%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP037^2 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 08:08:04 AM UTC 2026
% Result : Theorem 0.51s 0.41s
% Output : Refutation 0.51s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP037^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n020.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 19:41:05 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.21/0.26 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.51/0.41 % (1493481)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.51/0.41 % (1493492)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.51/0.41 % (1493492)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
% 0.51/0.41 % (1493492)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=3191843537:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.51/0.41 % (1493486)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2386309418:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.51/0.41 % (1493487)lrs+10_16_si=on:nwc=1.5:random_seed=3085134341:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.51/0.41 % (1493488)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2157601980:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.51/0.41 % (1493490)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2552301635:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.51/0.41 % (1493489)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=372881855: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)
% 0.51/0.41 % (1493491)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1196817157:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.51/0.41 % (1493488)Instruction limit reached!
% 0.51/0.41 % (1493488)------------------------------
% 0.51/0.41 % (1493488)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.51/0.41 % (1493488)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.51/0.41 % (1493488)CaDiCaL version: 2.1.3
% 0.51/0.41 % (1493488)Termination reason: Instruction limit
% 0.51/0.41 % (1493488)Termination phase: shuffling
% 0.51/0.41 % (1493488)Time elapsed: 0.002 s
% 0.51/0.41 % (1493488)Peak memory usage: 10 MB
% 0.51/0.41 % (1493488)Instructions burned: 3 (million)
% 0.51/0.41 % (1493487)Instruction limit reached!
% 0.51/0.41 % (1493487)------------------------------
% 0.51/0.41 % (1493487)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.51/0.41 % (1493487)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.51/0.41 % (1493487)CaDiCaL version: 2.1.3
% 0.51/0.41 % (1493487)Termination reason: Instruction limit
% 0.51/0.41 % (1493487)Termination phase: shuffling
% 0.51/0.41 % (1493487)Time elapsed: 0.011 s
% 0.51/0.41 % (1493487)Peak memory usage: 10 MB
% 0.51/0.41 % (1493487)Instructions burned: 19 (million)
% 0.51/0.41 % (1493490)Instruction limit reached!
% 0.51/0.41 % (1493490)------------------------------
% 0.51/0.41 % (1493490)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.51/0.41 % (1493490)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.51/0.41 % (1493490)CaDiCaL version: 2.1.3
% 0.51/0.41 % (1493490)Termination reason: Instruction limit
% 0.51/0.41 % (1493490)Termination phase: Property scanning
% 0.51/0.41 % (1493490)Time elapsed: 0.014 s
% 0.51/0.41 % (1493490)Peak memory usage: 11 MB
% 0.51/0.41 % (1493490)Instructions burned: 29 (million)
% 0.51/0.41 % (1493500)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2972861092:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.51/0.41 % (1493500)Instruction limit reached!
% 0.51/0.41 % (1493500)------------------------------
% 0.51/0.41 % (1493500)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.51/0.41 % (1493500)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.51/0.41 % (1493500)CaDiCaL version: 2.1.3
% 0.51/0.41 % (1493500)Termination reason: Instruction limit
% 0.51/0.41 % (1493500)Termination phase: shuffling
% 0.51/0.41 % (1493500)Time elapsed: 0.002 s
% 0.51/0.41 % (1493500)Peak memory usage: 10 MB
% 0.51/0.41 % (1493500)Instructions burned: 2 (million)
% 0.51/0.41 % (1493502)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.51/0.41 % (1493501)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=4232965647:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.51/0.41 % (1493492)Instruction limit reached!
% 0.51/0.41 % (1493492)------------------------------
% 0.51/0.41 % (1493492)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.51/0.41 % (1493492)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.51/0.41 % (1493492)CaDiCaL version: 2.1.3
% 0.51/0.41 % (1493492)Termination reason: Instruction limit
% 0.51/0.41 % (1493492)Termination phase: Saturation
% 0.51/0.41 % (1493492)Time elapsed: 0.041 s
% 0.51/0.41 % (1493492)Peak memory usage: 14 MB
% 0.51/0.41 % (1493492)Instructions burned: 161 (million)
% 0.51/0.41 % (1493502)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1726519594:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.51/0.41 % (1493501)Instruction limit reached!
% 0.51/0.41 % (1493501)------------------------------
% 0.51/0.41 % (1493501)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.51/0.41 % (1493501)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.51/0.41 % (1493501)CaDiCaL version: 2.1.3
% 0.51/0.41 % (1493501)Termination reason: Instruction limit
% 0.51/0.41 % (1493501)Termination phase: shuffling
% 0.51/0.41 % (1493501)Time elapsed: 0.004 s
% 0.51/0.41 % (1493501)Peak memory usage: 10 MB
% 0.51/0.41 % (1493501)Instructions burned: 7 (million)
% 0.51/0.41 % (1493502)Instruction limit reached!
% 0.51/0.41 % (1493502)------------------------------
% 0.51/0.41 % (1493502)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.51/0.41 % (1493502)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.51/0.41 % (1493502)CaDiCaL version: 2.1.3
% 0.51/0.41 % (1493502)Termination reason: Instruction limit
% 0.51/0.41 % (1493502)Termination phase: shuffling
% 0.51/0.41 % (1493502)Time elapsed: 0.004 s
% 0.51/0.41 % (1493502)Peak memory usage: 10 MB
% 0.51/0.41 % (1493502)Instructions burned: 8 (million)
% 0.51/0.41 % (1493491)Instruction limit reached!
% 0.51/0.41 % (1493491)------------------------------
% 0.51/0.41 % (1493491)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.51/0.41 % (1493491)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.51/0.41 % (1493491)CaDiCaL version: 2.1.3
% 0.51/0.41 % (1493491)Termination reason: Instruction limit
% 0.51/0.41 % (1493491)Termination phase: Property scanning
% 0.51/0.41 % (1493491)Time elapsed: 0.038 s
% 0.51/0.41 % (1493491)Peak memory usage: 12 MB
% 0.51/0.41 % (1493491)Instructions burned: 75 (million)
% 0.51/0.41 % (1493507)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
% 0.51/0.41 % (1493507)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.51/0.41 % (1493507)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=1937104008:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.51/0.41 % (1493486)Instruction limit reached!
% 0.51/0.41 % (1493486)------------------------------
% 0.51/0.41 % (1493486)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.51/0.41 % (1493486)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.51/0.41 % (1493486)CaDiCaL version: 2.1.3
% 0.51/0.41 % (1493486)Termination reason: Instruction limit
% 0.51/0.41 % (1493486)Termination phase: Function definition elimination
% 0.51/0.41 % (1493486)Time elapsed: 0.044 s
% 0.51/0.41 % (1493486)Peak memory usage: 12 MB
% 0.51/0.41 % (1493486)Instructions burned: 89 (million)
% 0.51/0.41 % (1493504)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=4281910141:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.51/0.41 % (1493504)Instruction limit reached!
% 0.51/0.41 % (1493504)------------------------------
% 0.51/0.41 % (1493504)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.51/0.41 % (1493504)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.51/0.41 % (1493504)CaDiCaL version: 2.1.3
% 0.51/0.41 % (1493504)Termination reason: Instruction limit
% 0.51/0.41 % (1493504)Termination phase: shuffling
% 0.51/0.41 % (1493504)Time elapsed: 0.006 s
% 0.51/0.41 % (1493504)Peak memory usage: 11 MB
% 0.51/0.41 % (1493504)Instructions burned: 12 (million)
% 0.51/0.41 % (1493507)Instruction limit reached!
% 0.51/0.41 % (1493507)------------------------------
% 0.51/0.41 % (1493507)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.51/0.41 % (1493507)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.51/0.41 % (1493507)CaDiCaL version: 2.1.3
% 0.51/0.41 % (1493507)Termination reason: Instruction limit
% 0.51/0.41 % (1493507)Termination phase: shuffling
% 0.51/0.41 % (1493507)Time elapsed: 0.007 s
% 0.51/0.41 % (1493507)Peak memory usage: 10 MB
% 0.51/0.41 % (1493507)Instructions burned: 29 (million)
% 0.51/0.41 % (1493508)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=820576828:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.51/0.41 % (1493510)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.51/0.41 % (1493509)lrs+10_1_si=on:cs=on:random_seed=2458980819:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.51/0.41 % (1493510)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=3672574800:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.51/0.41 % (1493510)Instruction limit reached!
% 0.51/0.41 % (1493510)------------------------------
% 0.51/0.41 % (1493510)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.51/0.41 % (1493510)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.51/0.41 % (1493510)CaDiCaL version: 2.1.3
% 0.51/0.41 % (1493510)Termination reason: Instruction limit
% 0.51/0.41 % (1493510)Termination phase: shuffling
% 0.51/0.41 % (1493510)Time elapsed: 0.002 s
% 0.51/0.41 % (1493510)Peak memory usage: 10 MB
% 0.51/0.41 % (1493510)Instructions burned: 3 (million)
% 0.51/0.41 % (1493515)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2380058293:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 0.51/0.41 % (1493509)Instruction limit reached!
% 0.51/0.41 % (1493509)------------------------------
% 0.51/0.41 % (1493509)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.51/0.41 % (1493509)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.51/0.41 % (1493509)CaDiCaL version: 2.1.3
% 0.51/0.41 % (1493509)Termination reason: Instruction limit
% 0.51/0.41 % (1493509)Termination phase: shuffling
% 0.51/0.41 % (1493509)Time elapsed: 0.005 s
% 0.51/0.41 % (1493509)Peak memory usage: 10 MB
% 0.51/0.41 % (1493509)Instructions burned: 10 (million)
% 0.51/0.41 % (1493513)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=2522697854:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.51/0.41 % (1493515)Instruction limit reached!
% 0.51/0.41 % (1493515)------------------------------
% 0.51/0.41 % (1493515)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.51/0.41 % (1493515)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.51/0.41 % (1493515)CaDiCaL version: 2.1.3
% 0.51/0.41 % (1493515)Termination reason: Instruction limit
% 0.51/0.41 % (1493515)Termination phase: Property scanning
% 0.51/0.41 % (1493515)Time elapsed: 0.007 s
% 0.51/0.41 % (1493515)Peak memory usage: 11 MB
% 0.51/0.41 % (1493515)Instructions burned: 29 (million)
% 0.51/0.41 % (1493514)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=3299167780:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 0.51/0.41 % (1493519)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=1426204744:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.51/0.41 % (1493523)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=1918190140:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 0.51/0.41 % (1493489) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1493481-1493489"...
% 0.51/0.41 % (1493521)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=1908503633:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 0.51/0.41 % (1493513)Instruction limit reached!
% 0.51/0.41 % (1493513)------------------------------
% 0.51/0.41 % (1493513)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.51/0.41 % (1493513)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.51/0.41 % (1493513)CaDiCaL version: 2.1.3
% 0.51/0.41 % (1493513)Termination reason: Instruction limit
% 0.51/0.41 % (1493513)Termination phase: SInE selection
% 0.51/0.41 % (1493513)Time elapsed: 0.019 s
% 0.51/0.41 % (1493513)Peak memory usage: 11 MB
% 0.51/0.41 % (1493513)Instructions burned: 39 (million)
% 0.51/0.41 % (1493489)...printing done.
% 0.51/0.41 % (1493523)Instruction limit reached!
% 0.51/0.41 % (1493523)------------------------------
% 0.51/0.41 % (1493523)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.51/0.41 % (1493523)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.51/0.41 % (1493523)CaDiCaL version: 2.1.3
% 0.51/0.41 % (1493523)Termination reason: Instruction limit
% 0.51/0.41 % (1493523)Termination phase: shuffling
% 0.51/0.41 % (1493523)Time elapsed: 0.004 s
% 0.51/0.41 % (1493523)Peak memory usage: 10 MB
% 0.51/0.41 % (1493523)Instructions burned: 16 (million)
% 0.51/0.41 % (1493489)Refutation found. Thanks to Tanya!
% 0.51/0.41 % SZS status Theorem for theBenchmark
% 0.51/0.41 % SZS output start Proof for theBenchmark
% 0.51/0.41 thf(type_def_5, type, denota1663640101rp_ext: ($tType * $tType * $tType * $tType) > $tType).
% 0.51/0.41 thf(type_def_6, type, frechet_good_interp: ($tType * $tType * $tType) > $tType).
% 0.51/0.41 thf(type_def_7, type, frechet_strm: ($tType * $tType) > $tType).
% 0.51/0.41 thf(type_def_8, type, finite_Cartesian_vec: ($tType * $tType) > $tType).
% 0.51/0.41 thf(type_def_9, type, product_unit: $tType).
% 0.51/0.41 thf(type_def_10, type, product_prod: ($tType * $tType) > $tType).
% 0.51/0.41 thf(type_def_11, type, formula: ($tType * $tType * $tType) > $tType).
% 0.51/0.41 thf(type_def_12, type, sum_sum: ($tType * $tType) > $tType).
% 0.51/0.41 thf(type_def_13, type, trm: ($tType * $tType) > $tType).
% 0.51/0.41 thf(type_def_14, type, real: $tType).
% 0.51/0.41 thf(type_def_15, type, list: $tType > $tType).
% 0.51/0.41 thf(type_def_16, type, set: $tType > $tType).
% 0.51/0.41 thf(type_def_17, type, sz: $tType).
% 0.51/0.41 thf(type_def_18, type, sf: $tType).
% 0.51/0.41 thf(type_def_19, type, sc: $tType).
% 0.51/0.41 thf(type_def_20, type, c: $tType).
% 0.51/0.41 thf(type_def_21, type, b: $tType).
% 0.51/0.41 thf(type_def_22, type, a: $tType).
% 0.51/0.41 thf(type_def_23, type, sTfun: ($tType * $tType) > $tType).
% 0.51/0.41 thf(func_def_0, type, cARD_1: !>[X0: $tType]:($o)).
% 0.51/0.41 thf(func_def_1, type, type: !>[X0: $tType]:($o)).
% 0.51/0.41 thf(func_def_2, type, zero: !>[X0: $tType]:($o)).
% 0.51/0.41 thf(func_def_3, type, top: !>[X0: $tType]:($o)).
% 0.51/0.41 thf(func_def_4, type, finite_finite: !>[X0: $tType]:($o)).
% 0.51/0.41 thf(func_def_5, type, linorder: !>[X0: $tType]:($o)).
% 0.51/0.41 thf(func_def_6, type, euclid1678468529ng_gcd: !>[X0: $tType]:($o)).
% 0.51/0.41 thf(func_def_7, type, euclid1155270486miring: !>[X0: $tType]:($o)).
% 0.51/0.41 thf(func_def_8, type, denotational_Vagree: !>[X0: $tType]:((product_prod @ finite_Cartesian_vec @ real @ X0 @ finite_Cartesian_vec @ real @ X0 > product_prod @ finite_Cartesian_vec @ real @ X0 @ finite_Cartesian_vec @ real @ X0 > set @ sum_sum @ X0 @ X0 > $o))).
% 0.51/0.41 thf(func_def_9, type, denota2078997598vative: !>[X0: $tType, X1: $tType, X2: $tType]:((denota1663640101rp_ext @ X0 @ X1 @ X2 @ product_unit > trm @ X0 @ X2 > product_prod @ finite_Cartesian_vec @ real @ X2 @ finite_Cartesian_vec @ real @ X2 > real))).
% 0.51/0.41 thf(func_def_10, type, denota594965758rm_sem: !>[X0: $tType, X1: $tType, X2: $tType]:((denota1663640101rp_ext @ X0 @ X1 @ X2 @ product_unit > trm @ X0 @ X2 > product_prod @ finite_Cartesian_vec @ real @ X2 @ finite_Cartesian_vec @ real @ X2 > real))).
% 0.51/0.41 thf(func_def_11, type, denotational_frechet: !>[X0: $tType, X1: $tType, X2: $tType]:((denota1663640101rp_ext @ X0 @ X1 @ X2 @ product_unit > trm @ X0 @ X2 > finite_Cartesian_vec @ real @ X2 > finite_Cartesian_vec @ real @ X2 > real))).
% 0.51/0.41 thf(func_def_12, type, denota2077489681interp: !>[X0: $tType, X1: $tType, X2: $tType]:((denota1663640101rp_ext @ X0 @ X1 @ X2 @ product_unit > $o))).
% 0.51/0.41 thf(func_def_13, type, freche457001096interp: !>[X0: $tType, X1: $tType, X2: $tType]:((denota1663640101rp_ext @ X0 @ X1 @ X2 @ product_unit > frechet_good_interp @ X0 @ X1 @ X2 > $o))).
% 0.51/0.41 thf(func_def_14, type, frechet_cr_strm: !>[X0: $tType, X1: $tType]:((trm @ X0 @ X1 > frechet_strm @ X0 @ X1 > $o))).
% 0.51/0.41 thf(func_def_15, type, freche227871258interp: !>[X0: $tType, X1: $tType, X2: $tType]:((denota1663640101rp_ext @ X0 @ X1 @ X2 @ product_unit > frechet_good_interp @ X0 @ X1 @ X2))).
% 0.51/0.41 thf(func_def_16, type, freche229654227interp: !>[X0: $tType, X1: $tType, X2: $tType]:((frechet_good_interp @ X0 @ X1 @ X2 > denota1663640101rp_ext @ X0 @ X1 @ X2 @ product_unit))).
% 0.51/0.41 thf(func_def_17, type, frechet_raw_term: !>[X0: $tType, X1: $tType]:((frechet_strm @ X0 @ X1 > trm @ X0 @ X1))).
% 0.51/0.41 thf(func_def_18, type, frechet_simple_term: !>[X0: $tType, X1: $tType]:((trm @ X0 @ X1 > frechet_strm @ X0 @ X1))).
% 0.51/0.41 thf(func_def_19, type, zero_zero: !>[X0: $tType]:(X0)).
% 0.51/0.41 thf(func_def_20, type, ids: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X0 > X0 > X1 > X1 > X1 > X2 > X2 > X2 > X2 > $o))).
% 0.51/0.41 thf(func_def_21, type, if: !>[X0: $tType]:(($o > X0 > X0 > X0))).
% 0.51/0.41 thf(func_def_22, type, top_top: !>[X0: $tType]:(X0)).
% 0.51/0.41 thf(func_def_23, type, product_Pair: !>[X0: $tType, X1: $tType]:((X0 > X1 > product_prod @ X0 @ X1))).
% 0.51/0.41 thf(func_def_24, type, produc2004651681e_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 0.51/0.41 thf(func_def_25, type, product_map_prod: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((X0 > X1) > (X2 > X3) > product_prod @ X0 @ X2 > product_prod @ X1 @ X3))).
% 0.51/0.41 thf(func_def_26, type, product_rec_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 0.51/0.41 thf(func_def_27, type, product_fst: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 0.51/0.41 thf(func_def_28, type, product_snd: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1))).
% 0.51/0.41 thf(func_def_29, type, product_swap: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > product_prod @ X1 @ X0))).
% 0.51/0.41 thf(func_def_30, type, domainp: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > X0 > $o))).
% 0.51/0.41 thf(func_def_31, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 0.51/0.41 thf(func_def_32, type, image: !>[X0: $tType, X1: $tType]:(((X0 > X1) > set @ X0 > set @ X1))).
% 0.51/0.41 thf(func_def_33, type, static_FVDiff: !>[X0: $tType, X1: $tType]:((trm @ X0 @ X1 > set @ sum_sum @ X1 @ X1))).
% 0.51/0.41 thf(func_def_34, type, predicational: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > formula @ X1 @ X0 @ X2))).
% 0.51/0.41 thf(func_def_35, type, dfree: !>[X0: $tType, X1: $tType]:((trm @ X0 @ X1 > $o))).
% 0.51/0.41 thf(func_def_36, type, dsafe: !>[X0: $tType, X1: $tType]:((trm @ X0 @ X1 > $o))).
% 0.51/0.41 thf(func_def_37, type, ffree: !>[X0: $tType, X1: $tType, X2: $tType]:((formula @ X0 @ X1 @ X2 > $o))).
% 0.51/0.41 thf(func_def_38, type, prop: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > (X0 > trm @ X1 @ X0) > formula @ X1 @ X2 @ X0))).
% 0.51/0.41 thf(func_def_39, type, set1_formula: !>[X0: $tType, X1: $tType, X2: $tType]:((formula @ X0 @ X1 @ X2 > set @ X0))).
% 0.51/0.41 thf(func_def_40, type, p: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > formula @ X1 @ X0 @ X2))).
% 0.51/0.41 thf(func_def_41, type, empty: !>[X0: $tType, X1: $tType]:((X0 > trm @ X1 @ X0))).
% 0.51/0.41 thf(func_def_42, type, f0: !>[X0: $tType, X1: $tType]:((X0 > trm @ X0 @ X1))).
% 0.51/0.41 thf(func_def_43, type, f1: !>[X0: $tType, X1: $tType]:((X0 > X1 > X0 > trm @ X1 @ X0))).
% 0.51/0.41 thf(func_def_44, type, p1: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X0 > X0 > formula @ X1 @ X2 @ X0))).
% 0.51/0.41 thf(func_def_45, type, singleton: !>[X0: $tType, X1: $tType]:((X0 > trm @ X1 @ X0 > X0 > trm @ X1 @ X0))).
% 0.51/0.41 thf(func_def_46, type, singleton_rel: !>[X0: $tType, X1: $tType]:((product_prod @ trm @ X0 @ X1 @ X1 > product_prod @ trm @ X0 @ X1 @ X1 > $o))).
% 0.51/0.41 thf(func_def_47, type, const: !>[X0: $tType, X1: $tType]:((real > trm @ X0 @ X1))).
% 0.51/0.41 thf(func_def_48, type, diffVar: !>[X0: $tType, X1: $tType]:((X0 > trm @ X1 @ X0))).
% 0.51/0.41 thf(func_def_49, type, differential: !>[X0: $tType, X1: $tType]:((trm @ X0 @ X1 > trm @ X0 @ X1))).
% 0.51/0.41 thf(func_def_50, type, function: !>[X0: $tType, X1: $tType]:((X0 > (X1 > trm @ X0 @ X1) > trm @ X0 @ X1))).
% 0.51/0.41 thf(func_def_51, type, plus: !>[X0: $tType, X1: $tType]:((trm @ X0 @ X1 > trm @ X0 @ X1 > trm @ X0 @ X1))).
% 0.51/0.41 thf(func_def_52, type, times: !>[X0: $tType, X1: $tType]:((trm @ X0 @ X1 > trm @ X0 @ X1 > trm @ X0 @ X1))).
% 0.51/0.41 thf(func_def_53, type, var: !>[X0: $tType, X1: $tType]:((X0 > trm @ X1 @ X0))).
% 0.51/0.41 thf(func_def_54, type, set_trm: !>[X0: $tType, X1: $tType]:((trm @ X0 @ X1 > set @ X0))).
% 0.51/0.41 thf(func_def_55, type, left_unique: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > $o))).
% 0.51/0.41 thf(func_def_56, type, right_unique: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > $o))).
% 0.51/0.41 thf(func_def_57, type, accp: !>[X0: $tType]:(((X0 > X0 > $o) > X0 > $o))).
% 0.51/0.41 thf(func_def_58, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.51/0.41 thf(func_def_59, type, i: denota1663640101rp_ext @ a @ b @ c @ product_unit).
% 0.51/0.41 thf(func_def_60, type, nu: product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c).
% 0.51/0.41 thf(func_def_61, type, nu2: product_prod @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c).
% 0.51/0.41 thf(func_def_62, type, args: (c > trm @ a @ c)).
% 0.51/0.41 thf(func_def_63, type, i2: c).
% 0.51/0.41 thf(func_def_64, type, var2: a).
% 0.51/0.41 thf(func_def_65, type, vid1: sz).
% 0.51/0.41 thf(func_def_66, type, vid2: sz).
% 0.51/0.41 thf(func_def_67, type, vid3: sz).
% 0.51/0.41 thf(func_def_71, type, db0: !>[X0: $tType]:(X0)).
% 0.51/0.41 thf(func_def_72, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.51/0.41 thf(func_def_73, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.51/0.41 thf(func_def_74, type, db1: !>[X0: $tType]:(X0)).
% 0.51/0.41 thf(func_def_75, type, db2: !>[X0: $tType]:(X0)).
% 0.51/0.41 thf(func_def_76, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.51/0.41 thf(func_def_77, type, vAND: ($o > $o > $o)).
% 0.51/0.41 thf(func_def_78, type, db3: !>[X0: $tType]:(X0)).
% 0.51/0.41 thf(func_def_79, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.51/0.41 thf(func_def_80, type, vIMP: ($o > $o > $o)).
% 0.51/0.41 thf(func_def_81, type, vOR: ($o > $o > $o)).
% 0.51/0.41 thf(func_def_82, type, sP0: !>[X0: $tType, X1: $tType]:(((trm @ X1 @ X0 > $o) > $o))).
% 0.51/0.41 thf(func_def_83, type, sP1: !>[X0: $tType, X1: $tType]:(((trm @ X1 @ X0 > $o) > $o))).
% 0.51/0.41 thf(func_def_84, type, sP2: !>[X0: $tType, X1: $tType]:(((trm @ X1 @ X0 > $o) > $o))).
% 0.51/0.41 thf(func_def_85, type, sP3: !>[X0: $tType, X1: $tType]:((trm @ X1 @ X0 > $o))).
% 0.51/0.41 thf(func_def_86, type, sP4: !>[X0: $tType, X1: $tType]:(((trm @ X1 @ X0 > $o) > $o))).
% 0.51/0.41 thf(func_def_87, type, sP5: !>[X0: $tType, X1: $tType]:((trm @ X1 @ X0 > X1 > $o))).
% 0.51/0.41 thf(func_def_88, type, sP6: !>[X0: $tType, X1: $tType]:((X1 > trm @ X1 @ X0 > $o))).
% 0.51/0.41 thf(func_def_89, type, sP7: !>[X0: $tType, X1: $tType]:((trm @ X1 @ X0 > $o))).
% 0.51/0.41 thf(func_def_90, type, sK8: (product_prod @ denota1663640101rp_ext @ sf @ sc @ sz @ product_unit @ product_prod @ list @ formula @ sf @ sc @ sz @ list @ formula @ sf @ sc @ sz > product_prod @ list @ formula @ sf @ sc @ sz @ list @ formula @ sf @ sc @ sz)).
% 0.51/0.41 thf(func_def_91, type, sK9: (product_prod @ denota1663640101rp_ext @ sf @ sc @ sz @ product_unit @ product_prod @ list @ formula @ sf @ sc @ sz @ list @ formula @ sf @ sc @ sz > denota1663640101rp_ext @ sf @ sc @ sz @ product_unit)).
% 0.51/0.41 thf(func_def_92, type, sK10: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > X0 > X1))).
% 0.51/0.41 thf(func_def_93, type, sK11: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X0 > X1))).
% 0.51/0.41 thf(func_def_94, type, sK12: !>[X0: $tType, X1: $tType]:((set @ X0 > (X0 > X1) > (X0 > X1) > X0))).
% 0.51/0.41 thf(func_def_95, type, sK13: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X1 @ product_prod @ X0 @ X2 > $o) > X1))).
% 0.51/0.41 thf(func_def_96, type, sK14: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X1 @ product_prod @ X0 @ X2 > $o) > X0))).
% 0.51/0.41 thf(func_def_97, type, sK15: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X1 @ product_prod @ X0 @ X2 > $o) > X2))).
% 0.51/0.41 thf(func_def_98, type, sK16: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0 > X1))).
% 0.51/0.41 thf(func_def_99, type, sK17: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X1 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X0 @ X4 > $o) > X0))).
% 0.51/0.41 thf(func_def_100, type, sK18: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X1 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X0 @ X4 > $o) > X3))).
% 0.51/0.41 thf(func_def_101, type, sK19: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X1 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X0 @ X4 > $o) > X1))).
% 0.51/0.41 thf(func_def_102, type, sK20: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X1 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X0 @ X4 > $o) > X4))).
% 0.51/0.41 thf(func_def_103, type, sK21: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X1 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X0 @ X4 > $o) > X2))).
% 0.51/0.41 thf(func_def_104, type, sK22: !>[X0: $tType, X1: $tType]:(((X0 > trm @ X1 @ X0) > X0))).
% 0.51/0.41 thf(func_def_105, type, sK23: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > X0))).
% 0.51/0.41 thf(func_def_106, type, sK24: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > X1))).
% 0.51/0.41 thf(func_def_107, type, sK25: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ product_prod @ X3 @ product_prod @ X5 @ product_prod @ X0 @ X4 > $o) > X4))).
% 0.51/0.41 thf(func_def_108, type, sK26: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ product_prod @ X3 @ product_prod @ X5 @ product_prod @ X0 @ X4 > $o) > X2))).
% 0.51/0.41 thf(func_def_109, type, sK27: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ product_prod @ X3 @ product_prod @ X5 @ product_prod @ X0 @ X4 > $o) > X5))).
% 0.51/0.41 thf(func_def_110, type, sK28: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ product_prod @ X3 @ product_prod @ X5 @ product_prod @ X0 @ X4 > $o) > X1))).
% 0.51/0.41 thf(func_def_111, type, sK29: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ product_prod @ X3 @ product_prod @ X5 @ product_prod @ X0 @ X4 > $o) > X0))).
% 0.51/0.41 thf(func_def_112, type, sK30: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ product_prod @ X3 @ product_prod @ X5 @ product_prod @ X0 @ X4 > $o) > X3))).
% 0.51/0.41 thf(func_def_113, type, sK31: !>[X0: $tType, X1: $tType]:(((product_prod @ X0 @ X1 > $o) > X1))).
% 0.51/0.41 thf(func_def_114, type, sK32: !>[X0: $tType, X1: $tType]:(((product_prod @ X0 @ X1 > $o) > X0))).
% 0.51/0.41 thf(func_def_115, type, sK33: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > X0))).
% 0.51/0.41 thf(func_def_116, type, sK34: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > X1))).
% 0.51/0.41 thf(func_def_117, type, sK35: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ denota1663640101rp_ext @ X0 @ X2 @ X1 @ product_unit @ product_prod @ list @ formula @ X0 @ X2 @ X1 @ list @ formula @ X0 @ X2 @ X1 > product_prod @ list @ formula @ X0 @ X2 @ X1 @ list @ formula @ X0 @ X2 @ X1))).
% 0.51/0.41 thf(func_def_118, type, sK36: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ denota1663640101rp_ext @ X0 @ X2 @ X1 @ product_unit @ product_prod @ list @ formula @ X0 @ X2 @ X1 @ list @ formula @ X0 @ X2 @ X1 > denota1663640101rp_ext @ X0 @ X2 @ X1 @ product_unit))).
% 0.51/0.41 thf(func_def_119, type, sK37: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X1))).
% 0.51/0.41 thf(func_def_120, type, sK38: !>[X0: $tType, X1: $tType]:((X1 > (X0 > X1) > X0))).
% 0.51/0.41 thf(func_def_121, type, sK39: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X1 @ product_prod @ X5 @ product_prod @ X2 @ product_prod @ X4 @ product_prod @ X3 @ X0 > X0))).
% 0.51/0.41 thf(func_def_122, type, sK40: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X1 @ product_prod @ X5 @ product_prod @ X2 @ product_prod @ X4 @ product_prod @ X3 @ X0 > X2))).
% 0.51/0.41 thf(func_def_123, type, sK41: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X1 @ product_prod @ X5 @ product_prod @ X2 @ product_prod @ X4 @ product_prod @ X3 @ X0 > X3))).
% 0.51/0.41 thf(func_def_124, type, sK42: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X1 @ product_prod @ X5 @ product_prod @ X2 @ product_prod @ X4 @ product_prod @ X3 @ X0 > X6))).
% 0.51/0.41 thf(func_def_125, type, sK43: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X1 @ product_prod @ X5 @ product_prod @ X2 @ product_prod @ X4 @ product_prod @ X3 @ X0 > X5))).
% 0.51/0.41 thf(func_def_126, type, sK44: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X1 @ product_prod @ X5 @ product_prod @ X2 @ product_prod @ X4 @ product_prod @ X3 @ X0 > X1))).
% 0.51/0.41 thf(func_def_127, type, sK45: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X1 @ product_prod @ X5 @ product_prod @ X2 @ product_prod @ X4 @ product_prod @ X3 @ X0 > X4))).
% 0.51/0.41 thf(func_def_128, type, sK46: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X1 > X0))).
% 0.51/0.41 thf(func_def_129, type, sK47: !>[X0: $tType]:((product_prod @ X0 @ X0 > X0))).
% 0.51/0.41 thf(func_def_130, type, sK48: !>[X0: $tType]:((product_prod @ X0 @ X0 > X0))).
% 0.51/0.41 thf(func_def_131, type, sK49: !>[X0: $tType, X1: $tType, X2: $tType]:(((denota1663640101rp_ext @ X2 @ X0 @ X1 @ product_unit > product_prod @ list @ formula @ X2 @ X0 @ X1 @ list @ formula @ X2 @ X0 @ X1 > $o) > product_prod @ list @ formula @ X2 @ X0 @ X1 @ list @ formula @ X2 @ X0 @ X1))).
% 0.51/0.41 thf(func_def_132, type, sK50: !>[X0: $tType, X1: $tType, X2: $tType]:(((denota1663640101rp_ext @ X2 @ X0 @ X1 @ product_unit > product_prod @ list @ formula @ X2 @ X0 @ X1 @ list @ formula @ X2 @ X0 @ X1 > $o) > denota1663640101rp_ext @ X2 @ X0 @ X1 @ product_unit))).
% 0.51/0.41 thf(func_def_133, type, sK51: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X0 > X1) > X1))).
% 0.51/0.41 thf(func_def_134, type, sK52: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X2 @ product_prod @ X4 @ product_prod @ X0 @ product_prod @ X1 @ X3 > X0))).
% 0.51/0.41 thf(func_def_135, type, sK53: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X2 @ product_prod @ X4 @ product_prod @ X0 @ product_prod @ X1 @ X3 > X4))).
% 0.51/0.41 thf(func_def_136, type, sK54: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X2 @ product_prod @ X4 @ product_prod @ X0 @ product_prod @ X1 @ X3 > X1))).
% 0.51/0.41 thf(func_def_137, type, sK55: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X2 @ product_prod @ X4 @ product_prod @ X0 @ product_prod @ X1 @ X3 > X3))).
% 0.51/0.41 thf(func_def_138, type, sK56: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X2 @ product_prod @ X4 @ product_prod @ X0 @ product_prod @ X1 @ X3 > X5))).
% 0.51/0.41 thf(func_def_139, type, sK57: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X2 @ product_prod @ X4 @ product_prod @ X0 @ product_prod @ X1 @ X3 > X2))).
% 0.51/0.41 thf(func_def_140, type, sK58: !>[X0: $tType, X1: $tType]:(((X1 > $o) > set @ X0 > (X0 > X1) > X0))).
% 0.51/0.41 thf(func_def_141, type, sK59: !>[X0: $tType]:((product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ X0 > X0))).
% 0.51/0.41 thf(func_def_142, type, sK60: !>[X0: $tType]:((product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ X0 > X0))).
% 0.51/0.41 thf(func_def_143, type, sK61: !>[X0: $tType]:((product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ X0 > X0))).
% 0.51/0.41 thf(func_def_144, type, sK62: !>[X0: $tType]:((product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ X0 > X0))).
% 0.51/0.41 thf(func_def_145, type, sK63: !>[X0: $tType]:((product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ X0 > X0))).
% 0.51/0.41 thf(func_def_146, type, sK64: !>[X0: $tType]:((product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ X0 > X0))).
% 0.51/0.41 thf(func_def_147, type, sK65: !>[X0: $tType, X1: $tType]:((trm @ X0 @ X1 > real))).
% 0.51/0.41 thf(func_def_148, type, sK66: !>[X0: $tType, X1: $tType]:((trm @ X0 @ X1 > X1))).
% 0.51/0.41 thf(func_def_149, type, sK67: !>[X0: $tType, X1: $tType]:((trm @ X0 @ X1 > X0))).
% 0.51/0.41 thf(func_def_150, type, sK68: !>[X0: $tType, X1: $tType]:((trm @ X0 @ X1 > X1 > trm @ X0 @ X1))).
% 0.51/0.41 thf(func_def_151, type, sK69: !>[X0: $tType, X1: $tType]:((trm @ X0 @ X1 > X1))).
% 0.51/0.41 thf(func_def_152, type, sK70: !>[X0: $tType, X1: $tType]:((trm @ X0 @ X1 > trm @ X0 @ X1))).
% 0.51/0.41 thf(func_def_153, type, sK71: !>[X0: $tType, X1: $tType]:((trm @ X0 @ X1 > trm @ X0 @ X1))).
% 0.51/0.41 thf(func_def_154, type, sK72: !>[X0: $tType, X1: $tType]:((trm @ X0 @ X1 > trm @ X0 @ X1))).
% 0.51/0.41 thf(func_def_155, type, sK73: !>[X0: $tType, X1: $tType]:((trm @ X0 @ X1 > trm @ X0 @ X1))).
% 0.51/0.41 thf(func_def_156, type, sK74: !>[X0: $tType, X1: $tType]:((trm @ X0 @ X1 > trm @ X0 @ X1))).
% 0.51/0.41 thf(func_def_157, type, sK75: !>[X0: $tType, X1: $tType]:(((trm @ X1 @ X0 > $o) > trm @ X1 @ X0))).
% 0.51/0.41 thf(func_def_158, type, sK76: !>[X0: $tType, X1: $tType]:(((trm @ X1 @ X0 > $o) > trm @ X1 @ X0))).
% 0.51/0.41 thf(func_def_159, type, sK77: !>[X0: $tType, X1: $tType]:(((trm @ X0 @ X1 > $o) > trm @ X0 @ X1))).
% 0.51/0.41 thf(func_def_160, type, sK78: !>[X0: $tType, X1: $tType]:(((trm @ X0 @ X1 > $o) > trm @ X0 @ X1))).
% 0.51/0.41 thf(func_def_161, type, sK79: !>[X0: $tType, X1: $tType]:(((trm @ X0 @ X1 > $o) > trm @ X0 @ X1))).
% 0.51/0.41 thf(func_def_162, type, sK80: !>[X0: $tType, X1: $tType]:(((trm @ X0 @ X1 > $o) > real))).
% 0.51/0.41 thf(func_def_163, type, sK81: !>[X0: $tType, X1: $tType]:(((trm @ X0 @ X1 > $o) > X1 > trm @ X0 @ X1))).
% 0.51/0.41 thf(func_def_164, type, sK82: !>[X0: $tType, X1: $tType]:(((trm @ X0 @ X1 > $o) > X0))).
% 0.51/0.41 thf(func_def_165, type, sK83: !>[X0: $tType, X1: $tType]:(((trm @ X0 @ X1 > $o) > X1))).
% 0.51/0.41 thf(func_def_166, type, sK84: !>[X0: $tType, X1: $tType]:(((trm @ X0 @ X1 > $o) > X1))).
% 0.51/0.41 thf(func_def_167, type, sK85: !>[X0: $tType, X1: $tType]:(((X1 > X0) > set @ X1 > (X0 > $o) > X0))).
% 0.51/0.41 thf(func_def_168, type, sK86: !>[X0: $tType, X1: $tType]:(((X0 > trm @ X1 @ X0) > X0))).
% 0.51/0.41 thf(func_def_169, type, sK87: !>[X0: $tType, X1: $tType]:(((trm @ X1 @ X0 > X0 > $o) > trm @ X1 @ X0))).
% 0.51/0.41 thf(func_def_170, type, sK88: !>[X0: $tType, X1: $tType]:(((trm @ X1 @ X0 > X0 > $o) > X0))).
% 0.51/0.41 thf(func_def_171, type, sK89: !>[X0: $tType, X1: $tType]:(((trm @ X1 @ X0 > $o) > trm @ X1 @ X0))).
% 0.51/0.41 thf(func_def_172, type, sK90: !>[X0: $tType, X1: $tType]:(((trm @ X1 @ X0 > $o) > trm @ X1 @ X0))).
% 0.51/0.41 thf(func_def_173, type, sK91: !>[X0: $tType, X1: $tType]:(((trm @ X1 @ X0 > $o) > trm @ X1 @ X0))).
% 0.51/0.41 thf(func_def_174, type, sK92: !>[X0: $tType, X1: $tType]:(((trm @ X1 @ X0 > $o) > trm @ X1 @ X0))).
% 0.51/0.41 thf(func_def_175, type, sK93: !>[X0: $tType, X1: $tType]:(((trm @ X1 @ X0 > $o) > real))).
% 0.51/0.41 thf(func_def_176, type, sK94: !>[X0: $tType, X1: $tType]:(((trm @ X1 @ X0 > $o) > X0))).
% 0.51/0.41 thf(func_def_177, type, sK95: !>[X0: $tType, X1: $tType]:(((trm @ X1 @ X0 > $o) > trm @ X1 @ X0))).
% 0.51/0.41 thf(func_def_178, type, sK96: !>[X0: $tType, X1: $tType]:(((trm @ X1 @ X0 > $o) > X1))).
% 0.51/0.41 thf(func_def_179, type, sK97: !>[X0: $tType, X1: $tType]:(((trm @ X1 @ X0 > $o) > X0 > trm @ X1 @ X0))).
% 0.51/0.41 thf(func_def_180, type, sK98: !>[X0: $tType, X1: $tType]:(((trm @ X1 @ X0 > $o) > X0))).
% 0.51/0.41 thf(func_def_181, type, sK99: !>[X0: $tType, X1: $tType]:((product_prod @ trm @ X1 @ X0 @ X0 > trm @ X1 @ X0))).
% 0.51/0.41 thf(func_def_182, type, sK100: !>[X0: $tType, X1: $tType]:((product_prod @ trm @ X1 @ X0 @ X0 > X0))).
% 0.51/0.41 thf(func_def_183, type, sK101: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > X1) > X0))).
% 0.51/0.41 thf(func_def_184, type, sK102: !>[X0: $tType]:(X0)).
% 0.51/0.41 thf(func_def_185, type, sK103: !>[X0: $tType, X1: $tType]:(((X1 > trm @ X0 @ X1) > trm @ X0 @ X1))).
% 0.51/0.41 thf(func_def_186, type, sK104: !>[X0: $tType, X1: $tType]:((X0 > product_prod @ X1 @ X0 > X1))).
% 0.51/0.41 thf(func_def_187, type, sK105: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > X1))).
% 0.51/0.41 thf(func_def_188, type, sK106: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > X1))).
% 0.51/0.41 thf(func_def_189, type, sK107: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > X0))).
% 0.51/0.41 thf(func_def_190, type, sK108: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X3 @ product_prod @ X1 @ product_prod @ X0 @ product_prod @ X2 @ X4 > X3))).
% 0.51/0.41 thf(func_def_191, type, sK109: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X3 @ product_prod @ X1 @ product_prod @ X0 @ product_prod @ X2 @ X4 > X2))).
% 0.51/0.41 thf(func_def_192, type, sK110: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X3 @ product_prod @ X1 @ product_prod @ X0 @ product_prod @ X2 @ X4 > X1))).
% 0.51/0.41 thf(func_def_193, type, sK111: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X3 @ product_prod @ X1 @ product_prod @ X0 @ product_prod @ X2 @ X4 > X0))).
% 0.51/0.41 thf(func_def_194, type, sK112: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X3 @ product_prod @ X1 @ product_prod @ X0 @ product_prod @ X2 @ X4 > X4))).
% 0.51/0.41 thf(func_def_195, type, sK113: !>[X0: $tType, X1: $tType]:((X0 > (X0 > X1 > $o) > X1))).
% 0.51/0.41 thf(func_def_196, type, sK114: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.51/0.41 thf(func_def_197, type, sK115: !>[X0: $tType, X1: $tType]:(((product_prod @ X0 @ X1 > $o) > X1))).
% 0.51/0.41 thf(func_def_198, type, sK116: !>[X0: $tType, X1: $tType]:(((product_prod @ X0 @ X1 > $o) > X0))).
% 0.51/0.41 thf(func_def_199, type, sK117: !>[X0: $tType, X1: $tType]:((trm @ X1 @ X0 > trm @ X1 @ X0))).
% 0.51/0.41 thf(func_def_200, type, sK118: !>[X0: $tType, X1: $tType]:((trm @ X1 @ X0 > trm @ X1 @ X0))).
% 0.51/0.41 thf(func_def_201, type, sK119: !>[X0: $tType, X1: $tType]:((trm @ X0 @ X1 > trm @ X0 @ X1))).
% 0.51/0.41 thf(func_def_202, type, sK120: !>[X0: $tType, X1: $tType]:((trm @ X0 @ X1 > X1 > trm @ X0 @ X1))).
% 0.51/0.41 thf(func_def_203, type, sK121: !>[X0: $tType, X1: $tType]:((trm @ X0 @ X1 > X0))).
% 0.51/0.41 thf(func_def_204, type, sK122: !>[X0: $tType, X1: $tType]:((trm @ X0 @ X1 > X1))).
% 0.51/0.41 thf(func_def_205, type, sK123: !>[X0: $tType, X1: $tType]:((trm @ X0 @ X1 > trm @ X0 @ X1))).
% 0.51/0.41 thf(func_def_206, type, sK124: !>[X0: $tType, X1: $tType]:((trm @ X0 @ X1 > trm @ X0 @ X1))).
% 0.51/0.41 thf(func_def_207, type, sK125: !>[X0: $tType, X1: $tType]:((trm @ X0 @ X1 > X1))).
% 0.51/0.41 thf(func_def_208, type, sK126: !>[X0: $tType, X1: $tType]:((trm @ X0 @ X1 > real))).
% 0.51/0.41 thf(func_def_209, type, sK127: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ denota1663640101rp_ext @ X0 @ X1 @ X2 @ product_unit @ X0 > denota1663640101rp_ext @ X0 @ X1 @ X2 @ product_unit))).
% 0.51/0.41 thf(func_def_210, type, sK128: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ denota1663640101rp_ext @ X0 @ X1 @ X2 @ product_unit @ X0 > X0))).
% 0.51/0.41 thf(func_def_211, type, sK129: !>[X0: $tType]:((set @ X0 > X0))).
% 0.51/0.41 thf(func_def_212, type, sK130: !>[X0: $tType, X1: $tType]:(((trm @ X1 @ X0 > $o) > trm @ X1 @ X0))).
% 0.51/0.41 thf(func_def_213, type, sK131: !>[X0: $tType, X1: $tType]:(((trm @ X1 @ X0 > $o) > trm @ X1 @ X0))).
% 0.51/0.41 thf(func_def_214, type, sK132: !>[X0: $tType, X1: $tType]:(((trm @ X1 @ X0 > $o) > trm @ X1 @ X0))).
% 0.51/0.41 thf(func_def_215, type, sK133: !>[X0: $tType, X1: $tType]:(((trm @ X1 @ X0 > $o) > trm @ X1 @ X0))).
% 0.51/0.41 thf(func_def_216, type, sK134: !>[X0: $tType, X1: $tType]:(((trm @ X1 @ X0 > $o) > X1))).
% 0.51/0.41 thf(func_def_217, type, sK135: !>[X0: $tType, X1: $tType]:(((trm @ X1 @ X0 > $o) > X0 > trm @ X1 @ X0))).
% 0.51/0.41 thf(func_def_218, type, sK136: !>[X0: $tType, X1: $tType]:(((trm @ X1 @ X0 > $o) > real))).
% 0.51/0.41 thf(func_def_219, type, sK137: !>[X0: $tType, X1: $tType]:(((trm @ X1 @ X0 > $o) > X0))).
% 0.51/0.41 thf(func_def_220, type, sK138: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((X2 > X1) > (X0 > X3) > set @ product_prod @ X2 @ X0 > product_prod @ X1 @ X3 > X2))).
% 0.51/0.41 thf(func_def_221, type, sK139: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((X2 > X1) > (X0 > X3) > set @ product_prod @ X2 @ X0 > product_prod @ X1 @ X3 > X0))).
% 0.51/0.41 thf(func_def_222, type, sK140: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X1 @ X2 > X1))).
% 0.51/0.41 thf(func_def_223, type, sK141: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X1 @ X2 > X0))).
% 0.51/0.41 thf(func_def_224, type, sK142: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X1 @ X2 > X2))).
% 0.51/0.41 thf(func_def_225, type, sK143: !>[X0: $tType, X1: $tType]:(((X0 > X1) > set @ X0 > X1 > X0))).
% 0.51/0.42 thf(func_def_226, type, sK144: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X5 @ product_prod @ X1 @ product_prod @ X6 @ product_prod @ X0 @ product_prod @ X3 @ product_prod @ X2 @ X4 > $o) > X0))).
% 0.51/0.42 thf(func_def_227, type, sK145: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X5 @ product_prod @ X1 @ product_prod @ X6 @ product_prod @ X0 @ product_prod @ X3 @ product_prod @ X2 @ X4 > $o) > X5))).
% 0.51/0.42 thf(func_def_228, type, sK146: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X5 @ product_prod @ X1 @ product_prod @ X6 @ product_prod @ X0 @ product_prod @ X3 @ product_prod @ X2 @ X4 > $o) > X6))).
% 0.51/0.42 thf(func_def_229, type, sK147: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X5 @ product_prod @ X1 @ product_prod @ X6 @ product_prod @ X0 @ product_prod @ X3 @ product_prod @ X2 @ X4 > $o) > X3))).
% 0.51/0.42 thf(func_def_230, type, sK148: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X5 @ product_prod @ X1 @ product_prod @ X6 @ product_prod @ X0 @ product_prod @ X3 @ product_prod @ X2 @ X4 > $o) > X4))).
% 0.51/0.42 thf(func_def_231, type, sK149: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X5 @ product_prod @ X1 @ product_prod @ X6 @ product_prod @ X0 @ product_prod @ X3 @ product_prod @ X2 @ X4 > $o) > X1))).
% 0.51/0.42 thf(func_def_232, type, sK150: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X5 @ product_prod @ X1 @ product_prod @ X6 @ product_prod @ X0 @ product_prod @ X3 @ product_prod @ X2 @ X4 > $o) > X2))).
% 0.51/0.42 thf(func_def_233, type, sK151: !>[X0: $tType, X1: $tType]:((X1 > trm @ X1 @ X0 > trm @ X1 @ X0))).
% 0.51/0.42 thf(func_def_234, type, sK152: !>[X0: $tType, X1: $tType]:((X1 > trm @ X1 @ X0 > trm @ X1 @ X0))).
% 0.51/0.42 thf(func_def_235, type, sK153: !>[X0: $tType, X1: $tType]:((trm @ X1 @ X0 > X1 > X0 > trm @ X1 @ X0))).
% 0.51/0.42 thf(func_def_236, type, sK154: !>[X0: $tType, X1: $tType]:((trm @ X1 @ X0 > X1 > X1))).
% 0.51/0.42 thf(func_def_237, type, sK155: !>[X0: $tType, X1: $tType]:((trm @ X1 @ X0 > X1 > trm @ X1 @ X0))).
% 0.51/0.42 thf(func_def_238, type, sK156: !>[X0: $tType, X1: $tType]:((trm @ X0 @ X1 > X0 > trm @ X0 @ X1))).
% 0.51/0.42 thf(func_def_239, type, sK157: !>[X0: $tType, X1: $tType]:((trm @ X0 @ X1 > X0 > trm @ X0 @ X1))).
% 0.51/0.42 thf(func_def_240, type, sK158: !>[X0: $tType, X1: $tType]:((trm @ X0 @ X1 > X0 > trm @ X0 @ X1))).
% 0.51/0.42 thf(func_def_241, type, sK159: !>[X0: $tType, X1: $tType]:((trm @ X0 @ X1 > X0 > trm @ X0 @ X1))).
% 0.51/0.42 thf(func_def_242, type, sK160: !>[X0: $tType, X1: $tType]:((trm @ X0 @ X1 > X0 > trm @ X0 @ X1))).
% 0.51/0.42 thf(func_def_243, type, sK161: !>[X0: $tType, X1: $tType]:((trm @ X0 @ X1 > X0 > trm @ X0 @ X1))).
% 0.51/0.42 thf(func_def_244, type, sK162: !>[X0: $tType, X1: $tType]:((trm @ X0 @ X1 > X0 > trm @ X0 @ X1))).
% 0.51/0.42 thf(func_def_245, type, sK163: !>[X0: $tType, X1: $tType]:((trm @ X0 @ X1 > X0 > X1 > trm @ X0 @ X1))).
% 0.51/0.42 thf(func_def_246, type, sK164: !>[X0: $tType]:((product_prod @ trm @ X0 @ sz @ sz > trm @ X0 @ sz))).
% 0.51/0.42 thf(func_def_247, type, sK165: !>[X0: $tType]:((product_prod @ trm @ X0 @ sz @ sz > sz))).
% 0.51/0.42 thf(func_def_248, type, sK166: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > X1))).
% 0.51/0.42 thf(func_def_249, type, sK167: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > X0))).
% 0.51/0.42 thf(func_def_250, type, sK168: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > X1))).
% 0.51/0.42 thf(func_def_251, type, sK169: !>[X0: $tType, X1: $tType]:(((X0 > trm @ X1 @ X0) > X0))).
% 0.51/0.42 thf(func_def_252, type, sK170: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X0 @ product_prod @ X3 @ product_prod @ X1 @ X2 > $o) > X2))).
% 0.51/0.42 thf(func_def_253, type, sK171: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X0 @ product_prod @ X3 @ product_prod @ X1 @ X2 > $o) > X0))).
% 0.51/0.42 thf(func_def_254, type, sK172: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X0 @ product_prod @ X3 @ product_prod @ X1 @ X2 > $o) > X3))).
% 0.51/0.42 thf(func_def_255, type, sK173: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X0 @ product_prod @ X3 @ product_prod @ X1 @ X2 > $o) > X1))).
% 0.51/0.42 thf(func_def_256, type, sK174: !>[X0: $tType, X1: $tType]:(((X0 > trm @ X1 @ X0) > X0))).
% 0.51/0.42 thf(func_def_257, type, sK175: !>[X0: $tType, X1: $tType]:(((X1 > $o) > (X1 > X0 > $o) > X0))).
% 0.51/0.42 thf(func_def_258, type, sK176: !>[X0: $tType, X1: $tType]:(((X1 > $o) > (X1 > X0 > $o) > X1))).
% 0.51/0.42 thf(func_def_259, type, sK177: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X1 @ product_prod @ X0 @ X2 > X2))).
% 0.51/0.42 thf(func_def_260, type, sK178: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X1 @ product_prod @ X0 @ X2 > X0))).
% 0.51/0.42 thf(func_def_261, type, sK179: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X1 @ product_prod @ X0 @ X2 > X1))).
% 0.51/0.42 thf(func_def_262, type, sK180: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X1 @ product_prod @ X0 @ X2 > X3))).
% 0.51/0.42 thf(func_def_263, type, sK181: !>[X0: $tType, X1: $tType]:((trm @ X1 @ X0 > trm @ X1 @ X0))).
% 0.51/0.42 thf(func_def_264, type, sK182: !>[X0: $tType, X1: $tType]:((trm @ X1 @ X0 > trm @ X1 @ X0))).
% 0.51/0.42 thf(func_def_265, type, sK183: !>[X0: $tType, X1: $tType]:((trm @ X1 @ X0 > real))).
% 0.51/0.42 thf(func_def_266, type, sK184: !>[X0: $tType, X1: $tType]:((trm @ X1 @ X0 > X0 > trm @ X1 @ X0))).
% 0.51/0.42 thf(func_def_267, type, sK185: !>[X0: $tType, X1: $tType]:((trm @ X1 @ X0 > X1))).
% 0.51/0.42 thf(func_def_268, type, sK186: !>[X0: $tType, X1: $tType]:((trm @ X1 @ X0 > X0))).
% 0.51/0.42 thf(func_def_269, type, sK187: !>[X0: $tType, X1: $tType]:((trm @ X1 @ X0 > trm @ X1 @ X0))).
% 0.51/0.42 thf(func_def_270, type, sK188: !>[X0: $tType, X1: $tType]:((trm @ X1 @ X0 > trm @ X1 @ X0))).
% 0.51/0.42 thf(func_def_271, type, sK189: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1))).
% 0.51/0.42 thf(func_def_272, type, sK190: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 0.51/0.42 thf(func_def_273, type, vNOT: ($o > $o)).
% 0.51/0.42 thf(f1,axiom,(
% 0.51/0.42 ! [X8 : c] : (dfree @ a @ c @ (args @ X8))),
% 0.51/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_free)).
% 0.51/0.42 thf(f288,conjecture,(
% 0.51/0.42 (dfree @ a @ c @ (args @ i2))),
% 0.51/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 0.51/0.42 thf(f289,negated_conjecture,(
% 0.51/0.42 ~(dfree @ a @ c @ (args @ i2))),
% 0.51/0.42 inference(negated_conjecture,[status(cth)],[f288])).
% 0.51/0.42 thf(f479,plain,(
% 0.51/0.42 ! [X0 : c] : (dfree @ a @ c @ (args @ X0))),
% 0.51/0.42 inference(rectify,[],[f1])).
% 0.51/0.42 thf(f480,plain,(
% 0.51/0.42 ! [X0 : c] : (((dfree @ a @ c @ (args @ X0))) = $true)),
% 0.51/0.42 inference(fool_elimination,[],[f479])).
% 0.51/0.42 thf(f583,plain,(
% 0.51/0.42 ~(dfree @ a @ c @ (args @ i2))),
% 0.51/0.42 inference(rectify,[],[f289])).
% 0.51/0.42 thf(f584,plain,(
% 0.51/0.42 ~ (((dfree @ a @ c @ (args @ i2))) = $true)),
% 0.51/0.42 inference(fool_elimination,[],[f583])).
% 0.51/0.42 thf(f749,plain,(
% 0.51/0.42 (((dfree @ a @ c @ (args @ i2))) != $true)),
% 0.51/0.42 inference(flattening,[],[f584])).
% 0.51/0.42 thf(f1380,plain,(
% 0.51/0.42 ( ! [X0 : c] : ((((dfree @ a @ c @ (args @ X0))) = $true)) )),
% 0.51/0.42 inference(cnf_transformation,[],[f480])).
% 0.51/0.42 thf(f1451,plain,(
% 0.51/0.42 (((dfree @ a @ c @ (args @ i2))) != $true)),
% 0.51/0.42 inference(cnf_transformation,[],[f749])).
% 0.51/0.42 thf(f1938,definition,(
% 0.51/0.42 spl191_28 <=> (((dfree @ a @ c @ (args @ i2))) = $true)),
% 0.51/0.42 introduced(definition,[new_symbols(definition,[spl191_28])],[avatar_definition])).
% 0.51/0.42 thf(f1940,plain,(
% 0.51/0.42 (((dfree @ a @ c @ (args @ i2))) != $true) | spl191_28),
% 0.51/0.42 inference(avatar_component_clause,[],[f1938])).
% 0.51/0.42 thf(f1941,plain,(
% 0.51/0.42 ~spl191_28),
% 0.51/0.42 inference(avatar_split_clause,[],[f1451,f1938])).
% 0.51/0.42 thf(f1973,plain,(
% 0.51/0.42 $false | spl191_28),
% 0.51/0.42 inference(forward_subsumption_resolution,[],[f1940,f1380])).
% 0.51/0.42 thf(f1974,plain,(
% 0.51/0.42 spl191_28),
% 0.51/0.42 inference(avatar_contradiction_clause,[],[f1973])).
% 0.51/0.42 cnf(s36, plain, ~spl191_28, inference(sat_conversion,[],[f1941])).
% 0.51/0.42 cnf(s46, plain, spl191_28, inference(sat_conversion,[],[f1974])).
% 0.51/0.42 cnf(s47, plain, $false, inference(rat,[],[s36,s46])).
% 0.51/0.42 thf(f1975,plain,(
% 0.51/0.42 $false),
% 0.51/0.42 inference(avatar_sat_refutation,[],[s47])).
% 0.51/0.42 % SZS output end Proof for theBenchmark
% 0.51/0.42 % (1493489)------------------------------
% 0.51/0.42 % (1493489)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.51/0.42 % (1493489)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.51/0.42 % (1493489)CaDiCaL version: 2.1.3
% 0.51/0.42 % (1493489)Termination reason: Refutation
% 0.51/0.42 % (1493489)Time elapsed: 0.082 s
% 0.51/0.42 % (1493489)Peak memory usage: 15 MB
% 0.51/0.42 % (1493489)Instructions burned: 165 (million)
% 0.51/0.42 % (1493481)Success in time 0.141 s
% 0.51/0.42 % Vampire exiting
%------------------------------------------------------------------------------