%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP114^2 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 08:08:24 AM UTC 2026
% Result : Theorem 0.59s 0.39s
% Output : Refutation 0.59s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP114^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.19 % Computer : n018.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Sep 29 19:57:56 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.22 Running higher-order theorem proving
% 0.22/0.27 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.59/0.39 % (565320)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.59/0.39 % (565325)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3615541974:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.59/0.39 % (565328)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=3808782200:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.59/0.39 % (565326)lrs+10_16_si=on:nwc=1.5:random_seed=2760861541:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.59/0.39 % (565329)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3613016406:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.59/0.39 % (565327)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=24353891:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.59/0.39 % (565327)Instruction limit reached!
% 0.59/0.39 % (565327)------------------------------
% 0.59/0.39 % (565327)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.59/0.39 % (565327)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.39 % (565327)CaDiCaL version: 2.1.3
% 0.59/0.39 % (565327)Termination reason: Instruction limit
% 0.59/0.39 % (565327)Termination phase: shuffling
% 0.59/0.39 % (565327)Time elapsed: 0.003 s
% 0.59/0.39 % (565327)Peak memory usage: 10 MB
% 0.59/0.39 % (565327)Instructions burned: 5 (million)
% 0.59/0.39 % (565326)Instruction limit reached!
% 0.59/0.39 % (565326)------------------------------
% 0.59/0.39 % (565326)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.59/0.39 % (565326)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.39 % (565326)CaDiCaL version: 2.1.3
% 0.59/0.39 % (565326)Termination reason: Instruction limit
% 0.59/0.39 % (565326)Termination phase: Property scanning
% 0.59/0.39 % (565326)Time elapsed: 0.009 s
% 0.59/0.39 % (565326)Peak memory usage: 10 MB
% 0.59/0.39 % (565326)Instructions burned: 19 (million)
% 0.59/0.39 % (565331)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.59/0.39 % (565331)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.59/0.39 % (565325)Instruction limit reached!
% 0.59/0.39 % (565325)------------------------------
% 0.59/0.39 % (565325)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.59/0.39 % (565325)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.39 % (565325)CaDiCaL version: 2.1.3
% 0.59/0.39 % (565325)Termination reason: Instruction limit
% 0.59/0.39 % (565325)Termination phase: Saturation
% 0.59/0.39 % (565325)Time elapsed: 0.023 s
% 0.59/0.39 % (565325)Peak memory usage: 13 MB
% 0.59/0.39 % (565325)Instructions burned: 91 (million)
% 0.59/0.39 % (565331)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=398999384:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.59/0.39 % (565330)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2683261543:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.59/0.39 % (565337)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=612005881:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.59/0.39 % (565339)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.59/0.39 % (565329)Instruction limit reached!
% 0.59/0.39 % (565329)------------------------------
% 0.59/0.39 % (565329)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.59/0.39 % (565329)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.39 % (565329)CaDiCaL version: 2.1.3
% 0.59/0.39 % (565329)Termination reason: Instruction limit
% 0.59/0.39 % (565329)Termination phase: Naming
% 0.59/0.39 % (565329)Time elapsed: 0.024 s
% 0.59/0.39 % (565329)Peak memory usage: 11 MB
% 0.59/0.39 % (565329)Instructions burned: 25 (million)
% 0.59/0.39 % (565337)Instruction limit reached!
% 0.59/0.39 % (565337)------------------------------
% 0.59/0.39 % (565337)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.59/0.39 % (565337)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.39 % (565337)CaDiCaL version: 2.1.3
% 0.59/0.39 % (565337)Termination reason: Instruction limit
% 0.59/0.39 % (565337)Termination phase: shuffling
% 0.59/0.39 % (565337)Time elapsed: 0.003 s
% 0.59/0.39 % (565337)Peak memory usage: 10 MB
% 0.59/0.39 % (565337)Instructions burned: 5 (million)
% 0.59/0.39 % (565339)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2255878672:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.59/0.39 % (565338)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3200136753:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.59/0.39 % (565339)Instruction limit reached!
% 0.59/0.39 % (565339)------------------------------
% 0.59/0.39 % (565339)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.59/0.39 % (565339)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.39 % (565339)CaDiCaL version: 2.1.3
% 0.59/0.39 % (565339)Termination reason: Instruction limit
% 0.59/0.39 % (565339)Termination phase: shuffling
% 0.59/0.39 % (565339)Time elapsed: 0.002 s
% 0.59/0.39 % (565339)Peak memory usage: 10 MB
% 0.59/0.39 % (565339)Instructions burned: 9 (million)
% 0.59/0.39 % (565338)Instruction limit reached!
% 0.59/0.39 % (565338)------------------------------
% 0.59/0.39 % (565338)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.59/0.39 % (565338)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.39 % (565338)CaDiCaL version: 2.1.3
% 0.59/0.39 % (565338)Termination reason: Instruction limit
% 0.59/0.39 % (565338)Termination phase: shuffling
% 0.59/0.39 % (565338)Time elapsed: 0.003 s
% 0.59/0.39 % (565338)Peak memory usage: 10 MB
% 0.59/0.39 % (565338)Instructions burned: 5 (million)
% 0.59/0.39 % (565347)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=1470518537:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.59/0.39 % (565345)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.59/0.39 % (565345)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.59/0.39 % (565345)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=1577541363:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.59/0.39 % (565348)lrs+10_1_si=on:cs=on:random_seed=4255829128:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.59/0.39 % (565348)Instruction limit reached!
% 0.59/0.39 % (565348)------------------------------
% 0.59/0.39 % (565348)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.59/0.39 % (565348)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.39 % (565348)CaDiCaL version: 2.1.3
% 0.59/0.39 % (565348)Termination reason: Instruction limit
% 0.59/0.39 % (565348)Termination phase: shuffling
% 0.59/0.39 % (565348)Time elapsed: 0.005 s
% 0.59/0.39 % (565348)Peak memory usage: 10 MB
% 0.59/0.39 % (565348)Instructions burned: 9 (million)
% 0.59/0.39 % (565330)Instruction limit reached!
% 0.59/0.39 % (565330)------------------------------
% 0.59/0.39 % (565330)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.59/0.39 % (565330)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.39 % (565330)CaDiCaL version: 2.1.3
% 0.59/0.39 % (565330)Termination reason: Instruction limit
% 0.59/0.39 % (565330)Termination phase: Saturation
% 0.59/0.39 % (565330)Time elapsed: 0.036 s
% 0.59/0.39 % (565330)Peak memory usage: 13 MB
% 0.59/0.39 % (565330)Instructions burned: 76 (million)
% 0.59/0.39 % (565328) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-565320-565328"...
% 0.59/0.39 % (565345)Instruction limit reached!
% 0.59/0.39 % (565345)------------------------------
% 0.59/0.39 % (565345)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.59/0.39 % (565345)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.39 % (565345)CaDiCaL version: 2.1.3
% 0.59/0.39 % (565345)Termination reason: Instruction limit
% 0.59/0.39 % (565345)Termination phase: Property scanning
% 0.59/0.39 % (565345)Time elapsed: 0.013 s
% 0.59/0.39 % (565345)Peak memory usage: 10 MB
% 0.59/0.39 % (565345)Instructions burned: 29 (million)
% 0.59/0.39 % (565347)Instruction limit reached!
% 0.59/0.39 % (565347)------------------------------
% 0.59/0.39 % (565347)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.59/0.39 % (565347)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.39 % (565343)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2632900659:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.59/0.39 % (565347)CaDiCaL version: 2.1.3
% 0.59/0.39 % (565347)Termination reason: Instruction limit
% 0.59/0.39 % (565347)Termination phase: Saturation
% 0.59/0.39 % (565347)Time elapsed: 0.020 s
% 0.59/0.39 % (565347)Peak memory usage: 12 MB
% 0.59/0.39 % (565347)Instructions burned: 89 (million)
% 0.59/0.39 % (565328)...printing done.
% 0.59/0.39 % (565328)Refutation found. Thanks to Tanya!
% 0.59/0.39 % SZS status Theorem for theBenchmark
% 0.59/0.39 % SZS output start Proof for theBenchmark
% 0.59/0.39 thf(type_def_5, type, extended_ereal: $tType).
% 0.59/0.39 thf(type_def_6, type, extended_enat: $tType).
% 0.59/0.39 thf(type_def_7, type, real: $tType).
% 0.59/0.39 thf(type_def_8, type, set: $tType > $tType).
% 0.59/0.39 thf(type_def_9, type, num: $tType).
% 0.59/0.39 thf(type_def_10, type, nat: $tType).
% 0.59/0.39 thf(type_def_11, type, a: $tType).
% 0.59/0.39 thf(type_def_12, type, sTfun: ($tType * $tType) > $tType).
% 0.59/0.39 thf(func_def_0, type, type: !>[X0: $tType]:($o)).
% 0.59/0.39 thf(func_def_1, type, zero: !>[X0: $tType]:($o)).
% 0.59/0.39 thf(func_def_2, type, numeral: !>[X0: $tType]:($o)).
% 0.59/0.39 thf(func_def_3, type, uminus: !>[X0: $tType]:($o)).
% 0.59/0.39 thf(func_def_4, type, ord: !>[X0: $tType]:($o)).
% 0.59/0.39 thf(func_def_5, type, ring_char_0: !>[X0: $tType]:($o)).
% 0.59/0.39 thf(func_def_6, type, neg_numeral: !>[X0: $tType]:($o)).
% 0.59/0.39 thf(func_def_7, type, order: !>[X0: $tType]:($o)).
% 0.59/0.39 thf(func_def_8, type, group_add: !>[X0: $tType]:($o)).
% 0.59/0.39 thf(func_def_9, type, linorder: !>[X0: $tType]:($o)).
% 0.59/0.39 thf(func_def_10, type, preorder: !>[X0: $tType]:($o)).
% 0.59/0.39 thf(func_def_11, type, semiring_char_0: !>[X0: $tType]:($o)).
% 0.59/0.39 thf(func_def_12, type, linordered_idom: !>[X0: $tType]:($o)).
% 0.59/0.39 thf(func_def_13, type, linordered_field: !>[X0: $tType]:($o)).
% 0.59/0.39 thf(func_def_14, type, boolean_algebra: !>[X0: $tType]:($o)).
% 0.59/0.39 thf(func_def_15, type, ordered_ab_group_add: !>[X0: $tType]:($o)).
% 0.59/0.39 thf(func_def_16, type, linord219039673up_add: !>[X0: $tType]:($o)).
% 0.59/0.39 thf(func_def_17, type, ordere142940540dd_abs: !>[X0: $tType]:($o)).
% 0.59/0.39 thf(func_def_18, type, real_V2090557954_space: !>[X0: $tType]:($o)).
% 0.59/0.39 thf(func_def_19, type, linord1659791738miring: !>[X0: $tType]:($o)).
% 0.59/0.39 thf(func_def_20, type, topolo259154727pology: !>[X0: $tType]:($o)).
% 0.59/0.39 thf(func_def_21, type, topolo503727757_space: !>[X0: $tType]:($o)).
% 0.59/0.39 thf(func_def_22, type, canoni770627133id_add: !>[X0: $tType]:($o)).
% 0.59/0.39 thf(func_def_23, type, extended_enat2: (nat > extended_enat)).
% 0.59/0.39 thf(func_def_24, type, extended_case_enat: !>[X0: $tType]:(((nat > X0) > X0 > extended_enat > X0))).
% 0.59/0.39 thf(func_def_25, type, extended_rec_enat: !>[X0: $tType]:(((nat > X0) > X0 > extended_enat > X0))).
% 0.59/0.39 thf(func_def_26, type, extend1396239628finity: !>[X0: $tType]:(X0)).
% 0.59/0.39 thf(func_def_27, type, extended_the_enat: (extended_enat > nat)).
% 0.59/0.39 thf(func_def_28, type, extended_MInfty: extended_ereal).
% 0.59/0.39 thf(func_def_29, type, extended_PInfty: extended_ereal).
% 0.59/0.39 thf(func_def_30, type, extended_ereal2: (real > extended_ereal)).
% 0.59/0.39 thf(func_def_31, type, extended_size_ereal: (extended_ereal > nat)).
% 0.59/0.39 thf(func_def_32, type, extend1771934483f_enat: (extended_enat > extended_ereal)).
% 0.59/0.39 thf(func_def_33, type, extend1716541707_ereal: (extended_ereal > real)).
% 0.59/0.39 thf(func_def_34, type, abs_abs: !>[X0: $tType]:((X0 > X0))).
% 0.59/0.39 thf(func_def_35, type, uminus_uminus: !>[X0: $tType]:((X0 > X0))).
% 0.59/0.39 thf(func_def_36, type, zero_zero: !>[X0: $tType]:(X0)).
% 0.59/0.39 thf(func_def_37, type, lower_107104146le_lsc: !>[X0: $tType, X1: $tType]:(((X0 > X1) > $o))).
% 0.59/0.39 thf(func_def_38, type, lower_582600101lsc_at: !>[X0: $tType, X1: $tType]:((X0 > (X0 > X1) > $o))).
% 0.59/0.39 thf(func_def_39, type, lower_1879122655c_hull: !>[X0: $tType]:(((X0 > extended_ereal) > X0 > extended_ereal))).
% 0.59/0.39 thf(func_def_40, type, neg_numeral_dbl: !>[X0: $tType]:((X0 > X0))).
% 0.59/0.39 thf(func_def_41, type, neg_numeral_sub: !>[X0: $tType]:((num > num > X0))).
% 0.59/0.39 thf(func_def_42, type, numeral_numeral: !>[X0: $tType]:((num > X0))).
% 0.59/0.39 thf(func_def_43, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.59/0.39 thf(func_def_44, type, order_Greatest: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.59/0.39 thf(func_def_45, type, order_antimono: !>[X0: $tType, X1: $tType]:(((X0 > X1) > $o))).
% 0.59/0.39 thf(func_def_46, type, order_strict_mono: !>[X0: $tType, X1: $tType]:(((X0 > X1) > $o))).
% 0.59/0.39 thf(func_def_47, type, divide_divide: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.59/0.39 thf(func_def_48, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.59/0.39 thf(func_def_49, type, f: (a > extended_ereal)).
% 0.59/0.39 thf(func_def_50, type, g: (a > extended_ereal)).
% 0.59/0.39 thf(func_def_51, type, x: a).
% 0.59/0.39 thf(func_def_55, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.59/0.39 thf(func_def_56, type, vIMP: ($o > $o > $o)).
% 0.59/0.39 thf(func_def_57, type, db1: !>[X0: $tType]:(X0)).
% 0.59/0.39 thf(func_def_58, type, db0: !>[X0: $tType]:(X0)).
% 0.59/0.39 thf(func_def_59, type, db2: !>[X0: $tType]:(X0)).
% 0.59/0.39 thf(func_def_60, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.59/0.39 thf(func_def_61, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.59/0.39 thf(func_def_62, type, vOR: ($o > $o > $o)).
% 0.59/0.39 thf(func_def_63, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.59/0.39 thf(func_def_64, type, vAND: ($o > $o > $o)).
% 0.59/0.39 thf(func_def_65, type, sP0: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 0.59/0.39 thf(func_def_66, type, sP1: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 0.59/0.39 thf(func_def_67, type, sP2: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 0.59/0.39 thf(func_def_68, type, sP3: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 0.59/0.39 thf(func_def_69, type, sP4: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 0.59/0.39 thf(func_def_70, type, sP5: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 0.59/0.39 thf(func_def_71, type, sP6: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 0.59/0.39 thf(func_def_72, type, sP7: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 0.59/0.39 thf(func_def_73, type, sP8: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 0.59/0.39 thf(func_def_74, type, sP9: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 0.59/0.39 thf(func_def_75, type, sP10: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 0.59/0.39 thf(func_def_76, type, sP11: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 0.59/0.39 thf(func_def_77, type, sP12: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 0.59/0.39 thf(func_def_78, type, sP13: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 0.59/0.39 thf(func_def_79, type, sP14: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 0.59/0.39 thf(func_def_80, type, sP15: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 0.59/0.39 thf(func_def_81, type, sP16: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 0.59/0.39 thf(func_def_82, type, sP17: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 0.59/0.39 thf(func_def_83, type, sP18: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 0.59/0.39 thf(func_def_84, type, sP19: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 0.59/0.39 thf(func_def_85, type, sP20: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 0.59/0.39 thf(func_def_86, type, sP21: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 0.59/0.39 thf(func_def_87, type, sP22: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 0.59/0.39 thf(func_def_88, type, sP23: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 0.59/0.39 thf(func_def_89, type, sP24: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 0.59/0.39 thf(func_def_90, type, sP25: (extended_ereal > extended_ereal > $o)).
% 0.59/0.39 thf(func_def_91, type, sP26: (extended_ereal > extended_ereal > $o)).
% 0.59/0.39 thf(func_def_92, type, sP27: (extended_ereal > extended_ereal > $o)).
% 0.59/0.39 thf(func_def_93, type, sP28: (extended_ereal > extended_ereal > $o)).
% 0.59/0.39 thf(func_def_94, type, sP29: (extended_ereal > extended_ereal > $o)).
% 0.59/0.39 thf(func_def_95, type, sP30: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.59/0.39 thf(func_def_96, type, sP31: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.59/0.39 thf(func_def_97, type, sK32: !>[X0: $tType]:(((X0 > $o) > X0 > X0))).
% 0.59/0.40 thf(func_def_98, type, sK33: ((extended_ereal > $o) > real)).
% 0.59/0.40 thf(func_def_99, type, sK34: (extended_ereal > extended_ereal > real)).
% 0.59/0.40 thf(func_def_100, type, sK35: (set @ extended_ereal > extended_ereal)).
% 0.59/0.40 thf(func_def_101, type, sK36: (extended_ereal > set @ extended_ereal > extended_ereal)).
% 0.59/0.40 thf(func_def_102, type, sK37: (extended_ereal > real)).
% 0.59/0.40 thf(func_def_103, type, sK38: (extended_ereal > real)).
% 0.59/0.40 thf(func_def_104, type, sK39: (extended_ereal > real)).
% 0.59/0.40 thf(func_def_105, type, sK40: (extended_ereal > real)).
% 0.59/0.40 thf(func_def_106, type, sK41: (extended_ereal > real)).
% 0.59/0.40 thf(func_def_107, type, sK42: (extended_ereal > real)).
% 0.59/0.40 thf(func_def_108, type, sK43: (extended_ereal > real)).
% 0.59/0.40 thf(func_def_109, type, sK44: (extended_ereal > real)).
% 0.59/0.40 thf(func_def_110, type, sK45: (extended_ereal > real)).
% 0.59/0.40 thf(func_def_111, type, sK46: (extended_ereal > real)).
% 0.59/0.40 thf(func_def_112, type, sK47: (extended_ereal > real)).
% 0.59/0.40 thf(func_def_113, type, sK48: (extended_ereal > real)).
% 0.59/0.40 thf(func_def_114, type, sK49: (extended_ereal > real)).
% 0.59/0.40 thf(func_def_115, type, sK50: (extended_ereal > real)).
% 0.59/0.40 thf(func_def_116, type, sK51: (extended_ereal > real)).
% 0.59/0.40 thf(func_def_117, type, sK52: (extended_ereal > real)).
% 0.59/0.40 thf(func_def_118, type, sK53: (extended_ereal > real)).
% 0.59/0.40 thf(func_def_119, type, sK54: (extended_ereal > real)).
% 0.59/0.40 thf(func_def_120, type, sK55: (extended_ereal > real)).
% 0.59/0.40 thf(func_def_121, type, sK56: (extended_ereal > real)).
% 0.59/0.40 thf(func_def_122, type, sK57: (extended_ereal > real)).
% 0.59/0.40 thf(func_def_123, type, sK58: (extended_ereal > real)).
% 0.59/0.40 thf(func_def_124, type, sK59: (extended_ereal > real)).
% 0.59/0.40 thf(func_def_125, type, sK60: (extended_ereal > real)).
% 0.59/0.40 thf(func_def_126, type, sK61: (extended_ereal > real)).
% 0.59/0.40 thf(func_def_127, type, sK62: (extended_ereal > real)).
% 0.59/0.40 thf(func_def_128, type, sK63: (extended_ereal > real)).
% 0.59/0.40 thf(func_def_129, type, sK64: ((extended_ereal > extended_ereal > $o) > real)).
% 0.59/0.40 thf(func_def_130, type, sK65: ((extended_ereal > extended_ereal > $o) > real)).
% 0.59/0.40 thf(func_def_131, type, sK66: ((extended_ereal > extended_ereal > $o) > extended_ereal)).
% 0.59/0.40 thf(func_def_132, type, sK67: ((extended_ereal > extended_ereal > $o) > real)).
% 0.59/0.40 thf(func_def_133, type, sK68: ((extended_ereal > extended_ereal > $o) > extended_ereal)).
% 0.59/0.40 thf(func_def_134, type, sK69: ((extended_ereal > extended_ereal > $o) > real)).
% 0.59/0.40 thf(func_def_135, type, sK70: ((nat > $o) > nat > nat)).
% 0.59/0.40 thf(func_def_136, type, sK71: !>[X0: $tType]:(((X0 > extended_ereal) > (X0 > extended_ereal) > X0))).
% 0.59/0.40 thf(func_def_137, type, sK72: !>[X0: $tType]:(((X0 > extended_ereal) > (X0 > extended_ereal) > X0))).
% 0.59/0.40 thf(func_def_138, type, sK73: !>[X0: $tType]:(((X0 > extended_ereal) > (X0 > extended_ereal) > X0 > extended_ereal))).
% 0.59/0.40 thf(func_def_139, type, sK74: !>[X0: $tType]:(((X0 > extended_ereal) > (X0 > extended_ereal) > X0))).
% 0.59/0.40 thf(func_def_140, type, sK75: (nat > (nat > $o) > nat)).
% 0.59/0.40 thf(func_def_141, type, sK76: ((nat > $o) > nat)).
% 0.59/0.40 thf(func_def_142, type, sK77: ((extended_ereal > $o) > real)).
% 0.59/0.40 thf(func_def_143, type, sK78: (extended_ereal > real)).
% 0.59/0.40 thf(func_def_144, type, sK79: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.59/0.40 thf(func_def_145, type, sK80: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.59/0.40 thf(func_def_146, type, sK81: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.59/0.40 thf(func_def_147, type, sK82: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.59/0.40 thf(func_def_148, type, sK83: !>[X0: $tType]:(((X0 > extended_ereal) > (X0 > extended_ereal) > X0))).
% 0.59/0.40 thf(func_def_149, type, sK84: ((extended_ereal > extended_ereal > $o) > real)).
% 0.59/0.40 thf(func_def_150, type, sK85: ((extended_ereal > extended_ereal > $o) > real)).
% 0.59/0.40 thf(func_def_151, type, sK86: ((extended_ereal > extended_ereal > $o) > real)).
% 0.59/0.40 thf(func_def_152, type, sK87: ((extended_ereal > extended_ereal > $o) > real)).
% 0.59/0.40 thf(func_def_153, type, sK88: ((extended_ereal > extended_ereal > $o) > real)).
% 0.59/0.40 thf(func_def_154, type, sK89: ((extended_ereal > extended_ereal > $o) > real)).
% 0.59/0.40 thf(func_def_155, type, sK90: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.59/0.40 thf(func_def_156, type, sK91: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.59/0.40 thf(func_def_157, type, sK92: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.59/0.40 thf(func_def_158, type, sK93: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.59/0.40 thf(func_def_159, type, sK94: ((extended_ereal > $o) > real)).
% 0.59/0.40 thf(func_def_160, type, sK95: (extended_ereal > real)).
% 0.59/0.40 thf(func_def_161, type, sK96: (extended_ereal > real)).
% 0.59/0.40 thf(func_def_162, type, sK97: (extended_ereal > real)).
% 0.59/0.40 thf(func_def_163, type, sK98: (extended_ereal > real)).
% 0.59/0.40 thf(func_def_164, type, sK99: (extended_ereal > real)).
% 0.59/0.40 thf(func_def_165, type, sK100: (extended_ereal > real)).
% 0.59/0.40 thf(func_def_166, type, sK101: (nat > (nat > $o) > nat)).
% 0.59/0.40 thf(func_def_167, type, sK102: (extended_ereal > real)).
% 0.59/0.40 thf(func_def_168, type, sK103: ((extended_ereal > extended_ereal > $o) > real)).
% 0.59/0.40 thf(func_def_169, type, sK104: ((extended_ereal > extended_ereal > $o) > extended_ereal)).
% 0.59/0.40 thf(func_def_170, type, sK105: ((extended_ereal > extended_ereal > $o) > real)).
% 0.59/0.40 thf(func_def_171, type, sK106: ((extended_ereal > extended_ereal > $o) > real)).
% 0.59/0.40 thf(func_def_172, type, sK107: ((extended_ereal > extended_ereal > $o) > extended_ereal)).
% 0.59/0.40 thf(func_def_173, type, sK108: ((extended_ereal > extended_ereal > $o) > real)).
% 0.59/0.40 thf(func_def_174, type, sK109: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.59/0.40 thf(func_def_175, type, sK110: (extended_ereal > extended_ereal > real)).
% 0.59/0.40 thf(func_def_176, type, sK111: ((nat > $o) > nat > nat)).
% 0.59/0.40 thf(func_def_177, type, sK112: (extended_ereal > real > real)).
% 0.59/0.40 thf(func_def_178, type, sK113: (extended_ereal > real)).
% 0.59/0.40 thf(func_def_179, type, sK114: ((extended_ereal > $o) > real)).
% 0.59/0.40 thf(func_def_180, type, sK115: (set @ extended_ereal > extended_ereal)).
% 0.59/0.40 thf(func_def_181, type, sK116: (extended_ereal > set @ extended_ereal > extended_ereal)).
% 0.59/0.40 thf(func_def_182, type, sK117: (extended_enat > nat)).
% 0.59/0.40 thf(func_def_183, type, sK118: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.59/0.40 thf(func_def_184, type, sK119: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.59/0.40 thf(func_def_185, type, sK120: (extended_ereal > real)).
% 0.59/0.40 thf(func_def_186, type, sK121: (extended_ereal > real)).
% 0.59/0.40 thf(func_def_187, type, sK122: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > X1) > X0))).
% 0.59/0.40 thf(func_def_188, type, sK123: (extended_ereal > real)).
% 0.59/0.40 thf(func_def_189, type, sK124: (extended_ereal > real)).
% 0.59/0.40 thf(func_def_190, type, sK125: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.59/0.40 thf(func_def_191, type, sK126: !>[X0: $tType]:((X0 > (X0 > $o) > X0))).
% 0.59/0.40 thf(func_def_192, type, sK127: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.59/0.40 thf(func_def_193, type, sK128: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.59/0.40 thf(func_def_194, type, sK129: (extended_ereal > real)).
% 0.59/0.40 thf(func_def_195, type, sK130: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.59/0.40 thf(func_def_196, type, sK131: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.59/0.40 thf(func_def_197, type, sK132: (extended_ereal > real)).
% 0.59/0.40 thf(func_def_198, type, vNOT: ($o > $o)).
% 0.59/0.40 thf(f1,axiom,(
% 0.59/0.40 ! [X3 : a] : (ord_less_eq @ extended_ereal @ (g @ X3) @ (f @ X3))),
% 0.59/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_assms)).
% 0.59/0.40 thf(f325,conjecture,(
% 0.59/0.40 (ord_less_eq @ extended_ereal @ (g @ x) @ (f @ x))),
% 0.59/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 0.59/0.40 thf(f326,negated_conjecture,(
% 0.59/0.40 ~(ord_less_eq @ extended_ereal @ (g @ x) @ (f @ x))),
% 0.59/0.40 inference(negated_conjecture,[status(cth)],[f325])).
% 0.59/0.40 thf(f398,plain,(
% 0.59/0.40 ! [X0 : a] : (ord_less_eq @ extended_ereal @ (g @ X0) @ (f @ X0))),
% 0.59/0.40 inference(rectify,[],[f1])).
% 0.59/0.40 thf(f399,plain,(
% 0.59/0.40 ! [X0 : a] : (((ord_less_eq @ extended_ereal @ (g @ X0) @ (f @ X0))) = $true)),
% 0.59/0.40 inference(fool_elimination,[],[f398])).
% 0.59/0.40 thf(f632,plain,(
% 0.59/0.40 ~(ord_less_eq @ extended_ereal @ (g @ x) @ (f @ x))),
% 0.59/0.40 inference(rectify,[],[f326])).
% 0.59/0.40 thf(f633,plain,(
% 0.59/0.40 ~ (((ord_less_eq @ extended_ereal @ (g @ x) @ (f @ x))) = $true)),
% 0.59/0.40 inference(fool_elimination,[],[f632])).
% 0.59/0.40 thf(f838,plain,(
% 0.59/0.40 (((ord_less_eq @ extended_ereal @ (g @ x) @ (f @ x))) != $true)),
% 0.59/0.40 inference(flattening,[],[f633])).
% 0.59/0.40 thf(f1406,plain,(
% 0.59/0.40 (((ord_less_eq @ extended_ereal @ (g @ x) @ (f @ x))) != $true)),
% 0.59/0.40 inference(cnf_transformation,[],[f838])).
% 0.59/0.40 thf(f1574,plain,(
% 0.59/0.40 ( ! [X0 : a] : ((((ord_less_eq @ extended_ereal @ (g @ X0) @ (f @ X0))) = $true)) )),
% 0.59/0.40 inference(cnf_transformation,[],[f399])).
% 0.59/0.40 thf(f2380,definition,(
% 0.59/0.40 spl133_60 <=> (((ord_less_eq @ extended_ereal @ (g @ x) @ (f @ x))) = $true)),
% 0.59/0.40 introduced(definition,[new_symbols(definition,[spl133_60])],[avatar_definition])).
% 0.59/0.40 thf(f2382,plain,(
% 0.59/0.40 (((ord_less_eq @ extended_ereal @ (g @ x) @ (f @ x))) != $true) | spl133_60),
% 0.59/0.40 inference(avatar_component_clause,[],[f2380])).
% 0.59/0.40 thf(f2383,plain,(
% 0.59/0.40 ~spl133_60),
% 0.59/0.40 inference(avatar_split_clause,[],[f1406,f2380])).
% 0.59/0.40 thf(f2577,plain,(
% 0.59/0.40 $false | spl133_60),
% 0.59/0.40 inference(forward_subsumption_resolution,[],[f2382,f1574])).
% 0.59/0.40 thf(f2578,plain,(
% 0.59/0.40 spl133_60),
% 0.59/0.40 inference(avatar_contradiction_clause,[],[f2577])).
% 0.59/0.40 cnf(s64, plain, ~spl133_60, inference(sat_conversion,[],[f2383])).
% 0.59/0.40 cnf(s108, plain, spl133_60, inference(sat_conversion,[],[f2578])).
% 0.59/0.40 cnf(s109, plain, $false, inference(rat,[],[s64,s108])).
% 0.59/0.40 thf(f2579,plain,(
% 0.59/0.40 $false),
% 0.59/0.40 inference(avatar_sat_refutation,[],[s109])).
% 0.59/0.40 % SZS output end Proof for theBenchmark
% 0.59/0.40 % (565328)------------------------------
% 0.59/0.40 % (565328)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.59/0.40 % (565328)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.40 % (565328)CaDiCaL version: 2.1.3
% 0.59/0.40 % (565328)Termination reason: Refutation
% 0.59/0.40 % (565328)Time elapsed: 0.059 s
% 0.59/0.40 % (565328)Peak memory usage: 14 MB
% 0.59/0.40 % (565328)Instructions burned: 119 (million)
% 0.59/0.40 % (565320)Success in time 0.113 s
% 0.59/0.40 % Vampire exiting
%------------------------------------------------------------------------------