%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP147^2 : 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 : n016.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 08:10:53 AM UTC 2026
% Result : Theorem 2.47s 0.60s
% Output : Refutation 2.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP147^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.17 % Computer : n016.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Sep 29 20:05:54 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.20 Running first-order model finding
% 0.08/0.20 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
% 2.47/0.60 % (841217)Will run a generic schedule for satisfiability detection.
% 2.47/0.60 % (841228)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3953267291:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 2.47/0.60 % (841223)% WARNING: option uhcvi not known.
% 2.47/0.60 % (841222)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1736459722_2999 on theBenchmark for (2999ds/0Mi)
% 2.47/0.60 % (841223)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2591796829:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 2.47/0.60 % (841227)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3271122713:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 2.47/0.60 % (841225)dis+10_1_sil=32000:sp=arity:random_seed=446321483:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 2.47/0.60 % (841226)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4224845526:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 2.47/0.60 % (841224)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1534051772:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 2.47/0.60 % (841223)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.47/0.60 % (841226)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.47/0.60 % (841228)Instruction limit reached!
% 2.47/0.60 % (841228)------------------------------
% 2.47/0.60 % (841228)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.47/0.60 % (841228)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.47/0.60 % (841228)CaDiCaL version: 2.1.3
% 2.47/0.60 % (841228)Termination reason: Instruction limit
% 2.47/0.60 % (841228)Termination phase: Saturation
% 2.47/0.60 % (841228)Time elapsed: 0.040 s
% 2.47/0.60 % (841228)Peak memory usage: 14 MB
% 2.47/0.60 % (841228)Instructions burned: 162 (million)
% 2.47/0.60 % Exception at run slice level
% 2.47/0.60 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.47/0.60 % (841223)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 2.47/0.60 % (841236)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=969021682:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 2.47/0.60 % (841225)Instruction limit reached!
% 2.47/0.60 % (841225)------------------------------
% 2.47/0.60 % (841225)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.47/0.60 % (841225)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.47/0.60 % (841225)CaDiCaL version: 2.1.3
% 2.47/0.60 % (841225)Termination reason: Instruction limit
% 2.47/0.60 % (841225)Termination phase: Saturation
% 2.47/0.60 % (841225)Time elapsed: 0.045 s
% 2.47/0.60 % (841225)Peak memory usage: 12 MB
% 2.47/0.60 % (841225)Instructions burned: 104 (million)
% 2.47/0.60 % (841226)Instruction limit reached!
% 2.47/0.60 % (841226)------------------------------
% 2.47/0.60 % (841226)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.47/0.60 % (841226)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.47/0.60 % (841226)CaDiCaL version: 2.1.3
% 2.47/0.60 % (841226)Termination reason: Instruction limit
% 2.47/0.60 % (841226)Termination phase: Saturation
% 2.47/0.60 % (841226)Time elapsed: 0.051 s
% 2.47/0.60 % (841226)Peak memory usage: 12 MB
% 2.47/0.60 % (841226)Instructions burned: 117 (million)
% 2.47/0.60 % (841237)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1755759944:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 2.47/0.60 % Exception at run slice level
% 2.47/0.60 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.47/0.60 % (841227)Instruction limit reached!
% 2.47/0.60 % (841227)------------------------------
% 2.47/0.60 % (841227)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.47/0.60 % (841227)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.47/0.60 % (841227)CaDiCaL version: 2.1.3
% 2.47/0.60 % (841227)Termination reason: Instruction limit
% 2.47/0.60 % (841227)Termination phase: Saturation
% 2.47/0.60 % (841227)Time elapsed: 0.062 s
% 2.47/0.60 % (841227)Peak memory usage: 13 MB
% 2.47/0.60 % (841227)Instructions burned: 132 (million)
% 2.47/0.60 % (841239)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=3932358316:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 2.47/0.60 % (841241)ott-21_1_sil=16000:fs=off:random_seed=1954348073:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 2.47/0.60 % (841242)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2214059665:i=477:bd=all_2999 on theBenchmark for (2999ds/477Mi)
% 2.47/0.60 % (841243)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=2327592463:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 2.47/0.60 % (841239)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.47/0.60 % (841239)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 2.47/0.60 % Exception at run slice level
% 2.47/0.60 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.47/0.60 % (841237)Instruction limit reached!
% 2.47/0.60 % (841237)------------------------------
% 2.47/0.60 % (841237)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.47/0.60 % (841237)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.47/0.60 % (841237)CaDiCaL version: 2.1.3
% 2.47/0.60 % (841237)Termination reason: Instruction limit
% 2.47/0.60 % (841237)Termination phase: Saturation
% 2.47/0.60 % (841237)Time elapsed: 0.060 s
% 2.47/0.60 % (841237)Peak memory usage: 13 MB
% 2.47/0.60 % (841237)Instructions burned: 133 (million)
% 2.47/0.60 % (841248)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=2228914309:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 2.47/0.60 % (841249)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=1494260918:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 2.47/0.60 % (841241)Instruction limit reached!
% 2.47/0.60 % (841241)------------------------------
% 2.47/0.60 % (841241)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.47/0.60 % (841241)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.47/0.60 % (841241)CaDiCaL version: 2.1.3
% 2.47/0.60 % (841241)Termination reason: Instruction limit
% 2.47/0.60 % (841241)Termination phase: Saturation
% 2.47/0.60 % (841241)Time elapsed: 0.082 s
% 2.47/0.60 % (841241)Peak memory usage: 13 MB
% 2.47/0.60 % (841241)Instructions burned: 182 (million)
% 2.47/0.60 % (841252)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=1663275622: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)
% 2.47/0.60 % Exception at run slice level
% 2.47/0.60 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.47/0.60 % (841252)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.47/0.60 % (841254)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=848051131:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 2.47/0.60 % (841242)Instruction limit reached!
% 2.47/0.60 % (841242)------------------------------
% 2.47/0.60 % (841242)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.47/0.60 % (841242)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.47/0.60 % (841242)CaDiCaL version: 2.1.3
% 2.47/0.60 % (841242)Termination reason: Instruction limit
% 2.47/0.60 % (841242)Termination phase: Saturation
% 2.47/0.60 % (841242)Time elapsed: 0.143 s
% 2.47/0.60 % (841242)Peak memory usage: 14 MB
% 2.47/0.60 % (841242)Instructions burned: 479 (million)
% 2.47/0.60 % (841254)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.47/0.60 % (841256)fmb+10_1_sil=64000:random_seed=2641848114:i=22061:nm=2:gsp=on_2997 on theBenchmark for (2997ds/22061Mi)
% 2.47/0.60 % (841256)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.47/0.60 % Exception at run slice level
% 2.47/0.60 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.47/0.60 % (841258)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=4215414015:i=9515:nm=5_2997 on theBenchmark for (2997ds/9515Mi)
% 2.47/0.60 % Exception at run slice level
% 2.47/0.60 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.47/0.60 % (841260)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=1189851609:fmbsr=1.7:i=920_2996 on theBenchmark for (2996ds/920Mi)
% 2.47/0.60 % (841248) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-841217-841248"...
% 2.47/0.60 % (841248)...printing done.
% 2.47/0.60 % (841248)Refutation found. Thanks to Tanya!
% 2.47/0.60 % SZS status Theorem for theBenchmark
% 2.47/0.60 % SZS output start Proof for theBenchmark
% 2.47/0.60 thf(type_def_5, type, real: $tType).
% 2.47/0.60 thf(type_def_6, type, set: $tType > $tType).
% 2.47/0.60 thf(type_def_7, type, a: $tType).
% 2.47/0.60 thf(type_def_8, type, sTfun: ($tType * $tType) > $tType).
% 2.47/0.60 thf(func_def_0, type, finite_finite: !>[X0: $tType]:($o)).
% 2.47/0.60 thf(func_def_1, type, countable: !>[X0: $tType]:($o)).
% 2.47/0.60 thf(func_def_2, type, one: !>[X0: $tType]:($o)).
% 2.47/0.60 thf(func_def_3, type, zero: !>[X0: $tType]:($o)).
% 2.47/0.60 thf(func_def_4, type, abs_if: !>[X0: $tType]:($o)).
% 2.47/0.60 thf(func_def_5, type, neg_numeral: !>[X0: $tType]:($o)).
% 2.47/0.60 thf(func_def_6, type, group_add: !>[X0: $tType]:($o)).
% 2.47/0.60 thf(func_def_7, type, monoid_add: !>[X0: $tType]:($o)).
% 2.47/0.60 thf(func_def_8, type, idom_abs_sgn: !>[X0: $tType]:($o)).
% 2.47/0.60 thf(func_def_9, type, zero_neq_one: !>[X0: $tType]:($o)).
% 2.47/0.60 thf(func_def_10, type, ab_group_add: !>[X0: $tType]:($o)).
% 2.47/0.60 thf(func_def_11, type, zero_less_one: !>[X0: $tType]:($o)).
% 2.47/0.60 thf(func_def_12, type, semigroup_add: !>[X0: $tType]:($o)).
% 2.47/0.60 thf(func_def_13, type, linordered_idom: !>[X0: $tType]:($o)).
% 2.47/0.60 thf(func_def_14, type, linordered_ring: !>[X0: $tType]:($o)).
% 2.47/0.60 thf(func_def_15, type, comm_monoid_add: !>[X0: $tType]:($o)).
% 2.47/0.60 thf(func_def_16, type, ab_semigroup_add: !>[X0: $tType]:($o)).
% 2.47/0.60 thf(func_def_17, type, cancel_semigroup_add: !>[X0: $tType]:($o)).
% 2.47/0.60 thf(func_def_18, type, ordered_ab_group_add: !>[X0: $tType]:($o)).
% 2.47/0.60 thf(func_def_19, type, cancel1352612707id_add: !>[X0: $tType]:($o)).
% 2.47/0.60 thf(func_def_20, type, linord219039673up_add: !>[X0: $tType]:($o)).
% 2.47/0.60 thf(func_def_21, type, ordere216010020id_add: !>[X0: $tType]:($o)).
% 2.47/0.60 thf(func_def_22, type, ordere142940540dd_abs: !>[X0: $tType]:($o)).
% 2.47/0.60 thf(func_def_23, type, ordere779506340up_add: !>[X0: $tType]:($o)).
% 2.47/0.60 thf(func_def_24, type, real_V2090557954_space: !>[X0: $tType]:($o)).
% 2.47/0.60 thf(func_def_25, type, linord1659791738miring: !>[X0: $tType]:($o)).
% 2.47/0.60 thf(func_def_26, type, canoni770627133id_add: !>[X0: $tType]:($o)).
% 2.47/0.60 thf(func_def_27, type, ordere1818651114id_add: !>[X0: $tType]:($o)).
% 2.47/0.60 thf(func_def_28, type, ordere236663937imp_le: !>[X0: $tType]:($o)).
% 2.47/0.60 thf(func_def_29, type, ordere223160158up_add: !>[X0: $tType]:($o)).
% 2.47/0.60 thf(func_def_30, type, ordere516151231imp_le: !>[X0: $tType]:($o)).
% 2.47/0.60 thf(func_def_31, type, execut510477386_space: !>[X0: $tType]:($o)).
% 2.47/0.60 thf(func_def_32, type, elemen1815086676c_ball: !>[X0: $tType]:((X0 > real > set @ X0))).
% 2.47/0.60 thf(func_def_33, type, auto_l1112008849e_ivl0: !>[X0: $tType]:(((X0 > X0) > set @ X0 > X0 > set @ real))).
% 2.47/0.60 thf(func_def_34, type, auto_ll_on_flow0: !>[X0: $tType]:(((X0 > X0) > set @ X0 > X0 > real > X0))).
% 2.47/0.60 thf(func_def_35, type, abs_abs: !>[X0: $tType]:((X0 > X0))).
% 2.47/0.60 thf(func_def_36, type, one_one: !>[X0: $tType]:(X0)).
% 2.47/0.60 thf(func_def_37, type, plus_plus: !>[X0: $tType]:((X0 > X0 > X0))).
% 2.47/0.60 thf(func_def_38, type, uminus_uminus: !>[X0: $tType]:((X0 > X0))).
% 2.47/0.60 thf(func_def_39, type, zero_zero: !>[X0: $tType]:(X0)).
% 2.47/0.60 thf(func_def_40, type, if: !>[X0: $tType]:(($o > X0 > X0 > X0))).
% 2.47/0.60 thf(func_def_41, type, initia826609931terval: (set @ real > $o)).
% 2.47/0.60 thf(func_def_42, type, limit_1335059408_point: !>[X0: $tType]:(((X0 > X0) > set @ X0 > X0 > X0 > $o))).
% 2.47/0.60 thf(func_def_43, type, limit_1052139091_point: !>[X0: $tType]:(((X0 > X0) > set @ X0 > X0 > X0 > $o))).
% 2.47/0.60 thf(func_def_44, type, line_open_segment: !>[X0: $tType]:((X0 > X0 > set @ X0))).
% 2.47/0.60 thf(func_def_45, type, bot_bot: !>[X0: $tType]:(X0)).
% 2.47/0.60 thf(func_def_46, type, ord_less: !>[X0: $tType]:((X0 > X0 > $o))).
% 2.47/0.60 thf(func_def_47, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 2.47/0.60 thf(func_def_48, type, top_top: !>[X0: $tType]:(X0)).
% 2.47/0.60 thf(func_def_49, type, period385816147_orbit: !>[X0: $tType]:(((X0 > X0) > set @ X0 > X0 > $o))).
% 2.47/0.60 thf(func_def_50, type, period1153813292period: !>[X0: $tType]:(((X0 > X0) > set @ X0 > X0 > real))).
% 2.47/0.60 thf(func_def_51, type, period862636932_orbit: !>[X0: $tType]:(((X0 > X0) > set @ X0 > X0 > $o))).
% 2.47/0.60 thf(func_def_52, type, poinca272511729egment: !>[X0: $tType]:(((X0 > X0) > set @ X0 > X0 > X0 > $o))).
% 2.47/0.60 thf(func_def_53, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 2.47/0.60 thf(func_def_54, type, topolo2071040574ous_on: !>[X0: $tType, X1: $tType]:((set @ X0 > (X0 > X1) > $o))).
% 2.47/0.60 thf(func_def_55, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 2.47/0.60 thf(func_def_56, type, x: set @ a).
% 2.47/0.60 thf(func_def_57, type, a2: a).
% 2.47/0.60 thf(func_def_58, type, b: a).
% 2.47/0.60 thf(func_def_59, type, f: (a > a)).
% 2.47/0.60 thf(func_def_60, type, p: a).
% 2.47/0.60 thf(func_def_61, type, thesisa: $o).
% 2.47/0.60 thf(func_def_62, type, x2: a).
% 2.47/0.60 thf(func_def_66, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 2.47/0.60 thf(func_def_67, type, vNOT: ($o > $o)).
% 2.47/0.60 thf(func_def_68, type, db0: !>[X0: $tType]:(X0)).
% 2.47/0.60 thf(func_def_69, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 2.47/0.60 thf(func_def_70, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 2.47/0.60 thf(func_def_71, type, vAND: ($o > $o > $o)).
% 2.47/0.60 thf(func_def_72, type, vOR: ($o > $o > $o)).
% 2.47/0.60 thf(func_def_73, type, db1: !>[X0: $tType]:(X0)).
% 2.47/0.60 thf(func_def_74, type, db2: !>[X0: $tType]:(X0)).
% 2.47/0.60 thf(func_def_75, type, sK0: real).
% 2.47/0.60 thf(func_def_76, type, sK1: (a > real)).
% 2.47/0.60 thf(func_def_77, type, sK2: ((a > real) > real > a)).
% 2.47/0.60 thf(func_def_78, type, sK3: ((a > real) > real > a)).
% 2.47/0.60 thf(func_def_79, type, sK4: (real > a > a > a > real)).
% 2.47/0.60 thf(func_def_80, type, sK5: (real > a > a > a > a > real)).
% 2.47/0.60 thf(func_def_81, type, sK6: (a > a)).
% 2.47/0.60 thf(func_def_82, type, sK7: (a > a)).
% 2.47/0.60 thf(func_def_83, type, sK8: (a > a)).
% 2.47/0.60 thf(func_def_84, type, sK9: (a > a)).
% 2.47/0.60 thf(func_def_85, type, sK10: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 2.47/0.60 thf(func_def_86, type, sK11: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 2.47/0.60 thf(func_def_87, type, sK12: ((a > a) > set @ a > a)).
% 2.47/0.60 thf(func_def_88, type, sK13: ((a > a) > set @ a > a)).
% 2.47/0.60 thf(func_def_89, type, sK14: ((a > a) > set @ a > a)).
% 2.47/0.60 thf(func_def_90, type, sK15: ((a > a) > set @ a > a)).
% 2.47/0.60 thf(func_def_91, type, sK16: (a > real)).
% 2.47/0.60 thf(func_def_92, type, sK17: (a > real)).
% 2.47/0.60 thf(func_def_93, type, sK18: !>[X0: $tType]:((X0 > X0 > X0))).
% 2.47/0.60 thf(func_def_94, type, sK19: ((a > real) > real > a)).
% 2.47/0.60 thf(func_def_95, type, sK20: ((a > real) > real > a)).
% 2.47/0.60 thf(func_def_96, type, sK21: (a > real)).
% 2.47/0.60 thf(func_def_97, type, sK22: (a > real)).
% 2.47/0.60 thf(f4,axiom,(
% 2.47/0.60 ~ ! [X0 : real] : ((ord_less @ real @ zero_zero @ real @ X0) => ! [X1 : (a > real)] : ((topolo2071040574ous_on @ a @ real @ (elemen1815086676c_ball @ a @ p @ X0) @ X1) => (! [X2 : a] : ((member @ a @ X2 @ (elemen1815086676c_ball @ a @ p @ X0)) => (member @ a @ (auto_ll_on_flow0 @ a @ f @ x @ X2 @ (X1 @ X2)) @ (line_open_segment @ a @ a2 @ b))) => (! [X2 : a] : ((member @ a @ X2 @ (elemen1815086676c_ball @ a @ p @ X0)) => (ord_less @ real @ (abs_abs @ real @ (X1 @ X2)) @ one_one @ real)) => ((topolo2071040574ous_on @ a @ real @ (elemen1815086676c_ball @ a @ p @ X0) @ X1) => (((X1 @ p)) != zero_zero @ real))))))),
% 2.47/0.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062d_At_O_A_092_060lbrakk_0620_A_060_Ad_059_Acontinuous__on_A_Iball_Ap_Ad_J_At_059_A_092_060And_062y_O_Ay_A_092_060in_062_Aball_Ap_Ad_A_092_060Longrightarrow_062_Aflow0_Ay_A_It_Ay_J_A_092_060in_062_A_123a_060_N_N_060b_125_059_A_092_060And_062y_O_Ay_A_092_060in_062_Aball_Ap_Ad_A_092_060Longrightarrow_062_A_092_060bar_062t_Ay_092_060bar_062_A_060_A1_059_Acontinuous__on_A_Iball_Ap_Ad_J_At_059_At_Ap_A_061_A0_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062)).
% 2.47/0.60 thf(f5,axiom,(
% 2.47/0.60 ! [X0 : real,X1 : (a > real)] : ((ord_less @ real @ zero_zero @ real @ X0) => ((topolo2071040574ous_on @ a @ real @ (elemen1815086676c_ball @ a @ p @ X0) @ X1) => ((((X1 @ p)) = zero_zero @ real) => (! [X2 : a] : ((member @ a @ X2 @ (elemen1815086676c_ball @ a @ p @ X0)) => (ord_less @ real @ (abs_abs @ real @ (X1 @ X2)) @ one_one @ real)) => (! [X2 : a] : ((member @ a @ X2 @ (elemen1815086676c_ball @ a @ p @ X0)) => (member @ a @ (auto_ll_on_flow0 @ a @ f @ x @ X2 @ (X1 @ X2)) @ (line_open_segment @ a @ a2 @ b))) => thesisa)))))),
% 2.47/0.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_that)).
% 2.47/0.60 thf(f320,conjecture,(
% 2.47/0.60 thesisa),
% 2.47/0.60 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1)).
% 2.47/0.60 thf(f321,negated_conjecture,(
% 2.47/0.60 ~thesisa),
% 2.47/0.60 inference(negated_conjecture,[status(cth)],[f320])).
% 2.47/0.60 thf(f328,plain,(
% 2.47/0.60 ~ ! [X0 : real] : ((ord_less @ real @ zero_zero @ real @ X0) => ! [X1 : (a > real)] : ((topolo2071040574ous_on @ a @ real @ (elemen1815086676c_ball @ a @ p @ X0) @ X1) => (! [X2 : a] : ((member @ a @ X2 @ (elemen1815086676c_ball @ a @ p @ X0)) => (member @ a @ (auto_ll_on_flow0 @ a @ f @ x @ X2 @ (X1 @ X2)) @ (line_open_segment @ a @ a2 @ b))) => (! [X3 : a] : ((member @ a @ X3 @ (elemen1815086676c_ball @ a @ p @ X0)) => (ord_less @ real @ (abs_abs @ real @ (X1 @ X3)) @ one_one @ real)) => ((topolo2071040574ous_on @ a @ real @ (elemen1815086676c_ball @ a @ p @ X0) @ X1) => (((X1 @ p)) != zero_zero @ real))))))),
% 2.47/0.60 inference(rectify,[],[f4])).
% 2.47/0.60 thf(f329,plain,(
% 2.47/0.60 ~ ! [X0 : real] : ((((ord_less @ real @ zero_zero @ real @ X0)) = $true) => ! [X1 : (a > real)] : ((((topolo2071040574ous_on @ a @ real @ (elemen1815086676c_ball @ a @ p @ X0) @ X1)) = $true) => (! [X2 : a] : ((((member @ a @ X2 @ (elemen1815086676c_ball @ a @ p @ X0))) = $true) => (((member @ a @ (auto_ll_on_flow0 @ a @ f @ x @ X2 @ (X1 @ X2)) @ (line_open_segment @ a @ a2 @ b))) = $true)) => (! [X3 : a] : (($true = ((member @ a @ X3 @ (elemen1815086676c_ball @ a @ p @ X0)))) => ($true = ((ord_less @ real @ (abs_abs @ real @ (X1 @ X3)) @ one_one @ real)))) => ((((topolo2071040574ous_on @ a @ real @ (elemen1815086676c_ball @ a @ p @ X0) @ X1)) = $true) => (zero_zero @ real != ((X1 @ p))))))))),
% 2.47/0.60 inference(fool_elimination,[],[f328])).
% 2.47/0.60 thf(f330,plain,(
% 2.47/0.60 ! [X0 : real,X1 : (a > real)] : ((ord_less @ real @ zero_zero @ real @ X0) => ((topolo2071040574ous_on @ a @ real @ (elemen1815086676c_ball @ a @ p @ X0) @ X1) => ((((X1 @ p)) = zero_zero @ real) => (! [X2 : a] : ((member @ a @ X2 @ (elemen1815086676c_ball @ a @ p @ X0)) => (ord_less @ real @ (abs_abs @ real @ (X1 @ X2)) @ one_one @ real)) => (! [X3 : a] : ((member @ a @ X3 @ (elemen1815086676c_ball @ a @ p @ X0)) => (member @ a @ (auto_ll_on_flow0 @ a @ f @ x @ X3 @ (X1 @ X3)) @ (line_open_segment @ a @ a2 @ b))) => thesisa)))))),
% 2.47/0.60 inference(rectify,[],[f5])).
% 2.47/0.60 thf(f331,plain,(
% 2.47/0.60 ! [X0 : real,X1 : (a > real)] : ((((ord_less @ real @ zero_zero @ real @ X0)) = $true) => ((((topolo2071040574ous_on @ a @ real @ (elemen1815086676c_ball @ a @ p @ X0) @ X1)) = $true) => ((zero_zero @ real = ((X1 @ p))) => (! [X2 : a] : ((((member @ a @ X2 @ (elemen1815086676c_ball @ a @ p @ X0))) = $true) => (((ord_less @ real @ (abs_abs @ real @ (X1 @ X2)) @ one_one @ real)) = $true)) => (! [X3 : a] : (($true = ((member @ a @ X3 @ (elemen1815086676c_ball @ a @ p @ X0)))) => ($true = ((member @ a @ (auto_ll_on_flow0 @ a @ f @ x @ X3 @ (X1 @ X3)) @ (line_open_segment @ a @ a2 @ b))))) => (thesisa = $true))))))),
% 2.47/0.60 inference(fool_elimination,[],[f330])).
% 2.47/0.60 thf(f937,plain,(
% 2.47/0.60 ~thesisa),
% 2.47/0.60 inference(rectify,[],[f321])).
% 2.47/0.60 thf(f938,plain,(
% 2.47/0.60 ~ (thesisa = $true)),
% 2.47/0.60 inference(fool_elimination,[],[f937])).
% 2.47/0.60 thf(f955,plain,(
% 2.47/0.60 (thesisa != $true)),
% 2.47/0.60 inference(flattening,[],[f938])).
% 2.47/0.60 thf(f958,plain,(
% 2.47/0.60 ? [X0 : real] : (? [X1 : (a > real)] : (((((zero_zero @ real = ((X1 @ p))) & (((topolo2071040574ous_on @ a @ real @ (elemen1815086676c_ball @ a @ p @ X0) @ X1)) = $true)) & ! [X3 : a] : (($true = ((ord_less @ real @ (abs_abs @ real @ (X1 @ X3)) @ one_one @ real))) | ($true != ((member @ a @ X3 @ (elemen1815086676c_ball @ a @ p @ X0)))))) & ! [X2 : a] : ((((member @ a @ (auto_ll_on_flow0 @ a @ f @ x @ X2 @ (X1 @ X2)) @ (line_open_segment @ a @ a2 @ b))) = $true) | (((member @ a @ X2 @ (elemen1815086676c_ball @ a @ p @ X0))) != $true))) & (((topolo2071040574ous_on @ a @ real @ (elemen1815086676c_ball @ a @ p @ X0) @ X1)) = $true)) & (((ord_less @ real @ zero_zero @ real @ X0)) = $true))),
% 2.47/0.60 inference(ennf_transformation,[],[f329])).
% 2.47/0.60 thf(f959,plain,(
% 2.47/0.60 ? [X0 : real] : (? [X1 : (a > real)] : ((zero_zero @ real = ((X1 @ p))) & (((topolo2071040574ous_on @ a @ real @ (elemen1815086676c_ball @ a @ p @ X0) @ X1)) = $true) & ! [X3 : a] : (($true = ((ord_less @ real @ (abs_abs @ real @ (X1 @ X3)) @ one_one @ real))) | ($true != ((member @ a @ X3 @ (elemen1815086676c_ball @ a @ p @ X0))))) & ! [X2 : a] : ((((member @ a @ (auto_ll_on_flow0 @ a @ f @ x @ X2 @ (X1 @ X2)) @ (line_open_segment @ a @ a2 @ b))) = $true) | (((member @ a @ X2 @ (elemen1815086676c_ball @ a @ p @ X0))) != $true)) & (((topolo2071040574ous_on @ a @ real @ (elemen1815086676c_ball @ a @ p @ X0) @ X1)) = $true)) & (((ord_less @ real @ zero_zero @ real @ X0)) = $true))),
% 2.47/0.60 inference(flattening,[],[f958])).
% 2.47/0.60 thf(f960,plain,(
% 2.47/0.60 ! [X0 : real,X1 : (a > real)] : ((((((thesisa = $true) | ? [X3 : a] : (($true != ((member @ a @ (auto_ll_on_flow0 @ a @ f @ x @ X3 @ (X1 @ X3)) @ (line_open_segment @ a @ a2 @ b)))) & ($true = ((member @ a @ X3 @ (elemen1815086676c_ball @ a @ p @ X0)))))) | ? [X2 : a] : ((((ord_less @ real @ (abs_abs @ real @ (X1 @ X2)) @ one_one @ real)) != $true) & (((member @ a @ X2 @ (elemen1815086676c_ball @ a @ p @ X0))) = $true))) | (zero_zero @ real != ((X1 @ p)))) | (((topolo2071040574ous_on @ a @ real @ (elemen1815086676c_ball @ a @ p @ X0) @ X1)) != $true)) | (((ord_less @ real @ zero_zero @ real @ X0)) != $true))),
% 2.47/0.60 inference(ennf_transformation,[],[f331])).
% 2.47/0.60 thf(f961,plain,(
% 2.47/0.60 ! [X0 : real,X1 : (a > real)] : ((thesisa = $true) | ? [X3 : a] : (($true != ((member @ a @ (auto_ll_on_flow0 @ a @ f @ x @ X3 @ (X1 @ X3)) @ (line_open_segment @ a @ a2 @ b)))) & ($true = ((member @ a @ X3 @ (elemen1815086676c_ball @ a @ p @ X0))))) | ? [X2 : a] : ((((ord_less @ real @ (abs_abs @ real @ (X1 @ X2)) @ one_one @ real)) != $true) & (((member @ a @ X2 @ (elemen1815086676c_ball @ a @ p @ X0))) = $true)) | (zero_zero @ real != ((X1 @ p))) | (((topolo2071040574ous_on @ a @ real @ (elemen1815086676c_ball @ a @ p @ X0) @ X1)) != $true) | (((ord_less @ real @ zero_zero @ real @ X0)) != $true))),
% 2.47/0.60 inference(flattening,[],[f960])).
% 2.47/0.60 thf(f1287,plain,(
% 2.47/0.60 ? [X0 : real] : (? [X1 : (a > real)] : ((zero_zero @ real = ((X1 @ p))) & (((topolo2071040574ous_on @ a @ real @ (elemen1815086676c_ball @ a @ p @ X0) @ X1)) = $true) & ! [X2 : a] : ((((ord_less @ real @ (abs_abs @ real @ (X1 @ X2)) @ one_one @ real)) = $true) | (((member @ a @ X2 @ (elemen1815086676c_ball @ a @ p @ X0))) != $true)) & ! [X3 : a] : (($true = ((member @ a @ (auto_ll_on_flow0 @ a @ f @ x @ X3 @ (X1 @ X3)) @ (line_open_segment @ a @ a2 @ b)))) | ($true != ((member @ a @ X3 @ (elemen1815086676c_ball @ a @ p @ X0))))) & (((topolo2071040574ous_on @ a @ real @ (elemen1815086676c_ball @ a @ p @ X0) @ X1)) = $true)) & (((ord_less @ real @ zero_zero @ real @ X0)) = $true))),
% 2.47/0.60 inference(rectify,[],[f959])).
% 2.47/0.60 thf(f1288,plain,(
% 2.47/0.60 ((zero_zero @ real = ((sK1 @ p))) & ($true = ((topolo2071040574ous_on @ a @ real @ (elemen1815086676c_ball @ a @ p @ sK0) @ sK1))) & ! [X2 : a] : (($true = ((ord_less @ real @ (abs_abs @ real @ (sK1 @ X2)) @ one_one @ real))) | ($true != ((member @ a @ X2 @ (elemen1815086676c_ball @ a @ p @ sK0))))) & ! [X3 : a] : (($true = ((member @ a @ (auto_ll_on_flow0 @ a @ f @ x @ X3 @ (sK1 @ X3)) @ (line_open_segment @ a @ a2 @ b)))) | ($true != ((member @ a @ X3 @ (elemen1815086676c_ball @ a @ p @ sK0))))) & ($true = ((topolo2071040574ous_on @ a @ real @ (elemen1815086676c_ball @ a @ p @ sK0) @ sK1)))) & ($true = ((ord_less @ real @ zero_zero @ real @ sK0)))),
% 2.47/0.60 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f1287])).
% 2.47/0.60 thf(f1289,plain,(
% 2.47/0.60 ! [X0 : real,X1 : (a > real)] : ((thesisa = $true) | ? [X2 : a] : ((((member @ a @ (auto_ll_on_flow0 @ a @ f @ x @ X2 @ (X1 @ X2)) @ (line_open_segment @ a @ a2 @ b))) != $true) & (((member @ a @ X2 @ (elemen1815086676c_ball @ a @ p @ X0))) = $true)) | ? [X3 : a] : (($true != ((ord_less @ real @ (abs_abs @ real @ (X1 @ X3)) @ one_one @ real))) & ($true = ((member @ a @ X3 @ (elemen1815086676c_ball @ a @ p @ X0))))) | (zero_zero @ real != ((X1 @ p))) | (((topolo2071040574ous_on @ a @ real @ (elemen1815086676c_ball @ a @ p @ X0) @ X1)) != $true) | (((ord_less @ real @ zero_zero @ real @ X0)) != $true))),
% 2.47/0.60 inference(rectify,[],[f961])).
% 2.47/0.60 thf(f1290,plain,(
% 2.47/0.60 ! [X0 : real,X1 : (a > real)] : ((thesisa = $true) | (($true != ((member @ a @ (auto_ll_on_flow0 @ a @ f @ x @ (sK2 @ X1 @ X0) @ (X1 @ (sK2 @ X1 @ X0))) @ (line_open_segment @ a @ a2 @ b)))) & ($true = ((member @ a @ (sK2 @ X1 @ X0) @ (elemen1815086676c_ball @ a @ p @ X0))))) | (($true != ((ord_less @ real @ (abs_abs @ real @ (X1 @ (sK3 @ X1 @ X0))) @ one_one @ real))) & ($true = ((member @ a @ (sK3 @ X1 @ X0) @ (elemen1815086676c_ball @ a @ p @ X0))))) | (zero_zero @ real != ((X1 @ p))) | (((topolo2071040574ous_on @ a @ real @ (elemen1815086676c_ball @ a @ p @ X0) @ X1)) != $true) | (((ord_less @ real @ zero_zero @ real @ X0)) != $true))),
% 2.47/0.60 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP]),skolemize(X3,sK3 @ X1 @ X0),skolemize(X3,sK3 @ X1 @ X0)],[f1289])).
% 2.47/0.60 thf(f1309,plain,(
% 2.47/0.60 ($true = ((ord_less @ real @ zero_zero @ real @ sK0)))),
% 2.47/0.60 inference(cnf_transformation,[],[f1288])).
% 2.47/0.60 thf(f1310,plain,(
% 2.47/0.60 ($true = ((topolo2071040574ous_on @ a @ real @ (elemen1815086676c_ball @ a @ p @ sK0) @ sK1)))),
% 2.47/0.60 inference(cnf_transformation,[],[f1288])).
% 2.47/0.60 thf(f1311,plain,(
% 2.47/0.60 ( ! [X3 : a] : (($true != ((member @ a @ X3 @ (elemen1815086676c_ball @ a @ p @ sK0)))) | ($true = ((member @ a @ (auto_ll_on_flow0 @ a @ f @ x @ X3 @ (sK1 @ X3)) @ (line_open_segment @ a @ a2 @ b))))) )),
% 2.47/0.60 inference(cnf_transformation,[],[f1288])).
% 2.47/0.60 thf(f1312,plain,(
% 2.47/0.60 ( ! [X2 : a] : (($true != ((member @ a @ X2 @ (elemen1815086676c_ball @ a @ p @ sK0)))) | ($true = ((ord_less @ real @ (abs_abs @ real @ (sK1 @ X2)) @ one_one @ real)))) )),
% 2.47/0.60 inference(cnf_transformation,[],[f1288])).
% 2.47/0.60 thf(f1314,plain,(
% 2.47/0.60 (zero_zero @ real = ((sK1 @ p)))),
% 2.47/0.60 inference(cnf_transformation,[],[f1288])).
% 2.47/0.60 thf(f1315,plain,(
% 2.47/0.60 ( ! [X0 : real,X1 : (a > real)] : ((thesisa = $true) | ($true = ((member @ a @ (sK2 @ X1 @ X0) @ (elemen1815086676c_ball @ a @ p @ X0)))) | ($true = ((member @ a @ (sK3 @ X1 @ X0) @ (elemen1815086676c_ball @ a @ p @ X0)))) | (zero_zero @ real != ((X1 @ p))) | (((topolo2071040574ous_on @ a @ real @ (elemen1815086676c_ball @ a @ p @ X0) @ X1)) != $true) | (((ord_less @ real @ zero_zero @ real @ X0)) != $true)) )),
% 2.47/0.60 inference(cnf_transformation,[],[f1290])).
% 2.47/0.60 thf(f1316,plain,(
% 2.47/0.60 ( ! [X0 : real,X1 : (a > real)] : ((thesisa = $true) | ($true = ((member @ a @ (sK2 @ X1 @ X0) @ (elemen1815086676c_ball @ a @ p @ X0)))) | ($true != ((ord_less @ real @ (abs_abs @ real @ (X1 @ (sK3 @ X1 @ X0))) @ one_one @ real))) | (zero_zero @ real != ((X1 @ p))) | (((topolo2071040574ous_on @ a @ real @ (elemen1815086676c_ball @ a @ p @ X0) @ X1)) != $true) | (((ord_less @ real @ zero_zero @ real @ X0)) != $true)) )),
% 2.47/0.60 inference(cnf_transformation,[],[f1290])).
% 2.47/0.60 thf(f1317,plain,(
% 2.47/0.60 ( ! [X0 : real,X1 : (a > real)] : ((thesisa = $true) | ($true != ((member @ a @ (auto_ll_on_flow0 @ a @ f @ x @ (sK2 @ X1 @ X0) @ (X1 @ (sK2 @ X1 @ X0))) @ (line_open_segment @ a @ a2 @ b)))) | ($true = ((member @ a @ (sK3 @ X1 @ X0) @ (elemen1815086676c_ball @ a @ p @ X0)))) | (zero_zero @ real != ((X1 @ p))) | (((topolo2071040574ous_on @ a @ real @ (elemen1815086676c_ball @ a @ p @ X0) @ X1)) != $true) | (((ord_less @ real @ zero_zero @ real @ X0)) != $true)) )),
% 2.47/0.60 inference(cnf_transformation,[],[f1290])).
% 2.47/0.60 thf(f1318,plain,(
% 2.47/0.60 ( ! [X0 : real,X1 : (a > real)] : ((thesisa = $true) | ($true != ((member @ a @ (auto_ll_on_flow0 @ a @ f @ x @ (sK2 @ X1 @ X0) @ (X1 @ (sK2 @ X1 @ X0))) @ (line_open_segment @ a @ a2 @ b)))) | ($true != ((ord_less @ real @ (abs_abs @ real @ (X1 @ (sK3 @ X1 @ X0))) @ one_one @ real))) | (zero_zero @ real != ((X1 @ p))) | (((topolo2071040574ous_on @ a @ real @ (elemen1815086676c_ball @ a @ p @ X0) @ X1)) != $true) | (((ord_less @ real @ zero_zero @ real @ X0)) != $true)) )),
% 2.47/0.60 inference(cnf_transformation,[],[f1290])).
% 2.47/0.60 thf(f1653,plain,(
% 2.47/0.60 (thesisa != $true)),
% 2.47/0.60 inference(cnf_transformation,[],[f955])).
% 2.47/0.60 thf(f2147,plain,(
% 2.47/0.60 ( ! [X0 : real,X1 : (a > real)] : ((((topolo2071040574ous_on @ a @ real @ (elemen1815086676c_ball @ a @ p @ X0) @ X1)) != $true) | ($true = ((member @ a @ (sK3 @ X1 @ X0) @ (elemen1815086676c_ball @ a @ p @ X0)))) | (zero_zero @ real != ((X1 @ p))) | ($true = ((member @ a @ (sK2 @ X1 @ X0) @ (elemen1815086676c_ball @ a @ p @ X0)))) | (((ord_less @ real @ zero_zero @ real @ X0)) != $true)) )),
% 2.47/0.60 inference(forward_subsumption_resolution,[],[f1315,f1653])).
% 2.47/0.60 thf(f2148,plain,(
% 2.47/0.60 ( ! [X0 : real,X1 : (a > real)] : (($true != ((ord_less @ real @ (abs_abs @ real @ (X1 @ (sK3 @ X1 @ X0))) @ one_one @ real))) | ($true = ((member @ a @ (sK2 @ X1 @ X0) @ (elemen1815086676c_ball @ a @ p @ X0)))) | (zero_zero @ real != ((X1 @ p))) | (((topolo2071040574ous_on @ a @ real @ (elemen1815086676c_ball @ a @ p @ X0) @ X1)) != $true) | (((ord_less @ real @ zero_zero @ real @ X0)) != $true)) )),
% 2.47/0.60 inference(forward_subsumption_resolution,[],[f1316,f1653])).
% 2.47/0.60 thf(f2149,plain,(
% 2.47/0.60 ( ! [X0 : real,X1 : (a > real)] : (($true != ((member @ a @ (auto_ll_on_flow0 @ a @ f @ x @ (sK2 @ X1 @ X0) @ (X1 @ (sK2 @ X1 @ X0))) @ (line_open_segment @ a @ a2 @ b)))) | ($true = ((member @ a @ (sK3 @ X1 @ X0) @ (elemen1815086676c_ball @ a @ p @ X0)))) | (zero_zero @ real != ((X1 @ p))) | (((topolo2071040574ous_on @ a @ real @ (elemen1815086676c_ball @ a @ p @ X0) @ X1)) != $true) | (((ord_less @ real @ zero_zero @ real @ X0)) != $true)) )),
% 2.47/0.60 inference(forward_subsumption_resolution,[],[f1317,f1653])).
% 2.47/0.60 thf(f2150,plain,(
% 2.47/0.60 ( ! [X0 : real,X1 : (a > real)] : (($true != ((member @ a @ (auto_ll_on_flow0 @ a @ f @ x @ (sK2 @ X1 @ X0) @ (X1 @ (sK2 @ X1 @ X0))) @ (line_open_segment @ a @ a2 @ b)))) | ($true != ((ord_less @ real @ (abs_abs @ real @ (X1 @ (sK3 @ X1 @ X0))) @ one_one @ real))) | (zero_zero @ real != ((X1 @ p))) | (((topolo2071040574ous_on @ a @ real @ (elemen1815086676c_ball @ a @ p @ X0) @ X1)) != $true) | (((ord_less @ real @ zero_zero @ real @ X0)) != $true)) )),
% 2.47/0.60 inference(forward_subsumption_resolution,[],[f1318,f1653])).
% 2.47/0.60 thf(f3185,plain,(
% 2.47/0.60 ($true != $true) | ($true = ((member @ a @ (sK3 @ sK1 @ sK0) @ (elemen1815086676c_ball @ a @ p @ sK0)))) | (zero_zero @ real != ((sK1 @ p))) | ($true = ((member @ a @ (sK2 @ sK1 @ sK0) @ (elemen1815086676c_ball @ a @ p @ sK0)))) | ($true != ((ord_less @ real @ zero_zero @ real @ sK0)))),
% 2.47/0.60 inference(constrained_superposition,[],[f2147,f1310])).
% 2.47/0.60 thf(f3188,plain,(
% 2.47/0.60 ($true = ((member @ a @ (sK3 @ sK1 @ sK0) @ (elemen1815086676c_ball @ a @ p @ sK0)))) | (zero_zero @ real != ((sK1 @ p))) | ($true = ((member @ a @ (sK2 @ sK1 @ sK0) @ (elemen1815086676c_ball @ a @ p @ sK0)))) | ($true != ((ord_less @ real @ zero_zero @ real @ sK0)))),
% 2.47/0.60 inference(trivial_inequality_removal,[],[f3185])).
% 2.47/0.60 thf(f3190,plain,(
% 2.47/0.60 ($true = ((member @ a @ (sK3 @ sK1 @ sK0) @ (elemen1815086676c_ball @ a @ p @ sK0)))) | ($true = ((member @ a @ (sK2 @ sK1 @ sK0) @ (elemen1815086676c_ball @ a @ p @ sK0)))) | ($true != ((ord_less @ real @ zero_zero @ real @ sK0)))),
% 2.47/0.60 inference(forward_subsumption_resolution,[],[f3188,f1314])).
% 2.47/0.60 thf(f3192,plain,(
% 2.47/0.60 ($true = ((member @ a @ (sK3 @ sK1 @ sK0) @ (elemen1815086676c_ball @ a @ p @ sK0)))) | ($true = ((member @ a @ (sK2 @ sK1 @ sK0) @ (elemen1815086676c_ball @ a @ p @ sK0))))),
% 2.47/0.60 inference(forward_subsumption_resolution,[],[f3190,f1309])).
% 2.47/0.60 thf(f3203,definition,(
% 2.47/0.60 spl23_42 <=> ($true = ((member @ a @ (sK2 @ sK1 @ sK0) @ (elemen1815086676c_ball @ a @ p @ sK0))))),
% 2.47/0.60 introduced(definition,[new_symbols(definition,[spl23_42])],[avatar_definition])).
% 2.47/0.60 thf(f3205,plain,(
% 2.47/0.60 ($true = ((member @ a @ (sK2 @ sK1 @ sK0) @ (elemen1815086676c_ball @ a @ p @ sK0)))) | ~spl23_42),
% 2.47/0.60 inference(avatar_component_clause,[],[f3203])).
% 2.47/0.60 thf(f3207,definition,(
% 2.47/0.60 spl23_43 <=> ($true = ((member @ a @ (sK3 @ sK1 @ sK0) @ (elemen1815086676c_ball @ a @ p @ sK0))))),
% 2.47/0.60 introduced(definition,[new_symbols(definition,[spl23_43])],[avatar_definition])).
% 2.47/0.60 thf(f3208,plain,(
% 2.47/0.60 ($true != ((member @ a @ (sK3 @ sK1 @ sK0) @ (elemen1815086676c_ball @ a @ p @ sK0)))) | spl23_43),
% 2.47/0.60 inference(avatar_component_clause,[],[f3207])).
% 2.47/0.60 thf(f3209,plain,(
% 2.47/0.60 ($true = ((member @ a @ (sK3 @ sK1 @ sK0) @ (elemen1815086676c_ball @ a @ p @ sK0)))) | ~spl23_43),
% 2.47/0.60 inference(avatar_component_clause,[],[f3207])).
% 2.47/0.60 thf(f3210,plain,(
% 2.47/0.60 spl23_42 | spl23_43),
% 2.47/0.60 inference(avatar_split_clause,[],[f3192,f3207,f3203])).
% 2.47/0.60 thf(f3795,plain,(
% 2.47/0.60 ($true != $true) | ($true = ((ord_less @ real @ (abs_abs @ real @ (sK1 @ (sK3 @ sK1 @ sK0))) @ one_one @ real))) | ~spl23_43),
% 2.47/0.60 inference(constrained_superposition,[],[f1312,f3209])).
% 2.47/0.60 thf(f3796,plain,(
% 2.47/0.60 ($true = ((ord_less @ real @ (abs_abs @ real @ (sK1 @ (sK3 @ sK1 @ sK0))) @ one_one @ real))) | ~spl23_43),
% 2.47/0.60 inference(trivial_inequality_removal,[],[f3795])).
% 2.47/0.60 thf(f3800,plain,(
% 2.47/0.60 ( ! [X0 : real] : (($true != $true) | ($true = ((member @ a @ (sK2 @ (^[Y0 : a]: (sK1 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ X0) @ (elemen1815086676c_ball @ a @ p @ X0)))) | (zero_zero @ real != (((^[Y0 : a]: (sK1 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ p))) | ($true != ((topolo2071040574ous_on @ a @ real @ (elemen1815086676c_ball @ a @ p @ X0) @ (^[Y0 : a]: (sK1 @ ((^[Y1 : a]: (Y1)) @ Y0)))))) | (((ord_less @ real @ zero_zero @ real @ X0)) != $true) | (sK0 != X0)) ) | ~spl23_43),
% 2.47/0.60 inference(constrained_superposition,[],[f2148,f3796])).
% 2.47/0.60 thf(f3806,plain,(
% 2.47/0.60 ( ! [X0 : real] : (($true = ((member @ a @ (sK2 @ (^[Y0 : a]: (sK1 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ X0) @ (elemen1815086676c_ball @ a @ p @ X0)))) | (zero_zero @ real != (((^[Y0 : a]: (sK1 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ p))) | ($true != ((topolo2071040574ous_on @ a @ real @ (elemen1815086676c_ball @ a @ p @ X0) @ (^[Y0 : a]: (sK1 @ ((^[Y1 : a]: (Y1)) @ Y0)))))) | (((ord_less @ real @ zero_zero @ real @ X0)) != $true) | (sK0 != X0)) ) | ~spl23_43),
% 2.47/0.60 inference(trivial_inequality_removal,[],[f3800])).
% 2.47/0.60 thf(f3807,plain,(
% 2.47/0.60 ( ! [X0 : real] : (($true = ((member @ a @ (sK2 @ sK1 @ X0) @ (elemen1815086676c_ball @ a @ p @ X0)))) | (zero_zero @ real != ((sK1 @ p))) | ($true != ((topolo2071040574ous_on @ a @ real @ (elemen1815086676c_ball @ a @ p @ X0) @ sK1))) | (((ord_less @ real @ zero_zero @ real @ X0)) != $true) | (sK0 != X0)) ) | ~spl23_43),
% 2.47/0.60 inference(beta-eta_normalization,[],[f3806])).
% 2.47/0.60 thf(f3810,plain,(
% 2.47/0.60 ( ! [X0 : real] : (($true != ((topolo2071040574ous_on @ a @ real @ (elemen1815086676c_ball @ a @ p @ X0) @ sK1))) | ($true = ((member @ a @ (sK2 @ sK1 @ X0) @ (elemen1815086676c_ball @ a @ p @ X0)))) | (((ord_less @ real @ zero_zero @ real @ X0)) != $true) | (sK0 != X0)) ) | ~spl23_43),
% 2.47/0.60 inference(forward_subsumption_resolution,[],[f3807,f1314])).
% 2.47/0.60 thf(f4065,plain,(
% 2.47/0.60 ($true != $true) | ($true = ((member @ a @ (sK2 @ sK1 @ sK0) @ (elemen1815086676c_ball @ a @ p @ sK0)))) | ($true != ((ord_less @ real @ zero_zero @ real @ sK0))) | (sK0 != sK0) | ~spl23_43),
% 2.47/0.60 inference(constrained_superposition,[],[f3810,f1310])).
% 2.47/0.60 thf(f4066,plain,(
% 2.47/0.60 ($true = ((member @ a @ (sK2 @ sK1 @ sK0) @ (elemen1815086676c_ball @ a @ p @ sK0)))) | ($true != ((ord_less @ real @ zero_zero @ real @ sK0))) | ~spl23_43),
% 2.47/0.60 inference(trivial_inequality_removal,[],[f4065])).
% 2.47/0.60 thf(f4068,plain,(
% 2.47/0.60 ($true = ((member @ a @ (sK2 @ sK1 @ sK0) @ (elemen1815086676c_ball @ a @ p @ sK0)))) | ~spl23_43),
% 2.47/0.60 inference(forward_subsumption_resolution,[],[f4066,f1309])).
% 2.47/0.60 thf(f4069,plain,(
% 2.47/0.60 spl23_42 | ~spl23_43),
% 2.47/0.60 inference(avatar_split_clause,[],[f4068,f3207,f3203])).
% 2.47/0.60 thf(f4742,plain,(
% 2.47/0.60 ($true != $true) | ($true = ((member @ a @ (auto_ll_on_flow0 @ a @ f @ x @ (sK2 @ sK1 @ sK0) @ (sK1 @ (sK2 @ sK1 @ sK0))) @ (line_open_segment @ a @ a2 @ b)))) | ~spl23_42),
% 2.47/0.60 inference(constrained_superposition,[],[f1311,f3205])).
% 2.47/0.60 thf(f4751,plain,(
% 2.47/0.60 ($true = ((member @ a @ (auto_ll_on_flow0 @ a @ f @ x @ (sK2 @ sK1 @ sK0) @ (sK1 @ (sK2 @ sK1 @ sK0))) @ (line_open_segment @ a @ a2 @ b)))) | ~spl23_42),
% 2.47/0.60 inference(trivial_inequality_removal,[],[f4742])).
% 2.47/0.60 thf(f4798,plain,(
% 2.47/0.60 ($true != $true) | ($true = ((member @ a @ (sK3 @ sK1 @ sK0) @ (elemen1815086676c_ball @ a @ p @ sK0)))) | (zero_zero @ real != ((sK1 @ p))) | ($true != ((topolo2071040574ous_on @ a @ real @ (elemen1815086676c_ball @ a @ p @ sK0) @ sK1))) | ($true != ((ord_less @ real @ zero_zero @ real @ sK0))) | ~spl23_42),
% 2.47/0.60 inference(constrained_superposition,[],[f2149,f4751])).
% 2.47/0.60 thf(f4799,plain,(
% 2.47/0.60 ($true != $true) | ($true != ((ord_less @ real @ (abs_abs @ real @ (sK1 @ (sK3 @ sK1 @ sK0))) @ one_one @ real))) | (zero_zero @ real != ((sK1 @ p))) | ($true != ((topolo2071040574ous_on @ a @ real @ (elemen1815086676c_ball @ a @ p @ sK0) @ sK1))) | ($true != ((ord_less @ real @ zero_zero @ real @ sK0))) | ~spl23_42),
% 2.47/0.60 inference(constrained_superposition,[],[f2150,f4751])).
% 2.47/0.60 thf(f4800,plain,(
% 2.47/0.60 ($true != ((ord_less @ real @ (abs_abs @ real @ (sK1 @ (sK3 @ sK1 @ sK0))) @ one_one @ real))) | (zero_zero @ real != ((sK1 @ p))) | ($true != ((topolo2071040574ous_on @ a @ real @ (elemen1815086676c_ball @ a @ p @ sK0) @ sK1))) | ($true != ((ord_less @ real @ zero_zero @ real @ sK0))) | ~spl23_42),
% 2.47/0.60 inference(trivial_inequality_removal,[],[f4799])).
% 2.47/0.60 thf(f4801,plain,(
% 2.47/0.60 ($true = ((member @ a @ (sK3 @ sK1 @ sK0) @ (elemen1815086676c_ball @ a @ p @ sK0)))) | (zero_zero @ real != ((sK1 @ p))) | ($true != ((topolo2071040574ous_on @ a @ real @ (elemen1815086676c_ball @ a @ p @ sK0) @ sK1))) | ($true != ((ord_less @ real @ zero_zero @ real @ sK0))) | ~spl23_42),
% 2.47/0.60 inference(trivial_inequality_removal,[],[f4798])).
% 2.47/0.60 thf(f4802,plain,(
% 2.47/0.60 (zero_zero @ real != ((sK1 @ p))) | ($true != ((topolo2071040574ous_on @ a @ real @ (elemen1815086676c_ball @ a @ p @ sK0) @ sK1))) | ($true != ((ord_less @ real @ zero_zero @ real @ sK0))) | (~spl23_42 | ~spl23_43)),
% 2.47/0.60 inference(forward_subsumption_resolution,[],[f4800,f3796])).
% 2.47/0.60 thf(f4804,plain,(
% 2.47/0.60 ($true != ((topolo2071040574ous_on @ a @ real @ (elemen1815086676c_ball @ a @ p @ sK0) @ sK1))) | ($true != ((ord_less @ real @ zero_zero @ real @ sK0))) | (~spl23_42 | ~spl23_43)),
% 2.47/0.60 inference(forward_subsumption_resolution,[],[f4802,f1314])).
% 2.47/0.60 thf(f4805,plain,(
% 2.47/0.60 ($true != ((ord_less @ real @ zero_zero @ real @ sK0))) | (~spl23_42 | ~spl23_43)),
% 2.47/0.60 inference(forward_subsumption_resolution,[],[f4804,f1310])).
% 2.47/0.60 thf(f4806,plain,(
% 2.47/0.60 $false | (~spl23_42 | ~spl23_43)),
% 2.47/0.60 inference(forward_subsumption_resolution,[],[f4805,f1309])).
% 2.47/0.60 thf(f4807,plain,(
% 2.47/0.60 ~spl23_42 | ~spl23_43),
% 2.47/0.60 inference(avatar_contradiction_clause,[],[f4806])).
% 2.47/0.60 thf(f4809,plain,(
% 2.47/0.60 (zero_zero @ real != ((sK1 @ p))) | ($true != ((topolo2071040574ous_on @ a @ real @ (elemen1815086676c_ball @ a @ p @ sK0) @ sK1))) | ($true != ((ord_less @ real @ zero_zero @ real @ sK0))) | (~spl23_42 | spl23_43)),
% 2.47/0.60 inference(forward_subsumption_resolution,[],[f4801,f3208])).
% 2.47/0.60 thf(f4811,plain,(
% 2.47/0.60 ($true != ((topolo2071040574ous_on @ a @ real @ (elemen1815086676c_ball @ a @ p @ sK0) @ sK1))) | ($true != ((ord_less @ real @ zero_zero @ real @ sK0))) | (~spl23_42 | spl23_43)),
% 2.47/0.60 inference(forward_subsumption_resolution,[],[f4809,f1314])).
% 2.47/0.60 thf(f4813,plain,(
% 2.47/0.60 ($true != ((ord_less @ real @ zero_zero @ real @ sK0))) | (~spl23_42 | spl23_43)),
% 2.47/0.60 inference(forward_subsumption_resolution,[],[f4811,f1310])).
% 2.47/0.60 thf(f4814,plain,(
% 2.47/0.60 $false | (~spl23_42 | spl23_43)),
% 2.47/0.60 inference(forward_subsumption_resolution,[],[f4813,f1309])).
% 2.47/0.60 thf(f4815,plain,(
% 2.47/0.60 ~spl23_42 | spl23_43),
% 2.47/0.60 inference(avatar_contradiction_clause,[],[f4814])).
% 2.47/0.60 cnf(s41, plain, spl23_42 | spl23_43, inference(sat_conversion,[],[f3210])).
% 2.47/0.60 cnf(s54, plain, spl23_42 | ~spl23_43, inference(sat_conversion,[],[f4069])).
% 2.47/0.60 cnf(s87, plain, ~spl23_42 | ~spl23_43, inference(sat_conversion,[],[f4807])).
% 2.47/0.60 cnf(s88, plain, ~spl23_42 | spl23_43, inference(sat_conversion,[],[f4815])).
% 2.47/0.60 cnf(s103, plain, spl23_42, inference(rat,[],[s41,s54])).
% 2.47/0.60 cnf(s104, plain, spl23_43, inference(rat,[],[s88,s103])).
% 2.47/0.60 cnf(s105, plain, $false, inference(rat,[],[s87,s104,s103])).
% 2.47/0.60 thf(f4816,plain,(
% 2.47/0.60 $false),
% 2.47/0.60 inference(avatar_sat_refutation,[],[s105])).
% 2.47/0.60 % SZS output end Proof for theBenchmark
% 2.47/0.60 % (841248)------------------------------
% 2.47/0.60 % (841248)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.47/0.60 % (841248)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.47/0.60 % (841248)CaDiCaL version: 2.1.3
% 2.47/0.60 % (841248)Termination reason: Refutation
% 2.47/0.60 % (841248)Time elapsed: 0.222 s
% 2.47/0.60 % (841248)Peak memory usage: 15 MB
% 2.47/0.60 % (841248)Instructions burned: 429 (million)
% 2.47/0.60 % (841217)Success in time 0.394 s
% 2.47/0.60 % Vampire exiting
%------------------------------------------------------------------------------