%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : DAT115^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 07:48:22 AM UTC 2026
% Result : Theorem 0.46s 0.24s
% Output : Refutation 0.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : DAT115^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Tue Sep 29 17:57:33 UTC 2026
% 0.00/0.10 % CPUTime :
% 0.00/0.10 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.12 Running higher-order theorem proving
% 0.09/0.15 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
% 0.46/0.23 % (468210)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.46/0.23 % (468236)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.46/0.23 % (468236)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
% 0.46/0.23 % (468229)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1451644246:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.46/0.23 % (468230)lrs+10_16_si=on:nwc=1.5:random_seed=2971220185:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.46/0.23 % (468231)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3168894037:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.46/0.23 % (468235)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1951241025:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.46/0.23 % (468233)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2315889243:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.46/0.23 % (468232)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=2879461047: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)
% 0.46/0.23 % (468236)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=640862170:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.46/0.23 % (468231)Instruction limit reached!
% 0.46/0.23 % (468231)------------------------------
% 0.46/0.23 % (468231)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.46/0.23 % (468231)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.46/0.23 % (468231)CaDiCaL version: 2.1.3
% 0.46/0.23 % (468231)Termination reason: Instruction limit
% 0.46/0.23 % (468231)Termination phase: shuffling
% 0.46/0.23 % (468231)Time elapsed: 0.002 s
% 0.46/0.23 % (468231)Peak memory usage: 10 MB
% 0.46/0.23 % (468231)Instructions burned: 7 (million)
% 0.46/0.23 % (468230)Instruction limit reached!
% 0.46/0.23 % (468230)------------------------------
% 0.46/0.23 % (468230)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.46/0.23 % (468230)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.46/0.23 % (468230)CaDiCaL version: 2.1.3
% 0.46/0.23 % (468230)Termination reason: Instruction limit
% 0.46/0.23 % (468230)Termination phase: shuffling
% 0.46/0.23 % (468230)Time elapsed: 0.005 s
% 0.46/0.23 % (468230)Peak memory usage: 10 MB
% 0.46/0.23 % (468230)Instructions burned: 20 (million)
% 0.46/0.23 % (468233)Instruction limit reached!
% 0.46/0.23 % (468233)------------------------------
% 0.46/0.23 % (468233)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.46/0.23 % (468233)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.46/0.23 % (468233)CaDiCaL version: 2.1.3
% 0.46/0.23 % (468233)Termination reason: Instruction limit
% 0.46/0.23 % (468233)Termination phase: Property scanning
% 0.46/0.23 % (468233)Time elapsed: 0.006 s
% 0.46/0.23 % (468233)Peak memory usage: 10 MB
% 0.46/0.23 % (468233)Instructions burned: 25 (million)
% 0.46/0.23 % (468249)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1624204163:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.46/0.23 % (468249)Instruction limit reached!
% 0.46/0.23 % (468249)------------------------------
% 0.46/0.23 % (468249)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.46/0.23 % (468249)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.46/0.23 % (468249)CaDiCaL version: 2.1.3
% 0.46/0.23 % (468249)Termination reason: Instruction limit
% 0.46/0.23 % (468249)Termination phase: shuffling
% 0.46/0.23 % (468249)Time elapsed: 0.001 s
% 0.46/0.23 % (468249)Peak memory usage: 10 MB
% 0.46/0.23 % (468249)Instructions burned: 3 (million)
% 0.46/0.23 % (468251)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.46/0.23 % (468250)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3701316809:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.46/0.23 % (468251)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1803134812:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.46/0.23 % (468250)Instruction limit reached!
% 0.46/0.23 % (468250)------------------------------
% 0.46/0.23 % (468250)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.46/0.23 % (468250)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.46/0.23 % (468250)CaDiCaL version: 2.1.3
% 0.46/0.23 % (468250)Termination reason: Instruction limit
% 0.46/0.23 % (468250)Termination phase: shuffling
% 0.46/0.23 % (468250)Time elapsed: 0.002 s
% 0.46/0.23 % (468250)Peak memory usage: 10 MB
% 0.46/0.23 % (468250)Instructions burned: 8 (million)
% 0.46/0.23 % (468251)Instruction limit reached!
% 0.46/0.23 % (468251)------------------------------
% 0.46/0.23 % (468251)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.46/0.23 % (468251)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.46/0.23 % (468251)CaDiCaL version: 2.1.3
% 0.46/0.23 % (468251)Termination reason: Instruction limit
% 0.46/0.23 % (468251)Termination phase: shuffling
% 0.46/0.23 % (468251)Time elapsed: 0.002 s
% 0.46/0.23 % (468251)Peak memory usage: 10 MB
% 0.46/0.23 % (468251)Instructions burned: 7 (million)
% 0.46/0.23 % (468235)Instruction limit reached!
% 0.46/0.23 % (468235)------------------------------
% 0.46/0.23 % (468235)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.46/0.23 % (468235)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.46/0.23 % (468235)CaDiCaL version: 2.1.3
% 0.46/0.23 % (468235)Termination reason: Instruction limit
% 0.46/0.23 % (468235)Termination phase: Property scanning
% 0.46/0.23 % (468235)Time elapsed: 0.020 s
% 0.46/0.23 % (468235)Peak memory usage: 12 MB
% 0.46/0.23 % (468235)Instructions burned: 79 (million)
% 0.46/0.23 % (468229)Instruction limit reached!
% 0.46/0.23 % (468229)------------------------------
% 0.46/0.23 % (468229)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.46/0.23 % (468229)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.46/0.23 % (468229)CaDiCaL version: 2.1.3
% 0.46/0.23 % (468229)Termination reason: Instruction limit
% 0.46/0.23 % (468229)Termination phase: Property scanning
% 0.46/0.23 % (468229)Time elapsed: 0.022 s
% 0.46/0.23 % (468229)Peak memory usage: 12 MB
% 0.46/0.23 % (468229)Instructions burned: 88 (million)
% 0.46/0.23 % (468256)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=3916992636:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.46/0.23 % (468260)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
% 0.46/0.23 % (468260)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.46/0.23 % (468256)Instruction limit reached!
% 0.46/0.23 % (468256)------------------------------
% 0.46/0.23 % (468256)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.46/0.24 % (468256)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.46/0.24 % (468256)CaDiCaL version: 2.1.3
% 0.46/0.24 % (468256)Termination reason: Instruction limit
% 0.46/0.24 % (468256)Termination phase: shuffling
% 0.46/0.24 % (468256)Time elapsed: 0.004 s
% 0.46/0.24 % (468256)Peak memory usage: 10 MB
% 0.46/0.24 % (468256)Instructions burned: 16 (million)
% 0.46/0.24 % (468260)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3047819098:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.46/0.24 % (468261)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=2726513110:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.46/0.24 % (468262)lrs+10_1_si=on:cs=on:random_seed=2367900825:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.46/0.24 % (468263)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.46/0.24 % (468263)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=683038101:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.46/0.24 % (468262)Instruction limit reached!
% 0.46/0.24 % (468262)------------------------------
% 0.46/0.24 % (468262)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.46/0.24 % (468262)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.46/0.24 % (468262)CaDiCaL version: 2.1.3
% 0.46/0.24 % (468262)Termination reason: Instruction limit
% 0.46/0.24 % (468262)Termination phase: Property scanning
% 0.46/0.24 % (468262)Time elapsed: 0.006 s
% 0.46/0.24 % (468262)Peak memory usage: 10 MB
% 0.46/0.24 % (468262)Instructions burned: 23 (million)
% 0.46/0.24 % (468263)Instruction limit reached!
% 0.46/0.24 % (468263)------------------------------
% 0.46/0.24 % (468263)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.46/0.24 % (468263)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.46/0.24 % (468263)CaDiCaL version: 2.1.3
% 0.46/0.24 % (468263)Termination reason: Instruction limit
% 0.46/0.24 % (468263)Termination phase: shuffling
% 0.46/0.24 % (468263)Time elapsed: 0.003 s
% 0.46/0.24 % (468263)Peak memory usage: 10 MB
% 0.46/0.24 % (468263)Instructions burned: 14 (million)
% 0.46/0.24 % (468260)Instruction limit reached!
% 0.46/0.24 % (468260)------------------------------
% 0.46/0.24 % (468260)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.46/0.24 % (468260)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.46/0.24 % (468260)CaDiCaL version: 2.1.3
% 0.46/0.24 % (468260)Termination reason: Instruction limit
% 0.46/0.24 % (468260)Termination phase: shuffling
% 0.46/0.24 % (468260)Time elapsed: 0.009 s
% 0.46/0.24 % (468260)Peak memory usage: 10 MB
% 0.46/0.24 % (468260)Instructions burned: 30 (million)
% 0.46/0.24 % (468266)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=2002242758:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.46/0.24 % (468236)Instruction limit reached!
% 0.46/0.24 % (468236)------------------------------
% 0.46/0.24 % (468236)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.46/0.24 % (468236)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.46/0.24 % (468236)CaDiCaL version: 2.1.3
% 0.46/0.24 % (468236)Termination reason: Instruction limit
% 0.46/0.24 % (468236)Termination phase: Saturation
% 0.46/0.24 % (468236)Time elapsed: 0.044 s
% 0.46/0.24 % (468236)Peak memory usage: 14 MB
% 0.46/0.24 % (468236)Instructions burned: 160 (million)
% 0.46/0.24 % (468270)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=4264283756:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.46/0.24 % (468271)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2217227365:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/25Mi)
% 0.46/0.24 % (468272)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=3975492520:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2999 on theBenchmark for (2999ds/14Mi)
% 0.46/0.24 % (468266)Instruction limit reached!
% 0.46/0.24 % (468266)------------------------------
% 0.46/0.24 % (468266)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.46/0.24 % (468266)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.46/0.24 % (468266)CaDiCaL version: 2.1.3
% 0.46/0.24 % (468266)Termination reason: Instruction limit
% 0.46/0.24 % (468266)Termination phase: Preprocessing 3
% 0.46/0.24 % (468266)Time elapsed: 0.010 s
% 0.46/0.24 % (468266)Peak memory usage: 11 MB
% 0.46/0.24 % (468266)Instructions burned: 40 (million)
% 0.46/0.24 % (468261)Instruction limit reached!
% 0.46/0.24 % (468261)------------------------------
% 0.46/0.24 % (468261)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.46/0.24 % (468261)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.46/0.24 % (468261)CaDiCaL version: 2.1.3
% 0.46/0.24 % (468261)Termination reason: Instruction limit
% 0.46/0.24 % (468261)Termination phase: Preprocessing 3
% 0.46/0.24 % (468261)Time elapsed: 0.019 s
% 0.46/0.24 % (468261)Peak memory usage: 11 MB
% 0.46/0.24 % (468261)Instructions burned: 86 (million)
% 0.46/0.24 % (468232) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-468210-468232"...
% 0.46/0.24 % (468232)...printing done.
% 0.46/0.24 % (468232)Refutation found. Thanks to Tanya!
% 0.46/0.24 % SZS status Theorem for theBenchmark
% 0.46/0.24 % SZS output start Proof for theBenchmark
% 0.46/0.24 thf(type_def_5, type, coindu1593790203_llist: $tType > $tType).
% 0.46/0.24 thf(type_def_6, type, product_prod: ($tType * $tType) > $tType).
% 0.46/0.24 thf(type_def_7, type, set: $tType > $tType).
% 0.46/0.24 thf(type_def_8, type, itself: $tType > $tType).
% 0.46/0.24 thf(type_def_9, type, a: $tType).
% 0.46/0.24 thf(type_def_10, type, sTfun: ($tType * $tType) > $tType).
% 0.46/0.24 thf(func_def_0, type, type: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.46/0.24 thf(func_def_1, type, lattice: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.46/0.24 thf(func_def_2, type, linorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.46/0.24 thf(func_def_3, type, semilattice_sup: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.46/0.24 thf(func_def_4, type, coindu1928975208n_lset: !>[X0: $tType]:((set @ X0 > coindu1593790203_llist @ X0 > set @ X0))).
% 0.46/0.24 thf(func_def_5, type, coindu268472904append: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.46/0.24 thf(func_def_6, type, coindu1213758845finite: !>[X0: $tType]:((coindu1593790203_llist @ X0 > $o))).
% 0.46/0.24 thf(func_def_7, type, coindu1121789889_LCons: !>[X0: $tType]:((X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.46/0.24 thf(func_def_8, type, coindu1598213697e_LNil: !>[X0: $tType]:(coindu1593790203_llist @ X0)).
% 0.46/0.24 thf(func_def_9, type, coindu882539134_llist: !>[X0: $tType, X1: $tType]:((X0 > (X1 > coindu1593790203_llist @ X1 > X0) > coindu1593790203_llist @ X1 > X0))).
% 0.46/0.24 thf(func_def_10, type, coindu1244876290_llist: !>[X0: $tType, X1: $tType]:(((X0 > $o) > (X0 > X1) > (X0 > $o) > (X0 > coindu1593790203_llist @ X1) > (X0 > X0) > X0 > coindu1593790203_llist @ X1))).
% 0.46/0.24 thf(func_def_11, type, coindu1046438764le_lhd: !>[X0: $tType]:((coindu1593790203_llist @ X0 > X0))).
% 0.46/0.24 thf(func_def_12, type, coindu987187967t_all2: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X1 > $o))).
% 0.46/0.24 thf(func_def_13, type, coindu335574135_lnull: !>[X0: $tType]:((coindu1593790203_llist @ X0 > $o))).
% 0.46/0.24 thf(func_def_14, type, coindu1112613586e_lset: !>[X0: $tType]:((coindu1593790203_llist @ X0 > set @ X0))).
% 0.46/0.24 thf(func_def_15, type, coindu1047225960le_ltl: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.46/0.24 thf(func_def_16, type, coindu567634248member: !>[X0: $tType]:((X0 > coindu1593790203_llist @ X0 > $o))).
% 0.46/0.24 thf(func_def_17, type, coindu1696667936prefix: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o))).
% 0.46/0.24 thf(func_def_18, type, coindu1599971794_llist: !>[X0: $tType, X1: $tType]:(((X0 > $o) > (X0 > X1) > (X0 > X0) > X0 > coindu1593790203_llist @ X1))).
% 0.46/0.24 thf(func_def_19, type, if: !>[X0: $tType]:(($o > X0 > X0 > X0))).
% 0.46/0.24 thf(func_def_20, type, sup_sup: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.46/0.24 thf(func_def_21, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.46/0.24 thf(func_def_22, type, product_Pair: !>[X0: $tType, X1: $tType]:((X0 > X1 > product_prod @ X0 @ X1))).
% 0.46/0.24 thf(func_def_23, type, produc2004651681e_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 0.46/0.24 thf(func_def_24, type, product_rec_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 0.46/0.24 thf(func_def_25, type, type2: !>[X0: $tType]:(itself @ X0)).
% 0.46/0.24 thf(func_def_26, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 0.46/0.24 thf(func_def_27, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.46/0.24 thf(func_def_28, type, xs: coindu1593790203_llist @ a).
% 0.46/0.24 thf(func_def_29, type, ys: coindu1593790203_llist @ a).
% 0.46/0.24 thf(func_def_30, type, zs: coindu1593790203_llist @ a).
% 0.46/0.24 thf(func_def_34, type, vOR: ($o > $o > $o)).
% 0.46/0.24 thf(func_def_35, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.46/0.24 thf(func_def_36, type, vAND: ($o > $o > $o)).
% 0.46/0.24 thf(func_def_37, type, db1: !>[X0: $tType]:(X0)).
% 0.46/0.24 thf(func_def_38, type, db0: !>[X0: $tType]:(X0)).
% 0.46/0.24 thf(func_def_39, type, db2: !>[X0: $tType]:(X0)).
% 0.46/0.24 thf(func_def_40, type, db3: !>[X0: $tType]:(X0)).
% 0.46/0.24 thf(func_def_41, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.46/0.24 thf(func_def_42, type, db4: !>[X0: $tType]:(X0)).
% 0.46/0.24 thf(func_def_43, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.46/0.24 thf(func_def_44, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.46/0.24 thf(func_def_45, type, vIMP: ($o > $o > $o)).
% 0.46/0.24 thf(func_def_46, type, vNOT: ($o > $o)).
% 0.46/0.24 thf(func_def_47, type, db5: !>[X0: $tType]:(X0)).
% 0.46/0.24 thf(func_def_48, type, sK0: !>[X0: $tType]:(((X0 > $o) > set @ X0 > set @ X0 > X0))).
% 0.46/0.24 thf(func_def_49, type, sK1: !>[X0: $tType]:(((X0 > $o) > set @ X0 > X0))).
% 0.46/0.24 thf(func_def_50, type, sK2: !>[X0: $tType]:(((X0 > $o) > set @ X0 > X0))).
% 0.46/0.24 thf(func_def_51, type, sK3: !>[X0: $tType]:((X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.46/0.24 thf(func_def_52, type, sK4: !>[X0: $tType]:((X0 > coindu1593790203_llist @ X0 > X0))).
% 0.46/0.24 thf(func_def_53, type, sK5: !>[X0: $tType]:((X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.46/0.24 thf(func_def_54, type, sK6: !>[X0: $tType, X1: $tType]:((coindu1593790203_llist @ X1 > coindu1593790203_llist @ X0 > (X0 > X1 > $o) > (X0 > X1 > $o) > X1))).
% 0.46/0.24 thf(func_def_55, type, sK7: !>[X0: $tType, X1: $tType]:((coindu1593790203_llist @ X1 > coindu1593790203_llist @ X0 > (X0 > X1 > $o) > (X0 > X1 > $o) > X0))).
% 0.46/0.24 thf(func_def_56, type, sK8: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 0.46/0.24 thf(func_def_57, type, sK9: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 0.46/0.24 thf(func_def_58, type, sK10: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > X0))).
% 0.46/0.24 thf(func_def_59, type, sK11: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > X1))).
% 0.46/0.24 thf(func_def_60, type, sK12: !>[X0: $tType]:((set @ product_prod @ coindu1593790203_llist @ X0 @ coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.46/0.24 thf(func_def_61, type, sK13: !>[X0: $tType]:((set @ product_prod @ coindu1593790203_llist @ X0 @ coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.46/0.24 thf(func_def_62, type, sK14: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 0.46/0.24 thf(func_def_63, type, sK15: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X1 @ product_prod @ X2 @ X0 > X2))).
% 0.46/0.24 thf(func_def_64, type, sK16: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X1 @ product_prod @ X2 @ X0 > X1))).
% 0.46/0.24 thf(func_def_65, type, sK17: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X1 @ product_prod @ X2 @ X0 > X0))).
% 0.46/0.24 thf(func_def_66, type, sK18: !>[X0: $tType]:((X0 > (coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 0.46/0.24 thf(func_def_67, type, sK19: !>[X0: $tType]:((X0 > (coindu1593790203_llist @ X0 > $o) > X0))).
% 0.46/0.24 thf(func_def_68, type, sK20: !>[X0: $tType]:((X0 > (coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 0.46/0.24 thf(func_def_69, type, sK21: !>[X0: $tType]:(((X0 > $o) > set @ X0 > X0))).
% 0.46/0.24 thf(func_def_70, type, sK22: !>[X0: $tType]:((set @ X0 > (X0 > $o) > X0))).
% 0.46/0.24 thf(func_def_71, type, sK23: !>[X0: $tType]:((set @ X0 > (X0 > $o) > set @ X0 > X0))).
% 0.46/0.24 thf(func_def_72, type, sK24: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 0.46/0.24 thf(func_def_73, type, sK25: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 0.46/0.24 thf(func_def_74, type, sK26: !>[X0: $tType]:((X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.46/0.24 thf(func_def_75, type, sK27: !>[X0: $tType, X1: $tType]:(((product_prod @ X0 @ X1 > $o) > X1))).
% 0.46/0.24 thf(func_def_76, type, sK28: !>[X0: $tType, X1: $tType]:(((product_prod @ X0 @ X1 > $o) > X0))).
% 0.46/0.24 thf(func_def_77, type, sK29: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X1 @ product_prod @ X3 @ product_prod @ X2 @ X0 > X1))).
% 0.46/0.24 thf(func_def_78, type, sK30: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X1 @ product_prod @ X3 @ product_prod @ X2 @ X0 > X0))).
% 0.46/0.24 thf(func_def_79, type, sK31: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X1 @ product_prod @ X3 @ product_prod @ X2 @ X0 > X3))).
% 0.46/0.24 thf(func_def_80, type, sK32: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X1 @ product_prod @ X3 @ product_prod @ X2 @ X0 > X2))).
% 0.46/0.24 thf(func_def_81, type, sK33: !>[X0: $tType]:(((X0 > coindu1593790203_llist @ X0 > $o) > X0))).
% 0.46/0.24 thf(func_def_82, type, sK34: !>[X0: $tType]:(((X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 0.46/0.24 thf(func_def_83, type, sK35: !>[X0: $tType]:(((X0 > coindu1593790203_llist @ X0 > $o) > X0))).
% 0.46/0.24 thf(func_def_84, type, sK36: !>[X0: $tType]:(((X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 0.46/0.24 thf(func_def_85, type, sK37: !>[X0: $tType]:(((X0 > coindu1593790203_llist @ X0 > $o) > X0))).
% 0.46/0.24 thf(func_def_86, type, sK38: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X4 @ product_prod @ X5 @ product_prod @ X0 @ product_prod @ X1 @ product_prod @ X3 @ X2 > X0))).
% 0.46/0.24 thf(func_def_87, type, sK39: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X4 @ product_prod @ X5 @ product_prod @ X0 @ product_prod @ X1 @ product_prod @ X3 @ X2 > X1))).
% 0.46/0.24 thf(func_def_88, type, sK40: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X4 @ product_prod @ X5 @ product_prod @ X0 @ product_prod @ X1 @ product_prod @ X3 @ X2 > X4))).
% 0.46/0.24 thf(func_def_89, type, sK41: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X4 @ product_prod @ X5 @ product_prod @ X0 @ product_prod @ X1 @ product_prod @ X3 @ X2 > X3))).
% 0.46/0.24 thf(func_def_90, type, sK42: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X4 @ product_prod @ X5 @ product_prod @ X0 @ product_prod @ X1 @ product_prod @ X3 @ X2 > X2))).
% 0.46/0.24 thf(func_def_91, type, sK43: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X4 @ product_prod @ X5 @ product_prod @ X0 @ product_prod @ X1 @ product_prod @ X3 @ X2 > X5))).
% 0.46/0.24 thf(func_def_92, type, sK44: !>[X0: $tType]:((coindu1593790203_llist @ X0 > X0 > coindu1593790203_llist @ X0))).
% 0.46/0.24 thf(func_def_93, type, sK45: !>[X0: $tType]:((coindu1593790203_llist @ X0 > X0 > coindu1593790203_llist @ X0))).
% 0.46/0.24 thf(func_def_94, type, sK46: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 0.46/0.24 thf(func_def_95, type, sK47: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 0.46/0.24 thf(func_def_96, type, sK48: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.46/0.24 thf(func_def_97, type, sK49: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.46/0.24 thf(func_def_98, type, sK50: !>[X0: $tType, X1: $tType]:((coindu1593790203_llist @ X1 > (X1 > X0 > $o) > (X1 > X0 > $o) > coindu1593790203_llist @ X0 > X1))).
% 0.46/0.24 thf(func_def_99, type, sK51: !>[X0: $tType, X1: $tType]:((coindu1593790203_llist @ X1 > (X1 > X0 > $o) > (X1 > X0 > $o) > coindu1593790203_llist @ X0 > X0))).
% 0.46/0.24 thf(func_def_100, type, sK52: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.46/0.24 thf(func_def_101, type, sK53: !>[X0: $tType]:((X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.46/0.24 thf(func_def_102, type, sK54: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.46/0.24 thf(func_def_103, type, sK55: !>[X0: $tType]:((coindu1593790203_llist @ X0 > X0))).
% 0.46/0.24 thf(func_def_104, type, sK56: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X0 > $o) > X2))).
% 0.46/0.24 thf(func_def_105, type, sK57: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X0 > $o) > X0))).
% 0.46/0.24 thf(func_def_106, type, sK58: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X0 > $o) > X1))).
% 0.46/0.24 thf(func_def_107, type, sK59: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X0 > $o) > X3))).
% 0.46/0.24 thf(func_def_108, type, sK60: !>[X0: $tType]:((X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.46/0.24 thf(func_def_109, type, sK61: !>[X0: $tType]:((X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.46/0.24 thf(func_def_110, type, sK62: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X3 @ product_prod @ X1 @ product_prod @ X4 @ product_prod @ X2 @ X0 > $o) > X1))).
% 0.46/0.24 thf(func_def_111, type, sK63: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X3 @ product_prod @ X1 @ product_prod @ X4 @ product_prod @ X2 @ X0 > $o) > X0))).
% 0.46/0.24 thf(func_def_112, type, sK64: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X3 @ product_prod @ X1 @ product_prod @ X4 @ product_prod @ X2 @ X0 > $o) > X4))).
% 0.46/0.24 thf(func_def_113, type, sK65: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X3 @ product_prod @ X1 @ product_prod @ X4 @ product_prod @ X2 @ X0 > $o) > X3))).
% 0.46/0.24 thf(func_def_114, type, sK66: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X3 @ product_prod @ X1 @ product_prod @ X4 @ product_prod @ X2 @ X0 > $o) > X2))).
% 0.46/0.24 thf(func_def_115, type, sK67: !>[X0: $tType]:(((X0 > X0 > $o) > coindu1593790203_llist @ X0 > X0))).
% 0.46/0.24 thf(func_def_116, type, sK68: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1))).
% 0.46/0.24 thf(func_def_117, type, sK69: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 0.46/0.24 thf(func_def_118, type, sK70: !>[X0: $tType]:((coindu1593790203_llist @ X0 > X0))).
% 0.46/0.24 thf(func_def_119, type, sK71: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.46/0.24 thf(func_def_120, type, sK72: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > $o) > X0 > X0))).
% 0.46/0.24 thf(func_def_121, type, sK73: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > $o) > X0 > coindu1593790203_llist @ X0))).
% 0.46/0.24 thf(func_def_122, type, sK74: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > $o) > X0 > coindu1593790203_llist @ X0))).
% 0.46/0.24 thf(func_def_123, type, sK75: !>[X0: $tType, X1: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X1 > (X0 > X1 > $o) > coindu1593790203_llist @ X0))).
% 0.46/0.24 thf(func_def_124, type, sK76: !>[X0: $tType, X1: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X1 > (X0 > X1 > $o) > X0))).
% 0.46/0.24 thf(func_def_125, type, sK77: !>[X0: $tType, X1: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X1 > (X0 > X1 > $o) > coindu1593790203_llist @ X1))).
% 0.46/0.24 thf(func_def_126, type, sK78: !>[X0: $tType, X1: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X1 > (X0 > X1 > $o) > X1))).
% 0.46/0.24 thf(func_def_127, type, sK79: !>[X0: $tType]:((coindu1593790203_llist @ X0 > X0 > coindu1593790203_llist @ X0))).
% 0.46/0.24 thf(func_def_128, type, sK80: !>[X0: $tType]:((coindu1593790203_llist @ X0 > X0 > coindu1593790203_llist @ X0))).
% 0.46/0.24 thf(func_def_129, type, sK81: !>[X0: $tType]:((coindu1593790203_llist @ X0 > X0 > X0))).
% 0.46/0.24 thf(func_def_130, type, sK82: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.46/0.24 thf(func_def_131, type, sK83: !>[X0: $tType]:((coindu1593790203_llist @ X0 > X0))).
% 0.46/0.24 thf(func_def_132, type, sK84: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.46/0.24 thf(func_def_133, type, sK85: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.46/0.24 thf(func_def_134, type, sK86: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > X0))).
% 0.46/0.24 thf(func_def_135, type, sK87: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.46/0.24 thf(func_def_136, type, sK88: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X1 @ product_prod @ X2 @ X0 > $o) > X0))).
% 0.46/0.24 thf(func_def_137, type, sK89: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X1 @ product_prod @ X2 @ X0 > $o) > X2))).
% 0.46/0.24 thf(func_def_138, type, sK90: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X1 @ product_prod @ X2 @ X0 > $o) > X1))).
% 0.46/0.24 thf(func_def_139, type, sK91: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0))).
% 0.46/0.24 thf(func_def_140, type, sK92: !>[X0: $tType]:((coindu1593790203_llist @ X0 > X0))).
% 0.46/0.24 thf(func_def_141, type, sK93: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.46/0.24 thf(func_def_142, type, sK94: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.46/0.24 thf(func_def_143, type, sK95: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 0.46/0.24 thf(func_def_144, type, sK96: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 0.46/0.24 thf(func_def_145, type, sK97: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 0.46/0.24 thf(func_def_146, type, sK98: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 0.46/0.24 thf(func_def_147, type, sK99: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 0.46/0.24 thf(func_def_148, type, sK100: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 0.46/0.24 thf(func_def_149, type, sK101: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 0.46/0.24 thf(func_def_150, type, sK102: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.46/0.24 thf(func_def_151, type, sK103: !>[X0: $tType, X1: $tType]:(((product_prod @ X0 @ X1 > $o) > X1))).
% 0.46/0.24 thf(func_def_152, type, sK104: !>[X0: $tType, X1: $tType]:(((product_prod @ X0 @ X1 > $o) > X0))).
% 0.46/0.24 thf(func_def_153, type, sK105: !>[X0: $tType]:(((X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 0.46/0.24 thf(func_def_154, type, sK106: !>[X0: $tType]:(((X0 > coindu1593790203_llist @ X0 > $o) > X0))).
% 0.46/0.24 thf(func_def_155, type, sK107: !>[X0: $tType]:(((X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 0.46/0.24 thf(func_def_156, type, sK108: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X4 @ product_prod @ X0 @ X1 > X0))).
% 0.46/0.24 thf(func_def_157, type, sK109: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X4 @ product_prod @ X0 @ X1 > X4))).
% 0.46/0.24 thf(func_def_158, type, sK110: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X4 @ product_prod @ X0 @ X1 > X3))).
% 0.46/0.24 thf(func_def_159, type, sK111: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X4 @ product_prod @ X0 @ X1 > X2))).
% 0.46/0.24 thf(func_def_160, type, sK112: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X4 @ product_prod @ X0 @ X1 > X1))).
% 0.46/0.24 thf(func_def_161, type, sK113: !>[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 @ X0 @ product_prod @ X2 @ product_prod @ X3 @ X4 > $o) > X0))).
% 0.46/0.24 thf(func_def_162, type, sK114: !>[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 @ X0 @ product_prod @ X2 @ product_prod @ X3 @ X4 > $o) > X1))).
% 0.46/0.24 thf(func_def_163, type, sK115: !>[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 @ X0 @ product_prod @ X2 @ product_prod @ X3 @ X4 > $o) > X2))).
% 0.46/0.24 thf(func_def_164, type, sK116: !>[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 @ X0 @ product_prod @ X2 @ product_prod @ X3 @ X4 > $o) > X4))).
% 0.46/0.24 thf(func_def_165, type, sK117: !>[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 @ X0 @ product_prod @ X2 @ product_prod @ X3 @ X4 > $o) > X3))).
% 0.46/0.24 thf(func_def_166, type, sK118: !>[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 @ X0 @ product_prod @ X2 @ product_prod @ X3 @ X4 > $o) > X5))).
% 0.46/0.24 thf(func_def_167, type, sK119: !>[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 @ X0 @ product_prod @ X2 @ product_prod @ X3 @ X4 > $o) > X6))).
% 0.46/0.24 thf(func_def_168, type, sK120: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 0.46/0.24 thf(func_def_169, type, sK121: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > $o) > X0))).
% 0.46/0.24 thf(func_def_170, type, sK122: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X0 @ product_prod @ X5 @ product_prod @ X2 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X6 @ X1 > X4))).
% 0.46/0.24 thf(func_def_171, type, sK123: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X0 @ product_prod @ X5 @ product_prod @ X2 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X6 @ X1 > X0))).
% 0.46/0.24 thf(func_def_172, type, sK124: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X0 @ product_prod @ X5 @ product_prod @ X2 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X6 @ X1 > X6))).
% 0.46/0.24 thf(func_def_173, type, sK125: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X0 @ product_prod @ X5 @ product_prod @ X2 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X6 @ X1 > X1))).
% 0.46/0.24 thf(func_def_174, type, sK126: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X0 @ product_prod @ X5 @ product_prod @ X2 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X6 @ X1 > X5))).
% 0.46/0.24 thf(func_def_175, type, sK127: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X0 @ product_prod @ X5 @ product_prod @ X2 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X6 @ X1 > X2))).
% 0.46/0.24 thf(func_def_176, type, sK128: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X0 @ product_prod @ X5 @ product_prod @ X2 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X6 @ X1 > X3))).
% 0.46/0.24 thf(func_def_177, type, sK129: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X5 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X0 @ product_prod @ X1 @ X4 > $o) > X0))).
% 0.46/0.24 thf(func_def_178, type, sK130: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X5 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X0 @ product_prod @ X1 @ X4 > $o) > X1))).
% 0.46/0.24 thf(func_def_179, type, sK131: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X5 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X0 @ product_prod @ X1 @ X4 > $o) > X5))).
% 0.46/0.24 thf(func_def_180, type, sK132: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X5 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X0 @ product_prod @ X1 @ X4 > $o) > X3))).
% 0.46/0.24 thf(func_def_181, type, sK133: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X5 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X0 @ product_prod @ X1 @ X4 > $o) > X2))).
% 0.46/0.24 thf(func_def_182, type, sK134: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X5 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X0 @ product_prod @ X1 @ X4 > $o) > X4))).
% 0.46/0.24 thf(func_def_183, type, sK135: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.46/0.24 thf(func_def_184, type, sK136: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 0.46/0.24 thf(func_def_185, type, sK137: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 0.46/0.24 thf(func_def_186, type, sK138: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 0.46/0.24 thf(func_def_187, type, sK139: !>[X0: $tType]:(((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0))).
% 0.46/0.24 thf(f2,axiom,(
% 0.46/0.24 (coindu1213758845finite @ a @ xs) => (coindu1696667936prefix @ a @ ys @ zs)),
% 0.46/0.24 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__092_060open_062lfinite_Axs_A_092_060longrightarrow_062_Ays_A_092_060sqsubseteq_062_Azs_092_060close_062)).
% 0.46/0.24 thf(f6,axiom,(
% 0.46/0.24 ! [X0 : $tType,X1 : coindu1593790203_llist @ X0,X2 : coindu1593790203_llist @ X0] : (coindu1696667936prefix @ X0 @ X1 @ (coindu268472904append @ X0 @ X1 @ X2))),
% 0.46/0.24 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_lprefix__lappend)).
% 0.46/0.24 thf(f8,axiom,(
% 0.46/0.24 ! [X0 : $tType,X3 : coindu1593790203_llist @ X0,X2 : coindu1593790203_llist @ X0,X1 : coindu1593790203_llist @ X0] : ((coindu1696667936prefix @ X0 @ X1 @ X2) => (coindu1696667936prefix @ X0 @ (coindu268472904append @ X0 @ X3 @ X1) @ (coindu268472904append @ X0 @ X3 @ X2)))),
% 0.46/0.24 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_lprefix__lappend__sameI)).
% 0.46/0.24 thf(f13,axiom,(
% 0.46/0.24 ! [X0 : $tType,X1 : coindu1593790203_llist @ X0,X2 : coindu1593790203_llist @ X0] : (~(coindu1213758845finite @ X0 @ X1) => (((coindu268472904append @ X0 @ X1 @ X2)) = X1))),
% 0.46/0.24 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_lappend__inf)).
% 0.46/0.24 thf(f266,conjecture,(
% 0.46/0.24 (coindu1696667936prefix @ a @ (coindu268472904append @ a @ xs @ ys) @ (coindu268472904append @ a @ xs @ zs))),
% 0.46/0.24 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 0.46/0.24 thf(f267,negated_conjecture,(
% 0.46/0.24 ~(coindu1696667936prefix @ a @ (coindu268472904append @ a @ xs @ ys) @ (coindu268472904append @ a @ xs @ zs))),
% 0.46/0.24 inference(negated_conjecture,[status(cth)],[f266])).
% 0.46/0.24 thf(f326,plain,(
% 0.46/0.24 ! [X0 : $tType,X1 : coindu1593790203_llist @ X0,X2 : coindu1593790203_llist @ X0] : (~(coindu1213758845finite @ X0 @ X1) => (((coindu268472904append @ X0 @ X1 @ X2)) = X1))),
% 0.46/0.24 inference(rectify,[],[f13])).
% 0.46/0.24 thf(f327,plain,(
% 0.46/0.24 ! [X0 : $tType,X1 : coindu1593790203_llist @ X0,X2 : coindu1593790203_llist @ X0] : (~ (((coindu1213758845finite @ X0 @ X1)) = $true) => (((coindu268472904append @ X0 @ X1 @ X2)) = X1))),
% 0.46/0.24 inference(fool_elimination,[],[f326])).
% 0.46/0.24 thf(f366,plain,(
% 0.46/0.24 (coindu1213758845finite @ a @ xs) => (coindu1696667936prefix @ a @ ys @ zs)),
% 0.46/0.24 inference(rectify,[],[f2])).
% 0.46/0.24 thf(f367,plain,(
% 0.46/0.24 (((coindu1213758845finite @ a @ xs)) = $true) => (((coindu1696667936prefix @ a @ ys @ zs)) = $true)),
% 0.46/0.24 inference(fool_elimination,[],[f366])).
% 0.46/0.24 thf(f477,plain,(
% 0.46/0.24 ! [X0 : $tType,X1 : coindu1593790203_llist @ X0,X2 : coindu1593790203_llist @ X0,X3 : coindu1593790203_llist @ X0] : ((coindu1696667936prefix @ X0 @ X3 @ X2) => (coindu1696667936prefix @ X0 @ (coindu268472904append @ X0 @ X1 @ X3) @ (coindu268472904append @ X0 @ X1 @ X2)))),
% 0.46/0.24 inference(rectify,[],[f8])).
% 0.46/0.24 thf(f478,plain,(
% 0.46/0.24 ! [X0 : $tType,X3 : coindu1593790203_llist @ X0,X1 : coindu1593790203_llist @ X0,X2 : coindu1593790203_llist @ X0] : ((((coindu1696667936prefix @ X0 @ X3 @ X2)) = $true) => (((coindu1696667936prefix @ X0 @ (coindu268472904append @ X0 @ X1 @ X3) @ (coindu268472904append @ X0 @ X1 @ X2))) = $true))),
% 0.46/0.24 inference(fool_elimination,[],[f477])).
% 0.46/0.24 thf(f570,plain,(
% 0.46/0.24 ! [X0 : $tType,X1 : coindu1593790203_llist @ X0,X2 : coindu1593790203_llist @ X0] : (coindu1696667936prefix @ X0 @ X1 @ (coindu268472904append @ X0 @ X1 @ X2))),
% 0.46/0.24 inference(rectify,[],[f6])).
% 0.46/0.24 thf(f571,plain,(
% 0.46/0.24 ! [X0 : $tType,X2 : coindu1593790203_llist @ X0,X1 : coindu1593790203_llist @ X0] : (((coindu1696667936prefix @ X0 @ X1 @ (coindu268472904append @ X0 @ X1 @ X2))) = $true)),
% 0.46/0.24 inference(fool_elimination,[],[f570])).
% 0.46/0.24 thf(f588,plain,(
% 0.46/0.24 ~(coindu1696667936prefix @ a @ (coindu268472904append @ a @ xs @ ys) @ (coindu268472904append @ a @ xs @ zs))),
% 0.46/0.24 inference(rectify,[],[f267])).
% 0.46/0.24 thf(f589,plain,(
% 0.46/0.24 ~ (((coindu1696667936prefix @ a @ (coindu268472904append @ a @ xs @ ys) @ (coindu268472904append @ a @ xs @ zs))) = $true)),
% 0.46/0.24 inference(fool_elimination,[],[f588])).
% 0.46/0.24 thf(f720,plain,(
% 0.46/0.24 ! [X0 : $tType,X2 : coindu1593790203_llist @ X0,X1 : coindu1593790203_llist @ X0] : ((((coindu1213758845finite @ X0 @ X1)) != $true) => (((coindu268472904append @ X0 @ X1 @ X2)) = X1))),
% 0.46/0.24 inference(flattening,[],[f327])).
% 0.46/0.24 thf(f766,plain,(
% 0.46/0.24 (((coindu1696667936prefix @ a @ (coindu268472904append @ a @ xs @ ys) @ (coindu268472904append @ a @ xs @ zs))) != $true)),
% 0.46/0.24 inference(flattening,[],[f589])).
% 0.46/0.24 thf(f802,plain,(
% 0.46/0.24 (((coindu1696667936prefix @ a @ ys @ zs)) = $true) | (((coindu1213758845finite @ a @ xs)) != $true)),
% 0.46/0.24 inference(ennf_transformation,[],[f367])).
% 0.46/0.24 thf(f898,plain,(
% 0.46/0.24 ! [X0 : $tType,X2 : coindu1593790203_llist @ X0,X1 : coindu1593790203_llist @ X0] : ((((coindu1213758845finite @ X0 @ X1)) = $true) | (((coindu268472904append @ X0 @ X1 @ X2)) = X1))),
% 0.46/0.24 inference(ennf_transformation,[],[f720])).
% 0.46/0.24 thf(f986,plain,(
% 0.46/0.24 ! [X0 : $tType,X3 : coindu1593790203_llist @ X0,X1 : coindu1593790203_llist @ X0,X2 : coindu1593790203_llist @ X0] : ((((coindu1696667936prefix @ X0 @ X3 @ X2)) != $true) | (((coindu1696667936prefix @ X0 @ (coindu268472904append @ X0 @ X1 @ X3) @ (coindu268472904append @ X0 @ X1 @ X2))) = $true))),
% 0.46/0.24 inference(ennf_transformation,[],[f478])).
% 0.46/0.24 thf(f1099,plain,(
% 0.46/0.24 ! [X0 : $tType,X1 : coindu1593790203_llist @ X0,X2 : coindu1593790203_llist @ X0] : (((coindu1696667936prefix @ X0 @ X2 @ (coindu268472904append @ X0 @ X2 @ X1))) = $true)),
% 0.46/0.24 inference(rectify,[],[f571])).
% 0.46/0.24 thf(f1188,plain,(
% 0.46/0.24 ! [X0 : $tType,X1 : coindu1593790203_llist @ X0,X2 : coindu1593790203_llist @ X0] : ((((coindu1213758845finite @ X0 @ X2)) = $true) | (((coindu268472904append @ X0 @ X2 @ X1)) = X2))),
% 0.46/0.24 inference(rectify,[],[f898])).
% 0.46/0.24 thf(f1250,plain,(
% 0.46/0.24 ! [X0 : $tType,X1 : coindu1593790203_llist @ X0,X2 : coindu1593790203_llist @ X0,X3 : coindu1593790203_llist @ X0] : ((((coindu1696667936prefix @ X0 @ X1 @ X3)) != $true) | ($true = ((coindu1696667936prefix @ X0 @ (coindu268472904append @ X0 @ X2 @ X1) @ (coindu268472904append @ X0 @ X2 @ X3)))))),
% 0.46/0.24 inference(rectify,[],[f986])).
% 0.46/0.24 thf(f1412,plain,(
% 0.46/0.24 ( ! [X0 : $tType,X2 : coindu1593790203_llist @ X0,X1 : coindu1593790203_llist @ X0] : ((((coindu1696667936prefix @ X0 @ X2 @ (coindu268472904append @ X0 @ X2 @ X1))) = $true)) )),
% 0.46/0.24 inference(cnf_transformation,[],[f1099])).
% 0.46/0.24 thf(f1532,plain,(
% 0.46/0.24 (((coindu1696667936prefix @ a @ (coindu268472904append @ a @ xs @ ys) @ (coindu268472904append @ a @ xs @ zs))) != $true)),
% 0.46/0.24 inference(cnf_transformation,[],[f766])).
% 0.46/0.24 thf(f1568,plain,(
% 0.46/0.24 ( ! [X0 : $tType,X2 : coindu1593790203_llist @ X0,X1 : coindu1593790203_llist @ X0] : ((((coindu268472904append @ X0 @ X2 @ X1)) = X2) | (((coindu1213758845finite @ X0 @ X2)) = $true)) )),
% 0.46/0.24 inference(cnf_transformation,[],[f1188])).
% 0.46/0.24 thf(f1634,plain,(
% 0.46/0.24 (((coindu1696667936prefix @ a @ ys @ zs)) = $true) | (((coindu1213758845finite @ a @ xs)) != $true)),
% 0.46/0.24 inference(cnf_transformation,[],[f802])).
% 0.46/0.24 thf(f1680,plain,(
% 0.46/0.24 ( ! [X0 : $tType,X2 : coindu1593790203_llist @ X0,X3 : coindu1593790203_llist @ X0,X1 : coindu1593790203_llist @ X0] : (($true = ((coindu1696667936prefix @ X0 @ (coindu268472904append @ X0 @ X2 @ X1) @ (coindu268472904append @ X0 @ X2 @ X3)))) | (((coindu1696667936prefix @ X0 @ X1 @ X3)) != $true)) )),
% 0.46/0.24 inference(cnf_transformation,[],[f1250])).
% 0.46/0.24 thf(f1798,definition,(
% 0.46/0.24 spl140_4 <=> (((coindu1696667936prefix @ a @ (coindu268472904append @ a @ xs @ ys) @ (coindu268472904append @ a @ xs @ zs))) = $true)),
% 0.46/0.24 introduced(definition,[new_symbols(definition,[spl140_4])],[avatar_definition])).
% 0.46/0.24 thf(f1800,plain,(
% 0.46/0.24 (((coindu1696667936prefix @ a @ (coindu268472904append @ a @ xs @ ys) @ (coindu268472904append @ a @ xs @ zs))) != $true) | spl140_4),
% 0.46/0.24 inference(avatar_component_clause,[],[f1798])).
% 0.46/0.24 thf(f1801,plain,(
% 0.46/0.24 ~spl140_4),
% 0.46/0.24 inference(avatar_split_clause,[],[f1532,f1798])).
% 0.46/0.24 thf(f1803,definition,(
% 0.46/0.24 spl140_5 <=> (((coindu1696667936prefix @ a @ ys @ zs)) = $true)),
% 0.46/0.24 introduced(definition,[new_symbols(definition,[spl140_5])],[avatar_definition])).
% 0.46/0.24 thf(f1805,plain,(
% 0.46/0.24 (((coindu1696667936prefix @ a @ ys @ zs)) = $true) | ~spl140_5),
% 0.46/0.24 inference(avatar_component_clause,[],[f1803])).
% 0.46/0.24 thf(f1807,definition,(
% 0.46/0.24 spl140_6 <=> (((coindu1213758845finite @ a @ xs)) = $true)),
% 0.46/0.24 introduced(definition,[new_symbols(definition,[spl140_6])],[avatar_definition])).
% 0.46/0.24 thf(f1810,plain,(
% 0.46/0.24 spl140_5 | ~spl140_6),
% 0.46/0.24 inference(avatar_split_clause,[],[f1634,f1807,f1803])).
% 0.46/0.24 thf(f1871,plain,(
% 0.46/0.24 (((coindu1696667936prefix @ a @ xs @ (coindu268472904append @ a @ xs @ zs))) != $true) | (((coindu1213758845finite @ a @ xs)) = $true) | spl140_4),
% 0.46/0.24 inference(superposition,[],[f1800,f1568])).
% 0.46/0.24 thf(f1917,plain,(
% 0.46/0.24 (((coindu1213758845finite @ a @ xs)) = $true) | spl140_4),
% 0.46/0.24 inference(forward_subsumption_resolution,[],[f1871,f1412])).
% 0.46/0.24 thf(f1919,plain,(
% 0.46/0.24 spl140_6 | spl140_4),
% 0.46/0.24 inference(avatar_split_clause,[],[f1917,f1798,f1807])).
% 0.46/0.24 thf(f2222,plain,(
% 0.46/0.24 (((coindu1696667936prefix @ a @ ys @ zs)) != $true) | ($true != $true) | spl140_4),
% 0.46/0.24 inference(superposition,[],[f1800,f1680])).
% 0.46/0.24 thf(f2226,plain,(
% 0.46/0.24 (((coindu1696667936prefix @ a @ ys @ zs)) != $true) | spl140_4),
% 0.46/0.24 inference(trivial_inequality_removal,[],[f2222])).
% 0.46/0.24 thf(f2233,plain,(
% 0.46/0.24 $false | (spl140_4 | ~spl140_5)),
% 0.46/0.24 inference(forward_subsumption_resolution,[],[f2226,f1805])).
% 0.46/0.24 thf(f2234,plain,(
% 0.46/0.24 spl140_4 | ~spl140_5),
% 0.46/0.24 inference(avatar_contradiction_clause,[],[f2233])).
% 0.46/0.24 cnf(s4, plain, ~spl140_4, inference(sat_conversion,[],[f1801])).
% 0.46/0.24 cnf(s5, plain, spl140_5 | ~spl140_6, inference(sat_conversion,[],[f1810])).
% 0.46/0.24 cnf(s15, plain, spl140_4 | spl140_6, inference(sat_conversion,[],[f1919])).
% 0.46/0.24 cnf(s21, plain, spl140_4 | ~spl140_5, inference(sat_conversion,[],[f2234])).
% 0.46/0.24 cnf(s24, plain, ~spl140_5, inference(rat,[],[s21,s4])).
% 0.46/0.24 cnf(s25, plain, spl140_6, inference(rat,[],[s15,s4])).
% 0.46/0.24 cnf(s28, plain, $false, inference(rat,[],[s5,s25,s24])).
% 0.46/0.24 thf(f2239,plain,(
% 0.46/0.24 $false),
% 0.46/0.24 inference(avatar_sat_refutation,[],[s28])).
% 0.46/0.24 % SZS output end Proof for theBenchmark
% 0.46/0.24 % (468232)------------------------------
% 0.46/0.24 % (468232)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.46/0.24 % (468232)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.46/0.24 % (468232)CaDiCaL version: 2.1.3
% 0.46/0.24 % (468232)Termination reason: Refutation
% 0.46/0.24 % (468232)Time elapsed: 0.051 s
% 0.46/0.24 % (468232)Peak memory usage: 15 MB
% 0.46/0.24 % (468232)Instructions burned: 185 (million)
% 0.46/0.24 % (468210)Success in time 0.081 s
% 0.46/0.24 % Vampire exiting
%------------------------------------------------------------------------------