%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP112^2 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n008.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 08:10:44 AM UTC 2026
% Result : Theorem 3.03s 0.77s
% Output : Refutation 3.03s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP112^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.20 % Computer : n008.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 19:56:09 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.23 Running first-order model finding
% 0.08/0.23 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
% 3.03/0.77 % (3654315)Will run a generic schedule for satisfiability detection.
% 3.03/0.77 % (3654323)dis+10_1_sil=32000:sp=arity:random_seed=2315231287:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 3.03/0.77 % (3654321)% WARNING: option uhcvi not known.
% 3.03/0.77 % (3654320)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3195315907_2999 on theBenchmark for (2999ds/0Mi)
% 3.03/0.77 % (3654321)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=776951093:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 3.03/0.77 % (3654322)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2064893281:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 3.03/0.77 % (3654324)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1868611614:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 3.03/0.77 % (3654326)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4246703767:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 3.03/0.77 % (3654325)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4166375833:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 3.03/0.77 % (3654323)Instruction limit reached!
% 3.03/0.77 % (3654323)------------------------------
% 3.03/0.77 % (3654323)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.03/0.77 % (3654323)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.03/0.77 % (3654323)CaDiCaL version: 2.1.3
% 3.03/0.77 % (3654323)Termination reason: Instruction limit
% 3.03/0.77 % (3654323)Termination phase: Saturation
% 3.03/0.77 % (3654323)Time elapsed: 0.025 s
% 3.03/0.77 % (3654323)Peak memory usage: 12 MB
% 3.03/0.77 % (3654323)Instructions burned: 105 (million)
% 3.03/0.77 % (3654321)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.03/0.77 % (3654324)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.03/0.77 % (3654334)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3635497486:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 3.03/0.77 % Exception at run slice level
% 3.03/0.77 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.03/0.77 % (3654321)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.03/0.77 % Exception at run slice level
% 3.03/0.77 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.03/0.77 % (3654324)Instruction limit reached!
% 3.03/0.77 % (3654324)------------------------------
% 3.03/0.77 % (3654324)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.03/0.77 % (3654324)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.03/0.77 % (3654324)CaDiCaL version: 2.1.3
% 3.03/0.77 % (3654324)Termination reason: Instruction limit
% 3.03/0.77 % (3654324)Termination phase: Saturation
% 3.03/0.77 % (3654324)Time elapsed: 0.053 s
% 3.03/0.77 % (3654324)Peak memory usage: 13 MB
% 3.03/0.77 % (3654324)Instructions burned: 117 (million)
% 3.03/0.77 % (3654337)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=3655614824:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 3.03/0.77 % (3654337)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.03/0.77 % (3654336)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=109490018:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 3.03/0.77 % (3654326)Instruction limit reached!
% 3.03/0.77 % (3654326)------------------------------
% 3.03/0.77 % (3654326)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.03/0.77 % (3654326)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.03/0.77 % (3654326)CaDiCaL version: 2.1.3
% 3.03/0.77 % (3654326)Termination reason: Instruction limit
% 3.03/0.77 % (3654326)Termination phase: Saturation
% 3.03/0.77 % (3654326)Time elapsed: 0.072 s
% 3.03/0.77 % (3654326)Peak memory usage: 14 MB
% 3.03/0.77 % (3654326)Instructions burned: 159 (million)
% 3.03/0.77 % (3654338)ott-21_1_sil=16000:fs=off:random_seed=2355274427:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 3.03/0.77 % (3654337)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.03/0.77 % (3654341)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=698890958:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 3.03/0.77 % (3654325)Instruction limit reached!
% 3.03/0.77 % (3654325)------------------------------
% 3.03/0.77 % (3654325)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.03/0.77 % (3654325)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.03/0.77 % (3654325)CaDiCaL version: 2.1.3
% 3.03/0.77 % (3654325)Termination reason: Instruction limit
% 3.03/0.77 % (3654325)Termination phase: Saturation
% 3.03/0.77 % (3654325)Time elapsed: 0.106 s
% 3.03/0.77 % (3654325)Peak memory usage: 13 MB
% 3.03/0.77 % (3654325)Instructions burned: 131 (million)
% 3.03/0.77 % (3654336)Instruction limit reached!
% 3.03/0.77 % (3654336)------------------------------
% 3.03/0.77 % (3654336)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.03/0.77 % (3654336)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.03/0.77 % (3654336)CaDiCaL version: 2.1.3
% 3.03/0.77 % (3654336)Termination reason: Instruction limit
% 3.03/0.77 % (3654336)Termination phase: Saturation
% 3.03/0.77 % (3654336)Time elapsed: 0.066 s
% 3.03/0.77 % (3654336)Peak memory usage: 13 MB
% 3.03/0.77 % (3654336)Instructions burned: 132 (million)
% 3.03/0.77 % (3654344)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=393762060:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 3.03/0.77 % (3654346)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=1420339638:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 3.03/0.77 % (3654338)Instruction limit reached!
% 3.03/0.77 % (3654338)------------------------------
% 3.03/0.77 % (3654338)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.03/0.77 % (3654338)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.03/0.77 % (3654338)CaDiCaL version: 2.1.3
% 3.03/0.77 % (3654338)Termination reason: Instruction limit
% 3.03/0.77 % (3654338)Termination phase: Saturation
% 3.03/0.77 % (3654338)Time elapsed: 0.102 s
% 3.03/0.77 % (3654338)Peak memory usage: 13 MB
% 3.03/0.77 % (3654338)Instructions burned: 186 (million)
% 3.03/0.77 % (3654348)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=3940451570:i=889:ins=1_2997 on theBenchmark for (2997ds/889Mi)
% 3.03/0.77 % Exception at run slice level
% 3.03/0.77 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.03/0.77 % (3654337)Instruction limit reached!
% 3.03/0.77 % (3654337)------------------------------
% 3.03/0.77 % (3654337)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.03/0.77 % (3654337)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.03/0.77 % (3654337)CaDiCaL version: 2.1.3
% 3.03/0.77 % (3654337)Termination reason: Instruction limit
% 3.03/0.77 % (3654337)Termination phase: Saturation
% 3.03/0.77 % (3654337)Time elapsed: 0.177 s
% 3.03/0.77 % (3654337)Peak memory usage: 16 MB
% 3.03/0.77 % (3654337)Instructions burned: 688 (million)
% 3.03/0.77 % (3654350)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=3986532633:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2997 on theBenchmark for (2997ds/692Mi)
% 3.03/0.77 % (3654351)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=476839541:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 3.03/0.77 % Exception at run slice level
% 3.03/0.77 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.03/0.77 % (3654351)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.03/0.77 % (3654354)fmb+10_1_sil=64000:random_seed=4099736731:i=22061:nm=2:gsp=on_2996 on theBenchmark for (2996ds/22061Mi)
% 3.03/0.77 % (3654350)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.03/0.77 % (3654354)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.03/0.77 % (3654341)Instruction limit reached!
% 3.03/0.77 % (3654341)------------------------------
% 3.03/0.77 % (3654341)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.03/0.77 % (3654341)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.03/0.77 % (3654341)CaDiCaL version: 2.1.3
% 3.03/0.77 % (3654341)Termination reason: Instruction limit
% 3.03/0.77 % (3654341)Termination phase: Saturation
% 3.03/0.77 % (3654341)Time elapsed: 0.247 s
% 3.03/0.77 % (3654341)Peak memory usage: 14 MB
% 3.03/0.77 % (3654341)Instructions burned: 478 (million)
% 3.03/0.77 % Exception at run slice level
% 3.03/0.77 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.03/0.77 % (3654356)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=2689718959:i=9515:nm=5_2995 on theBenchmark for (2995ds/9515Mi)
% 3.03/0.77 % (3654357)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=1484487742:fmbsr=1.7:i=920_2995 on theBenchmark for (2995ds/920Mi)
% 3.03/0.77 % Exception at run slice level
% 3.03/0.77 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.03/0.77 % (3654360)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=1596885371:i=5131_2995 on theBenchmark for (2995ds/5131Mi)
% 3.03/0.77 % Exception at run slice level
% 3.03/0.77 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.03/0.77 % (3654360)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.03/0.77 % (3654362)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=124063574:i=1472:ins=7:fdi=8:gsp=on_2995 on theBenchmark for (2995ds/1472Mi)
% 3.03/0.77 % (3654350) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3654315-3654350"...
% 3.03/0.77 % (3654350)...printing done.
% 3.03/0.77 % (3654351)Instruction limit reached!
% 3.03/0.77 % (3654351)------------------------------
% 3.03/0.77 % (3654351)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.03/0.77 % (3654351)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.03/0.77 % (3654351)CaDiCaL version: 2.1.3
% 3.03/0.77 % (3654351)Termination reason: Instruction limit
% 3.03/0.77 % (3654351)Termination phase: Saturation
% 3.03/0.77 % (3654351)Time elapsed: 0.222 s
% 3.03/0.77 % (3654351)Peak memory usage: 20 MB
% 3.03/0.77 % (3654351)Instructions burned: 879 (million)
% 3.03/0.77 % (3654350)Refutation found. Thanks to Tanya!
% 3.03/0.77 % SZS status Theorem for theBenchmark
% 3.03/0.77 % SZS output start Proof for theBenchmark
% 3.03/0.77 thf(type_def_5, type, extended_ereal: $tType).
% 3.03/0.77 thf(type_def_6, type, filter: $tType > $tType).
% 3.03/0.77 thf(type_def_7, type, real: $tType).
% 3.03/0.77 thf(type_def_8, type, set: $tType > $tType).
% 3.03/0.77 thf(type_def_9, type, nat: $tType).
% 3.03/0.77 thf(type_def_10, type, int: $tType).
% 3.03/0.77 thf(type_def_11, type, a: $tType).
% 3.03/0.77 thf(type_def_12, type, sTfun: ($tType * $tType) > $tType).
% 3.03/0.77 thf(func_def_0, type, finite_finite: !>[X0: $tType]:($o)).
% 3.03/0.77 thf(func_def_1, type, type: !>[X0: $tType]:($o)).
% 3.03/0.77 thf(func_def_2, type, countable: !>[X0: $tType]:($o)).
% 3.03/0.77 thf(func_def_3, type, uminus: !>[X0: $tType]:($o)).
% 3.03/0.77 thf(func_def_4, type, ord: !>[X0: $tType]:($o)).
% 3.03/0.77 thf(func_def_5, type, order: !>[X0: $tType]:($o)).
% 3.03/0.77 thf(func_def_6, type, group_add: !>[X0: $tType]:($o)).
% 3.03/0.77 thf(func_def_7, type, linorder: !>[X0: $tType]:($o)).
% 3.03/0.77 thf(func_def_8, type, preorder: !>[X0: $tType]:($o)).
% 3.03/0.77 thf(func_def_9, type, ab_group_add: !>[X0: $tType]:($o)).
% 3.03/0.77 thf(func_def_10, type, semigroup_add: !>[X0: $tType]:($o)).
% 3.03/0.77 thf(func_def_11, type, comm_monoid_add: !>[X0: $tType]:($o)).
% 3.03/0.77 thf(func_def_12, type, ab_semigroup_add: !>[X0: $tType]:($o)).
% 3.03/0.77 thf(func_def_13, type, boolean_algebra: !>[X0: $tType]:($o)).
% 3.03/0.77 thf(func_def_14, type, cancel_semigroup_add: !>[X0: $tType]:($o)).
% 3.03/0.77 thf(func_def_15, type, ordered_ab_group_add: !>[X0: $tType]:($o)).
% 3.03/0.77 thf(func_def_16, type, topological_t2_space: !>[X0: $tType]:($o)).
% 3.03/0.77 thf(func_def_17, type, topolo799126099up_add: !>[X0: $tType]:($o)).
% 3.03/0.77 thf(func_def_18, type, topolo1314133330id_add: !>[X0: $tType]:($o)).
% 3.03/0.77 thf(func_def_19, type, ordere779506340up_add: !>[X0: $tType]:($o)).
% 3.03/0.77 thf(func_def_20, type, real_V2090557954_space: !>[X0: $tType]:($o)).
% 3.03/0.77 thf(func_def_21, type, topolo47006728_space: !>[X0: $tType]:($o)).
% 3.03/0.77 thf(func_def_22, type, linord1659791738miring: !>[X0: $tType]:($o)).
% 3.03/0.77 thf(func_def_23, type, topolo259154727pology: !>[X0: $tType]:($o)).
% 3.03/0.77 thf(func_def_24, type, comple187826305attice: !>[X0: $tType]:($o)).
% 3.03/0.77 thf(func_def_25, type, comple1035589618norder: !>[X0: $tType]:($o)).
% 3.03/0.77 thf(func_def_26, type, topolo2117631714pology: !>[X0: $tType]:($o)).
% 3.03/0.77 thf(func_def_27, type, topolo503727757_space: !>[X0: $tType]:($o)).
% 3.03/0.77 thf(func_def_28, type, canoni770627133id_add: !>[X0: $tType]:($o)).
% 3.03/0.78 thf(func_def_29, type, real_V55928688vector: !>[X0: $tType]:($o)).
% 3.03/0.78 thf(func_def_30, type, ordere236663937imp_le: !>[X0: $tType]:($o)).
% 3.03/0.78 thf(func_def_31, type, topolo2135403230pology: !>[X0: $tType]:($o)).
% 3.03/0.78 thf(func_def_32, type, extend1396239628finity: !>[X0: $tType]:(X0)).
% 3.03/0.78 thf(func_def_33, type, extended_case_ereal: !>[X0: $tType]:(((real > X0) > X0 > X0 > extended_ereal > X0))).
% 3.03/0.78 thf(func_def_34, type, extended_ereal2: (real > extended_ereal)).
% 3.03/0.78 thf(func_def_35, type, at_bot: !>[X0: $tType]:(filter @ X0)).
% 3.03/0.78 thf(func_def_36, type, at_top: !>[X0: $tType]:(filter @ X0)).
% 3.03/0.78 thf(func_def_37, type, filterlim: !>[X0: $tType, X1: $tType]:(((X0 > X1) > filter @ X1 > filter @ X0 > $o))).
% 3.03/0.78 thf(func_def_38, type, comp: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1) > (X2 > X0) > X2 > X1))).
% 3.03/0.78 thf(func_def_39, type, plus_plus: !>[X0: $tType]:((X0 > X0 > X0))).
% 3.03/0.78 thf(func_def_40, type, uminus_uminus: !>[X0: $tType]:((X0 > X0))).
% 3.03/0.78 thf(func_def_41, type, ex1: !>[X0: $tType]:(((X0 > $o) > $o))).
% 3.03/0.78 thf(func_def_42, type, uniq: !>[X0: $tType]:(((X0 > $o) > $o))).
% 3.03/0.78 thf(func_def_43, type, liminf_Liminf: !>[X0: $tType, X1: $tType]:((filter @ X0 > (X0 > X1) > X1))).
% 3.03/0.78 thf(func_def_44, type, lower_582600101lsc_at: !>[X0: $tType, X1: $tType]:((X0 > (X0 > X1) > $o))).
% 3.03/0.78 thf(func_def_45, type, lower_708585518usc_at: !>[X0: $tType, X1: $tType]:((X0 > (X0 > X1) > $o))).
% 3.03/0.78 thf(func_def_46, type, semiring_1_of_nat: !>[X0: $tType]:((nat > X0))).
% 3.03/0.78 thf(func_def_47, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 3.03/0.78 thf(func_def_48, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 3.03/0.78 thf(func_def_49, type, topological_monoseq: !>[X0: $tType]:(((nat > X0) > $o))).
% 3.03/0.78 thf(func_def_50, type, topolo1920029354e_nhds: !>[X0: $tType]:((X0 > filter @ X0))).
% 3.03/0.78 thf(func_def_51, type, topolo1334162427filter: !>[X0: $tType]:((filter @ X0 > $o))).
% 3.03/0.78 thf(func_def_52, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 3.03/0.78 thf(func_def_53, type, a2: extended_ereal).
% 3.03/0.78 thf(func_def_54, type, f: (a > extended_ereal)).
% 3.03/0.78 thf(func_def_55, type, x0: a).
% 3.03/0.78 thf(func_def_56, type, x: (nat > a)).
% 3.03/0.78 thf(func_def_60, type, db0: !>[X0: $tType]:(X0)).
% 3.03/0.78 thf(func_def_61, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 3.03/0.78 thf(func_def_62, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 3.03/0.78 thf(func_def_63, type, db2: !>[X0: $tType]:(X0)).
% 3.03/0.78 thf(func_def_64, type, db1: !>[X0: $tType]:(X0)).
% 3.03/0.78 thf(func_def_65, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 3.03/0.78 thf(func_def_66, type, vIMP: ($o > $o > $o)).
% 3.03/0.78 thf(func_def_67, type, vAND: ($o > $o > $o)).
% 3.03/0.78 thf(func_def_68, type, db4: !>[X0: $tType]:(X0)).
% 3.03/0.78 thf(func_def_69, type, db3: !>[X0: $tType]:(X0)).
% 3.03/0.78 thf(func_def_70, type, vOR: ($o > $o > $o)).
% 3.03/0.78 thf(func_def_71, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 3.03/0.78 thf(func_def_72, type, vNOT: ($o > $o)).
% 3.03/0.78 thf(func_def_73, type, sP0: !>[X0: $tType]:((X0 > (nat > X0) > $o))).
% 3.03/0.78 thf(func_def_74, type, sP1: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 3.03/0.78 thf(func_def_75, type, sP2: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 3.03/0.78 thf(func_def_76, type, sP3: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 3.03/0.78 thf(func_def_77, type, sP4: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 3.03/0.78 thf(func_def_78, type, sP5: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 3.03/0.78 thf(func_def_79, type, sP6: !>[X0: $tType]:(((X0 > X0 > $o) > $o))).
% 3.03/0.78 thf(func_def_80, type, sP7: !>[X0: $tType]:(((X0 > $o) > $o))).
% 3.03/0.78 thf(func_def_81, type, sP8: !>[X0: $tType]:(((X0 > $o) > $o))).
% 3.03/0.78 thf(func_def_82, type, sP9: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 3.03/0.78 thf(func_def_83, type, sP10: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 3.03/0.78 thf(func_def_84, type, sP11: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 3.03/0.78 thf(func_def_85, type, sP12: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 3.03/0.78 thf(func_def_86, type, sP13: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 3.03/0.78 thf(func_def_87, type, sP14: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 3.03/0.78 thf(func_def_88, type, sP15: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 3.03/0.78 thf(func_def_89, type, sP16: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 3.03/0.78 thf(func_def_90, type, sP17: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 3.03/0.78 thf(func_def_91, type, sP18: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 3.03/0.78 thf(func_def_92, type, sP19: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 3.03/0.78 thf(func_def_93, type, sP20: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 3.03/0.78 thf(func_def_94, type, sP21: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 3.03/0.78 thf(func_def_95, type, sP22: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 3.03/0.78 thf(func_def_96, type, sP23: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 3.03/0.78 thf(func_def_97, type, sP24: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 3.03/0.78 thf(func_def_98, type, sP25: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 3.03/0.78 thf(func_def_99, type, sP26: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 3.03/0.78 thf(func_def_100, type, sP27: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 3.03/0.78 thf(func_def_101, type, sP28: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 3.03/0.78 thf(func_def_102, type, sP29: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 3.03/0.78 thf(func_def_103, type, sP30: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 3.03/0.78 thf(func_def_104, type, sP31: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 3.03/0.78 thf(func_def_105, type, sP32: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 3.03/0.78 thf(func_def_106, type, sP33: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 3.03/0.78 thf(func_def_107, type, sP34: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 3.03/0.78 thf(func_def_108, type, sP35: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 3.03/0.78 thf(func_def_109, type, sP36: (extended_ereal > extended_ereal > $o)).
% 3.03/0.78 thf(func_def_110, type, sP37: (extended_ereal > extended_ereal > $o)).
% 3.03/0.78 thf(func_def_111, type, sP38: (extended_ereal > extended_ereal > $o)).
% 3.03/0.78 thf(func_def_112, type, sP39: (extended_ereal > extended_ereal > $o)).
% 3.03/0.78 thf(func_def_113, type, sP40: (extended_ereal > extended_ereal > $o)).
% 3.03/0.78 thf(func_def_114, type, sP41: (extended_ereal > extended_ereal > $o)).
% 3.03/0.78 thf(func_def_115, type, sP42: (extended_ereal > extended_ereal > $o)).
% 3.03/0.78 thf(func_def_116, type, sP43: (extended_ereal > extended_ereal > $o)).
% 3.03/0.78 thf(func_def_117, type, sP44: (extended_ereal > extended_ereal > $o)).
% 3.03/0.78 thf(func_def_118, type, sP45: ((nat > extended_ereal) > (nat > extended_ereal) > $o)).
% 3.03/0.78 thf(func_def_119, type, sP46: ((nat > $o) > nat > $o)).
% 3.03/0.78 thf(func_def_120, type, sP47: (extended_ereal > real > extended_ereal > $o)).
% 3.03/0.78 thf(func_def_121, type, sP48: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 3.03/0.78 thf(func_def_122, type, sP49: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 3.03/0.78 thf(func_def_123, type, sP50: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 3.03/0.78 thf(func_def_124, type, sP51: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 3.03/0.78 thf(func_def_125, type, sP52: (extended_ereal > extended_ereal > $o)).
% 3.03/0.78 thf(func_def_126, type, sK53: !>[X0: $tType]:(((nat > extended_ereal) > (nat > X0) > (X0 > extended_ereal) > nat))).
% 3.03/0.78 thf(func_def_127, type, sK54: (set @ extended_ereal > extended_ereal)).
% 3.03/0.78 thf(func_def_128, type, sK55: (extended_ereal > set @ extended_ereal > extended_ereal)).
% 3.03/0.78 thf(func_def_129, type, sK56: (set @ extended_ereal > extended_ereal)).
% 3.03/0.78 thf(func_def_130, type, sK57: (extended_ereal > set @ extended_ereal > extended_ereal)).
% 3.03/0.78 thf(func_def_131, type, sK58: !>[X0: $tType]:(((nat > X0) > (nat > X0) > nat > nat))).
% 3.03/0.78 thf(func_def_132, type, sK59: !>[X0: $tType]:((nat > (nat > X0) > (nat > X0) > nat))).
% 3.03/0.78 thf(func_def_133, type, sK60: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 3.03/0.78 thf(func_def_134, type, sK61: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 3.03/0.78 thf(func_def_135, type, sK62: !>[X0: $tType]:((X0 > nat > (nat > X0) > nat))).
% 3.03/0.78 thf(func_def_136, type, sK63: !>[X0: $tType]:((X0 > nat > (nat > X0) > nat))).
% 3.03/0.78 thf(func_def_137, type, sK64: !>[X0: $tType]:((nat > X0 > (nat > X0) > nat))).
% 3.03/0.78 thf(func_def_138, type, sK65: !>[X0: $tType]:((nat > X0 > (nat > X0) > nat))).
% 3.03/0.78 thf(func_def_139, type, sK66: !>[X0: $tType]:(((nat > X0) > X0))).
% 3.03/0.78 thf(func_def_140, type, sK67: !>[X0: $tType]:(((nat > X0) > nat))).
% 3.03/0.78 thf(func_def_141, type, sK68: !>[X0: $tType]:(((nat > X0) > nat))).
% 3.03/0.78 thf(func_def_142, type, sK69: !>[X0: $tType]:(((nat > X0) > X0))).
% 3.03/0.78 thf(func_def_143, type, sK70: !>[X0: $tType]:(((nat > X0) > nat))).
% 3.03/0.78 thf(func_def_144, type, sK71: !>[X0: $tType]:(((nat > X0) > nat))).
% 3.03/0.78 thf(func_def_145, type, sK72: !>[X0: $tType]:(((nat > X0) > nat))).
% 3.03/0.78 thf(func_def_146, type, sK73: !>[X0: $tType]:(((nat > X0) > nat))).
% 3.03/0.78 thf(func_def_147, type, sK74: !>[X0: $tType]:(((nat > X0) > nat))).
% 3.03/0.78 thf(func_def_148, type, sK75: !>[X0: $tType]:(((nat > X0) > nat))).
% 3.03/0.78 thf(func_def_149, type, sK76: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 3.03/0.78 thf(func_def_150, type, sK77: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 3.03/0.78 thf(func_def_151, type, sK78: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 3.03/0.78 thf(func_def_152, type, sK79: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 3.03/0.78 thf(func_def_153, type, sK80: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 3.03/0.78 thf(func_def_154, type, sK81: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 3.03/0.78 thf(func_def_155, type, sK82: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 3.03/0.78 thf(func_def_156, type, sK83: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 3.03/0.78 thf(func_def_157, type, sK84: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 3.03/0.78 thf(func_def_158, type, sK85: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 3.03/0.78 thf(func_def_159, type, sK86: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 3.03/0.78 thf(func_def_160, type, sK87: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 3.03/0.78 thf(func_def_161, type, sK88: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 3.03/0.78 thf(func_def_162, type, sK89: !>[X0: $tType]:((X0 > (X0 > $o) > X0))).
% 3.03/0.78 thf(func_def_163, type, sK90: !>[X0: $tType]:(((X0 > $o) > X0))).
% 3.03/0.78 thf(func_def_164, type, sK91: !>[X0: $tType]:(((X0 > $o) > X0))).
% 3.03/0.78 thf(func_def_165, type, sK92: !>[X0: $tType]:(((X0 > $o) > X0))).
% 3.03/0.78 thf(func_def_166, type, sK93: (real > (nat > extended_ereal) > nat)).
% 3.03/0.78 thf(func_def_167, type, sK94: (real > nat > (nat > extended_ereal) > nat)).
% 3.03/0.78 thf(func_def_168, type, sK95: (extended_ereal > extended_ereal > real)).
% 3.03/0.78 thf(func_def_169, type, sK96: ((extended_ereal > $o) > real)).
% 3.03/0.78 thf(func_def_170, type, sK97: (extended_ereal > real)).
% 3.03/0.78 thf(func_def_171, type, sK98: ((extended_ereal > extended_ereal > $o) > real)).
% 3.03/0.78 thf(func_def_172, type, sK99: ((extended_ereal > extended_ereal > $o) > real)).
% 3.03/0.78 thf(func_def_173, type, sK100: ((extended_ereal > extended_ereal > $o) > real)).
% 3.03/0.78 thf(func_def_174, type, sK101: ((extended_ereal > extended_ereal > $o) > real)).
% 3.03/0.78 thf(func_def_175, type, sK102: ((extended_ereal > extended_ereal > $o) > real)).
% 3.03/0.78 thf(func_def_176, type, sK103: ((extended_ereal > extended_ereal > $o) > real)).
% 3.03/0.78 thf(func_def_177, type, sK104: ((extended_ereal > extended_ereal > $o) > real)).
% 3.03/0.78 thf(func_def_178, type, sK105: ((extended_ereal > extended_ereal > $o) > real)).
% 3.03/0.78 thf(func_def_179, type, sK106: ((extended_ereal > extended_ereal > $o) > extended_ereal)).
% 3.03/0.78 thf(func_def_180, type, sK107: ((extended_ereal > extended_ereal > $o) > extended_ereal)).
% 3.03/0.78 thf(func_def_181, type, sK108: ((extended_ereal > extended_ereal > $o) > real)).
% 3.03/0.78 thf(func_def_182, type, sK109: ((extended_ereal > extended_ereal > $o) > real)).
% 3.03/0.78 thf(func_def_183, type, sK110: ((extended_ereal > extended_ereal > $o) > real)).
% 3.03/0.78 thf(func_def_184, type, sK111: ((extended_ereal > extended_ereal > $o) > real)).
% 3.03/0.78 thf(func_def_185, type, sK112: ((extended_ereal > extended_ereal > $o) > extended_ereal)).
% 3.03/0.78 thf(func_def_186, type, sK113: ((extended_ereal > extended_ereal > $o) > extended_ereal)).
% 3.03/0.78 thf(func_def_187, type, sK114: ((extended_ereal > extended_ereal > $o) > real)).
% 3.03/0.78 thf(func_def_188, type, sK115: ((extended_ereal > extended_ereal > $o) > real)).
% 3.03/0.78 thf(func_def_189, type, sK116: ((extended_ereal > $o) > real)).
% 3.03/0.78 thf(func_def_190, type, sK117: (extended_ereal > real)).
% 3.03/0.78 thf(func_def_191, type, sK118: (extended_ereal > real)).
% 3.03/0.78 thf(func_def_192, type, sK119: (extended_ereal > real)).
% 3.03/0.78 thf(func_def_193, type, sK120: (extended_ereal > real)).
% 3.03/0.78 thf(func_def_194, type, sK121: (extended_ereal > real)).
% 3.03/0.78 thf(func_def_195, type, sK122: (extended_ereal > real)).
% 3.03/0.78 thf(func_def_196, type, sK123: (extended_ereal > real)).
% 3.03/0.78 thf(func_def_197, type, sK124: (extended_ereal > real)).
% 3.03/0.78 thf(func_def_198, type, sK125: (extended_ereal > real)).
% 3.03/0.78 thf(func_def_199, type, sK126: (extended_ereal > real)).
% 3.03/0.78 thf(func_def_200, type, sK127: (extended_ereal > real)).
% 3.03/0.78 thf(func_def_201, type, sK128: (extended_ereal > real)).
% 3.03/0.78 thf(func_def_202, type, sK129: (extended_ereal > real)).
% 3.03/0.78 thf(func_def_203, type, sK130: (extended_ereal > real)).
% 3.03/0.78 thf(func_def_204, type, sK131: (extended_ereal > real)).
% 3.03/0.78 thf(func_def_205, type, sK132: (extended_ereal > real)).
% 3.03/0.78 thf(func_def_206, type, sK133: (extended_ereal > real)).
% 3.03/0.78 thf(func_def_207, type, sK134: (extended_ereal > real)).
% 3.03/0.78 thf(func_def_208, type, sK135: (extended_ereal > real)).
% 3.03/0.78 thf(func_def_209, type, sK136: (extended_ereal > real)).
% 3.03/0.78 thf(func_def_210, type, sK137: (extended_ereal > real)).
% 3.03/0.78 thf(func_def_211, type, sK138: (extended_ereal > real)).
% 3.03/0.78 thf(func_def_212, type, sK139: (extended_ereal > real)).
% 3.03/0.78 thf(func_def_213, type, sK140: (extended_ereal > real)).
% 3.03/0.78 thf(func_def_214, type, sK141: (extended_ereal > real)).
% 3.03/0.78 thf(func_def_215, type, sK142: (extended_ereal > real)).
% 3.03/0.78 thf(func_def_216, type, sK143: (extended_ereal > real)).
% 3.03/0.78 thf(func_def_217, type, sK144: (extended_ereal > real)).
% 3.03/0.78 thf(func_def_218, type, sK145: (extended_ereal > real)).
% 3.03/0.78 thf(func_def_219, type, sK146: (extended_ereal > real)).
% 3.03/0.78 thf(func_def_220, type, sK147: (extended_ereal > real)).
% 3.03/0.78 thf(func_def_221, type, sK148: (extended_ereal > real)).
% 3.03/0.78 thf(func_def_222, type, sK149: (extended_ereal > real)).
% 3.03/0.78 thf(func_def_223, type, sK150: (extended_ereal > real)).
% 3.03/0.78 thf(func_def_224, type, sK151: (extended_ereal > real)).
% 3.03/0.78 thf(func_def_225, type, sK152: (extended_ereal > real)).
% 3.03/0.78 thf(func_def_226, type, sK153: (extended_ereal > real)).
% 3.03/0.78 thf(func_def_227, type, sK154: (real > (nat > extended_ereal) > nat)).
% 3.03/0.78 thf(func_def_228, type, sK155: !>[X0: $tType]:((X0 > X0 > X0))).
% 3.03/0.78 thf(func_def_229, type, sK156: !>[X0: $tType]:((X0 > (real > X0) > nat > real))).
% 3.03/0.78 thf(func_def_230, type, sK157: (nat > nat > nat)).
% 3.03/0.78 thf(func_def_231, type, sK158: ((nat > $o) > nat > nat)).
% 3.03/0.78 thf(func_def_232, type, sK159: ((nat > $o) > nat)).
% 3.03/0.78 thf(func_def_233, type, sK160: (extended_ereal > extended_ereal > extended_ereal > real)).
% 3.03/0.78 thf(func_def_234, type, sK161: (extended_ereal > real)).
% 3.03/0.78 thf(func_def_235, type, sK162: (extended_ereal > real)).
% 3.03/0.78 thf(func_def_236, type, sK163: (extended_ereal > real > extended_ereal > real)).
% 3.03/0.78 thf(func_def_237, type, sK164: !>[X0: $tType]:((X0 > (real > X0) > nat > real))).
% 3.03/0.78 thf(func_def_238, type, sK165: (real > (nat > extended_ereal) > nat)).
% 3.03/0.78 thf(func_def_239, type, sK166: ((nat > extended_ereal) > real)).
% 3.03/0.78 thf(func_def_240, type, sK167: (nat > (nat > extended_ereal) > nat)).
% 3.03/0.78 thf(func_def_241, type, sK168: (real > (nat > extended_ereal) > nat)).
% 3.03/0.78 thf(func_def_242, type, sK169: ((nat > extended_ereal) > real)).
% 3.03/0.78 thf(func_def_243, type, sK170: (nat > (nat > extended_ereal) > nat)).
% 3.03/0.78 thf(func_def_244, type, sK171: !>[X0: $tType]:(((X0 > $o) > X0))).
% 3.03/0.78 thf(func_def_245, type, sK172: !>[X0: $tType]:(((X0 > $o) > X0))).
% 3.03/0.78 thf(f2,axiom,(
% 3.03/0.78 (filterlim @ nat @ extended_ereal @ (comp @ a @ extended_ereal @ nat @ f @ x) @ (topolo1920029354e_nhds @ extended_ereal @ a2) @ at_top @ nat)),
% 3.03/0.78 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_x__def_I2_J)).
% 3.03/0.78 thf(f5,axiom,(
% 3.03/0.78 ! [X0 : $tType,X1 : (X0 > extended_ereal),X2 : extended_ereal,X3 : filter @ X0] : ((filterlim @ X0 @ extended_ereal @ X1 @ (topolo1920029354e_nhds @ extended_ereal @ X2) @ X3) => (filterlim @ X0 @ extended_ereal @ (^[X4 : X0] : ((uminus_uminus @ extended_ereal @ (X1 @ X4)))) @ (topolo1920029354e_nhds @ extended_ereal @ (uminus_uminus @ extended_ereal @ X2)) @ X3))),
% 3.03/0.78 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_tendsto__uminus__ereal)).
% 3.03/0.78 thf(f21,axiom,(
% 3.03/0.78 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (comp @ X2 @ X1 @ X0 = (^[X3 : (X2 > X1), X4 : (X0 > X2), X5 : X0] : ((X3 @ (X4 @ X5)))))),
% 3.03/0.78 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_comp__apply)).
% 3.03/0.78 thf(f382,conjecture,(
% 3.03/0.78 (filterlim @ nat @ extended_ereal @ (^[X0 : nat] : ((uminus_uminus @ extended_ereal @ (f @ (x @ X0))))) @ (topolo1920029354e_nhds @ extended_ereal @ (uminus_uminus @ extended_ereal @ a2)) @ at_top @ nat)),
% 3.03/0.78 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 3.03/0.78 thf(f383,negated_conjecture,(
% 3.03/0.78 ~(filterlim @ nat @ extended_ereal @ (^[X0 : nat] : ((uminus_uminus @ extended_ereal @ (f @ (x @ X0))))) @ (topolo1920029354e_nhds @ extended_ereal @ (uminus_uminus @ extended_ereal @ a2)) @ at_top @ nat)),
% 3.03/0.78 inference(negated_conjecture,[status(cth)],[f382])).
% 3.03/0.78 thf(f386,plain,(
% 3.03/0.78 (filterlim @ nat @ extended_ereal @ (comp @ a @ extended_ereal @ nat @ f @ x) @ (topolo1920029354e_nhds @ extended_ereal @ a2) @ at_top @ nat)),
% 3.03/0.78 inference(rectify,[],[f2])).
% 3.03/0.78 thf(f387,plain,(
% 3.03/0.78 (((filterlim @ nat @ extended_ereal @ (comp @ a @ extended_ereal @ nat @ f @ x) @ (topolo1920029354e_nhds @ extended_ereal @ a2) @ at_top @ nat)) = $true)),
% 3.03/0.78 inference(fool_elimination,[],[f386])).
% 3.03/0.78 thf(f392,plain,(
% 3.03/0.78 ! [X0 : $tType,X1 : (X0 > extended_ereal),X2 : extended_ereal,X3 : filter @ X0] : ((filterlim @ X0 @ extended_ereal @ X1 @ (topolo1920029354e_nhds @ extended_ereal @ X2) @ X3) => (filterlim @ X0 @ extended_ereal @ (^[X4 : X0] : ((uminus_uminus @ extended_ereal @ (X1 @ X4)))) @ (topolo1920029354e_nhds @ extended_ereal @ (uminus_uminus @ extended_ereal @ X2)) @ X3))),
% 3.03/0.78 inference(rectify,[],[f5])).
% 3.03/0.78 thf(f393,plain,(
% 3.03/0.78 ! [X0 : $tType,X1 : (X0 > extended_ereal),X2 : extended_ereal,X3 : filter @ X0] : ((((filterlim @ X0 @ extended_ereal @ X1 @ (topolo1920029354e_nhds @ extended_ereal @ X2) @ X3)) = $true) => ($true = ((filterlim @ X0 @ extended_ereal @ (^[Y0 : X0]: (uminus_uminus @ extended_ereal @ (X1 @ Y0))) @ (topolo1920029354e_nhds @ extended_ereal @ (uminus_uminus @ extended_ereal @ X2)) @ X3))))),
% 3.03/0.78 inference(fool_elimination,[],[f392])).
% 3.03/0.78 thf(f420,plain,(
% 3.03/0.78 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (comp @ X2 @ X1 @ X0 = (^[Y0 : X2 > X1]: ((^[Y1 : X0 > X2]: ((^[Y2 : X0]: (Y0 @ (Y1 @ Y2))))))))),
% 3.03/0.78 inference(fool_elimination,[],[f21])).
% 3.03/0.78 thf(f1054,plain,(
% 3.03/0.78 ~(filterlim @ nat @ extended_ereal @ (^[X0 : nat] : ((uminus_uminus @ extended_ereal @ (f @ (x @ X0))))) @ (topolo1920029354e_nhds @ extended_ereal @ (uminus_uminus @ extended_ereal @ a2)) @ at_top @ nat)),
% 3.03/0.78 inference(rectify,[],[f383])).
% 3.03/0.78 thf(f1055,plain,(
% 3.03/0.78 ~ ($true = ((filterlim @ nat @ extended_ereal @ (^[Y0 : nat]: (uminus_uminus @ extended_ereal @ (f @ (x @ Y0)))) @ (topolo1920029354e_nhds @ extended_ereal @ (uminus_uminus @ extended_ereal @ a2)) @ at_top @ nat)))),
% 3.03/0.78 inference(fool_elimination,[],[f1054])).
% 3.03/0.78 thf(f1066,plain,(
% 3.03/0.78 ($true != ((filterlim @ nat @ extended_ereal @ (^[Y0 : nat]: (uminus_uminus @ extended_ereal @ (f @ (x @ Y0)))) @ (topolo1920029354e_nhds @ extended_ereal @ (uminus_uminus @ extended_ereal @ a2)) @ at_top @ nat)))),
% 3.03/0.78 inference(flattening,[],[f1055])).
% 3.03/0.78 thf(f1068,plain,(
% 3.03/0.78 ! [X0 : $tType,X1 : (X0 > extended_ereal),X2 : extended_ereal,X3 : filter @ X0] : (($true = ((filterlim @ X0 @ extended_ereal @ (^[Y0 : X0]: (uminus_uminus @ extended_ereal @ (X1 @ Y0))) @ (topolo1920029354e_nhds @ extended_ereal @ (uminus_uminus @ extended_ereal @ X2)) @ X3))) | (((filterlim @ X0 @ extended_ereal @ X1 @ (topolo1920029354e_nhds @ extended_ereal @ X2) @ X3)) != $true))),
% 3.03/0.78 inference(ennf_transformation,[],[f393])).
% 3.03/0.78 thf(f1594,plain,(
% 3.03/0.78 (((filterlim @ nat @ extended_ereal @ (comp @ a @ extended_ereal @ nat @ f @ x) @ (topolo1920029354e_nhds @ extended_ereal @ a2) @ at_top @ nat)) = $true)),
% 3.03/0.78 inference(cnf_transformation,[],[f387])).
% 3.03/0.78 thf(f1597,plain,(
% 3.03/0.78 ( ! [X0 : $tType,X2 : extended_ereal,X3 : filter @ X0,X1 : (X0 > extended_ereal)] : ((((filterlim @ X0 @ extended_ereal @ X1 @ (topolo1920029354e_nhds @ extended_ereal @ X2) @ X3)) != $true) | ($true = ((filterlim @ X0 @ extended_ereal @ (^[Y0 : X0]: (uminus_uminus @ extended_ereal @ (X1 @ Y0))) @ (topolo1920029354e_nhds @ extended_ereal @ (uminus_uminus @ extended_ereal @ X2)) @ X3)))) )),
% 3.03/0.78 inference(cnf_transformation,[],[f1068])).
% 3.03/0.78 thf(f1613,plain,(
% 3.03/0.78 ( ! [X1 : $tType,X0 : $tType,X2 : $tType] : ((comp @ X2 @ X1 @ X0 = (^[Y0 : X2 > X1]: ((^[Y1 : X0 > X2]: ((^[Y2 : X0]: (Y0 @ (Y1 @ Y2))))))))) )),
% 3.03/0.78 inference(cnf_transformation,[],[f420])).
% 3.03/0.78 thf(f2143,plain,(
% 3.03/0.78 ($true != ((filterlim @ nat @ extended_ereal @ (^[Y0 : nat]: (uminus_uminus @ extended_ereal @ (f @ (x @ Y0)))) @ (topolo1920029354e_nhds @ extended_ereal @ (uminus_uminus @ extended_ereal @ a2)) @ at_top @ nat)))),
% 3.03/0.78 inference(cnf_transformation,[],[f1066])).
% 3.03/0.78 thf(f2147,plain,(
% 3.03/0.78 ($true = ((filterlim @ nat @ extended_ereal @ ((^[Y0 : a > extended_ereal]: ((^[Y1 : nat > a]: ((^[Y2 : nat]: (Y0 @ (Y1 @ Y2))))))) @ f @ x) @ (topolo1920029354e_nhds @ extended_ereal @ a2) @ at_top @ nat)))),
% 3.03/0.78 inference(definition_unfolding,[],[f1594,f1613])).
% 3.03/0.78 thf(f2595,plain,(
% 3.03/0.78 ($true = ((filterlim @ nat @ extended_ereal @ (^[Y0 : nat]: (f @ (x @ Y0))) @ (topolo1920029354e_nhds @ extended_ereal @ a2) @ at_top @ nat)))),
% 3.03/0.78 inference(beta-eta_normalization,[],[f2147])).
% 3.03/0.78 thf(f5581,plain,(
% 3.03/0.78 ($true != $true) | ($true = ((filterlim @ nat @ extended_ereal @ (^[Y0 : nat]: (uminus_uminus @ extended_ereal @ ((^[Y1 : nat]: (f @ (x @ Y1))) @ Y0))) @ (topolo1920029354e_nhds @ extended_ereal @ (uminus_uminus @ extended_ereal @ a2)) @ at_top @ nat)))),
% 3.03/0.78 inference(constrained_superposition,[],[f1597,f2595])).
% 3.03/0.78 thf(f5585,plain,(
% 3.03/0.78 ($true = ((filterlim @ nat @ extended_ereal @ (^[Y0 : nat]: (uminus_uminus @ extended_ereal @ ((^[Y1 : nat]: (f @ (x @ Y1))) @ Y0))) @ (topolo1920029354e_nhds @ extended_ereal @ (uminus_uminus @ extended_ereal @ a2)) @ at_top @ nat)))),
% 3.03/0.78 inference(trivial_inequality_removal,[],[f5581])).
% 3.03/0.78 thf(f5586,plain,(
% 3.03/0.78 ($true = ((filterlim @ nat @ extended_ereal @ (^[Y0 : nat]: (uminus_uminus @ extended_ereal @ (f @ (x @ Y0)))) @ (topolo1920029354e_nhds @ extended_ereal @ (uminus_uminus @ extended_ereal @ a2)) @ at_top @ nat)))),
% 3.03/0.78 inference(beta-eta_normalization,[],[f5585])).
% 3.03/0.78 thf(f5589,plain,(
% 3.03/0.78 $false),
% 3.03/0.78 inference(forward_subsumption_resolution,[],[f5586,f2143])).
% 3.03/0.78 % SZS output end Proof for theBenchmark
% 3.03/0.78 % (3654350)------------------------------
% 3.03/0.78 % (3654350)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.03/0.78 % (3654350)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.03/0.78 % (3654350)CaDiCaL version: 2.1.3
% 3.03/0.78 % (3654350)Termination reason: Refutation
% 3.03/0.78 % (3654350)Time elapsed: 0.224 s
% 3.03/0.78 % (3654350)Peak memory usage: 17 MB
% 3.03/0.78 % (3654350)Instructions burned: 373 (million)
% 3.03/0.78 % (3654315)Success in time 0.533 s
% 3.03/0.78 % Vampire exiting
%------------------------------------------------------------------------------