%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP075^1 : 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 : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:08:14 AM UTC 2026
% Result : Theorem 0.52s 0.40s
% Output : Refutation 0.52s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP075^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n017.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 19:43:07 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 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
% 0.52/0.40 % (804662)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.52/0.40 % (804671)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3359521225:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.52/0.40 % (804673)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.52/0.40 % (804673)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
% 0.52/0.40 % (804668)lrs+10_16_si=on:nwc=1.5:random_seed=985014683:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.52/0.40 % (804671)Instruction limit reached!
% 0.52/0.40 % (804671)------------------------------
% 0.52/0.40 % (804671)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.52/0.40 % (804671)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.52/0.40 % (804671)CaDiCaL version: 2.1.3
% 0.52/0.40 % (804671)Termination reason: Instruction limit
% 0.52/0.40 % (804671)Termination phase: shuffling
% 0.52/0.40 % (804667)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=674289091:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.52/0.40 % (804671)Time elapsed: 0.006 s
% 0.52/0.40 % (804671)Peak memory usage: 10 MB
% 0.52/0.40 % (804671)Instructions burned: 25 (million)
% 0.52/0.40 % (804669)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3711167361:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.52/0.40 % (804670)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=989729553: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)
% 0.52/0.40 % (804672)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2561863838:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.52/0.40 % (804673)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=421442963:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.52/0.40 % (804669)Instruction limit reached!
% 0.52/0.40 % (804669)------------------------------
% 0.52/0.40 % (804669)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.52/0.40 % (804669)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.52/0.40 % (804669)CaDiCaL version: 2.1.3
% 0.52/0.40 % (804669)Termination reason: Instruction limit
% 0.52/0.40 % (804669)Termination phase: shuffling
% 0.52/0.40 % (804669)Time elapsed: 0.002 s
% 0.52/0.40 % (804669)Peak memory usage: 10 MB
% 0.52/0.40 % (804669)Instructions burned: 3 (million)
% 0.52/0.40 % (804668)Instruction limit reached!
% 0.52/0.40 % (804668)------------------------------
% 0.52/0.40 % (804668)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.52/0.40 % (804668)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.52/0.40 % (804668)CaDiCaL version: 2.1.3
% 0.52/0.40 % (804668)Termination reason: Instruction limit
% 0.52/0.40 % (804668)Termination phase: Property scanning
% 0.52/0.40 % (804668)Time elapsed: 0.009 s
% 0.52/0.40 % (804668)Peak memory usage: 10 MB
% 0.52/0.40 % (804668)Instructions burned: 20 (million)
% 0.52/0.40 % (804678)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2041308464:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.52/0.40 % (804678)Instruction limit reached!
% 0.52/0.40 % (804678)------------------------------
% 0.52/0.40 % (804678)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.52/0.40 % (804678)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.52/0.40 % (804678)CaDiCaL version: 2.1.3
% 0.52/0.40 % (804678)Termination reason: Instruction limit
% 0.52/0.40 % (804678)Termination phase: shuffling
% 0.52/0.40 % (804678)Time elapsed: 0.001 s
% 0.52/0.40 % (804678)Peak memory usage: 10 MB
% 0.52/0.40 % (804678)Instructions burned: 5 (million)
% 0.52/0.40 % (804682)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2568130724:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.52/0.40 % (804685)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2110395595:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.52/0.40 % (804683)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.52/0.40 % (804682)Instruction limit reached!
% 0.52/0.40 % (804682)------------------------------
% 0.52/0.40 % (804682)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.52/0.40 % (804682)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.52/0.40 % (804682)CaDiCaL version: 2.1.3
% 0.52/0.40 % (804682)Termination reason: Instruction limit
% 0.52/0.40 % (804682)Termination phase: shuffling
% 0.52/0.40 % (804682)Time elapsed: 0.003 s
% 0.52/0.40 % (804682)Peak memory usage: 10 MB
% 0.52/0.40 % (804682)Instructions burned: 5 (million)
% 0.52/0.40 % (804685)Instruction limit reached!
% 0.52/0.40 % (804685)------------------------------
% 0.52/0.40 % (804685)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.52/0.40 % (804685)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.52/0.40 % (804685)CaDiCaL version: 2.1.3
% 0.52/0.40 % (804685)Termination reason: Instruction limit
% 0.52/0.40 % (804685)Termination phase: Property scanning
% 0.52/0.40 % (804685)Time elapsed: 0.003 s
% 0.52/0.40 % (804685)Peak memory usage: 10 MB
% 0.52/0.40 % (804685)Instructions burned: 14 (million)
% 0.52/0.40 % (804683)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1522690055:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.52/0.40 % (804683)Instruction limit reached!
% 0.52/0.40 % (804683)------------------------------
% 0.52/0.40 % (804683)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.52/0.40 % (804683)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.52/0.40 % (804683)CaDiCaL version: 2.1.3
% 0.52/0.40 % (804683)Termination reason: Instruction limit
% 0.52/0.40 % (804683)Termination phase: shuffling
% 0.52/0.40 % (804683)Time elapsed: 0.003 s
% 0.52/0.40 % (804683)Peak memory usage: 10 MB
% 0.52/0.40 % (804683)Instructions burned: 7 (million)
% 0.52/0.40 % (804672)Instruction limit reached!
% 0.52/0.40 % (804672)------------------------------
% 0.52/0.40 % (804672)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.52/0.40 % (804672)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.52/0.40 % (804672)CaDiCaL version: 2.1.3
% 0.52/0.40 % (804672)Termination reason: Instruction limit
% 0.52/0.40 % (804672)Termination phase: Property scanning
% 0.52/0.40 % (804672)Time elapsed: 0.035 s
% 0.52/0.40 % (804672)Peak memory usage: 12 MB
% 0.52/0.40 % (804672)Instructions burned: 77 (million)
% 0.52/0.40 % (804688)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
% 0.52/0.40 % (804688)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.52/0.40 % (804688)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3038150404:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.52/0.40 % (804667)Instruction limit reached!
% 0.52/0.40 % (804667)------------------------------
% 0.52/0.40 % (804667)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.52/0.40 % (804667)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.52/0.40 % (804667)CaDiCaL version: 2.1.3
% 0.52/0.40 % (804667)Termination reason: Instruction limit
% 0.52/0.40 % (804667)Termination phase: Property scanning
% 0.52/0.40 % (804667)Time elapsed: 0.039 s
% 0.52/0.40 % (804667)Peak memory usage: 12 MB
% 0.52/0.40 % (804667)Instructions burned: 89 (million)
% 0.52/0.40 % (804688)Instruction limit reached!
% 0.52/0.40 % (804688)------------------------------
% 0.52/0.40 % (804688)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.52/0.40 % (804688)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.52/0.40 % (804688)CaDiCaL version: 2.1.3
% 0.52/0.40 % (804688)Termination reason: Instruction limit
% 0.52/0.40 % (804688)Termination phase: Property scanning
% 0.52/0.40 % (804688)Time elapsed: 0.007 s
% 0.52/0.40 % (804688)Peak memory usage: 10 MB
% 0.52/0.40 % (804688)Instructions burned: 32 (million)
% 0.52/0.40 % (804689)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=725573895:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.52/0.40 % (804691)lrs+10_1_si=on:cs=on:random_seed=194305842:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.52/0.40 % (804692)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.52/0.40 % (804691)Instruction limit reached!
% 0.52/0.40 % (804691)------------------------------
% 0.52/0.40 % (804691)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.52/0.40 % (804691)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.52/0.40 % (804691)CaDiCaL version: 2.1.3
% 0.52/0.40 % (804691)Termination reason: Instruction limit
% 0.52/0.40 % (804691)Termination phase: shuffling
% 0.52/0.40 % (804691)Time elapsed: 0.004 s
% 0.52/0.40 % (804691)Peak memory usage: 10 MB
% 0.52/0.40 % (804691)Instructions burned: 8 (million)
% 0.52/0.40 % (804692)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=1841998662:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.52/0.40 % (804695)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=10648295:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.52/0.40 % (804692)Instruction limit reached!
% 0.52/0.40 % (804692)------------------------------
% 0.52/0.40 % (804692)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.52/0.40 % (804692)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.52/0.40 % (804692)CaDiCaL version: 2.1.3
% 0.52/0.40 % (804692)Termination reason: Instruction limit
% 0.52/0.40 % (804692)Termination phase: shuffling
% 0.52/0.40 % (804692)Time elapsed: 0.002 s
% 0.52/0.40 % (804692)Peak memory usage: 10 MB
% 0.52/0.40 % (804692)Instructions burned: 3 (million)
% 0.52/0.40 % (804694)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=6918195:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.52/0.40 % (804673)Instruction limit reached!
% 0.52/0.40 % (804673)------------------------------
% 0.52/0.40 % (804673)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.52/0.40 % (804673)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.52/0.40 % (804673)CaDiCaL version: 2.1.3
% 0.52/0.40 % (804673)Termination reason: Instruction limit
% 0.52/0.40 % (804673)Termination phase: Saturation
% 0.52/0.40 % (804673)Time elapsed: 0.067 s
% 0.52/0.40 % (804673)Peak memory usage: 13 MB
% 0.52/0.40 % (804673)Instructions burned: 158 (million)
% 0.52/0.40 % (804695) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-804662-804695"...
% 0.52/0.40 % (804695)...printing done.
% 0.52/0.40 % (804695)Refutation found. Thanks to Tanya!
% 0.52/0.40 % SZS status Theorem for theBenchmark
% 0.52/0.40 % SZS output start Proof for theBenchmark
% 0.52/0.40 thf(type_def_5, type, set_HF_Mirabelle_hf: $tType).
% 0.52/0.40 thf(type_def_6, type, hF_Mirabelle_hf: $tType).
% 0.52/0.40 thf(type_def_7, type, nat: $tType).
% 0.52/0.40 thf(type_def_8, type, int: $tType).
% 0.52/0.40 thf(type_def_9, type, sTfun: ($tType * $tType) > $tType).
% 0.52/0.40 thf(func_def_0, type, minus_1668263787e_hf_o: ((hF_Mirabelle_hf > $o) > (hF_Mirabelle_hf > $o) > hF_Mirabelle_hf > $o)).
% 0.52/0.40 thf(func_def_1, type, minus_minus_o: ($o > $o > $o)).
% 0.52/0.40 thf(func_def_2, type, minus_1232880740lle_hf: (hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.52/0.40 thf(func_def_3, type, minus_minus_int: (int > int > int)).
% 0.52/0.40 thf(func_def_4, type, minus_minus_nat: (nat > nat > nat)).
% 0.52/0.40 thf(func_def_5, type, minus_1450406810lle_hf: (set_HF_Mirabelle_hf > set_HF_Mirabelle_hf > set_HF_Mirabelle_hf)).
% 0.52/0.40 thf(func_def_6, type, zero_z189798548lle_hf: hF_Mirabelle_hf).
% 0.52/0.40 thf(func_def_7, type, zero_zero_int: int).
% 0.52/0.40 thf(func_def_8, type, zero_zero_nat: nat).
% 0.52/0.40 thf(func_def_9, type, hF_Mirabelle_HBall: (hF_Mirabelle_hf > (hF_Mirabelle_hf > $o) > $o)).
% 0.52/0.40 thf(func_def_10, type, hF_Mirabelle_HBex: (hF_Mirabelle_hf > (hF_Mirabelle_hf > $o) > $o)).
% 0.52/0.40 thf(func_def_11, type, hF_Mir818139703ollect: ((hF_Mirabelle_hf > $o) > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.52/0.40 thf(func_def_12, type, hF_Mirabelle_HF: (set_HF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.52/0.40 thf(func_def_13, type, hF_Mirabelle_HInter: (hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.52/0.40 thf(func_def_14, type, hF_Mirabelle_HUnion: (hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.52/0.40 thf(func_def_15, type, hF_Mir1248913145eplace: (hF_Mirabelle_hf > (hF_Mirabelle_hf > hF_Mirabelle_hf > $o) > hF_Mirabelle_hf)).
% 0.52/0.40 thf(func_def_16, type, hF_Mirabelle_RepFun: (hF_Mirabelle_hf > (hF_Mirabelle_hf > hF_Mirabelle_hf) > hF_Mirabelle_hf)).
% 0.52/0.40 thf(func_def_17, type, hF_Mirabelle_Replace: (hF_Mirabelle_hf > (hF_Mirabelle_hf > hF_Mirabelle_hf > $o) > hF_Mirabelle_hf)).
% 0.52/0.40 thf(func_def_18, type, hF_Mirabelle_hcard: (hF_Mirabelle_hf > nat)).
% 0.52/0.40 thf(func_def_19, type, hF_Mirabelle_Abs_hf: (nat > hF_Mirabelle_hf)).
% 0.52/0.40 thf(func_def_20, type, hF_Mirabelle_hfset: (hF_Mirabelle_hf > set_HF_Mirabelle_hf)).
% 0.52/0.40 thf(func_def_21, type, hF_Mirabelle_hfst: (hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.52/0.40 thf(func_def_22, type, hF_Mirabelle_hinsert: (hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.52/0.40 thf(func_def_23, type, hF_Mirabelle_hmem: (hF_Mirabelle_hf > hF_Mirabelle_hf > $o)).
% 0.52/0.40 thf(func_def_24, type, hF_Mirabelle_hpair: (hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.52/0.40 thf(func_def_25, type, hF_Mirabelle_hsnd: (hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.52/0.40 thf(func_def_26, type, the_HF_Mirabelle_hf: ((hF_Mirabelle_hf > $o) > hF_Mirabelle_hf)).
% 0.52/0.40 thf(func_def_27, type, if_HF_Mirabelle_hf: ($o > hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.52/0.40 thf(func_def_28, type, inf_in307783154e_hf_o: ((hF_Mirabelle_hf > $o) > (hF_Mirabelle_hf > $o) > hF_Mirabelle_hf > $o)).
% 0.52/0.40 thf(func_def_29, type, inf_inf_o: ($o > $o > $o)).
% 0.52/0.40 thf(func_def_30, type, inf_in956532509lle_hf: (hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.52/0.40 thf(func_def_31, type, inf_inf_int: (int > int > int)).
% 0.52/0.40 thf(func_def_32, type, inf_inf_nat: (nat > nat > nat)).
% 0.52/0.40 thf(func_def_33, type, inf_in923488851lle_hf: (set_HF_Mirabelle_hf > set_HF_Mirabelle_hf > set_HF_Mirabelle_hf)).
% 0.52/0.40 thf(func_def_34, type, semiri2019852685at_int: (nat > int)).
% 0.52/0.40 thf(func_def_35, type, semiri1382578993at_nat: (nat > nat)).
% 0.52/0.40 thf(func_def_36, type, bot_bo1263054448e_hf_o: (hF_Mirabelle_hf > $o)).
% 0.52/0.40 thf(func_def_37, type, bot_bot_o: $o).
% 0.52/0.40 thf(func_def_38, type, bot_bo1001194783lle_hf: hF_Mirabelle_hf).
% 0.52/0.40 thf(func_def_39, type, bot_bot_nat: nat).
% 0.52/0.40 thf(func_def_40, type, bot_bo53200981lle_hf: set_HF_Mirabelle_hf).
% 0.52/0.40 thf(func_def_41, type, least_917110455lle_hf: ((hF_Mirabelle_hf > hF_Mirabelle_hf > $o) > (hF_Mirabelle_hf > $o) > hF_Mirabelle_hf)).
% 0.52/0.40 thf(func_def_42, type, ord_le616625840e_hf_o: ((hF_Mirabelle_hf > $o) > (hF_Mirabelle_hf > $o) > $o)).
% 0.52/0.40 thf(func_def_43, type, ord_le1310584031lle_hf: (hF_Mirabelle_hf > hF_Mirabelle_hf > $o)).
% 0.52/0.40 thf(func_def_44, type, ord_less_int: (int > int > $o)).
% 0.52/0.40 thf(func_def_45, type, ord_less_nat: (nat > nat > $o)).
% 0.52/0.40 thf(func_def_46, type, ord_le1344122901lle_hf: (set_HF_Mirabelle_hf > set_HF_Mirabelle_hf > $o)).
% 0.52/0.40 thf(func_def_47, type, collec2046588256lle_hf: ((hF_Mirabelle_hf > $o) > set_HF_Mirabelle_hf)).
% 0.52/0.40 thf(func_def_48, type, is_emp566801209lle_hf: (set_HF_Mirabelle_hf > $o)).
% 0.52/0.40 thf(func_def_49, type, member1367349282lle_hf: (hF_Mirabelle_hf > set_HF_Mirabelle_hf > $o)).
% 0.52/0.40 thf(func_def_50, type, a: hF_Mirabelle_hf).
% 0.52/0.40 thf(func_def_51, type, p: $o).
% 0.52/0.40 thf(func_def_53, type, vNOT: ($o > $o)).
% 0.52/0.40 thf(func_def_54, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.52/0.40 thf(func_def_57, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.52/0.40 thf(func_def_58, type, vAND: ($o > $o > $o)).
% 0.52/0.40 thf(func_def_59, type, db0: !>[X0: $tType]:(X0)).
% 0.52/0.40 thf(func_def_60, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.52/0.40 thf(func_def_61, type, vIMP: ($o > $o > $o)).
% 0.52/0.40 thf(func_def_62, type, db1: !>[X0: $tType]:(X0)).
% 0.52/0.40 thf(func_def_63, type, db2: !>[X0: $tType]:(X0)).
% 0.52/0.40 thf(func_def_64, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.52/0.40 thf(func_def_65, type, vOR: ($o > $o > $o)).
% 0.52/0.40 thf(func_def_66, type, db3: !>[X0: $tType]:(X0)).
% 0.52/0.40 thf(func_def_67, type, db4: !>[X0: $tType]:(X0)).
% 0.52/0.40 thf(func_def_68, type, sK0: (hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.52/0.40 thf(func_def_69, type, sK1: ((hF_Mirabelle_hf > $o) > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.52/0.40 thf(func_def_70, type, sK2: (hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.52/0.40 thf(func_def_71, type, sK3: (hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.52/0.40 thf(func_def_72, type, sK4: (hF_Mirabelle_hf > (hF_Mirabelle_hf > hF_Mirabelle_hf) > hF_Mirabelle_hf)).
% 0.52/0.40 thf(func_def_73, type, sK5: ((hF_Mirabelle_hf > $o) > (hF_Mirabelle_hf > $o) > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.52/0.40 thf(func_def_74, type, sK6: (hF_Mirabelle_hf > (hF_Mirabelle_hf > hF_Mirabelle_hf > $o) > hF_Mirabelle_hf)).
% 0.52/0.40 thf(func_def_75, type, sK7: (hF_Mirabelle_hf > (hF_Mirabelle_hf > hF_Mirabelle_hf > $o) > hF_Mirabelle_hf)).
% 0.52/0.40 thf(func_def_76, type, sK8: (hF_Mirabelle_hf > (hF_Mirabelle_hf > hF_Mirabelle_hf > $o) > hF_Mirabelle_hf)).
% 0.52/0.40 thf(func_def_77, type, sK9: (hF_Mirabelle_hf > (hF_Mirabelle_hf > hF_Mirabelle_hf > $o) > hF_Mirabelle_hf)).
% 0.52/0.40 thf(func_def_78, type, sK10: ((hF_Mirabelle_hf > $o) > hF_Mirabelle_hf > hF_Mirabelle_hf)).
% 0.52/0.40 thf(func_def_79, type, sK11: hF_Mirabelle_hf).
% 0.52/0.40 thf(func_def_80, type, sK12: hF_Mirabelle_hf).
% 0.52/0.40 thf(func_def_81, type, sK13: hF_Mirabelle_hf).
% 0.52/0.40 thf(f6,axiom,(
% 0.52/0.40 (hF_Mirabelle_HBex = (^[X0 : hF_Mirabelle_hf, X1 : (hF_Mirabelle_hf > $o)] : (? [X2 : hF_Mirabelle_hf] : ((hF_Mirabelle_hmem @ X2 @ X0) & (X1 @ X2)))))),
% 0.52/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_HBex__def)).
% 0.52/0.40 thf(f54,axiom,(
% 0.52/0.40 ! [X0 : hF_Mirabelle_hf] : ((X0 != zero_z189798548lle_hf) => ? [X1 : hF_Mirabelle_hf] : ((hF_Mirabelle_hmem @ X1 @ X0) & (((inf_in956532509lle_hf @ X1 @ X0)) = zero_z189798548lle_hf)))),
% 0.52/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_foundation)).
% 0.52/0.40 thf(f55,axiom,(
% 0.52/0.40 ! [X0 : hF_Mirabelle_hf] : ~(hF_Mirabelle_hmem @ X0 @ zero_z189798548lle_hf)),
% 0.52/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_hemptyE)).
% 0.52/0.40 thf(f355,conjecture,(
% 0.52/0.40 (((hF_Mirabelle_HBex @ a @ (^[X0 : hF_Mirabelle_hf] : (p)))) = p & ? [X0 : hF_Mirabelle_hf] : (hF_Mirabelle_hmem @ X0 @ a))),
% 0.52/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 0.52/0.40 thf(f356,negated_conjecture,(
% 0.52/0.40 ~ (((hF_Mirabelle_HBex @ a @ (^[X0 : hF_Mirabelle_hf] : (p)))) = p & ? [X0 : hF_Mirabelle_hf] : (hF_Mirabelle_hmem @ X0 @ a))),
% 0.52/0.40 inference(negated_conjecture,[status(cth)],[f355])).
% 0.52/0.40 thf(f476,plain,(
% 0.52/0.40 ! [X0 : hF_Mirabelle_hf] : ~(hF_Mirabelle_hmem @ X0 @ zero_z189798548lle_hf)),
% 0.52/0.40 inference(rectify,[],[f55])).
% 0.52/0.40 thf(f477,plain,(
% 0.52/0.40 ! [X0 : hF_Mirabelle_hf] : ~ (((hF_Mirabelle_hmem @ X0 @ zero_z189798548lle_hf)) = $true)),
% 0.52/0.40 inference(fool_elimination,[],[f476])).
% 0.52/0.40 thf(f547,plain,(
% 0.52/0.40 ~ (((hF_Mirabelle_HBex @ a @ (^[X0 : hF_Mirabelle_hf] : (p)))) = p & ? [X1 : hF_Mirabelle_hf] : (hF_Mirabelle_hmem @ X1 @ a))),
% 0.52/0.40 inference(rectify,[],[f356])).
% 0.52/0.40 thf(f548,plain,(
% 0.52/0.40 ~ ((((?? @ hF_Mirabelle_hf @ (^[Y0 : hF_Mirabelle_hf]: (hF_Mirabelle_hmem @ Y0 @ a))) & p)) = ((hF_Mirabelle_HBex @ a @ (^[Y0 : hF_Mirabelle_hf]: (p)))))),
% 0.52/0.40 inference(fool_elimination,[],[f547])).
% 0.52/0.40 thf(f611,plain,(
% 0.52/0.40 (hF_Mirabelle_HBex = (^[X0 : hF_Mirabelle_hf, X1 : (hF_Mirabelle_hf > $o)] : (? [X2 : hF_Mirabelle_hf] : ((hF_Mirabelle_hmem @ X2 @ X0) & (X1 @ X2)))))),
% 0.52/0.40 inference(rectify,[],[f6])).
% 0.52/0.40 thf(f612,plain,(
% 0.52/0.40 (hF_Mirabelle_HBex = (^[Y0 : hF_Mirabelle_hf]: ((^[Y1 : hF_Mirabelle_hf > $o]: (?? @ hF_Mirabelle_hf @ (^[Y2 : hF_Mirabelle_hf]: ((Y1 @ Y2) & (hF_Mirabelle_hmem @ Y2 @ Y0))))))))),
% 0.52/0.40 inference(fool_elimination,[],[f611])).
% 0.52/0.40 thf(f631,plain,(
% 0.52/0.40 ! [X0 : hF_Mirabelle_hf] : ((X0 != zero_z189798548lle_hf) => ? [X1 : hF_Mirabelle_hf] : ((hF_Mirabelle_hmem @ X1 @ X0) & (((inf_in956532509lle_hf @ X1 @ X0)) = zero_z189798548lle_hf)))),
% 0.52/0.40 inference(rectify,[],[f54])).
% 0.52/0.40 thf(f632,plain,(
% 0.52/0.40 ! [X0 : hF_Mirabelle_hf] : ((zero_z189798548lle_hf != X0) => ? [X1 : hF_Mirabelle_hf] : ((zero_z189798548lle_hf = ((inf_in956532509lle_hf @ X1 @ X0))) & (((hF_Mirabelle_hmem @ X1 @ X0)) = $true)))),
% 0.52/0.40 inference(fool_elimination,[],[f631])).
% 0.52/0.40 thf(f715,plain,(
% 0.52/0.40 ((((?? @ hF_Mirabelle_hf @ (^[Y0 : hF_Mirabelle_hf]: (hF_Mirabelle_hmem @ Y0 @ a))) & p)) != ((hF_Mirabelle_HBex @ a @ (^[Y0 : hF_Mirabelle_hf]: (p)))))),
% 0.52/0.40 inference(flattening,[],[f548])).
% 0.52/0.40 thf(f717,plain,(
% 0.52/0.40 ! [X0 : hF_Mirabelle_hf] : (((hF_Mirabelle_hmem @ X0 @ zero_z189798548lle_hf)) != $true)),
% 0.52/0.40 inference(flattening,[],[f477])).
% 0.52/0.40 thf(f732,plain,(
% 0.52/0.40 ! [X0 : hF_Mirabelle_hf] : (? [X1 : hF_Mirabelle_hf] : ((zero_z189798548lle_hf = ((inf_in956532509lle_hf @ X1 @ X0))) & (((hF_Mirabelle_hmem @ X1 @ X0)) = $true)) | (zero_z189798548lle_hf = X0))),
% 0.52/0.40 inference(ennf_transformation,[],[f632])).
% 0.52/0.40 thf(f735,plain,(
% 0.52/0.40 ! [X0 : hF_Mirabelle_hf] : (((zero_z189798548lle_hf = ((inf_in956532509lle_hf @ (sK0 @ X0) @ X0))) & ($true = ((hF_Mirabelle_hmem @ (sK0 @ X0) @ X0)))) | (zero_z189798548lle_hf = X0))),
% 0.52/0.40 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X1,sK0 @ X0)],[f732])).
% 0.52/0.40 thf(f752,plain,(
% 0.52/0.40 ( ! [X0 : hF_Mirabelle_hf] : (($true = ((hF_Mirabelle_hmem @ (sK0 @ X0) @ X0))) | (zero_z189798548lle_hf = X0)) )),
% 0.52/0.40 inference(cnf_transformation,[],[f735])).
% 0.52/0.40 thf(f781,plain,(
% 0.52/0.40 ((((?? @ hF_Mirabelle_hf @ (^[Y0 : hF_Mirabelle_hf]: (hF_Mirabelle_hmem @ Y0 @ a))) & p)) != ((hF_Mirabelle_HBex @ a @ (^[Y0 : hF_Mirabelle_hf]: (p)))))),
% 0.52/0.40 inference(cnf_transformation,[],[f715])).
% 0.52/0.40 thf(f782,plain,(
% 0.52/0.40 ( ! [X0 : hF_Mirabelle_hf] : ((((hF_Mirabelle_hmem @ X0 @ zero_z189798548lle_hf)) != $true)) )),
% 0.52/0.40 inference(cnf_transformation,[],[f717])).
% 0.52/0.40 thf(f783,plain,(
% 0.52/0.40 (hF_Mirabelle_HBex = (^[Y0 : hF_Mirabelle_hf]: ((^[Y1 : hF_Mirabelle_hf > $o]: (?? @ hF_Mirabelle_hf @ (^[Y2 : hF_Mirabelle_hf]: ((Y1 @ Y2) & (hF_Mirabelle_hmem @ Y2 @ Y0))))))))),
% 0.52/0.40 inference(cnf_transformation,[],[f612])).
% 0.52/0.40 thf(f794,plain,(
% 0.52/0.40 ((((?? @ hF_Mirabelle_hf @ (^[Y0 : hF_Mirabelle_hf]: (hF_Mirabelle_hmem @ Y0 @ a))) & p)) != (((^[Y0 : hF_Mirabelle_hf]: ((^[Y1 : hF_Mirabelle_hf > $o]: (?? @ hF_Mirabelle_hf @ (^[Y2 : hF_Mirabelle_hf]: ((Y1 @ Y2) & (hF_Mirabelle_hmem @ Y2 @ Y0))))))) @ a @ (^[Y0 : hF_Mirabelle_hf]: (p)))))),
% 0.52/0.40 inference(definition_unfolding,[],[f781,f783])).
% 0.52/0.40 thf(f808,plain,(
% 0.52/0.40 ((((^[Y0 : hF_Mirabelle_hf]: ((^[Y1 : hF_Mirabelle_hf > $o]: (?? @ hF_Mirabelle_hf @ (^[Y2 : hF_Mirabelle_hf]: ((Y1 @ Y2) & (hF_Mirabelle_hmem @ Y2 @ Y0))))))) @ a @ (^[Y0 : hF_Mirabelle_hf]: (p)))) = $true) | ((((?? @ hF_Mirabelle_hf @ (^[Y0 : hF_Mirabelle_hf]: (hF_Mirabelle_hmem @ Y0 @ a))) & p)) = $true)),
% 0.52/0.40 inference(xor_proxy_clausification,[],[f794])).
% 0.52/0.40 thf(f809,plain,(
% 0.52/0.40 ((((?? @ hF_Mirabelle_hf @ (^[Y0 : hF_Mirabelle_hf]: (hF_Mirabelle_hmem @ Y0 @ a))) & p)) = $false) | ((((^[Y0 : hF_Mirabelle_hf]: ((^[Y1 : hF_Mirabelle_hf > $o]: (?? @ hF_Mirabelle_hf @ (^[Y2 : hF_Mirabelle_hf]: ((Y1 @ Y2) & (hF_Mirabelle_hmem @ Y2 @ Y0))))))) @ a @ (^[Y0 : hF_Mirabelle_hf]: (p)))) = $false)),
% 0.52/0.40 inference(xor_proxy_clausification,[],[f794])).
% 0.52/0.40 thf(f810,plain,(
% 0.52/0.40 (((?? @ hF_Mirabelle_hf @ (^[Y0 : hF_Mirabelle_hf]: (hF_Mirabelle_hmem @ Y0 @ a)))) = $false) | (p = $false) | ((((^[Y0 : hF_Mirabelle_hf]: ((^[Y1 : hF_Mirabelle_hf > $o]: (?? @ hF_Mirabelle_hf @ (^[Y2 : hF_Mirabelle_hf]: ((Y1 @ Y2) & (hF_Mirabelle_hmem @ Y2 @ Y0))))))) @ a @ (^[Y0 : hF_Mirabelle_hf]: (p)))) = $false)),
% 0.52/0.40 inference(and_proxy_clausification,[],[f809])).
% 0.52/0.40 thf(f811,plain,(
% 0.52/0.40 ( ! [X1 : hF_Mirabelle_hf] : (((((^[Y0 : hF_Mirabelle_hf]: ((^[Y1 : hF_Mirabelle_hf > $o]: (?? @ hF_Mirabelle_hf @ (^[Y2 : hF_Mirabelle_hf]: ((Y1 @ Y2) & (hF_Mirabelle_hmem @ Y2 @ Y0))))))) @ a @ (^[Y0 : hF_Mirabelle_hf]: (p)))) = $false) | ((((^[Y0 : hF_Mirabelle_hf]: (hF_Mirabelle_hmem @ Y0 @ a)) @ X1)) = $false) | (p = $false)) )),
% 0.52/0.40 inference(pi_proxy_clausification,[],[f810])).
% 0.52/0.40 thf(f812,plain,(
% 0.52/0.40 ( ! [X1 : hF_Mirabelle_hf] : ((p = $false) | (((hF_Mirabelle_hmem @ X1 @ a)) = $false) | (((?? @ hF_Mirabelle_hf @ (^[Y0 : hF_Mirabelle_hf]: (p & (hF_Mirabelle_hmem @ Y0 @ a))))) = $false)) )),
% 0.52/0.40 inference(beta-eta_normalization,[],[f811])).
% 0.52/0.40 thf(f813,plain,(
% 0.52/0.40 ( ! [X2 : hF_Mirabelle_hf,X1 : hF_Mirabelle_hf] : (((((^[Y0 : hF_Mirabelle_hf]: (p & (hF_Mirabelle_hmem @ Y0 @ a))) @ X2)) = $false) | (((hF_Mirabelle_hmem @ X1 @ a)) = $false) | (p = $false)) )),
% 0.52/0.40 inference(pi_proxy_clausification,[],[f812])).
% 0.52/0.40 thf(f814,plain,(
% 0.52/0.40 ( ! [X2 : hF_Mirabelle_hf,X1 : hF_Mirabelle_hf] : ((((hF_Mirabelle_hmem @ X1 @ a)) = $false) | (p = $false) | (((p & (hF_Mirabelle_hmem @ X2 @ a))) = $false)) )),
% 0.52/0.40 inference(beta-eta_normalization,[],[f813])).
% 0.52/0.40 thf(f815,plain,(
% 0.52/0.40 ( ! [X2 : hF_Mirabelle_hf,X1 : hF_Mirabelle_hf] : ((p = $false) | (((hF_Mirabelle_hmem @ X1 @ a)) = $false) | (((hF_Mirabelle_hmem @ X2 @ a)) = $false) | (p = $false)) )),
% 0.52/0.40 inference(and_proxy_clausification,[],[f814])).
% 0.52/0.40 thf(f816,plain,(
% 0.52/0.40 ( ! [X2 : hF_Mirabelle_hf,X1 : hF_Mirabelle_hf] : ((p = $false) | (((hF_Mirabelle_hmem @ X1 @ a)) = $false) | (((hF_Mirabelle_hmem @ X2 @ a)) = $false)) )),
% 0.52/0.40 inference(duplicate_literal_removal,[],[f815])).
% 0.52/0.40 thf(f817,plain,(
% 0.52/0.40 ((((^[Y0 : hF_Mirabelle_hf]: ((^[Y1 : hF_Mirabelle_hf > $o]: (?? @ hF_Mirabelle_hf @ (^[Y2 : hF_Mirabelle_hf]: ((Y1 @ Y2) & (hF_Mirabelle_hmem @ Y2 @ Y0))))))) @ a @ (^[Y0 : hF_Mirabelle_hf]: (p)))) = $true) | (p = $true)),
% 0.52/0.40 inference(and_proxy_clausification,[],[f808])).
% 0.52/0.40 thf(f818,plain,(
% 0.52/0.40 ((((^[Y0 : hF_Mirabelle_hf]: ((^[Y1 : hF_Mirabelle_hf > $o]: (?? @ hF_Mirabelle_hf @ (^[Y2 : hF_Mirabelle_hf]: ((Y1 @ Y2) & (hF_Mirabelle_hmem @ Y2 @ Y0))))))) @ a @ (^[Y0 : hF_Mirabelle_hf]: (p)))) = $true) | ($true = ((?? @ hF_Mirabelle_hf @ (^[Y0 : hF_Mirabelle_hf]: (hF_Mirabelle_hmem @ Y0 @ a)))))),
% 0.52/0.40 inference(and_proxy_clausification,[],[f808])).
% 0.52/0.40 thf(f819,plain,(
% 0.52/0.40 ($true = (((^[Y0 : hF_Mirabelle_hf]: (hF_Mirabelle_hmem @ Y0 @ a)) @ sK11))) | ((((^[Y0 : hF_Mirabelle_hf]: ((^[Y1 : hF_Mirabelle_hf > $o]: (?? @ hF_Mirabelle_hf @ (^[Y2 : hF_Mirabelle_hf]: ((Y1 @ Y2) & (hF_Mirabelle_hmem @ Y2 @ Y0))))))) @ a @ (^[Y0 : hF_Mirabelle_hf]: (p)))) = $true)),
% 0.52/0.40 inference(sigma_proxy_clausification,[],[f818])).
% 0.52/0.40 thf(f820,plain,(
% 0.52/0.40 ($true = ((hF_Mirabelle_hmem @ sK11 @ a))) | ($true = ((?? @ hF_Mirabelle_hf @ (^[Y0 : hF_Mirabelle_hf]: (p & (hF_Mirabelle_hmem @ Y0 @ a))))))),
% 0.52/0.40 inference(beta-eta_normalization,[],[f819])).
% 0.52/0.40 thf(f821,plain,(
% 0.52/0.40 ($true = (((^[Y0 : hF_Mirabelle_hf]: (p & (hF_Mirabelle_hmem @ Y0 @ a))) @ sK12))) | ($true = ((hF_Mirabelle_hmem @ sK11 @ a)))),
% 0.52/0.40 inference(sigma_proxy_clausification,[],[f820])).
% 0.52/0.40 thf(f822,plain,(
% 0.52/0.40 ($true = ((p & (hF_Mirabelle_hmem @ sK12 @ a)))) | ($true = ((hF_Mirabelle_hmem @ sK11 @ a)))),
% 0.52/0.40 inference(beta-eta_normalization,[],[f821])).
% 0.52/0.40 thf(f823,plain,(
% 0.52/0.40 ($true = ((hF_Mirabelle_hmem @ sK12 @ a))) | ($true = ((hF_Mirabelle_hmem @ sK11 @ a)))),
% 0.52/0.40 inference(and_proxy_clausification,[],[f822])).
% 0.52/0.40 thf(f825,plain,(
% 0.52/0.40 (p = $true) | ($true = ((?? @ hF_Mirabelle_hf @ (^[Y0 : hF_Mirabelle_hf]: (p & (hF_Mirabelle_hmem @ Y0 @ a))))))),
% 0.52/0.40 inference(beta-eta_normalization,[],[f817])).
% 0.52/0.40 thf(f826,plain,(
% 0.52/0.40 ($true = (((^[Y0 : hF_Mirabelle_hf]: (p & (hF_Mirabelle_hmem @ Y0 @ a))) @ sK13))) | (p = $true)),
% 0.52/0.40 inference(sigma_proxy_clausification,[],[f825])).
% 0.52/0.40 thf(f827,plain,(
% 0.52/0.40 (p = $true) | ($true = ((p & (hF_Mirabelle_hmem @ sK13 @ a))))),
% 0.52/0.40 inference(beta-eta_normalization,[],[f826])).
% 0.52/0.40 thf(f829,plain,(
% 0.52/0.40 (p = $true) | (p = $true)),
% 0.52/0.40 inference(and_proxy_clausification,[],[f827])).
% 0.52/0.40 thf(f830,plain,(
% 0.52/0.40 (p = $true)),
% 0.52/0.40 inference(duplicate_literal_removal,[],[f829])).
% 0.52/0.40 thf(f832,definition,(
% 0.52/0.40 spl14_1 <=> ! [X1 : hF_Mirabelle_hf] : (((hF_Mirabelle_hmem @ X1 @ a)) = $false)),
% 0.52/0.40 introduced(definition,[new_symbols(definition,[spl14_1])],[avatar_definition])).
% 0.52/0.40 thf(f833,plain,(
% 0.52/0.40 ( ! [X1 : hF_Mirabelle_hf] : ((((hF_Mirabelle_hmem @ X1 @ a)) = $false)) ) | ~spl14_1),
% 0.52/0.40 inference(avatar_component_clause,[],[f832])).
% 0.52/0.40 thf(f835,definition,(
% 0.52/0.40 spl14_2 <=> (p = $false)),
% 0.52/0.40 introduced(definition,[new_symbols(definition,[spl14_2])],[avatar_definition])).
% 0.52/0.40 thf(f837,plain,(
% 0.52/0.40 (p = $false) | ~spl14_2),
% 0.52/0.40 inference(avatar_component_clause,[],[f835])).
% 0.52/0.40 thf(f838,plain,(
% 0.52/0.40 spl14_1 | spl14_2 | spl14_1),
% 0.52/0.40 inference(avatar_split_clause,[],[f816,f832,f835,f832])).
% 0.52/0.40 thf(f840,definition,(
% 0.52/0.40 spl14_3 <=> (p = $true)),
% 0.52/0.40 introduced(definition,[new_symbols(definition,[spl14_3])],[avatar_definition])).
% 0.52/0.40 thf(f842,plain,(
% 0.52/0.40 (p = $true) | ~spl14_3),
% 0.52/0.40 inference(avatar_component_clause,[],[f840])).
% 0.52/0.40 thf(f844,definition,(
% 0.52/0.40 spl14_4 <=> ($true = ((hF_Mirabelle_hmem @ sK11 @ a)))),
% 0.52/0.40 introduced(definition,[new_symbols(definition,[spl14_4])],[avatar_definition])).
% 0.52/0.40 thf(f846,plain,(
% 0.52/0.40 ($true = ((hF_Mirabelle_hmem @ sK11 @ a))) | ~spl14_4),
% 0.52/0.40 inference(avatar_component_clause,[],[f844])).
% 0.52/0.40 thf(f849,definition,(
% 0.52/0.40 spl14_5 <=> ($true = ((hF_Mirabelle_hmem @ sK12 @ a)))),
% 0.52/0.40 introduced(definition,[new_symbols(definition,[spl14_5])],[avatar_definition])).
% 0.52/0.40 thf(f851,plain,(
% 0.52/0.40 ($true = ((hF_Mirabelle_hmem @ sK12 @ a))) | ~spl14_5),
% 0.52/0.40 inference(avatar_component_clause,[],[f849])).
% 0.52/0.40 thf(f852,plain,(
% 0.52/0.40 spl14_4 | spl14_5),
% 0.52/0.40 inference(avatar_split_clause,[],[f823,f849,f844])).
% 0.52/0.40 thf(f853,plain,(
% 0.52/0.40 spl14_3),
% 0.52/0.40 inference(avatar_split_clause,[],[f830,f840])).
% 0.52/0.40 thf(f859,plain,(
% 0.52/0.40 ($true = $false) | (~spl14_2 | ~spl14_3)),
% 0.52/0.40 inference(forward_demodulation,[],[f842,f837])).
% 0.52/0.40 thf(f860,plain,(
% 0.52/0.40 $false | (~spl14_2 | ~spl14_3)),
% 0.52/0.40 inference(trivial_inequality_removal,[],[f859])).
% 0.52/0.40 thf(f861,plain,(
% 0.52/0.40 ~spl14_2 | ~spl14_3),
% 0.52/0.40 inference(avatar_contradiction_clause,[],[f860])).
% 0.52/0.40 thf(f868,plain,(
% 0.52/0.40 ($true = $false) | (zero_z189798548lle_hf = a) | ~spl14_1),
% 0.52/0.40 inference(superposition,[],[f752,f833])).
% 0.52/0.40 thf(f880,plain,(
% 0.52/0.40 (zero_z189798548lle_hf = a) | ~spl14_1),
% 0.52/0.40 inference(trivial_inequality_removal,[],[f868])).
% 0.52/0.40 thf(f920,plain,(
% 0.52/0.40 ($true = ((hF_Mirabelle_hmem @ sK11 @ zero_z189798548lle_hf))) | (~spl14_1 | ~spl14_4)),
% 0.52/0.40 inference(superposition,[],[f846,f880])).
% 0.52/0.40 thf(f939,plain,(
% 0.52/0.40 $false | (~spl14_1 | ~spl14_4)),
% 0.52/0.40 inference(forward_subsumption_resolution,[],[f920,f782])).
% 0.52/0.40 thf(f940,plain,(
% 0.52/0.40 ~spl14_1 | ~spl14_4),
% 0.52/0.40 inference(avatar_contradiction_clause,[],[f939])).
% 0.52/0.40 thf(f942,plain,(
% 0.52/0.40 ($true = $false) | (~spl14_1 | ~spl14_5)),
% 0.52/0.40 inference(forward_demodulation,[],[f851,f833])).
% 0.52/0.40 thf(f943,plain,(
% 0.52/0.40 $false | (~spl14_1 | ~spl14_5)),
% 0.52/0.40 inference(trivial_inequality_removal,[],[f942])).
% 0.52/0.40 thf(f944,plain,(
% 0.52/0.40 ~spl14_1 | ~spl14_5),
% 0.52/0.40 inference(avatar_contradiction_clause,[],[f943])).
% 0.52/0.40 cnf(s1, plain, spl14_1 | spl14_1 | spl14_2, inference(sat_conversion,[],[f838])).
% 0.52/0.40 cnf(s2, plain, spl14_1 | spl14_2, inference(rat,[],[s1])).
% 0.52/0.40 cnf(s4, plain, spl14_4 | spl14_5, inference(sat_conversion,[],[f852])).
% 0.52/0.40 cnf(s5, plain, spl14_3, inference(sat_conversion,[],[f853])).
% 0.52/0.40 cnf(s7, plain, ~spl14_2 | ~spl14_3, inference(sat_conversion,[],[f861])).
% 0.52/0.40 cnf(s10, plain, ~spl14_1 | ~spl14_4, inference(sat_conversion,[],[f940])).
% 0.52/0.40 cnf(s11, plain, ~spl14_1 | ~spl14_5, inference(sat_conversion,[],[f944])).
% 0.52/0.40 cnf(s12, plain, ~spl14_2, inference(rat,[],[s7,s5])).
% 0.52/0.40 cnf(s13, plain, spl14_1, inference(rat,[],[s2,s12])).
% 0.52/0.40 cnf(s14, plain, ~spl14_5, inference(rat,[],[s11,s13])).
% 0.52/0.40 cnf(s15, plain, ~spl14_4, inference(rat,[],[s10,s13])).
% 0.52/0.40 cnf(s16, plain, $false, inference(rat,[],[s4,s14,s15])).
% 0.52/0.40 thf(f945,plain,(
% 0.52/0.40 $false),
% 0.52/0.40 inference(avatar_sat_refutation,[],[s16])).
% 0.52/0.40 % SZS output end Proof for theBenchmark
% 0.52/0.40 % (804695)------------------------------
% 0.52/0.40 % (804695)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.52/0.40 % (804695)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.52/0.40 % (804695)CaDiCaL version: 2.1.3
% 0.52/0.40 % (804695)Termination reason: Refutation
% 0.52/0.40 % (804695)Time elapsed: 0.013 s
% 0.52/0.40 % (804695)Peak memory usage: 13 MB
% 0.52/0.40 % (804695)Instructions burned: 46 (million)
% 0.52/0.40 % (804662)Success in time 0.119 s
% 0.52/0.40 % Vampire exiting
%------------------------------------------------------------------------------