%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO877^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 08:48:31 AM UTC 2026
% Result : Theorem 0.78s 0.58s
% Output : Refutation 0.78s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SYO877^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.30 % Computer : n003.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8046.5625MB
% 0.11/0.30 % OS : Linux 6.8.0-71-generic
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % WCLimit : 300
% 0.11/0.30 % DateTime : Tue Sep 29 17:25:14 UTC 2026
% 0.11/0.30 % CPUTime :
% 0.11/0.30 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.29/0.36 Running higher-order theorem proving
% 0.33/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.78/0.58 % (2795448)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.78/0.58 % (2795453)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=753979606:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.78/0.58 % (2795459)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.78/0.58 % (2795459)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
% 0.78/0.58 % (2795457)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=885562376:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.78/0.58 % (2795456)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=3967018605: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)
% 0.78/0.58 % (2795459)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=804170316:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.78/0.58 % (2795454)lrs+10_16_si=on:nwc=1.5:random_seed=3637893277:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.78/0.58 % (2795455)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1018647888:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.78/0.58 % (2795458)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=4287836046:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.78/0.58 % (2795455)Instruction limit reached!
% 0.78/0.58 % (2795455)------------------------------
% 0.78/0.58 % (2795455)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.78/0.58 % (2795455)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.78/0.58 % (2795455)CaDiCaL version: 2.1.3
% 0.78/0.58 % (2795455)Termination reason: Instruction limit
% 0.78/0.58 % (2795455)Termination phase: shuffling
% 0.78/0.58 % (2795455)Time elapsed: 0.003 s
% 0.78/0.58 % (2795455)Peak memory usage: 10 MB
% 0.78/0.58 % (2795455)Instructions burned: 3 (million)
% 0.78/0.58 % (2795454)Instruction limit reached!
% 0.78/0.58 % (2795454)------------------------------
% 0.78/0.58 % (2795454)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.78/0.58 % (2795454)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.78/0.58 % (2795454)CaDiCaL version: 2.1.3
% 0.78/0.58 % (2795454)Termination reason: Instruction limit
% 0.78/0.58 % (2795454)Termination phase: Property scanning
% 0.78/0.58 % (2795454)Time elapsed: 0.016 s
% 0.78/0.58 % (2795454)Peak memory usage: 10 MB
% 0.78/0.58 % (2795454)Instructions burned: 18 (million)
% 0.78/0.58 % (2795453)Instruction limit reached!
% 0.78/0.58 % (2795453)------------------------------
% 0.78/0.58 % (2795453)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.78/0.58 % (2795453)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.78/0.58 % (2795453)CaDiCaL version: 2.1.3
% 0.78/0.58 % (2795453)Termination reason: Instruction limit
% 0.78/0.58 % (2795453)Termination phase: Saturation
% 0.78/0.58 % (2795453)Time elapsed: 0.033 s
% 0.78/0.58 % (2795453)Peak memory usage: 12 MB
% 0.78/0.58 % (2795453)Instructions burned: 89 (million)
% 0.78/0.58 % (2795457)Instruction limit reached!
% 0.78/0.58 % (2795457)------------------------------
% 0.78/0.58 % (2795457)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.78/0.58 % (2795457)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.78/0.58 % (2795457)CaDiCaL version: 2.1.3
% 0.78/0.58 % (2795457)Termination reason: Instruction limit
% 0.78/0.58 % (2795457)Termination phase: Property scanning
% 0.78/0.58 % (2795457)Time elapsed: 0.020 s
% 0.78/0.58 % (2795457)Peak memory usage: 10 MB
% 0.78/0.58 % (2795457)Instructions burned: 25 (million)
% 0.78/0.58 % (2795469)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.78/0.58 % (2795469)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3946273268:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.78/0.58 % (2795469)Instruction limit reached!
% 0.78/0.58 % (2795469)------------------------------
% 0.78/0.58 % (2795469)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.78/0.58 % (2795469)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.78/0.58 % (2795469)CaDiCaL version: 2.1.3
% 0.78/0.58 % (2795469)Termination reason: Instruction limit
% 0.78/0.58 % (2795469)Termination phase: shuffling
% 0.78/0.58 % (2795469)Time elapsed: 0.004 s
% 0.78/0.58 % (2795469)Peak memory usage: 10 MB
% 0.78/0.58 % (2795469)Instructions burned: 9 (million)
% 0.78/0.58 % (2795468)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=379254013:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.78/0.58 % (2795470)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=3738757868:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.78/0.58 % (2795467)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2104083483:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.78/0.58 % (2795468)Instruction limit reached!
% 0.78/0.58 % (2795468)------------------------------
% 0.78/0.58 % (2795468)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.78/0.58 % (2795468)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.78/0.58 % (2795468)CaDiCaL version: 2.1.3
% 0.78/0.58 % (2795468)Termination reason: Instruction limit
% 0.78/0.58 % (2795468)Termination phase: shuffling
% 0.78/0.58 % (2795468)Time elapsed: 0.005 s
% 0.78/0.58 % (2795468)Peak memory usage: 10 MB
% 0.78/0.58 % (2795468)Instructions burned: 6 (million)
% 0.78/0.58 % (2795472)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
% 0.78/0.58 % (2795472)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.78/0.58 % (2795458)Instruction limit reached!
% 0.78/0.58 % (2795458)------------------------------
% 0.78/0.58 % (2795458)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.78/0.58 % (2795458)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.78/0.58 % (2795458)CaDiCaL version: 2.1.3
% 0.78/0.58 % (2795458)Termination reason: Instruction limit
% 0.78/0.58 % (2795458)Termination phase: Function definition elimination
% 0.78/0.58 % (2795458)Time elapsed: 0.054 s
% 0.78/0.58 % (2795458)Peak memory usage: 11 MB
% 0.78/0.58 % (2795458)Instructions burned: 76 (million)
% 0.78/0.58 % (2795467)Instruction limit reached!
% 0.78/0.58 % (2795467)------------------------------
% 0.78/0.58 % (2795467)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.78/0.58 % (2795467)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.78/0.58 % (2795467)CaDiCaL version: 2.1.3
% 0.78/0.58 % (2795467)Termination reason: Instruction limit
% 0.78/0.58 % (2795467)Termination phase: shuffling
% 0.78/0.58 % (2795467)Time elapsed: 0.003 s
% 0.78/0.58 % (2795467)Peak memory usage: 10 MB
% 0.78/0.58 % (2795467)Instructions burned: 2 (million)
% 0.78/0.58 % (2795472)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=1667849998:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.78/0.58 % (2795470)Instruction limit reached!
% 0.78/0.58 % (2795470)------------------------------
% 0.78/0.58 % (2795470)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.78/0.58 % (2795470)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.78/0.58 % (2795470)CaDiCaL version: 2.1.3
% 0.78/0.58 % (2795470)Termination reason: Instruction limit
% 0.78/0.58 % (2795470)Termination phase: shuffling
% 0.78/0.58 % (2795470)Time elapsed: 0.010 s
% 0.78/0.58 % (2795470)Peak memory usage: 10 MB
% 0.78/0.58 % (2795470)Instructions burned: 12 (million)
% 0.78/0.58 % (2795472)Instruction limit reached!
% 0.78/0.58 % (2795472)------------------------------
% 0.78/0.58 % (2795472)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.78/0.58 % (2795472)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.78/0.58 % (2795472)CaDiCaL version: 2.1.3
% 0.78/0.58 % (2795472)Termination reason: Instruction limit
% 0.78/0.58 % (2795472)Termination phase: Property scanning
% 0.78/0.58 % (2795472)Time elapsed: 0.012 s
% 0.78/0.58 % (2795472)Peak memory usage: 10 MB
% 0.78/0.58 % (2795472)Instructions burned: 30 (million)
% 0.78/0.58 % (2795459) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2795448-2795459"...
% 0.78/0.58 % (2795478)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.78/0.58 % (2795481)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=1787689080:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 0.78/0.58 % (2795478)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=2864233579:i=2:add=on:rtra=on_2998 on theBenchmark for (2998ds/2Mi)
% 0.78/0.58 % (2795477)lrs+10_1_si=on:cs=on:random_seed=4140859482:i=8:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/8Mi)
% 0.78/0.58 % (2795476)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=3642172703:i=86:piset=equals:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/86Mi)
% 0.78/0.58 % (2795478)Instruction limit reached!
% 0.78/0.58 % (2795478)------------------------------
% 0.78/0.58 % (2795478)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.78/0.58 % (2795478)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.78/0.58 % (2795478)CaDiCaL version: 2.1.3
% 0.78/0.58 % (2795478)Termination reason: Instruction limit
% 0.78/0.58 % (2795478)Termination phase: shuffling
% 0.78/0.58 % (2795478)Time elapsed: 0.003 s
% 0.78/0.58 % (2795478)Peak memory usage: 9 MB
% 0.78/0.58 % (2795478)Instructions burned: 2 (million)
% 0.78/0.58 % (2795480)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=960439789:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 0.78/0.58 % (2795477)Instruction limit reached!
% 0.78/0.58 % (2795477)------------------------------
% 0.78/0.58 % (2795477)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.78/0.58 % (2795477)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.78/0.58 % (2795477)CaDiCaL version: 2.1.3
% 0.78/0.58 % (2795477)Termination reason: Instruction limit
% 0.78/0.58 % (2795477)Termination phase: shuffling
% 0.78/0.58 % (2795477)Time elapsed: 0.007 s
% 0.78/0.58 % (2795477)Peak memory usage: 10 MB
% 0.78/0.58 % (2795477)Instructions burned: 9 (million)
% 0.78/0.58 % (2795459)...printing done.
% 0.78/0.58 % (2795459)Refutation found. Thanks to Tanya!
% 0.78/0.58 % SZS status Theorem for theBenchmark
% 0.78/0.58 % SZS output start Proof for theBenchmark
% 0.78/0.58 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.78/0.58 thf(func_def_0, type, c_Eps_i: (($i > $o) > $i)).
% 0.78/0.58 thf(func_def_1, type, c_False: $o).
% 0.78/0.58 thf(func_def_2, type, c_True: $o).
% 0.78/0.58 thf(func_def_3, type, c_not: ($o > $o)).
% 0.78/0.58 thf(func_def_4, type, c_and: ($o > $o > $o)).
% 0.78/0.58 thf(func_def_5, type, c_or: ($o > $o > $o)).
% 0.78/0.58 thf(func_def_6, type, c_iff: ($o > $o > $o)).
% 0.78/0.58 thf(func_def_7, type, c_In: ($i > $i > $o)).
% 0.78/0.58 thf(func_def_8, type, c_Subq: ($i > $i > $o)).
% 0.78/0.58 thf(func_def_10, type, c_Union: ($i > $i)).
% 0.78/0.58 thf(func_def_11, type, c_Power: ($i > $i)).
% 0.78/0.58 thf(func_def_12, type, c_Repl: ($i > ($i > $i) > $i)).
% 0.78/0.58 thf(func_def_13, type, c_TransSet: ($i > $o)).
% 0.78/0.58 thf(func_def_14, type, c_atleast2: ($i > $o)).
% 0.78/0.58 thf(func_def_15, type, c_atleast3: ($i > $o)).
% 0.78/0.58 thf(func_def_16, type, c_atleast4: ($i > $o)).
% 0.78/0.58 thf(func_def_17, type, c_atleast5: ($i > $o)).
% 0.78/0.58 thf(func_def_18, type, c_atleast6: ($i > $o)).
% 0.78/0.58 thf(func_def_19, type, c_exactly2: ($i > $o)).
% 0.78/0.58 thf(func_def_20, type, c_exactly3: ($i > $o)).
% 0.78/0.58 thf(func_def_21, type, c_exactly4: ($i > $o)).
% 0.78/0.58 thf(func_def_22, type, c_exactly5: ($i > $o)).
% 0.78/0.58 thf(func_def_23, type, c_exu_i: (($i > $o) > $o)).
% 0.78/0.58 thf(func_def_24, type, c_reflexive_i: (($i > $i > $o) > $o)).
% 0.78/0.58 thf(func_def_25, type, c_irreflexive_i: (($i > $i > $o) > $o)).
% 0.78/0.58 thf(func_def_26, type, c_symmetric_i: (($i > $i > $o) > $o)).
% 0.78/0.58 thf(func_def_27, type, c_antisymmetric_i: (($i > $i > $o) > $o)).
% 0.78/0.58 thf(func_def_28, type, c_transitive_i: (($i > $i > $o) > $o)).
% 0.78/0.58 thf(func_def_29, type, c_eqreln_i: (($i > $i > $o) > $o)).
% 0.78/0.58 thf(func_def_30, type, c_per_i: (($i > $i > $o) > $o)).
% 0.78/0.58 thf(func_def_31, type, c_linear_i: (($i > $i > $o) > $o)).
% 0.78/0.58 thf(func_def_32, type, c_trichotomous_or_i: (($i > $i > $o) > $o)).
% 0.78/0.58 thf(func_def_33, type, c_partialorder_i: (($i > $i > $o) > $o)).
% 0.78/0.58 thf(func_def_34, type, c_totalorder_i: (($i > $i > $o) > $o)).
% 0.78/0.58 thf(func_def_35, type, c_strictpartialorder_i: (($i > $i > $o) > $o)).
% 0.78/0.58 thf(func_def_36, type, c_stricttotalorder_i: (($i > $i > $o) > $o)).
% 0.78/0.58 thf(func_def_37, type, c_If_i: ($o > $i > $i > $i)).
% 0.78/0.58 thf(func_def_38, type, c_exactly1of2: ($o > $o > $o)).
% 0.78/0.58 thf(func_def_39, type, c_exactly1of3: ($o > $o > $o > $o)).
% 0.78/0.58 thf(func_def_40, type, c_nIn: ($i > $i > $o)).
% 0.78/0.58 thf(func_def_41, type, c_nSubq: ($i > $i > $o)).
% 0.78/0.58 thf(func_def_42, type, c_UPair: ($i > $i > $i)).
% 0.78/0.58 thf(func_def_43, type, c_Sing: ($i > $i)).
% 0.78/0.58 thf(func_def_44, type, c_binunion: ($i > $i > $i)).
% 0.78/0.58 thf(func_def_45, type, c_SetAdjoin: ($i > $i > $i)).
% 0.78/0.58 thf(func_def_46, type, c_famunion: ($i > ($i > $i) > $i)).
% 0.78/0.58 thf(func_def_47, type, c_Sep: ($i > ($i > $o) > $i)).
% 0.78/0.58 thf(func_def_48, type, c_ReplSep: ($i > ($i > $o) > ($i > $i) > $i)).
% 0.78/0.58 thf(func_def_49, type, c_binintersect: ($i > $i > $i)).
% 0.78/0.58 thf(func_def_50, type, c_setminus: ($i > $i > $i)).
% 0.78/0.58 thf(func_def_51, type, c_inj: ($i > $i > ($i > $i) > $o)).
% 0.78/0.58 thf(func_def_52, type, c_bij: ($i > $i > ($i > $i) > $o)).
% 0.78/0.58 thf(func_def_53, type, c_atleastp: ($i > $i > $o)).
% 0.78/0.58 thf(func_def_54, type, c_equip: ($i > $i > $o)).
% 0.78/0.58 thf(func_def_55, type, c_In_rec_poly_G_i: (($i > ($i > $i) > $i) > $i > $i > $o)).
% 0.78/0.58 thf(func_def_56, type, c_In_rec_poly_i: (($i > ($i > $i) > $i) > $i > $i)).
% 0.78/0.58 thf(func_def_57, type, c_ordsucc: ($i > $i)).
% 0.78/0.58 thf(func_def_58, type, c_nat_p: ($i > $o)).
% 0.78/0.58 thf(func_def_59, type, c_nat_primrec: ($i > ($i > $i > $i) > $i > $i)).
% 0.78/0.58 thf(func_def_60, type, c_add_nat: ($i > $i > $i)).
% 0.78/0.58 thf(func_def_61, type, c_mul_nat: ($i > $i > $i)).
% 0.78/0.58 thf(func_def_62, type, c_ordinal: ($i > $o)).
% 0.78/0.58 thf(func_def_63, type, c_V_: ($i > $i)).
% 0.78/0.58 thf(func_def_64, type, c_Inj1: ($i > $i)).
% 0.78/0.58 thf(func_def_65, type, c_Inj0: ($i > $i)).
% 0.78/0.58 thf(func_def_66, type, c_Unj: ($i > $i)).
% 0.78/0.58 thf(func_def_67, type, c_combine_funcs: ($i > $i > ($i > $i) > ($i > $i) > $i > $i)).
% 0.78/0.58 thf(func_def_68, type, c_setsum: ($i > $i > $i)).
% 0.78/0.58 thf(func_def_69, type, c_proj0: ($i > $i)).
% 0.78/0.58 thf(func_def_70, type, c_proj1: ($i > $i)).
% 0.78/0.58 thf(func_def_71, type, c_binrep: ($i > $i > $i)).
% 0.78/0.58 thf(func_def_72, type, c_lam: ($i > ($i > $i) > $i)).
% 0.78/0.58 thf(func_def_73, type, c_setprod: ($i > $i > $i)).
% 0.78/0.58 thf(func_def_74, type, c_ap: ($i > $i > $i)).
% 0.78/0.58 thf(func_def_75, type, c_setsum_p: ($i > $o)).
% 0.78/0.58 thf(func_def_76, type, c_tuple_p: ($i > $i > $o)).
% 0.78/0.58 thf(func_def_77, type, c_Pi: ($i > ($i > $i) > $i)).
% 0.78/0.58 thf(func_def_78, type, c_setexp: ($i > $i > $i)).
% 0.78/0.58 thf(func_def_79, type, c_Sep2: ($i > ($i > $i) > ($i > $i > $o) > $i)).
% 0.78/0.58 thf(func_def_80, type, c_set_of_pairs: ($i > $o)).
% 0.78/0.58 thf(func_def_81, type, c_lam2: ($i > ($i > $i) > ($i > $i > $i) > $i)).
% 0.78/0.58 thf(func_def_82, type, c_PNoEq_: ($i > ($i > $o) > ($i > $o) > $o)).
% 0.78/0.58 thf(func_def_83, type, c_PNoLt_: ($i > ($i > $o) > ($i > $o) > $o)).
% 0.78/0.58 thf(func_def_84, type, c_PNoLt: ($i > ($i > $o) > $i > ($i > $o) > $o)).
% 0.78/0.58 thf(func_def_85, type, c_PNoLe: ($i > ($i > $o) > $i > ($i > $o) > $o)).
% 0.78/0.58 thf(func_def_86, type, c_PNo_downc: (($i > ($i > $o) > $o) > $i > ($i > $o) > $o)).
% 0.78/0.58 thf(func_def_87, type, c_PNo_upc: (($i > ($i > $o) > $o) > $i > ($i > $o) > $o)).
% 0.78/0.58 thf(func_def_88, type, c_SNoElts_: ($i > $i)).
% 0.78/0.58 thf(func_def_89, type, c_SNo_: ($i > $i > $o)).
% 0.78/0.58 thf(func_def_90, type, c_PSNo: ($i > ($i > $o) > $i)).
% 0.78/0.58 thf(func_def_91, type, c_SNo: ($i > $o)).
% 0.78/0.58 thf(func_def_92, type, c_SNoLev: ($i > $i)).
% 0.78/0.58 thf(func_def_93, type, c_SNoEq_: ($i > $i > $i > $o)).
% 0.78/0.58 thf(func_def_94, type, c_SNoLt: ($i > $i > $o)).
% 0.78/0.58 thf(func_def_95, type, c_SNoLe: ($i > $i > $o)).
% 0.78/0.58 thf(func_def_96, type, c_binop_on: ($i > ($i > $i > $i) > $o)).
% 0.78/0.58 thf(func_def_97, type, c_Loop: ($i > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > $i > $o)).
% 0.78/0.58 thf(func_def_98, type, c_Loop_with_defs: ($i > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > $i > ($i > $i > $i) > ($i > $i > $i > $i) > ($i > $i > $i) > ($i > $i > $i > $i) > ($i > $i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > $o)).
% 0.78/0.58 thf(func_def_99, type, c_Loop_with_defs_cex1: ($i > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > $i > ($i > $i > $i) > ($i > $i > $i > $i) > ($i > $i > $i) > ($i > $i > $i > $i) > ($i > $i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > $o)).
% 0.78/0.58 thf(func_def_100, type, c_Loop_with_defs_cex2: ($i > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > $i > ($i > $i > $i) > ($i > $i > $i > $i) > ($i > $i > $i) > ($i > $i > $i > $i) > ($i > $i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > ($i > $i > $i) > $o)).
% 0.78/0.58 thf(func_def_101, type, c_combinator: ($i > $o)).
% 0.78/0.58 thf(func_def_102, type, c_combinator_equiv: ($i > $i > $o)).
% 0.78/0.58 thf(func_def_103, type, c_equip_mod: ($i > $i > $i > $o)).
% 0.78/0.58 thf(func_def_105, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.78/0.58 thf(func_def_106, type, db1: !>[X0: $tType]:(X0)).
% 0.78/0.58 thf(func_def_107, type, db0: !>[X0: $tType]:(X0)).
% 0.78/0.58 thf(func_def_108, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.78/0.58 thf(func_def_109, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.78/0.58 thf(func_def_110, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.78/0.58 thf(func_def_111, type, vIMP: ($o > $o > $o)).
% 0.78/0.58 thf(func_def_112, type, db2: !>[X0: $tType]:(X0)).
% 0.78/0.58 thf(func_def_113, type, db3: !>[X0: $tType]:(X0)).
% 0.78/0.58 thf(func_def_114, type, db5: !>[X0: $tType]:(X0)).
% 0.78/0.58 thf(func_def_117, type, db4: !>[X0: $tType]:(X0)).
% 0.78/0.58 thf(func_def_118, type, db13: !>[X0: $tType]:(X0)).
% 0.78/0.58 thf(func_def_119, type, db12: !>[X0: $tType]:(X0)).
% 0.78/0.58 thf(func_def_120, type, db11: !>[X0: $tType]:(X0)).
% 0.78/0.58 thf(func_def_121, type, db10: !>[X0: $tType]:(X0)).
% 0.78/0.58 thf(func_def_122, type, db9: !>[X0: $tType]:(X0)).
% 0.78/0.58 thf(func_def_123, type, db8: !>[X0: $tType]:(X0)).
% 0.78/0.58 thf(func_def_124, type, db7: !>[X0: $tType]:(X0)).
% 0.78/0.58 thf(func_def_125, type, db6: !>[X0: $tType]:(X0)).
% 0.78/0.58 thf(func_def_126, type, db14: !>[X0: $tType]:(X0)).
% 0.78/0.58 thf(func_def_127, type, db15: !>[X0: $tType]:(X0)).
% 0.78/0.58 thf(func_def_128, type, db16: !>[X0: $tType]:(X0)).
% 0.78/0.58 thf(func_def_129, type, db17: !>[X0: $tType]:(X0)).
% 0.78/0.58 thf(func_def_130, type, db18: !>[X0: $tType]:(X0)).
% 0.78/0.58 thf(func_def_131, type, sP0: (($i > $o) > $i > $o)).
% 0.78/0.58 thf(func_def_132, type, sP1: (($i > $o) > $i > $o)).
% 0.78/0.58 thf(func_def_133, type, sP2: (($i > $o) > $o)).
% 0.78/0.58 thf(func_def_134, type, sP3: (($i > $o) > $o)).
% 0.78/0.58 thf(func_def_135, type, sP4: (($i > $o) > $o)).
% 0.78/0.58 thf(func_def_136, type, sK5: (($i > $o) > $i)).
% 0.78/0.58 thf(func_def_137, type, sK6: (($i > $o) > $i)).
% 0.78/0.58 thf(func_def_138, type, sK7: (($i > $o) > $i)).
% 0.78/0.58 thf(func_def_139, type, sK8: (($i > $o) > $i)).
% 0.78/0.58 thf(func_def_140, type, sK9: (($i > $o) > $i > $i > $i)).
% 0.78/0.58 thf(func_def_141, type, sK10: (($i > $o) > $i > $i)).
% 0.78/0.58 thf(func_def_142, type, sK11: (($i > $o) > $i)).
% 0.78/0.58 thf(func_def_143, type, sF12: $o).
% 0.78/0.58 thf(func_def_144, type, sF13: $o).
% 0.78/0.58 thf(func_def_145, type, sK14: ($i > $i > $i)).
% 0.78/0.58 thf(func_def_146, type, sK15: ($o > $o > $o)).
% 0.78/0.58 thf(func_def_147, type, sK16: ($o > $o > $o)).
% 0.78/0.58 thf(func_def_148, type, sK17: $o).
% 0.78/0.58 thf(func_def_149, type, sK18: ($i > $i > $i)).
% 0.78/0.58 thf(func_def_150, type, sK19: ($i > $i > $i)).
% 0.78/0.58 thf(func_def_151, type, sK20: $o).
% 0.78/0.58 thf(func_def_152, type, sK21: ($i > $i > $i)).
% 0.78/0.58 thf(func_def_153, type, sK22: ($i > $i > $i > $o)).
% 0.78/0.58 thf(func_def_155, type, sK24: ($i > $i)).
% 0.78/0.58 thf(func_def_157, type, sK26: ($i > $o)).
% 0.78/0.58 thf(func_def_159, type, sK28: ($i > $i > $i)).
% 0.78/0.58 thf(func_def_160, type, sK29: $o).
% 0.78/0.58 thf(func_def_161, type, sK30: ($i > $i > ($i > $i) > $i)).
% 0.78/0.58 thf(func_def_162, type, sK31: (($i > $i) > $i > $i > $i > $o)).
% 0.78/0.58 thf(f13,axiom,(
% 0.78/0.58 (c_not = (^[X0 : $o] : (X0 => c_False)))),
% 0.78/0.58 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax13)).
% 0.78/0.58 thf(f14,axiom,(
% 0.78/0.58 (c_and = (^[X0 : $o, X1 : $o] : (! [X2 : $o] : ((X0 => (X1 => X2)) => X2))))),
% 0.78/0.58 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax14)).
% 0.78/0.58 thf(f109,conjecture,(
% 0.78/0.58 (c_not @ ! [X1 : ($i > $i > $i),X6 : $i,X2 : ($i > $o),X3 : ($i > $o),X7 : $i,X4 : ($i > $i),X0 : ($i > $i > $o),X5 : $i] : (c_and @ (X6 = ((X1 @ (X1 @ X5 @ (X1 @ X7 @ (X1 @ (X1 @ (X1 @ (X1 @ X6 @ (X1 @ (X1 @ X5 @ (X1 @ X5 @ (X1 @ (X1 @ X5 @ (X1 @ (X4 @ X5) @ (X1 @ (X1 @ X7 @ (X1 @ X6 @ (X1 @ X6 @ X6))) @ X5))) @ (X1 @ (X4 @ (X1 @ (X1 @ (X4 @ X7) @ X5) @ (X1 @ X5 @ X5))) @ (X1 @ X6 @ (X1 @ X6 @ (X1 @ (X1 @ (X1 @ X5 @ (X1 @ (X1 @ X5 @ (X1 @ (X4 @ X6) @ X7)) @ (X4 @ (X1 @ X7 @ X5)))) @ X6) @ (X4 @ (X1 @ (X1 @ X7 @ (X1 @ X5 @ (X1 @ (X4 @ (X1 @ X5 @ X7)) @ X5))) @ (X1 @ (X1 @ (X1 @ X6 @ (X1 @ (X4 @ X5) @ X6)) @ X6) @ (X4 @ (X4 @ (X1 @ (X1 @ (X1 @ (X1 @ X5 @ (X1 @ (X1 @ X6 @ (X1 @ (X1 @ X7 @ X5) @ X7)) @ X6)) @ X7) @ (X1 @ X7 @ (X1 @ X5 @ X5))) @ X6))))))))))))) @ (X1 @ (X1 @ (X1 @ (X1 @ (X1 @ X6 @ (X1 @ X5 @ X5)) @ (X4 @ (X4 @ (X1 @ X7 @ (X4 @ (X4 @ (X1 @ X7 @ X5))))))) @ X5) @ X6) @ (X1 @ X6 @ X7)))) @ X5) @ X5) @ (X4 @ X6)))) @ (X1 @ (X1 @ (X4 @ (X1 @ (X4 @ (X1 @ (X1 @ (X1 @ (X1 @ X7 @ (X1 @ (X4 @ (X4 @ (X1 @ (X1 @ X5 @ X6) @ X7))) @ (X4 @ (X1 @ X5 @ X5)))) @ X5) @ (X4 @ X5)) @ (X1 @ (X1 @ (X1 @ (X1 @ (X1 @ X5 @ X7) @ (X4 @ (X4 @ (X4 @ X7)))) @ X7) @ X6) @ X5))) @ (X1 @ (X1 @ (X1 @ X6 @ X5) @ (X4 @ X6)) @ X6))) @ X7) @ X6)))) @ ? [X8 : $i] : (X3 @ (X4 @ X5))))),
% 0.78/0.58 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj)).
% 0.78/0.58 thf(f110,negated_conjecture,(
% 0.78/0.58 ~(c_not @ ! [X1 : ($i > $i > $i),X6 : $i,X2 : ($i > $o),X3 : ($i > $o),X7 : $i,X4 : ($i > $i),X0 : ($i > $i > $o),X5 : $i] : (c_and @ (X6 = ((X1 @ (X1 @ X5 @ (X1 @ X7 @ (X1 @ (X1 @ (X1 @ (X1 @ X6 @ (X1 @ (X1 @ X5 @ (X1 @ X5 @ (X1 @ (X1 @ X5 @ (X1 @ (X4 @ X5) @ (X1 @ (X1 @ X7 @ (X1 @ X6 @ (X1 @ X6 @ X6))) @ X5))) @ (X1 @ (X4 @ (X1 @ (X1 @ (X4 @ X7) @ X5) @ (X1 @ X5 @ X5))) @ (X1 @ X6 @ (X1 @ X6 @ (X1 @ (X1 @ (X1 @ X5 @ (X1 @ (X1 @ X5 @ (X1 @ (X4 @ X6) @ X7)) @ (X4 @ (X1 @ X7 @ X5)))) @ X6) @ (X4 @ (X1 @ (X1 @ X7 @ (X1 @ X5 @ (X1 @ (X4 @ (X1 @ X5 @ X7)) @ X5))) @ (X1 @ (X1 @ (X1 @ X6 @ (X1 @ (X4 @ X5) @ X6)) @ X6) @ (X4 @ (X4 @ (X1 @ (X1 @ (X1 @ (X1 @ X5 @ (X1 @ (X1 @ X6 @ (X1 @ (X1 @ X7 @ X5) @ X7)) @ X6)) @ X7) @ (X1 @ X7 @ (X1 @ X5 @ X5))) @ X6))))))))))))) @ (X1 @ (X1 @ (X1 @ (X1 @ (X1 @ X6 @ (X1 @ X5 @ X5)) @ (X4 @ (X4 @ (X1 @ X7 @ (X4 @ (X4 @ (X1 @ X7 @ X5))))))) @ X5) @ X6) @ (X1 @ X6 @ X7)))) @ X5) @ X5) @ (X4 @ X6)))) @ (X1 @ (X1 @ (X4 @ (X1 @ (X4 @ (X1 @ (X1 @ (X1 @ (X1 @ X7 @ (X1 @ (X4 @ (X4 @ (X1 @ (X1 @ X5 @ X6) @ X7))) @ (X4 @ (X1 @ X5 @ X5)))) @ X5) @ (X4 @ X5)) @ (X1 @ (X1 @ (X1 @ (X1 @ (X1 @ X5 @ X7) @ (X4 @ (X4 @ (X4 @ X7)))) @ X7) @ X6) @ X5))) @ (X1 @ (X1 @ (X1 @ X6 @ X5) @ (X4 @ X6)) @ X6))) @ X7) @ X6)))) @ ? [X8 : $i] : (X3 @ (X4 @ X5))))),
% 0.78/0.58 inference(negated_conjecture,[status(cth)],[f109])).
% 0.78/0.58 thf(f139,plain,(
% 0.78/0.58 (c_not = (^[X0 : $o] : (X0 => c_False)))),
% 0.78/0.58 inference(rectify,[],[f13])).
% 0.78/0.58 thf(f140,plain,(
% 0.78/0.58 (c_not = (^[Y0 : $o]: (Y0 => c_False)))),
% 0.78/0.58 inference(fool_elimination,[],[f139])).
% 0.78/0.58 thf(f148,plain,(
% 0.78/0.58 ~(c_not @ ! [X0 : ($i > $i > $i),X1 : $i,X3 : ($i > $o),X4 : $i,X5 : ($i > $i),X7 : $i] : (c_and @ (((X0 @ (X0 @ X7 @ (X0 @ X4 @ (X0 @ (X0 @ (X0 @ (X0 @ X1 @ (X0 @ (X0 @ X7 @ (X0 @ X7 @ (X0 @ (X0 @ X7 @ (X0 @ (X5 @ X7) @ (X0 @ (X0 @ X4 @ (X0 @ X1 @ (X0 @ X1 @ X1))) @ X7))) @ (X0 @ (X5 @ (X0 @ (X0 @ (X5 @ X4) @ X7) @ (X0 @ X7 @ X7))) @ (X0 @ X1 @ (X0 @ X1 @ (X0 @ (X0 @ (X0 @ X7 @ (X0 @ (X0 @ X7 @ (X0 @ (X5 @ X1) @ X4)) @ (X5 @ (X0 @ X4 @ X7)))) @ X1) @ (X5 @ (X0 @ (X0 @ X4 @ (X0 @ X7 @ (X0 @ (X5 @ (X0 @ X7 @ X4)) @ X7))) @ (X0 @ (X0 @ (X0 @ X1 @ (X0 @ (X5 @ X7) @ X1)) @ X1) @ (X5 @ (X5 @ (X0 @ (X0 @ (X0 @ (X0 @ X7 @ (X0 @ (X0 @ X1 @ (X0 @ (X0 @ X4 @ X7) @ X4)) @ X1)) @ X4) @ (X0 @ X4 @ (X0 @ X7 @ X7))) @ X1))))))))))))) @ (X0 @ (X0 @ (X0 @ (X0 @ (X0 @ X1 @ (X0 @ X7 @ X7)) @ (X5 @ (X5 @ (X0 @ X4 @ (X5 @ (X5 @ (X0 @ X4 @ X7))))))) @ X7) @ X1) @ (X0 @ X1 @ X4)))) @ X7) @ X7) @ (X5 @ X1)))) @ (X0 @ (X0 @ (X5 @ (X0 @ (X5 @ (X0 @ (X0 @ (X0 @ (X0 @ X4 @ (X0 @ (X5 @ (X5 @ (X0 @ (X0 @ X7 @ X1) @ X4))) @ (X5 @ (X0 @ X7 @ X7)))) @ X7) @ (X5 @ X7)) @ (X0 @ (X0 @ (X0 @ (X0 @ (X0 @ X7 @ X4) @ (X5 @ (X5 @ (X5 @ X4)))) @ X4) @ X1) @ X7))) @ (X0 @ (X0 @ (X0 @ X1 @ X7) @ (X5 @ X1)) @ X1))) @ X4) @ X1))) = X1) @ (X3 @ (X5 @ X7))))),
% 0.78/0.58 inference(rectify,[],[f110])).
% 0.78/0.58 thf(f149,plain,(
% 0.78/0.58 ~ (((c_not @ (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: (!! @ $i @ (^[Y4 : $i]: (!! @ ($i > $i > $i) @ (^[Y5 : $i > $i > $i]: (c_and @ ((Y5 @ (Y5 @ Y0 @ (Y5 @ Y2 @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ Y4 @ (Y5 @ (Y5 @ Y0 @ (Y5 @ Y0 @ (Y5 @ (Y5 @ Y0 @ (Y5 @ (Y1 @ Y0) @ (Y5 @ (Y5 @ Y2 @ (Y5 @ Y4 @ (Y5 @ Y4 @ Y4))) @ Y0))) @ (Y5 @ (Y1 @ (Y5 @ (Y5 @ (Y1 @ Y2) @ Y0) @ (Y5 @ Y0 @ Y0))) @ (Y5 @ Y4 @ (Y5 @ Y4 @ (Y5 @ (Y5 @ (Y5 @ Y0 @ (Y5 @ (Y5 @ Y0 @ (Y5 @ (Y1 @ Y4) @ Y2)) @ (Y1 @ (Y5 @ Y2 @ Y0)))) @ Y4) @ (Y1 @ (Y5 @ (Y5 @ Y2 @ (Y5 @ Y0 @ (Y5 @ (Y1 @ (Y5 @ Y0 @ Y2)) @ Y0))) @ (Y5 @ (Y5 @ (Y5 @ Y4 @ (Y5 @ (Y1 @ Y0) @ Y4)) @ Y4) @ (Y1 @ (Y1 @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ Y0 @ (Y5 @ (Y5 @ Y4 @ (Y5 @ (Y5 @ Y2 @ Y0) @ Y2)) @ Y4)) @ Y2) @ (Y5 @ Y2 @ (Y5 @ Y0 @ Y0))) @ Y4))))))))))))) @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ Y4 @ (Y5 @ Y0 @ Y0)) @ (Y1 @ (Y1 @ (Y5 @ Y2 @ (Y1 @ (Y1 @ (Y5 @ Y2 @ Y0))))))) @ Y0) @ Y4) @ (Y5 @ Y4 @ Y2)))) @ Y0) @ Y0) @ (Y1 @ Y4)))) @ (Y5 @ (Y5 @ (Y1 @ (Y5 @ (Y1 @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ Y2 @ (Y5 @ (Y1 @ (Y1 @ (Y5 @ (Y5 @ Y0 @ Y4) @ Y2))) @ (Y1 @ (Y5 @ Y0 @ Y0)))) @ Y0) @ (Y1 @ Y0)) @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ Y0 @ Y2) @ (Y1 @ (Y1 @ (Y1 @ Y2)))) @ Y2) @ Y4) @ Y0))) @ (Y5 @ (Y5 @ (Y5 @ Y4 @ Y0) @ (Y1 @ Y4)) @ Y4))) @ Y2) @ Y4)) = Y4) @ (Y3 @ (Y1 @ Y0))))))))))))))))) = $true)),
% 0.78/0.58 inference(fool_elimination,[],[f148])).
% 0.78/0.58 thf(f161,plain,(
% 0.78/0.58 (c_and = (^[X0 : $o, X1 : $o] : (! [X2 : $o] : ((X0 => (X1 => X2)) => X2))))),
% 0.78/0.58 inference(rectify,[],[f14])).
% 0.78/0.58 thf(f162,plain,(
% 0.78/0.58 (c_and = (^[Y0 : $o]: ((^[Y1 : $o]: (!! @ $o @ (^[Y2 : $o]: ((Y0 => (Y1 => Y2)) => Y2)))))))),
% 0.78/0.58 inference(fool_elimination,[],[f161])).
% 0.78/0.58 thf(f308,plain,(
% 0.78/0.58 (((c_not @ (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: (!! @ $i @ (^[Y4 : $i]: (!! @ ($i > $i > $i) @ (^[Y5 : $i > $i > $i]: (c_and @ ((Y5 @ (Y5 @ Y0 @ (Y5 @ Y2 @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ Y4 @ (Y5 @ (Y5 @ Y0 @ (Y5 @ Y0 @ (Y5 @ (Y5 @ Y0 @ (Y5 @ (Y1 @ Y0) @ (Y5 @ (Y5 @ Y2 @ (Y5 @ Y4 @ (Y5 @ Y4 @ Y4))) @ Y0))) @ (Y5 @ (Y1 @ (Y5 @ (Y5 @ (Y1 @ Y2) @ Y0) @ (Y5 @ Y0 @ Y0))) @ (Y5 @ Y4 @ (Y5 @ Y4 @ (Y5 @ (Y5 @ (Y5 @ Y0 @ (Y5 @ (Y5 @ Y0 @ (Y5 @ (Y1 @ Y4) @ Y2)) @ (Y1 @ (Y5 @ Y2 @ Y0)))) @ Y4) @ (Y1 @ (Y5 @ (Y5 @ Y2 @ (Y5 @ Y0 @ (Y5 @ (Y1 @ (Y5 @ Y0 @ Y2)) @ Y0))) @ (Y5 @ (Y5 @ (Y5 @ Y4 @ (Y5 @ (Y1 @ Y0) @ Y4)) @ Y4) @ (Y1 @ (Y1 @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ Y0 @ (Y5 @ (Y5 @ Y4 @ (Y5 @ (Y5 @ Y2 @ Y0) @ Y2)) @ Y4)) @ Y2) @ (Y5 @ Y2 @ (Y5 @ Y0 @ Y0))) @ Y4))))))))))))) @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ Y4 @ (Y5 @ Y0 @ Y0)) @ (Y1 @ (Y1 @ (Y5 @ Y2 @ (Y1 @ (Y1 @ (Y5 @ Y2 @ Y0))))))) @ Y0) @ Y4) @ (Y5 @ Y4 @ Y2)))) @ Y0) @ Y0) @ (Y1 @ Y4)))) @ (Y5 @ (Y5 @ (Y1 @ (Y5 @ (Y1 @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ Y2 @ (Y5 @ (Y1 @ (Y1 @ (Y5 @ (Y5 @ Y0 @ Y4) @ Y2))) @ (Y1 @ (Y5 @ Y0 @ Y0)))) @ Y0) @ (Y1 @ Y0)) @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ Y0 @ Y2) @ (Y1 @ (Y1 @ (Y1 @ Y2)))) @ Y2) @ Y4) @ Y0))) @ (Y5 @ (Y5 @ (Y5 @ Y4 @ Y0) @ (Y1 @ Y4)) @ Y4))) @ Y2) @ Y4)) = Y4) @ (Y3 @ (Y1 @ Y0))))))))))))))))) != $true)),
% 0.78/0.58 inference(flattening,[],[f149])).
% 0.78/0.58 thf(f318,definition,(
% 0.78/0.58 ! [X1 : $i,X0 : ($i > $o)] : (? [X2 : $i] : ((((c_In @ X2 @ X1)) = $true) & (((X0 @ X2)) != $true)) | ~ ($true = ((sP0 @ X0 @ X1))))),
% 0.78/0.58 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 0.78/0.58 thf(f339,plain,(
% 0.78/0.58 ! [X1 : $i,X0 : ($i > $o)] : (? [X2 : $i] : ((((c_In @ X2 @ X1)) = $true) & (((X0 @ X2)) != $true)) | ($true != ((sP0 @ X0 @ X1))))),
% 0.78/0.58 inference(nnf_transformation,[],[f318])).
% 0.78/0.58 thf(f340,plain,(
% 0.78/0.58 ! [X0 : $i,X1 : ($i > $o)] : (? [X2 : $i] : ((((c_In @ X2 @ X0)) = $true) & (((X1 @ X2)) != $true)) | ($true != ((sP0 @ X1 @ X0))))),
% 0.78/0.58 inference(rectify,[],[f339])).
% 0.78/0.58 thf(f341,plain,(
% 0.78/0.58 ! [X0 : $i,X1 : ($i > $o)] : (((((c_In @ (sK10 @ X1 @ X0) @ X0)) = $true) & (((X1 @ (sK10 @ X1 @ X0))) != $true)) | ($true != ((sP0 @ X1 @ X0))))),
% 0.78/0.58 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X1,sK5 @ X0)],[f340])).
% 0.78/0.58 thf(f365,plain,(
% 0.78/0.58 (((c_not @ (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: (!! @ $i @ (^[Y4 : $i]: (!! @ ($i > $i > $i) @ (^[Y5 : $i > $i > $i]: (c_and @ ((Y5 @ (Y5 @ Y0 @ (Y5 @ Y2 @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ Y4 @ (Y5 @ (Y5 @ Y0 @ (Y5 @ Y0 @ (Y5 @ (Y5 @ Y0 @ (Y5 @ (Y1 @ Y0) @ (Y5 @ (Y5 @ Y2 @ (Y5 @ Y4 @ (Y5 @ Y4 @ Y4))) @ Y0))) @ (Y5 @ (Y1 @ (Y5 @ (Y5 @ (Y1 @ Y2) @ Y0) @ (Y5 @ Y0 @ Y0))) @ (Y5 @ Y4 @ (Y5 @ Y4 @ (Y5 @ (Y5 @ (Y5 @ Y0 @ (Y5 @ (Y5 @ Y0 @ (Y5 @ (Y1 @ Y4) @ Y2)) @ (Y1 @ (Y5 @ Y2 @ Y0)))) @ Y4) @ (Y1 @ (Y5 @ (Y5 @ Y2 @ (Y5 @ Y0 @ (Y5 @ (Y1 @ (Y5 @ Y0 @ Y2)) @ Y0))) @ (Y5 @ (Y5 @ (Y5 @ Y4 @ (Y5 @ (Y1 @ Y0) @ Y4)) @ Y4) @ (Y1 @ (Y1 @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ Y0 @ (Y5 @ (Y5 @ Y4 @ (Y5 @ (Y5 @ Y2 @ Y0) @ Y2)) @ Y4)) @ Y2) @ (Y5 @ Y2 @ (Y5 @ Y0 @ Y0))) @ Y4))))))))))))) @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ Y4 @ (Y5 @ Y0 @ Y0)) @ (Y1 @ (Y1 @ (Y5 @ Y2 @ (Y1 @ (Y1 @ (Y5 @ Y2 @ Y0))))))) @ Y0) @ Y4) @ (Y5 @ Y4 @ Y2)))) @ Y0) @ Y0) @ (Y1 @ Y4)))) @ (Y5 @ (Y5 @ (Y1 @ (Y5 @ (Y1 @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ Y2 @ (Y5 @ (Y1 @ (Y1 @ (Y5 @ (Y5 @ Y0 @ Y4) @ Y2))) @ (Y1 @ (Y5 @ Y0 @ Y0)))) @ Y0) @ (Y1 @ Y0)) @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ Y0 @ Y2) @ (Y1 @ (Y1 @ (Y1 @ Y2)))) @ Y2) @ Y4) @ Y0))) @ (Y5 @ (Y5 @ (Y5 @ Y4 @ Y0) @ (Y1 @ Y4)) @ Y4))) @ Y2) @ Y4)) = Y4) @ (Y3 @ (Y1 @ Y0))))))))))))))))) != $true)),
% 0.78/0.58 inference(cnf_transformation,[],[f308])).
% 0.78/0.58 thf(f401,plain,(
% 0.78/0.58 ( ! [X0 : $i,X1 : ($i > $o)] : (($true != ((sP0 @ X1 @ X0))) | (((X1 @ (sK10 @ X1 @ X0))) != $true)) )),
% 0.78/0.58 inference(cnf_transformation,[],[f341])).
% 0.78/0.58 thf(f453,plain,(
% 0.78/0.58 (c_and = (^[Y0 : $o]: ((^[Y1 : $o]: (!! @ $o @ (^[Y2 : $o]: ((Y0 => (Y1 => Y2)) => Y2)))))))),
% 0.78/0.58 inference(cnf_transformation,[],[f162])).
% 0.78/0.58 thf(f463,plain,(
% 0.78/0.58 (c_not = (^[Y0 : $o]: (Y0 => c_False)))),
% 0.78/0.58 inference(cnf_transformation,[],[f140])).
% 0.78/0.58 thf(f555,plain,(
% 0.78/0.58 ((((^[Y0 : $o]: (Y0 => c_False)) @ (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: (!! @ $i @ (^[Y4 : $i]: (!! @ ($i > $i > $i) @ (^[Y5 : $i > $i > $i]: ((^[Y6 : $o]: ((^[Y7 : $o]: (!! @ $o @ (^[Y8 : $o]: ((Y6 => (Y7 => Y8)) => Y8)))))) @ ((Y5 @ (Y5 @ Y0 @ (Y5 @ Y2 @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ Y4 @ (Y5 @ (Y5 @ Y0 @ (Y5 @ Y0 @ (Y5 @ (Y5 @ Y0 @ (Y5 @ (Y1 @ Y0) @ (Y5 @ (Y5 @ Y2 @ (Y5 @ Y4 @ (Y5 @ Y4 @ Y4))) @ Y0))) @ (Y5 @ (Y1 @ (Y5 @ (Y5 @ (Y1 @ Y2) @ Y0) @ (Y5 @ Y0 @ Y0))) @ (Y5 @ Y4 @ (Y5 @ Y4 @ (Y5 @ (Y5 @ (Y5 @ Y0 @ (Y5 @ (Y5 @ Y0 @ (Y5 @ (Y1 @ Y4) @ Y2)) @ (Y1 @ (Y5 @ Y2 @ Y0)))) @ Y4) @ (Y1 @ (Y5 @ (Y5 @ Y2 @ (Y5 @ Y0 @ (Y5 @ (Y1 @ (Y5 @ Y0 @ Y2)) @ Y0))) @ (Y5 @ (Y5 @ (Y5 @ Y4 @ (Y5 @ (Y1 @ Y0) @ Y4)) @ Y4) @ (Y1 @ (Y1 @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ Y0 @ (Y5 @ (Y5 @ Y4 @ (Y5 @ (Y5 @ Y2 @ Y0) @ Y2)) @ Y4)) @ Y2) @ (Y5 @ Y2 @ (Y5 @ Y0 @ Y0))) @ Y4))))))))))))) @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ Y4 @ (Y5 @ Y0 @ Y0)) @ (Y1 @ (Y1 @ (Y5 @ Y2 @ (Y1 @ (Y1 @ (Y5 @ Y2 @ Y0))))))) @ Y0) @ Y4) @ (Y5 @ Y4 @ Y2)))) @ Y0) @ Y0) @ (Y1 @ Y4)))) @ (Y5 @ (Y5 @ (Y1 @ (Y5 @ (Y1 @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ Y2 @ (Y5 @ (Y1 @ (Y1 @ (Y5 @ (Y5 @ Y0 @ Y4) @ Y2))) @ (Y1 @ (Y5 @ Y0 @ Y0)))) @ Y0) @ (Y1 @ Y0)) @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ Y0 @ Y2) @ (Y1 @ (Y1 @ (Y1 @ Y2)))) @ Y2) @ Y4) @ Y0))) @ (Y5 @ (Y5 @ (Y5 @ Y4 @ Y0) @ (Y1 @ Y4)) @ Y4))) @ Y2) @ Y4)) = Y4) @ (Y3 @ (Y1 @ Y0))))))))))))))))) != $true)),
% 0.78/0.58 inference(definition_unfolding,[],[f365,f463,f453])).
% 0.78/0.58 thf(f562,definition,(
% 0.78/0.58 (sF12 = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: (!! @ $i @ (^[Y4 : $i]: (!! @ ($i > $i > $i) @ (^[Y5 : $i > $i > $i]: ((^[Y6 : $o]: ((^[Y7 : $o]: (!! @ $o @ (^[Y8 : $o]: ((Y6 => (Y7 => Y8)) => Y8)))))) @ ((Y5 @ (Y5 @ Y0 @ (Y5 @ Y2 @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ Y4 @ (Y5 @ (Y5 @ Y0 @ (Y5 @ Y0 @ (Y5 @ (Y5 @ Y0 @ (Y5 @ (Y1 @ Y0) @ (Y5 @ (Y5 @ Y2 @ (Y5 @ Y4 @ (Y5 @ Y4 @ Y4))) @ Y0))) @ (Y5 @ (Y1 @ (Y5 @ (Y5 @ (Y1 @ Y2) @ Y0) @ (Y5 @ Y0 @ Y0))) @ (Y5 @ Y4 @ (Y5 @ Y4 @ (Y5 @ (Y5 @ (Y5 @ Y0 @ (Y5 @ (Y5 @ Y0 @ (Y5 @ (Y1 @ Y4) @ Y2)) @ (Y1 @ (Y5 @ Y2 @ Y0)))) @ Y4) @ (Y1 @ (Y5 @ (Y5 @ Y2 @ (Y5 @ Y0 @ (Y5 @ (Y1 @ (Y5 @ Y0 @ Y2)) @ Y0))) @ (Y5 @ (Y5 @ (Y5 @ Y4 @ (Y5 @ (Y1 @ Y0) @ Y4)) @ Y4) @ (Y1 @ (Y1 @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ Y0 @ (Y5 @ (Y5 @ Y4 @ (Y5 @ (Y5 @ Y2 @ Y0) @ Y2)) @ Y4)) @ Y2) @ (Y5 @ Y2 @ (Y5 @ Y0 @ Y0))) @ Y4))))))))))))) @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ Y4 @ (Y5 @ Y0 @ Y0)) @ (Y1 @ (Y1 @ (Y5 @ Y2 @ (Y1 @ (Y1 @ (Y5 @ Y2 @ Y0))))))) @ Y0) @ Y4) @ (Y5 @ Y4 @ Y2)))) @ Y0) @ Y0) @ (Y1 @ Y4)))) @ (Y5 @ (Y5 @ (Y1 @ (Y5 @ (Y1 @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ Y2 @ (Y5 @ (Y1 @ (Y1 @ (Y5 @ (Y5 @ Y0 @ Y4) @ Y2))) @ (Y1 @ (Y5 @ Y0 @ Y0)))) @ Y0) @ (Y1 @ Y0)) @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ Y0 @ Y2) @ (Y1 @ (Y1 @ (Y1 @ Y2)))) @ Y2) @ Y4) @ Y0))) @ (Y5 @ (Y5 @ (Y5 @ Y4 @ Y0) @ (Y1 @ Y4)) @ Y4))) @ Y2) @ Y4)) = Y4) @ (Y3 @ (Y1 @ Y0)))))))))))))))))),
% 0.78/0.58 introduced(definition,[new_symbols(definition,[sF12])],[function_definition])).
% 0.78/0.58 thf(f563,definition,(
% 0.78/0.58 (sF13 = (((^[Y0 : $o]: (Y0 => c_False)) @ sF12)))),
% 0.78/0.58 introduced(definition,[new_symbols(definition,[sF13])],[function_definition])).
% 0.78/0.58 thf(f564,plain,(
% 0.78/0.58 ((((^[Y0 : $o]: (Y0 => c_False)) @ sF12)) = sF13)),
% 0.78/0.58 inference(reorient_equations,[],[f563])).
% 0.78/0.58 thf(f565,plain,(
% 0.78/0.58 (sF13 != $true)),
% 0.78/0.58 inference(definition_folding,[],[f555,f564,f562])).
% 0.78/0.58 thf(f653,plain,(
% 0.78/0.58 (sF13 = $true) | ((((^[Y0 : $o]: (Y0 => c_False)) @ sF12)) = $false)),
% 0.78/0.58 inference(iff_proxy_clausification,[],[f564])).
% 0.78/0.58 thf(f654,plain,(
% 0.78/0.58 (sF13 = $true) | ($false = ((sF12 => c_False)))),
% 0.78/0.58 inference(beta-eta_normalization,[],[f653])).
% 0.78/0.58 thf(f655,plain,(
% 0.78/0.58 (sF13 = $true) | (c_False = $false)),
% 0.78/0.58 inference(imp_proxy_clausification,[],[f654])).
% 0.78/0.58 thf(f656,plain,(
% 0.78/0.58 (sF13 = $true) | (sF12 = $true)),
% 0.78/0.58 inference(imp_proxy_clausification,[],[f654])).
% 0.78/0.58 thf(f687,plain,(
% 0.78/0.58 (sF12 = $false) | ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: (!! @ $i @ (^[Y4 : $i]: (!! @ ($i > $i > $i) @ (^[Y5 : $i > $i > $i]: ((^[Y6 : $o]: ((^[Y7 : $o]: (!! @ $o @ (^[Y8 : $o]: ((Y6 => (Y7 => Y8)) => Y8)))))) @ ((Y5 @ (Y5 @ Y0 @ (Y5 @ Y2 @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ Y4 @ (Y5 @ (Y5 @ Y0 @ (Y5 @ Y0 @ (Y5 @ (Y5 @ Y0 @ (Y5 @ (Y1 @ Y0) @ (Y5 @ (Y5 @ Y2 @ (Y5 @ Y4 @ (Y5 @ Y4 @ Y4))) @ Y0))) @ (Y5 @ (Y1 @ (Y5 @ (Y5 @ (Y1 @ Y2) @ Y0) @ (Y5 @ Y0 @ Y0))) @ (Y5 @ Y4 @ (Y5 @ Y4 @ (Y5 @ (Y5 @ (Y5 @ Y0 @ (Y5 @ (Y5 @ Y0 @ (Y5 @ (Y1 @ Y4) @ Y2)) @ (Y1 @ (Y5 @ Y2 @ Y0)))) @ Y4) @ (Y1 @ (Y5 @ (Y5 @ Y2 @ (Y5 @ Y0 @ (Y5 @ (Y1 @ (Y5 @ Y0 @ Y2)) @ Y0))) @ (Y5 @ (Y5 @ (Y5 @ Y4 @ (Y5 @ (Y1 @ Y0) @ Y4)) @ Y4) @ (Y1 @ (Y1 @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ Y0 @ (Y5 @ (Y5 @ Y4 @ (Y5 @ (Y5 @ Y2 @ Y0) @ Y2)) @ Y4)) @ Y2) @ (Y5 @ Y2 @ (Y5 @ Y0 @ Y0))) @ Y4))))))))))))) @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ Y4 @ (Y5 @ Y0 @ Y0)) @ (Y1 @ (Y1 @ (Y5 @ Y2 @ (Y1 @ (Y1 @ (Y5 @ Y2 @ Y0))))))) @ Y0) @ Y4) @ (Y5 @ Y4 @ Y2)))) @ Y0) @ Y0) @ (Y1 @ Y4)))) @ (Y5 @ (Y5 @ (Y1 @ (Y5 @ (Y1 @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ Y2 @ (Y5 @ (Y1 @ (Y1 @ (Y5 @ (Y5 @ Y0 @ Y4) @ Y2))) @ (Y1 @ (Y5 @ Y0 @ Y0)))) @ Y0) @ (Y1 @ Y0)) @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ Y0 @ Y2) @ (Y1 @ (Y1 @ (Y1 @ Y2)))) @ Y2) @ Y4) @ Y0))) @ (Y5 @ (Y5 @ (Y5 @ Y4 @ Y0) @ (Y1 @ Y4)) @ Y4))) @ Y2) @ Y4)) = Y4) @ (Y3 @ (Y1 @ Y0)))))))))))))))))),
% 0.78/0.58 inference(iff_proxy_clausification,[],[f562])).
% 0.78/0.58 thf(f688,plain,(
% 0.78/0.58 ( ! [X1 : $i] : ((sF12 = $false) | ((((^[Y0 : $i]: (!! @ ($i > $i) @ (^[Y1 : $i > $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: (!! @ $i @ (^[Y4 : $i]: (!! @ ($i > $i > $i) @ (^[Y5 : $i > $i > $i]: ((^[Y6 : $o]: ((^[Y7 : $o]: (!! @ $o @ (^[Y8 : $o]: ((Y6 => (Y7 => Y8)) => Y8)))))) @ ((Y5 @ (Y5 @ Y0 @ (Y5 @ Y2 @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ Y4 @ (Y5 @ (Y5 @ Y0 @ (Y5 @ Y0 @ (Y5 @ (Y5 @ Y0 @ (Y5 @ (Y1 @ Y0) @ (Y5 @ (Y5 @ Y2 @ (Y5 @ Y4 @ (Y5 @ Y4 @ Y4))) @ Y0))) @ (Y5 @ (Y1 @ (Y5 @ (Y5 @ (Y1 @ Y2) @ Y0) @ (Y5 @ Y0 @ Y0))) @ (Y5 @ Y4 @ (Y5 @ Y4 @ (Y5 @ (Y5 @ (Y5 @ Y0 @ (Y5 @ (Y5 @ Y0 @ (Y5 @ (Y1 @ Y4) @ Y2)) @ (Y1 @ (Y5 @ Y2 @ Y0)))) @ Y4) @ (Y1 @ (Y5 @ (Y5 @ Y2 @ (Y5 @ Y0 @ (Y5 @ (Y1 @ (Y5 @ Y0 @ Y2)) @ Y0))) @ (Y5 @ (Y5 @ (Y5 @ Y4 @ (Y5 @ (Y1 @ Y0) @ Y4)) @ Y4) @ (Y1 @ (Y1 @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ Y0 @ (Y5 @ (Y5 @ Y4 @ (Y5 @ (Y5 @ Y2 @ Y0) @ Y2)) @ Y4)) @ Y2) @ (Y5 @ Y2 @ (Y5 @ Y0 @ Y0))) @ Y4))))))))))))) @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ Y4 @ (Y5 @ Y0 @ Y0)) @ (Y1 @ (Y1 @ (Y5 @ Y2 @ (Y1 @ (Y1 @ (Y5 @ Y2 @ Y0))))))) @ Y0) @ Y4) @ (Y5 @ Y4 @ Y2)))) @ Y0) @ Y0) @ (Y1 @ Y4)))) @ (Y5 @ (Y5 @ (Y1 @ (Y5 @ (Y1 @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ Y2 @ (Y5 @ (Y1 @ (Y1 @ (Y5 @ (Y5 @ Y0 @ Y4) @ Y2))) @ (Y1 @ (Y5 @ Y0 @ Y0)))) @ Y0) @ (Y1 @ Y0)) @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ (Y5 @ Y0 @ Y2) @ (Y1 @ (Y1 @ (Y1 @ Y2)))) @ Y2) @ Y4) @ Y0))) @ (Y5 @ (Y5 @ (Y5 @ Y4 @ Y0) @ (Y1 @ Y4)) @ Y4))) @ Y2) @ Y4)) = Y4) @ (Y3 @ (Y1 @ Y0)))))))))))))) @ X1)) = $true)) )),
% 0.78/0.58 inference(pi_proxy_clausification,[],[f687])).
% 0.78/0.58 thf(f689,plain,(
% 0.78/0.58 ( ! [X1 : $i] : ((((!! @ ($i > $i) @ (^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $i) @ (^[Y4 : $i > $i > $i]: (!! @ $o @ (^[Y5 : $o]: ((((Y4 @ (Y4 @ X1 @ (Y4 @ Y1 @ (Y4 @ (Y4 @ (Y4 @ (Y4 @ Y3 @ (Y4 @ (Y4 @ X1 @ (Y4 @ X1 @ (Y4 @ (Y4 @ X1 @ (Y4 @ (Y0 @ X1) @ (Y4 @ (Y4 @ Y1 @ (Y4 @ Y3 @ (Y4 @ Y3 @ Y3))) @ X1))) @ (Y4 @ (Y0 @ (Y4 @ (Y4 @ (Y0 @ Y1) @ X1) @ (Y4 @ X1 @ X1))) @ (Y4 @ Y3 @ (Y4 @ Y3 @ (Y4 @ (Y4 @ (Y4 @ X1 @ (Y4 @ (Y4 @ X1 @ (Y4 @ (Y0 @ Y3) @ Y1)) @ (Y0 @ (Y4 @ Y1 @ X1)))) @ Y3) @ (Y0 @ (Y4 @ (Y4 @ Y1 @ (Y4 @ X1 @ (Y4 @ (Y0 @ (Y4 @ X1 @ Y1)) @ X1))) @ (Y4 @ (Y4 @ (Y4 @ Y3 @ (Y4 @ (Y0 @ X1) @ Y3)) @ Y3) @ (Y0 @ (Y0 @ (Y4 @ (Y4 @ (Y4 @ (Y4 @ X1 @ (Y4 @ (Y4 @ Y3 @ (Y4 @ (Y4 @ Y1 @ X1) @ Y1)) @ Y3)) @ Y1) @ (Y4 @ Y1 @ (Y4 @ X1 @ X1))) @ Y3))))))))))))) @ (Y4 @ (Y4 @ (Y4 @ (Y4 @ (Y4 @ Y3 @ (Y4 @ X1 @ X1)) @ (Y0 @ (Y0 @ (Y4 @ Y1 @ (Y0 @ (Y0 @ (Y4 @ Y1 @ X1))))))) @ X1) @ Y3) @ (Y4 @ Y3 @ Y1)))) @ X1) @ X1) @ (Y0 @ Y3)))) @ (Y4 @ (Y4 @ (Y0 @ (Y4 @ (Y0 @ (Y4 @ (Y4 @ (Y4 @ (Y4 @ Y1 @ (Y4 @ (Y0 @ (Y0 @ (Y4 @ (Y4 @ X1 @ Y3) @ Y1))) @ (Y0 @ (Y4 @ X1 @ X1)))) @ X1) @ (Y0 @ X1)) @ (Y4 @ (Y4 @ (Y4 @ (Y4 @ (Y4 @ X1 @ Y1) @ (Y0 @ (Y0 @ (Y0 @ Y1)))) @ Y1) @ Y3) @ X1))) @ (Y4 @ (Y4 @ (Y4 @ Y3 @ X1) @ (Y0 @ Y3)) @ Y3))) @ Y1) @ Y3)) = Y3) => ((Y2 @ (Y0 @ X1)) => Y5)) => Y5)))))))))))))) = $true) | (sF12 = $false)) )),
% 0.78/0.58 inference(beta-eta_normalization,[],[f688])).
% 0.78/0.58 thf(f690,plain,(
% 0.78/0.58 ( ! [X2 : ($i > $i),X1 : $i] : ((sF12 = $false) | ((((^[Y0 : $i > $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $i) @ (^[Y4 : $i > $i > $i]: (!! @ $o @ (^[Y5 : $o]: ((((Y4 @ (Y4 @ X1 @ (Y4 @ Y1 @ (Y4 @ (Y4 @ (Y4 @ (Y4 @ Y3 @ (Y4 @ (Y4 @ X1 @ (Y4 @ X1 @ (Y4 @ (Y4 @ X1 @ (Y4 @ (Y0 @ X1) @ (Y4 @ (Y4 @ Y1 @ (Y4 @ Y3 @ (Y4 @ Y3 @ Y3))) @ X1))) @ (Y4 @ (Y0 @ (Y4 @ (Y4 @ (Y0 @ Y1) @ X1) @ (Y4 @ X1 @ X1))) @ (Y4 @ Y3 @ (Y4 @ Y3 @ (Y4 @ (Y4 @ (Y4 @ X1 @ (Y4 @ (Y4 @ X1 @ (Y4 @ (Y0 @ Y3) @ Y1)) @ (Y0 @ (Y4 @ Y1 @ X1)))) @ Y3) @ (Y0 @ (Y4 @ (Y4 @ Y1 @ (Y4 @ X1 @ (Y4 @ (Y0 @ (Y4 @ X1 @ Y1)) @ X1))) @ (Y4 @ (Y4 @ (Y4 @ Y3 @ (Y4 @ (Y0 @ X1) @ Y3)) @ Y3) @ (Y0 @ (Y0 @ (Y4 @ (Y4 @ (Y4 @ (Y4 @ X1 @ (Y4 @ (Y4 @ Y3 @ (Y4 @ (Y4 @ Y1 @ X1) @ Y1)) @ Y3)) @ Y1) @ (Y4 @ Y1 @ (Y4 @ X1 @ X1))) @ Y3))))))))))))) @ (Y4 @ (Y4 @ (Y4 @ (Y4 @ (Y4 @ Y3 @ (Y4 @ X1 @ X1)) @ (Y0 @ (Y0 @ (Y4 @ Y1 @ (Y0 @ (Y0 @ (Y4 @ Y1 @ X1))))))) @ X1) @ Y3) @ (Y4 @ Y3 @ Y1)))) @ X1) @ X1) @ (Y0 @ Y3)))) @ (Y4 @ (Y4 @ (Y0 @ (Y4 @ (Y0 @ (Y4 @ (Y4 @ (Y4 @ (Y4 @ Y1 @ (Y4 @ (Y0 @ (Y0 @ (Y4 @ (Y4 @ X1 @ Y3) @ Y1))) @ (Y0 @ (Y4 @ X1 @ X1)))) @ X1) @ (Y0 @ X1)) @ (Y4 @ (Y4 @ (Y4 @ (Y4 @ (Y4 @ X1 @ Y1) @ (Y0 @ (Y0 @ (Y0 @ Y1)))) @ Y1) @ Y3) @ X1))) @ (Y4 @ (Y4 @ (Y4 @ Y3 @ X1) @ (Y0 @ Y3)) @ Y3))) @ Y1) @ Y3)) = Y3) => ((Y2 @ (Y0 @ X1)) => Y5)) => Y5)))))))))))) @ X2)) = $true)) )),
% 0.78/0.58 inference(pi_proxy_clausification,[],[f689])).
% 0.78/0.58 thf(f691,plain,(
% 0.78/0.58 ( ! [X2 : ($i > $i),X1 : $i] : ((sF12 = $false) | ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $i) @ (^[Y3 : $i > $i > $i]: (!! @ $o @ (^[Y4 : $o]: ((((Y3 @ (Y3 @ X1 @ (Y3 @ Y0 @ (Y3 @ (Y3 @ (Y3 @ (Y3 @ Y2 @ (Y3 @ (Y3 @ X1 @ (Y3 @ X1 @ (Y3 @ (Y3 @ X1 @ (Y3 @ (X2 @ X1) @ (Y3 @ (Y3 @ Y0 @ (Y3 @ Y2 @ (Y3 @ Y2 @ Y2))) @ X1))) @ (Y3 @ (X2 @ (Y3 @ (Y3 @ (X2 @ Y0) @ X1) @ (Y3 @ X1 @ X1))) @ (Y3 @ Y2 @ (Y3 @ Y2 @ (Y3 @ (Y3 @ (Y3 @ X1 @ (Y3 @ (Y3 @ X1 @ (Y3 @ (X2 @ Y2) @ Y0)) @ (X2 @ (Y3 @ Y0 @ X1)))) @ Y2) @ (X2 @ (Y3 @ (Y3 @ Y0 @ (Y3 @ X1 @ (Y3 @ (X2 @ (Y3 @ X1 @ Y0)) @ X1))) @ (Y3 @ (Y3 @ (Y3 @ Y2 @ (Y3 @ (X2 @ X1) @ Y2)) @ Y2) @ (X2 @ (X2 @ (Y3 @ (Y3 @ (Y3 @ (Y3 @ X1 @ (Y3 @ (Y3 @ Y2 @ (Y3 @ (Y3 @ Y0 @ X1) @ Y0)) @ Y2)) @ Y0) @ (Y3 @ Y0 @ (Y3 @ X1 @ X1))) @ Y2))))))))))))) @ (Y3 @ (Y3 @ (Y3 @ (Y3 @ (Y3 @ Y2 @ (Y3 @ X1 @ X1)) @ (X2 @ (X2 @ (Y3 @ Y0 @ (X2 @ (X2 @ (Y3 @ Y0 @ X1))))))) @ X1) @ Y2) @ (Y3 @ Y2 @ Y0)))) @ X1) @ X1) @ (X2 @ Y2)))) @ (Y3 @ (Y3 @ (X2 @ (Y3 @ (X2 @ (Y3 @ (Y3 @ (Y3 @ (Y3 @ Y0 @ (Y3 @ (X2 @ (X2 @ (Y3 @ (Y3 @ X1 @ Y2) @ Y0))) @ (X2 @ (Y3 @ X1 @ X1)))) @ X1) @ (X2 @ X1)) @ (Y3 @ (Y3 @ (Y3 @ (Y3 @ (Y3 @ X1 @ Y0) @ (X2 @ (X2 @ (X2 @ Y0)))) @ Y0) @ Y2) @ X1))) @ (Y3 @ (Y3 @ (Y3 @ Y2 @ X1) @ (X2 @ Y2)) @ Y2))) @ Y0) @ Y2)) = Y2) => ((Y1 @ (X2 @ X1)) => Y4)) => Y4)))))))))))))) )),
% 0.78/0.58 inference(beta-eta_normalization,[],[f690])).
% 0.78/0.58 thf(f692,plain,(
% 0.78/0.58 ( ! [X2 : ($i > $i),X3 : $i,X1 : $i] : (((((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $i) @ (^[Y3 : $i > $i > $i]: (!! @ $o @ (^[Y4 : $o]: ((((Y3 @ (Y3 @ X1 @ (Y3 @ Y0 @ (Y3 @ (Y3 @ (Y3 @ (Y3 @ Y2 @ (Y3 @ (Y3 @ X1 @ (Y3 @ X1 @ (Y3 @ (Y3 @ X1 @ (Y3 @ (X2 @ X1) @ (Y3 @ (Y3 @ Y0 @ (Y3 @ Y2 @ (Y3 @ Y2 @ Y2))) @ X1))) @ (Y3 @ (X2 @ (Y3 @ (Y3 @ (X2 @ Y0) @ X1) @ (Y3 @ X1 @ X1))) @ (Y3 @ Y2 @ (Y3 @ Y2 @ (Y3 @ (Y3 @ (Y3 @ X1 @ (Y3 @ (Y3 @ X1 @ (Y3 @ (X2 @ Y2) @ Y0)) @ (X2 @ (Y3 @ Y0 @ X1)))) @ Y2) @ (X2 @ (Y3 @ (Y3 @ Y0 @ (Y3 @ X1 @ (Y3 @ (X2 @ (Y3 @ X1 @ Y0)) @ X1))) @ (Y3 @ (Y3 @ (Y3 @ Y2 @ (Y3 @ (X2 @ X1) @ Y2)) @ Y2) @ (X2 @ (X2 @ (Y3 @ (Y3 @ (Y3 @ (Y3 @ X1 @ (Y3 @ (Y3 @ Y2 @ (Y3 @ (Y3 @ Y0 @ X1) @ Y0)) @ Y2)) @ Y0) @ (Y3 @ Y0 @ (Y3 @ X1 @ X1))) @ Y2))))))))))))) @ (Y3 @ (Y3 @ (Y3 @ (Y3 @ (Y3 @ Y2 @ (Y3 @ X1 @ X1)) @ (X2 @ (X2 @ (Y3 @ Y0 @ (X2 @ (X2 @ (Y3 @ Y0 @ X1))))))) @ X1) @ Y2) @ (Y3 @ Y2 @ Y0)))) @ X1) @ X1) @ (X2 @ Y2)))) @ (Y3 @ (Y3 @ (X2 @ (Y3 @ (X2 @ (Y3 @ (Y3 @ (Y3 @ (Y3 @ Y0 @ (Y3 @ (X2 @ (X2 @ (Y3 @ (Y3 @ X1 @ Y2) @ Y0))) @ (X2 @ (Y3 @ X1 @ X1)))) @ X1) @ (X2 @ X1)) @ (Y3 @ (Y3 @ (Y3 @ (Y3 @ (Y3 @ X1 @ Y0) @ (X2 @ (X2 @ (X2 @ Y0)))) @ Y0) @ Y2) @ X1))) @ (Y3 @ (Y3 @ (Y3 @ Y2 @ X1) @ (X2 @ Y2)) @ Y2))) @ Y0) @ Y2)) = Y2) => ((Y1 @ (X2 @ X1)) => Y4)) => Y4)))))))))) @ X3)) = $true) | (sF12 = $false)) )),
% 0.78/0.58 inference(pi_proxy_clausification,[],[f691])).
% 0.78/0.58 thf(f693,plain,(
% 0.78/0.58 ( ! [X2 : ($i > $i),X3 : $i,X1 : $i] : ((((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $i) @ (^[Y2 : $i > $i > $i]: (!! @ $o @ (^[Y3 : $o]: ((((Y2 @ (Y2 @ X1 @ (Y2 @ X3 @ (Y2 @ (Y2 @ (Y2 @ (Y2 @ Y1 @ (Y2 @ (Y2 @ X1 @ (Y2 @ X1 @ (Y2 @ (Y2 @ X1 @ (Y2 @ (X2 @ X1) @ (Y2 @ (Y2 @ X3 @ (Y2 @ Y1 @ (Y2 @ Y1 @ Y1))) @ X1))) @ (Y2 @ (X2 @ (Y2 @ (Y2 @ (X2 @ X3) @ X1) @ (Y2 @ X1 @ X1))) @ (Y2 @ Y1 @ (Y2 @ Y1 @ (Y2 @ (Y2 @ (Y2 @ X1 @ (Y2 @ (Y2 @ X1 @ (Y2 @ (X2 @ Y1) @ X3)) @ (X2 @ (Y2 @ X3 @ X1)))) @ Y1) @ (X2 @ (Y2 @ (Y2 @ X3 @ (Y2 @ X1 @ (Y2 @ (X2 @ (Y2 @ X1 @ X3)) @ X1))) @ (Y2 @ (Y2 @ (Y2 @ Y1 @ (Y2 @ (X2 @ X1) @ Y1)) @ Y1) @ (X2 @ (X2 @ (Y2 @ (Y2 @ (Y2 @ (Y2 @ X1 @ (Y2 @ (Y2 @ Y1 @ (Y2 @ (Y2 @ X3 @ X1) @ X3)) @ Y1)) @ X3) @ (Y2 @ X3 @ (Y2 @ X1 @ X1))) @ Y1))))))))))))) @ (Y2 @ (Y2 @ (Y2 @ (Y2 @ (Y2 @ Y1 @ (Y2 @ X1 @ X1)) @ (X2 @ (X2 @ (Y2 @ X3 @ (X2 @ (X2 @ (Y2 @ X3 @ X1))))))) @ X1) @ Y1) @ (Y2 @ Y1 @ X3)))) @ X1) @ X1) @ (X2 @ Y1)))) @ (Y2 @ (Y2 @ (X2 @ (Y2 @ (X2 @ (Y2 @ (Y2 @ (Y2 @ (Y2 @ X3 @ (Y2 @ (X2 @ (X2 @ (Y2 @ (Y2 @ X1 @ Y1) @ X3))) @ (X2 @ (Y2 @ X1 @ X1)))) @ X1) @ (X2 @ X1)) @ (Y2 @ (Y2 @ (Y2 @ (Y2 @ (Y2 @ X1 @ X3) @ (X2 @ (X2 @ (X2 @ X3)))) @ X3) @ Y1) @ X1))) @ (Y2 @ (Y2 @ (Y2 @ Y1 @ X1) @ (X2 @ Y1)) @ Y1))) @ X3) @ Y1)) = Y1) => ((Y0 @ (X2 @ X1)) => Y3)) => Y3)))))))))) = $true) | (sF12 = $false)) )),
% 0.78/0.58 inference(beta-eta_normalization,[],[f692])).
% 0.78/0.58 thf(f694,plain,(
% 0.78/0.58 ( ! [X2 : ($i > $i),X3 : $i,X1 : $i,X4 : ($i > $o)] : ((sF12 = $false) | ((((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $i) @ (^[Y2 : $i > $i > $i]: (!! @ $o @ (^[Y3 : $o]: ((((Y2 @ (Y2 @ X1 @ (Y2 @ X3 @ (Y2 @ (Y2 @ (Y2 @ (Y2 @ Y1 @ (Y2 @ (Y2 @ X1 @ (Y2 @ X1 @ (Y2 @ (Y2 @ X1 @ (Y2 @ (X2 @ X1) @ (Y2 @ (Y2 @ X3 @ (Y2 @ Y1 @ (Y2 @ Y1 @ Y1))) @ X1))) @ (Y2 @ (X2 @ (Y2 @ (Y2 @ (X2 @ X3) @ X1) @ (Y2 @ X1 @ X1))) @ (Y2 @ Y1 @ (Y2 @ Y1 @ (Y2 @ (Y2 @ (Y2 @ X1 @ (Y2 @ (Y2 @ X1 @ (Y2 @ (X2 @ Y1) @ X3)) @ (X2 @ (Y2 @ X3 @ X1)))) @ Y1) @ (X2 @ (Y2 @ (Y2 @ X3 @ (Y2 @ X1 @ (Y2 @ (X2 @ (Y2 @ X1 @ X3)) @ X1))) @ (Y2 @ (Y2 @ (Y2 @ Y1 @ (Y2 @ (X2 @ X1) @ Y1)) @ Y1) @ (X2 @ (X2 @ (Y2 @ (Y2 @ (Y2 @ (Y2 @ X1 @ (Y2 @ (Y2 @ Y1 @ (Y2 @ (Y2 @ X3 @ X1) @ X3)) @ Y1)) @ X3) @ (Y2 @ X3 @ (Y2 @ X1 @ X1))) @ Y1))))))))))))) @ (Y2 @ (Y2 @ (Y2 @ (Y2 @ (Y2 @ Y1 @ (Y2 @ X1 @ X1)) @ (X2 @ (X2 @ (Y2 @ X3 @ (X2 @ (X2 @ (Y2 @ X3 @ X1))))))) @ X1) @ Y1) @ (Y2 @ Y1 @ X3)))) @ X1) @ X1) @ (X2 @ Y1)))) @ (Y2 @ (Y2 @ (X2 @ (Y2 @ (X2 @ (Y2 @ (Y2 @ (Y2 @ (Y2 @ X3 @ (Y2 @ (X2 @ (X2 @ (Y2 @ (Y2 @ X1 @ Y1) @ X3))) @ (X2 @ (Y2 @ X1 @ X1)))) @ X1) @ (X2 @ X1)) @ (Y2 @ (Y2 @ (Y2 @ (Y2 @ (Y2 @ X1 @ X3) @ (X2 @ (X2 @ (X2 @ X3)))) @ X3) @ Y1) @ X1))) @ (Y2 @ (Y2 @ (Y2 @ Y1 @ X1) @ (X2 @ Y1)) @ Y1))) @ X3) @ Y1)) = Y1) => ((Y0 @ (X2 @ X1)) => Y3)) => Y3)))))))) @ X4)) = $true)) )),
% 0.78/0.58 inference(pi_proxy_clausification,[],[f693])).
% 0.78/0.58 thf(f695,plain,(
% 0.78/0.58 ( ! [X2 : ($i > $i),X3 : $i,X1 : $i,X4 : ($i > $o)] : ((sF12 = $false) | (((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $i) @ (^[Y1 : $i > $i > $i]: (!! @ $o @ (^[Y2 : $o]: ((((Y1 @ (Y1 @ X1 @ (Y1 @ X3 @ (Y1 @ (Y1 @ (Y1 @ (Y1 @ Y0 @ (Y1 @ (Y1 @ X1 @ (Y1 @ X1 @ (Y1 @ (Y1 @ X1 @ (Y1 @ (X2 @ X1) @ (Y1 @ (Y1 @ X3 @ (Y1 @ Y0 @ (Y1 @ Y0 @ Y0))) @ X1))) @ (Y1 @ (X2 @ (Y1 @ (Y1 @ (X2 @ X3) @ X1) @ (Y1 @ X1 @ X1))) @ (Y1 @ Y0 @ (Y1 @ Y0 @ (Y1 @ (Y1 @ (Y1 @ X1 @ (Y1 @ (Y1 @ X1 @ (Y1 @ (X2 @ Y0) @ X3)) @ (X2 @ (Y1 @ X3 @ X1)))) @ Y0) @ (X2 @ (Y1 @ (Y1 @ X3 @ (Y1 @ X1 @ (Y1 @ (X2 @ (Y1 @ X1 @ X3)) @ X1))) @ (Y1 @ (Y1 @ (Y1 @ Y0 @ (Y1 @ (X2 @ X1) @ Y0)) @ Y0) @ (X2 @ (X2 @ (Y1 @ (Y1 @ (Y1 @ (Y1 @ X1 @ (Y1 @ (Y1 @ Y0 @ (Y1 @ (Y1 @ X3 @ X1) @ X3)) @ Y0)) @ X3) @ (Y1 @ X3 @ (Y1 @ X1 @ X1))) @ Y0))))))))))))) @ (Y1 @ (Y1 @ (Y1 @ (Y1 @ (Y1 @ Y0 @ (Y1 @ X1 @ X1)) @ (X2 @ (X2 @ (Y1 @ X3 @ (X2 @ (X2 @ (Y1 @ X3 @ X1))))))) @ X1) @ Y0) @ (Y1 @ Y0 @ X3)))) @ X1) @ X1) @ (X2 @ Y0)))) @ (Y1 @ (Y1 @ (X2 @ (Y1 @ (X2 @ (Y1 @ (Y1 @ (Y1 @ (Y1 @ X3 @ (Y1 @ (X2 @ (X2 @ (Y1 @ (Y1 @ X1 @ Y0) @ X3))) @ (X2 @ (Y1 @ X1 @ X1)))) @ X1) @ (X2 @ X1)) @ (Y1 @ (Y1 @ (Y1 @ (Y1 @ (Y1 @ X1 @ X3) @ (X2 @ (X2 @ (X2 @ X3)))) @ X3) @ Y0) @ X1))) @ (Y1 @ (Y1 @ (Y1 @ Y0 @ X1) @ (X2 @ Y0)) @ Y0))) @ X3) @ Y0)) = Y0) => ((X4 @ (X2 @ X1)) => Y2)) => Y2)))))))) = $true)) )),
% 0.78/0.58 inference(beta-eta_normalization,[],[f694])).
% 0.78/0.58 thf(f696,plain,(
% 0.78/0.58 ( ! [X2 : ($i > $i),X3 : $i,X1 : $i,X4 : ($i > $o),X5 : $i] : (((((^[Y0 : $i]: (!! @ ($i > $i > $i) @ (^[Y1 : $i > $i > $i]: (!! @ $o @ (^[Y2 : $o]: ((((Y1 @ (Y1 @ X1 @ (Y1 @ X3 @ (Y1 @ (Y1 @ (Y1 @ (Y1 @ Y0 @ (Y1 @ (Y1 @ X1 @ (Y1 @ X1 @ (Y1 @ (Y1 @ X1 @ (Y1 @ (X2 @ X1) @ (Y1 @ (Y1 @ X3 @ (Y1 @ Y0 @ (Y1 @ Y0 @ Y0))) @ X1))) @ (Y1 @ (X2 @ (Y1 @ (Y1 @ (X2 @ X3) @ X1) @ (Y1 @ X1 @ X1))) @ (Y1 @ Y0 @ (Y1 @ Y0 @ (Y1 @ (Y1 @ (Y1 @ X1 @ (Y1 @ (Y1 @ X1 @ (Y1 @ (X2 @ Y0) @ X3)) @ (X2 @ (Y1 @ X3 @ X1)))) @ Y0) @ (X2 @ (Y1 @ (Y1 @ X3 @ (Y1 @ X1 @ (Y1 @ (X2 @ (Y1 @ X1 @ X3)) @ X1))) @ (Y1 @ (Y1 @ (Y1 @ Y0 @ (Y1 @ (X2 @ X1) @ Y0)) @ Y0) @ (X2 @ (X2 @ (Y1 @ (Y1 @ (Y1 @ (Y1 @ X1 @ (Y1 @ (Y1 @ Y0 @ (Y1 @ (Y1 @ X3 @ X1) @ X3)) @ Y0)) @ X3) @ (Y1 @ X3 @ (Y1 @ X1 @ X1))) @ Y0))))))))))))) @ (Y1 @ (Y1 @ (Y1 @ (Y1 @ (Y1 @ Y0 @ (Y1 @ X1 @ X1)) @ (X2 @ (X2 @ (Y1 @ X3 @ (X2 @ (X2 @ (Y1 @ X3 @ X1))))))) @ X1) @ Y0) @ (Y1 @ Y0 @ X3)))) @ X1) @ X1) @ (X2 @ Y0)))) @ (Y1 @ (Y1 @ (X2 @ (Y1 @ (X2 @ (Y1 @ (Y1 @ (Y1 @ (Y1 @ X3 @ (Y1 @ (X2 @ (X2 @ (Y1 @ (Y1 @ X1 @ Y0) @ X3))) @ (X2 @ (Y1 @ X1 @ X1)))) @ X1) @ (X2 @ X1)) @ (Y1 @ (Y1 @ (Y1 @ (Y1 @ (Y1 @ X1 @ X3) @ (X2 @ (X2 @ (X2 @ X3)))) @ X3) @ Y0) @ X1))) @ (Y1 @ (Y1 @ (Y1 @ Y0 @ X1) @ (X2 @ Y0)) @ Y0))) @ X3) @ Y0)) = Y0) => ((X4 @ (X2 @ X1)) => Y2)) => Y2)))))) @ X5)) = $true) | (sF12 = $false)) )),
% 0.78/0.58 inference(pi_proxy_clausification,[],[f695])).
% 0.78/0.58 thf(f697,plain,(
% 0.78/0.58 ( ! [X2 : ($i > $i),X3 : $i,X1 : $i,X4 : ($i > $o),X5 : $i] : ((((!! @ ($i > $i > $i) @ (^[Y0 : $i > $i > $i]: (!! @ $o @ (^[Y1 : $o]: ((((Y0 @ (Y0 @ X1 @ (Y0 @ X3 @ (Y0 @ (Y0 @ (Y0 @ (Y0 @ X5 @ (Y0 @ (Y0 @ X1 @ (Y0 @ X1 @ (Y0 @ (Y0 @ X1 @ (Y0 @ (X2 @ X1) @ (Y0 @ (Y0 @ X3 @ (Y0 @ X5 @ (Y0 @ X5 @ X5))) @ X1))) @ (Y0 @ (X2 @ (Y0 @ (Y0 @ (X2 @ X3) @ X1) @ (Y0 @ X1 @ X1))) @ (Y0 @ X5 @ (Y0 @ X5 @ (Y0 @ (Y0 @ (Y0 @ X1 @ (Y0 @ (Y0 @ X1 @ (Y0 @ (X2 @ X5) @ X3)) @ (X2 @ (Y0 @ X3 @ X1)))) @ X5) @ (X2 @ (Y0 @ (Y0 @ X3 @ (Y0 @ X1 @ (Y0 @ (X2 @ (Y0 @ X1 @ X3)) @ X1))) @ (Y0 @ (Y0 @ (Y0 @ X5 @ (Y0 @ (X2 @ X1) @ X5)) @ X5) @ (X2 @ (X2 @ (Y0 @ (Y0 @ (Y0 @ (Y0 @ X1 @ (Y0 @ (Y0 @ X5 @ (Y0 @ (Y0 @ X3 @ X1) @ X3)) @ X5)) @ X3) @ (Y0 @ X3 @ (Y0 @ X1 @ X1))) @ X5))))))))))))) @ (Y0 @ (Y0 @ (Y0 @ (Y0 @ (Y0 @ X5 @ (Y0 @ X1 @ X1)) @ (X2 @ (X2 @ (Y0 @ X3 @ (X2 @ (X2 @ (Y0 @ X3 @ X1))))))) @ X1) @ X5) @ (Y0 @ X5 @ X3)))) @ X1) @ X1) @ (X2 @ X5)))) @ (Y0 @ (Y0 @ (X2 @ (Y0 @ (X2 @ (Y0 @ (Y0 @ (Y0 @ (Y0 @ X3 @ (Y0 @ (X2 @ (X2 @ (Y0 @ (Y0 @ X1 @ X5) @ X3))) @ (X2 @ (Y0 @ X1 @ X1)))) @ X1) @ (X2 @ X1)) @ (Y0 @ (Y0 @ (Y0 @ (Y0 @ (Y0 @ X1 @ X3) @ (X2 @ (X2 @ (X2 @ X3)))) @ X3) @ X5) @ X1))) @ (Y0 @ (Y0 @ (Y0 @ X5 @ X1) @ (X2 @ X5)) @ X5))) @ X3) @ X5)) = X5) => ((X4 @ (X2 @ X1)) => Y1)) => Y1)))))) = $true) | (sF12 = $false)) )),
% 0.78/0.58 inference(beta-eta_normalization,[],[f696])).
% 0.78/0.58 thf(f698,plain,(
% 0.78/0.58 ( ! [X2 : ($i > $i),X3 : $i,X1 : $i,X6 : ($i > $i > $i),X4 : ($i > $o),X5 : $i] : ((sF12 = $false) | ((((^[Y0 : $i > $i > $i]: (!! @ $o @ (^[Y1 : $o]: ((((Y0 @ (Y0 @ X1 @ (Y0 @ X3 @ (Y0 @ (Y0 @ (Y0 @ (Y0 @ X5 @ (Y0 @ (Y0 @ X1 @ (Y0 @ X1 @ (Y0 @ (Y0 @ X1 @ (Y0 @ (X2 @ X1) @ (Y0 @ (Y0 @ X3 @ (Y0 @ X5 @ (Y0 @ X5 @ X5))) @ X1))) @ (Y0 @ (X2 @ (Y0 @ (Y0 @ (X2 @ X3) @ X1) @ (Y0 @ X1 @ X1))) @ (Y0 @ X5 @ (Y0 @ X5 @ (Y0 @ (Y0 @ (Y0 @ X1 @ (Y0 @ (Y0 @ X1 @ (Y0 @ (X2 @ X5) @ X3)) @ (X2 @ (Y0 @ X3 @ X1)))) @ X5) @ (X2 @ (Y0 @ (Y0 @ X3 @ (Y0 @ X1 @ (Y0 @ (X2 @ (Y0 @ X1 @ X3)) @ X1))) @ (Y0 @ (Y0 @ (Y0 @ X5 @ (Y0 @ (X2 @ X1) @ X5)) @ X5) @ (X2 @ (X2 @ (Y0 @ (Y0 @ (Y0 @ (Y0 @ X1 @ (Y0 @ (Y0 @ X5 @ (Y0 @ (Y0 @ X3 @ X1) @ X3)) @ X5)) @ X3) @ (Y0 @ X3 @ (Y0 @ X1 @ X1))) @ X5))))))))))))) @ (Y0 @ (Y0 @ (Y0 @ (Y0 @ (Y0 @ X5 @ (Y0 @ X1 @ X1)) @ (X2 @ (X2 @ (Y0 @ X3 @ (X2 @ (X2 @ (Y0 @ X3 @ X1))))))) @ X1) @ X5) @ (Y0 @ X5 @ X3)))) @ X1) @ X1) @ (X2 @ X5)))) @ (Y0 @ (Y0 @ (X2 @ (Y0 @ (X2 @ (Y0 @ (Y0 @ (Y0 @ (Y0 @ X3 @ (Y0 @ (X2 @ (X2 @ (Y0 @ (Y0 @ X1 @ X5) @ X3))) @ (X2 @ (Y0 @ X1 @ X1)))) @ X1) @ (X2 @ X1)) @ (Y0 @ (Y0 @ (Y0 @ (Y0 @ (Y0 @ X1 @ X3) @ (X2 @ (X2 @ (X2 @ X3)))) @ X3) @ X5) @ X1))) @ (Y0 @ (Y0 @ (Y0 @ X5 @ X1) @ (X2 @ X5)) @ X5))) @ X3) @ X5)) = X5) => ((X4 @ (X2 @ X1)) => Y1)) => Y1)))) @ X6)) = $true)) )),
% 0.78/0.58 inference(pi_proxy_clausification,[],[f697])).
% 0.78/0.58 thf(f699,plain,(
% 0.78/0.58 ( ! [X2 : ($i > $i),X3 : $i,X1 : $i,X6 : ($i > $i > $i),X4 : ($i > $o),X5 : $i] : ((((!! @ $o @ (^[Y0 : $o]: ((((X6 @ (X6 @ X1 @ (X6 @ X3 @ (X6 @ (X6 @ (X6 @ (X6 @ X5 @ (X6 @ (X6 @ X1 @ (X6 @ X1 @ (X6 @ (X6 @ X1 @ (X6 @ (X2 @ X1) @ (X6 @ (X6 @ X3 @ (X6 @ X5 @ (X6 @ X5 @ X5))) @ X1))) @ (X6 @ (X2 @ (X6 @ (X6 @ (X2 @ X3) @ X1) @ (X6 @ X1 @ X1))) @ (X6 @ X5 @ (X6 @ X5 @ (X6 @ (X6 @ (X6 @ X1 @ (X6 @ (X6 @ X1 @ (X6 @ (X2 @ X5) @ X3)) @ (X2 @ (X6 @ X3 @ X1)))) @ X5) @ (X2 @ (X6 @ (X6 @ X3 @ (X6 @ X1 @ (X6 @ (X2 @ (X6 @ X1 @ X3)) @ X1))) @ (X6 @ (X6 @ (X6 @ X5 @ (X6 @ (X2 @ X1) @ X5)) @ X5) @ (X2 @ (X2 @ (X6 @ (X6 @ (X6 @ (X6 @ X1 @ (X6 @ (X6 @ X5 @ (X6 @ (X6 @ X3 @ X1) @ X3)) @ X5)) @ X3) @ (X6 @ X3 @ (X6 @ X1 @ X1))) @ X5))))))))))))) @ (X6 @ (X6 @ (X6 @ (X6 @ (X6 @ X5 @ (X6 @ X1 @ X1)) @ (X2 @ (X2 @ (X6 @ X3 @ (X2 @ (X2 @ (X6 @ X3 @ X1))))))) @ X1) @ X5) @ (X6 @ X5 @ X3)))) @ X1) @ X1) @ (X2 @ X5)))) @ (X6 @ (X6 @ (X2 @ (X6 @ (X2 @ (X6 @ (X6 @ (X6 @ (X6 @ X3 @ (X6 @ (X2 @ (X2 @ (X6 @ (X6 @ X1 @ X5) @ X3))) @ (X2 @ (X6 @ X1 @ X1)))) @ X1) @ (X2 @ X1)) @ (X6 @ (X6 @ (X6 @ (X6 @ (X6 @ X1 @ X3) @ (X2 @ (X2 @ (X2 @ X3)))) @ X3) @ X5) @ X1))) @ (X6 @ (X6 @ (X6 @ X5 @ X1) @ (X2 @ X5)) @ X5))) @ X3) @ X5)) = X5) => ((X4 @ (X2 @ X1)) => Y0)) => Y0)))) = $true) | (sF12 = $false)) )),
% 0.78/0.58 inference(beta-eta_normalization,[],[f698])).
% 0.78/0.58 thf(f700,plain,(
% 0.78/0.58 ( ! [X2 : ($i > $i),X3 : $i,X1 : $i,X6 : ($i > $i > $i),X7 : $o,X4 : ($i > $o),X5 : $i] : (((((^[Y0 : $o]: ((((X6 @ (X6 @ X1 @ (X6 @ X3 @ (X6 @ (X6 @ (X6 @ (X6 @ X5 @ (X6 @ (X6 @ X1 @ (X6 @ X1 @ (X6 @ (X6 @ X1 @ (X6 @ (X2 @ X1) @ (X6 @ (X6 @ X3 @ (X6 @ X5 @ (X6 @ X5 @ X5))) @ X1))) @ (X6 @ (X2 @ (X6 @ (X6 @ (X2 @ X3) @ X1) @ (X6 @ X1 @ X1))) @ (X6 @ X5 @ (X6 @ X5 @ (X6 @ (X6 @ (X6 @ X1 @ (X6 @ (X6 @ X1 @ (X6 @ (X2 @ X5) @ X3)) @ (X2 @ (X6 @ X3 @ X1)))) @ X5) @ (X2 @ (X6 @ (X6 @ X3 @ (X6 @ X1 @ (X6 @ (X2 @ (X6 @ X1 @ X3)) @ X1))) @ (X6 @ (X6 @ (X6 @ X5 @ (X6 @ (X2 @ X1) @ X5)) @ X5) @ (X2 @ (X2 @ (X6 @ (X6 @ (X6 @ (X6 @ X1 @ (X6 @ (X6 @ X5 @ (X6 @ (X6 @ X3 @ X1) @ X3)) @ X5)) @ X3) @ (X6 @ X3 @ (X6 @ X1 @ X1))) @ X5))))))))))))) @ (X6 @ (X6 @ (X6 @ (X6 @ (X6 @ X5 @ (X6 @ X1 @ X1)) @ (X2 @ (X2 @ (X6 @ X3 @ (X2 @ (X2 @ (X6 @ X3 @ X1))))))) @ X1) @ X5) @ (X6 @ X5 @ X3)))) @ X1) @ X1) @ (X2 @ X5)))) @ (X6 @ (X6 @ (X2 @ (X6 @ (X2 @ (X6 @ (X6 @ (X6 @ (X6 @ X3 @ (X6 @ (X2 @ (X2 @ (X6 @ (X6 @ X1 @ X5) @ X3))) @ (X2 @ (X6 @ X1 @ X1)))) @ X1) @ (X2 @ X1)) @ (X6 @ (X6 @ (X6 @ (X6 @ (X6 @ X1 @ X3) @ (X2 @ (X2 @ (X2 @ X3)))) @ X3) @ X5) @ X1))) @ (X6 @ (X6 @ (X6 @ X5 @ X1) @ (X2 @ X5)) @ X5))) @ X3) @ X5)) = X5) => ((X4 @ (X2 @ X1)) => Y0)) => Y0)) @ X7)) = $true) | (sF12 = $false)) )),
% 0.78/0.58 inference(pi_proxy_clausification,[],[f699])).
% 0.78/0.58 thf(f701,plain,(
% 0.78/0.58 ( ! [X2 : ($i > $i),X3 : $i,X1 : $i,X6 : ($i > $i > $i),X7 : $o,X4 : ($i > $o),X5 : $i] : ((sF12 = $false) | ((((((X6 @ (X6 @ X1 @ (X6 @ X3 @ (X6 @ (X6 @ (X6 @ (X6 @ X5 @ (X6 @ (X6 @ X1 @ (X6 @ X1 @ (X6 @ (X6 @ X1 @ (X6 @ (X2 @ X1) @ (X6 @ (X6 @ X3 @ (X6 @ X5 @ (X6 @ X5 @ X5))) @ X1))) @ (X6 @ (X2 @ (X6 @ (X6 @ (X2 @ X3) @ X1) @ (X6 @ X1 @ X1))) @ (X6 @ X5 @ (X6 @ X5 @ (X6 @ (X6 @ (X6 @ X1 @ (X6 @ (X6 @ X1 @ (X6 @ (X2 @ X5) @ X3)) @ (X2 @ (X6 @ X3 @ X1)))) @ X5) @ (X2 @ (X6 @ (X6 @ X3 @ (X6 @ X1 @ (X6 @ (X2 @ (X6 @ X1 @ X3)) @ X1))) @ (X6 @ (X6 @ (X6 @ X5 @ (X6 @ (X2 @ X1) @ X5)) @ X5) @ (X2 @ (X2 @ (X6 @ (X6 @ (X6 @ (X6 @ X1 @ (X6 @ (X6 @ X5 @ (X6 @ (X6 @ X3 @ X1) @ X3)) @ X5)) @ X3) @ (X6 @ X3 @ (X6 @ X1 @ X1))) @ X5))))))))))))) @ (X6 @ (X6 @ (X6 @ (X6 @ (X6 @ X5 @ (X6 @ X1 @ X1)) @ (X2 @ (X2 @ (X6 @ X3 @ (X2 @ (X2 @ (X6 @ X3 @ X1))))))) @ X1) @ X5) @ (X6 @ X5 @ X3)))) @ X1) @ X1) @ (X2 @ X5)))) @ (X6 @ (X6 @ (X2 @ (X6 @ (X2 @ (X6 @ (X6 @ (X6 @ (X6 @ X3 @ (X6 @ (X2 @ (X2 @ (X6 @ (X6 @ X1 @ X5) @ X3))) @ (X2 @ (X6 @ X1 @ X1)))) @ X1) @ (X2 @ X1)) @ (X6 @ (X6 @ (X6 @ (X6 @ (X6 @ X1 @ X3) @ (X2 @ (X2 @ (X2 @ X3)))) @ X3) @ X5) @ X1))) @ (X6 @ (X6 @ (X6 @ X5 @ X1) @ (X2 @ X5)) @ X5))) @ X3) @ X5)) = X5) => ((X4 @ (X2 @ X1)) => X7)) => X7)) = $true)) )),
% 0.78/0.58 inference(beta-eta_normalization,[],[f700])).
% 0.78/0.58 thf(f702,plain,(
% 0.78/0.58 ( ! [X2 : ($i > $i),X3 : $i,X1 : $i,X6 : ($i > $i > $i),X7 : $o,X4 : ($i > $o),X5 : $i] : (($true = X7) | ($false = ((((X6 @ (X6 @ X1 @ (X6 @ X3 @ (X6 @ (X6 @ (X6 @ (X6 @ X5 @ (X6 @ (X6 @ X1 @ (X6 @ X1 @ (X6 @ (X6 @ X1 @ (X6 @ (X2 @ X1) @ (X6 @ (X6 @ X3 @ (X6 @ X5 @ (X6 @ X5 @ X5))) @ X1))) @ (X6 @ (X2 @ (X6 @ (X6 @ (X2 @ X3) @ X1) @ (X6 @ X1 @ X1))) @ (X6 @ X5 @ (X6 @ X5 @ (X6 @ (X6 @ (X6 @ X1 @ (X6 @ (X6 @ X1 @ (X6 @ (X2 @ X5) @ X3)) @ (X2 @ (X6 @ X3 @ X1)))) @ X5) @ (X2 @ (X6 @ (X6 @ X3 @ (X6 @ X1 @ (X6 @ (X2 @ (X6 @ X1 @ X3)) @ X1))) @ (X6 @ (X6 @ (X6 @ X5 @ (X6 @ (X2 @ X1) @ X5)) @ X5) @ (X2 @ (X2 @ (X6 @ (X6 @ (X6 @ (X6 @ X1 @ (X6 @ (X6 @ X5 @ (X6 @ (X6 @ X3 @ X1) @ X3)) @ X5)) @ X3) @ (X6 @ X3 @ (X6 @ X1 @ X1))) @ X5))))))))))))) @ (X6 @ (X6 @ (X6 @ (X6 @ (X6 @ X5 @ (X6 @ X1 @ X1)) @ (X2 @ (X2 @ (X6 @ X3 @ (X2 @ (X2 @ (X6 @ X3 @ X1))))))) @ X1) @ X5) @ (X6 @ X5 @ X3)))) @ X1) @ X1) @ (X2 @ X5)))) @ (X6 @ (X6 @ (X2 @ (X6 @ (X2 @ (X6 @ (X6 @ (X6 @ (X6 @ X3 @ (X6 @ (X2 @ (X2 @ (X6 @ (X6 @ X1 @ X5) @ X3))) @ (X2 @ (X6 @ X1 @ X1)))) @ X1) @ (X2 @ X1)) @ (X6 @ (X6 @ (X6 @ (X6 @ (X6 @ X1 @ X3) @ (X2 @ (X2 @ (X2 @ X3)))) @ X3) @ X5) @ X1))) @ (X6 @ (X6 @ (X6 @ X5 @ X1) @ (X2 @ X5)) @ X5))) @ X3) @ X5)) = X5) => ((X4 @ (X2 @ X1)) => X7)))) | (sF12 = $false)) )),
% 0.78/0.58 inference(imp_proxy_clausification,[],[f701])).
% 0.78/0.58 thf(f703,plain,(
% 0.78/0.58 ( ! [X2 : ($i > $i),X1 : $i,X7 : $o,X4 : ($i > $o)] : (($true = X7) | (sF12 = $false) | ($false = (((X4 @ (X2 @ X1)) => X7)))) )),
% 0.78/0.58 inference(imp_proxy_clausification,[],[f702])).
% 0.78/0.58 thf(f707,plain,(
% 0.78/0.58 ( ! [X2 : ($i > $i),X1 : $i,X7 : $o,X4 : ($i > $o)] : ((((X4 @ (X2 @ X1))) = $true) | (sF12 = $false) | ($true = X7)) )),
% 0.78/0.58 inference(imp_proxy_clausification,[],[f703])).
% 0.78/0.58 thf(f758,definition,(
% 0.78/0.58 spl32_1 <=> ! [X2 : $o] : ($true = X2)),
% 0.78/0.58 introduced(definition,[new_symbols(definition,[spl32_1])],[avatar_definition])).
% 0.78/0.58 thf(f759,plain,(
% 0.78/0.58 ( ! [X2 : $o] : (($true = X2)) ) | ~spl32_1),
% 0.78/0.58 inference(avatar_component_clause,[],[f758])).
% 0.78/0.58 thf(f781,definition,(
% 0.78/0.58 spl32_7 <=> (c_False = $false)),
% 0.78/0.58 introduced(definition,[new_symbols(definition,[spl32_7])],[avatar_definition])).
% 0.78/0.58 thf(f783,plain,(
% 0.78/0.58 (c_False = $false) | ~spl32_7),
% 0.78/0.58 inference(avatar_component_clause,[],[f781])).
% 0.78/0.58 thf(f815,definition,(
% 0.78/0.58 spl32_14 <=> (sF12 = $true)),
% 0.78/0.58 introduced(definition,[new_symbols(definition,[spl32_14])],[avatar_definition])).
% 0.78/0.58 thf(f817,plain,(
% 0.78/0.58 (sF12 = $true) | ~spl32_14),
% 0.78/0.58 inference(avatar_component_clause,[],[f815])).
% 0.78/0.58 thf(f819,definition,(
% 0.78/0.58 spl32_15 <=> (sF13 = $true)),
% 0.78/0.58 introduced(definition,[new_symbols(definition,[spl32_15])],[avatar_definition])).
% 0.78/0.58 thf(f822,plain,(
% 0.78/0.58 spl32_14 | spl32_15),
% 0.78/0.58 inference(avatar_split_clause,[],[f656,f819,f815])).
% 0.78/0.58 thf(f823,plain,(
% 0.78/0.58 spl32_7 | spl32_15),
% 0.78/0.58 inference(avatar_split_clause,[],[f655,f819,f781])).
% 0.78/0.58 thf(f825,definition,(
% 0.78/0.58 spl32_16 <=> (sF12 = $false)),
% 0.78/0.58 introduced(definition,[new_symbols(definition,[spl32_16])],[avatar_definition])).
% 0.78/0.58 thf(f827,plain,(
% 0.78/0.58 (sF12 = $false) | ~spl32_16),
% 0.78/0.58 inference(avatar_component_clause,[],[f825])).
% 0.78/0.58 thf(f859,definition,(
% 0.78/0.58 spl32_24 <=> ! [X2 : ($i > $i),X1 : $i,X4 : ($i > $o)] : (((X4 @ (X2 @ X1))) = $true)),
% 0.78/0.58 introduced(definition,[new_symbols(definition,[spl32_24])],[avatar_definition])).
% 0.78/0.58 thf(f860,plain,(
% 0.78/0.58 ( ! [X2 : ($i > $i),X1 : $i,X4 : ($i > $o)] : ((((X4 @ (X2 @ X1))) = $true)) ) | ~spl32_24),
% 0.78/0.58 inference(avatar_component_clause,[],[f859])).
% 0.78/0.58 thf(f861,plain,(
% 0.78/0.58 spl32_16 | spl32_24 | spl32_1),
% 0.78/0.58 inference(avatar_split_clause,[],[f707,f758,f859,f825])).
% 0.78/0.58 thf(f901,plain,(
% 0.78/0.58 ~spl32_15),
% 0.78/0.58 inference(avatar_split_clause,[],[f565,f819])).
% 0.78/0.58 thf(f906,plain,(
% 0.78/0.58 ($false = $true) | (~spl32_14 | ~spl32_16)),
% 0.78/0.58 inference(forward_demodulation,[],[f817,f827])).
% 0.78/0.58 thf(f907,plain,(
% 0.78/0.58 $false | (~spl32_14 | ~spl32_16)),
% 0.78/0.58 inference(trivial_inequality_removal,[],[f906])).
% 0.78/0.58 thf(f908,plain,(
% 0.78/0.58 ~spl32_14 | ~spl32_16),
% 0.78/0.58 inference(avatar_contradiction_clause,[],[f907])).
% 0.78/0.58 thf(f962,plain,(
% 0.78/0.58 ( ! [X0 : $i,X1 : ($i > $o)] : (($true != ((sP0 @ X1 @ X0)))) ) | ~spl32_24),
% 0.78/0.58 inference(forward_subsumption_resolution,[],[f401,f860])).
% 0.78/0.58 thf(f964,plain,(
% 0.78/0.58 ($true != $true) | ~spl32_24),
% 0.78/0.58 inference(constrained_superposition,[],[f962,f860])).
% 0.78/0.58 thf(f974,plain,(
% 0.78/0.58 $false | ~spl32_24),
% 0.78/0.58 inference(trivial_inequality_removal,[],[f964])).
% 0.78/0.58 thf(f975,plain,(
% 0.78/0.58 ~spl32_24),
% 0.78/0.58 inference(avatar_contradiction_clause,[],[f974])).
% 0.78/0.58 thf(f983,plain,(
% 0.78/0.58 ($false = $true) | (~spl32_1 | ~spl32_7)),
% 0.78/0.58 inference(constrained_superposition,[],[f783,f759])).
% 0.78/0.58 thf(f996,plain,(
% 0.78/0.58 $false | (~spl32_1 | ~spl32_7)),
% 0.78/0.58 inference(trivial_inequality_removal,[],[f983])).
% 0.78/0.58 thf(f997,plain,(
% 0.78/0.58 ~spl32_1 | ~spl32_7),
% 0.78/0.58 inference(avatar_contradiction_clause,[],[f996])).
% 0.78/0.58 cnf(s12, plain, spl32_14 | spl32_15, inference(sat_conversion,[],[f822])).
% 0.78/0.58 cnf(s13, plain, spl32_7 | spl32_15, inference(sat_conversion,[],[f823])).
% 0.78/0.58 cnf(s24, plain, spl32_1 | spl32_16 | spl32_24, inference(sat_conversion,[],[f861])).
% 0.78/0.58 cnf(s36, plain, ~spl32_15, inference(sat_conversion,[],[f901])).
% 0.78/0.58 cnf(s39, plain, ~spl32_14 | ~spl32_16, inference(sat_conversion,[],[f908])).
% 0.78/0.58 cnf(s40, plain, ~spl32_24, inference(sat_conversion,[],[f975])).
% 0.78/0.58 cnf(s41, plain, ~spl32_1 | ~spl32_7, inference(sat_conversion,[],[f997])).
% 0.78/0.58 cnf(s46, plain, spl32_1 | spl32_16, inference(rat,[],[s24,s40])).
% 0.78/0.58 cnf(s47, plain, spl32_7, inference(rat,[],[s13,s36])).
% 0.78/0.58 cnf(s48, plain, ~spl32_1, inference(rat,[],[s41,s47])).
% 0.78/0.58 cnf(s54, plain, spl32_16, inference(rat,[],[s46,s48])).
% 0.78/0.58 cnf(s59, plain, ~spl32_14, inference(rat,[],[s39,s54])).
% 0.78/0.58 cnf(s61, plain, $false, inference(rat,[],[s12,s36,s59])).
% 0.78/0.58 thf(f1019,plain,(
% 0.78/0.58 $false),
% 0.78/0.58 inference(avatar_sat_refutation,[],[s61])).
% 0.78/0.58 % SZS output end Proof for theBenchmark
% 0.78/0.58 % (2795459)------------------------------
% 0.78/0.58 % (2795459)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.78/0.58 % (2795459)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.78/0.58 % (2795459)CaDiCaL version: 2.1.3
% 0.78/0.58 % (2795459)Termination reason: Refutation
% 0.78/0.58 % (2795459)Time elapsed: 0.099 s
% 0.78/0.58 % (2795459)Peak memory usage: 14 MB
% 0.78/0.58 % (2795459)Instructions burned: 127 (million)
% 0.78/0.58 % (2795448)Success in time 0.158 s
% 0.78/0.58 % Vampire exiting
%------------------------------------------------------------------------------