%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP119^2 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:08:25 AM UTC 2026
% Result : ContradictoryAxioms 0.61s 0.41s
% Output : Refutation 0.61s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP119^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n006.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 19:56:10 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.26 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
% 0.61/0.41 % (1229095)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.61/0.41 % (1229122)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=804329064:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.61/0.41 % (1229124)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.61/0.41 % (1229124)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
% 0.61/0.41 % (1229122)Instruction limit reached!
% 0.61/0.41 % (1229122)------------------------------
% 0.61/0.41 % (1229122)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.41 % (1229122)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.41 % (1229122)CaDiCaL version: 2.1.3
% 0.61/0.41 % (1229122)Termination reason: Instruction limit
% 0.61/0.41 % (1229122)Termination phase: Property scanning
% 0.61/0.41 % (1229122)Time elapsed: 0.006 s
% 0.61/0.41 % (1229122)Peak memory usage: 10 MB
% 0.61/0.41 % (1229122)Instructions burned: 24 (million)
% 0.61/0.41 % (1229118)lrs+10_16_si=on:nwc=1.5:random_seed=833058572:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.61/0.41 % (1229117)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3843742501:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.61/0.41 % (1229123)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=528784289:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.61/0.41 % (1229120)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1280196398:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.61/0.41 % (1229121)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=4067106584: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)
% 0.61/0.41 % (1229124)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=1959210931:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.61/0.41 % (1229120)Instruction limit reached!
% 0.61/0.41 % (1229120)------------------------------
% 0.61/0.41 % (1229120)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.41 % (1229120)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.41 % (1229120)CaDiCaL version: 2.1.3
% 0.61/0.41 % (1229120)Termination reason: Instruction limit
% 0.61/0.41 % (1229120)Termination phase: shuffling
% 0.61/0.41 % (1229120)Time elapsed: 0.002 s
% 0.61/0.41 % (1229120)Peak memory usage: 10 MB
% 0.61/0.41 % (1229120)Instructions burned: 4 (million)
% 0.61/0.41 % (1229118)Instruction limit reached!
% 0.61/0.41 % (1229118)------------------------------
% 0.61/0.41 % (1229118)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.41 % (1229118)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.41 % (1229118)CaDiCaL version: 2.1.3
% 0.61/0.41 % (1229118)Termination reason: Instruction limit
% 0.61/0.41 % (1229118)Termination phase: Property scanning
% 0.61/0.41 % (1229118)Time elapsed: 0.010 s
% 0.61/0.41 % (1229118)Peak memory usage: 10 MB
% 0.61/0.41 % (1229118)Instructions burned: 20 (million)
% 0.61/0.41 % (1229128)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=795772847:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.61/0.41 % (1229128)Instruction limit reached!
% 0.61/0.41 % (1229128)------------------------------
% 0.61/0.41 % (1229128)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.41 % (1229128)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.41 % (1229128)CaDiCaL version: 2.1.3
% 0.61/0.41 % (1229128)Termination reason: Instruction limit
% 0.61/0.41 % (1229128)Termination phase: shuffling
% 0.61/0.41 % (1229128)Time elapsed: 0.001 s
% 0.61/0.41 % (1229128)Peak memory usage: 10 MB
% 0.61/0.41 % (1229128)Instructions burned: 6 (million)
% 0.61/0.41 % (1229139)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=918479950:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.61/0.41 % (1229135)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1165029872:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.61/0.41 % (1229135)Instruction limit reached!
% 0.61/0.41 % (1229135)------------------------------
% 0.61/0.41 % (1229135)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.41 % (1229135)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.41 % (1229135)CaDiCaL version: 2.1.3
% 0.61/0.41 % (1229135)Termination reason: Instruction limit
% 0.61/0.41 % (1229135)Termination phase: shuffling
% 0.61/0.41 % (1229135)Time elapsed: 0.004 s
% 0.61/0.41 % (1229135)Peak memory usage: 10 MB
% 0.61/0.41 % (1229135)Instructions burned: 7 (million)
% 0.61/0.41 % (1229139)Instruction limit reached!
% 0.61/0.41 % (1229139)------------------------------
% 0.61/0.41 % (1229139)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.41 % (1229139)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.41 % (1229139)CaDiCaL version: 2.1.3
% 0.61/0.41 % (1229139)Termination reason: Instruction limit
% 0.61/0.41 % (1229139)Termination phase: shuffling
% 0.61/0.41 % (1229139)Time elapsed: 0.004 s
% 0.61/0.41 % (1229139)Peak memory usage: 10 MB
% 0.61/0.41 % (1229139)Instructions burned: 16 (million)
% 0.61/0.41 % (1229138)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.61/0.41 % (1229138)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3484984821:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.61/0.41 % (1229138)Instruction limit reached!
% 0.61/0.41 % (1229138)------------------------------
% 0.61/0.41 % (1229138)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.41 % (1229138)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.41 % (1229138)CaDiCaL version: 2.1.3
% 0.61/0.41 % (1229138)Termination reason: Instruction limit
% 0.61/0.41 % (1229138)Termination phase: shuffling
% 0.61/0.41 % (1229138)Time elapsed: 0.004 s
% 0.61/0.41 % (1229138)Peak memory usage: 10 MB
% 0.61/0.41 % (1229138)Instructions burned: 7 (million)
% 0.61/0.41 % (1229123)Instruction limit reached!
% 0.61/0.41 % (1229123)------------------------------
% 0.61/0.41 % (1229123)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.41 % (1229123)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.41 % (1229123)CaDiCaL version: 2.1.3
% 0.61/0.41 % (1229123)Termination reason: Instruction limit
% 0.61/0.41 % (1229123)Termination phase: Property scanning
% 0.61/0.41 % (1229123)Time elapsed: 0.037 s
% 0.61/0.41 % (1229123)Peak memory usage: 12 MB
% 0.61/0.41 % (1229123)Instructions burned: 78 (million)
% 0.61/0.41 % (1229146)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=3701625798:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.61/0.41 % (1229145)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
% 0.61/0.41 % (1229145)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.61/0.41 % (1229117)Instruction limit reached!
% 0.61/0.41 % (1229117)------------------------------
% 0.61/0.41 % (1229117)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.41 % (1229117)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.41 % (1229117)CaDiCaL version: 2.1.3
% 0.61/0.41 % (1229117)Termination reason: Instruction limit
% 0.61/0.41 % (1229117)Termination phase: Property scanning
% 0.61/0.41 % (1229117)Time elapsed: 0.044 s
% 0.61/0.41 % (1229117)Peak memory usage: 12 MB
% 0.61/0.41 % (1229117)Instructions burned: 94 (million)
% 0.61/0.41 % (1229145)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=15261015:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.61/0.41 % (1229151)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.61/0.41 % (1229150)lrs+10_1_si=on:cs=on:random_seed=754903445:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.61/0.41 % (1229151)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=2425686211:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.61/0.41 % (1229151)Instruction limit reached!
% 0.61/0.41 % (1229151)------------------------------
% 0.61/0.41 % (1229151)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.41 % (1229151)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.41 % (1229146)Instruction limit reached!
% 0.61/0.41 % (1229146)------------------------------
% 0.61/0.41 % (1229146)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.41 % (1229151)CaDiCaL version: 2.1.3
% 0.61/0.41 % (1229151)Termination reason: Instruction limit
% 0.61/0.41 % (1229151)Termination phase: shuffling
% 0.61/0.41 % (1229151)Time elapsed: 0.002 s
% 0.61/0.41 % (1229151)Peak memory usage: 10 MB
% 0.61/0.41 % (1229146)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.41 % (1229151)Instructions burned: 4 (million)
% 0.61/0.41 % (1229146)CaDiCaL version: 2.1.3
% 0.61/0.41 % (1229146)Termination reason: Instruction limit
% 0.61/0.41 % (1229146)Termination phase: Property scanning
% 0.61/0.41 % (1229146)Time elapsed: 0.021 s
% 0.61/0.41 % (1229146)Peak memory usage: 11 MB
% 0.61/0.41 % (1229146)Instructions burned: 86 (million)
% 0.61/0.41 % (1229145)Instruction limit reached!
% 0.61/0.41 % (1229145)------------------------------
% 0.61/0.41 % (1229145)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.41 % (1229145)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.41 % (1229145)CaDiCaL version: 2.1.3
% 0.61/0.41 % (1229145)Termination reason: Instruction limit
% 0.61/0.41 % (1229145)Termination phase: shuffling
% 0.61/0.41 % (1229145)Time elapsed: 0.014 s
% 0.61/0.41 % (1229145)Peak memory usage: 10 MB
% 0.61/0.41 % (1229145)Instructions burned: 28 (million)
% 0.61/0.41 % (1229150)Instruction limit reached!
% 0.61/0.41 % (1229150)------------------------------
% 0.61/0.41 % (1229150)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.41 % (1229150)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.41 % (1229150)CaDiCaL version: 2.1.3
% 0.61/0.41 % (1229150)Termination reason: Instruction limit
% 0.61/0.41 % (1229150)Termination phase: shuffling
% 0.61/0.41 % (1229150)Time elapsed: 0.004 s
% 0.61/0.41 % (1229150)Peak memory usage: 10 MB
% 0.61/0.41 % (1229150)Instructions burned: 8 (million)
% 0.61/0.41 % (1229154)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=663728276:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.61/0.41 % (1229163)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=2926024533:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 0.61/0.41 % (1229166)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=2998310847:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.61/0.41 % (1229167)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=2065935239:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 0.61/0.41 % (1229154)Instruction limit reached!
% 0.61/0.41 % (1229154)------------------------------
% 0.61/0.41 % (1229154)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.41 % (1229154)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.41 % (1229154)CaDiCaL version: 2.1.3
% 0.61/0.41 % (1229154)Termination reason: Instruction limit
% 0.61/0.41 % (1229154)Termination phase: Saturation
% 0.61/0.41 % (1229154)Time elapsed: 0.018 s
% 0.61/0.41 % (1229154)Peak memory usage: 12 MB
% 0.61/0.41 % (1229154)Instructions burned: 39 (million)
% 0.61/0.41 % (1229166)Instruction limit reached!
% 0.61/0.41 % (1229166)------------------------------
% 0.61/0.41 % (1229166)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.41 % (1229166)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.41 % (1229166)CaDiCaL version: 2.1.3
% 0.61/0.41 % (1229166)Termination reason: Instruction limit
% 0.61/0.41 % (1229166)Termination phase: shuffling
% 0.61/0.41 % (1229166)Time elapsed: 0.007 s
% 0.61/0.41 % (1229166)Peak memory usage: 10 MB
% 0.61/0.41 % (1229166)Instructions burned: 15 (million)
% 0.61/0.41 % (1229121) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1229095-1229121"...
% 0.61/0.41 % (1229165)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=3294699549:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 0.61/0.41 % (1229121)...printing done.
% 0.61/0.41 % (1229121)Refutation found. Thanks to Tanya!
% 0.61/0.41 % SZS status ContradictoryAxioms for theBenchmark
% 0.61/0.41 % SZS output start Proof for theBenchmark
% 0.61/0.41 thf(type_def_5, type, list: $tType > $tType).
% 0.61/0.41 thf(type_def_6, type, a: $tType).
% 0.61/0.41 thf(type_def_7, type, sTfun: ($tType * $tType) > $tType).
% 0.61/0.41 thf(func_def_0, type, type: !>[X0: $tType]:($o)).
% 0.61/0.41 thf(func_def_1, type, ord: !>[X0: $tType]:($o)).
% 0.61/0.41 thf(func_def_2, type, linorder: !>[X0: $tType]:($o)).
% 0.61/0.41 thf(func_def_3, type, finite_comp_fun_idem: !>[X0: $tType, X1: $tType]:(((X0 > X1 > X1) > $o))).
% 0.61/0.41 thf(func_def_4, type, abel_semigroup: !>[X0: $tType]:(((X0 > X0 > X0) > $o))).
% 0.61/0.41 thf(func_def_5, type, abel_s1917375468axioms: !>[X0: $tType]:(((X0 > X0 > X0) > $o))).
% 0.61/0.41 thf(func_def_6, type, semigroup: !>[X0: $tType]:(((X0 > X0 > X0) > $o))).
% 0.61/0.41 thf(func_def_7, type, semilattice: !>[X0: $tType]:(((X0 > X0 > X0) > $o))).
% 0.61/0.41 thf(func_def_8, type, semilattice_axioms: !>[X0: $tType]:(((X0 > X0 > X0) > $o))).
% 0.61/0.41 thf(func_def_9, type, lattices_is_arg_max: !>[X0: $tType, X1: $tType]:(((X0 > X0 > $o) > (X1 > X0) > (X1 > $o) > X1 > $o))).
% 0.61/0.41 thf(func_def_10, type, lattices_is_arg_min: !>[X0: $tType, X1: $tType]:(((X0 > X0 > $o) > (X1 > X0) > (X1 > $o) > X1 > $o))).
% 0.61/0.41 thf(func_def_11, type, lattic35693393ce_set: !>[X0: $tType]:(((X0 > X0 > X0) > $o))).
% 0.61/0.41 thf(func_def_12, type, append: !>[X0: $tType]:((list @ X0 > list @ X0 > list @ X0))).
% 0.61/0.41 thf(func_def_13, type, bind: !>[X0: $tType, X1: $tType]:((list @ X0 > (X0 > list @ X1) > list @ X1))).
% 0.61/0.41 thf(func_def_14, type, butlast: !>[X0: $tType]:((list @ X0 > list @ X0))).
% 0.61/0.41 thf(func_def_15, type, concat: !>[X0: $tType]:((list @ list @ X0 > list @ X0))).
% 0.61/0.41 thf(func_def_16, type, insert: !>[X0: $tType]:((X0 > list @ X0 > list @ X0))).
% 0.61/0.41 thf(func_def_17, type, last: !>[X0: $tType]:((list @ X0 > X0))).
% 0.61/0.41 thf(func_def_18, type, cons: !>[X0: $tType]:((X0 > list @ X0 > list @ X0))).
% 0.61/0.41 thf(func_def_19, type, nil: !>[X0: $tType]:(list @ X0)).
% 0.61/0.41 thf(func_def_20, type, list_ex1: !>[X0: $tType]:(((X0 > $o) > list @ X0 > $o))).
% 0.61/0.41 thf(func_def_21, type, maps: !>[X0: $tType, X1: $tType]:(((X0 > list @ X1) > list @ X0 > list @ X1))).
% 0.61/0.41 thf(func_def_22, type, lexordp: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > list @ X0 > $o))).
% 0.61/0.41 thf(func_def_23, type, lexordp_eq: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > list @ X0 > $o))).
% 0.61/0.41 thf(func_def_24, type, product_lists: !>[X0: $tType]:((list @ list @ X0 > list @ list @ X0))).
% 0.61/0.41 thf(func_def_25, type, rotate1: !>[X0: $tType]:((list @ X0 > list @ X0))).
% 0.61/0.41 thf(func_def_26, type, subseqs: !>[X0: $tType]:((list @ X0 > list @ list @ X0))).
% 0.61/0.41 thf(func_def_27, type, modula1618706180attice: !>[X0: $tType]:(((X0 > X0 > X0) > (X0 > X0 > $o) > (X0 > X0 > X0) > X0 > X0 > X0 > $o))).
% 0.61/0.41 thf(func_def_28, type, modula1192512645attice: !>[X0: $tType]:(((X0 > X0 > X0) > (X0 > X0 > $o) > (X0 > X0 > X0) > X0 > X0 > X0 > $o))).
% 0.61/0.41 thf(func_def_29, type, modula105138637_a_aux: !>[X0: $tType]:(((X0 > X0 > X0) > (X0 > X0 > X0) > X0 > X0 > X0 > X0))).
% 0.61/0.41 thf(func_def_30, type, modula477145868_b_aux: !>[X0: $tType]:(((X0 > X0 > X0) > (X0 > X0 > X0) > X0 > X0 > X0 > X0))).
% 0.61/0.41 thf(func_def_31, type, modula849153099_c_aux: !>[X0: $tType]:(((X0 > X0 > X0) > (X0 > X0 > X0) > X0 > X0 > X0 > X0))).
% 0.61/0.41 thf(func_def_32, type, modula1221160330_d_aux: !>[X0: $tType]:(((X0 > X0 > X0) > (X0 > X0 > X0) > X0 > X0 > X0 > X0))).
% 0.61/0.41 thf(func_def_33, type, modula1593167561_e_aux: !>[X0: $tType]:(((X0 > X0 > X0) > (X0 > X0 > X0) > X0 > X0 > X0 > X0))).
% 0.61/0.41 thf(func_def_34, type, modula141148890istrib: !>[X0: $tType]:(((X0 > X0 > X0) > (X0 > X0 > $o) > (X0 > X0 > X0) > X0 > X0 > X0 > $o))).
% 0.61/0.41 thf(func_def_35, type, transp: !>[X0: $tType]:(((X0 > X0 > $o) > $o))).
% 0.61/0.41 thf(func_def_36, type, a2: a).
% 0.61/0.41 thf(func_def_37, type, b: a).
% 0.61/0.41 thf(func_def_38, type, c: a).
% 0.61/0.41 thf(func_def_39, type, inf: (a > a > a)).
% 0.61/0.41 thf(func_def_40, type, less: (a > a > $o)).
% 0.61/0.41 thf(func_def_41, type, sup: (a > a > a)).
% 0.61/0.41 thf(func_def_45, type, vAND: ($o > $o > $o)).
% 0.61/0.41 thf(func_def_46, type, db1: !>[X0: $tType]:(X0)).
% 0.61/0.41 thf(func_def_47, type, db0: !>[X0: $tType]:(X0)).
% 0.61/0.41 thf(func_def_48, type, vNOT: ($o > $o)).
% 0.61/0.41 thf(func_def_49, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.61/0.41 thf(func_def_50, type, db2: !>[X0: $tType]:(X0)).
% 0.61/0.41 thf(func_def_51, type, db4: !>[X0: $tType]:(X0)).
% 0.61/0.41 thf(func_def_52, type, db3: !>[X0: $tType]:(X0)).
% 0.61/0.41 thf(func_def_53, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.61/0.41 thf(func_def_54, type, vOR: ($o > $o > $o)).
% 0.61/0.41 thf(func_def_55, type, db6: !>[X0: $tType]:(X0)).
% 0.61/0.41 thf(func_def_56, type, db5: !>[X0: $tType]:(X0)).
% 0.61/0.41 thf(func_def_57, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.61/0.41 thf(func_def_58, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.61/0.41 thf(func_def_59, type, sP0: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > list @ X0 > $o))).
% 0.61/0.41 thf(func_def_60, type, sP1: (list @ a > list @ a > $o)).
% 0.61/0.41 thf(func_def_61, type, sP2: (list @ a > list @ a > $o)).
% 0.61/0.41 thf(func_def_62, type, sP3: (list @ a > list @ a > $o)).
% 0.61/0.41 thf(func_def_63, type, sK4: !>[X0: $tType]:((list @ X0 > list @ X0))).
% 0.61/0.41 thf(func_def_64, type, sK5: !>[X0: $tType]:((list @ X0 > X0))).
% 0.61/0.41 thf(func_def_65, type, sK6: !>[X0: $tType]:(((list @ X0 > $o) > X0))).
% 0.61/0.41 thf(func_def_66, type, sK7: !>[X0: $tType]:(((list @ X0 > $o) > list @ X0))).
% 0.61/0.41 thf(func_def_67, type, sK8: !>[X0: $tType]:(((list @ X0 > $o) > X0))).
% 0.61/0.41 thf(func_def_68, type, sK9: !>[X0: $tType]:((((X0 > X0 > $o) > list @ X0 > $o) > list @ X0))).
% 0.61/0.41 thf(func_def_69, type, sK10: !>[X0: $tType]:((((X0 > X0 > $o) > list @ X0 > $o) > X0))).
% 0.61/0.41 thf(func_def_70, type, sK11: !>[X0: $tType]:((((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o))).
% 0.61/0.41 thf(func_def_71, type, sK12: !>[X0: $tType]:((((X0 > X0 > $o) > list @ X0 > $o) > X0))).
% 0.61/0.41 thf(func_def_72, type, sK13: !>[X0: $tType]:((((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o))).
% 0.61/0.41 thf(func_def_73, type, sK14: !>[X0: $tType]:((((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o))).
% 0.61/0.41 thf(func_def_74, type, sK15: !>[X0: $tType]:((((X0 > X0 > $o) > list @ X0 > $o) > X0))).
% 0.61/0.41 thf(func_def_75, type, sK16: !>[X0: $tType]:(((list @ X0 > $o) > list @ X0))).
% 0.61/0.41 thf(func_def_76, type, sK17: !>[X0: $tType]:(((list @ X0 > $o) > X0))).
% 0.61/0.41 thf(func_def_77, type, sK18: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.61/0.41 thf(func_def_78, type, sK19: !>[X0: $tType]:(((list @ X0 > $o) > list @ X0))).
% 0.61/0.41 thf(func_def_79, type, sK20: !>[X0: $tType]:(((list @ X0 > $o) > X0))).
% 0.61/0.41 thf(func_def_80, type, sK21: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 0.61/0.41 thf(func_def_81, type, sK22: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 0.61/0.41 thf(func_def_82, type, sK23: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 0.61/0.41 thf(func_def_83, type, sK24: !>[X0: $tType]:(((list @ X0 > $o) > X0))).
% 0.61/0.41 thf(func_def_84, type, sK25: !>[X0: $tType]:(((list @ X0 > $o) > X0))).
% 0.61/0.41 thf(func_def_85, type, sK26: !>[X0: $tType]:(((list @ X0 > $o) > X0))).
% 0.61/0.41 thf(func_def_86, type, sK27: !>[X0: $tType]:(((list @ X0 > $o) > list @ X0))).
% 0.61/0.41 thf(func_def_87, type, sK28: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 0.61/0.41 thf(func_def_88, type, sK29: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 0.61/0.41 thf(func_def_89, type, sK30: a).
% 0.61/0.41 thf(func_def_90, type, sK31: a).
% 0.61/0.41 thf(func_def_91, type, sK32: a).
% 0.61/0.41 thf(func_def_92, type, sK33: !>[X0: $tType]:((list @ X0 > list @ X0 > X0 > list @ X0 > list @ X0))).
% 0.61/0.41 thf(func_def_93, type, sK34: ((list @ a > list @ a > $o) > a)).
% 0.61/0.41 thf(func_def_94, type, sK35: ((list @ a > list @ a > $o) > a)).
% 0.61/0.41 thf(func_def_95, type, sK36: ((list @ a > list @ a > $o) > list @ a)).
% 0.61/0.41 thf(func_def_96, type, sK37: ((list @ a > list @ a > $o) > list @ a)).
% 0.61/0.41 thf(func_def_97, type, sK38: ((list @ a > list @ a > $o) > list @ a)).
% 0.61/0.41 thf(func_def_98, type, sK39: ((list @ a > list @ a > $o) > list @ a)).
% 0.61/0.41 thf(func_def_99, type, sK40: ((list @ a > list @ a > $o) > a)).
% 0.61/0.41 thf(func_def_100, type, sK41: ((list @ a > list @ a > $o) > list @ a)).
% 0.61/0.41 thf(func_def_101, type, sK42: ((list @ a > list @ a > $o) > a)).
% 0.61/0.41 thf(func_def_102, type, sK43: !>[X0: $tType, X1: $tType]:((((X1 > X0) > list @ X1 > $o) > X1 > X0))).
% 0.61/0.41 thf(func_def_103, type, sK44: !>[X0: $tType, X1: $tType]:((((X1 > X0) > list @ X1 > $o) > X1))).
% 0.61/0.41 thf(func_def_104, type, sK45: !>[X0: $tType, X1: $tType]:((((X1 > X0) > list @ X1 > $o) > X1))).
% 0.61/0.41 thf(func_def_105, type, sK46: !>[X0: $tType, X1: $tType]:((((X1 > X0) > list @ X1 > $o) > list @ X1))).
% 0.61/0.41 thf(func_def_106, type, sK47: !>[X0: $tType, X1: $tType]:((((X1 > X0) > list @ X1 > $o) > X1 > X0))).
% 0.61/0.41 thf(func_def_107, type, sK48: !>[X0: $tType, X1: $tType]:((((X1 > X0) > list @ X1 > $o) > X1))).
% 0.61/0.41 thf(func_def_108, type, sK49: !>[X0: $tType, X1: $tType]:((((X1 > X0) > list @ X1 > $o) > X1 > X0))).
% 0.61/0.41 thf(func_def_109, type, sK50: a).
% 0.61/0.41 thf(func_def_110, type, sK51: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > X1) > X0))).
% 0.61/0.41 thf(func_def_111, type, sK52: !>[X0: $tType]:((list @ X0 > list @ X0 > X0 > list @ X0 > list @ X0))).
% 0.61/0.41 thf(func_def_112, type, sK53: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > a) > X0))).
% 0.61/0.41 thf(func_def_113, type, sK54: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > list @ X0 > X0))).
% 0.61/0.41 thf(func_def_114, type, sK55: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > list @ X0 > X0))).
% 0.61/0.41 thf(func_def_115, type, sK56: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > list @ X0 > list @ X0))).
% 0.61/0.41 thf(func_def_116, type, sK57: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > list @ X0 > list @ X0))).
% 0.61/0.41 thf(func_def_117, type, sK58: !>[X0: $tType]:((list @ X0 > list @ X0))).
% 0.61/0.41 thf(func_def_118, type, sK59: !>[X0: $tType]:((list @ X0 > X0))).
% 0.61/0.41 thf(func_def_119, type, sK60: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > list @ X0 > X0))).
% 0.61/0.41 thf(func_def_120, type, sK61: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > list @ X0 > list @ X0))).
% 0.61/0.41 thf(func_def_121, type, sK62: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > list @ X0 > X0))).
% 0.61/0.41 thf(func_def_122, type, sK63: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > list @ X0 > list @ X0))).
% 0.61/0.41 thf(func_def_123, type, sK64: !>[X0: $tType]:((list @ X0 > list @ X0))).
% 0.61/0.41 thf(func_def_124, type, sK65: !>[X0: $tType]:((list @ X0 > X0))).
% 0.61/0.41 thf(func_def_125, type, sK66: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > list @ X0 > X0))).
% 0.61/0.41 thf(func_def_126, type, sK67: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > list @ X0 > list @ X0))).
% 0.61/0.41 thf(func_def_127, type, sK68: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > list @ X0 > X0))).
% 0.61/0.41 thf(func_def_128, type, sK69: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > list @ X0 > list @ X0))).
% 0.61/0.41 thf(func_def_129, type, sK70: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > list @ X0 > X0))).
% 0.61/0.41 thf(func_def_130, type, sK71: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > list @ X0 > X0))).
% 0.61/0.41 thf(func_def_131, type, sK72: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > list @ X0 > list @ X0))).
% 0.61/0.41 thf(func_def_132, type, sK73: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > list @ X0 > list @ X0))).
% 0.61/0.41 thf(func_def_133, type, sK74: ((list @ a > list @ a > $o) > a)).
% 0.61/0.41 thf(func_def_134, type, sK75: ((list @ a > list @ a > $o) > a)).
% 0.61/0.41 thf(func_def_135, type, sK76: ((list @ a > list @ a > $o) > list @ a)).
% 0.61/0.41 thf(func_def_136, type, sK77: ((list @ a > list @ a > $o) > list @ a)).
% 0.61/0.41 thf(func_def_137, type, sK78: ((list @ a > list @ a > $o) > a)).
% 0.61/0.41 thf(func_def_138, type, sK79: ((list @ a > list @ a > $o) > list @ a)).
% 0.61/0.41 thf(func_def_139, type, sK80: ((list @ a > list @ a > $o) > a)).
% 0.61/0.41 thf(func_def_140, type, sK81: ((list @ a > list @ a > $o) > a)).
% 0.61/0.41 thf(func_def_141, type, sK82: ((list @ a > list @ a > $o) > list @ a)).
% 0.61/0.41 thf(func_def_142, type, sK83: ((list @ a > list @ a > $o) > list @ a)).
% 0.61/0.41 thf(func_def_143, type, sK84: (list @ a > list @ a > a)).
% 0.61/0.41 thf(func_def_144, type, sK85: (list @ a > list @ a > a)).
% 0.61/0.41 thf(func_def_145, type, sK86: (list @ a > list @ a > list @ a)).
% 0.61/0.41 thf(func_def_146, type, sK87: (list @ a > list @ a > list @ a)).
% 0.61/0.41 thf(func_def_147, type, sK88: (list @ a > list @ a > a)).
% 0.61/0.41 thf(func_def_148, type, sK89: (list @ a > list @ a > a)).
% 0.61/0.41 thf(func_def_149, type, sK90: (list @ a > list @ a > list @ a)).
% 0.61/0.41 thf(func_def_150, type, sK91: (list @ a > list @ a > list @ a)).
% 0.61/0.41 thf(func_def_151, type, sK92: !>[X0: $tType]:(((list @ X0 > $o) > list @ X0))).
% 0.61/0.41 thf(func_def_152, type, sK93: !>[X0: $tType]:(((list @ X0 > $o) > X0))).
% 0.61/0.41 thf(func_def_153, type, sK94: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.61/0.41 thf(func_def_154, type, sK95: a).
% 0.61/0.41 thf(func_def_155, type, sK96: a).
% 0.61/0.41 thf(func_def_156, type, sK97: a).
% 0.61/0.41 thf(func_def_157, type, sK98: (list @ a > list @ a > list @ a)).
% 0.61/0.41 thf(func_def_158, type, sK99: (list @ a > list @ a > a)).
% 0.61/0.41 thf(func_def_159, type, sK100: (list @ a > list @ a > a)).
% 0.61/0.41 thf(func_def_160, type, sK101: (list @ a > list @ a > list @ a)).
% 0.61/0.41 thf(func_def_161, type, sK102: (list @ a > list @ a > a)).
% 0.61/0.41 thf(func_def_162, type, sK103: (list @ a > list @ a > a)).
% 0.61/0.41 thf(func_def_163, type, sK104: (list @ a > list @ a > list @ a)).
% 0.61/0.41 thf(func_def_164, type, sK105: (list @ a > list @ a > list @ a)).
% 0.61/0.41 thf(func_def_165, type, sK106: (list @ a > list @ a)).
% 0.61/0.41 thf(func_def_166, type, sK107: (list @ a > a)).
% 0.61/0.41 thf(func_def_167, type, sK108: !>[X0: $tType, X1: $tType]:(((list @ X0 > list @ X1 > $o) > X0))).
% 0.61/0.41 thf(func_def_168, type, sK109: !>[X0: $tType, X1: $tType]:(((list @ X0 > list @ X1 > $o) > list @ X0))).
% 0.61/0.41 thf(func_def_169, type, sK110: !>[X0: $tType, X1: $tType]:(((list @ X0 > list @ X1 > $o) > X0))).
% 0.61/0.41 thf(func_def_170, type, sK111: !>[X0: $tType, X1: $tType]:(((list @ X0 > list @ X1 > $o) > list @ X1))).
% 0.61/0.41 thf(func_def_171, type, sK112: !>[X0: $tType, X1: $tType]:(((list @ X0 > list @ X1 > $o) > list @ X0))).
% 0.61/0.41 thf(func_def_172, type, sK113: !>[X0: $tType, X1: $tType]:(((list @ X0 > list @ X1 > $o) > X1))).
% 0.61/0.41 thf(func_def_173, type, sK114: !>[X0: $tType, X1: $tType]:(((list @ X0 > list @ X1 > $o) > list @ X1))).
% 0.61/0.41 thf(func_def_174, type, sK115: !>[X0: $tType, X1: $tType]:(((list @ X0 > list @ X1 > $o) > X1))).
% 0.61/0.41 thf(func_def_175, type, sK116: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > (X0 > X0 > $o) > X0))).
% 0.61/0.41 thf(func_def_176, type, sK117: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > (X0 > X0 > $o) > list @ X0))).
% 0.61/0.41 thf(func_def_177, type, sK118: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > (X0 > X0 > $o) > list @ X0))).
% 0.61/0.41 thf(func_def_178, type, sK119: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > (X0 > X0 > $o) > X0))).
% 0.61/0.41 thf(func_def_179, type, sK120: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > list @ X0))).
% 0.61/0.41 thf(func_def_180, type, sK121: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > X0))).
% 0.61/0.41 thf(func_def_181, type, sK122: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > (X0 > X0 > $o) > list @ X0))).
% 0.61/0.41 thf(func_def_182, type, sK123: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > (X0 > X0 > $o) > X0))).
% 0.61/0.41 thf(func_def_183, type, sK124: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > (X0 > X0 > $o) > list @ X0))).
% 0.61/0.41 thf(func_def_184, type, sK125: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > (X0 > X0 > $o) > X0))).
% 0.61/0.41 thf(func_def_185, type, sK126: !>[X0: $tType]:((list @ X0 > list @ X0))).
% 0.61/0.41 thf(func_def_186, type, sK127: !>[X0: $tType]:((list @ X0 > X0))).
% 0.61/0.41 thf(func_def_187, type, sK128: (list @ a > list @ a > a)).
% 0.61/0.41 thf(func_def_188, type, sK129: (list @ a > list @ a > list @ a)).
% 0.61/0.41 thf(func_def_189, type, sK130: (list @ a > list @ a > a)).
% 0.61/0.41 thf(func_def_190, type, sK131: (list @ a > list @ a > list @ a)).
% 0.61/0.41 thf(func_def_191, type, sK132: (list @ a > list @ a > a)).
% 0.61/0.41 thf(func_def_192, type, sK133: (list @ a > list @ a > a)).
% 0.61/0.41 thf(func_def_193, type, sK134: (list @ a > list @ a > list @ a)).
% 0.61/0.41 thf(func_def_194, type, sK135: (list @ a > list @ a > list @ a)).
% 0.61/0.41 thf(func_def_195, type, sK136: (list @ a > list @ a > list @ a)).
% 0.61/0.41 thf(func_def_196, type, sK137: !>[X0: $tType]:((list @ X0 > list @ X0))).
% 0.61/0.41 thf(func_def_197, type, sK138: !>[X0: $tType]:((list @ X0 > X0))).
% 0.61/0.41 thf(func_def_198, type, sK139: !>[X0: $tType]:(((list @ X0 > $o) > list @ X0))).
% 0.61/0.41 thf(func_def_199, type, sK140: !>[X0: $tType]:(((list @ X0 > $o) > X0))).
% 0.61/0.41 thf(func_def_200, type, sK141: !>[X0: $tType]:((list @ list @ X0 > list @ X0 > list @ X0 > list @ list @ X0))).
% 0.61/0.41 thf(func_def_201, type, sK142: !>[X0: $tType]:((list @ list @ X0 > list @ X0 > list @ X0 > list @ list @ X0))).
% 0.61/0.41 thf(func_def_202, type, sK143: !>[X0: $tType]:((list @ list @ X0 > list @ X0 > list @ X0 > list @ X0))).
% 0.61/0.41 thf(func_def_203, type, sK144: !>[X0: $tType]:((list @ list @ X0 > list @ X0 > list @ X0 > list @ X0))).
% 0.61/0.41 thf(func_def_204, type, sK145: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > list @ X0))).
% 0.61/0.41 thf(func_def_205, type, sK146: !>[X0: $tType]:(((X0 > X0 > $o) > (list @ X0 > list @ X0 > $o) > list @ X0))).
% 0.61/0.41 thf(func_def_206, type, sK147: !>[X0: $tType]:(((X0 > X0 > $o) > (list @ X0 > list @ X0 > $o) > list @ X0))).
% 0.61/0.41 thf(func_def_207, type, sK148: !>[X0: $tType]:(((X0 > X0 > $o) > (list @ X0 > list @ X0 > $o) > X0))).
% 0.61/0.41 thf(func_def_208, type, sK149: !>[X0: $tType]:(((X0 > X0 > $o) > (list @ X0 > list @ X0 > $o) > X0))).
% 0.61/0.41 thf(func_def_209, type, sK150: !>[X0: $tType]:(((X0 > X0 > $o) > (list @ X0 > list @ X0 > $o) > X0))).
% 0.61/0.41 thf(func_def_210, type, sK151: !>[X0: $tType]:(((X0 > X0 > $o) > (list @ X0 > list @ X0 > $o) > X0))).
% 0.61/0.41 thf(func_def_211, type, sK152: !>[X0: $tType]:(((X0 > X0 > $o) > (list @ X0 > list @ X0 > $o) > list @ X0))).
% 0.61/0.41 thf(func_def_212, type, sK153: !>[X0: $tType]:(((X0 > X0 > $o) > (list @ X0 > list @ X0 > $o) > list @ X0))).
% 0.61/0.41 thf(func_def_213, type, sK154: !>[X0: $tType]:(((list @ X0 > $o) > X0))).
% 0.61/0.41 thf(func_def_214, type, sK155: !>[X0: $tType]:(((list @ X0 > $o) > list @ X0))).
% 0.61/0.41 thf(func_def_215, type, sK156: !>[X0: $tType]:(((list @ X0 > $o) > X0))).
% 0.61/0.41 thf(func_def_216, type, sK157: !>[X0: $tType]:(((list @ X0 > $o) > X0))).
% 0.61/0.41 thf(func_def_217, type, sK158: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > X0))).
% 0.61/0.41 thf(func_def_218, type, sK159: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > list @ X0))).
% 0.61/0.41 thf(func_def_219, type, sK160: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > list @ X0))).
% 0.61/0.41 thf(func_def_220, type, sK161: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > list @ X0))).
% 0.61/0.41 thf(func_def_221, type, sK162: !>[X0: $tType]:(((list @ X0 > $o) > X0))).
% 0.61/0.41 thf(func_def_222, type, sK163: !>[X0: $tType]:(((list @ X0 > $o) > list @ X0))).
% 0.61/0.41 thf(func_def_223, type, sK164: !>[X0: $tType]:(((list @ X0 > $o) > X0))).
% 0.61/0.41 thf(func_def_224, type, sK165: (list @ a > list @ a > list @ a)).
% 0.61/0.41 thf(func_def_225, type, sK166: (list @ a > list @ a > a)).
% 0.61/0.41 thf(func_def_226, type, sK167: (list @ a > list @ a > list @ a)).
% 0.61/0.41 thf(func_def_227, type, sK168: (list @ a > list @ a > a)).
% 0.61/0.41 thf(func_def_228, type, sK169: (list @ a > list @ a > a)).
% 0.61/0.41 thf(func_def_229, type, sK170: (list @ a > list @ a > list @ a)).
% 0.61/0.41 thf(func_def_230, type, sK171: (list @ a > list @ a > a)).
% 0.61/0.41 thf(func_def_231, type, sK172: (list @ a > list @ a > list @ a)).
% 0.61/0.41 thf(func_def_232, type, sK173: (list @ a > list @ a > list @ a)).
% 0.61/0.41 thf(func_def_233, type, sK174: (list @ a > list @ a > a)).
% 0.61/0.41 thf(func_def_234, type, sK175: !>[X0: $tType]:((list @ X0 > list @ X0 > list @ X0 > list @ X0 > list @ X0))).
% 0.61/0.41 thf(func_def_235, type, sK176: !>[X0: $tType]:((list @ X0 > list @ list @ X0 > list @ X0 > list @ X0))).
% 0.61/0.41 thf(func_def_236, type, sK177: !>[X0: $tType]:((list @ X0 > list @ list @ X0 > list @ X0 > list @ list @ X0))).
% 0.61/0.41 thf(func_def_237, type, sK178: !>[X0: $tType]:((list @ X0 > list @ list @ X0 > list @ X0 > list @ X0))).
% 0.61/0.41 thf(func_def_238, type, sK179: !>[X0: $tType]:((list @ X0 > list @ list @ X0 > list @ X0 > list @ list @ X0))).
% 0.61/0.41 thf(func_def_239, type, sK180: !>[X0: $tType]:((list @ X0 > X0))).
% 0.61/0.41 thf(func_def_240, type, sK181: !>[X0: $tType]:((list @ X0 > X0))).
% 0.61/0.41 thf(func_def_241, type, sK182: !>[X0: $tType]:((list @ X0 > list @ X0))).
% 0.61/0.41 thf(func_def_242, type, sK183: !>[X0: $tType]:((list @ X0 > X0))).
% 0.61/0.41 thf(func_def_243, type, sK184: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > a) > X0))).
% 0.61/0.41 thf(func_def_244, type, sK185: !>[X0: $tType, X1: $tType]:((((X0 > X1) > list @ X0 > list @ X1 > $o) > X0 > X1))).
% 0.61/0.41 thf(func_def_245, type, sK186: !>[X0: $tType, X1: $tType]:((((X0 > X1) > list @ X0 > list @ X1 > $o) > list @ X1))).
% 0.61/0.41 thf(func_def_246, type, sK187: !>[X0: $tType, X1: $tType]:((((X0 > X1) > list @ X0 > list @ X1 > $o) > X0))).
% 0.61/0.41 thf(func_def_247, type, sK188: !>[X0: $tType, X1: $tType]:((((X0 > X1) > list @ X0 > list @ X1 > $o) > list @ X0))).
% 0.61/0.41 thf(func_def_248, type, sK189: !>[X0: $tType, X1: $tType]:((((X0 > X1) > list @ X0 > list @ X1 > $o) > X0 > X1))).
% 0.61/0.41 thf(func_def_249, type, sK190: !>[X0: $tType, X1: $tType]:((((X0 > X1) > list @ X0 > list @ X1 > $o) > list @ X1))).
% 0.61/0.41 thf(func_def_250, type, sK191: !>[X0: $tType]:((((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o))).
% 0.61/0.41 thf(func_def_251, type, sK192: !>[X0: $tType]:((((X0 > X0 > $o) > list @ X0 > $o) > X0))).
% 0.61/0.41 thf(func_def_252, type, sK193: !>[X0: $tType]:((((X0 > X0 > $o) > list @ X0 > $o) > list @ X0))).
% 0.61/0.41 thf(func_def_253, type, sK194: !>[X0: $tType]:((((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o))).
% 0.61/0.41 thf(func_def_254, type, sK195: a).
% 0.61/0.41 thf(func_def_255, type, sK196: !>[X0: $tType]:((list @ X0 > X0))).
% 0.61/0.41 thf(func_def_256, type, sK197: !>[X0: $tType]:((list @ X0 > list @ X0))).
% 0.61/0.41 thf(func_def_257, type, sK198: !>[X0: $tType]:((list @ list @ X0 > list @ list @ X0))).
% 0.61/0.41 thf(func_def_258, type, sK199: !>[X0: $tType]:((list @ list @ X0 > list @ list @ X0))).
% 0.61/0.41 thf(func_def_259, type, sK200: !>[X0: $tType]:((list @ list @ X0 > X0))).
% 0.61/0.41 thf(func_def_260, type, sK201: !>[X0: $tType]:((list @ list @ X0 > list @ X0))).
% 0.61/0.41 thf(func_def_261, type, sK202: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > list @ X0))).
% 0.61/0.41 thf(func_def_262, type, sK203: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > list @ X0))).
% 0.61/0.41 thf(func_def_263, type, sK204: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > list @ X0))).
% 0.61/0.41 thf(func_def_264, type, sK205: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > X0))).
% 0.61/0.41 thf(func_def_265, type, sK206: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > X0))).
% 0.61/0.41 thf(func_def_266, type, sK207: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > list @ X0))).
% 0.61/0.41 thf(f17,axiom,(
% 0.61/0.41 ! [X0 : a] : ~(less @ X0 @ X0)),
% 0.61/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_local_Oorder_Oirrefl)).
% 0.61/0.41 thf(f56,axiom,(
% 0.61/0.41 ! [X0 : a] : (((sup @ X0 @ X0)) = X0)),
% 0.61/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_local_Osup__idem)).
% 0.61/0.41 thf(f260,axiom,(
% 0.61/0.41 (((inf @ c @ (sup @ b @ c))) = b)),
% 0.61/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1)).
% 0.61/0.41 thf(f262,axiom,(
% 0.61/0.41 (less @ b @ (sup @ b @ c))),
% 0.61/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_3)).
% 0.61/0.41 thf(f263,axiom,(
% 0.61/0.41 (((inf @ c @ (sup @ b @ c))) = c)),
% 0.61/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_4)).
% 0.61/0.41 thf(f272,plain,(
% 0.61/0.41 ! [X0 : a] : ~(less @ X0 @ X0)),
% 0.61/0.41 inference(rectify,[],[f17])).
% 0.61/0.41 thf(f273,plain,(
% 0.61/0.41 ! [X0 : a] : ~ (((less @ X0 @ X0)) = $true)),
% 0.61/0.41 inference(fool_elimination,[],[f272])).
% 0.61/0.41 thf(f369,plain,(
% 0.61/0.41 (less @ b @ (sup @ b @ c))),
% 0.61/0.41 inference(rectify,[],[f262])).
% 0.61/0.41 thf(f370,plain,(
% 0.61/0.41 (((less @ b @ (sup @ b @ c))) = $true)),
% 0.61/0.41 inference(fool_elimination,[],[f369])).
% 0.61/0.41 thf(f583,plain,(
% 0.61/0.41 ! [X0 : a] : (((less @ X0 @ X0)) != $true)),
% 0.61/0.41 inference(flattening,[],[f273])).
% 0.61/0.41 thf(f1121,plain,(
% 0.61/0.41 ( ! [X0 : a] : ((((less @ X0 @ X0)) != $true)) )),
% 0.61/0.41 inference(cnf_transformation,[],[f583])).
% 0.61/0.41 thf(f1142,plain,(
% 0.61/0.41 (((less @ b @ (sup @ b @ c))) = $true)),
% 0.61/0.41 inference(cnf_transformation,[],[f370])).
% 0.61/0.41 thf(f1144,plain,(
% 0.61/0.41 (c = ((inf @ c @ (sup @ b @ c))))),
% 0.61/0.41 inference(cnf_transformation,[],[f263])).
% 0.61/0.41 thf(f1276,plain,(
% 0.61/0.41 (b = ((inf @ c @ (sup @ b @ c))))),
% 0.61/0.41 inference(cnf_transformation,[],[f260])).
% 0.61/0.41 thf(f1389,plain,(
% 0.61/0.41 ( ! [X0 : a] : ((((sup @ X0 @ X0)) = X0)) )),
% 0.61/0.41 inference(cnf_transformation,[],[f56])).
% 0.61/0.41 thf(f1656,definition,(
% 0.61/0.41 spl208_3 <=> (((less @ b @ (sup @ b @ c))) = $true)),
% 0.61/0.41 introduced(definition,[new_symbols(definition,[spl208_3])],[avatar_definition])).
% 0.61/0.41 thf(f1658,plain,(
% 0.61/0.41 (((less @ b @ (sup @ b @ c))) = $true) | ~spl208_3),
% 0.61/0.41 inference(avatar_component_clause,[],[f1656])).
% 0.61/0.41 thf(f1659,plain,(
% 0.61/0.41 spl208_3),
% 0.61/0.41 inference(avatar_split_clause,[],[f1142,f1656])).
% 0.61/0.41 thf(f1671,definition,(
% 0.61/0.41 spl208_6 <=> (b = ((inf @ c @ (sup @ b @ c))))),
% 0.61/0.41 introduced(definition,[new_symbols(definition,[spl208_6])],[avatar_definition])).
% 0.61/0.41 thf(f1673,plain,(
% 0.61/0.41 (b = ((inf @ c @ (sup @ b @ c)))) | ~spl208_6),
% 0.61/0.41 inference(avatar_component_clause,[],[f1671])).
% 0.61/0.41 thf(f1674,plain,(
% 0.61/0.41 spl208_6),
% 0.61/0.41 inference(avatar_split_clause,[],[f1276,f1671])).
% 0.61/0.41 thf(f1684,definition,(
% 0.61/0.41 spl208_9 <=> (c = ((inf @ c @ (sup @ b @ c))))),
% 0.61/0.41 introduced(definition,[new_symbols(definition,[spl208_9])],[avatar_definition])).
% 0.61/0.41 thf(f1686,plain,(
% 0.61/0.41 (c = ((inf @ c @ (sup @ b @ c)))) | ~spl208_9),
% 0.61/0.41 inference(avatar_component_clause,[],[f1684])).
% 0.61/0.41 thf(f1687,plain,(
% 0.61/0.41 spl208_9),
% 0.61/0.41 inference(avatar_split_clause,[],[f1144,f1684])).
% 0.61/0.41 thf(f1834,definition,(
% 0.61/0.41 spl208_34 <=> (b = c)),
% 0.61/0.41 introduced(definition,[new_symbols(definition,[spl208_34])],[avatar_definition])).
% 0.61/0.41 thf(f1836,plain,(
% 0.61/0.41 (b = c) | ~spl208_34),
% 0.61/0.41 inference(avatar_component_clause,[],[f1834])).
% 0.61/0.41 thf(f1841,plain,(
% 0.61/0.41 (b = c) | (~spl208_6 | ~spl208_9)),
% 0.61/0.41 inference(superposition,[],[f1673,f1686])).
% 0.61/0.41 thf(f1843,plain,(
% 0.61/0.41 spl208_34 | ~spl208_6 | ~spl208_9),
% 0.61/0.41 inference(avatar_split_clause,[],[f1841,f1684,f1671,f1834])).
% 0.61/0.41 thf(f1844,plain,(
% 0.61/0.41 (((less @ c @ (sup @ c @ c))) = $true) | (~spl208_3 | ~spl208_34)),
% 0.61/0.41 inference(superposition,[],[f1658,f1836])).
% 0.61/0.41 thf(f1850,plain,(
% 0.61/0.41 ($true = ((less @ c @ c))) | (~spl208_3 | ~spl208_34)),
% 0.61/0.41 inference(forward_demodulation,[],[f1844,f1389])).
% 0.61/0.41 thf(f1851,plain,(
% 0.61/0.41 $false | (~spl208_3 | ~spl208_34)),
% 0.61/0.41 inference(forward_subsumption_resolution,[],[f1850,f1121])).
% 0.61/0.41 thf(f1852,plain,(
% 0.61/0.41 ~spl208_3 | ~spl208_34),
% 0.61/0.41 inference(avatar_contradiction_clause,[],[f1851])).
% 0.61/0.41 cnf(s3, plain, spl208_3, inference(sat_conversion,[],[f1659])).
% 0.61/0.41 cnf(s6, plain, spl208_6, inference(sat_conversion,[],[f1674])).
% 0.61/0.42 cnf(s8, plain, spl208_9, inference(sat_conversion,[],[f1687])).
% 0.61/0.42 cnf(s39, plain, ~spl208_6 | ~spl208_9 | spl208_34, inference(sat_conversion,[],[f1843])).
% 0.61/0.42 cnf(s44, plain, ~spl208_3 | ~spl208_34, inference(sat_conversion,[],[f1852])).
% 0.61/0.42 cnf(s48, plain, spl208_34, inference(rat,[],[s39,s8,s6])).
% 0.61/0.42 cnf(s49, plain, ~spl208_3, inference(rat,[],[s44,s48])).
% 0.61/0.42 cnf(s50, plain, $false, inference(rat,[],[s3,s49])).
% 0.61/0.42 thf(f1853,plain,(
% 0.61/0.42 $false),
% 0.61/0.42 inference(avatar_sat_refutation,[],[s50])).
% 0.61/0.42 % SZS output end Proof for theBenchmark
% 0.61/0.42 % (1229121)------------------------------
% 0.61/0.42 % (1229121)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.42 % (1229121)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.42 % (1229121)CaDiCaL version: 2.1.3
% 0.61/0.42 % (1229121)Termination reason: Refutation
% 0.61/0.42 % (1229121)Time elapsed: 0.088 s
% 0.61/0.42 % (1229121)Peak memory usage: 14 MB
% 0.61/0.42 % (1229121)Instructions burned: 165 (million)
% 0.61/0.42 % (1229095)Success in time 0.146 s
% 0.61/0.42 % Vampire exiting
%------------------------------------------------------------------------------