%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWX181^1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 08:40:40 AM UTC 2026
% Result : Theorem 2.70s 0.71s
% Output : Refutation 2.70s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX181^1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n019.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 16:10:18 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.25 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
% 0.67/0.42 % (981239)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.67/0.42 % (981250)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.67/0.42 % (981250)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
% 0.67/0.42 % (981250)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=139679238:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.67/0.42 % (981245)lrs+10_16_si=on:nwc=1.5:random_seed=711841288:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.67/0.42 % (981246)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2596670318:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.67/0.42 % (981246)Instruction limit reached!
% 0.67/0.42 % (981246)------------------------------
% 0.67/0.42 % (981246)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.42 % (981246)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.42 % (981246)CaDiCaL version: 2.1.3
% 0.67/0.42 % (981246)Termination reason: Instruction limit
% 0.67/0.42 % (981246)Termination phase: shuffling
% 0.67/0.42 % (981246)Time elapsed: 0.002 s
% 0.67/0.42 % (981246)Peak memory usage: 10 MB
% 0.67/0.42 % (981246)Instructions burned: 4 (million)
% 0.67/0.42 % (981249)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1290694025:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.67/0.42 % (981247)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=1895500145: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)
% 0.67/0.42 % (981245)Instruction limit reached!
% 0.67/0.42 % (981245)------------------------------
% 0.67/0.42 % (981245)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.42 % (981245)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.42 % (981245)CaDiCaL version: 2.1.3
% 0.67/0.42 % (981245)Termination reason: Instruction limit
% 0.67/0.42 % (981245)Termination phase: Property scanning
% 0.67/0.42 % (981245)Time elapsed: 0.008 s
% 0.67/0.42 % (981245)Peak memory usage: 10 MB
% 0.67/0.42 % (981245)Instructions burned: 19 (million)
% 0.67/0.42 % (981248)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1884196338:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.67/0.42 % (981244)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1657943068:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.67/0.42 % (981255)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3185837625:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.67/0.42 % (981255)Instruction limit reached!
% 0.67/0.42 % (981255)------------------------------
% 0.67/0.42 % (981255)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.42 % (981255)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.42 % (981255)CaDiCaL version: 2.1.3
% 0.67/0.42 % (981255)Termination reason: Instruction limit
% 0.67/0.42 % (981255)Termination phase: shuffling
% 0.67/0.42 % (981255)Time elapsed: 0.002 s
% 0.67/0.42 % (981255)Peak memory usage: 10 MB
% 0.67/0.42 % (981255)Instructions burned: 4 (million)
% 0.67/0.42 % (981257)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3514004875:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.67/0.42 % (981257)Instruction limit reached!
% 0.67/0.42 % (981257)------------------------------
% 0.67/0.42 % (981257)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.42 % (981257)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.42 % (981257)CaDiCaL version: 2.1.3
% 0.67/0.42 % (981257)Termination reason: Instruction limit
% 0.67/0.42 % (981257)Termination phase: shuffling
% 0.67/0.42 % (981257)Time elapsed: 0.003 s
% 0.67/0.42 % (981257)Peak memory usage: 10 MB
% 0.67/0.42 % (981257)Instructions burned: 7 (million)
% 0.67/0.42 % (981249)Instruction limit reached!
% 0.67/0.46 % (981249)------------------------------
% 0.67/0.46 % (981249)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.46 % (981249)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.46 % (981249)CaDiCaL version: 2.1.3
% 0.67/0.46 % (981249)Termination reason: Instruction limit
% 0.67/0.46 % (981249)Termination phase: Saturation
% 0.67/0.46 % (981249)Time elapsed: 0.033 s
% 0.67/0.46 % (981249)Peak memory usage: 13 MB
% 0.67/0.46 % (981249)Instructions burned: 77 (million)
% 0.67/0.46 % (981261)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.67/0.46 % (981261)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=102365336:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.67/0.46 % (981261)Instruction limit reached!
% 0.67/0.46 % (981261)------------------------------
% 0.67/0.46 % (981261)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.46 % (981261)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.46 % (981261)CaDiCaL version: 2.1.3
% 0.67/0.46 % (981261)Termination reason: Instruction limit
% 0.67/0.46 % (981261)Termination phase: shuffling
% 0.67/0.46 % (981261)Time elapsed: 0.004 s
% 0.67/0.46 % (981261)Peak memory usage: 10 MB
% 0.67/0.46 % (981261)Instructions burned: 9 (million)
% 0.67/0.46 % (981263)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=3341601745:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.67/0.46 % (981264)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
% 0.67/0.46 % (981264)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.67/0.46 % (981248)Instruction limit reached!
% 0.67/0.46 % (981248)------------------------------
% 0.67/0.46 % (981248)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.46 % (981248)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.46 % (981248)CaDiCaL version: 2.1.3
% 0.67/0.46 % (981248)Termination reason: Instruction limit
% 0.67/0.46 % (981248)Termination phase: Property scanning
% 0.67/0.46 % (981248)Time elapsed: 0.034 s
% 0.67/0.46 % (981248)Peak memory usage: 11 MB
% 0.67/0.46 % (981248)Instructions burned: 33 (million)
% 0.67/0.46 % (981264)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=228491835:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.67/0.46 % (981263)Instruction limit reached!
% 0.67/0.46 % (981263)------------------------------
% 0.67/0.46 % (981263)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.46 % (981263)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.46 % (981263)CaDiCaL version: 2.1.3
% 0.67/0.46 % (981263)Termination reason: Instruction limit
% 0.67/0.46 % (981263)Termination phase: Property scanning
% 0.67/0.46 % (981263)Time elapsed: 0.006 s
% 0.67/0.46 % (981263)Peak memory usage: 10 MB
% 0.67/0.46 % (981263)Instructions burned: 13 (million)
% 0.67/0.46 % (981250)Instruction limit reached!
% 0.67/0.46 % (981250)------------------------------
% 0.67/0.46 % (981250)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.46 % (981250)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.46 % (981250)CaDiCaL version: 2.1.3
% 0.67/0.46 % (981250)Termination reason: Instruction limit
% 0.67/0.46 % (981250)Termination phase: Saturation
% 0.67/0.46 % (981250)Time elapsed: 0.064 s
% 0.67/0.46 % (981250)Peak memory usage: 14 MB
% 0.67/0.46 % (981250)Instructions burned: 157 (million)
% 0.67/0.46 % (981266)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=3366478791:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.67/0.46 % (981264)Instruction limit reached!
% 0.67/0.46 % (981264)------------------------------
% 0.67/0.46 % (981264)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.46 % (981264)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.51 % (981264)CaDiCaL version: 2.1.3
% 0.67/0.51 % (981264)Termination reason: Instruction limit
% 0.67/0.51 % (981264)Termination phase: Property scanning
% 0.67/0.51 % (981264)Time elapsed: 0.013 s
% 0.67/0.51 % (981264)Peak memory usage: 10 MB
% 0.67/0.51 % (981264)Instructions burned: 29 (million)
% 0.67/0.51 % (981270)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.67/0.51 % (981244)Instruction limit reached!
% 0.67/0.51 % (981244)------------------------------
% 0.67/0.51 % (981244)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.51 % (981244)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.51 % (981244)CaDiCaL version: 2.1.3
% 0.67/0.51 % (981244)Termination reason: Instruction limit
% 0.67/0.51 % (981244)Termination phase: Saturation
% 0.67/0.51 % (981244)Time elapsed: 0.057 s
% 0.67/0.51 % (981244)Peak memory usage: 13 MB
% 0.67/0.51 % (981244)Instructions burned: 87 (million)
% 0.67/0.51 % (981270)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=306956441:i=2:add=on:rtra=on_2998 on theBenchmark for (2998ds/2Mi)
% 0.67/0.51 % (981268)lrs+10_1_si=on:cs=on:random_seed=2949226945:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.67/0.51 % (981270)Instruction limit reached!
% 0.67/0.51 % (981270)------------------------------
% 0.67/0.51 % (981270)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.51 % (981270)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.51 % (981270)CaDiCaL version: 2.1.3
% 0.67/0.51 % (981270)Termination reason: Instruction limit
% 0.67/0.51 % (981270)Termination phase: shuffling
% 0.67/0.51 % (981270)Time elapsed: 0.002 s
% 0.67/0.51 % (981270)Peak memory usage: 10 MB
% 0.67/0.51 % (981270)Instructions burned: 4 (million)
% 0.67/0.51 % (981268)Instruction limit reached!
% 0.67/0.51 % (981268)------------------------------
% 0.67/0.51 % (981268)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.51 % (981268)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.51 % (981268)CaDiCaL version: 2.1.3
% 0.67/0.51 % (981268)Termination reason: Instruction limit
% 0.67/0.51 % (981268)Termination phase: shuffling
% 0.67/0.51 % (981268)Time elapsed: 0.004 s
% 0.67/0.51 % (981268)Peak memory usage: 10 MB
% 0.67/0.51 % (981268)Instructions burned: 9 (million)
% 0.67/0.51 % (981271)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=2618329063:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 0.67/0.51 % (981273)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=523685940:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 0.67/0.51 % (981275)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=436187828:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 0.67/0.51 % (981277)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=1206345870:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.67/0.51 % (981271)Refutation not found, incomplete strategy
% 0.67/0.51 % (981271)------------------------------
% 0.67/0.51 % (981271)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.51 % (981271)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.51 % (981271)CaDiCaL version: 2.1.3
% 0.67/0.51 % (981271)Termination reason: Refutation not found, incomplete strategy
% 0.67/0.51 % (981271)Time elapsed: 0.013 s
% 0.67/0.51 % (981271)Peak memory usage: 13 MB
% 0.67/0.51 % (981271)Instructions burned: 25 (million)
% 0.67/0.51 % (981271)------------------------------
% 0.67/0.51 % (981271)------------------------------
% 0.67/0.51 % (981278)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=3681159159:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 0.67/0.51 % (981266)Instruction limit reached!
% 0.67/0.51 % (981266)------------------------------
% 0.67/0.51 % (981266)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.67/0.51 % (981266)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.67/0.51 % (981266)CaDiCaL version: 2.1.3
% 0.67/0.51 % (981266)Termination reason: Instruction limit
% 1.57/0.56 % (981266)Termination phase: Saturation
% 1.57/0.56 % (981266)Time elapsed: 0.039 s
% 1.57/0.56 % (981266)Peak memory usage: 14 MB
% 1.57/0.56 % (981266)Instructions burned: 88 (million)
% 1.57/0.56 % (981277)Instruction limit reached!
% 1.57/0.56 % (981277)------------------------------
% 1.57/0.56 % (981277)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.57/0.56 % (981277)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.57/0.56 % (981277)CaDiCaL version: 2.1.3
% 1.57/0.56 % (981277)Termination reason: Instruction limit
% 1.57/0.56 % (981277)Termination phase: Property scanning
% 1.57/0.56 % (981277)Time elapsed: 0.009 s
% 1.57/0.56 % (981277)Peak memory usage: 10 MB
% 1.57/0.56 % (981277)Instructions burned: 15 (million)
% 1.57/0.56 % (981275)Instruction limit reached!
% 1.57/0.56 % (981275)------------------------------
% 1.57/0.56 % (981275)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.57/0.56 % (981275)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.57/0.56 % (981275)CaDiCaL version: 2.1.3
% 1.57/0.56 % (981275)Termination reason: Instruction limit
% 1.57/0.57 % (981275)Termination phase: Preprocessing 3
% 1.57/0.57 % (981275)Time elapsed: 0.015 s
% 1.57/0.57 % (981275)Peak memory usage: 11 MB
% 1.57/0.57 % (981275)Instructions burned: 27 (million)
% 1.57/0.57 % (981284)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=4004625960:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 1.57/0.57 % (981285)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=947989148:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2998 on theBenchmark for (2998ds/2Mi)
% 1.57/0.57 % (981285)Instruction limit reached!
% 1.57/0.57 % (981285)------------------------------
% 1.57/0.57 % (981285)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.57/0.57 % (981285)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.57/0.57 % (981285)CaDiCaL version: 2.1.3
% 1.57/0.57 % (981285)Termination reason: Instruction limit
% 1.57/0.57 % (981285)Termination phase: shuffling
% 1.57/0.57 % (981285)Time elapsed: 0.002 s
% 1.57/0.57 % (981285)Peak memory usage: 10 MB
% 1.57/0.57 % (981285)Instructions burned: 3 (million)
% 1.57/0.57 % (981284)Instruction limit reached!
% 1.57/0.57 % (981284)------------------------------
% 1.57/0.57 % (981284)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.57/0.57 % (981284)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.57/0.57 % (981284)CaDiCaL version: 2.1.3
% 1.57/0.57 % (981284)Termination reason: Instruction limit
% 1.57/0.57 % (981284)Termination phase: Property scanning
% 1.57/0.57 % (981284)Time elapsed: 0.007 s
% 1.57/0.57 % (981284)Peak memory usage: 10 MB
% 1.57/0.57 % (981284)Instructions burned: 15 (million)
% 1.57/0.57 % (981287)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=4203533570:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.57/0.57 % (981286)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=1195698352:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.57/0.57 % (981287)Instruction limit reached!
% 1.57/0.57 % (981287)------------------------------
% 1.57/0.57 % (981287)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.57/0.57 % (981287)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.57/0.57 % (981287)CaDiCaL version: 2.1.3
% 1.57/0.57 % (981287)Termination reason: Instruction limit
% 1.57/0.57 % (981287)Termination phase: Preprocessing 3
% 1.57/0.57 % (981287)Time elapsed: 0.011 s
% 1.57/0.57 % (981287)Peak memory usage: 10 MB
% 1.57/0.57 % (981287)Instructions burned: 25 (million)
% 1.57/0.57 % (981290)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=1526489831:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 1.57/0.57 % (981286)Instruction limit reached!
% 1.57/0.57 % (981286)------------------------------
% 1.57/0.57 % (981286)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.57/0.57 % (981286)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.57/0.57 % (981286)CaDiCaL version: 2.1.3
% 1.57/0.57 % (981286)Termination reason: Instruction limit
% 1.57/0.57 % (981286)Termination phase: Property scanning
% 1.57/0.57 % (981286)Time elapsed: 0.011 s
% 2.22/0.63 % (981286)Peak memory usage: 10 MB
% 2.22/0.63 % (981286)Instructions burned: 26 (million)
% 2.22/0.63 % (981294)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 2.22/0.63 % (981294)lrs+1010_4:1_slsqr=8,1:to=kbo:cha=on:drc=off:si=on:sp=arity:lcm=predicate:uwa=off:fd=preordered:gs=on:nwc=5:s2agt=32:slsqc=1:kmz=on:updr=off:chr=on:pe=on:slsq=on:random_seed=3711691189:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 2.22/0.63 % (981294)Instruction limit reached!
% 2.22/0.63 % (981294)------------------------------
% 2.22/0.63 % (981294)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.22/0.63 % (981294)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.22/0.63 % (981294)CaDiCaL version: 2.1.3
% 2.22/0.63 % (981294)Termination reason: Instruction limit
% 2.22/0.63 % (981294)Termination phase: shuffling
% 2.22/0.63 % (981294)Time elapsed: 0.004 s
% 2.22/0.63 % (981294)Peak memory usage: 10 MB
% 2.22/0.63 % (981294)Instructions burned: 8 (million)
% 2.22/0.63 % (981292)WARNING Broken Constraint: if sine_to_age_generality_threshold(10) 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
% 2.22/0.63 % (981292)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 2.22/0.63 % (981296)dis+1004_50_to=lpo:drc=off:fde=unused:cnfonf=lazy_not_gen_be_off:si=on:sp=reverse_arity:spb=units:cbe=off:foolp=on:random_seed=4088325317:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 2.22/0.63 % (981292)ott+21_1_to=kbo:sil=128000:cnfonf=lazy_gen:bsd=on:si=on:sp=const_frequency:lma=off:uwa=off:foolp=on:s2agt=10:lwlo=on:random_seed=3078599443:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 2.22/0.63 % (981290)Instruction limit reached!
% 2.22/0.63 % (981290)------------------------------
% 2.22/0.63 % (981290)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.22/0.63 % (981290)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.22/0.63 % (981290)CaDiCaL version: 2.1.3
% 2.22/0.63 % (981290)Termination reason: Instruction limit
% 2.22/0.63 % (981290)Termination phase: Saturation
% 2.22/0.63 % (981290)Time elapsed: 0.028 s
% 2.22/0.63 % (981290)Peak memory usage: 13 MB
% 2.22/0.63 % (981290)Instructions burned: 60 (million)
% 2.22/0.63 % (981292)Instruction limit reached!
% 2.22/0.63 % (981292)------------------------------
% 2.22/0.63 % (981292)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.22/0.63 % (981292)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.22/0.63 % (981292)CaDiCaL version: 2.1.3
% 2.22/0.63 % (981292)Termination reason: Instruction limit
% 2.22/0.63 % (981292)Termination phase: Property scanning
% 2.22/0.63 % (981292)Time elapsed: 0.007 s
% 2.22/0.63 % (981292)Peak memory usage: 10 MB
% 2.22/0.63 % (981292)Instructions burned: 16 (million)
% 2.22/0.63 % (981296)Instruction limit reached!
% 2.22/0.63 % (981296)------------------------------
% 2.22/0.63 % (981296)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.22/0.63 % (981296)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.22/0.63 % (981296)CaDiCaL version: 2.1.3
% 2.22/0.63 % (981296)Termination reason: Instruction limit
% 2.22/0.63 % (981296)Termination phase: Property scanning
% 2.22/0.63 % (981296)Time elapsed: 0.013 s
% 2.22/0.63 % (981296)Peak memory usage: 10 MB
% 2.22/0.63 % (981296)Instructions burned: 31 (million)
% 2.22/0.63 % (981298)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=3901637129:i=7:hud=5:bd=preordered:rtra=on:bet=on_2997 on theBenchmark for (2997ds/7Mi)
% 2.22/0.63 % (981298)Instruction limit reached!
% 2.22/0.63 % (981298)------------------------------
% 2.22/0.63 % (981298)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.22/0.63 % (981298)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.22/0.63 % (981298)CaDiCaL version: 2.1.3
% 2.22/0.63 % (981298)Termination reason: Instruction limit
% 2.22/0.63 % (981298)Termination phase: shuffling
% 2.22/0.63 % (981298)Time elapsed: 0.004 s
% 2.22/0.63 % (981298)Peak memory usage: 10 MB
% 2.22/0.63 % (981298)Instructions burned: 7 (million)
% 2.22/0.63 % (981301)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=2405633497:i=23:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/23Mi)
% 2.70/0.70 % (981303)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=2304145024:i=1240:rtra=on:ixr=off_2997 on theBenchmark for (2997ds/1240Mi)
% 2.70/0.70 % (981302)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=1784339352:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2997 on theBenchmark for (2997ds/20Mi)
% 2.70/0.70 % (981301)Instruction limit reached!
% 2.70/0.70 % (981301)------------------------------
% 2.70/0.70 % (981301)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.70/0.70 % (981301)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.70/0.70 % (981301)CaDiCaL version: 2.1.3
% 2.70/0.70 % (981301)Termination reason: Instruction limit
% 2.70/0.70 % (981301)Termination phase: Property scanning
% 2.70/0.70 % (981301)Time elapsed: 0.010 s
% 2.70/0.70 % (981301)Peak memory usage: 10 MB
% 2.70/0.70 % (981301)Instructions burned: 24 (million)
% 2.70/0.70 % (981273)Instruction limit reached!
% 2.70/0.70 % (981273)------------------------------
% 2.70/0.70 % (981273)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.70/0.70 % (981273)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.70/0.70 % (981273)CaDiCaL version: 2.1.3
% 2.70/0.70 % (981273)Termination reason: Instruction limit
% 2.70/0.70 % (981273)Termination phase: Saturation
% 2.70/0.70 % (981273)Time elapsed: 0.119 s
% 2.70/0.70 % (981273)Peak memory usage: 14 MB
% 2.70/0.70 % (981273)Instructions burned: 251 (million)
% 2.70/0.70 % (981305)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=2478560505:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2997 on theBenchmark for (2997ds/143Mi)
% 2.70/0.70 % (981302)Instruction limit reached!
% 2.70/0.70 % (981302)------------------------------
% 2.70/0.70 % (981302)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.70/0.70 % (981302)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.70/0.70 % (981302)CaDiCaL version: 2.1.3
% 2.70/0.70 % (981302)Termination reason: Instruction limit
% 2.70/0.70 % (981302)Termination phase: SInE selection
% 2.70/0.70 % (981302)Time elapsed: 0.012 s
% 2.70/0.70 % (981302)Peak memory usage: 10 MB
% 2.70/0.70 % (981302)Instructions burned: 22 (million)
% 2.70/0.70 % (981309)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=2142816592:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/193Mi)
% 2.70/0.70 % (981310)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=665224715:i=42:hud=10:rtra=on_2997 on theBenchmark for (2997ds/42Mi)
% 2.70/0.70 % (981312)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 2.70/0.70 % (981278)Instruction limit reached!
% 2.70/0.70 % (981278)------------------------------
% 2.70/0.70 % (981278)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.70/0.70 % (981278)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.70/0.70 % (981278)CaDiCaL version: 2.1.3
% 2.70/0.70 % (981278)Termination reason: Instruction limit
% 2.70/0.70 % (981278)Termination phase: Saturation
% 2.70/0.70 % (981278)Time elapsed: 0.135 s
% 2.70/0.70 % (981278)Peak memory usage: 14 MB
% 2.70/0.70 % (981278)Instructions burned: 328 (million)
% 2.70/0.70 % (981312)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=157442020:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2997 on theBenchmark for (2997ds/7Mi)
% 2.70/0.70 % (981312)Instruction limit reached!
% 2.70/0.70 % (981312)------------------------------
% 2.70/0.70 % (981312)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.70/0.70 % (981312)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.70/0.70 % (981312)CaDiCaL version: 2.1.3
% 2.70/0.70 % (981312)Termination reason: Instruction limit
% 2.70/0.70 % (981312)Termination phase: shuffling
% 2.70/0.70 % (981312)Time elapsed: 0.004 s
% 2.70/0.70 % (981312)Peak memory usage: 10 MB
% 2.70/0.70 % (981312)Instructions burned: 8 (million)
% 2.70/0.70 % (981315)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=1261345018:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/181Mi)
% 2.70/0.70 % (981310)Instruction limit reached!
% 2.70/0.70 % (981310)------------------------------
% 2.70/0.70 % (981310)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.70/0.71 % (981310)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.70/0.71 % (981310)CaDiCaL version: 2.1.3
% 2.70/0.71 % (981310)Termination reason: Instruction limit
% 2.70/0.71 % (981310)Termination phase: Saturation
% 2.70/0.71 % (981310)Time elapsed: 0.025 s
% 2.70/0.71 % (981310)Peak memory usage: 12 MB
% 2.70/0.71 % (981310)Instructions burned: 42 (million)
% 2.70/0.71 % (981317)dis+10_8_sil=128000:plsq=on:plsqc=1:si=on:sp=unary_first:sos=on:lma=off:plsqr=64,1:uwa=interpreted_only:foolp=on:random_seed=101801136:st=3:avsq=on:i=169:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2997 on theBenchmark for (2997ds/169Mi)
% 2.70/0.71 % (981319)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 2.70/0.71 % (981315)Refutation not found, incomplete strategy
% 2.70/0.71 % (981315)------------------------------
% 2.70/0.71 % (981315)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.70/0.71 % (981315)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.70/0.71 % (981315)CaDiCaL version: 2.1.3
% 2.70/0.71 % (981315)Termination reason: Refutation not found, incomplete strategy
% 2.70/0.71 % (981315)Time elapsed: 0.029 s
% 2.70/0.71 % (981315)Peak memory usage: 13 MB
% 2.70/0.71 % (981315)Instructions burned: 25 (million)
% 2.70/0.71 % (981315)------------------------------
% 2.70/0.71 % (981315)------------------------------
% 2.70/0.71 % (981319)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=3542593558:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2996 on theBenchmark for (2996ds/6Mi)
% 2.70/0.71 % (981305)Instruction limit reached!
% 2.70/0.71 % (981305)------------------------------
% 2.70/0.71 % (981305)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.70/0.71 % (981305)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.70/0.71 % (981305)CaDiCaL version: 2.1.3
% 2.70/0.71 % (981305)Termination reason: Instruction limit
% 2.70/0.71 % (981305)Termination phase: Saturation
% 2.70/0.71 % (981305)Time elapsed: 0.078 s
% 2.70/0.71 % (981305)Peak memory usage: 14 MB
% 2.70/0.71 % (981305)Instructions burned: 143 (million)
% 2.70/0.71 % (981319)Instruction limit reached!
% 2.70/0.71 % (981319)------------------------------
% 2.70/0.71 % (981319)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.70/0.71 % (981319)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.70/0.71 % (981319)CaDiCaL version: 2.1.3
% 2.70/0.71 % (981319)Termination reason: Instruction limit
% 2.70/0.71 % (981319)Termination phase: shuffling
% 2.70/0.71 % (981319)Time elapsed: 0.006 s
% 2.70/0.71 % (981319)Peak memory usage: 10 MB
% 2.70/0.71 % (981319)Instructions burned: 7 (million)
% 2.70/0.71 % (981309)Instruction limit reached!
% 2.70/0.71 % (981309)------------------------------
% 2.70/0.71 % (981309)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.70/0.71 % (981309)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.70/0.71 % (981309)CaDiCaL version: 2.1.3
% 2.70/0.71 % (981309)Termination reason: Instruction limit
% 2.70/0.71 % (981309)Termination phase: Saturation
% 2.70/0.71 % (981309)Time elapsed: 0.081 s
% 2.70/0.71 % (981309)Peak memory usage: 14 MB
% 2.70/0.71 % (981309)Instructions burned: 195 (million)
% 2.70/0.71 % (981323)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=3546945490:i=19:add=on:rtra=on_2996 on theBenchmark for (2996ds/19Mi)
% 2.70/0.71 % (981324)ott+10_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:lma=off:plsqr=128,1:urr=ec_only:uwa=off:rp=on:nwc=20:br=off:random_seed=614181632:i=316:bs=unit_only:ins=25:rtra=on:ntd=on_2996 on theBenchmark for (2996ds/316Mi)
% 2.70/0.71 % (981321)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=4232450861:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2996 on theBenchmark for (2996ds/22Mi)
% 2.70/0.71 % (981323)Instruction limit reached!
% 2.70/0.71 % (981323)------------------------------
% 2.70/0.71 % (981323)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.70/0.71 % (981323)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.70/0.71 % (981323)CaDiCaL version: 2.1.3
% 2.70/0.71 % (981323)Termination reason: Instruction limit
% 2.70/0.71 % (981323)Termination phase: Property scanning
% 2.70/0.71 % (981323)Time elapsed: 0.008 s
% 2.70/0.71 % (981323)Peak memory usage: 10 MB
% 2.70/0.71 % (981323)Instructions burned: 20 (million)
% 2.70/0.71 % (981321)Instruction limit reached!
% 2.70/0.71 % (981321)------------------------------
% 2.70/0.71 % (981321)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.70/0.71 % (981321)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.70/0.71 % (981321)CaDiCaL version: 2.1.3
% 2.70/0.71 % (981321)Termination reason: Instruction limit
% 2.70/0.71 % (981321)Termination phase: Preprocessing 3
% 2.70/0.71 % (981321)Time elapsed: 0.010 s
% 2.70/0.71 % (981321)Peak memory usage: 10 MB
% 2.70/0.71 % (981321)Instructions burned: 24 (million)
% 2.70/0.71 % (981325)dis+1004_4:1_slsqr=1,2:to=lpo:plsq=on:fde=unused:e2e=on:si=on:spb=goal_then_units:acc=on:urr=on:uwa=off:fd=preordered:s2agt=16:slsqc=1:slsq=on:random_seed=2086425026:hsq=on:hsqr=16,1:s2a=on:i=853:add=off:bd=all:nm=64:rtra=on:gtg=position:c=on:ntd=on_2996 on theBenchmark for (2996ds/853Mi)
% 2.70/0.71 % (981329)dis+1003_3:4_to=kbo:plsq=on:prc=on:sims=off:e2e=on:si=on:spb=intro:acc=on:urr=on:uwa=off:foolp=on:s2agt=32:slsqc=3:slsq=on:random_seed=3821747246:hsq=on:hsqr=16,1:s2a=on:i=45:erml=3:slsql=off:rtra=on:gtg=exists_top:er=filter:ntd=on_2996 on theBenchmark for (2996ds/45Mi)
% 2.70/0.71 % (981303) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-981239-981303"...
% 2.70/0.71 % (981330)lrs+1002_1_sil=128000:fde=unused:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=3247428210:i=480:rtra=on_2996 on theBenchmark for (2996ds/480Mi)
% 2.70/0.71 % (981329)Instruction limit reached!
% 2.70/0.71 % (981329)------------------------------
% 2.70/0.71 % (981329)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.70/0.71 % (981329)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.70/0.71 % (981329)CaDiCaL version: 2.1.3
% 2.70/0.71 % (981329)Termination reason: Instruction limit
% 2.70/0.71 % (981329)Termination phase: Saturation
% 2.70/0.71 % (981329)Time elapsed: 0.020 s
% 2.70/0.71 % (981329)Peak memory usage: 12 MB
% 2.70/0.71 % (981329)Instructions burned: 45 (million)
% 2.70/0.71 % (981317)Instruction limit reached!
% 2.70/0.71 % (981317)------------------------------
% 2.70/0.71 % (981317)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.70/0.71 % (981317)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.70/0.71 % (981317)CaDiCaL version: 2.1.3
% 2.70/0.71 % (981317)Termination reason: Instruction limit
% 2.70/0.71 % (981317)Termination phase: Saturation
% 2.70/0.71 % (981317)Time elapsed: 0.096 s
% 2.70/0.71 % (981317)Peak memory usage: 13 MB
% 2.70/0.71 % (981317)Instructions burned: 169 (million)
% 2.70/0.71 % (981330)Refutation not found, incomplete strategy
% 2.70/0.71 % (981330)------------------------------
% 2.70/0.71 % (981330)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.70/0.71 % (981330)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.70/0.71 % (981330)CaDiCaL version: 2.1.3
% 2.70/0.71 % (981330)Termination reason: Refutation not found, incomplete strategy
% 2.70/0.71 % (981330)Time elapsed: 0.020 s
% 2.70/0.71 % (981330)Peak memory usage: 12 MB
% 2.70/0.71 % (981330)Instructions burned: 39 (million)
% 2.70/0.71 % (981330)------------------------------
% 2.70/0.71 % (981330)------------------------------
% 2.70/0.71 % (981325) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-981239-981325"...
% 2.70/0.71 % (981335)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 2.70/0.71 % (981334)dis+1010_40_sil=128000:si=on:uwa=off:nwc=1:sac=on:chr=on:avsqc=3:random_seed=3577220054:avsq=on:i=21:avsqr=8,1:kws=frequency:fgj=on:bd=all:rtra=on:fe=axiom:ntd=on_2995 on theBenchmark for (2995ds/21Mi)
% 2.70/0.71 % (981335)ott+1002_3_si=on:sp=weighted_frequency:spb=goal:cbe=off:slsqc=2:random_seed=3201435839:cts=off:uwa_fpi=on:i=200:av=off:fsr=off:rtra=on:ntd=on_2995 on theBenchmark for (2995ds/200Mi)
% 2.70/0.71 % (981334)Instruction limit reached!
% 2.70/0.71 % (981334)------------------------------
% 2.70/0.71 % (981334)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.70/0.71 % (981334)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.70/0.71 % (981334)CaDiCaL version: 2.1.3
% 2.70/0.71 % (981334)Termination reason: Instruction limit
% 2.70/0.71 % (981334)Termination phase: Preprocessing 3
% 2.70/0.71 % (981334)Time elapsed: 0.010 s
% 2.70/0.71 % (981334)Peak memory usage: 10 MB
% 2.70/0.71 % (981334)Instructions burned: 23 (million)
% 2.70/0.71 % (981336)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=969569754:s2a=on:i=13:kws=inv_frequency:bd=all:rtra=on_2995 on theBenchmark for (2995ds/13Mi)
% 2.70/0.71 % (981325)...printing done.
% 2.70/0.71 % (981325)Refutation found. Thanks to Tanya!
% 2.70/0.71 % SZS status Theorem for theBenchmark
% 2.70/0.71 % SZS output start Proof for theBenchmark
% 2.70/0.71 thf(type_def_5, type, unsorted: $tType).
% 2.70/0.71 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 2.70/0.71 thf(type_def_7, type, d_unsorted: $tType).
% 2.70/0.71 thf(func_def_0, type, subrel: (($i > $i > $o) > ($i > $i > $o) > $o)).
% 2.70/0.71 thf(func_def_1, type, inv: (($i > $i > $o) > $i > $i > $o)).
% 2.70/0.71 thf(func_def_2, type, idem: ((($i > $i > $o) > $i > $i > $o) > $o)).
% 2.70/0.71 thf(func_def_3, type, infl: ((($i > $i > $o) > $i > $i > $o) > $o)).
% 2.70/0.71 thf(func_def_4, type, mono: ((($i > $i > $o) > $i > $i > $o) > $o)).
% 2.70/0.71 thf(func_def_5, type, refl: (($i > $i > $o) > $o)).
% 2.70/0.71 thf(func_def_6, type, irrefl: (($i > $i > $o) > $o)).
% 2.70/0.71 thf(func_def_7, type, rc: (($i > $i > $o) > $i > $i > $o)).
% 2.70/0.71 thf(func_def_8, type, symm: (($i > $i > $o) > $o)).
% 2.70/0.71 thf(func_def_9, type, antisymm: (($i > $i > $o) > $o)).
% 2.70/0.71 thf(func_def_10, type, asymm: (($i > $i > $o) > $o)).
% 2.70/0.71 thf(func_def_11, type, sc: (($i > $i > $o) > $i > $i > $o)).
% 2.70/0.71 thf(func_def_12, type, trans: (($i > $i > $o) > $o)).
% 2.70/0.71 thf(func_def_13, type, tc: (($i > $i > $o) > $i > $i > $o)).
% 2.70/0.71 thf(func_def_14, type, trc: (($i > $i > $o) > $i > $i > $o)).
% 2.70/0.71 thf(func_def_15, type, trsc: (($i > $i > $o) > $i > $i > $o)).
% 2.70/0.71 thf(func_def_16, type, po: (($i > $i > $o) > $o)).
% 2.70/0.71 thf(func_def_17, type, so: (($i > $i > $o) > $o)).
% 2.70/0.71 thf(func_def_18, type, total: (($i > $i > $o) > $o)).
% 2.70/0.71 thf(func_def_19, type, term: (($i > $i > $o) > $o)).
% 2.70/0.71 thf(func_def_20, type, ind: (($i > $i > $o) > $o)).
% 2.70/0.71 thf(func_def_21, type, innf: (($i > $i > $o) > $i > $o)).
% 2.70/0.71 thf(func_def_22, type, nfof: (($i > $i > $o) > $i > $i > $o)).
% 2.70/0.71 thf(func_def_23, type, norm: (($i > $i > $o) > $o)).
% 2.70/0.71 thf(func_def_24, type, join: (($i > $i > $o) > $i > $i > $o)).
% 2.70/0.71 thf(func_def_25, type, lconfl: (($i > $i > $o) > $o)).
% 2.70/0.71 thf(func_def_26, type, sconfl: (($i > $i > $o) > $o)).
% 2.70/0.71 thf(func_def_27, type, confl: (($i > $i > $o) > $o)).
% 2.70/0.71 thf(func_def_28, type, cr: (($i > $i > $o) > $o)).
% 2.70/0.71 thf(func_def_29, type, d2unsorted: (d_unsorted > $i)).
% 2.70/0.71 thf(func_def_30, type, d_unsorted_0: d_unsorted).
% 2.70/0.71 thf(func_def_32, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 2.70/0.71 thf(func_def_33, type, vOR: ($o > $o > $o)).
% 2.70/0.71 thf(func_def_34, type, vNOT: ($o > $o)).
% 2.70/0.71 thf(func_def_35, type, db1: !>[X0: $tType]:(X0)).
% 2.70/0.71 thf(func_def_36, type, db2: !>[X0: $tType]:(X0)).
% 2.70/0.71 thf(func_def_37, type, db0: !>[X0: $tType]:(X0)).
% 2.70/0.71 thf(func_def_38, type, db3: !>[X0: $tType]:(X0)).
% 2.70/0.71 thf(func_def_39, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 2.70/0.71 thf(func_def_40, type, db5: !>[X0: $tType]:(X0)).
% 2.70/0.71 thf(func_def_41, type, db4: !>[X0: $tType]:(X0)).
% 2.70/0.71 thf(func_def_42, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 2.70/0.71 thf(func_def_43, type, db7: !>[X0: $tType]:(X0)).
% 2.70/0.71 thf(func_def_44, type, vAND: ($o > $o > $o)).
% 2.70/0.71 thf(func_def_45, type, db8: !>[X0: $tType]:(X0)).
% 2.70/0.71 thf(func_def_46, type, db9: !>[X0: $tType]:(X0)).
% 2.70/0.71 thf(func_def_47, type, db6: !>[X0: $tType]:(X0)).
% 2.70/0.71 thf(func_def_48, type, sK0: ($i > d_unsorted)).
% 2.70/0.71 thf(func_def_52, type, sK2: ($i > $i > $o)).
% 2.70/0.71 thf(func_def_56, type, sK6: ($i > $i)).
% 2.70/0.71 thf(func_def_57, type, sK7: (($i > $i > $o) > ($i > $i > $o) > $i)).
% 2.70/0.71 thf(func_def_58, type, sK8: (($i > $i > $o) > $i)).
% 2.70/0.71 thf(func_def_59, type, sK9: (($i > $i > $o) > $i)).
% 2.70/0.71 thf(func_def_60, type, sK10: (($i > $i > $o) > ($i > $i > $o) > $i)).
% 2.70/0.71 thf(func_def_61, type, sK11: (($i > $i > $o) > $i)).
% 2.70/0.71 thf(func_def_62, type, sK12: (($i > $i > $o) > $i)).
% 2.70/0.71 thf(func_def_63, type, sK13: ($i > ($i > $i > $o) > $i > $i > $i > $o)).
% 2.70/0.71 thf(func_def_64, type, sK14: ($i > $i > $o)).
% 2.70/0.71 thf(func_def_65, type, sK15: (($i > $i > $o) > $i)).
% 2.70/0.71 thf(func_def_66, type, sK16: (($i > $i > $o) > ($i > $i > $o) > $i)).
% 2.70/0.71 thf(func_def_67, type, sK17: (($i > $i > $o) > ($i > $i > $o) > $i)).
% 2.70/0.71 thf(func_def_68, type, sK18: (($i > $i > $o) > $i)).
% 2.70/0.71 thf(func_def_69, type, sK19: (($i > $i > $o) > $i)).
% 2.70/0.71 thf(func_def_70, type, sK20: (($i > $i > $o) > ($i > $i > $o) > $i)).
% 2.70/0.71 thf(func_def_71, type, sK21: (($i > $i > $o) > ($i > $i > $o) > $i)).
% 2.70/0.71 thf(func_def_72, type, sK22: (($i > $i > $o) > $i)).
% 2.70/0.71 thf(func_def_73, type, sK23: (($i > $i > $o) > $i)).
% 2.70/0.71 thf(func_def_74, type, sK24: (($i > $i > $o) > $i)).
% 2.70/0.71 thf(func_def_75, type, sK25: (($i > $i > $o) > $i)).
% 2.70/0.71 thf(func_def_76, type, sK26: (($i > $i > $o) > $i)).
% 2.70/0.71 thf(func_def_77, type, sK27: (($i > $i > $o) > $i)).
% 2.70/0.71 thf(func_def_78, type, sK28: (($i > $i > $o) > $i)).
% 2.70/0.71 thf(func_def_79, type, sK29: ($i > ($i > $i > $o) > $i > $i > $i > $o)).
% 2.70/0.71 thf(func_def_80, type, sK30: ($i > ($i > $i > $o) > $i > $i > $i > $o)).
% 2.70/0.71 thf(func_def_83, type, sK33: ($i > $i > $o)).
% 2.70/0.71 thf(func_def_84, type, sK34: ($i > $i > $o)).
% 2.70/0.71 thf(func_def_85, type, sK35: (($i > $i > $o) > $i)).
% 2.70/0.71 thf(func_def_86, type, sK36: (($i > $i > $o) > $i)).
% 2.70/0.71 thf(func_def_87, type, sK37: (($i > $i > $o) > $i)).
% 2.70/0.71 thf(func_def_88, type, sK38: (($i > $i > $o) > $i)).
% 2.70/0.71 thf(func_def_89, type, sK39: (($i > $i > $o) > $i)).
% 2.70/0.71 thf(func_def_90, type, sK40: (($i > $i > $o) > $i)).
% 2.70/0.71 thf(func_def_91, type, sK41: (($i > $i > $o) > $i)).
% 2.70/0.71 thf(func_def_92, type, sK42: (($i > $i > $o) > $i)).
% 2.70/0.71 thf(func_def_93, type, sK43: (($i > $i > $o) > $i)).
% 2.70/0.71 thf(func_def_94, type, sK44: (($i > $i > $o) > $i)).
% 2.70/0.71 thf(func_def_95, type, sK45: (($i > $i > $o) > $i)).
% 2.70/0.71 thf(func_def_96, type, sK46: (($i > $i > $o) > $i)).
% 2.70/0.71 thf(f1,axiom,(
% 2.70/0.71 (sc = (^[X4 : ($i > $i > $o), X6 : $i, X7 : $i] : ((X4 @ X7 @ X6) | (X4 @ X6 @ X7)))) & ((^[X4 : ($i > $i > $o)] : (! [X19 : $i,X18 : ($i > $o)] : (~(X18 @ X19) | ~ ! [X6 : $i] : (~ ! [X7 : $i] : (~(X18 @ X7) | ~(X4 @ X6 @ X7)) | ~(X18 @ X6))))) = term) & (mono = (^[X8 : (($i > $i > $o) > $i > $i > $o)] : (! [X10 : $i,X5 : ($i > $i > $o),X4 : ($i > $i > $o),X9 : $i] : (~(X8 @ X4 @ X9 @ X10) | ~ ! [X6 : $i,X7 : $i] : ((X5 @ X6 @ X7) | ~(X4 @ X6 @ X7)) | (X8 @ X5 @ X9 @ X10))))) & (trsc = (^[X4 : ($i > $i > $o), X16 : $i, X17 : $i] : ((X16 = X17) | ! [X5 : ($i > $i > $o)] : (~ ! [X13 : $i,X11 : $i,X12 : $i] : (~(X5 @ X12 @ X13) | (X5 @ X12 @ X11) | ~(X5 @ X13 @ X11)) | (X5 @ X17 @ X16) | ~ ! [X15 : $i,X14 : $i] : (~(X4 @ X14 @ X15) | (X5 @ X14 @ X15))) | ! [X5 : ($i > $i > $o)] : (~ ! [X15 : $i,X14 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | ~ ! [X11 : $i,X13 : $i,X12 : $i] : ((X5 @ X12 @ X11) | ~(X5 @ X13 @ X11) | ~(X5 @ X12 @ X13)) | (X5 @ X16 @ X17))))) & ((^[X4 : ($i > $i > $o), X6 : $i] : (! [X7 : $i] : ~(X4 @ X6 @ X7))) = innf) & ((^[X4 : ($i > $i > $o)] : (! [X6 : $i,X7 : $i] : (~(X4 @ X6 @ X7) | ~(X4 @ X7 @ X6)))) = asymm) & ((^[X4 : ($i > $i > $o)] : (! [X7 : $i,X6 : $i] : (~(X4 @ X7 @ X6) | ~(X4 @ X6 @ X7)) & ! [X7 : $i,X6 : $i,X11 : $i] : (~(X4 @ X6 @ X7) | ~(X4 @ X7 @ X11) | (X4 @ X6 @ X11)))) = so) & (ind = (^[X4 : ($i > $i > $o)] : (! [X21 : $i,X20 : ($i > $o)] : ((X20 @ X21) | ~ ! [X6 : $i] : (~ ! [X7 : $i] : ((X20 @ X7) | ~ ! [X5 : ($i > $i > $o)] : (~ ! [X13 : $i,X12 : $i,X11 : $i] : ((X5 @ X12 @ X11) | ~(X5 @ X13 @ X11) | ~(X5 @ X12 @ X13)) | (X5 @ X6 @ X7) | ~ ! [X14 : $i,X15 : $i] : (~(X4 @ X14 @ X15) | (X5 @ X14 @ X15)))) | (X20 @ X6)))))) & (antisymm = (^[X4 : ($i > $i > $o)] : (! [X6 : $i,X7 : $i] : (~(X4 @ X6 @ X7) | ~(X4 @ X7 @ X6) | (X6 = X7))))) & (trc = (^[X4 : ($i > $i > $o), X16 : $i, X17 : $i] : ((X16 = X17) | ! [X5 : ($i > $i > $o)] : (~ ! [X15 : $i,X14 : $i] : (~(X4 @ X14 @ X15) | (X5 @ X14 @ X15)) | ~ ! [X12 : $i,X13 : $i,X11 : $i] : (~(X5 @ X13 @ X11) | ~(X5 @ X12 @ X13) | (X5 @ X12 @ X11)) | (X5 @ X16 @ X17))))) & (join = (^[X4 : ($i > $i > $o), X6 : $i, X7 : $i] : (~((X6 != X7) & ! [X27 : $i] : (~ ! [X5 : ($i > $i > $o)] : (~ ! [X15 : $i,X14 : $i] : (~(X4 @ X14 @ X15) | (X5 @ X14 @ X15)) | ~ ! [X13 : $i,X26 : $i,X12 : $i] : (~(X5 @ X12 @ X13) | (X5 @ X12 @ X26) | ~(X5 @ X13 @ X26)) | (X5 @ X6 @ X27)) | ~ ! [X5 : ($i > $i > $o)] : (~ ! [X25 : $i,X13 : $i,X12 : $i] : (~(X5 @ X12 @ X13) | ~(X5 @ X13 @ X25) | (X5 @ X12 @ X25)) | (X5 @ X7 @ X27) | ~ ! [X14 : $i,X15 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)))) & ~ ! [X5 : ($i > $i > $o)] : (~ ! [X15 : $i,X14 : $i] : (~(X4 @ X14 @ X15) | (X5 @ X14 @ X15)) | (X5 @ X7 @ X6) | ~ ! [X13 : $i,X12 : $i,X25 : $i] : (~(X5 @ X13 @ X25) | (X5 @ X12 @ X25) | ~(X5 @ X12 @ X13))) & ~ ! [X5 : ($i > $i > $o)] : (~ ! [X13 : $i,X26 : $i,X12 : $i] : (~(X5 @ X13 @ X26) | ~(X5 @ X12 @ X13) | (X5 @ X12 @ X26)) | ~ ! [X14 : $i,X15 : $i] : (~(X4 @ X14 @ X15) | (X5 @ X14 @ X15)) | (X5 @ X6 @ X7)))))) & (inv = (^[X4 : ($i > $i > $o), X6 : $i, X7 : $i] : ((X4 @ X7 @ X6)))) & ! [X0 : $i] : ? [X1 : d_unsorted] : (X0 = ((d2unsorted @ X1))) & (nfof = (^[X4 : ($i > $i > $o), X6 : $i, X7 : $i] : (! [X22 : $i] : ~(X4 @ X6 @ X22) & (! [X5 : ($i > $i > $o)] : ((X5 @ X7 @ X6) | ~ ! [X14 : $i,X15 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | ~ ! [X11 : $i,X13 : $i,X12 : $i] : ((X5 @ X12 @ X11) | ~(X5 @ X12 @ X13) | ~(X5 @ X13 @ X11))) | (X6 = X7))))) & ((^[X4 : ($i > $i > $o)] : (! [X37 : ($i > $i > $o),X36 : ($i > $i > $o),X6 : $i,X7 : $i] : (~ ! [X13 : $i,X25 : $i,X12 : $i] : (~(X36 @ X13 @ X25) | ~(X36 @ X12 @ X13) | (X36 @ X12 @ X25)) | ~ ! [X13 : $i,X26 : $i,X12 : $i] : (~(X37 @ X13 @ X26) | (X37 @ X12 @ X26) | ~(X37 @ X12 @ X13)) | (~ ! [X5 : ($i > $i > $o)] : ((X5 @ X7 @ X6) | ~ ! [X13 : $i,X12 : $i,X11 : $i] : (~(X5 @ X13 @ X11) | ~(X5 @ X12 @ X13) | (X5 @ X12 @ X11)) | ~ ! [X15 : $i,X14 : $i] : (~(X4 @ X14 @ X15) | (X5 @ X14 @ X15))) & ~ ! [X5 : ($i > $i > $o)] : ((X5 @ X6 @ X7) | ~ ! [X11 : $i,X13 : $i,X12 : $i] : (~(X5 @ X13 @ X11) | ~(X5 @ X12 @ X13) | (X5 @ X12 @ X11)) | ~ ! [X15 : $i,X14 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15))) & (X6 != X7)) | ~ ! [X27 : $i] : (~ ! [X5 : ($i > $i > $o)] : ((X5 @ X7 @ X27) | ~ ! [X12 : $i,X13 : $i,X25 : $i] : (~(X5 @ X13 @ X25) | (X5 @ X12 @ X25) | ~(X5 @ X12 @ X13)) | ~ ! [X14 : $i,X15 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15))) | ~ ! [X5 : ($i > $i > $o)] : (~ ! [X14 : $i,X15 : $i] : (~(X4 @ X14 @ X15) | (X5 @ X14 @ X15)) | (X5 @ X6 @ X27) | ~ ! [X26 : $i,X13 : $i,X12 : $i] : (~(X5 @ X12 @ X13) | ~(X5 @ X13 @ X26) | (X5 @ X12 @ X26)))) | ~ ! [X15 : $i,X14 : $i] : ((X36 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | (X36 @ X7 @ X6) | (X37 @ X6 @ X7) | ~ ! [X14 : $i,X15 : $i] : (~(X4 @ X14 @ X15) | (X37 @ X14 @ X15)) | (X6 = X7)))) = cr) & ! [X1 : d_unsorted] : (X1 = d_unsorted_0) & ((^[X4 : ($i > $i > $o)] : (! [X7 : $i,X6 : $i,X11 : $i] : ((X4 @ X6 @ X11) | ~(X4 @ X6 @ X7) | ~(X4 @ X7 @ X11)) & ! [X6 : $i] : (X4 @ X6 @ X6) & ! [X7 : $i,X6 : $i] : (~(X4 @ X7 @ X6) | (X6 = X7) | ~(X4 @ X6 @ X7)))) = po) & ((^[X4 : ($i > $i > $o)] : (! [X11 : $i,X6 : $i,X33 : ($i > $i > $o),X7 : $i,X34 : ($i > $i > $o)] : (~ ! [X13 : $i,X12 : $i,X25 : $i] : (~(X33 @ X13 @ X25) | ~(X33 @ X12 @ X13) | (X33 @ X12 @ X25)) | ~ ! [X14 : $i,X15 : $i] : ((X34 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | ~ ! [X14 : $i,X15 : $i] : ((X33 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | (X34 @ X11 @ X7) | (X33 @ X7 @ X11) | ((X6 != X7) & ~ ! [X5 : ($i > $i > $o)] : ((X5 @ X6 @ X7) | ~ ! [X14 : $i,X15 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | ~ ! [X13 : $i,X12 : $i,X35 : $i] : (~(X5 @ X12 @ X13) | ~(X5 @ X13 @ X35) | (X5 @ X12 @ X35)))) | (X7 = X11) | ~ ! [X26 : $i,X12 : $i,X13 : $i] : (~(X34 @ X13 @ X26) | (X34 @ X12 @ X26) | ~(X34 @ X12 @ X13)) | ~ ! [X27 : $i] : (~ ! [X5 : ($i > $i > $o)] : (~ ! [X26 : $i,X12 : $i,X13 : $i] : (~(X5 @ X12 @ X13) | ~(X5 @ X13 @ X26) | (X5 @ X12 @ X26)) | ~ ! [X14 : $i,X15 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | (X5 @ X11 @ X27)) | ~ ! [X5 : ($i > $i > $o)] : ((X5 @ X7 @ X27) | ~ ! [X13 : $i,X25 : $i,X12 : $i] : (~(X5 @ X12 @ X13) | ~(X5 @ X13 @ X25) | (X5 @ X12 @ X25)) | ~ ! [X14 : $i,X15 : $i] : (~(X4 @ X14 @ X15) | (X5 @ X14 @ X15)))) | ((X6 != X11) & ~ ! [X5 : ($i > $i > $o)] : (~ ! [X14 : $i,X15 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | ~ ! [X26 : $i,X12 : $i,X13 : $i] : (~(X5 @ X13 @ X26) | (X5 @ X12 @ X26) | ~(X5 @ X12 @ X13)) | (X5 @ X6 @ X11)))))) = confl) & ((^[X4 : ($i > $i > $o)] : (! [X6 : $i] : (X4 @ X6 @ X6))) = refl) & ! [X2 : d_unsorted,X3 : d_unsorted] : ((((d2unsorted @ X2)) = ((d2unsorted @ X3))) => (X2 = X3)) & ((^[X4 : ($i > $i > $o)] : (! [X6 : $i,X7 : $i,X28 : ($i > $i > $o),X11 : $i,X29 : ($i > $i > $o)] : (~ ! [X27 : $i] : (~ ! [X5 : ($i > $i > $o)] : (~ ! [X15 : $i,X14 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | (X5 @ X7 @ X27) | ~ ! [X25 : $i,X13 : $i,X12 : $i] : ((X5 @ X12 @ X25) | ~(X5 @ X12 @ X13) | ~(X5 @ X13 @ X25))) | ~ ! [X5 : ($i > $i > $o)] : (~ ! [X15 : $i,X14 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | ~ ! [X12 : $i,X13 : $i,X26 : $i] : (~(X5 @ X12 @ X13) | (X5 @ X12 @ X26) | ~(X5 @ X13 @ X26)) | (X5 @ X11 @ X27))) | (X29 @ X11 @ X7) | ~ ! [X14 : $i,X15 : $i] : (~(X4 @ X14 @ X15) | (X29 @ X14 @ X15)) | ~ ! [X12 : $i,X25 : $i,X13 : $i] : (~(X28 @ X13 @ X25) | ~(X28 @ X12 @ X13) | (X28 @ X12 @ X25)) | ~(X4 @ X6 @ X11) | (X7 = X11) | ~(X4 @ X6 @ X7) | ~ ! [X13 : $i,X12 : $i,X26 : $i] : ((X29 @ X12 @ X26) | ~(X29 @ X12 @ X13) | ~(X29 @ X13 @ X26)) | (X28 @ X7 @ X11) | ~ ! [X15 : $i,X14 : $i] : ((X28 @ X14 @ X15) | ~(X4 @ X14 @ X15))))) = lconfl) & (rc = (^[X4 : ($i > $i > $o), X6 : $i, X7 : $i] : ((X4 @ X6 @ X7) | (X6 = X7)))) & ((^[X4 : ($i > $i > $o)] : (! [X6 : $i,X23 : $i] : (~(X4 @ X6 @ X23) | ~ ! [X24 : $i] : (~ ! [X5 : ($i > $i > $o)] : (~ ! [X14 : $i,X15 : $i] : ((X5 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | (X5 @ X6 @ X24) | ~ ! [X11 : $i,X13 : $i,X12 : $i] : (~(X5 @ X12 @ X13) | (X5 @ X12 @ X11) | ~(X5 @ X13 @ X11))) | ~ ! [X22 : $i] : ~(X4 @ X24 @ X22))))) = norm) & (subrel = (^[X4 : ($i > $i > $o), X5 : ($i > $i > $o)] : (! [X7 : $i,X6 : $i] : ((X5 @ X6 @ X7) | ~(X4 @ X6 @ X7))))) & ((^[X4 : ($i > $i > $o)] : (! [X7 : $i,X6 : $i] : ((X4 @ X7 @ X6) | ~(X4 @ X6 @ X7)))) = symm) & (irrefl = (^[X4 : ($i > $i > $o)] : (! [X6 : $i] : ~(X4 @ X6 @ X6)))) & ((^[X4 : ($i > $i > $o)] : (! [X7 : $i,X6 : $i] : ((X4 @ X7 @ X6) | (X4 @ X6 @ X7) | (X6 = X7)))) = total) & (tc = (^[X4 : ($i > $i > $o), X6 : $i, X7 : $i] : (! [X5 : ($i > $i > $o)] : (~ ! [X15 : $i,X14 : $i] : (~(X4 @ X14 @ X15) | (X5 @ X14 @ X15)) | (X5 @ X6 @ X7) | ~ ! [X13 : $i,X11 : $i,X12 : $i] : (~(X5 @ X13 @ X11) | ~(X5 @ X12 @ X13) | (X5 @ X12 @ X11)))))) & (idem = (^[X8 : (($i > $i > $o) > $i > $i > $o)] : (! [X4 : ($i > $i > $o)] : (((X8 @ X4)) = ((X8 @ (X8 @ X4))))))) & ((^[X4 : ($i > $i > $o)] : (! [X6 : $i,X11 : $i,X7 : $i] : (~(X4 @ X6 @ X7) | (X4 @ X6 @ X11) | ~(X4 @ X7 @ X11)))) = trans) & (sconfl = (^[X4 : ($i > $i > $o)] : (! [X6 : $i,X31 : ($i > $i > $o),X30 : ($i > $i > $o),X7 : $i,X11 : $i] : (~ ! [X12 : $i,X13 : $i,X26 : $i] : (~(X31 @ X13 @ X26) | ~(X31 @ X12 @ X13) | (X31 @ X12 @ X26)) | (X31 @ X11 @ X7) | (X30 @ X7 @ X11) | ~(X4 @ X6 @ X11) | ~ ! [X27 : $i] : (~ ! [X5 : ($i > $i > $o)] : ((X5 @ X7 @ X27) | ~ ! [X25 : $i,X12 : $i,X13 : $i] : (~(X5 @ X12 @ X13) | ~(X5 @ X13 @ X25) | (X5 @ X12 @ X25)) | ~ ! [X14 : $i,X15 : $i] : (~(X4 @ X14 @ X15) | (X5 @ X14 @ X15))) | ~ ! [X5 : ($i > $i > $o)] : ((X5 @ X11 @ X27) | ~ ! [X26 : $i,X13 : $i,X12 : $i] : (~(X5 @ X13 @ X26) | ~(X5 @ X12 @ X13) | (X5 @ X12 @ X26)) | ~ ! [X15 : $i,X14 : $i] : (~(X4 @ X14 @ X15) | (X5 @ X14 @ X15)))) | ((X6 != X7) & ~ ! [X5 : ($i > $i > $o)] : (~ ! [X32 : $i,X13 : $i,X12 : $i] : (~(X5 @ X13 @ X32) | (X5 @ X12 @ X32) | ~(X5 @ X12 @ X13)) | (X5 @ X6 @ X7) | ~ ! [X15 : $i,X14 : $i] : (~(X4 @ X14 @ X15) | (X5 @ X14 @ X15)))) | ~ ! [X14 : $i,X15 : $i] : ((X30 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | ~ ! [X14 : $i,X15 : $i] : ((X31 @ X14 @ X15) | ~(X4 @ X14 @ X15)) | (X7 = X11) | ~ ! [X12 : $i,X25 : $i,X13 : $i] : (~(X30 @ X12 @ X13) | (X30 @ X12 @ X25) | ~(X30 @ X13 @ X25)))))) & (infl = (^[X8 : (($i > $i > $o) > $i > $i > $o)] : (! [X7 : $i,X4 : ($i > $i > $o),X6 : $i] : ((X8 @ X4 @ X6 @ X7) | ~(X4 @ X6 @ X7)))))),
% 2.70/0.71 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sev441_1)).
% 2.70/0.71 thf(f2,conjecture,(
% 2.70/0.71 ((^[X0 : ($i > $i > $o)] : ((sc @ (rc @ (tc @ X0))))) = trsc)),
% 2.70/0.71 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitive_reflexive_symmetric_closure)).
% 2.70/0.71 thf(f3,negated_conjecture,(
% 2.70/0.71 ~ ((^[X0 : ($i > $i > $o)] : ((sc @ (rc @ (tc @ X0))))) = trsc)),
% 2.70/0.71 inference(negated_conjecture,[status(cth)],[f2])).
% 2.70/0.71 thf(f4,plain,(
% 2.70/0.71 (sc = (^[X0 : ($i > $i > $o), X1 : $i, X2 : $i] : ((X0 @ X2 @ X1) | (X0 @ X1 @ X2)))) & ((^[X3 : ($i > $i > $o)] : (! [X4 : $i,X5 : ($i > $o)] : (~(X5 @ X4) | ~ ! [X6 : $i] : (~ ! [X7 : $i] : (~(X5 @ X7) | ~(X3 @ X6 @ X7)) | ~(X5 @ X6))))) = term) & (mono = (^[X8 : (($i > $i > $o) > $i > $i > $o)] : (! [X9 : $i,X10 : ($i > $i > $o),X11 : ($i > $i > $o),X12 : $i] : (~(X8 @ X11 @ X12 @ X9) | ~ ! [X13 : $i,X14 : $i] : ((X10 @ X13 @ X14) | ~(X11 @ X13 @ X14)) | (X8 @ X10 @ X12 @ X9))))) & (trsc = (^[X15 : ($i > $i > $o), X16 : $i, X17 : $i] : ((X16 = X17) | ! [X18 : ($i > $i > $o)] : (~ ! [X19 : $i,X20 : $i,X21 : $i] : (~(X18 @ X21 @ X19) | (X18 @ X21 @ X20) | ~(X18 @ X19 @ X20)) | (X18 @ X17 @ X16) | ~ ! [X22 : $i,X23 : $i] : (~(X15 @ X23 @ X22) | (X18 @ X23 @ X22))) | ! [X24 : ($i > $i > $o)] : (~ ! [X25 : $i,X26 : $i] : ((X24 @ X26 @ X25) | ~(X15 @ X26 @ X25)) | ~ ! [X27 : $i,X28 : $i,X29 : $i] : ((X24 @ X29 @ X27) | ~(X24 @ X28 @ X27) | ~(X24 @ X29 @ X28)) | (X24 @ X16 @ X17))))) & ((^[X30 : ($i > $i > $o), X31 : $i] : (! [X32 : $i] : ~(X30 @ X31 @ X32))) = innf) & ((^[X33 : ($i > $i > $o)] : (! [X34 : $i,X35 : $i] : (~(X33 @ X34 @ X35) | ~(X33 @ X35 @ X34)))) = asymm) & ((^[X36 : ($i > $i > $o)] : (! [X37 : $i,X38 : $i] : (~(X36 @ X37 @ X38) | ~(X36 @ X38 @ X37)) & ! [X39 : $i,X40 : $i,X41 : $i] : (~(X36 @ X40 @ X39) | ~(X36 @ X39 @ X41) | (X36 @ X40 @ X41)))) = so) & (ind = (^[X42 : ($i > $i > $o)] : (! [X43 : $i,X44 : ($i > $o)] : ((X44 @ X43) | ~ ! [X45 : $i] : (~ ! [X46 : $i] : ((X44 @ X46) | ~ ! [X47 : ($i > $i > $o)] : (~ ! [X48 : $i,X49 : $i,X50 : $i] : ((X47 @ X49 @ X50) | ~(X47 @ X48 @ X50) | ~(X47 @ X49 @ X48)) | (X47 @ X45 @ X46) | ~ ! [X51 : $i,X52 : $i] : (~(X42 @ X51 @ X52) | (X47 @ X51 @ X52)))) | (X44 @ X45)))))) & (antisymm = (^[X53 : ($i > $i > $o)] : (! [X54 : $i,X55 : $i] : (~(X53 @ X54 @ X55) | ~(X53 @ X55 @ X54) | (X54 = X55))))) & (trc = (^[X56 : ($i > $i > $o), X57 : $i, X58 : $i] : ((X57 = X58) | ! [X59 : ($i > $i > $o)] : (~ ! [X60 : $i,X61 : $i] : (~(X56 @ X61 @ X60) | (X59 @ X61 @ X60)) | ~ ! [X62 : $i,X63 : $i,X64 : $i] : (~(X59 @ X63 @ X64) | ~(X59 @ X62 @ X63) | (X59 @ X62 @ X64)) | (X59 @ X57 @ X58))))) & (join = (^[X65 : ($i > $i > $o), X66 : $i, X67 : $i] : (~((X66 != X67) & ! [X68 : $i] : (~ ! [X69 : ($i > $i > $o)] : (~ ! [X70 : $i,X71 : $i] : (~(X65 @ X71 @ X70) | (X69 @ X71 @ X70)) | ~ ! [X72 : $i,X73 : $i,X74 : $i] : (~(X69 @ X74 @ X72) | (X69 @ X74 @ X73) | ~(X69 @ X72 @ X73)) | (X69 @ X66 @ X68)) | ~ ! [X75 : ($i > $i > $o)] : (~ ! [X76 : $i,X77 : $i,X78 : $i] : (~(X75 @ X78 @ X77) | ~(X75 @ X77 @ X76) | (X75 @ X78 @ X76)) | (X75 @ X67 @ X68) | ~ ! [X79 : $i,X80 : $i] : ((X75 @ X79 @ X80) | ~(X65 @ X79 @ X80)))) & ~ ! [X81 : ($i > $i > $o)] : (~ ! [X82 : $i,X83 : $i] : (~(X65 @ X83 @ X82) | (X81 @ X83 @ X82)) | (X81 @ X67 @ X66) | ~ ! [X84 : $i,X85 : $i,X86 : $i] : (~(X81 @ X84 @ X86) | (X81 @ X85 @ X86) | ~(X81 @ X85 @ X84))) & ~ ! [X87 : ($i > $i > $o)] : (~ ! [X88 : $i,X89 : $i,X90 : $i] : (~(X87 @ X88 @ X89) | ~(X87 @ X90 @ X88) | (X87 @ X90 @ X89)) | ~ ! [X91 : $i,X92 : $i] : (~(X65 @ X91 @ X92) | (X87 @ X91 @ X92)) | (X87 @ X66 @ X67)))))) & (inv = (^[X93 : ($i > $i > $o), X94 : $i, X95 : $i] : ((X93 @ X95 @ X94)))) & ! [X96 : $i] : ? [X97 : d_unsorted] : (((d2unsorted @ X97)) = X96) & (nfof = (^[X98 : ($i > $i > $o), X99 : $i, X100 : $i] : (! [X101 : $i] : ~(X98 @ X99 @ X101) & (! [X102 : ($i > $i > $o)] : ((X102 @ X100 @ X99) | ~ ! [X103 : $i,X104 : $i] : ((X102 @ X103 @ X104) | ~(X98 @ X103 @ X104)) | ~ ! [X105 : $i,X106 : $i,X107 : $i] : ((X102 @ X107 @ X105) | ~(X102 @ X107 @ X106) | ~(X102 @ X106 @ X105))) | (X99 = X100))))) & ((^[X108 : ($i > $i > $o)] : (! [X109 : ($i > $i > $o),X110 : ($i > $i > $o),X111 : $i,X112 : $i] : (~ ! [X113 : $i,X114 : $i,X115 : $i] : (~(X110 @ X113 @ X114) | ~(X110 @ X115 @ X113) | (X110 @ X115 @ X114)) | ~ ! [X116 : $i,X117 : $i,X118 : $i] : (~(X109 @ X116 @ X117) | (X109 @ X118 @ X117) | ~(X109 @ X118 @ X116)) | (~ ! [X119 : ($i > $i > $o)] : ((X119 @ X112 @ X111) | ~ ! [X120 : $i,X121 : $i,X122 : $i] : (~(X119 @ X120 @ X122) | ~(X119 @ X121 @ X120) | (X119 @ X121 @ X122)) | ~ ! [X123 : $i,X124 : $i] : (~(X108 @ X124 @ X123) | (X119 @ X124 @ X123))) & ~ ! [X125 : ($i > $i > $o)] : ((X125 @ X111 @ X112) | ~ ! [X126 : $i,X127 : $i,X128 : $i] : (~(X125 @ X127 @ X126) | ~(X125 @ X128 @ X127) | (X125 @ X128 @ X126)) | ~ ! [X129 : $i,X130 : $i] : ((X125 @ X130 @ X129) | ~(X108 @ X130 @ X129))) & (X111 != X112)) | ~ ! [X131 : $i] : (~ ! [X132 : ($i > $i > $o)] : ((X132 @ X112 @ X131) | ~ ! [X133 : $i,X134 : $i,X135 : $i] : (~(X132 @ X134 @ X135) | (X132 @ X133 @ X135) | ~(X132 @ X133 @ X134)) | ~ ! [X136 : $i,X137 : $i] : ((X132 @ X136 @ X137) | ~(X108 @ X136 @ X137))) | ~ ! [X138 : ($i > $i > $o)] : (~ ! [X139 : $i,X140 : $i] : (~(X108 @ X139 @ X140) | (X138 @ X139 @ X140)) | (X138 @ X111 @ X131) | ~ ! [X141 : $i,X142 : $i,X143 : $i] : (~(X138 @ X143 @ X142) | ~(X138 @ X142 @ X141) | (X138 @ X143 @ X141)))) | ~ ! [X144 : $i,X145 : $i] : ((X110 @ X145 @ X144) | ~(X108 @ X145 @ X144)) | (X110 @ X112 @ X111) | (X109 @ X111 @ X112) | ~ ! [X146 : $i,X147 : $i] : (~(X108 @ X146 @ X147) | (X109 @ X146 @ X147)) | (X111 = X112)))) = cr) & ! [X148 : d_unsorted] : (d_unsorted_0 = X148) & ((^[X149 : ($i > $i > $o)] : (! [X150 : $i,X151 : $i,X152 : $i] : ((X149 @ X151 @ X152) | ~(X149 @ X151 @ X150) | ~(X149 @ X150 @ X152)) & ! [X153 : $i] : (X149 @ X153 @ X153) & ! [X154 : $i,X155 : $i] : (~(X149 @ X154 @ X155) | (X154 = X155) | ~(X149 @ X155 @ X154)))) = po) & ((^[X156 : ($i > $i > $o)] : (! [X157 : $i,X158 : $i,X159 : ($i > $i > $o),X160 : $i,X161 : ($i > $i > $o)] : (~ ! [X162 : $i,X163 : $i,X164 : $i] : (~(X159 @ X162 @ X164) | ~(X159 @ X163 @ X162) | (X159 @ X163 @ X164)) | ~ ! [X165 : $i,X166 : $i] : ((X161 @ X165 @ X166) | ~(X156 @ X165 @ X166)) | ~ ! [X167 : $i,X168 : $i] : ((X159 @ X167 @ X168) | ~(X156 @ X167 @ X168)) | (X161 @ X157 @ X160) | (X159 @ X160 @ X157) | ((X158 != X160) & ~ ! [X169 : ($i > $i > $o)] : ((X169 @ X158 @ X160) | ~ ! [X170 : $i,X171 : $i] : ((X169 @ X170 @ X171) | ~(X156 @ X170 @ X171)) | ~ ! [X172 : $i,X173 : $i,X174 : $i] : (~(X169 @ X173 @ X172) | ~(X169 @ X172 @ X174) | (X169 @ X173 @ X174)))) | (X157 = X160) | ~ ! [X175 : $i,X176 : $i,X177 : $i] : (~(X161 @ X177 @ X175) | (X161 @ X176 @ X175) | ~(X161 @ X176 @ X177)) | ~ ! [X178 : $i] : (~ ! [X179 : ($i > $i > $o)] : (~ ! [X180 : $i,X181 : $i,X182 : $i] : (~(X179 @ X181 @ X182) | ~(X179 @ X182 @ X180) | (X179 @ X181 @ X180)) | ~ ! [X183 : $i,X184 : $i] : ((X179 @ X183 @ X184) | ~(X156 @ X183 @ X184)) | (X179 @ X157 @ X178)) | ~ ! [X185 : ($i > $i > $o)] : ((X185 @ X160 @ X178) | ~ ! [X186 : $i,X187 : $i,X188 : $i] : (~(X185 @ X188 @ X186) | ~(X185 @ X186 @ X187) | (X185 @ X188 @ X187)) | ~ ! [X189 : $i,X190 : $i] : (~(X156 @ X189 @ X190) | (X185 @ X189 @ X190)))) | ((X157 != X158) & ~ ! [X191 : ($i > $i > $o)] : (~ ! [X192 : $i,X193 : $i] : ((X191 @ X192 @ X193) | ~(X156 @ X192 @ X193)) | ~ ! [X194 : $i,X195 : $i,X196 : $i] : (~(X191 @ X196 @ X194) | (X191 @ X195 @ X194) | ~(X191 @ X195 @ X196)) | (X191 @ X158 @ X157)))))) = confl) & ((^[X197 : ($i > $i > $o)] : (! [X198 : $i] : (X197 @ X198 @ X198))) = refl) & ! [X199 : d_unsorted,X200 : d_unsorted] : ((((d2unsorted @ X200)) = ((d2unsorted @ X199))) => (X199 = X200)) & ((^[X201 : ($i > $i > $o)] : (! [X202 : $i,X203 : $i,X204 : ($i > $i > $o),X205 : $i,X206 : ($i > $i > $o)] : (~ ! [X207 : $i] : (~ ! [X208 : ($i > $i > $o)] : (~ ! [X209 : $i,X210 : $i] : ((X208 @ X210 @ X209) | ~(X201 @ X210 @ X209)) | (X208 @ X203 @ X207) | ~ ! [X211 : $i,X212 : $i,X213 : $i] : ((X208 @ X213 @ X211) | ~(X208 @ X213 @ X212) | ~(X208 @ X212 @ X211))) | ~ ! [X214 : ($i > $i > $o)] : (~ ! [X215 : $i,X216 : $i] : ((X214 @ X216 @ X215) | ~(X201 @ X216 @ X215)) | ~ ! [X217 : $i,X218 : $i,X219 : $i] : (~(X214 @ X217 @ X218) | (X214 @ X217 @ X219) | ~(X214 @ X218 @ X219)) | (X214 @ X205 @ X207))) | (X206 @ X205 @ X203) | ~ ! [X220 : $i,X221 : $i] : (~(X201 @ X220 @ X221) | (X206 @ X220 @ X221)) | ~ ! [X222 : $i,X223 : $i,X224 : $i] : (~(X204 @ X224 @ X223) | ~(X204 @ X222 @ X224) | (X204 @ X222 @ X223)) | ~(X201 @ X202 @ X205) | (X203 = X205) | ~(X201 @ X202 @ X203) | ~ ! [X225 : $i,X226 : $i,X227 : $i] : ((X206 @ X226 @ X227) | ~(X206 @ X226 @ X225) | ~(X206 @ X225 @ X227)) | (X204 @ X203 @ X205) | ~ ! [X228 : $i,X229 : $i] : ((X204 @ X229 @ X228) | ~(X201 @ X229 @ X228))))) = lconfl) & (rc = (^[X230 : ($i > $i > $o), X231 : $i, X232 : $i] : ((X230 @ X231 @ X232) | (X231 = X232)))) & ((^[X233 : ($i > $i > $o)] : (! [X234 : $i,X235 : $i] : (~(X233 @ X234 @ X235) | ~ ! [X236 : $i] : (~ ! [X237 : ($i > $i > $o)] : (~ ! [X238 : $i,X239 : $i] : ((X237 @ X238 @ X239) | ~(X233 @ X238 @ X239)) | (X237 @ X234 @ X236) | ~ ! [X240 : $i,X241 : $i,X242 : $i] : (~(X237 @ X242 @ X241) | (X237 @ X242 @ X240) | ~(X237 @ X241 @ X240))) | ~ ! [X243 : $i] : ~(X233 @ X236 @ X243))))) = norm) & (subrel = (^[X244 : ($i > $i > $o), X245 : ($i > $i > $o)] : (! [X246 : $i,X247 : $i] : ((X245 @ X247 @ X246) | ~(X244 @ X247 @ X246))))) & ((^[X248 : ($i > $i > $o)] : (! [X249 : $i,X250 : $i] : ((X248 @ X249 @ X250) | ~(X248 @ X250 @ X249)))) = symm) & (irrefl = (^[X251 : ($i > $i > $o)] : (! [X252 : $i] : ~(X251 @ X252 @ X252)))) & ((^[X253 : ($i > $i > $o)] : (! [X254 : $i,X255 : $i] : ((X253 @ X254 @ X255) | (X253 @ X255 @ X254) | (X254 = X255)))) = total) & (tc = (^[X256 : ($i > $i > $o), X257 : $i, X258 : $i] : (! [X259 : ($i > $i > $o)] : (~ ! [X260 : $i,X261 : $i] : (~(X256 @ X261 @ X260) | (X259 @ X261 @ X260)) | (X259 @ X257 @ X258) | ~ ! [X262 : $i,X263 : $i,X264 : $i] : (~(X259 @ X262 @ X263) | ~(X259 @ X264 @ X262) | (X259 @ X264 @ X263)))))) & (idem = (^[X265 : (($i > $i > $o) > $i > $i > $o)] : (! [X266 : ($i > $i > $o)] : (((X265 @ (X265 @ X266))) = ((X265 @ X266)))))) & ((^[X267 : ($i > $i > $o)] : (! [X268 : $i,X269 : $i,X270 : $i] : (~(X267 @ X268 @ X270) | (X267 @ X268 @ X269) | ~(X267 @ X270 @ X269)))) = trans) & (sconfl = (^[X271 : ($i > $i > $o)] : (! [X272 : $i,X273 : ($i > $i > $o),X274 : ($i > $i > $o),X275 : $i,X276 : $i] : (~ ! [X277 : $i,X278 : $i,X279 : $i] : (~(X273 @ X278 @ X279) | ~(X273 @ X277 @ X278) | (X273 @ X277 @ X279)) | (X273 @ X276 @ X275) | (X274 @ X275 @ X276) | ~(X271 @ X272 @ X276) | ~ ! [X280 : $i] : (~ ! [X281 : ($i > $i > $o)] : ((X281 @ X275 @ X280) | ~ ! [X282 : $i,X283 : $i,X284 : $i] : (~(X281 @ X283 @ X284) | ~(X281 @ X284 @ X282) | (X281 @ X283 @ X282)) | ~ ! [X285 : $i,X286 : $i] : (~(X271 @ X285 @ X286) | (X281 @ X285 @ X286))) | ~ ! [X287 : ($i > $i > $o)] : ((X287 @ X276 @ X280) | ~ ! [X288 : $i,X289 : $i,X290 : $i] : (~(X287 @ X289 @ X288) | ~(X287 @ X290 @ X289) | (X287 @ X290 @ X288)) | ~ ! [X291 : $i,X292 : $i] : (~(X271 @ X292 @ X291) | (X287 @ X292 @ X291)))) | ((X272 != X275) & ~ ! [X293 : ($i > $i > $o)] : (~ ! [X294 : $i,X295 : $i,X296 : $i] : (~(X293 @ X295 @ X294) | (X293 @ X296 @ X294) | ~(X293 @ X296 @ X295)) | (X293 @ X272 @ X275) | ~ ! [X297 : $i,X298 : $i] : (~(X271 @ X298 @ X297) | (X293 @ X298 @ X297)))) | ~ ! [X299 : $i,X300 : $i] : ((X274 @ X299 @ X300) | ~(X271 @ X299 @ X300)) | ~ ! [X301 : $i,X302 : $i] : ((X273 @ X301 @ X302) | ~(X271 @ X301 @ X302)) | (X275 = X276) | ~ ! [X303 : $i,X304 : $i,X305 : $i] : (~(X274 @ X303 @ X305) | (X274 @ X303 @ X304) | ~(X274 @ X305 @ X304)))))) & (infl = (^[X306 : (($i > $i > $o) > $i > $i > $o)] : (! [X307 : $i,X308 : ($i > $i > $o),X309 : $i] : ((X306 @ X308 @ X309 @ X307) | ~(X308 @ X309 @ X307)))))),
% 2.70/0.71 inference(rectify,[],[f1])).
% 2.70/0.71 thf(f5,plain,(
% 2.70/0.71 (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y0 @ Y2 @ Y1)))))))) & (term = (^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y1 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y0 @ Y3 @ Y4)) | (~ (Y1 @ Y4)))))))))) | (~ (Y1 @ Y2))))))))) & (mono = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((Y0 @ Y3 @ Y1 @ Y4) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y2 @ Y6 @ Y5)) | (Y3 @ Y6 @ Y5)))))))) | (~ (Y0 @ Y2 @ Y1 @ Y4))))))))))))) & (trsc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y5 @ Y6))) | (Y3 @ Y4 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5)))))))))) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5)))))))) | (Y3 @ Y2 @ Y1)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y4 @ Y6)))))))))))))) | (Y1 = Y2)))))))) & (innf = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2)))))))) & (asymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y2 @ Y1))))))))) & (so = (^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) | (~ (Y0 @ Y3 @ Y1))) | (~ (Y0 @ Y2 @ Y3))))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y2 @ Y1)))))))))) & (ind = (^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6)))))))) | (Y5 @ Y3 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y7 @ Y8)) | (~ (Y5 @ Y8 @ Y6))) | (Y5 @ Y7 @ Y6))))))))))))) | (Y1 @ Y4))))))))) | (Y1 @ Y2)))))))) & (antisymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((Y2 = Y1) | (~ (Y0 @ Y1 @ Y2))) | (~ (Y0 @ Y2 @ Y1))))))))) & (trc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y6 @ Y4) | (~ (Y3 @ Y6 @ Y5))) | (~ (Y3 @ Y5 @ Y4))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5))))))))))) | (Y1 = Y2)))))))) & (join = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (~ ((((~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y5) | (~ (Y3 @ Y4 @ Y6))) | (~ (Y3 @ Y6 @ Y5)))))))))))))) & (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y5 @ Y6)) | (Y3 @ Y5 @ Y4)) | (~ (Y3 @ Y6 @ Y4)))))))))) | (Y3 @ Y2 @ Y1)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5))))))))))))) & (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y5))))))) | (Y4 @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y5 @ Y7) | (~ (Y4 @ Y6 @ Y7))) | (~ (Y4 @ Y5 @ Y6)))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y1 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y6)) | (Y4 @ Y5 @ Y6)) | (~ (Y4 @ Y5 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6)))))))))))))))) & (~ (Y1 = Y2)))))))))) & (inv = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (Y0 @ Y2 @ Y1))))))) & ! [X96 : $i] : ? [X97 : d_unsorted] : (((d2unsorted @ X97)) = X96) & (nfof = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((Y1 = Y2) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y5 @ Y6)) | (~ (Y3 @ Y4 @ Y5))) | (Y3 @ Y4 @ Y6))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (Y3 @ Y2 @ Y1))))) & (!! @ $i @ (^[Y3 : $i]: (~ (Y0 @ Y1 @ Y3))))))))))) & (cr = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((((((((Y2 = Y1) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y6 @ Y5) | (~ (Y0 @ Y6 @ Y5))))))))) | (Y4 @ Y2 @ Y1)) | (Y3 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y3 @ Y5 @ Y6)))))))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y7 @ Y9) | (~ (Y6 @ Y8 @ Y9))) | (~ (Y6 @ Y7 @ Y8)))))))))) | (Y6 @ Y2 @ Y5)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7)))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y8)) | (Y6 @ Y9 @ Y7)) | (~ (Y6 @ Y8 @ Y7))))))))))) | (Y6 @ Y1 @ Y5)))))))))) | (((~ (Y2 = Y1)) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y5 @ Y6 @ Y7))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y6 @ Y8) | (~ (Y5 @ Y6 @ Y7))) | (~ (Y5 @ Y7 @ Y8))))))))))) | (Y5 @ Y2 @ Y1)))))) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y7 @ Y6) | (~ (Y5 @ Y7 @ Y8))) | (~ (Y5 @ Y8 @ Y6))))))))))) | (Y5 @ Y1 @ Y2))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y5 @ Y7)) | (Y4 @ Y5 @ Y6)) | (~ (Y4 @ Y7 @ Y6))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y3 @ Y5 @ Y6) | (~ (Y3 @ Y5 @ Y7))) | (~ (Y3 @ Y7 @ Y6))))))))))))))))))))) & ! [X148 : d_unsorted] : (d_unsorted_0 = X148) & (po = (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (Y2 = Y1)) | (~ (Y0 @ Y2 @ Y1))))))) & (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y1)) | (~ (Y0 @ Y2 @ Y3))) | (Y0 @ Y2 @ Y1))))))))))) & (confl = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((((((((((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y4 @ Y5) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y9)) | (~ (Y6 @ Y7 @ Y9))))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7))))))))))) & (~ (Y5 = Y4))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y9 @ Y8) | (~ (Y0 @ Y9 @ Y8)))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y8 @ Y9) | (~ (Y7 @ Y10 @ Y9))) | (~ (Y7 @ Y8 @ Y10))))))))))) | (Y7 @ Y2 @ Y6))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y5 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8)))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y9 @ Y10) | (~ (Y7 @ Y8 @ Y10))) | (~ (Y7 @ Y9 @ Y8))))))))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y7 @ Y6)) | (Y1 @ Y7 @ Y8)) | (~ (Y1 @ Y6 @ Y8))))))))))) | (Y5 = Y2)) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y8 @ Y7) | (~ (Y6 @ Y9 @ Y7))) | (~ (Y6 @ Y8 @ Y9)))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7)))))))) | (Y6 @ Y4 @ Y2))))) & (~ (Y4 = Y2)))) | (Y3 @ Y2 @ Y5)) | (Y1 @ Y5 @ Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y3 @ Y7 @ Y6)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y1 @ Y7 @ Y6)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y3 @ Y7 @ Y6) | (~ (Y3 @ Y7 @ Y8))) | (~ (Y3 @ Y8 @ Y6))))))))))))))))))))))) & (refl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))))) & ! [X199 : d_unsorted,X200 : d_unsorted] : ((((d2unsorted @ X200)) = ((d2unsorted @ X199))) => (X199 = X200)) & (lconfl = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((((((((((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y3 @ Y6 @ Y7))))))) | (Y3 @ Y4 @ Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y8 @ Y6)) | (~ (Y1 @ Y7 @ Y8))) | (Y1 @ Y7 @ Y6)))))))))) | (~ (Y0 @ Y5 @ Y4))) | (Y4 = Y2)) | (~ (Y0 @ Y5 @ Y2))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y3 @ Y8 @ Y7) | (~ (Y3 @ Y8 @ Y6))) | (~ (Y3 @ Y6 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y1 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (Y1 @ Y2 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y2 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y8)) | (Y7 @ Y10 @ Y8)) | (~ (Y7 @ Y10 @ Y9))))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y10)) | (~ (Y7 @ Y8 @ Y9))) | (Y7 @ Y8 @ Y10))))))))) | (Y7 @ Y4 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9)))))))))))))))))))))))))))) & (rc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y1 = Y2) | (Y0 @ Y1 @ Y2)))))))) & (norm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: (~ (Y0 @ Y3 @ Y4))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y7)) | (Y4 @ Y5 @ Y7)) | (~ (Y4 @ Y5 @ Y6)))))))))) | (Y4 @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y5))))))))))))))) | (~ (Y0 @ Y2 @ Y1))))))))) & (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y2 @ Y3)))))))))) & (symm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y2 @ Y1)))))))) & (irrefl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1)))))) & (total = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((Y2 = Y1) | (Y0 @ Y1 @ Y2)) | (Y0 @ Y2 @ Y1)))))))) & (tc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y5) | (~ (Y3 @ Y4 @ Y6))) | (~ (Y3 @ Y6 @ Y5)))))))))) | (Y3 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5))))))))))))))))) & (idem = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((Y0 @ (Y0 @ Y1)) = (Y0 @ Y1)))))) & (trans = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y3 @ Y1))))))))))) & (sconfl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (!! @ $i @ (^[Y5 : $i]: ((((((((((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y3 @ Y6 @ Y7)) | (Y3 @ Y8 @ Y7)) | (~ (Y3 @ Y8 @ Y6)))))))))) | (Y2 = Y1)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y4 @ Y7 @ Y6)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y3 @ Y7 @ Y6)))))))) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y7 @ Y8) | (~ (Y0 @ Y7 @ Y8)))))))) | (Y6 @ Y5 @ Y2)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y9)) | (~ (Y6 @ Y8 @ Y9)))))))))))))) & (~ (Y5 = Y2)))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9)))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y8 @ Y10) | (~ (Y7 @ Y8 @ Y9))) | (~ (Y7 @ Y9 @ Y10))))))))))) | (Y7 @ Y1 @ Y6))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y9 @ Y8) | (~ (Y0 @ Y9 @ Y8)))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y9 @ Y10) | (~ (Y7 @ Y8 @ Y10))) | (~ (Y7 @ Y9 @ Y8))))))))))) | (Y7 @ Y2 @ Y6)))))))))) | (~ (Y0 @ Y5 @ Y1))) | (Y3 @ Y2 @ Y1)) | (Y4 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y4 @ Y8 @ Y6) | (~ (Y4 @ Y8 @ Y7))) | (~ (Y4 @ Y7 @ Y6))))))))))))))))))))))) & (infl = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y2 @ Y1 @ Y3)) | (Y0 @ Y2 @ Y1 @ Y3))))))))))),
% 2.70/0.71 inference(fool_elimination,[],[f4])).
% 2.70/0.71 thf(f6,plain,(
% 2.70/0.71 ~ (trsc = (^[Y0 : $i > $i > $o]: (sc @ (rc @ (tc @ Y0)))))),
% 2.70/0.71 inference(fool_elimination,[],[f3])).
% 2.70/0.71 thf(f7,plain,(
% 2.70/0.71 (mono = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((Y0 @ Y3 @ Y1 @ Y4) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y2 @ Y6 @ Y5)) | (Y3 @ Y6 @ Y5)))))))) | (~ (Y0 @ Y2 @ Y1 @ Y4))))))))))))) & (asymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y2 @ Y1))))))))) & (nfof = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((Y1 = Y2) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y5 @ Y6)) | (~ (Y3 @ Y4 @ Y5))) | (Y3 @ Y4 @ Y6))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (Y3 @ Y2 @ Y1))))) & (!! @ $i @ (^[Y3 : $i]: (~ (Y0 @ Y1 @ Y3))))))))))) & (innf = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2)))))))) & (cr = (^[Y0 : $i > $i > $o]: (!! 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@ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y5 @ Y6 @ Y7))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y6 @ Y8) | (~ (Y5 @ Y6 @ Y7))) | (~ (Y5 @ Y7 @ Y8))))))))))) | (Y5 @ Y2 @ Y1)))))) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y7 @ Y6) | (~ (Y5 @ Y7 @ Y8))) | (~ (Y5 @ Y8 @ Y6))))))))))) | (Y5 @ Y1 @ Y2))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y5 @ Y7)) | (Y4 @ Y5 @ Y6)) | (~ (Y4 @ Y7 @ Y6))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y3 @ Y5 @ Y6) | (~ (Y3 @ Y5 @ Y7))) | (~ (Y3 @ Y7 @ Y6))))))))))))))))))))) & (total = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((Y2 = Y1) | (Y0 @ Y1 @ Y2)) | (Y0 @ Y2 @ Y1)))))))) & (sconfl = (^[Y0 : $i > $i > $o]: (!! 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@ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y8 @ Y10) | (~ (Y7 @ Y8 @ Y9))) | (~ (Y7 @ Y9 @ Y10))))))))))) | (Y7 @ Y1 @ Y6))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y9 @ Y8) | (~ (Y0 @ Y9 @ Y8)))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y9 @ Y10) | (~ (Y7 @ Y8 @ Y10))) | (~ (Y7 @ Y9 @ Y8))))))))))) | (Y7 @ Y2 @ Y6)))))))))) | (~ (Y0 @ Y5 @ Y1))) | (Y3 @ Y2 @ Y1)) | (Y4 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y4 @ Y8 @ Y6) | (~ (Y4 @ Y8 @ Y7))) | (~ (Y4 @ Y7 @ Y6))))))))))))))))))))))) & (trc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y6 @ Y4) | (~ (Y3 @ Y6 @ Y5))) | (~ (Y3 @ Y5 @ Y4))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5))))))))))) | (Y1 = Y2)))))))) & (inv = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (Y0 @ Y2 @ Y1))))))) & (join = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (~ ((((~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y5) | (~ (Y3 @ Y4 @ Y6))) | (~ (Y3 @ Y6 @ Y5)))))))))))))) & (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y5 @ Y6)) | (Y3 @ Y5 @ Y4)) | (~ (Y3 @ Y6 @ Y4)))))))))) | (Y3 @ Y2 @ Y1)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5))))))))))))) & (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y5))))))) | (Y4 @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y5 @ Y7) | (~ (Y4 @ Y6 @ Y7))) | (~ (Y4 @ Y5 @ Y6)))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y1 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y6)) | (Y4 @ Y5 @ Y6)) | (~ (Y4 @ Y5 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6)))))))))))))))) & (~ (Y1 = Y2)))))))))) & (symm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y2 @ Y1)))))))) & (lconfl = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((((((((((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y3 @ Y6 @ Y7))))))) | (Y3 @ Y4 @ Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y8 @ Y6)) | (~ (Y1 @ Y7 @ Y8))) | (Y1 @ Y7 @ Y6)))))))))) | (~ (Y0 @ Y5 @ Y4))) | (Y4 = Y2)) | (~ (Y0 @ Y5 @ Y2))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y3 @ Y8 @ Y7) | (~ (Y3 @ Y8 @ Y6))) | (~ (Y3 @ Y6 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y1 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (Y1 @ Y2 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y2 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y8)) | (Y7 @ Y10 @ Y8)) | (~ (Y7 @ Y10 @ Y9))))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y10)) | (~ (Y7 @ Y8 @ Y9))) | (Y7 @ Y8 @ Y10))))))))) | (Y7 @ Y4 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9)))))))))))))))))))))))))))) & (trans = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! 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@ $i @ (^[Y3 : $i]: ((~ (Y2 @ Y1 @ Y3)) | (Y0 @ Y2 @ Y1 @ Y3)))))))))) & (norm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: (~ (Y0 @ Y3 @ Y4))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y7)) | (Y4 @ Y5 @ Y7)) | (~ (Y4 @ Y5 @ Y6)))))))))) | (Y4 @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y5))))))))))))))) | (~ (Y0 @ Y2 @ Y1))))))))) & (idem = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((Y0 @ (Y0 @ Y1)) = (Y0 @ Y1)))))) & (ind = (^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6)))))))) | (Y5 @ Y3 @ Y4)) | (~ (!! 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[X0 : $i] : ? [X1 : d_unsorted] : (((d2unsorted @ X1)) = X0) & (trsc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y5 @ Y6))) | (Y3 @ Y4 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5)))))))))) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5)))))))) | (Y3 @ Y2 @ Y1)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y4 @ Y6)))))))))))))) | (Y1 = Y2)))))))) & ! [X3 : d_unsorted,X4 : d_unsorted] : ((((d2unsorted @ X3)) = ((d2unsorted @ X4))) => (X3 = X4)) & (confl = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((((((((((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y4 @ Y5) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y9)) | (~ (Y6 @ Y7 @ Y9))))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7))))))))))) & (~ (Y5 = Y4))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y9 @ Y8) | (~ (Y0 @ Y9 @ Y8)))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y8 @ Y9) | (~ (Y7 @ Y10 @ Y9))) | (~ (Y7 @ Y8 @ Y10))))))))))) | (Y7 @ Y2 @ Y6))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y5 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8)))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y9 @ Y10) | (~ (Y7 @ Y8 @ Y10))) | (~ (Y7 @ Y9 @ Y8))))))))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y7 @ Y6)) | (Y1 @ Y7 @ Y8)) | (~ (Y1 @ Y6 @ Y8))))))))))) | (Y5 = Y2)) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y8 @ Y7) | (~ (Y6 @ Y9 @ Y7))) | (~ (Y6 @ Y8 @ Y9)))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7)))))))) | (Y6 @ Y4 @ Y2))))) & (~ (Y4 = Y2)))) | (Y3 @ Y2 @ Y5)) | (Y1 @ Y5 @ Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y3 @ Y7 @ Y6)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y1 @ Y7 @ Y6)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y3 @ Y7 @ Y6) | (~ (Y3 @ Y7 @ Y8))) | (~ (Y3 @ Y8 @ Y6))))))))))))))))))))))) & (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y2 @ Y3)))))))))) & (irrefl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1)))))) & (tc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y5) | (~ (Y3 @ Y4 @ Y6))) | (~ (Y3 @ Y6 @ Y5)))))))))) | (Y3 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5))))))))))))))))) & ! [X2 : d_unsorted] : (d_unsorted_0 = X2) & (term = (^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y1 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y0 @ Y3 @ Y4)) | (~ (Y1 @ Y4)))))))))) | (~ (Y1 @ Y2))))))))) & (antisymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((Y2 = Y1) | (~ (Y0 @ Y1 @ Y2))) | (~ (Y0 @ Y2 @ Y1))))))))) & (refl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))),
% 2.70/0.71 inference(rectify,[],[f5])).
% 2.70/0.71 thf(f8,plain,(
% 2.70/0.71 (trsc != (^[Y0 : $i > $i > $o]: (sc @ (rc @ (tc @ Y0)))))),
% 2.70/0.71 inference(flattening,[],[f6])).
% 2.70/0.71 thf(f9,plain,(
% 2.70/0.71 (po = (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (Y2 = Y1)) | (~ (Y0 @ Y2 @ Y1))))))) & (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y1)) | (~ (Y0 @ Y2 @ Y3))) | (Y0 @ Y2 @ Y1))))))))))) & (tc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y5) | (~ (Y3 @ Y4 @ Y6))) | (~ (Y3 @ Y6 @ Y5)))))))))) | (Y3 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5))))))))))))))))) & (antisymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((Y2 = Y1) | (~ (Y0 @ Y1 @ Y2))) | (~ (Y0 @ Y2 @ Y1))))))))) & ! [X0 : $i] : ? [X1 : d_unsorted] : (((d2unsorted @ X1)) = X0) & (total = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((Y2 = Y1) | (Y0 @ Y1 @ Y2)) | (Y0 @ Y2 @ Y1)))))))) & (idem = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((Y0 @ (Y0 @ Y1)) = (Y0 @ Y1)))))) & (lconfl = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((((((((((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y3 @ Y6 @ Y7))))))) | (Y3 @ Y4 @ Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y8 @ Y6)) | (~ (Y1 @ Y7 @ Y8))) | (Y1 @ Y7 @ Y6)))))))))) | (~ (Y0 @ Y5 @ Y4))) | (Y4 = Y2)) | (~ (Y0 @ Y5 @ Y2))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y3 @ Y8 @ Y7) | (~ (Y3 @ Y8 @ Y6))) | (~ (Y3 @ Y6 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y1 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (Y1 @ Y2 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y2 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y8)) | (Y7 @ Y10 @ Y8)) | (~ (Y7 @ Y10 @ Y9))))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y10)) | (~ (Y7 @ Y8 @ Y9))) | (Y7 @ Y8 @ Y10))))))))) | (Y7 @ Y4 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9)))))))))))))))))))))))))))) & (nfof = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((Y1 = Y2) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y5 @ Y6)) | (~ (Y3 @ Y4 @ Y5))) | (Y3 @ Y4 @ Y6))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (Y3 @ Y2 @ Y1))))) & (!! @ $i @ (^[Y3 : $i]: (~ (Y0 @ Y1 @ Y3))))))))))) & (ind = (^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6)))))))) | (Y5 @ Y3 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y7 @ Y8)) | (~ (Y5 @ Y8 @ Y6))) | (Y5 @ Y7 @ Y6))))))))))))) | (Y1 @ Y4))))))))) | (Y1 @ Y2)))))))) & (rc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y1 = Y2) | (Y0 @ Y1 @ Y2)))))))) & ! [X3 : d_unsorted,X4 : d_unsorted] : ((((d2unsorted @ X3)) != ((d2unsorted @ X4))) | (X3 = X4)) & (mono = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((Y0 @ Y3 @ Y1 @ Y4) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y2 @ Y6 @ Y5)) | (Y3 @ Y6 @ Y5)))))))) | (~ (Y0 @ Y2 @ Y1 @ Y4))))))))))))) & (innf = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2)))))))) & (inv = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (Y0 @ Y2 @ Y1))))))) & (irrefl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1)))))) & (confl = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((((((((((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y4 @ Y5) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y9)) | (~ (Y6 @ Y7 @ Y9))))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7))))))))))) & (~ (Y5 = Y4))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y9 @ Y8) | (~ (Y0 @ Y9 @ Y8)))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y8 @ Y9) | (~ (Y7 @ Y10 @ Y9))) | (~ (Y7 @ Y8 @ Y10))))))))))) | (Y7 @ Y2 @ Y6))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y5 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8)))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y9 @ Y10) | (~ (Y7 @ Y8 @ Y10))) | (~ (Y7 @ Y9 @ Y8))))))))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y7 @ Y6)) | (Y1 @ Y7 @ Y8)) | (~ (Y1 @ Y6 @ Y8))))))))))) | (Y5 = Y2)) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y8 @ Y7) | (~ (Y6 @ Y9 @ Y7))) | (~ (Y6 @ Y8 @ Y9)))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7)))))))) | (Y6 @ Y4 @ Y2))))) & (~ (Y4 = Y2)))) | (Y3 @ Y2 @ Y5)) | (Y1 @ Y5 @ Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y3 @ Y7 @ Y6)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y1 @ Y7 @ Y6)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y3 @ Y7 @ Y6) | (~ (Y3 @ Y7 @ Y8))) | (~ (Y3 @ Y8 @ Y6))))))))))))))))))))))) & (refl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))))) & (norm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: (~ (Y0 @ Y3 @ Y4))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y7)) | (Y4 @ Y5 @ Y7)) | (~ (Y4 @ Y5 @ Y6)))))))))) | (Y4 @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y5))))))))))))))) | (~ (Y0 @ Y2 @ Y1))))))))) & ! [X2 : d_unsorted] : (d_unsorted_0 = X2) & (trc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y6 @ Y4) | (~ (Y3 @ Y6 @ Y5))) | (~ (Y3 @ Y5 @ Y4))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5))))))))))) | (Y1 = Y2)))))))) & (trans = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y3 @ Y1))))))))))) & (symm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y2 @ Y1)))))))) & (infl = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y2 @ Y1 @ Y3)) | (Y0 @ Y2 @ Y1 @ Y3)))))))))) & (so = (^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) | (~ (Y0 @ Y3 @ Y1))) | (~ (Y0 @ Y2 @ Y3))))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y2 @ Y1)))))))))) & (cr = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((((((((Y2 = Y1) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y6 @ Y5) | (~ (Y0 @ Y6 @ Y5))))))))) | (Y4 @ Y2 @ Y1)) | (Y3 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y3 @ Y5 @ Y6)))))))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y7 @ Y9) | (~ (Y6 @ Y8 @ Y9))) | (~ (Y6 @ Y7 @ Y8)))))))))) | (Y6 @ Y2 @ Y5)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7)))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y8)) | (Y6 @ Y9 @ Y7)) | (~ (Y6 @ Y8 @ Y7))))))))))) | (Y6 @ Y1 @ Y5)))))))))) | (((~ (Y2 = Y1)) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y5 @ Y6 @ Y7))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y6 @ Y8) | (~ (Y5 @ Y6 @ Y7))) | (~ (Y5 @ Y7 @ Y8))))))))))) | (Y5 @ Y2 @ Y1)))))) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y7 @ Y6) | (~ (Y5 @ Y7 @ Y8))) | (~ (Y5 @ Y8 @ Y6))))))))))) | (Y5 @ Y1 @ Y2))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y5 @ Y7)) | (Y4 @ Y5 @ Y6)) | (~ (Y4 @ Y7 @ Y6))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y3 @ Y5 @ Y6) | (~ (Y3 @ Y5 @ Y7))) | (~ (Y3 @ Y7 @ Y6))))))))))))))))))))) & (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y2 @ Y3)))))))))) & (join = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (~ ((((~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y5) | (~ (Y3 @ Y4 @ Y6))) | (~ (Y3 @ Y6 @ Y5)))))))))))))) & (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y5 @ Y6)) | (Y3 @ Y5 @ Y4)) | (~ (Y3 @ Y6 @ Y4)))))))))) | (Y3 @ Y2 @ Y1)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5))))))))))))) & (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y5))))))) | (Y4 @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y5 @ Y7) | (~ (Y4 @ Y6 @ Y7))) | (~ (Y4 @ Y5 @ Y6)))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y1 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y6)) | (Y4 @ Y5 @ Y6)) | (~ (Y4 @ Y5 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6)))))))))))))))) & (~ (Y1 = Y2)))))))))) & (asymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y2 @ Y1))))))))) & (sconfl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (!! @ $i @ (^[Y5 : $i]: ((((((((((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y3 @ Y6 @ Y7)) | (Y3 @ Y8 @ Y7)) | (~ (Y3 @ Y8 @ Y6)))))))))) | (Y2 = Y1)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y4 @ Y7 @ Y6)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y3 @ Y7 @ Y6)))))))) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y7 @ Y8) | (~ (Y0 @ Y7 @ Y8)))))))) | (Y6 @ Y5 @ Y2)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y9)) | (~ (Y6 @ Y8 @ Y9)))))))))))))) & (~ (Y5 = Y2)))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9)))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y8 @ Y10) | (~ (Y7 @ Y8 @ Y9))) | (~ (Y7 @ Y9 @ Y10))))))))))) | (Y7 @ Y1 @ Y6))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y9 @ Y8) | (~ (Y0 @ Y9 @ Y8)))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y9 @ Y10) | (~ (Y7 @ Y8 @ Y10))) | (~ (Y7 @ Y9 @ Y8))))))))))) | (Y7 @ Y2 @ Y6)))))))))) | (~ (Y0 @ Y5 @ Y1))) | (Y3 @ Y2 @ Y1)) | (Y4 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y4 @ Y8 @ Y6) | (~ (Y4 @ Y8 @ Y7))) | (~ (Y4 @ Y7 @ Y6))))))))))))))))))))))) & (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y0 @ Y2 @ Y1)))))))) & (term = (^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y1 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y0 @ Y3 @ Y4)) | (~ (Y1 @ Y4)))))))))) | (~ (Y1 @ Y2))))))))) & (trsc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y5 @ Y6))) | (Y3 @ Y4 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5)))))))))) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5)))))))) | (Y3 @ Y2 @ Y1)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y4 @ Y6)))))))))))))) | (Y1 = Y2))))))))),
% 2.70/0.71 inference(ennf_transformation,[],[f7])).
% 2.70/0.71 thf(f10,plain,(
% 2.70/0.71 (po = (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (Y2 = Y1)) | (~ (Y0 @ Y2 @ Y1))))))) & (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y1)) | (~ (Y0 @ Y2 @ Y3))) | (Y0 @ Y2 @ Y1))))))))))) & (tc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y5) | (~ (Y3 @ Y4 @ Y6))) | (~ (Y3 @ Y6 @ Y5)))))))))) | (Y3 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5))))))))))))))))) & (antisymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((Y2 = Y1) | (~ (Y0 @ Y1 @ Y2))) | (~ (Y0 @ Y2 @ Y1))))))))) & ! [X0 : $i] : ? [X1 : d_unsorted] : (((d2unsorted @ X1)) = X0) & (total = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((Y2 = Y1) | (Y0 @ Y1 @ Y2)) | (Y0 @ Y2 @ Y1)))))))) & (idem = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((Y0 @ (Y0 @ Y1)) = (Y0 @ Y1)))))) & (lconfl = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((((((((((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y3 @ Y6 @ Y7))))))) | (Y3 @ Y4 @ Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y8 @ Y6)) | (~ (Y1 @ Y7 @ Y8))) | (Y1 @ Y7 @ Y6)))))))))) | (~ (Y0 @ Y5 @ Y4))) | (Y4 = Y2)) | (~ (Y0 @ Y5 @ Y2))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y3 @ Y8 @ Y7) | (~ (Y3 @ Y8 @ Y6))) | (~ (Y3 @ Y6 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y1 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (Y1 @ Y2 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y2 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y8)) | (Y7 @ Y10 @ Y8)) | (~ (Y7 @ Y10 @ Y9))))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y10)) | (~ (Y7 @ Y8 @ Y9))) | (Y7 @ Y8 @ Y10))))))))) | (Y7 @ Y4 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9)))))))))))))))))))))))))))) & (nfof = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((Y1 = Y2) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y5 @ Y6)) | (~ (Y3 @ Y4 @ Y5))) | (Y3 @ Y4 @ Y6))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (Y3 @ Y2 @ Y1))))) & (!! @ $i @ (^[Y3 : $i]: (~ (Y0 @ Y1 @ Y3))))))))))) & (ind = (^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6)))))))) | (Y5 @ Y3 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y7 @ Y8)) | (~ (Y5 @ Y8 @ Y6))) | (Y5 @ Y7 @ Y6))))))))))))) | (Y1 @ Y4))))))))) | (Y1 @ Y2)))))))) & (rc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y1 = Y2) | (Y0 @ Y1 @ Y2)))))))) & ! [X2 : d_unsorted,X3 : d_unsorted] : ((((d2unsorted @ X2)) != ((d2unsorted @ X3))) | (X2 = X3)) & (mono = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((Y0 @ Y3 @ Y1 @ Y4) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y2 @ Y6 @ Y5)) | (Y3 @ Y6 @ Y5)))))))) | (~ (Y0 @ Y2 @ Y1 @ Y4))))))))))))) & (innf = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2)))))))) & (inv = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (Y0 @ Y2 @ Y1))))))) & (irrefl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1)))))) & (confl = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((((((((((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y4 @ Y5) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y9)) | (~ (Y6 @ Y7 @ Y9))))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7))))))))))) & (~ (Y5 = Y4))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y9 @ Y8) | (~ (Y0 @ Y9 @ Y8)))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y8 @ Y9) | (~ (Y7 @ Y10 @ Y9))) | (~ (Y7 @ Y8 @ Y10))))))))))) | (Y7 @ Y2 @ Y6))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y5 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8)))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y9 @ Y10) | (~ (Y7 @ Y8 @ Y10))) | (~ (Y7 @ Y9 @ Y8))))))))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y7 @ Y6)) | (Y1 @ Y7 @ Y8)) | (~ (Y1 @ Y6 @ Y8))))))))))) | (Y5 = Y2)) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y8 @ Y7) | (~ (Y6 @ Y9 @ Y7))) | (~ (Y6 @ Y8 @ Y9)))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7)))))))) | (Y6 @ Y4 @ Y2))))) & (~ (Y4 = Y2)))) | (Y3 @ Y2 @ Y5)) | (Y1 @ Y5 @ Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y3 @ Y7 @ Y6)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y1 @ Y7 @ Y6)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y3 @ Y7 @ Y6) | (~ (Y3 @ Y7 @ Y8))) | (~ (Y3 @ Y8 @ Y6))))))))))))))))))))))) & (refl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))))) & (norm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: (~ (Y0 @ Y3 @ Y4))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y7)) | (Y4 @ Y5 @ Y7)) | (~ (Y4 @ Y5 @ Y6)))))))))) | (Y4 @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y5))))))))))))))) | (~ (Y0 @ Y2 @ Y1))))))))) & ! [X4 : d_unsorted] : (d_unsorted_0 = X4) & (trc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y6 @ Y4) | (~ (Y3 @ Y6 @ Y5))) | (~ (Y3 @ Y5 @ Y4))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5))))))))))) | (Y1 = Y2)))))))) & (trans = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y3 @ Y1))))))))))) & (symm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y2 @ Y1)))))))) & (infl = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y2 @ Y1 @ Y3)) | (Y0 @ Y2 @ Y1 @ Y3)))))))))) & (so = (^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) | (~ (Y0 @ Y3 @ Y1))) | (~ (Y0 @ Y2 @ Y3))))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y2 @ Y1)))))))))) & (cr = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((((((((Y2 = Y1) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y6 @ Y5) | (~ (Y0 @ Y6 @ Y5))))))))) | (Y4 @ Y2 @ Y1)) | (Y3 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y3 @ Y5 @ Y6)))))))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y7 @ Y9) | (~ (Y6 @ Y8 @ Y9))) | (~ (Y6 @ Y7 @ Y8)))))))))) | (Y6 @ Y2 @ Y5)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7)))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y8)) | (Y6 @ Y9 @ Y7)) | (~ (Y6 @ Y8 @ Y7))))))))))) | (Y6 @ Y1 @ Y5)))))))))) | (((~ (Y2 = Y1)) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y5 @ Y6 @ Y7))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y6 @ Y8) | (~ (Y5 @ Y6 @ Y7))) | (~ (Y5 @ Y7 @ Y8))))))))))) | (Y5 @ Y2 @ Y1)))))) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y7 @ Y6) | (~ (Y5 @ Y7 @ Y8))) | (~ (Y5 @ Y8 @ Y6))))))))))) | (Y5 @ Y1 @ Y2))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y5 @ Y7)) | (Y4 @ Y5 @ Y6)) | (~ (Y4 @ Y7 @ Y6))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y3 @ Y5 @ Y6) | (~ (Y3 @ Y5 @ Y7))) | (~ (Y3 @ Y7 @ Y6))))))))))))))))))))) & (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y2 @ Y3)))))))))) & (join = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (~ ((((~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y5) | (~ (Y3 @ Y4 @ Y6))) | (~ (Y3 @ Y6 @ Y5)))))))))))))) & (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y5 @ Y6)) | (Y3 @ Y5 @ Y4)) | (~ (Y3 @ Y6 @ Y4)))))))))) | (Y3 @ Y2 @ Y1)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5))))))))))))) & (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y5))))))) | (Y4 @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y5 @ Y7) | (~ (Y4 @ Y6 @ Y7))) | (~ (Y4 @ Y5 @ Y6)))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y1 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y6)) | (Y4 @ Y5 @ Y6)) | (~ (Y4 @ Y5 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6)))))))))))))))) & (~ (Y1 = Y2)))))))))) & (asymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y2 @ Y1))))))))) & (sconfl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (!! @ $i @ (^[Y5 : $i]: ((((((((((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y3 @ Y6 @ Y7)) | (Y3 @ Y8 @ Y7)) | (~ (Y3 @ Y8 @ Y6)))))))))) | (Y2 = Y1)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y4 @ Y7 @ Y6)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y3 @ Y7 @ Y6)))))))) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y7 @ Y8) | (~ (Y0 @ Y7 @ Y8)))))))) | (Y6 @ Y5 @ Y2)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y9)) | (~ (Y6 @ Y8 @ Y9)))))))))))))) & (~ (Y5 = Y2)))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9)))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y8 @ Y10) | (~ (Y7 @ Y8 @ Y9))) | (~ (Y7 @ Y9 @ Y10))))))))))) | (Y7 @ Y1 @ Y6))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y9 @ Y8) | (~ (Y0 @ Y9 @ Y8)))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y9 @ Y10) | (~ (Y7 @ Y8 @ Y10))) | (~ (Y7 @ Y9 @ Y8))))))))))) | (Y7 @ Y2 @ Y6)))))))))) | (~ (Y0 @ Y5 @ Y1))) | (Y3 @ Y2 @ Y1)) | (Y4 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y4 @ Y8 @ Y6) | (~ (Y4 @ Y8 @ Y7))) | (~ (Y4 @ Y7 @ Y6))))))))))))))))))))))) & (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y0 @ Y2 @ Y1)))))))) & (term = (^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y1 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y0 @ Y3 @ Y4)) | (~ (Y1 @ Y4)))))))))) | (~ (Y1 @ Y2))))))))) & (trsc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y5 @ Y6))) | (Y3 @ Y4 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5)))))))))) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5)))))))) | (Y3 @ Y2 @ Y1)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y4 @ Y6)))))))))))))) | (Y1 = Y2))))))))),
% 2.70/0.71 inference(rectify,[],[f9])).
% 2.70/0.71 thf(f11,plain,(
% 2.70/0.71 (po = (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (Y2 = Y1)) | (~ (Y0 @ Y2 @ Y1))))))) & (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y1)) | (~ (Y0 @ Y2 @ Y3))) | (Y0 @ Y2 @ Y1))))))))))) & (tc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y5) | (~ (Y3 @ Y4 @ Y6))) | (~ (Y3 @ Y6 @ Y5)))))))))) | (Y3 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5))))))))))))))))) & (antisymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((Y2 = Y1) | (~ (Y0 @ Y1 @ Y2))) | (~ (Y0 @ Y2 @ Y1))))))))) & ! [X0 : $i] : (((d2unsorted @ (sK0 @ X0))) = X0) & (total = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((Y2 = Y1) | (Y0 @ Y1 @ Y2)) | (Y0 @ Y2 @ Y1)))))))) & (idem = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((Y0 @ (Y0 @ Y1)) = (Y0 @ Y1)))))) & (lconfl = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((((((((((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y3 @ Y6 @ Y7))))))) | (Y3 @ Y4 @ Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y8 @ Y6)) | (~ (Y1 @ Y7 @ Y8))) | (Y1 @ Y7 @ Y6)))))))))) | (~ (Y0 @ Y5 @ Y4))) | (Y4 = Y2)) | (~ (Y0 @ Y5 @ Y2))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y3 @ Y8 @ Y7) | (~ (Y3 @ Y8 @ Y6))) | (~ (Y3 @ Y6 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y1 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (Y1 @ Y2 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y2 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y8)) | (Y7 @ Y10 @ Y8)) | (~ (Y7 @ Y10 @ Y9))))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y10)) | (~ (Y7 @ Y8 @ Y9))) | (Y7 @ Y8 @ Y10))))))))) | (Y7 @ Y4 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9)))))))))))))))))))))))))))) & (nfof = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((Y1 = Y2) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y5 @ Y6)) | (~ (Y3 @ Y4 @ Y5))) | (Y3 @ Y4 @ Y6))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))) | (Y3 @ Y2 @ Y1))))) & (!! @ $i @ (^[Y3 : $i]: (~ (Y0 @ Y1 @ Y3))))))))))) & (ind = (^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6)))))))) | (Y5 @ Y3 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y7 @ Y8)) | (~ (Y5 @ Y8 @ Y6))) | (Y5 @ Y7 @ Y6))))))))))))) | (Y1 @ Y4))))))))) | (Y1 @ Y2)))))))) & (rc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y1 = Y2) | (Y0 @ Y1 @ Y2)))))))) & ! [X2 : d_unsorted,X3 : d_unsorted] : ((((d2unsorted @ X2)) != ((d2unsorted @ X3))) | (X2 = X3)) & (mono = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((Y0 @ Y3 @ Y1 @ Y4) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y2 @ Y6 @ Y5)) | (Y3 @ Y6 @ Y5)))))))) | (~ (Y0 @ Y2 @ Y1 @ Y4))))))))))))) & (innf = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2)))))))) & (inv = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (Y0 @ Y2 @ Y1))))))) & (irrefl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1)))))) & (confl = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((((((((((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y4 @ Y5) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y9)) | (~ (Y6 @ Y7 @ Y9))))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7))))))))))) & (~ (Y5 = Y4))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y9 @ Y8) | (~ (Y0 @ Y9 @ Y8)))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y8 @ Y9) | (~ (Y7 @ Y10 @ Y9))) | (~ (Y7 @ Y8 @ Y10))))))))))) | (Y7 @ Y2 @ Y6))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y5 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8)))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y9 @ Y10) | (~ (Y7 @ Y8 @ Y10))) | (~ (Y7 @ Y9 @ Y8))))))))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y7 @ Y6)) | (Y1 @ Y7 @ Y8)) | (~ (Y1 @ Y6 @ Y8))))))))))) | (Y5 = Y2)) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y8 @ Y7) | (~ (Y6 @ Y9 @ Y7))) | (~ (Y6 @ Y8 @ Y9)))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7)))))))) | (Y6 @ Y4 @ Y2))))) & (~ (Y4 = Y2)))) | (Y3 @ Y2 @ Y5)) | (Y1 @ Y5 @ Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y3 @ Y7 @ Y6)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y1 @ Y7 @ Y6)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y3 @ Y7 @ Y6) | (~ (Y3 @ Y7 @ Y8))) | (~ (Y3 @ Y8 @ Y6))))))))))))))))))))))) & (refl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))))) & (norm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: (~ (Y0 @ Y3 @ Y4))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y7)) | (Y4 @ Y5 @ Y7)) | (~ (Y4 @ Y5 @ Y6)))))))))) | (Y4 @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y5))))))))))))))) | (~ (Y0 @ Y2 @ Y1))))))))) & ! [X4 : d_unsorted] : (d_unsorted_0 = X4) & (trc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y6 @ Y4) | (~ (Y3 @ Y6 @ Y5))) | (~ (Y3 @ Y5 @ Y4))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5))))))))))) | (Y1 = Y2)))))))) & (trans = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y3 @ Y1))))))))))) & (symm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y2 @ Y1)))))))) & (infl = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y2 @ Y1 @ Y3)) | (Y0 @ Y2 @ Y1 @ Y3)))))))))) & (so = (^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) | (~ (Y0 @ Y3 @ Y1))) | (~ (Y0 @ Y2 @ Y3))))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y2 @ Y1)))))))))) & (cr = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((((((((Y2 = Y1) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y6 @ Y5) | (~ (Y0 @ Y6 @ Y5))))))))) | (Y4 @ Y2 @ Y1)) | (Y3 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y3 @ Y5 @ Y6)))))))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y7 @ Y9) | (~ (Y6 @ Y8 @ Y9))) | (~ (Y6 @ Y7 @ Y8)))))))))) | (Y6 @ Y2 @ Y5)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7)))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y8)) | (Y6 @ Y9 @ Y7)) | (~ (Y6 @ Y8 @ Y7))))))))))) | (Y6 @ Y1 @ Y5)))))))))) | (((~ (Y2 = Y1)) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y5 @ Y6 @ Y7))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y6 @ Y8) | (~ (Y5 @ Y6 @ Y7))) | (~ (Y5 @ Y7 @ Y8))))))))))) | (Y5 @ Y2 @ Y1)))))) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y7 @ Y6) | (~ (Y5 @ Y7 @ Y8))) | (~ (Y5 @ Y8 @ Y6))))))))))) | (Y5 @ Y1 @ Y2))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y5 @ Y7)) | (Y4 @ Y5 @ Y6)) | (~ (Y4 @ Y7 @ Y6))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y3 @ Y5 @ Y6) | (~ (Y3 @ Y5 @ Y7))) | (~ (Y3 @ Y7 @ Y6))))))))))))))))))))) & (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y2 @ Y3)))))))))) & (join = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (~ ((((~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y5) | (~ (Y3 @ Y4 @ Y6))) | (~ (Y3 @ Y6 @ Y5)))))))))))))) & (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y5 @ Y6)) | (Y3 @ Y5 @ Y4)) | (~ (Y3 @ Y6 @ Y4)))))))))) | (Y3 @ Y2 @ Y1)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5))))))))))))) & (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y5))))))) | (Y4 @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y5 @ Y7) | (~ (Y4 @ Y6 @ Y7))) | (~ (Y4 @ Y5 @ Y6)))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y1 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y6)) | (Y4 @ Y5 @ Y6)) | (~ (Y4 @ Y5 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y5 @ Y6) | (~ (Y0 @ Y5 @ Y6)))))))))))))))) & (~ (Y1 = Y2)))))))))) & (asymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y2 @ Y1))))))))) & (sconfl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (!! @ $i @ (^[Y5 : $i]: ((((((((((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y3 @ Y6 @ Y7)) | (Y3 @ Y8 @ Y7)) | (~ (Y3 @ Y8 @ Y6)))))))))) | (Y2 = Y1)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y4 @ Y7 @ Y6)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y3 @ Y7 @ Y6)))))))) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y7 @ Y8) | (~ (Y0 @ Y7 @ Y8)))))))) | (Y6 @ Y5 @ Y2)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y9)) | (~ (Y6 @ Y8 @ Y9)))))))))))))) & (~ (Y5 = Y2)))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9)))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y8 @ Y10) | (~ (Y7 @ Y8 @ Y9))) | (~ (Y7 @ Y9 @ Y10))))))))))) | (Y7 @ Y1 @ Y6))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y9 @ Y8) | (~ (Y0 @ Y9 @ Y8)))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y9 @ Y10) | (~ (Y7 @ Y8 @ Y10))) | (~ (Y7 @ Y9 @ Y8))))))))))) | (Y7 @ Y2 @ Y6)))))))))) | (~ (Y0 @ Y5 @ Y1))) | (Y3 @ Y2 @ Y1)) | (Y4 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y4 @ Y8 @ Y6) | (~ (Y4 @ Y8 @ Y7))) | (~ (Y4 @ Y7 @ Y6))))))))))))))))))))))) & (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y0 @ Y2 @ Y1)))))))) & (term = (^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y1 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y0 @ Y3 @ Y4)) | (~ (Y1 @ Y4)))))))))) | (~ (Y1 @ Y2))))))))) & (trsc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y5 @ Y6))) | (Y3 @ Y4 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5)))))))))) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5)))))))) | (Y3 @ Y2 @ Y1)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y4 @ Y6)))))))))))))) | (Y1 = Y2))))))))),
% 2.70/0.71 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X1,sK0 @ X0)],[f10])).
% 2.70/0.71 thf(f12,plain,(
% 2.70/0.71 (trsc != (^[Y0 : $i > $i > $o]: (sc @ (rc @ (tc @ Y0)))))),
% 2.70/0.71 inference(cnf_transformation,[],[f8])).
% 2.70/0.71 thf(f13,plain,(
% 2.70/0.71 (trsc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y5 @ Y6))) | (Y3 @ Y4 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5)))))))))) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5)))))))) | (Y3 @ Y2 @ Y1)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y4 @ Y6)))))))))))))) | (Y1 = Y2))))))))),
% 2.70/0.71 inference(cnf_transformation,[],[f11])).
% 2.70/0.71 thf(f15,plain,(
% 2.70/0.71 (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y0 @ Y2 @ Y1))))))))),
% 2.70/0.71 inference(cnf_transformation,[],[f11])).
% 2.70/0.71 thf(f26,plain,(
% 2.70/0.71 ( ! [X4 : d_unsorted] : ((d_unsorted_0 = X4)) )),
% 2.70/0.71 inference(cnf_transformation,[],[f11])).
% 2.70/0.71 thf(f35,plain,(
% 2.70/0.71 (rc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y1 = Y2) | (Y0 @ Y1 @ Y2))))))))),
% 2.70/0.71 inference(cnf_transformation,[],[f11])).
% 2.70/0.71 thf(f41,plain,(
% 2.70/0.71 ( ! [X0 : $i] : ((((d2unsorted @ (sK0 @ X0))) = X0)) )),
% 2.70/0.71 inference(cnf_transformation,[],[f11])).
% 2.70/0.71 thf(f48,definition,(
% 2.70/0.71 spl1_1 <=> (rc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y1 = Y2) | (Y0 @ Y1 @ Y2))))))))),
% 2.70/0.71 introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition])).
% 2.70/0.71 thf(f50,plain,(
% 2.70/0.71 (rc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y1 = Y2) | (Y0 @ Y1 @ Y2)))))))) | ~spl1_1),
% 2.70/0.71 inference(avatar_component_clause,[],[f48])).
% 2.70/0.71 thf(f51,plain,(
% 2.70/0.71 spl1_1),
% 2.70/0.71 inference(avatar_split_clause,[],[f35,f48])).
% 2.70/0.71 thf(f53,definition,(
% 2.70/0.71 spl1_2 <=> (trsc = (^[Y0 : $i > $i > $o]: (sc @ (rc @ (tc @ Y0)))))),
% 2.70/0.71 introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition])).
% 2.70/0.71 thf(f55,plain,(
% 2.70/0.71 (trsc != (^[Y0 : $i > $i > $o]: (sc @ (rc @ (tc @ Y0))))) | spl1_2),
% 2.70/0.71 inference(avatar_component_clause,[],[f53])).
% 2.70/0.71 thf(f56,plain,(
% 2.70/0.71 ~spl1_2),
% 2.70/0.71 inference(avatar_split_clause,[],[f12,f53])).
% 2.70/0.71 thf(f63,definition,(
% 2.70/0.71 spl1_4 <=> (trsc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y5 @ Y6))) | (Y3 @ Y4 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5)))))))))) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5)))))))) | (Y3 @ Y2 @ Y1)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y4 @ Y6)))))))))))))) | (Y1 = Y2))))))))),
% 2.70/0.72 introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition])).
% 2.70/0.72 thf(f65,plain,(
% 2.70/0.72 (trsc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y5 @ Y6))) | (Y3 @ Y4 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5)))))))))) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5)))))))) | (Y3 @ Y2 @ Y1)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y4 @ Y6)))))))))))))) | (Y1 = Y2)))))))) | ~spl1_4),
% 2.70/0.72 inference(avatar_component_clause,[],[f63])).
% 2.70/0.72 thf(f66,plain,(
% 2.70/0.72 spl1_4),
% 2.70/0.72 inference(avatar_split_clause,[],[f13,f63])).
% 2.70/0.72 thf(f68,definition,(
% 2.70/0.72 spl1_5 <=> (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y0 @ Y2 @ Y1))))))))),
% 2.70/0.72 introduced(definition,[new_symbols(definition,[spl1_5])],[avatar_definition])).
% 2.70/0.72 thf(f70,plain,(
% 2.70/0.72 (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y0 @ Y2 @ Y1)))))))) | ~spl1_5),
% 2.70/0.72 inference(avatar_component_clause,[],[f68])).
% 2.70/0.72 thf(f71,plain,(
% 2.70/0.72 spl1_5),
% 2.70/0.72 inference(avatar_split_clause,[],[f15,f68])).
% 2.70/0.72 thf(f80,plain,(
% 2.70/0.72 ( ! [X0 : $i] : ((((d2unsorted @ d_unsorted_0)) = X0)) )),
% 2.70/0.72 inference(superposition,[],[f41,f26])).
% 2.70/0.72 thf(f86,plain,(
% 2.70/0.72 ( ! [X1 : ($i > $i > $o)] : (((((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y1 = Y2) | (Y0 @ Y1 @ Y2))))))) @ X1)) = ((rc @ X1)))) ) | ~spl1_1),
% 2.70/0.72 inference(argument_congruence,[],[f50])).
% 2.70/0.72 thf(f87,plain,(
% 2.70/0.72 ( ! [X1 : ($i > $i > $o)] : (((^[Y0 : $i]: ((^[Y1 : $i]: ((Y0 = Y1) | (X1 @ Y0 @ Y1))))) = ((rc @ X1)))) ) | ~spl1_1),
% 2.70/0.72 inference(beta-eta_normalization,[],[f86])).
% 2.70/0.72 thf(f104,plain,(
% 2.70/0.72 ( ! [X0 : $i,X1 : $i] : ((X0 = X1)) )),
% 2.70/0.72 inference(superposition,[],[f80,f80])).
% 2.70/0.72 thf(f304,plain,(
% 2.70/0.72 ( ! [X1 : ($i > $i > $o)] : ((((sc @ X1)) = (((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y0 @ Y2 @ Y1))))))) @ X1)))) ) | ~spl1_5),
% 2.70/0.72 inference(argument_congruence,[],[f70])).
% 2.70/0.72 thf(f305,plain,(
% 2.70/0.72 ( ! [X1 : ($i > $i > $o)] : (((^[Y0 : $i]: ((^[Y1 : $i]: ((X1 @ Y0 @ Y1) | (X1 @ Y1 @ Y0))))) = ((sc @ X1)))) ) | ~spl1_5),
% 2.70/0.72 inference(beta-eta_normalization,[],[f304])).
% 2.70/0.72 thf(f308,plain,(
% 2.70/0.72 ((^[Y0 : $i > $i > $o]: (sc @ (rc @ (tc @ Y0)))) != (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y5 @ Y6))) | (Y3 @ Y4 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5)))))))))) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5)))))))) | (Y3 @ Y2 @ Y1)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y4 @ Y6)))))))))))))) | (Y1 = Y2)))))))) | (spl1_2 | ~spl1_4)),
% 2.70/0.72 inference(backward_demodulation,[],[f55,f65])).
% 2.70/0.72 thf(f312,definition,(
% 2.70/0.72 spl1_26 <=> ((^[Y0 : $i > $i > $o]: (sc @ (rc @ (tc @ Y0)))) = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y5 @ Y6))) | (Y3 @ Y4 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5)))))))))) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5)))))))) | (Y3 @ Y2 @ Y1)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y4 @ Y6)))))))))))))) | (Y1 = Y2))))))))),
% 2.70/0.72 introduced(definition,[new_symbols(definition,[spl1_26])],[avatar_definition])).
% 2.70/0.72 thf(f314,plain,(
% 2.70/0.72 ((^[Y0 : $i > $i > $o]: (sc @ (rc @ (tc @ Y0)))) != (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y5 @ Y6))) | (Y3 @ Y4 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5)))))))))) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5)))))))) | (Y3 @ Y2 @ Y1)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y4 @ Y6)))))))))))))) | (Y1 = Y2)))))))) | spl1_26),
% 2.70/0.72 inference(avatar_component_clause,[],[f312])).
% 2.70/0.72 thf(f315,plain,(
% 2.70/0.72 ~spl1_26 | spl1_2 | ~spl1_4),
% 2.70/0.72 inference(avatar_split_clause,[],[f308,f63,f53,f312])).
% 2.70/0.72 thf(f316,plain,(
% 2.70/0.72 ( ! [X2 : $i,X1 : ($i > $i > $o)] : ((((sc @ X1 @ X2)) = (((^[Y0 : $i]: ((^[Y1 : $i]: ((X1 @ Y0 @ Y1) | (X1 @ Y1 @ Y0))))) @ X2)))) ) | ~spl1_5),
% 2.70/0.72 inference(argument_congruence,[],[f305])).
% 2.70/0.72 thf(f317,plain,(
% 2.70/0.72 ( ! [X2 : $i,X1 : ($i > $i > $o)] : ((((sc @ X1 @ X2)) = (^[Y0 : $i]: ((X1 @ X2 @ Y0) | (X1 @ Y0 @ X2))))) ) | ~spl1_5),
% 2.70/0.72 inference(beta-eta_normalization,[],[f316])).
% 2.70/0.72 thf(f318,plain,(
% 2.70/0.72 ( ! [X2 : $i,X1 : ($i > $i > $o)] : ((((rc @ X1 @ X2)) = (((^[Y0 : $i]: ((^[Y1 : $i]: ((Y0 = Y1) | (X1 @ Y0 @ Y1))))) @ X2)))) ) | ~spl1_1),
% 2.70/0.72 inference(argument_congruence,[],[f87])).
% 2.70/0.72 thf(f319,plain,(
% 2.70/0.72 ( ! [X2 : $i,X1 : ($i > $i > $o)] : ((((rc @ X1 @ X2)) = (^[Y0 : $i]: ((X2 = Y0) | (X1 @ X2 @ Y0))))) ) | ~spl1_1),
% 2.70/0.72 inference(beta-eta_normalization,[],[f318])).
% 2.70/0.72 thf(f322,plain,(
% 2.70/0.72 ( ! [X2 : $i,X3 : $i,X1 : ($i > $i > $o)] : ((((sc @ X1 @ X2 @ X3)) = (((^[Y0 : $i]: ((X1 @ X2 @ Y0) | (X1 @ Y0 @ X2))) @ X3)))) ) | ~spl1_5),
% 2.70/0.72 inference(argument_congruence,[],[f317])).
% 2.70/0.72 thf(f323,plain,(
% 2.70/0.72 ( ! [X2 : $i,X3 : $i,X1 : ($i > $i > $o)] : ((((sc @ X1 @ X2 @ X3)) = $true) | ($false = (((^[Y0 : $i]: ((X1 @ X2 @ Y0) | (X1 @ Y0 @ X2))) @ X3)))) ) | ~spl1_5),
% 2.70/0.72 inference(iff_proxy_clausification,[],[f322])).
% 2.70/0.72 thf(f327,plain,(
% 2.70/0.72 ( ! [X2 : $i,X3 : $i,X1 : ($i > $i > $o)] : ((((sc @ X1 @ X2 @ X3)) = $true) | ($false = (((X1 @ X2 @ X3) | (X1 @ X3 @ X2))))) ) | ~spl1_5),
% 2.70/0.72 inference(beta-eta_normalization,[],[f323])).
% 2.70/0.72 thf(f328,plain,(
% 2.70/0.72 ( ! [X2 : $i,X3 : $i,X1 : ($i > $i > $o)] : ((((sc @ X1 @ X2 @ X3)) = $true) | ($false = ((X1 @ X3 @ X2)))) ) | ~spl1_5),
% 2.70/0.72 inference(or_proxy_clausification,[],[f327])).
% 2.70/0.72 thf(f332,plain,(
% 2.70/0.72 ( ! [X2 : $i,X3 : $i,X1 : ($i > $i > $o)] : (((((^[Y0 : $i]: ((X2 = Y0) | (X1 @ X2 @ Y0))) @ X3)) = ((rc @ X1 @ X2 @ X3)))) ) | ~spl1_1),
% 2.70/0.72 inference(argument_congruence,[],[f319])).
% 2.70/0.72 thf(f334,plain,(
% 2.70/0.72 ( ! [X2 : $i,X3 : $i,X1 : ($i > $i > $o)] : ((((rc @ X1 @ X2 @ X3)) = $true) | ((((^[Y0 : $i]: ((X2 = Y0) | (X1 @ X2 @ Y0))) @ X3)) = $false)) ) | ~spl1_1),
% 2.70/0.72 inference(iff_proxy_clausification,[],[f332])).
% 2.70/0.72 thf(f335,plain,(
% 2.70/0.72 ( ! [X2 : $i,X3 : $i,X1 : ($i > $i > $o)] : ((((rc @ X1 @ X2 @ X3)) = $true) | ($false = (((X2 = X3) | (X1 @ X2 @ X3))))) ) | ~spl1_1),
% 2.70/0.72 inference(beta-eta_normalization,[],[f334])).
% 2.70/0.72 thf(f337,plain,(
% 2.70/0.72 ( ! [X2 : $i,X3 : $i,X1 : ($i > $i > $o)] : ((((rc @ X1 @ X2 @ X3)) = $true) | ($false = ((X2 = X3)))) ) | ~spl1_1),
% 2.70/0.72 inference(or_proxy_clausification,[],[f335])).
% 2.70/0.72 thf(f338,plain,(
% 2.70/0.72 ( ! [X2 : $i,X3 : $i,X1 : ($i > $i > $o)] : ((X2 != X3) | (((rc @ X1 @ X2 @ X3)) = $true)) ) | ~spl1_1),
% 2.70/0.72 inference(equality_proxy_clausification,[],[f337])).
% 2.70/0.72 thf(f342,plain,(
% 2.70/0.72 ( ! [X2 : $i,X3 : $i,X1 : ($i > $i > $o)] : ((((rc @ X1 @ X2 @ X3)) = $true)) ) | ~spl1_1),
% 2.70/0.72 inference(forward_subsumption_resolution,[],[f338,f104])).
% 2.70/0.72 thf(f403,plain,(
% 2.70/0.72 ((((^[Y0 : $i > $i > $o]: (sc @ (rc @ (tc @ Y0)))) @ sK14)) != (((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y5 @ Y6))) | (Y3 @ Y4 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5)))))))))) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5)))))))) | (Y3 @ Y2 @ Y1)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y4 @ Y6)))))))))))))) | (Y1 = Y2))))))) @ sK14))) | spl1_26),
% 2.70/0.72 inference(negative_extensionality,[],[f314])).
% 2.70/0.72 thf(f404,plain,(
% 2.70/0.72 (((sc @ (rc @ (tc @ sK14)))) != (^[Y0 : $i]: ((^[Y1 : $i]: (((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((Y2 @ Y0 @ Y1) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y3 @ Y4)) | (~ (Y2 @ Y4 @ Y5))) | (Y2 @ Y3 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (sK14 @ Y3 @ Y4)) | (Y2 @ Y3 @ Y4)))))))))) | (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y3 @ Y4) | (~ (sK14 @ Y3 @ Y4)))))))) | (Y2 @ Y1 @ Y0)) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y4)) | (Y2 @ Y3 @ Y4)) | (~ (Y2 @ Y3 @ Y5)))))))))))))) | (Y0 = Y1)))))) | spl1_26),
% 2.70/0.72 inference(beta-eta_normalization,[],[f403])).
% 2.70/0.72 thf(f406,definition,(
% 2.70/0.72 spl1_27 <=> (((sc @ (rc @ (tc @ sK14)))) = (^[Y0 : $i]: ((^[Y1 : $i]: (((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((Y2 @ Y0 @ Y1) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y3 @ Y4)) | (~ (Y2 @ Y4 @ Y5))) | (Y2 @ Y3 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (sK14 @ Y3 @ Y4)) | (Y2 @ Y3 @ Y4)))))))))) | (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y3 @ Y4) | (~ (sK14 @ Y3 @ Y4)))))))) | (Y2 @ Y1 @ Y0)) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y4)) | (Y2 @ Y3 @ Y4)) | (~ (Y2 @ Y3 @ Y5)))))))))))))) | (Y0 = Y1))))))),
% 2.70/0.72 introduced(definition,[new_symbols(definition,[spl1_27])],[avatar_definition])).
% 2.70/0.72 thf(f408,plain,(
% 2.70/0.72 (((sc @ (rc @ (tc @ sK14)))) != (^[Y0 : $i]: ((^[Y1 : $i]: (((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((Y2 @ Y0 @ Y1) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y3 @ Y4)) | (~ (Y2 @ Y4 @ Y5))) | (Y2 @ Y3 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (sK14 @ Y3 @ Y4)) | (Y2 @ Y3 @ Y4)))))))))) | (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y3 @ Y4) | (~ (sK14 @ Y3 @ Y4)))))))) | (Y2 @ Y1 @ Y0)) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y4)) | (Y2 @ Y3 @ Y4)) | (~ (Y2 @ Y3 @ Y5)))))))))))))) | (Y0 = Y1)))))) | spl1_27),
% 2.70/0.72 inference(avatar_component_clause,[],[f406])).
% 2.70/0.72 thf(f409,plain,(
% 2.70/0.72 ~spl1_27 | spl1_26),
% 2.70/0.72 inference(avatar_split_clause,[],[f404,f312,f406])).
% 2.70/0.72 thf(f615,plain,(
% 2.70/0.72 ((((^[Y0 : $i]: ((^[Y1 : $i]: (((!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((Y2 @ Y0 @ Y1) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y3 @ Y4)) | (~ (Y2 @ Y4 @ Y5))) | (Y2 @ Y3 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (sK14 @ Y3 @ Y4)) | (Y2 @ Y3 @ Y4)))))))))) | (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y3 @ Y4) | (~ (sK14 @ Y3 @ Y4)))))))) | (Y2 @ Y1 @ Y0)) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y4)) | (Y2 @ Y3 @ Y4)) | (~ (Y2 @ Y3 @ Y5)))))))))))))) | (Y0 = Y1))))) @ sK31)) != ((sc @ (rc @ (tc @ sK14)) @ sK31))) | spl1_27),
% 2.70/0.72 inference(negative_extensionality,[],[f408])).
% 2.70/0.72 thf(f616,plain,(
% 2.70/0.72 ((^[Y0 : $i]: (((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((Y1 @ sK31 @ Y0) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y2 @ Y3)) | (~ (Y1 @ Y3 @ Y4))) | (Y1 @ Y2 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK14 @ Y2 @ Y3)) | (Y1 @ Y2 @ Y3)))))))))) | (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) | (~ (sK14 @ Y2 @ Y3)))))))) | (Y1 @ Y0 @ sK31)) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (Y1 @ Y2 @ Y3)) | (~ (Y1 @ Y2 @ Y4)))))))))))))) | (sK31 = Y0))) != ((sc @ (rc @ (tc @ sK14)) @ sK31))) | spl1_27),
% 2.70/0.72 inference(beta-eta_normalization,[],[f615])).
% 2.70/0.72 thf(f618,definition,(
% 2.70/0.72 spl1_28 <=> ((^[Y0 : $i]: (((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((Y1 @ sK31 @ Y0) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y2 @ Y3)) | (~ (Y1 @ Y3 @ Y4))) | (Y1 @ Y2 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK14 @ Y2 @ Y3)) | (Y1 @ Y2 @ Y3)))))))))) | (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) | (~ (sK14 @ Y2 @ Y3)))))))) | (Y1 @ Y0 @ sK31)) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (Y1 @ Y2 @ Y3)) | (~ (Y1 @ Y2 @ Y4)))))))))))))) | (sK31 = Y0))) = ((sc @ (rc @ (tc @ sK14)) @ sK31)))),
% 2.70/0.72 introduced(definition,[new_symbols(definition,[spl1_28])],[avatar_definition])).
% 2.70/0.72 thf(f620,plain,(
% 2.70/0.72 ((^[Y0 : $i]: (((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((Y1 @ sK31 @ Y0) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y2 @ Y3)) | (~ (Y1 @ Y3 @ Y4))) | (Y1 @ Y2 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK14 @ Y2 @ Y3)) | (Y1 @ Y2 @ Y3)))))))))) | (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) | (~ (sK14 @ Y2 @ Y3)))))))) | (Y1 @ Y0 @ sK31)) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (Y1 @ Y2 @ Y3)) | (~ (Y1 @ Y2 @ Y4)))))))))))))) | (sK31 = Y0))) != ((sc @ (rc @ (tc @ sK14)) @ sK31))) | spl1_28),
% 2.70/0.72 inference(avatar_component_clause,[],[f618])).
% 2.70/0.72 thf(f621,plain,(
% 2.70/0.72 ~spl1_28 | spl1_27),
% 2.70/0.72 inference(avatar_split_clause,[],[f616,f406,f618])).
% 2.70/0.72 thf(f622,plain,(
% 2.70/0.72 (((sc @ (rc @ (tc @ sK14)) @ sK31 @ sK32)) != (((^[Y0 : $i]: (((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((Y1 @ sK31 @ Y0) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y2 @ Y3)) | (~ (Y1 @ Y3 @ Y4))) | (Y1 @ Y2 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK14 @ Y2 @ Y3)) | (Y1 @ Y2 @ Y3)))))))))) | (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) | (~ (sK14 @ Y2 @ Y3)))))))) | (Y1 @ Y0 @ sK31)) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (Y1 @ Y2 @ Y3)) | (~ (Y1 @ Y2 @ Y4)))))))))))))) | (sK31 = Y0))) @ sK32))) | spl1_28),
% 2.70/0.72 inference(negative_extensionality,[],[f620])).
% 2.70/0.72 thf(f624,plain,(
% 2.70/0.72 ($false = (((^[Y0 : $i]: (((!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((Y1 @ sK31 @ Y0) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y2 @ Y3)) | (~ (Y1 @ Y3 @ Y4))) | (Y1 @ Y2 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (sK14 @ Y2 @ Y3)) | (Y1 @ Y2 @ Y3)))))))))) | (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) | (~ (sK14 @ Y2 @ Y3)))))))) | (Y1 @ Y0 @ sK31)) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y3)) | (Y1 @ Y2 @ Y3)) | (~ (Y1 @ Y2 @ Y4)))))))))))))) | (sK31 = Y0))) @ sK32))) | (((sc @ (rc @ (tc @ sK14)) @ sK31 @ sK32)) = $false) | spl1_28),
% 2.70/0.72 inference(xor_proxy_clausification,[],[f622])).
% 2.70/0.72 thf(f625,plain,(
% 2.70/0.72 (((sc @ (rc @ (tc @ sK14)) @ sK31 @ sK32)) = $false) | ($false = ((((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((Y0 @ sK31 @ sK32) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y2 @ Y3))) | (Y0 @ Y1 @ Y3)))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (sK14 @ Y1 @ Y2)) | (Y0 @ Y1 @ Y2)))))))))) | (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (~ (sK14 @ Y1 @ Y2)))))))) | (Y0 @ sK32 @ sK31)) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y2)) | (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y1 @ Y3)))))))))))))) | (sK31 = sK32)))) | spl1_28),
% 2.70/0.72 inference(beta-eta_normalization,[],[f624])).
% 2.70/0.72 thf(f626,plain,(
% 2.70/0.72 ($false = ((sK31 = sK32))) | (((sc @ (rc @ (tc @ sK14)) @ sK31 @ sK32)) = $false) | spl1_28),
% 2.70/0.72 inference(or_proxy_clausification,[],[f625])).
% 2.70/0.72 thf(f678,plain,(
% 2.70/0.72 (((sc @ (rc @ (tc @ sK14)) @ sK31 @ sK32)) = $false) | (sK31 != sK32) | spl1_28),
% 2.70/0.72 inference(equality_proxy_clausification,[],[f626])).
% 2.70/0.72 thf(f826,definition,(
% 2.70/0.72 spl1_29 <=> (((sc @ (rc @ (tc @ sK14)) @ sK31 @ sK32)) = $false)),
% 2.70/0.72 introduced(definition,[new_symbols(definition,[spl1_29])],[avatar_definition])).
% 2.70/0.72 thf(f828,plain,(
% 2.70/0.72 (((sc @ (rc @ (tc @ sK14)) @ sK31 @ sK32)) = $false) | ~spl1_29),
% 2.70/0.72 inference(avatar_component_clause,[],[f826])).
% 2.70/0.72 thf(f855,plain,(
% 2.70/0.72 (((sc @ (rc @ (tc @ sK14)) @ sK31 @ sK32)) = $false) | spl1_28),
% 2.70/0.72 inference(forward_subsumption_resolution,[],[f678,f104])).
% 2.70/0.72 thf(f856,plain,(
% 2.70/0.72 spl1_29 | spl1_28),
% 2.70/0.72 inference(avatar_split_clause,[],[f855,f618,f826])).
% 2.70/0.72 thf(f857,plain,(
% 2.70/0.72 ( ! [X0 : $i] : ((((sc @ (rc @ (tc @ sK14)) @ sK31 @ X0)) = $false)) ) | ~spl1_29),
% 2.70/0.72 inference(superposition,[],[f828,f104])).
% 2.70/0.72 thf(f873,plain,(
% 2.70/0.72 ( ! [X0 : $i,X1 : $i] : (($false = ((sc @ (rc @ (tc @ sK14)) @ X0 @ X1)))) ) | ~spl1_29),
% 2.70/0.72 inference(superposition,[],[f857,f104])).
% 2.70/0.72 thf(f883,plain,(
% 2.70/0.72 ( ! [X0 : $i,X1 : $i] : (($false = $true) | ($false = ((rc @ (tc @ sK14) @ X1 @ X0)))) ) | (~spl1_5 | ~spl1_29)),
% 2.70/0.72 inference(superposition,[],[f873,f328])).
% 2.70/0.72 thf(f888,plain,(
% 2.70/0.72 ( ! [X0 : $i,X1 : $i] : (($false = ((rc @ (tc @ sK14) @ X1 @ X0)))) ) | (~spl1_5 | ~spl1_29)),
% 2.70/0.72 inference(trivial_inequality_removal,[],[f883])).
% 2.70/0.72 thf(f898,plain,(
% 2.70/0.72 ($false = $true) | (~spl1_1 | ~spl1_5 | ~spl1_29)),
% 2.70/0.72 inference(forward_demodulation,[],[f888,f342])).
% 2.70/0.72 thf(f899,plain,(
% 2.70/0.72 $false | (~spl1_1 | ~spl1_5 | ~spl1_29)),
% 2.70/0.72 inference(trivial_inequality_removal,[],[f898])).
% 2.70/0.72 thf(f900,plain,(
% 2.70/0.72 ~spl1_1 | ~spl1_5 | ~spl1_29),
% 2.70/0.72 inference(avatar_contradiction_clause,[],[f899])).
% 2.70/0.72 cnf(s1, plain, spl1_1, inference(sat_conversion,[],[f51])).
% 2.70/0.72 cnf(s2, plain, ~spl1_2, inference(sat_conversion,[],[f56])).
% 2.70/0.72 cnf(s4, plain, spl1_4, inference(sat_conversion,[],[f66])).
% 2.70/0.72 cnf(s5, plain, spl1_5, inference(sat_conversion,[],[f71])).
% 2.70/0.72 cnf(s38, plain, spl1_2 | ~spl1_4 | ~spl1_26, inference(sat_conversion,[],[f315])).
% 2.70/0.72 cnf(s39, plain, spl1_26 | ~spl1_27, inference(sat_conversion,[],[f409])).
% 2.70/0.72 cnf(s40, plain, spl1_27 | ~spl1_28, inference(sat_conversion,[],[f621])).
% 2.70/0.72 cnf(s47, plain, spl1_28 | spl1_29, inference(sat_conversion,[],[f856])).
% 2.70/0.72 cnf(s53, plain, ~spl1_1 | ~spl1_5 | ~spl1_29, inference(sat_conversion,[],[f900])).
% 2.70/0.72 cnf(s54, plain, ~spl1_26, inference(rat,[],[s38,s4,s2])).
% 2.70/0.72 cnf(s56, plain, ~spl1_27, inference(rat,[],[s39,s54])).
% 2.70/0.72 cnf(s58, plain, ~spl1_28, inference(rat,[],[s40,s56])).
% 2.70/0.72 cnf(s60, plain, spl1_29, inference(rat,[],[s47,s58])).
% 2.70/0.72 cnf(s63, plain, ~spl1_1, inference(rat,[],[s53,s5,s60])).
% 2.70/0.72 cnf(s64, plain, $false, inference(rat,[],[s1,s63])).
% 2.70/0.72 thf(f901,plain,(
% 2.70/0.72 $false),
% 2.70/0.72 inference(avatar_sat_refutation,[],[s64])).
% 2.70/0.72 % SZS output end Proof for theBenchmark
% 2.70/0.72 % (981325)------------------------------
% 2.70/0.72 % (981325)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.70/0.72 % (981325)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.70/0.72 % (981325)CaDiCaL version: 2.1.3
% 2.70/0.72 % (981325)Termination reason: Refutation
% 2.70/0.72 % (981325)Time elapsed: 0.069 s
% 2.70/0.72 % (981325)Peak memory usage: 14 MB
% 2.70/0.72 % (981325)Instructions burned: 158 (million)
% 2.70/0.72 % (981239)Success in time 0.45 s
% 2.70/0.72 % Vampire exiting
%------------------------------------------------------------------------------