%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP072^2 : 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 : n011.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 08:08:13 AM UTC 2026
% Result : Theorem 0.55s 0.40s
% Output : Refutation 0.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP072^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n011.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 19:47:16 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 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
% 0.55/0.40 % (553454)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.55/0.40 % (553463)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3761812050:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.55/0.40 % (553465)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.55/0.40 % (553465)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
% 0.55/0.40 % (553461)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1820504956:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.55/0.40 % (553459)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=379857439:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.55/0.40 % (553460)lrs+10_16_si=on:nwc=1.5:random_seed=2116936060:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.55/0.40 % (553463)Instruction limit reached!
% 0.55/0.40 % (553463)------------------------------
% 0.55/0.40 % (553463)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.55/0.40 % (553463)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.55/0.40 % (553463)CaDiCaL version: 2.1.3
% 0.55/0.40 % (553463)Termination reason: Instruction limit
% 0.55/0.40 % (553463)Termination phase: Property scanning
% 0.55/0.40 % (553463)Time elapsed: 0.007 s
% 0.55/0.40 % (553463)Peak memory usage: 10 MB
% 0.55/0.40 % (553463)Instructions burned: 26 (million)
% 0.55/0.40 % (553462)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=795509865: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)
% 0.55/0.40 % (553464)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2802102373:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.55/0.40 % (553465)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=3760528783:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.55/0.40 % (553461)Instruction limit reached!
% 0.55/0.40 % (553461)------------------------------
% 0.55/0.40 % (553461)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.55/0.40 % (553461)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.55/0.40 % (553461)CaDiCaL version: 2.1.3
% 0.55/0.40 % (553461)Termination reason: Instruction limit
% 0.55/0.40 % (553461)Termination phase: shuffling
% 0.55/0.40 % (553461)Time elapsed: 0.002 s
% 0.55/0.40 % (553461)Peak memory usage: 10 MB
% 0.55/0.40 % (553461)Instructions burned: 3 (million)
% 0.55/0.40 % (553460)Instruction limit reached!
% 0.55/0.40 % (553460)------------------------------
% 0.55/0.40 % (553460)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.55/0.40 % (553460)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.55/0.40 % (553460)CaDiCaL version: 2.1.3
% 0.55/0.40 % (553460)Termination reason: Instruction limit
% 0.55/0.40 % (553460)Termination phase: Property scanning
% 0.55/0.40 % (553460)Time elapsed: 0.018 s
% 0.55/0.40 % (553460)Peak memory usage: 10 MB
% 0.55/0.40 % (553460)Instructions burned: 27 (million)
% 0.55/0.40 % (553474)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=116664162:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.55/0.40 % (553474)Instruction limit reached!
% 0.55/0.40 % (553474)------------------------------
% 0.55/0.40 % (553474)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.55/0.40 % (553474)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.55/0.40 % (553474)CaDiCaL version: 2.1.3
% 0.55/0.40 % (553474)Termination reason: Instruction limit
% 0.55/0.40 % (553474)Termination phase: shuffling
% 0.55/0.40 % (553474)Time elapsed: 0.002 s
% 0.55/0.40 % (553474)Peak memory usage: 10 MB
% 0.55/0.40 % (553474)Instructions burned: 6 (million)
% 0.55/0.40 % (553473)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3179948297:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.55/0.40 % (553473)Instruction limit reached!
% 0.55/0.40 % (553473)------------------------------
% 0.55/0.40 % (553473)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.55/0.40 % (553473)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.55/0.40 % (553473)CaDiCaL version: 2.1.3
% 0.55/0.40 % (553473)Termination reason: Instruction limit
% 0.55/0.40 % (553473)Termination phase: shuffling
% 0.55/0.40 % (553473)Time elapsed: 0.002 s
% 0.55/0.40 % (553473)Peak memory usage: 10 MB
% 0.55/0.40 % (553473)Instructions burned: 2 (million)
% 0.55/0.40 % (553477)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1504723492:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.55/0.40 % (553477)Instruction limit reached!
% 0.55/0.40 % (553477)------------------------------
% 0.55/0.40 % (553477)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.55/0.40 % (553477)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.55/0.40 % (553477)CaDiCaL version: 2.1.3
% 0.55/0.40 % (553477)Termination reason: Instruction limit
% 0.55/0.40 % (553477)Termination phase: shuffling
% 0.55/0.40 % (553477)Time elapsed: 0.003 s
% 0.55/0.40 % (553477)Peak memory usage: 10 MB
% 0.55/0.40 % (553477)Instructions burned: 13 (million)
% 0.55/0.40 % (553464)Instruction limit reached!
% 0.55/0.40 % (553464)------------------------------
% 0.55/0.40 % (553464)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.55/0.40 % (553464)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.55/0.40 % (553464)CaDiCaL version: 2.1.3
% 0.55/0.40 % (553464)Termination reason: Instruction limit
% 0.55/0.40 % (553464)Termination phase: Equality resolution with deletion
% 0.55/0.40 % (553464)Time elapsed: 0.036 s
% 0.55/0.40 % (553464)Peak memory usage: 12 MB
% 0.55/0.40 % (553464)Instructions burned: 76 (million)
% 0.55/0.40 % (553476)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.55/0.40 % (553459)Instruction limit reached!
% 0.55/0.40 % (553459)------------------------------
% 0.55/0.40 % (553459)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.55/0.40 % (553459)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.55/0.40 % (553459)CaDiCaL version: 2.1.3
% 0.55/0.40 % (553459)Termination reason: Instruction limit
% 0.55/0.40 % (553459)Termination phase: Property scanning
% 0.55/0.40 % (553459)Time elapsed: 0.042 s
% 0.55/0.40 % (553459)Peak memory usage: 12 MB
% 0.55/0.40 % (553459)Instructions burned: 88 (million)
% 0.55/0.40 % (553476)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3162009857:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.55/0.40 % (553479)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
% 0.55/0.40 % (553479)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.55/0.40 % (553481)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=1032501547:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.55/0.40 % (553479)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3551274209:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.55/0.40 % (553476)Instruction limit reached!
% 0.55/0.40 % (553476)------------------------------
% 0.55/0.40 % (553476)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.55/0.40 % (553476)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.55/0.40 % (553476)CaDiCaL version: 2.1.3
% 0.55/0.40 % (553476)Termination reason: Instruction limit
% 0.55/0.40 % (553476)Termination phase: shuffling
% 0.55/0.40 % (553476)Time elapsed: 0.007 s
% 0.55/0.40 % (553476)Peak memory usage: 10 MB
% 0.55/0.40 % (553476)Instructions burned: 8 (million)
% 0.55/0.40 % (553482)lrs+10_1_si=on:cs=on:random_seed=2854949967:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.55/0.40 % (553483)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.55/0.40 % (553483)ott+1002_20_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:plsqr=1,32:bce=on:uwa=interpreted_only:foolp=on:random_seed=2173250609:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.55/0.40 % (553482)Instruction limit reached!
% 0.55/0.40 % (553482)------------------------------
% 0.55/0.40 % (553482)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.55/0.40 % (553482)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.55/0.40 % (553482)CaDiCaL version: 2.1.3
% 0.55/0.40 % (553482)Termination reason: Instruction limit
% 0.55/0.40 % (553482)Termination phase: shuffling
% 0.55/0.40 % (553482)Time elapsed: 0.005 s
% 0.55/0.40 % (553482)Peak memory usage: 10 MB
% 0.55/0.40 % (553482)Instructions burned: 9 (million)
% 0.55/0.40 % (553483)Instruction limit reached!
% 0.55/0.40 % (553483)------------------------------
% 0.55/0.40 % (553483)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.55/0.40 % (553483)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.55/0.40 % (553483)CaDiCaL version: 2.1.3
% 0.55/0.40 % (553483)Termination reason: Instruction limit
% 0.55/0.40 % (553483)Termination phase: shuffling
% 0.55/0.40 % (553483)Time elapsed: 0.003 s
% 0.55/0.40 % (553483)Peak memory usage: 10 MB
% 0.55/0.40 % (553483)Instructions burned: 5 (million)
% 0.55/0.40 % (553479)Instruction limit reached!
% 0.55/0.40 % (553479)------------------------------
% 0.55/0.40 % (553479)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.55/0.40 % (553479)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.55/0.40 % (553479)CaDiCaL version: 2.1.3
% 0.55/0.40 % (553479)Termination reason: Instruction limit
% 0.55/0.40 % (553479)Termination phase: Property scanning
% 0.55/0.40 % (553479)Time elapsed: 0.014 s
% 0.55/0.40 % (553479)Peak memory usage: 11 MB
% 0.55/0.40 % (553479)Instructions burned: 30 (million)
% 0.55/0.40 % (553462) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-553454-553462"...
% 0.55/0.40 % (553481)Instruction limit reached!
% 0.55/0.40 % (553481)------------------------------
% 0.55/0.40 % (553481)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.55/0.40 % (553481)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.55/0.40 % (553481)CaDiCaL version: 2.1.3
% 0.55/0.40 % (553481)Termination reason: Instruction limit
% 0.55/0.40 % (553481)Termination phase: Property scanning
% 0.55/0.40 % (553481)Time elapsed: 0.020 s
% 0.55/0.40 % (553481)Peak memory usage: 11 MB
% 0.55/0.40 % (553481)Instructions burned: 87 (million)
% 0.55/0.40 % (553462)...printing done.
% 0.55/0.40 % (553487)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=740254076:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 0.55/0.40 % (553462)Refutation found. Thanks to Tanya!
% 0.55/0.40 % SZS status Theorem for theBenchmark
% 0.55/0.40 % SZS output start Proof for theBenchmark
% 0.55/0.40 thf(type_def_5, type, hF_Mirabelle_hf: $tType).
% 0.55/0.40 thf(type_def_6, type, set: $tType > $tType).
% 0.55/0.40 thf(type_def_7, type, nat: $tType).
% 0.55/0.40 thf(type_def_8, type, sTfun: ($tType * $tType) > $tType).
% 0.55/0.40 thf(func_def_0, type, type: !>[X0: $tType]:($o)).
% 0.55/0.40 thf(func_def_1, type, zero: !>[X0: $tType]:($o)).
% 0.55/0.40 thf(func_def_2, type, bot: !>[X0: $tType]:($o)).
% 0.55/0.40 thf(func_def_3, type, ord: !>[X0: $tType]:($o)).
% 0.55/0.40 thf(func_def_4, type, neg_numeral: !>[X0: $tType]:($o)).
% 0.55/0.40 thf(func_def_5, type, order: !>[X0: $tType]:($o)).
% 0.55/0.40 thf(func_def_6, type, group_add: !>[X0: $tType]:($o)).
% 0.55/0.40 thf(func_def_7, type, semiring_1: !>[X0: $tType]:($o)).
% 0.55/0.40 thf(func_def_8, type, finite_finite: !>[X0: $tType]:($o)).
% 0.55/0.40 thf(func_def_9, type, linorder: !>[X0: $tType]:($o)).
% 0.55/0.40 thf(func_def_10, type, preorder: !>[X0: $tType]:($o)).
% 0.55/0.40 thf(func_def_11, type, order_bot: !>[X0: $tType]:($o)).
% 0.55/0.40 thf(func_def_12, type, comm_monoid_diff: !>[X0: $tType]:($o)).
% 0.55/0.40 thf(func_def_13, type, semiring_bit_shifts: !>[X0: $tType]:($o)).
% 0.55/0.40 thf(func_def_14, type, ordered_ab_group_add: !>[X0: $tType]:($o)).
% 0.55/0.40 thf(func_def_15, type, cancel1352612707id_add: !>[X0: $tType]:($o)).
% 0.55/0.40 thf(func_def_16, type, cancel146912293up_add: !>[X0: $tType]:($o)).
% 0.55/0.40 thf(func_def_17, type, linord1659791738miring: !>[X0: $tType]:($o)).
% 0.55/0.40 thf(func_def_18, type, canoni770627133id_add: !>[X0: $tType]:($o)).
% 0.55/0.40 thf(func_def_19, type, unique788075200shifts: !>[X0: $tType]:($o)).
% 0.55/0.40 thf(func_def_20, type, finite_card: !>[X0: $tType]:((set @ X0 > nat))).
% 0.55/0.40 thf(func_def_21, type, finite_finite2: !>[X0: $tType]:((set @ X0 > $o))).
% 0.55/0.40 thf(func_def_22, type, inj_on: !>[X0: $tType, X1: $tType]:(((X0 > X1) > set @ X0 > $o))).
% 0.55/0.40 thf(func_def_23, type, minus_minus: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.55/0.40 thf(func_def_24, type, zero_zero: !>[X0: $tType]:(X0)).
% 0.55/0.40 thf(func_def_25, type, hF_Mirabelle_HF: (set @ hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.55/0.40 thf(func_def_26, type, hF_Mirabelle_Abs_hf: (nat > hF_Mirabelle_hf)).
% 0.55/0.40 thf(func_def_27, type, hF_Mirabelle_hfset: (hF_Mirabelle_hf > set @ hF_Mirabelle_hf)).
% 0.55/0.40 thf(func_def_28, type, hF_Mirabelle_hinsert: (hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.55/0.40 thf(func_def_29, type, hF_Mirabelle_hmem: (hF_Mirabelle_hf > hF_Mirabelle_hf > $o)).
% 0.55/0.40 thf(func_def_30, type, lattic1704895705min_on: !>[X0: $tType, X1: $tType]:(((X0 > X1) > set @ X0 > X0))).
% 0.55/0.40 thf(func_def_31, type, semiring_1_Nats: !>[X0: $tType]:(set @ X0)).
% 0.55/0.40 thf(func_def_32, type, semiri532925092at_aux: !>[X0: $tType]:(((X0 > X0) > nat > X0 > X0))).
% 0.55/0.40 thf(func_def_33, type, neg_numeral_dbl: !>[X0: $tType]:((X0 > X0))).
% 0.55/0.40 thf(func_def_34, type, bot_bot: !>[X0: $tType]:(X0)).
% 0.55/0.40 thf(func_def_35, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.55/0.40 thf(func_def_36, type, semiri2097166173op_bit: !>[X0: $tType]:((nat > X0 > X0))).
% 0.55/0.40 thf(func_def_37, type, semiri1924326578sh_bit: !>[X0: $tType]:((nat > X0 > X0))).
% 0.55/0.40 thf(func_def_38, type, inv_imagep: !>[X0: $tType, X1: $tType]:(((X0 > X0 > $o) > (X1 > X0) > X1 > X1 > $o))).
% 0.55/0.40 thf(func_def_39, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 0.55/0.40 thf(func_def_40, type, image: !>[X0: $tType, X1: $tType]:(((X0 > X1) > set @ X0 > set @ X1))).
% 0.55/0.40 thf(func_def_41, type, insert: !>[X0: $tType]:((X0 > set @ X0 > set @ X0))).
% 0.55/0.40 thf(func_def_42, type, is_empty: !>[X0: $tType]:((set @ X0 > $o))).
% 0.55/0.40 thf(func_def_43, type, is_singleton: !>[X0: $tType]:((set @ X0 > $o))).
% 0.55/0.40 thf(func_def_44, type, the_elem: !>[X0: $tType]:((set @ X0 > X0))).
% 0.55/0.40 thf(func_def_45, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.55/0.40 thf(func_def_46, type, z: hF_Mirabelle_hf).
% 0.55/0.40 thf(func_def_50, type, db1: !>[X0: $tType]:(X0)).
% 0.55/0.40 thf(func_def_51, type, db0: !>[X0: $tType]:(X0)).
% 0.55/0.40 thf(func_def_52, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.55/0.40 thf(func_def_53, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.55/0.40 thf(func_def_54, type, vAND: ($o > $o > $o)).
% 0.55/0.40 thf(func_def_55, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.55/0.40 thf(func_def_56, type, vIMP: ($o > $o > $o)).
% 0.55/0.40 thf(func_def_57, type, db2: !>[X0: $tType]:(X0)).
% 0.55/0.40 thf(func_def_58, type, db3: !>[X0: $tType]:(X0)).
% 0.55/0.40 thf(func_def_59, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.55/0.40 thf(func_def_60, type, vOR: ($o > $o > $o)).
% 0.55/0.40 thf(func_def_61, type, sP0: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.55/0.40 thf(func_def_62, type, sP1: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.55/0.40 thf(func_def_63, type, sK2: !>[X0: $tType]:((set @ X0 > set @ X0))).
% 0.55/0.40 thf(func_def_64, type, sK3: !>[X0: $tType]:((set @ X0 > X0))).
% 0.55/0.40 thf(func_def_65, type, sK4: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (set @ X1 > $o) > set @ X0 > set @ X1))).
% 0.55/0.40 thf(func_def_66, type, sK5: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (set @ X1 > $o) > set @ X0 > set @ X0))).
% 0.55/0.40 thf(func_def_67, type, sK6: !>[X0: $tType, X1: $tType]:(((X0 > X1) > set @ X0 > (set @ X1 > $o) > set @ X1))).
% 0.55/0.40 thf(func_def_68, type, sK7: !>[X0: $tType, X1: $tType]:(((X0 > X1) > set @ X0 > (set @ X1 > $o) > set @ X0))).
% 0.55/0.40 thf(func_def_69, type, sK8: !>[X0: $tType]:(((X0 > nat) > (X0 > $o) > X0))).
% 0.55/0.40 thf(func_def_70, type, sK9: !>[X0: $tType]:((set @ X0 > set @ X0))).
% 0.55/0.40 thf(func_def_71, type, sK10: !>[X0: $tType]:((set @ X0 > X0))).
% 0.55/0.40 thf(func_def_72, type, sK11: !>[X0: $tType]:((X0 > set @ X0 > X0))).
% 0.55/0.40 thf(func_def_73, type, sK12: !>[X0: $tType]:(((set @ X0 > $o) > set @ X0))).
% 0.55/0.40 thf(func_def_74, type, sK13: !>[X0: $tType]:(((set @ X0 > $o) > X0))).
% 0.55/0.40 thf(func_def_75, type, sK14: !>[X0: $tType]:(((set @ X0 > $o) > set @ X0))).
% 0.55/0.40 thf(func_def_76, type, sK15: ((nat > $o) > nat)).
% 0.55/0.40 thf(func_def_77, type, sK16: (nat > (nat > $o) > nat)).
% 0.55/0.40 thf(func_def_78, type, sK17: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 0.55/0.40 thf(func_def_79, type, sK18: !>[X0: $tType]:((set @ X0 > X0))).
% 0.55/0.40 thf(func_def_80, type, sK19: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.55/0.40 thf(func_def_81, type, sK20: (hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.55/0.40 thf(func_def_82, type, sK21: (hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.55/0.40 thf(func_def_83, type, sK22: !>[X0: $tType]:((set @ X0 > (set @ X0 > $o) > X0))).
% 0.55/0.40 thf(func_def_84, type, sK23: !>[X0: $tType]:((set @ X0 > (set @ X0 > $o) > set @ X0))).
% 0.55/0.40 thf(func_def_85, type, sK24: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.55/0.40 thf(func_def_86, type, sK25: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.55/0.40 thf(func_def_87, type, sK26: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.55/0.40 thf(func_def_88, type, sK27: !>[X0: $tType, X1: $tType]:((set @ X0 > set @ X1 > (X1 > X0) > set @ X1))).
% 0.55/0.40 thf(func_def_89, type, sK28: !>[X0: $tType]:(((set @ X0 > $o) > set @ X0))).
% 0.55/0.40 thf(func_def_90, type, sK29: !>[X0: $tType]:(((set @ X0 > $o) > X0))).
% 0.55/0.40 thf(func_def_91, type, sK30: !>[X0: $tType]:(((set @ X0 > $o) > X0))).
% 0.55/0.40 thf(func_def_92, type, sK31: !>[X0: $tType]:(((set @ X0 > $o) > X0))).
% 0.55/0.40 thf(func_def_93, type, sK32: !>[X0: $tType]:(((set @ X0 > $o) > set @ X0))).
% 0.55/0.40 thf(func_def_94, type, sK33: !>[X0: $tType]:((X0 > set @ X0 > set @ X0 > X0 > set @ X0))).
% 0.55/0.40 thf(func_def_95, type, sK34: !>[X0: $tType]:((X0 > set @ X0 > set @ X0))).
% 0.55/0.40 thf(func_def_96, type, sK35: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.55/0.40 thf(func_def_97, type, sK36: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.55/0.40 thf(func_def_98, type, sK37: !>[X0: $tType]:((nat > set @ X0 > set @ X0))).
% 0.55/0.40 thf(func_def_99, type, sK38: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > set @ X0 > set @ X1))).
% 0.55/0.40 thf(func_def_100, type, sK39: !>[X0: $tType]:(((set @ X0 > $o) > X0))).
% 0.55/0.40 thf(func_def_101, type, sK40: !>[X0: $tType]:(((set @ X0 > $o) > set @ X0))).
% 0.55/0.40 thf(func_def_102, type, sK41: !>[X0: $tType]:((set @ X0 > X0))).
% 0.55/0.40 thf(func_def_103, type, sK42: !>[X0: $tType]:((set @ X0 > X0))).
% 0.55/0.40 thf(func_def_104, type, sK43: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.55/0.40 thf(func_def_105, type, sK44: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.55/0.40 thf(func_def_106, type, sK45: !>[X0: $tType]:((set @ X0 > nat > set @ X0))).
% 0.55/0.40 thf(func_def_107, type, sK46: !>[X0: $tType]:((set @ set @ X0 > X0 > set @ X0))).
% 0.55/0.40 thf(func_def_108, type, sK47: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.55/0.40 thf(func_def_109, type, sK48: !>[X0: $tType, X1: $tType]:(((set @ X0 > $o) > (X0 > X1) > X0))).
% 0.55/0.40 thf(func_def_110, type, sK49: !>[X0: $tType, X1: $tType]:(((set @ X0 > $o) > (X0 > X1) > set @ X0))).
% 0.55/0.40 thf(func_def_111, type, sK50: !>[X0: $tType]:((set @ X0 > (set @ X0 > $o) > set @ X0))).
% 0.55/0.40 thf(func_def_112, type, sK51: !>[X0: $tType]:((set @ X0 > (set @ X0 > $o) > X0))).
% 0.55/0.40 thf(func_def_113, type, sK52: (nat > (nat > $o) > nat)).
% 0.55/0.40 thf(func_def_114, type, sK53: ((nat > $o) > nat)).
% 0.55/0.40 thf(func_def_115, type, sK54: !>[X0: $tType]:((set @ X0 > X0 > set @ X0))).
% 0.55/0.40 thf(func_def_116, type, sK55: !>[X0: $tType]:((set @ X0 > X0))).
% 0.55/0.40 thf(func_def_117, type, sK56: hF_Mirabelle_hf).
% 0.55/0.40 thf(func_def_118, type, sK57: !>[X0: $tType, X1: $tType]:(((X0 > X1) > set @ X1 > set @ X0 > set @ X0))).
% 0.55/0.40 thf(func_def_119, type, sK58: !>[X0: $tType, X1: $tType]:((set @ X0 > (X0 > X1 > $o) > X0 > X1))).
% 0.55/0.40 thf(func_def_120, type, sK59: !>[X0: $tType, X1: $tType]:((set @ X0 > (X0 > X1 > $o) > X0))).
% 0.55/0.40 thf(func_def_121, type, sK60: !>[X0: $tType, X1: $tType]:(((X1 > X0) > set @ X1 > X1))).
% 0.55/0.40 thf(func_def_122, type, sK61: !>[X0: $tType, X1: $tType]:(((X1 > X0) > set @ X1 > X1))).
% 0.55/0.40 thf(func_def_123, type, sK62: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.55/0.40 thf(func_def_124, type, sK63: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.55/0.40 thf(func_def_125, type, sK64: !>[X0: $tType, X1: $tType]:(((X1 > X0) > set @ X1 > set @ X0 > X0 > X1))).
% 0.55/0.40 thf(func_def_126, type, sK65: !>[X0: $tType, X1: $tType]:(((X1 > X0) > set @ X1 > set @ X0 > X0 > set @ X1))).
% 0.55/0.40 thf(func_def_127, type, sK66: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X0 > X1) > set @ X0 > X0))).
% 0.55/0.40 thf(func_def_128, type, sK67: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.55/0.40 thf(func_def_129, type, sK68: !>[X0: $tType]:((set @ X0 > X0))).
% 0.55/0.40 thf(func_def_130, type, sK69: !>[X0: $tType, X1: $tType]:(((X0 > X1) > set @ X0 > (X0 > X1) > X0))).
% 0.55/0.40 thf(func_def_131, type, sK70: !>[X0: $tType, X1: $tType]:((set @ X1 > set @ X0 > X1 > X0))).
% 0.55/0.40 thf(func_def_132, type, sK71: !>[X0: $tType]:((set @ X0 > X0))).
% 0.55/0.40 thf(func_def_133, type, sK72: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.55/0.40 thf(func_def_134, type, sK73: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.55/0.40 thf(func_def_135, type, sK74: !>[X0: $tType]:((set @ X0 > X0))).
% 0.55/0.40 thf(func_def_136, type, sK75: !>[X0: $tType]:((set @ X0 > X0))).
% 0.55/0.40 thf(func_def_137, type, sK76: !>[X0: $tType, X1: $tType]:((set @ X1 > (set @ X0 > $o) > (X1 > X0) > set @ X1))).
% 0.55/0.40 thf(func_def_138, type, sK77: !>[X0: $tType, X1: $tType]:((set @ X1 > (set @ X0 > $o) > (X1 > X0) > set @ X0))).
% 0.55/0.40 thf(func_def_139, type, sK78: !>[X0: $tType]:((nat > set @ X0 > set @ X0))).
% 0.55/0.40 thf(func_def_140, type, sK79: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > set @ X0 > set @ X1 > X0))).
% 0.55/0.40 thf(func_def_141, type, sK80: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > set @ X0 > set @ X1 > X1))).
% 0.55/0.40 thf(func_def_142, type, sK81: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > set @ X0 > set @ X1 > X1))).
% 0.55/0.40 thf(func_def_143, type, sK82: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > set @ X0 > set @ X1 > X1))).
% 0.55/0.40 thf(func_def_144, type, sK83: !>[X0: $tType, X1: $tType]:((set @ X1 > set @ X0 > (X0 > X1) > X0))).
% 0.55/0.40 thf(func_def_145, type, sK84: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.55/0.40 thf(func_def_146, type, sK85: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.55/0.40 thf(func_def_147, type, sK86: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.55/0.40 thf(func_def_148, type, sK87: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.55/0.40 thf(func_def_149, type, sK88: !>[X0: $tType]:((set @ X0 > X0 > X0))).
% 0.55/0.40 thf(func_def_150, type, sK89: !>[X0: $tType, X1: $tType]:((set @ X0 > set @ X1 > (X1 > X0) > X1))).
% 0.55/0.40 thf(func_def_151, type, sK90: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.55/0.40 thf(func_def_152, type, sK91: !>[X0: $tType]:((set @ X0 > X0))).
% 0.55/0.40 thf(func_def_153, type, vNOT: ($o > $o)).
% 0.55/0.40 thf(f3,axiom,(
% 0.55/0.40 ! [X0 : hF_Mirabelle_hf] : ~(hF_Mirabelle_hmem @ X0 @ zero_zero @ hF_Mirabelle_hf)),
% 0.55/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_hmem__hempty)).
% 0.55/0.40 thf(f4,axiom,(
% 0.55/0.40 ! [X0 : hF_Mirabelle_hf] : ((X0 != zero_zero @ hF_Mirabelle_hf) => ~ ! [X1 : hF_Mirabelle_hf,X2 : hF_Mirabelle_hf] : ((X0 = ((hF_Mirabelle_hinsert @ X1 @ X2))) => (hF_Mirabelle_hmem @ X1 @ X2)))),
% 0.55/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_hf__cases)).
% 0.55/0.40 thf(f5,axiom,(
% 0.55/0.40 ! [X2 : hF_Mirabelle_hf,X0 : hF_Mirabelle_hf,X1 : hF_Mirabelle_hf] : (((hF_Mirabelle_hmem @ X0 @ (hF_Mirabelle_hinsert @ X1 @ X2))) = (X0 = X1) | (hF_Mirabelle_hmem @ X0 @ X2))),
% 0.55/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_hmem__hinsert)).
% 0.55/0.40 thf(f290,conjecture,(
% 0.55/0.40 (! [X0 : hF_Mirabelle_hf] : ~(hF_Mirabelle_hmem @ X0 @ z) = (z = zero_zero @ hF_Mirabelle_hf))),
% 0.55/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 0.55/0.40 thf(f291,negated_conjecture,(
% 0.55/0.40 ~ (! [X0 : hF_Mirabelle_hf] : ~(hF_Mirabelle_hmem @ X0 @ z) = (z = zero_zero @ hF_Mirabelle_hf))),
% 0.55/0.40 inference(negated_conjecture,[status(cth)],[f290])).
% 0.55/0.40 thf(f322,plain,(
% 0.55/0.40 ! [X0 : hF_Mirabelle_hf,X1 : hF_Mirabelle_hf,X2 : hF_Mirabelle_hf] : (((hF_Mirabelle_hmem @ X1 @ (hF_Mirabelle_hinsert @ X2 @ X0))) = (X1 = X2) | (hF_Mirabelle_hmem @ X1 @ X0))),
% 0.55/0.40 inference(rectify,[],[f5])).
% 0.55/0.40 thf(f323,plain,(
% 0.55/0.40 ! [X0 : hF_Mirabelle_hf,X2 : hF_Mirabelle_hf,X1 : hF_Mirabelle_hf] : ((($true = ((hF_Mirabelle_hmem @ X1 @ X0))) | (X1 = X2)) <=> ($true = ((hF_Mirabelle_hmem @ X1 @ (hF_Mirabelle_hinsert @ X2 @ X0)))))),
% 0.55/0.40 inference(fool_elimination,[],[f322])).
% 0.55/0.40 thf(f597,plain,(
% 0.55/0.40 ! [X0 : hF_Mirabelle_hf] : ((X0 != zero_zero @ hF_Mirabelle_hf) => ~ ! [X1 : hF_Mirabelle_hf,X2 : hF_Mirabelle_hf] : ((X0 = ((hF_Mirabelle_hinsert @ X1 @ X2))) => (hF_Mirabelle_hmem @ X1 @ X2)))),
% 0.55/0.40 inference(rectify,[],[f4])).
% 0.55/0.40 thf(f598,plain,(
% 0.55/0.40 ! [X0 : hF_Mirabelle_hf] : ((zero_zero @ hF_Mirabelle_hf != X0) => ~ ! [X2 : hF_Mirabelle_hf,X1 : hF_Mirabelle_hf] : ((((hF_Mirabelle_hinsert @ X1 @ X2)) = X0) => (((hF_Mirabelle_hmem @ X1 @ X2)) = $true)))),
% 0.55/0.41 inference(fool_elimination,[],[f597])).
% 0.55/0.41 thf(f619,plain,(
% 0.55/0.41 ! [X0 : hF_Mirabelle_hf] : ~(hF_Mirabelle_hmem @ X0 @ zero_zero @ hF_Mirabelle_hf)),
% 0.55/0.41 inference(rectify,[],[f3])).
% 0.55/0.41 thf(f620,plain,(
% 0.55/0.41 ! [X0 : hF_Mirabelle_hf] : ~ (((hF_Mirabelle_hmem @ X0 @ zero_zero @ hF_Mirabelle_hf)) = $true)),
% 0.55/0.41 inference(fool_elimination,[],[f619])).
% 0.55/0.41 thf(f737,plain,(
% 0.55/0.41 ~ (! [X0 : hF_Mirabelle_hf] : ~(hF_Mirabelle_hmem @ X0 @ z) = (z = zero_zero @ hF_Mirabelle_hf))),
% 0.55/0.41 inference(rectify,[],[f291])).
% 0.55/0.41 thf(f738,plain,(
% 0.55/0.41 ~(! [X0 : hF_Mirabelle_hf] : ~ (((hF_Mirabelle_hmem @ X0 @ z)) = $true) <=> (zero_zero @ hF_Mirabelle_hf = z))),
% 0.55/0.41 inference(fool_elimination,[],[f737])).
% 0.55/0.41 thf(f839,plain,(
% 0.55/0.41 ! [X0 : hF_Mirabelle_hf] : (((hF_Mirabelle_hmem @ X0 @ zero_zero @ hF_Mirabelle_hf)) != $true)),
% 0.55/0.41 inference(flattening,[],[f620])).
% 0.55/0.41 thf(f850,plain,(
% 0.55/0.41 ~((zero_zero @ hF_Mirabelle_hf = z) <=> ! [X0 : hF_Mirabelle_hf] : (((hF_Mirabelle_hmem @ X0 @ z)) != $true))),
% 0.55/0.41 inference(flattening,[],[f738])).
% 0.55/0.41 thf(f880,plain,(
% 0.55/0.41 ! [X0 : hF_Mirabelle_hf] : ((zero_zero @ hF_Mirabelle_hf = X0) | ? [X2 : hF_Mirabelle_hf,X1 : hF_Mirabelle_hf] : ((((hF_Mirabelle_hmem @ X1 @ X2)) != $true) & (((hF_Mirabelle_hinsert @ X1 @ X2)) = X0)))),
% 0.55/0.41 inference(ennf_transformation,[],[f598])).
% 0.55/0.41 thf(f894,plain,(
% 0.55/0.41 ! [X0 : hF_Mirabelle_hf] : (((hF_Mirabelle_hmem @ X0 @ z)) != $true) <~> (zero_zero @ hF_Mirabelle_hf = z)),
% 0.55/0.41 inference(ennf_transformation,[],[f850])).
% 0.55/0.41 thf(f1170,plain,(
% 0.55/0.41 ! [X0 : hF_Mirabelle_hf] : ((zero_zero @ hF_Mirabelle_hf = X0) | ? [X1 : hF_Mirabelle_hf,X2 : hF_Mirabelle_hf] : (($true != ((hF_Mirabelle_hmem @ X2 @ X1))) & (((hF_Mirabelle_hinsert @ X2 @ X1)) = X0)))),
% 0.55/0.41 inference(rectify,[],[f880])).
% 0.55/0.41 thf(f1171,plain,(
% 0.55/0.41 ! [X0 : hF_Mirabelle_hf] : ((zero_zero @ hF_Mirabelle_hf = X0) | (($true != ((hF_Mirabelle_hmem @ (sK21 @ X0) @ (sK20 @ X0)))) & (((hF_Mirabelle_hinsert @ (sK21 @ X0) @ (sK20 @ X0))) = X0)))),
% 0.55/0.41 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP]),skolemize(X3,sK3 @ X0 @ X1),skolemize(X3,sK3 @ X0 @ X1)],[f1170])).
% 0.55/0.41 thf(f1268,plain,(
% 0.55/0.41 ((zero_zero @ hF_Mirabelle_hf != z) | ? [X0 : hF_Mirabelle_hf] : (((hF_Mirabelle_hmem @ X0 @ z)) = $true)) & ((zero_zero @ hF_Mirabelle_hf = z) | ! [X0 : hF_Mirabelle_hf] : (((hF_Mirabelle_hmem @ X0 @ z)) != $true))),
% 0.55/0.41 inference(nnf_transformation,[],[f894])).
% 0.55/0.41 thf(f1269,plain,(
% 0.55/0.41 ((zero_zero @ hF_Mirabelle_hf != z) | ? [X0 : hF_Mirabelle_hf] : (((hF_Mirabelle_hmem @ X0 @ z)) = $true)) & ((zero_zero @ hF_Mirabelle_hf = z) | ! [X1 : hF_Mirabelle_hf] : ($true != ((hF_Mirabelle_hmem @ X1 @ z))))),
% 0.55/0.41 inference(rectify,[],[f1268])).
% 0.55/0.41 thf(f1270,plain,(
% 0.55/0.41 ((zero_zero @ hF_Mirabelle_hf != z) | ($true = ((hF_Mirabelle_hmem @ sK56 @ z)))) & ((zero_zero @ hF_Mirabelle_hf = z) | ! [X1 : hF_Mirabelle_hf] : ($true != ((hF_Mirabelle_hmem @ X1 @ z))))),
% 0.55/0.41 inference(skolemize,[status(esa),new_symbols(skolem,[sK56]),skolemize(X0,sK56)],[f1269])).
% 0.55/0.41 thf(f1296,plain,(
% 0.55/0.41 ! [X0 : hF_Mirabelle_hf,X2 : hF_Mirabelle_hf,X1 : hF_Mirabelle_hf] : (((($true = ((hF_Mirabelle_hmem @ X1 @ X0))) | (X1 = X2)) | ($true != ((hF_Mirabelle_hmem @ X1 @ (hF_Mirabelle_hinsert @ X2 @ X0))))) & (($true = ((hF_Mirabelle_hmem @ X1 @ (hF_Mirabelle_hinsert @ X2 @ X0)))) | (($true != ((hF_Mirabelle_hmem @ X1 @ X0))) & (X1 != X2))))),
% 0.55/0.41 inference(nnf_transformation,[],[f323])).
% 0.55/0.41 thf(f1297,plain,(
% 0.55/0.41 ! [X0 : hF_Mirabelle_hf,X2 : hF_Mirabelle_hf,X1 : hF_Mirabelle_hf] : ((($true = ((hF_Mirabelle_hmem @ X1 @ X0))) | (X1 = X2) | ($true != ((hF_Mirabelle_hmem @ X1 @ (hF_Mirabelle_hinsert @ X2 @ X0))))) & (($true = ((hF_Mirabelle_hmem @ X1 @ (hF_Mirabelle_hinsert @ X2 @ X0)))) | (($true != ((hF_Mirabelle_hmem @ X1 @ X0))) & (X1 != X2))))),
% 0.55/0.41 inference(flattening,[],[f1296])).
% 0.55/0.41 thf(f1298,plain,(
% 0.55/0.41 ! [X0 : hF_Mirabelle_hf,X1 : hF_Mirabelle_hf,X2 : hF_Mirabelle_hf] : ((($true = ((hF_Mirabelle_hmem @ X2 @ X0))) | (X1 = X2) | ($true != ((hF_Mirabelle_hmem @ X2 @ (hF_Mirabelle_hinsert @ X1 @ X0))))) & (($true = ((hF_Mirabelle_hmem @ X2 @ (hF_Mirabelle_hinsert @ X1 @ X0)))) | (($true != ((hF_Mirabelle_hmem @ X2 @ X0))) & (X1 != X2))))),
% 0.55/0.41 inference(rectify,[],[f1297])).
% 0.55/0.41 thf(f1483,plain,(
% 0.55/0.41 ( ! [X0 : hF_Mirabelle_hf] : ((((hF_Mirabelle_hinsert @ (sK21 @ X0) @ (sK20 @ X0))) = X0) | (zero_zero @ hF_Mirabelle_hf = X0)) )),
% 0.55/0.41 inference(cnf_transformation,[],[f1171])).
% 0.55/0.41 thf(f1563,plain,(
% 0.55/0.41 ( ! [X0 : hF_Mirabelle_hf] : ((((hF_Mirabelle_hmem @ X0 @ zero_zero @ hF_Mirabelle_hf)) != $true)) )),
% 0.55/0.41 inference(cnf_transformation,[],[f839])).
% 0.55/0.41 thf(f1668,plain,(
% 0.55/0.41 ( ! [X1 : hF_Mirabelle_hf] : (($true != ((hF_Mirabelle_hmem @ X1 @ z))) | (zero_zero @ hF_Mirabelle_hf = z)) )),
% 0.55/0.41 inference(cnf_transformation,[],[f1270])).
% 0.55/0.41 thf(f1669,plain,(
% 0.55/0.41 ($true = ((hF_Mirabelle_hmem @ sK56 @ z))) | (zero_zero @ hF_Mirabelle_hf != z)),
% 0.55/0.41 inference(cnf_transformation,[],[f1270])).
% 0.55/0.41 thf(f1709,plain,(
% 0.55/0.41 ( ! [X2 : hF_Mirabelle_hf,X0 : hF_Mirabelle_hf,X1 : hF_Mirabelle_hf] : (($true = ((hF_Mirabelle_hmem @ X2 @ (hF_Mirabelle_hinsert @ X1 @ X0)))) | (X1 != X2)) )),
% 0.55/0.41 inference(cnf_transformation,[],[f1298])).
% 0.55/0.41 thf(f1899,plain,(
% 0.55/0.41 ( ! [X2 : hF_Mirabelle_hf,X0 : hF_Mirabelle_hf] : (($true = ((hF_Mirabelle_hmem @ X2 @ (hF_Mirabelle_hinsert @ X2 @ X0))))) )),
% 0.55/0.41 inference(equality_resolution,[],[f1709])).
% 0.55/0.41 thf(f1972,definition,(
% 0.55/0.41 spl92_4 <=> (zero_zero @ hF_Mirabelle_hf = z)),
% 0.55/0.41 introduced(definition,[new_symbols(definition,[spl92_4])],[avatar_definition])).
% 0.55/0.41 thf(f1973,plain,(
% 0.55/0.41 (zero_zero @ hF_Mirabelle_hf != z) | spl92_4),
% 0.55/0.41 inference(avatar_component_clause,[],[f1972])).
% 0.55/0.41 thf(f1974,plain,(
% 0.55/0.41 (zero_zero @ hF_Mirabelle_hf = z) | ~spl92_4),
% 0.55/0.41 inference(avatar_component_clause,[],[f1972])).
% 0.55/0.41 thf(f1976,definition,(
% 0.55/0.41 spl92_5 <=> ! [X1 : hF_Mirabelle_hf] : ($true != ((hF_Mirabelle_hmem @ X1 @ z)))),
% 0.55/0.41 introduced(definition,[new_symbols(definition,[spl92_5])],[avatar_definition])).
% 0.55/0.41 thf(f1977,plain,(
% 0.55/0.41 ( ! [X1 : hF_Mirabelle_hf] : (($true != ((hF_Mirabelle_hmem @ X1 @ z)))) ) | ~spl92_5),
% 0.55/0.41 inference(avatar_component_clause,[],[f1976])).
% 0.55/0.41 thf(f1978,plain,(
% 0.55/0.41 spl92_4 | spl92_5),
% 0.55/0.41 inference(avatar_split_clause,[],[f1668,f1976,f1972])).
% 0.55/0.41 thf(f2035,definition,(
% 0.55/0.41 spl92_17 <=> ($true = ((hF_Mirabelle_hmem @ sK56 @ z)))),
% 0.55/0.41 introduced(definition,[new_symbols(definition,[spl92_17])],[avatar_definition])).
% 0.55/0.41 thf(f2037,plain,(
% 0.55/0.41 ($true = ((hF_Mirabelle_hmem @ sK56 @ z))) | ~spl92_17),
% 0.55/0.41 inference(avatar_component_clause,[],[f2035])).
% 0.55/0.41 thf(f2038,plain,(
% 0.55/0.41 ~spl92_4 | spl92_17),
% 0.55/0.41 inference(avatar_split_clause,[],[f1669,f2035,f1972])).
% 0.55/0.41 thf(f2159,plain,(
% 0.55/0.41 ( ! [X0 : hF_Mirabelle_hf] : (($true = ((hF_Mirabelle_hmem @ (sK21 @ X0) @ X0))) | (zero_zero @ hF_Mirabelle_hf = X0)) )),
% 0.55/0.41 inference(superposition,[],[f1899,f1483])).
% 0.55/0.41 thf(f2170,plain,(
% 0.55/0.41 (zero_zero @ hF_Mirabelle_hf = z) | ($true != $true) | ~spl92_5),
% 0.55/0.41 inference(superposition,[],[f1977,f2159])).
% 0.55/0.41 thf(f2172,plain,(
% 0.55/0.41 (zero_zero @ hF_Mirabelle_hf = z) | ~spl92_5),
% 0.55/0.41 inference(trivial_inequality_removal,[],[f2170])).
% 0.55/0.41 thf(f2174,plain,(
% 0.55/0.41 $false | (spl92_4 | ~spl92_5)),
% 0.55/0.41 inference(forward_subsumption_resolution,[],[f2172,f1973])).
% 0.55/0.41 thf(f2175,plain,(
% 0.55/0.41 spl92_4 | ~spl92_5),
% 0.55/0.41 inference(avatar_contradiction_clause,[],[f2174])).
% 0.55/0.41 thf(f2176,plain,(
% 0.55/0.41 ($true = ((hF_Mirabelle_hmem @ sK56 @ zero_zero @ hF_Mirabelle_hf))) | (~spl92_4 | ~spl92_17)),
% 0.55/0.41 inference(forward_demodulation,[],[f2037,f1974])).
% 0.55/0.41 thf(f2177,plain,(
% 0.55/0.41 $false | (~spl92_4 | ~spl92_17)),
% 0.55/0.41 inference(forward_subsumption_resolution,[],[f2176,f1563])).
% 0.55/0.41 thf(f2178,plain,(
% 0.55/0.41 ~spl92_4 | ~spl92_17),
% 0.55/0.41 inference(avatar_contradiction_clause,[],[f2177])).
% 0.55/0.41 cnf(s4, plain, spl92_4 | spl92_5, inference(sat_conversion,[],[f1978])).
% 0.55/0.41 cnf(s16, plain, ~spl92_4 | spl92_17, inference(sat_conversion,[],[f2038])).
% 0.55/0.41 cnf(s39, plain, spl92_4 | ~spl92_5, inference(sat_conversion,[],[f2175])).
% 0.55/0.41 cnf(s40, plain, ~spl92_4 | ~spl92_17, inference(sat_conversion,[],[f2178])).
% 0.55/0.41 cnf(s44, plain, spl92_4, inference(rat,[],[s4,s39])).
% 0.55/0.41 cnf(s45, plain, ~spl92_17, inference(rat,[],[s40,s44])).
% 0.55/0.41 cnf(s46, plain, $false, inference(rat,[],[s16,s45,s44])).
% 0.55/0.41 thf(f2179,plain,(
% 0.55/0.41 $false),
% 0.55/0.41 inference(avatar_sat_refutation,[],[s46])).
% 0.55/0.41 % SZS output end Proof for theBenchmark
% 0.55/0.41 % (553462)------------------------------
% 0.55/0.41 % (553462)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.55/0.41 % (553462)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.55/0.41 % (553462)CaDiCaL version: 2.1.3
% 0.55/0.41 % (553462)Termination reason: Refutation
% 0.55/0.41 % (553462)Time elapsed: 0.068 s
% 0.55/0.41 % (553462)Peak memory usage: 14 MB
% 0.55/0.41 % (553462)Instructions burned: 133 (million)
% 0.55/0.41 % (553454)Success in time 0.127 s
% 0.55/0.41 % Vampire exiting
%------------------------------------------------------------------------------