
% 5.57/1.07 (funcGraphProp1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((func @ Y2 @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (kpair @ Y3 @ (ap @ Y2 @ Y1 @ Y0 @ Y3)) @ Y0)))))))))))))),
% 5.57/1.07 inference(cnf_transformation,[],[f19])).
% 5.57/1.07 thf(f31,plain,(
% 5.57/1.07 (infuncsetfunc = $true)),
% 5.57/1.07 inference(cnf_transformation,[],[f24])).
% 5.57/1.07 thf(f32,plain,(
% 5.57/1.07 (funcGraphProp1 = $true)),
% 5.57/1.07 inference(cnf_transformation,[],[f24])).
% 5.57/1.07 thf(f33,plain,(
% 5.57/1.07 ($true = ((in @ sK2 @ (funcSet @ sK0 @ sK1))))),
% 5.57/1.07 inference(cnf_transformation,[],[f24])).
% 5.57/1.07 thf(f34,plain,(
% 5.57/1.07 ($true = ((in @ sK3 @ sK0)))),
% 5.57/1.07 inference(cnf_transformation,[],[f24])).
% 5.57/1.07 thf(f35,plain,(
% 5.57/1.07 ($true != ((in @ (kpair @ sK3 @ (ap @ sK0 @ sK1 @ sK2 @ sK3)) @ sK2)))),
% 5.57/1.07 inference(cnf_transformation,[],[f24])).
% 5.57/1.07 thf(f37,definition,(
% 5.57/1.07 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 5.57/1.07 introduced(theory,[fool_exhaustiveness_axiom])).
% 5.57/1.07 thf(f38,plain,(
% 5.57/1.07 (ex1 = (^[Y0 : $i]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) & ((setadjoin @ Y3 @ emptyset) = Y2))))) @ (dsetconstr @ Y0 @ (^[Y2 : $i]: (Y1 @ Y2))))))))),
% 5.57/1.07 inference(definition_unfolding,[],[f26,f25])).
% 5.57/1.07 thf(f39,plain,(
% 5.57/1.07 (func = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (subset @ Y5 @ (cartprod @ Y3 @ Y4))))))) @ Y0 @ Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((^[Y4 : $i]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: (?? @ $i @ (^[Y7 : $i]: ((in @ Y7 @ Y6) & ((setadjoin @ Y7 @ emptyset) = Y6))))) @ (dsetconstr @ Y4 @ (^[Y6 : $i]: (Y5 @ Y6))))))) @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y2)))))))))))))),
% 5.57/1.07 inference(definition_unfolding,[],[f28,f27,f38])).
% 5.57/1.07 thf(f40,plain,(
% 5.57/1.07 ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (funcSet @ Y2 @ Y1)) => ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (((^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: (subset @ Y8 @ (cartprod @ Y6 @ Y7))))))) @ Y3 @ Y4 @ Y5) & (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y3) => ((^[Y7 : $i]: ((^[Y8 : $i > $o]: ((^[Y9 : $i]: (?? @ $i @ (^[Y10 : $i]: ((in @ Y10 @ Y9) & ((setadjoin @ Y10 @ emptyset) = Y9))))) @ (dsetconstr @ Y7 @ (^[Y9 : $i]: (Y8 @ Y9))))))) @ Y4 @ (^[Y7 : $i]: (in @ (kpair @ Y6 @ Y7) @ Y5)))))))))))) @ Y2 @ Y1 @ Y0))))))))))),
% 5.57/1.07 inference(definition_unfolding,[],[f29,f31,f39])).
% 5.57/1.07 thf(f41,plain,(
% 5.57/1.07 ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (((^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: (subset @ Y8 @ (cartprod @ Y6 @ Y7))))))) @ Y3 @ Y4 @ Y5) & (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y3) => ((^[Y7 : $i]: ((^[Y8 : $i > $o]: ((^[Y9 : $i]: (?? @ $i @ (^[Y10 : $i]: ((in @ Y10 @ Y9) & ((setadjoin @ Y10 @ emptyset) = Y9))))) @ (dsetconstr @ Y7 @ (^[Y9 : $i]: (Y8 @ Y9))))))) @ Y4 @ (^[Y7 : $i]: (in @ (kpair @ Y6 @ Y7) @ Y5)))))))))))) @ Y2 @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (kpair @ Y3 @ (ap @ Y2 @ Y1 @ Y0 @ Y3)) @ Y0)))))))))))))),
% 5.57/1.07 inference(definition_unfolding,[],[f30,f32,f39])).
% 5.57/1.07 thf(f42,plain,(
% 5.57/1.07 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (((^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: (subset @ Y8 @ (cartprod @ Y6 @ Y7))))))) @ Y3 @ Y4 @ Y5) & (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y3) => ((^[Y7 : $i]: ((^[Y8 : $i > $o]: ((^[Y9 : $i]: (?? @ $i @ (^[Y10 : $i]: ((in @ Y10 @ Y9) & ((setadjoin @ Y10 @ emptyset) = Y9))))) @ (dsetconstr @ Y7 @ (^[Y9 : $i]: (Y8 @ Y9))))))) @ Y4 @ (^[Y7 : $i]: (in @ (kpair @ Y6 @ Y7) @ Y5)))))))))))) @ Y2 @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y2) => (in @ (kpair @ Y3 @ (ap @ Y2 @ Y1 @ Y0 @ Y3)) @ Y0)))))))))) @ X1)))) )),
% 5.57/1.07 inference(pi_proxy_clausification,[],[f41])).
% 5.57/1.07 thf(f43,plain,(
% 5.57/1.07 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((subset @ X1 @ (cartprod @ Y1 @ Y0)) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ Y0 @ (^[Y4 : $i]: (in @ (kpair @ Y2 @ Y4) @ X1)))) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y0 @ (^[Y4 : $i]: (in @ (kpair @ Y2 @ Y4) @ X1))))))))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ (kpair @ Y2 @ (ap @ Y1 @ Y0 @ X1 @ Y2)) @ X1)))))))))))) )),
% 5.57/1.07 inference(beta-eta_normalization,[],[f42])).
% 5.57/1.07 thf(f44,plain,(
% 5.57/1.07 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((subset @ X1 @ (cartprod @ Y1 @ Y0)) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ Y0 @ (^[Y4 : $i]: (in @ (kpair @ Y2 @ Y4) @ X1)))) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y0 @ (^[Y4 : $i]: (in @ (kpair @ Y2 @ Y4) @ X1))))))))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (in @ (kpair @ Y2 @ (ap @ Y1 @ Y0 @ X1 @ Y2)) @ X1)))))))) @ X2)))) )),
% 5.57/1.07 inference(pi_proxy_clausification,[],[f43])).
% 5.57/1.07 thf(f45,plain,(
% 5.57/1.07 ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: (((subset @ X1 @ (cartprod @ Y0 @ X2)) & (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ X2 @ (^[Y3 : $i]: (in @ (kpair @ Y1 @ Y3) @ X1)))) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ X2 @ (^[Y3 : $i]: (in @ (kpair @ Y1 @ Y3) @ X1))))))))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ (kpair @ Y1 @ (ap @ Y0 @ X2 @ X1 @ Y1)) @ X1)))))))))) )),
% 5.57/1.07 inference(beta-eta_normalization,[],[f44])).
% 5.57/1.07 thf(f46,plain,(
% 5.57/1.07 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: (((subset @ X1 @ (cartprod @ Y0 @ X2)) & (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ X2 @ (^[Y3 : $i]: (in @ (kpair @ Y1 @ Y3) @ X1)))) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ X2 @ (^[Y3 : $i]: (in @ (kpair @ Y1 @ Y3) @ X1))))))))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (in @ (kpair @ Y1 @ (ap @ Y0 @ X2 @ X1 @ Y1)) @ X1)))))) @ X3)))) )),
% 5.57/1.07 inference(pi_proxy_clausification,[],[f45])).
% 5.57/1.07 thf(f47,plain,(
% 5.57/1.07 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((((subset @ X1 @ (cartprod @ X3 @ X2)) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X3) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ X2 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ X1)))) & ((setadjoin @ Y1 @ emptyset) = (dsetconstr @ X2 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ X1))))))))))) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X3) => (in @ (kpair @ Y0 @ (ap @ X3 @ X2 @ X1 @ Y0)) @ X1)))))))) )),
% 5.57/1.07 inference(beta-eta_normalization,[],[f46])).
% 5.57/1.07 thf(f48,plain,(
% 5.57/1.07 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (((subset @ X1 @ (cartprod @ X3 @ X2)) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X3) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ X2 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ X1)))) & ((setadjoin @ Y1 @ emptyset) = (dsetconstr @ X2 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ X1))))))))))))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X3) => (in @ (kpair @ Y0 @ (ap @ X3 @ X2 @ X1 @ Y0)) @ X1))))))) )),
% 5.57/1.07 inference(imp_proxy_clausification,[],[f47])).
% 5.57/1.07 thf(f49,plain,(
% 5.57/1.07 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X3) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ X2 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ X1)))) & ((setadjoin @ Y1 @ emptyset) = (dsetconstr @ X2 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ X1)))))))))))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X3) => (in @ (kpair @ Y0 @ (ap @ X3 @ X2 @ X1 @ Y0)) @ X1)))))) | ($false = ((subset @ X1 @ (cartprod @ X3 @ X2))))) )),
% 5.57/1.07 inference(and_proxy_clausification,[],[f48])).
% 5.57/1.07 thf(f50,plain,(
% 5.57/1.07 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (((^[Y0 : $i]: ((in @ Y0 @ X3) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ X2 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ X1)))) & ((setadjoin @ Y1 @ emptyset) = (dsetconstr @ X2 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ X1))))))))) @ (sK4 @ X3 @ X1 @ X2)))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X3) => (in @ (kpair @ Y0 @ (ap @ X3 @ X2 @ X1 @ Y0)) @ X1)))))) | ($false = ((subset @ X1 @ (cartprod @ X3 @ X2))))) )),
% 5.57/1.07 inference(sigma_proxy_clausification,[],[f49])).
% 5.57/1.07 thf(f51,plain,(
% 5.57/1.07 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = (((^[Y0 : $i]: ((in @ Y0 @ X3) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ X2 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ X1)))) & ((setadjoin @ Y1 @ emptyset) = (dsetconstr @ X2 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ X1))))))))) @ (sK4 @ X3 @ X1 @ X2)))) | ($true = (((^[Y0 : $i]: ((in @ Y0 @ X3) => (in @ (kpair @ Y0 @ (ap @ X3 @ X2 @ X1 @ Y0)) @ X1))) @ X4))) | ($false = ((subset @ X1 @ (cartprod @ X3 @ X2))))) )),
% 5.57/1.07 inference(pi_proxy_clausification,[],[f50])).
% 5.57/1.07 thf(f52,plain,(
% 5.57/1.07 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = (((in @ (sK4 @ X3 @ X1 @ X2) @ X3) => (?? @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ X2 @ (^[Y1 : $i]: (in @ (kpair @ (sK4 @ X3 @ X1 @ X2) @ Y1) @ X1)))) & ((setadjoin @ Y0 @ emptyset) = (dsetconstr @ X2 @ (^[Y1 : $i]: (in @ (kpair @ (sK4 @ X3 @ X1 @ X2) @ Y1) @ X1)))))))))) | ($true = (((in @ X4 @ X3) => (in @ (kpair @ X4 @ (ap @ X3 @ X2 @ X1 @ X4)) @ X1)))) | ($false = ((subset @ X1 @ (cartprod @ X3 @ X2))))) )),
% 5.57/1.07 inference(beta-eta_normalization,[],[f51])).
% 5.57/1.07 thf(f53,plain,(
% 5.57/1.07 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = ((?? @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ X2 @ (^[Y1 : $i]: (in @ (kpair @ (sK4 @ X3 @ X1 @ X2) @ Y1) @ X1)))) & ((setadjoin @ Y0 @ emptyset) = (dsetconstr @ X2 @ (^[Y1 : $i]: (in @ (kpair @ (sK4 @ X3 @ X1 @ X2) @ Y1) @ X1))))))))) | ($true = (((in @ X4 @ X3) => (in @ (kpair @ X4 @ (ap @ X3 @ X2 @ X1 @ X4)) @ X1)))) | ($false = ((subset @ X1 @ (cartprod @ X3 @ X2))))) )),
% 5.57/1.07 inference(imp_proxy_clausification,[],[f52])).
% 5.57/1.07 thf(f54,plain,(
% 5.57/1.07 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((in @ (sK4 @ X3 @ X1 @ X2) @ X3))) | ($true = (((in @ X4 @ X3) => (in @ (kpair @ X4 @ (ap @ X3 @ X2 @ X1 @ X4)) @ X1)))) | ($false = ((subset @ X1 @ (cartprod @ X3 @ X2))))) )),
% 5.57/1.07 inference(imp_proxy_clausification,[],[f52])).
% 5.57/1.07 thf(f55,plain,(
% 5.57/1.07 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((in @ (kpair @ X4 @ (ap @ X3 @ X2 @ X1 @ X4)) @ X1))) | ($true = ((in @ (sK4 @ X3 @ X1 @ X2) @ X3))) | ($false = ((subset @ X1 @ (cartprod @ X3 @ X2)))) | ($false = ((in @ X4 @ X3)))) )),
% 5.57/1.07 inference(imp_proxy_clausification,[],[f54])).
% 5.57/1.07 thf(f56,plain,(
% 5.57/1.07 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i,X5 : $i] : (($false = (((^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ X2 @ (^[Y1 : $i]: (in @ (kpair @ (sK4 @ X3 @ X1 @ X2) @ Y1) @ X1)))) & ((setadjoin @ Y0 @ emptyset) = (dsetconstr @ X2 @ (^[Y1 : $i]: (in @ (kpair @ (sK4 @ X3 @ X1 @ X2) @ Y1) @ X1)))))) @ X5))) | ($true = (((in @ X4 @ X3) => (in @ (kpair @ X4 @ (ap @ X3 @ X2 @ X1 @ X4)) @ X1)))) | ($false = ((subset @ X1 @ (cartprod @ X3 @ X2))))) )),
% 5.57/1.07 inference(pi_proxy_clausification,[],[f53])).
% 5.57/1.07 thf(f57,plain,(
% 5.57/1.07 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i,X5 : $i] : (($false = (((^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ X2 @ (^[Y1 : $i]: (in @ (kpair @ (sK4 @ X3 @ X1 @ X2) @ Y1) @ X1)))) & ((setadjoin @ Y0 @ emptyset) = (dsetconstr @ X2 @ (^[Y1 : $i]: (in @ (kpair @ (sK4 @ X3 @ X1 @ X2) @ Y1) @ X1)))))) @ X5))) | ($false = ((in @ X4 @ X3))) | ($false = ((subset @ X1 @ (cartprod @ X3 @ X2)))) | ($true = ((in @ (kpair @ X4 @ (ap @ X3 @ X2 @ X1 @ X4)) @ X1)))) )),
% 5.57/1.07 inference(imp_proxy_clausification,[],[f56])).
% 5.57/1.07 thf(f58,plain,(
% 5.57/1.07 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i,X5 : $i] : (($false = (((in @ X5 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (in @ (kpair @ (sK4 @ X3 @ X1 @ X2) @ Y0) @ X1)))) & ((setadjoin @ X5 @ emptyset) = (dsetconstr @ X2 @ (^[Y0 : $i]: (in @ (kpair @ (sK4 @ X3 @ X1 @ X2) @ Y0) @ X1))))))) | ($false = ((in @ X4 @ X3))) | ($false = ((subset @ X1 @ (cartprod @ X3 @ X2)))) | ($true = ((in @ (kpair @ X4 @ (ap @ X3 @ X2 @ X1 @ X4)) @ X1)))) )),
% 5.57/1.07 inference(beta-eta_normalization,[],[f57])).
% 5.57/1.07 thf(f59,plain,(
% 5.57/1.07 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i,X5 : $i] : (($false = (((setadjoin @ X5 @ emptyset) = (dsetconstr @ X2 @ (^[Y0 : $i]: (in @ (kpair @ (sK4 @ X3 @ X1 @ X2) @ Y0) @ X1)))))) | ($false = ((in @ X4 @ X3))) | ($false = ((subset @ X1 @ (cartprod @ X3 @ X2)))) | ($true = ((in @ (kpair @ X4 @ (ap @ X3 @ X2 @ X1 @ X4)) @ X1))) | ($false = ((in @ X5 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (in @ (kpair @ (sK4 @ X3 @ X1 @ X2) @ Y0) @ X1))))))) )),
% 5.57/1.07 inference(and_proxy_clausification,[],[f58])).
% 5.57/1.07 thf(f60,plain,(
% 5.57/1.07 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i,X5 : $i] : ((((dsetconstr @ X2 @ (^[Y0 : $i]: (in @ (kpair @ (sK4 @ X3 @ X1 @ X2) @ Y0) @ X1)))) != ((setadjoin @ X5 @ emptyset))) | ($false = ((in @ X4 @ X3))) | ($false = ((subset @ X1 @ (cartprod @ X3 @ X2)))) | ($true = ((in @ (kpair @ X4 @ (ap @ X3 @ X2 @ X1 @ X4)) @ X1))) | ($false = ((in @ X5 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (in @ (kpair @ (sK4 @ X3 @ X1 @ X2) @ Y0) @ X1))))))) )),
% 5.57/1.07 inference(equality_proxy_clausification,[],[f59])).
% 5.57/1.07 thf(f61,plain,(
% 5.57/1.07 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (funcSet @ Y2 @ Y1)) => ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (((^[Y6 : $i]: ((^[Y7 : $i]: ((^[Y8 : $i]: (subset @ Y8 @ (cartprod @ Y6 @ Y7))))))) @ Y3 @ Y4 @ Y5) & (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y3) => ((^[Y7 : $i]: ((^[Y8 : $i > $o]: ((^[Y9 : $i]: (?? @ $i @ (^[Y10 : $i]: ((in @ Y10 @ Y9) & ((setadjoin @ Y10 @ emptyset) = Y9))))) @ (dsetconstr @ Y7 @ (^[Y9 : $i]: (Y8 @ Y9))))))) @ Y4 @ (^[Y7 : $i]: (in @ (kpair @ Y6 @ Y7) @ Y5)))))))))))) @ Y2 @ Y1 @ Y0))))))) @ X1)))) )),
% 5.57/1.07 inference(pi_proxy_clausification,[],[f40])).
% 5.57/1.07 thf(f62,plain,(
% 5.57/1.07 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ X1 @ (funcSet @ Y1 @ Y0)) => ((subset @ X1 @ (cartprod @ Y1 @ Y0)) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ Y0 @ (^[Y4 : $i]: (in @ (kpair @ Y2 @ Y4) @ X1)))) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y0 @ (^[Y4 : $i]: (in @ (kpair @ Y2 @ Y4) @ X1))))))))))))))))))) )),
% 5.57/1.07 inference(beta-eta_normalization,[],[f61])).
% 5.57/1.07 thf(f63,plain,(
% 5.57/1.07 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ X1 @ (funcSet @ Y1 @ Y0)) => ((subset @ X1 @ (cartprod @ Y1 @ Y0)) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (dsetconstr @ Y0 @ (^[Y4 : $i]: (in @ (kpair @ Y2 @ Y4) @ X1)))) & ((setadjoin @ Y3 @ emptyset) = (dsetconstr @ Y0 @ (^[Y4 : $i]: (in @ (kpair @ Y2 @ Y4) @ X1))))))))))))))) @ X2)))) )),
% 5.57/1.07 inference(pi_proxy_clausification,[],[f62])).
% 5.57/1.07 thf(f64,plain,(
% 5.57/1.07 ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ X1 @ (funcSet @ Y0 @ X2)) => ((subset @ X1 @ (cartprod @ Y0 @ X2)) & (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ X2 @ (^[Y3 : $i]: (in @ (kpair @ Y1 @ Y3) @ X1)))) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ X2 @ (^[Y3 : $i]: (in @ (kpair @ Y1 @ Y3) @ X1))))))))))))))))) )),
% 5.57/1.07 inference(beta-eta_normalization,[],[f63])).
% 5.57/1.07 thf(f65,plain,(
% 5.57/1.07 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((in @ X1 @ (funcSet @ Y0 @ X2)) => ((subset @ X1 @ (cartprod @ Y0 @ X2)) & (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (dsetconstr @ X2 @ (^[Y3 : $i]: (in @ (kpair @ Y1 @ Y3) @ X1)))) & ((setadjoin @ Y2 @ emptyset) = (dsetconstr @ X2 @ (^[Y3 : $i]: (in @ (kpair @ Y1 @ Y3) @ X1))))))))))))) @ X3)))) )),
% 5.57/1.07 inference(pi_proxy_clausification,[],[f64])).
% 5.57/1.07 thf(f66,plain,(
% 5.57/1.07 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((in @ X1 @ (funcSet @ X3 @ X2)) => ((subset @ X1 @ (cartprod @ X3 @ X2)) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X3) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ X2 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ X1)))) & ((setadjoin @ Y1 @ emptyset) = (dsetconstr @ X2 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ X1))))))))))))))) )),
% 5.57/1.07 inference(beta-eta_normalization,[],[f65])).
% 5.57/1.07 thf(f67,plain,(
% 5.57/1.07 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((in @ X1 @ (funcSet @ X3 @ X2)))) | ($true = (((subset @ X1 @ (cartprod @ X3 @ X2)) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X3) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ X2 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ X1)))) & ((setadjoin @ Y1 @ emptyset) = (dsetconstr @ X2 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ X1)))))))))))))) )),
% 5.57/1.07 inference(imp_proxy_clausification,[],[f66])).
% 5.57/1.07 thf(f68,plain,(
% 5.57/1.07 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((in @ X1 @ (funcSet @ X3 @ X2)))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X3) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ X2 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ X1)))) & ((setadjoin @ Y1 @ emptyset) = (dsetconstr @ X2 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ X1))))))))))))) )),
% 5.57/1.07 inference(and_proxy_clausification,[],[f67])).
% 5.57/1.07 thf(f69,plain,(
% 5.57/1.07 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((subset @ X1 @ (cartprod @ X3 @ X2)))) | ($false = ((in @ X1 @ (funcSet @ X3 @ X2))))) )),
% 5.57/1.07 inference(and_proxy_clausification,[],[f67])).
% 5.57/1.07 thf(f70,plain,(
% 5.57/1.07 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = ((in @ X1 @ (funcSet @ X3 @ X2)))) | ($true = (((^[Y0 : $i]: ((in @ Y0 @ X3) => (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (dsetconstr @ X2 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ X1)))) & ((setadjoin @ Y1 @ emptyset) = (dsetconstr @ X2 @ (^[Y2 : $i]: (in @ (kpair @ Y0 @ Y2) @ X1))))))))) @ X4)))) )),
% 5.57/1.07 inference(pi_proxy_clausification,[],[f68])).
% 5.57/1.07 thf(f71,plain,(
% 5.57/1.07 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = ((in @ X1 @ (funcSet @ X3 @ X2)))) | ($true = (((in @ X4 @ X3) => (?? @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ X2 @ (^[Y1 : $i]: (in @ (kpair @ X4 @ Y1) @ X1)))) & ((setadjoin @ Y0 @ emptyset) = (dsetconstr @ X2 @ (^[Y1 : $i]: (in @ (kpair @ X4 @ Y1) @ X1))))))))))) )),
% 5.57/1.07 inference(beta-eta_normalization,[],[f70])).
% 5.57/1.07 thf(f72,plain,(
% 5.57/1.07 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = ((in @ X1 @ (funcSet @ X3 @ X2)))) | ($false = ((in @ X4 @ X3))) | ($true = ((?? @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ X2 @ (^[Y1 : $i]: (in @ (kpair @ X4 @ Y1) @ X1)))) & ((setadjoin @ Y0 @ emptyset) = (dsetconstr @ X2 @ (^[Y1 : $i]: (in @ (kpair @ X4 @ Y1) @ X1)))))))))) )),
% 5.57/1.07 inference(imp_proxy_clausification,[],[f71])).
% 5.57/1.07 thf(f73,plain,(
% 5.57/1.07 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = ((in @ X1 @ (funcSet @ X3 @ X2)))) | ($false = ((in @ X4 @ X3))) | ($true = (((^[Y0 : $i]: ((in @ Y0 @ (dsetconstr @ X2 @ (^[Y1 : $i]: (in @ (kpair @ X4 @ Y1) @ X1)))) & ((setadjoin @ Y0 @ emptyset) = (dsetconstr @ X2 @ (^[Y1 : $i]: (in @ (kpair @ X4 @ Y1) @ X1)))))) @ (sK5 @ X4 @ X1 @ X2))))) )),
% 5.57/1.07 inference(sigma_proxy_clausification,[],[f72])).
% 5.57/1.07 thf(f74,plain,(
% 5.57/1.07 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = ((in @ X1 @ (funcSet @ X3 @ X2)))) | ($false = ((in @ X4 @ X3))) | ($true = (((in @ (sK5 @ X4 @ X1 @ X2) @ (dsetconstr @ X2 @ (^[Y0 : $i]: (in @ (kpair @ X4 @ Y0) @ X1)))) & ((setadjoin @ (sK5 @ X4 @ X1 @ X2) @ emptyset) = (dsetconstr @ X2 @ (^[Y0 : $i]: (in @ (kpair @ X4 @ Y0) @ X1)))))))) )),
% 5.57/1.07 inference(beta-eta_normalization,[],[f73])).
% 5.57/1.07 thf(f75,plain,(
% 5.57/1.07 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = ((in @ X1 @ (funcSet @ X3 @ X2)))) | ($false = ((in @ X4 @ X3))) | ($true = (((setadjoin @ (sK5 @ X4 @ X1 @ X2) @ emptyset) = (dsetconstr @ X2 @ (^[Y0 : $i]: (in @ (kpair @ X4 @ Y0) @ X1))))))) )),
% 5.57/1.07 inference(and_proxy_clausification,[],[f74])).
% 5.57/1.07 thf(f76,plain,(
% 5.57/1.07 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = ((in @ X1 @ (funcSet @ X3 @ X2)))) | ($false = ((in @ X4 @ X3))) | ($true = ((in @ (sK5 @ X4 @ X1 @ X2) @ (dsetconstr @ X2 @ (^[Y0 : $i]: (in @ (kpair @ X4 @ Y0) @ X1))))))) )),
% 5.57/1.07 inference(and_proxy_clausification,[],[f74])).
% 5.57/1.07 thf(f77,plain,(
% 5.57/1.07 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = ((in @ X1 @ (funcSet @ X3 @ X2)))) | ($false = ((in @ X4 @ X3))) | (((dsetconstr @ X2 @ (^[Y0 : $i]: (in @ (kpair @ X4 @ Y0) @ X1)))) = ((setadjoin @ (sK5 @ X4 @ X1 @ X2) @ emptyset)))) )),
% 5.57/1.07 inference(equality_proxy_clausification,[],[f75])).
% 5.57/1.07 thf(f80,plain,(
% 5.57/1.07 ($true != $true) | (((in @ (kpair @ sK3 @ (ap @ sK0 @ sK1 @ sK2 @ sK3)) @ sK2)) = $false)),
% 5.57/1.07 inference(constrained_superposition,[],[f35,f37])).
% 5.57/1.07 thf(f82,plain,(
% 5.57/1.07 (((in @ (kpair @ sK3 @ (ap @ sK0 @ sK1 @ sK2 @ sK3)) @ sK2)) = $false)),
% 5.57/1.07 inference(trivial_inequality_removal,[],[f80])).
% 5.57/1.07 thf(f90,plain,(
% 5.57/1.07 ($true = $false) | ($true = ((in @ (sK4 @ sK0 @ sK2 @ sK1) @ sK0))) | ($false = ((subset @ sK2 @ (cartprod @ sK0 @ sK1)))) | (((in @ sK3 @ sK0)) = $false)),
% 5.57/1.07 inference(constrained_superposition,[],[f55,f82])).
% 5.57/1.07 thf(f95,plain,(
% 5.57/1.07 ($true = ((in @ (sK4 @ sK0 @ sK2 @ sK1) @ sK0))) | ($false = ((subset @ sK2 @ (cartprod @ sK0 @ sK1)))) | (((in @ sK3 @ sK0)) = $false)),
% 5.57/1.07 inference(trivial_inequality_removal,[],[f90])).
% 5.57/1.07 thf(f100,plain,(
% 5.57/1.07 ($true = $false) | ($true = ((in @ (sK4 @ sK0 @ sK2 @ sK1) @ sK0))) | ($false = ((subset @ sK2 @ (cartprod @ sK0 @ sK1))))),
% 5.57/1.07 inference(forward_demodulation,[],[f95,f34])).
% 5.57/1.07 thf(f101,plain,(
% 5.57/1.07 ($true = ((in @ (sK4 @ sK0 @ sK2 @ sK1) @ sK0))) | ($false = ((subset @ sK2 @ (cartprod @ sK0 @ sK1))))),
% 5.57/1.07 inference(trivial_inequality_removal,[],[f100])).
% 5.57/1.07 thf(f103,definition,(
% 5.57/1.07 spl6_1 <=> ($false = ((subset @ sK2 @ (cartprod @ sK0 @ sK1))))),
% 5.57/1.07 introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition])).
% 5.57/1.07 thf(f104,plain,(
% 5.57/1.07 ($false != ((subset @ sK2 @ (cartprod @ sK0 @ sK1)))) | spl6_1),
% 5.57/1.07 inference(avatar_component_clause,[],[f103])).
% 5.57/1.07 thf(f105,plain,(
% 5.57/1.07 ($false = ((subset @ sK2 @ (cartprod @ sK0 @ sK1)))) | ~spl6_1),
% 5.57/1.07 inference(avatar_component_clause,[],[f103])).
% 5.57/1.07 thf(f107,definition,(
% 5.57/1.07 spl6_2 <=> ($true = ((in @ (sK4 @ sK0 @ sK2 @ sK1) @ sK0)))),
% 5.57/1.07 introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition])).
% 5.57/1.07 thf(f109,plain,(
% 5.57/1.07 ($true = ((in @ (sK4 @ sK0 @ sK2 @ sK1) @ sK0))) | ~spl6_2),
% 5.57/1.07 inference(avatar_component_clause,[],[f107])).
% 5.57/1.07 thf(f112,plain,(
% 5.57/1.07 spl6_1 | spl6_2),
% 5.57/1.07 inference(avatar_split_clause,[],[f101,f107,f103])).
% 5.57/1.07 thf(f124,plain,(
% 5.57/1.07 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X6 : $i,X4 : $i,X5 : $i] : ((((setadjoin @ (sK5 @ X0 @ X1 @ X2) @ emptyset)) = ((setadjoin @ (sK5 @ X3 @ X4 @ X2) @ emptyset))) | ($false = ((in @ X4 @ (funcSet @ X5 @ X2)))) | ($false = ((in @ X3 @ X5))) | ($false = ((in @ X1 @ (funcSet @ X6 @ X2)))) | ($false = ((in @ X0 @ X6))) | ((^[Y0 : $i]: (X3)) != (^[Y0 : $i]: (X0))) | ((^[Y0 : $i]: (X1)) != (^[Y0 : $i]: (X4)))) )),
% 5.57/1.07 inference(constrained_superposition,[],[f77,f77])).
% 5.57/1.07 thf(f128,plain,(
% 5.57/1.07 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i,X5 : $i] : (($true = $false) | ($true = ((in @ (kpair @ X3 @ (ap @ X0 @ X2 @ X1 @ X3)) @ X1))) | ($false = ((subset @ X1 @ (cartprod @ X0 @ X2)))) | (((in @ X3 @ X0)) = $false) | ($false = ((in @ X4 @ (funcSet @ X0 @ X5)))) | (((dsetconstr @ X5 @ (^[Y0 : $i]: (in @ (kpair @ (sK4 @ X0 @ X1 @ X2) @ Y0) @ X4)))) = ((setadjoin @ (sK5 @ (sK4 @ X0 @ X1 @ X2) @ X4 @ X5) @ emptyset)))) )),
% 5.57/1.07 inference(constrained_superposition,[],[f55,f77])).
% 5.57/1.07 thf(f130,plain,(
% 5.57/1.07 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X6 : $i,X4 : $i,X5 : $i] : (($true = ((in @ (sK5 @ X3 @ X4 @ X2) @ (setadjoin @ (sK5 @ X0 @ X1 @ X2) @ emptyset)))) | ($false = ((in @ X4 @ (funcSet @ X5 @ X2)))) | ($false = ((in @ X3 @ X5))) | ($false = ((in @ X1 @ (funcSet @ X6 @ X2)))) | ($false = ((in @ X0 @ X6))) | ((^[Y0 : $i]: (X3)) != (^[Y0 : $i]: (X0))) | ((^[Y0 : $i]: (X1)) != (^[Y0 : $i]: (X4)))) )),
% 5.57/1.07 inference(constrained_superposition,[],[f76,f77])).
% 5.57/1.07 thf(f133,plain,(
% 5.57/1.07 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i,X5 : $i] : ((((dsetconstr @ X5 @ (^[Y0 : $i]: (in @ (kpair @ (sK4 @ X0 @ X1 @ X2) @ Y0) @ X4)))) = ((setadjoin @ (sK5 @ (sK4 @ X0 @ X1 @ X2) @ X4 @ X5) @ emptyset))) | ($true = ((in @ (kpair @ X3 @ (ap @ X0 @ X2 @ X1 @ X3)) @ X1))) | (((in @ X3 @ X0)) = $false) | ($false = ((in @ X4 @ (funcSet @ X0 @ X5)))) | ($false = ((subset @ X1 @ (cartprod @ X0 @ X2))))) )),
% 5.57/1.07 inference(trivial_inequality_removal,[],[f128])).
% 5.57/1.07 thf(f182,plain,(
% 5.57/1.07 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (($false != $false) | (((setadjoin @ (sK5 @ X3 @ X0 @ X2) @ emptyset)) = ((setadjoin @ (sK5 @ X4 @ X0 @ X2) @ emptyset))) | ($false = ((in @ X0 @ (funcSet @ X1 @ X2)))) | ($false = ((in @ X4 @ X1))) | ($false = ((in @ X3 @ X1))) | ((^[Y0 : $i]: (X3)) != (^[Y0 : $i]: (X4))) | ((^[Y0 : $i]: (X0)) != (^[Y0 : $i]: (X0)))) )),
% 5.57/1.07 inference(equality_factoring,[],[f124])).
% 5.57/1.07 thf(f189,plain,(
% 5.57/1.07 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : ((((setadjoin @ (sK5 @ X3 @ X0 @ X2) @ emptyset)) = ((setadjoin @ (sK5 @ X4 @ X0 @ X2) @ emptyset))) | ($false = ((in @ X0 @ (funcSet @ X1 @ X2)))) | ($false = ((in @ X4 @ X1))) | ($false = ((in @ X3 @ X1))) | ((^[Y0 : $i]: (X3)) != (^[Y0 : $i]: (X4)))) )),
% 5.57/1.07 inference(trivial_inequality_removal,[],[f182])).
% 5.57/1.07 thf(f250,plain,(
% 5.57/1.07 ( ! [X0 : $i,X1 : $i] : (($true = $false) | (((setadjoin @ (sK5 @ X0 @ sK2 @ sK1) @ emptyset)) = ((setadjoin @ (sK5 @ X1 @ sK2 @ sK1) @ emptyset))) | ($false = ((in @ X1 @ sK0))) | ($false = ((in @ X0 @ sK0))) | ((^[Y0 : $i]: (X1)) != (^[Y0 : $i]: (X0)))) )),
% 5.57/1.07 inference(constrained_superposition,[],[f33,f189])).
% 5.57/1.07 thf(f265,plain,(
% 5.57/1.07 ( ! [X0 : $i,X1 : $i] : ((((setadjoin @ (sK5 @ X0 @ sK2 @ sK1) @ emptyset)) = ((setadjoin @ (sK5 @ X1 @ sK2 @ sK1) @ emptyset))) | ($false = ((in @ X1 @ sK0))) | ($false = ((in @ X0 @ sK0))) | ((^[Y0 : $i]: (X1)) != (^[Y0 : $i]: (X0)))) )),
% 5.57/1.07 inference(trivial_inequality_removal,[],[f250])).
% 5.57/1.07 thf(f329,plain,(
% 5.57/1.07 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (($false != $false) | ($true = ((in @ (sK5 @ X3 @ X0 @ X2) @ (setadjoin @ (sK5 @ X4 @ X0 @ X2) @ emptyset)))) | ($false = ((in @ X0 @ (funcSet @ X1 @ X2)))) | ($false = ((in @ X3 @ X1))) | ($false = ((in @ X4 @ X1))) | ((^[Y0 : $i]: (X3)) != (^[Y0 : $i]: (X4))) | ((^[Y0 : $i]: (X0)) != (^[Y0 : $i]: (X0)))) )),
% 5.57/1.07 inference(equality_factoring,[],[f130])).
% 5.57/1.07 thf(f336,plain,(
% 5.57/1.07 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (($true = ((in @ (sK5 @ X3 @ X0 @ X2) @ (setadjoin @ (sK5 @ X4 @ X0 @ X2) @ emptyset)))) | ($false = ((in @ X0 @ (funcSet @ X1 @ X2)))) | ($false = ((in @ X3 @ X1))) | ($false = ((in @ X4 @ X1))) | ((^[Y0 : $i]: (X3)) != (^[Y0 : $i]: (X4)))) )),
% 5.57/1.07 inference(trivial_inequality_removal,[],[f329])).
% 5.57/1.07 thf(f505,plain,(
% 5.57/1.07 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($false != $false) | ($true = ((in @ (sK5 @ X0 @ X2 @ X3) @ (setadjoin @ (sK5 @ X0 @ X2 @ X3) @ emptyset)))) | ($false = ((in @ X2 @ (funcSet @ X1 @ X3)))) | ($false = ((in @ X0 @ X1))) | ((^[Y0 : $i]: (X0)) != (^[Y0 : $i]: (X0)))) )),
% 5.57/1.07 inference(equality_factoring,[],[f336])).
% 5.57/1.07 thf(f506,plain,(
% 5.57/1.07 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true = ((in @ (sK5 @ X0 @ X2 @ X3) @ (setadjoin @ (sK5 @ X0 @ X2 @ X3) @ emptyset)))) | ($false = ((in @ X2 @ (funcSet @ X1 @ X3)))) | ($false = ((in @ X0 @ X1)))) )),
% 5.57/1.07 inference(trivial_inequality_removal,[],[f505])).
% 5.57/1.07 thf(f569,plain,(
% 5.57/1.07 ( ! [X0 : $i,X1 : $i] : (($true = $false) | (((dsetconstr @ X0 @ (^[Y0 : $i]: (in @ (kpair @ (sK4 @ sK0 @ sK2 @ sK1) @ Y0) @ X1)))) = ((setadjoin @ (sK5 @ (sK4 @ sK0 @ sK2 @ sK1) @ X1 @ X0) @ emptyset))) | (((in @ sK3 @ sK0)) = $false) | ($false = ((in @ X1 @ (funcSet @ sK0 @ X0)))) | ($false = ((subset @ sK2 @ (cartprod @ sK0 @ sK1))))) )),
% 5.57/1.07 inference(constrained_superposition,[],[f133,f82])).
% 5.57/1.07 thf(f614,plain,(
% 5.57/1.07 ( ! [X0 : $i,X1 : $i] : ((((dsetconstr @ X0 @ (^[Y0 : $i]: (in @ (kpair @ (sK4 @ sK0 @ sK2 @ sK1) @ Y0) @ X1)))) = ((setadjoin @ (sK5 @ (sK4 @ sK0 @ sK2 @ sK1) @ X1 @ X0) @ emptyset))) | (((in @ sK3 @ sK0)) = $false) | ($false = ((in @ X1 @ (funcSet @ sK0 @ X0)))) | ($false = ((subset @ sK2 @ (cartprod @ sK0 @ sK1))))) )),
% 5.57/1.07 inference(trivial_inequality_removal,[],[f569])).
% 5.57/1.07 thf(f637,plain,(
% 5.57/1.07 ( ! [X0 : $i,X1 : $i] : (($true = $false) | (((dsetconstr @ X0 @ (^[Y0 : $i]: (in @ (kpair @ (sK4 @ sK0 @ sK2 @ sK1) @ Y0) @ X1)))) = ((setadjoin @ (sK5 @ (sK4 @ sK0 @ sK2 @ sK1) @ X1 @ X0) @ emptyset))) | ($false = ((in @ X1 @ (funcSet @ sK0 @ X0)))) | ($false = ((subset @ sK2 @ (cartprod @ sK0 @ sK1))))) )),
% 5.57/1.07 inference(forward_demodulation,[],[f614,f34])).
% 5.57/1.07 thf(f638,plain,(
% 5.57/1.07 ( ! [X0 : $i,X1 : $i] : ((((dsetconstr @ X0 @ (^[Y0 : $i]: (in @ (kpair @ (sK4 @ sK0 @ sK2 @ sK1) @ Y0) @ X1)))) = ((setadjoin @ (sK5 @ (sK4 @ sK0 @ sK2 @ sK1) @ X1 @ X0) @ emptyset))) | ($false = ((in @ X1 @ (funcSet @ sK0 @ X0)))) | ($false = ((subset @ sK2 @ (cartprod @ sK0 @ sK1))))) )),
% 5.57/1.07 inference(trivial_inequality_removal,[],[f637])).
% 5.57/1.07 thf(f640,definition,(
% 5.57/1.07 spl6_3 <=> ! [X0 : $i,X1 : $i] : ((((dsetconstr @ X0 @ (^[Y0 : $i]: (in @ (kpair @ (sK4 @ sK0 @ sK2 @ sK1) @ Y0) @ X1)))) = ((setadjoin @ (sK5 @ (sK4 @ sK0 @ sK2 @ sK1) @ X1 @ X0) @ emptyset))) | ($false = ((in @ X1 @ (funcSet @ sK0 @ X0)))))),
% 5.57/1.07 introduced(definition,[new_symbols(definition,[spl6_3])],[avatar_definition])).
% 5.57/1.07 thf(f641,plain,(
% 5.57/1.07 ( ! [X0 : $i,X1 : $i] : ((((dsetconstr @ X0 @ (^[Y0 : $i]: (in @ (kpair @ (sK4 @ sK0 @ sK2 @ sK1) @ Y0) @ X1)))) = ((setadjoin @ (sK5 @ (sK4 @ sK0 @ sK2 @ sK1) @ X1 @ X0) @ emptyset))) | ($false = ((in @ X1 @ (funcSet @ sK0 @ X0))))) ) | ~spl6_3),
% 5.57/1.07 inference(avatar_component_clause,[],[f640])).
% 5.57/1.07 thf(f644,plain,(
% 5.57/1.07 spl6_1 | spl6_3),
% 5.57/1.07 inference(avatar_split_clause,[],[f638,f640,f103])).
% 5.57/1.07 thf(f647,plain,(
% 5.57/1.07 ($true = $false) | (((in @ sK2 @ (funcSet @ sK0 @ sK1))) = $false) | ~spl6_1),
% 5.57/1.07 inference(constrained_superposition,[],[f69,f105])).
% 5.57/1.07 thf(f648,plain,(
% 5.57/1.07 (((in @ sK2 @ (funcSet @ sK0 @ sK1))) = $false) | ~spl6_1),
% 5.57/1.07 inference(trivial_inequality_removal,[],[f647])).
% 5.57/1.07 thf(f651,plain,(
% 5.57/1.07 ($true = $false) | ~spl6_1),
% 5.57/1.07 inference(constrained_superposition,[],[f648,f33])).
% 5.57/1.07 thf(f657,plain,(
% 5.57/1.07 $false | ~spl6_1),
% 5.57/1.07 inference(trivial_inequality_removal,[],[f651])).
% 5.57/1.07 thf(f658,plain,(
% 5.57/1.07 ~spl6_1),
% 5.57/1.07 inference(avatar_contradiction_clause,[],[f657])).
% 5.57/1.07 thf(f667,plain,(
% 5.57/1.07 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : ((((setadjoin @ (sK5 @ (sK4 @ sK0 @ sK2 @ sK1) @ X0 @ sK1) @ emptyset)) != ((setadjoin @ X2 @ emptyset))) | ($false = ((in @ X3 @ sK0))) | ($false = ((subset @ X1 @ (cartprod @ sK0 @ sK1)))) | ($true = ((in @ (kpair @ X3 @ (ap @ sK0 @ sK1 @ X1 @ X3)) @ X1))) | ($false = ((in @ X2 @ (setadjoin @ (sK5 @ (sK4 @ sK0 @ sK2 @ sK1) @ X0 @ sK1) @ emptyset)))) | ($false = ((in @ X0 @ (funcSet @ sK0 @ sK1)))) | ((^[Y0 : $i]: (X1)) != (^[Y0 : $i]: (sK2))) | ((^[Y0 : $i]: (X1)) != (^[Y0 : $i]: (X0)))) ) | ~spl6_3),
% 5.57/1.07 inference(constrained_superposition,[],[f60,f641])).
% 5.57/1.07 thf(f1171,plain,(
% 5.57/1.07 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : ((((setadjoin @ X1 @ emptyset)) != ((setadjoin @ (sK5 @ X0 @ sK2 @ sK1) @ emptyset))) | ($false = ((in @ X2 @ sK0))) | ($false = ((subset @ X3 @ (cartprod @ sK0 @ sK1)))) | ($true = ((in @ (kpair @ X2 @ (ap @ sK0 @ sK1 @ X3 @ X2)) @ X3))) | ($false = ((in @ X1 @ (setadjoin @ (sK5 @ X0 @ sK2 @ sK1) @ emptyset)))) | (((in @ sK2 @ (funcSet @ sK0 @ sK1))) = $false) | ((^[Y0 : $i]: (X3)) != (^[Y0 : $i]: (sK2))) | ((^[Y0 : $i]: (X3)) != (^[Y0 : $i]: (sK2))) | ($false = ((in @ (sK4 @ sK0 @ sK2 @ sK1) @ sK0))) | ($false = ((in @ X0 @ sK0))) | ((^[Y0 : $i]: (X0)) != (^[Y0 : $i]: (sK4 @ sK0 @ sK2 @ sK1)))) ) | ~spl6_3),
% 5.57/1.07 inference(constrained_superposition,[],[f667,f265])).
% 5.57/1.07 thf(f1203,plain,(
% 5.57/1.07 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : ((((setadjoin @ X1 @ emptyset)) != ((setadjoin @ (sK5 @ X0 @ sK2 @ sK1) @ emptyset))) | ($false = ((in @ X2 @ sK0))) | ($false = ((subset @ X3 @ (cartprod @ sK0 @ sK1)))) | ($true = ((in @ (kpair @ X2 @ (ap @ sK0 @ sK1 @ X3 @ X2)) @ X3))) | ($false = ((in @ X1 @ (setadjoin @ (sK5 @ X0 @ sK2 @ sK1) @ emptyset)))) | (((in @ sK2 @ (funcSet @ sK0 @ sK1))) = $false) | ((^[Y0 : $i]: (X3)) != (^[Y0 : $i]: (sK2))) | ($false = ((in @ (sK4 @ sK0 @ sK2 @ sK1) @ sK0))) | ($false = ((in @ X0 @ sK0))) | ((^[Y0 : $i]: (X0)) != (^[Y0 : $i]: (sK4 @ sK0 @ sK2 @ sK1)))) ) | ~spl6_3),
% 5.57/1.07 inference(duplicate_literal_removal,[],[f1171])).
% 5.57/1.07 thf(f1208,plain,(
% 5.57/1.07 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true = $false) | (((setadjoin @ X1 @ emptyset)) != ((setadjoin @ (sK5 @ X0 @ sK2 @ sK1) @ emptyset))) | ($false = ((in @ X2 @ sK0))) | ($false = ((subset @ X3 @ (cartprod @ sK0 @ sK1)))) | ($true = ((in @ (kpair @ X2 @ (ap @ sK0 @ sK1 @ X3 @ X2)) @ X3))) | ($false = ((in @ X1 @ (setadjoin @ (sK5 @ X0 @ sK2 @ sK1) @ emptyset)))) | ((^[Y0 : $i]: (X3)) != (^[Y0 : $i]: (sK2))) | ($false = ((in @ (sK4 @ sK0 @ sK2 @ sK1) @ sK0))) | ($false = ((in @ X0 @ sK0))) | ((^[Y0 : $i]: (X0)) != (^[Y0 : $i]: (sK4 @ sK0 @ sK2 @ sK1)))) ) | ~spl6_3),
% 5.57/1.07 inference(forward_demodulation,[],[f1203,f33])).
% 5.57/1.07 thf(f1209,plain,(
% 5.57/1.07 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : ((((setadjoin @ X1 @ emptyset)) != ((setadjoin @ (sK5 @ X0 @ sK2 @ sK1) @ emptyset))) | ($false = ((in @ X2 @ sK0))) | ($false = ((subset @ X3 @ (cartprod @ sK0 @ sK1)))) | ($true = ((in @ (kpair @ X2 @ (ap @ sK0 @ sK1 @ X3 @ X2)) @ X3))) | ($false = ((in @ X1 @ (setadjoin @ (sK5 @ X0 @ sK2 @ sK1) @ emptyset)))) | ((^[Y0 : $i]: (X3)) != (^[Y0 : $i]: (sK2))) | ($false = ((in @ (sK4 @ sK0 @ sK2 @ sK1) @ sK0))) | ($false = ((in @ X0 @ sK0))) | ((^[Y0 : $i]: (X0)) != (^[Y0 : $i]: (sK4 @ sK0 @ sK2 @ sK1)))) ) | ~spl6_3),
% 5.57/1.07 inference(trivial_inequality_removal,[],[f1208])).
% 5.57/1.07 thf(f1212,plain,(
% 5.57/1.07 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true = $false) | (((setadjoin @ X1 @ emptyset)) != ((setadjoin @ (sK5 @ X0 @ sK2 @ sK1) @ emptyset))) | ($false = ((in @ X2 @ sK0))) | ($false = ((subset @ X3 @ (cartprod @ sK0 @ sK1)))) | ($true = ((in @ (kpair @ X2 @ (ap @ sK0 @ sK1 @ X3 @ X2)) @ X3))) | ($false = ((in @ X1 @ (setadjoin @ (sK5 @ X0 @ sK2 @ sK1) @ emptyset)))) | ((^[Y0 : $i]: (X3)) != (^[Y0 : $i]: (sK2))) | ($false = ((in @ X0 @ sK0))) | ((^[Y0 : $i]: (X0)) != (^[Y0 : $i]: (sK4 @ sK0 @ sK2 @ sK1)))) ) | (~spl6_2 | ~spl6_3)),
% 5.57/1.07 inference(forward_demodulation,[],[f1209,f109])).
% 5.57/1.07 thf(f1213,plain,(
% 5.57/1.07 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : ((((setadjoin @ X1 @ emptyset)) != ((setadjoin @ (sK5 @ X0 @ sK2 @ sK1) @ emptyset))) | ($false = ((in @ X2 @ sK0))) | ($false = ((subset @ X3 @ (cartprod @ sK0 @ sK1)))) | ($true = ((in @ (kpair @ X2 @ (ap @ sK0 @ sK1 @ X3 @ X2)) @ X3))) | ($false = ((in @ X1 @ (setadjoin @ (sK5 @ X0 @ sK2 @ sK1) @ emptyset)))) | ((^[Y0 : $i]: (X3)) != (^[Y0 : $i]: (sK2))) | ($false = ((in @ X0 @ sK0))) | ((^[Y0 : $i]: (X0)) != (^[Y0 : $i]: (sK4 @ sK0 @ sK2 @ sK1)))) ) | (~spl6_2 | ~spl6_3)),
% 5.57/1.07 inference(trivial_inequality_removal,[],[f1212])).
% 5.57/1.07 thf(f1215,definition,(
% 5.57/1.07 spl6_12 <=> ! [X2 : $i,X3 : $i] : (($false = ((in @ X2 @ sK0))) | ((^[Y0 : $i]: (X3)) != (^[Y0 : $i]: (sK2))) | ($true = ((in @ (kpair @ X2 @ (ap @ sK0 @ sK1 @ X3 @ X2)) @ X3))) | ($false = ((subset @ X3 @ (cartprod @ sK0 @ sK1)))))),
% 5.57/1.07 introduced(definition,[new_symbols(definition,[spl6_12])],[avatar_definition])).
% 5.57/1.07 thf(f1216,plain,(
% 5.57/1.07 ( ! [X2 : $i,X3 : $i] : (($true = ((in @ (kpair @ X2 @ (ap @ sK0 @ sK1 @ X3 @ X2)) @ X3))) | ((^[Y0 : $i]: (X3)) != (^[Y0 : $i]: (sK2))) | ($false = ((in @ X2 @ sK0))) | ($false = ((subset @ X3 @ (cartprod @ sK0 @ sK1))))) ) | ~spl6_12),
% 5.57/1.07 inference(avatar_component_clause,[],[f1215])).
% 5.57/1.07 thf(f1218,definition,(
% 5.57/1.07 spl6_13 <=> ! [X0 : $i,X1 : $i] : ((((setadjoin @ X1 @ emptyset)) != ((setadjoin @ (sK5 @ X0 @ sK2 @ sK1) @ emptyset))) | ((^[Y0 : $i]: (X0)) != (^[Y0 : $i]: (sK4 @ sK0 @ sK2 @ sK1))) | ($false = ((in @ X0 @ sK0))) | ($false = ((in @ X1 @ (setadjoin @ (sK5 @ X0 @ sK2 @ sK1) @ emptyset)))))),
% 5.57/1.07 introduced(definition,[new_symbols(definition,[spl6_13])],[avatar_definition])).
% 5.57/1.07 thf(f1219,plain,(
% 5.57/1.07 ( ! [X0 : $i,X1 : $i] : (($false = ((in @ X1 @ (setadjoin @ (sK5 @ X0 @ sK2 @ sK1) @ emptyset)))) | ((^[Y0 : $i]: (X0)) != (^[Y0 : $i]: (sK4 @ sK0 @ sK2 @ sK1))) | ($false = ((in @ X0 @ sK0))) | (((setadjoin @ X1 @ emptyset)) != ((setadjoin @ (sK5 @ X0 @ sK2 @ sK1) @ emptyset)))) ) | ~spl6_13),
% 5.57/1.07 inference(avatar_component_clause,[],[f1218])).
% 5.57/1.07 thf(f1221,plain,(
% 5.57/1.07 spl6_12 | spl6_13 | ~spl6_2 | ~spl6_3),
% 5.57/1.07 inference(avatar_split_clause,[],[f1213,f640,f107,f1218,f1215])).
% 5.57/1.07 thf(f1688,plain,(
% 5.57/1.07 ($true != $true) | ((^[Y0 : $i]: (sK2)) != (^[Y0 : $i]: (sK2))) | (((in @ sK3 @ sK0)) = $false) | ($false = ((subset @ sK2 @ (cartprod @ sK0 @ sK1)))) | ~spl6_12),
% 5.57/1.07 inference(constrained_superposition,[],[f35,f1216])).
% 5.57/1.07 thf(f1689,plain,(
% 5.57/1.07 (((in @ sK3 @ sK0)) = $false) | ($false = ((subset @ sK2 @ (cartprod @ sK0 @ sK1)))) | ~spl6_12),
% 5.57/1.07 inference(trivial_inequality_removal,[],[f1688])).
% 5.57/1.07 thf(f1740,plain,(
% 5.57/1.07 (((in @ sK3 @ sK0)) = $false) | (spl6_1 | ~spl6_12)),
% 5.57/1.07 inference(forward_subsumption_resolution,[],[f1689,f104])).
% 5.57/1.07 thf(f1743,plain,(
% 5.57/1.07 ($true = $false) | (spl6_1 | ~spl6_12)),
% 5.57/1.07 inference(constrained_superposition,[],[f1740,f34])).
% 5.57/1.07 thf(f1749,plain,(
% 5.57/1.07 $false | (spl6_1 | ~spl6_12)),
% 5.57/1.07 inference(trivial_inequality_removal,[],[f1743])).
% 5.57/1.07 thf(f1750,plain,(
% 5.57/1.07 spl6_1 | ~spl6_12),
% 5.57/1.07 inference(avatar_contradiction_clause,[],[f1749])).
% 5.57/1.07 thf(f1779,plain,(
% 5.57/1.07 ( ! [X0 : $i,X1 : $i] : (($true = $false) | ($false = ((in @ sK2 @ (funcSet @ X1 @ sK1)))) | ($false = ((in @ X0 @ X1))) | ((^[Y0 : $i]: (X0)) != (^[Y0 : $i]: (sK4 @ sK0 @ sK2 @ sK1))) | ($false = ((in @ X0 @ sK0))) | (((setadjoin @ (sK5 @ X0 @ sK2 @ sK1) @ emptyset)) != ((setadjoin @ (sK5 @ X0 @ sK2 @ sK1) @ emptyset)))) ) | ~spl6_13),
% 5.57/1.07 inference(constrained_superposition,[],[f506,f1219])).
% 5.57/1.07 thf(f1788,plain,(
% 5.57/1.07 ( ! [X0 : $i,X1 : $i] : (((^[Y0 : $i]: (X0)) != (^[Y0 : $i]: (sK4 @ sK0 @ sK2 @ sK1))) | ($false = ((in @ X0 @ X1))) | ($false = ((in @ sK2 @ (funcSet @ X1 @ sK1)))) | ($false = ((in @ X0 @ sK0)))) ) | ~spl6_13),
% 5.57/1.07 inference(trivial_inequality_removal,[],[f1779])).
% 5.57/1.07 thf(f1937,plain,(
% 5.57/1.07 ( ! [X0 : $i,X1 : $i] : (((((^[Y0 : $i]: (X0)) @ (sK11 @ X0))) != (((^[Y0 : $i]: (sK4 @ sK0 @ sK2 @ sK1)) @ (sK11 @ X0)))) | ($false = ((in @ X0 @ X1))) | ($false = ((in @ sK2 @ (funcSet @ X1 @ sK1)))) | ($false = ((in @ X0 @ sK0)))) ) | ~spl6_13),
% 5.57/1.07 inference(negative_extensionality,[],[f1788])).
% 5.57/1.07 thf(f1939,plain,(
% 5.57/1.07 ( ! [X0 : $i,X1 : $i] : ((((sK4 @ sK0 @ sK2 @ sK1)) != X0) | ($false = ((in @ X0 @ X1))) | ($false = ((in @ sK2 @ (funcSet @ X1 @ sK1)))) | ($false = ((in @ X0 @ sK0)))) ) | ~spl6_13),
% 5.57/1.07 inference(beta-eta_normalization,[],[f1937])).
% 5.57/1.07 thf(f2049,plain,(
% 5.57/1.07 ( ! [X0 : $i] : (($false = ((in @ (sK4 @ sK0 @ sK2 @ sK1) @ X0))) | ($false = ((in @ sK2 @ (funcSet @ X0 @ sK1)))) | ($false = ((in @ (sK4 @ sK0 @ sK2 @ sK1) @ sK0)))) ) | ~spl6_13),
% 5.57/1.07 inference(equality_resolution,[],[f1939])).
% 5.57/1.07 thf(f2050,plain,(
% 5.57/1.07 ( ! [X0 : $i] : (($true = $false) | ($false = ((in @ (sK4 @ sK0 @ sK2 @ sK1) @ X0))) | ($false = ((in @ sK2 @ (funcSet @ X0 @ sK1))))) ) | (~spl6_2 | ~spl6_13)),
% 5.57/1.07 inference(forward_demodulation,[],[f2049,f109])).
% 5.57/1.07 thf(f2051,plain,(
% 5.57/1.07 ( ! [X0 : $i] : (($false = ((in @ (sK4 @ sK0 @ sK2 @ sK1) @ X0))) | ($false = ((in @ sK2 @ (funcSet @ X0 @ sK1))))) ) | (~spl6_2 | ~spl6_13)),
% 5.57/1.07 inference(trivial_inequality_removal,[],[f2050])).
% 5.57/1.07 thf(f2217,plain,(
% 5.57/1.07 ($true = $false) | (((in @ sK2 @ (funcSet @ sK0 @ sK1))) = $false) | (~spl6_2 | ~spl6_13)),
% 5.57/1.07 inference(constrained_superposition,[],[f109,f2051])).
% 5.57/1.07 thf(f2218,plain,(
% 5.57/1.07 (((in @ sK2 @ (funcSet @ sK0 @ sK1))) = $false) | (~spl6_2 | ~spl6_13)),
% 5.57/1.07 inference(trivial_inequality_removal,[],[f2217])).
% 5.57/1.07 thf(f2224,plain,(
% 5.57/1.07 ($true = $false) | (~spl6_2 | ~spl6_13)),
% 5.57/1.07 inference(constrained_superposition,[],[f2218,f33])).
% 5.57/1.07 thf(f2230,plain,(
% 5.57/1.07 $false | (~spl6_2 | ~spl6_13)),
% 5.57/1.07 inference(trivial_inequality_removal,[],[f2224])).
% 5.57/1.07 thf(f2231,plain,(
% 5.57/1.07 ~spl6_2 | ~spl6_13),
% 5.57/1.07 inference(avatar_contradiction_clause,[],[f2230])).
% 5.57/1.07 cnf(s3, plain, spl6_1 | spl6_2, inference(sat_conversion,[],[f112])).
% 5.57/1.07 cnf(s6, plain, spl6_1 | spl6_3, inference(sat_conversion,[],[f644])).
% 5.57/1.07 cnf(s8, plain, ~spl6_1, inference(sat_conversion,[],[f658])).
% 5.57/1.07 cnf(s18, plain, ~spl6_2 | ~spl6_3 | spl6_12 | spl6_13, inference(sat_conversion,[],[f1221])).
% 5.57/1.07 cnf(s24, plain, spl6_1 | ~spl6_12, inference(sat_conversion,[],[f1750])).
% 5.57/1.07 cnf(s37, plain, ~spl6_2 | ~spl6_13, inference(sat_conversion,[],[f2231])).
% 5.57/1.07 cnf(s42, plain, ~spl6_12, inference(rat,[],[s24,s8])).
% 5.57/1.07 cnf(s43, plain, spl6_3, inference(rat,[],[s6,s8])).
% 5.57/1.07 cnf(s44, plain, spl6_2, inference(rat,[],[s3,s8])).
% 5.57/1.07 cnf(s45, plain, ~spl6_13, inference(rat,[],[s37,s44])).
% 5.57/1.07 cnf(s48, plain, $false, inference(rat,[],[s18,s43,s42,s45,s44])).
% 5.57/1.07 thf(f2232,plain,(
% 5.57/1.07 $false),
% 5.57/1.07 inference(avatar_sat_refutation,[],[s48])).
% 5.57/1.07 % SZS output end Proof for theBenchmark
% 5.57/1.07 % (391721)------------------------------
% 5.57/1.07 % (391721)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.57/1.07 % (391721)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.57/1.07 % (391721)CaDiCaL version: 2.1.3
% 5.57/1.07 % (391721)Termination reason: Refutation
% 5.57/1.07 % (391721)Time elapsed: 0.380 s
% 5.57/1.07 % (391721)Peak memory usage: 16 MB
% 5.57/1.07 % (391721)Instructions burned: 846 (million)
% 5.57/1.07 % (391668)Success in time 0.838 s
% 5.57/1.07 % Vampire exiting
%------------------------------------------------------------------------------