%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP055^2 : 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 : n016.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 08:08:08 AM UTC 2026
% Result : Theorem 0.71s 0.40s
% Output : Refutation 0.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP055^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n016.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 19:49:05 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.25 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
% 0.71/0.40 % (819733)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.71/0.40 % (819742)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3013965030:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.71/0.40 % (819744)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.71/0.40 % (819744)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
% 0.71/0.40 % (819742)Instruction limit reached!
% 0.71/0.40 % (819742)------------------------------
% 0.71/0.40 % (819742)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.71/0.40 % (819742)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.71/0.40 % (819742)CaDiCaL version: 2.1.3
% 0.71/0.40 % (819742)Termination reason: Instruction limit
% 0.71/0.40 % (819742)Termination phase: Property scanning
% 0.71/0.40 % (819738)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2028906990:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.71/0.40 % (819742)Time elapsed: 0.006 s
% 0.71/0.40 % (819742)Peak memory usage: 10 MB
% 0.71/0.40 % (819742)Instructions burned: 26 (million)
% 0.71/0.40 % (819739)lrs+10_16_si=on:nwc=1.5:random_seed=894719821:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.71/0.40 % (819740)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1338045184:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.71/0.40 % (819741)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=4270025193: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)
% 0.71/0.40 % (819743)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3463754639:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.71/0.40 % (819744)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=781942446:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.71/0.40 % (819740)Instruction limit reached!
% 0.71/0.40 % (819740)------------------------------
% 0.71/0.40 % (819740)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.71/0.40 % (819740)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.71/0.40 % (819740)CaDiCaL version: 2.1.3
% 0.71/0.40 % (819740)Termination reason: Instruction limit
% 0.71/0.40 % (819740)Termination phase: shuffling
% 0.71/0.40 % (819740)Time elapsed: 0.003 s
% 0.71/0.40 % (819740)Peak memory usage: 10 MB
% 0.71/0.40 % (819740)Instructions burned: 5 (million)
% 0.71/0.40 % (819739)Instruction limit reached!
% 0.71/0.40 % (819739)------------------------------
% 0.71/0.40 % (819739)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.71/0.40 % (819739)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.71/0.40 % (819739)CaDiCaL version: 2.1.3
% 0.71/0.40 % (819739)Termination reason: Instruction limit
% 0.71/0.40 % (819739)Termination phase: shuffling
% 0.71/0.40 % (819739)Time elapsed: 0.008 s
% 0.71/0.40 % (819739)Peak memory usage: 10 MB
% 0.71/0.40 % (819739)Instructions burned: 18 (million)
% 0.71/0.40 % (819749)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2864428756:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.71/0.40 % (819749)Instruction limit reached!
% 0.71/0.40 % (819749)------------------------------
% 0.71/0.40 % (819749)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.71/0.40 % (819749)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.71/0.40 % (819749)CaDiCaL version: 2.1.3
% 0.71/0.40 % (819749)Termination reason: Instruction limit
% 0.71/0.40 % (819749)Termination phase: shuffling
% 0.71/0.40 % (819749)Time elapsed: 0.001 s
% 0.71/0.40 % (819749)Peak memory usage: 10 MB
% 0.71/0.40 % (819749)Instructions burned: 6 (million)
% 0.71/0.40 % (819753)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=196863944:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.71/0.40 % (819756)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1149065124:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.71/0.40 % (819754)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.71/0.40 % (819753)Instruction limit reached!
% 0.71/0.40 % (819753)------------------------------
% 0.71/0.40 % (819753)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.71/0.40 % (819753)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.71/0.40 % (819753)CaDiCaL version: 2.1.3
% 0.71/0.40 % (819753)Termination reason: Instruction limit
% 0.71/0.40 % (819753)Termination phase: shuffling
% 0.71/0.40 % (819753)Time elapsed: 0.003 s
% 0.71/0.40 % (819753)Peak memory usage: 10 MB
% 0.71/0.40 % (819753)Instructions burned: 6 (million)
% 0.71/0.40 % (819756)Instruction limit reached!
% 0.71/0.40 % (819756)------------------------------
% 0.71/0.40 % (819756)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.71/0.40 % (819756)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.71/0.40 % (819756)CaDiCaL version: 2.1.3
% 0.71/0.40 % (819756)Termination reason: Instruction limit
% 0.71/0.40 % (819756)Termination phase: shuffling
% 0.71/0.40 % (819756)Time elapsed: 0.004 s
% 0.71/0.40 % (819756)Peak memory usage: 10 MB
% 0.71/0.40 % (819756)Instructions burned: 17 (million)
% 0.71/0.40 % (819754)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3065173165:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.71/0.40 % (819759)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
% 0.71/0.40 % (819759)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.71/0.40 % (819743)Instruction limit reached!
% 0.71/0.40 % (819743)------------------------------
% 0.71/0.40 % (819743)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.71/0.40 % (819743)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.71/0.40 % (819743)CaDiCaL version: 2.1.3
% 0.71/0.40 % (819743)Termination reason: Instruction limit
% 0.71/0.40 % (819743)Termination phase: Property scanning
% 0.71/0.40 % (819743)Time elapsed: 0.037 s
% 0.71/0.40 % (819743)Peak memory usage: 12 MB
% 0.71/0.40 % (819743)Instructions burned: 76 (million)
% 0.71/0.40 % (819759)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=1487904198:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.71/0.40 % (819754)Instruction limit reached!
% 0.71/0.40 % (819754)------------------------------
% 0.71/0.40 % (819754)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.71/0.40 % (819754)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.71/0.40 % (819754)CaDiCaL version: 2.1.3
% 0.71/0.40 % (819754)Termination reason: Instruction limit
% 0.71/0.40 % (819754)Termination phase: shuffling
% 0.71/0.40 % (819754)Time elapsed: 0.007 s
% 0.71/0.40 % (819754)Peak memory usage: 10 MB
% 0.71/0.40 % (819754)Instructions burned: 7 (million)
% 0.71/0.40 % (819738)Instruction limit reached!
% 0.71/0.40 % (819738)------------------------------
% 0.71/0.40 % (819738)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.71/0.40 % (819738)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.71/0.40 % (819738)CaDiCaL version: 2.1.3
% 0.71/0.40 % (819738)Termination reason: Instruction limit
% 0.71/0.40 % (819738)Termination phase: Function definition elimination
% 0.71/0.40 % (819738)Time elapsed: 0.042 s
% 0.71/0.40 % (819738)Peak memory usage: 12 MB
% 0.71/0.40 % (819738)Instructions burned: 92 (million)
% 0.71/0.40 % (819759)Instruction limit reached!
% 0.71/0.40 % (819759)------------------------------
% 0.71/0.40 % (819759)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.71/0.40 % (819759)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.71/0.40 % (819759)CaDiCaL version: 2.1.3
% 0.71/0.40 % (819759)Termination reason: Instruction limit
% 0.71/0.40 % (819759)Termination phase: shuffling
% 0.71/0.40 % (819759)Time elapsed: 0.007 s
% 0.71/0.40 % (819759)Peak memory usage: 10 MB
% 0.71/0.40 % (819759)Instructions burned: 32 (million)
% 0.71/0.40 % (819760)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=3082466473:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.71/0.40 % (819762)lrs+10_1_si=on:cs=on:random_seed=724553395:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.71/0.40 % (819766)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=59574941:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.71/0.40 % (819762)Instruction limit reached!
% 0.71/0.40 % (819762)------------------------------
% 0.71/0.40 % (819762)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.71/0.40 % (819765)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=1016189594:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.71/0.40 % (819762)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.71/0.40 % (819762)CaDiCaL version: 2.1.3
% 0.71/0.40 % (819762)Termination reason: Instruction limit
% 0.71/0.40 % (819762)Termination phase: shuffling
% 0.71/0.40 % (819762)Time elapsed: 0.004 s
% 0.71/0.40 % (819762)Peak memory usage: 10 MB
% 0.71/0.40 % (819762)Instructions burned: 9 (million)
% 0.71/0.40 % (819764)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.71/0.40 % (819764)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=1560097484:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.71/0.40 % (819764)Instruction limit reached!
% 0.71/0.40 % (819764)------------------------------
% 0.71/0.40 % (819764)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.71/0.40 % (819764)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.71/0.40 % (819764)CaDiCaL version: 2.1.3
% 0.71/0.40 % (819764)Termination reason: Instruction limit
% 0.71/0.40 % (819764)Termination phase: shuffling
% 0.71/0.40 % (819764)Time elapsed: 0.002 s
% 0.71/0.40 % (819764)Peak memory usage: 10 MB
% 0.71/0.40 % (819764)Instructions burned: 3 (million)
% 0.71/0.40 % (819744)Instruction limit reached!
% 0.71/0.40 % (819744)------------------------------
% 0.71/0.40 % (819744)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.71/0.40 % (819744)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.71/0.40 % (819744)CaDiCaL version: 2.1.3
% 0.71/0.40 % (819744)Termination reason: Instruction limit
% 0.71/0.40 % (819744)Termination phase: Saturation
% 0.71/0.40 % (819744)Time elapsed: 0.075 s
% 0.71/0.40 % (819744)Peak memory usage: 14 MB
% 0.71/0.40 % (819744)Instructions burned: 157 (million)
% 0.71/0.40 % (819765)Instruction limit reached!
% 0.71/0.40 % (819765)------------------------------
% 0.71/0.40 % (819765)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.71/0.40 % (819765)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.71/0.40 % (819765)CaDiCaL version: 2.1.3
% 0.71/0.40 % (819765)Termination reason: Instruction limit
% 0.71/0.40 % (819765)Termination phase: SInE selection
% 0.71/0.40 % (819765)Time elapsed: 0.018 s
% 0.71/0.40 % (819765)Peak memory usage: 11 MB
% 0.71/0.40 % (819765)Instructions burned: 38 (million)
% 0.71/0.40 % (819771)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2196245683:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 0.71/0.40 % (819741) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-819733-819741"...
% 0.71/0.40 % (819766) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-819733-819766"...
% 0.71/0.40 % (819766)...printing done.
% 0.71/0.40 % (819773)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=2963057046:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.71/0.40 % (819741)...printing done.
% 0.71/0.40 % (819766)Refutation found. Thanks to Tanya!
% 0.71/0.40 % SZS status Theorem for theBenchmark
% 0.71/0.40 % SZS output start Proof for theBenchmark
% 0.71/0.40 thf(type_def_5, type, configuration_ext: ($tType * $tType * $tType * $tType) > $tType).
% 0.71/0.40 thf(type_def_6, type, messageValue: $tType > $tType).
% 0.71/0.40 thf(type_def_7, type, message: ($tType * $tType) > $tType).
% 0.71/0.40 thf(type_def_8, type, product_unit: $tType).
% 0.71/0.40 thf(type_def_9, type, list: $tType > $tType).
% 0.71/0.40 thf(type_def_10, type, set: $tType > $tType).
% 0.71/0.40 thf(type_def_11, type, nat: $tType).
% 0.71/0.40 thf(type_def_12, type, int: $tType).
% 0.71/0.40 thf(type_def_13, type, v: $tType).
% 0.71/0.40 thf(type_def_14, type, s: $tType).
% 0.71/0.40 thf(type_def_15, type, p: $tType).
% 0.71/0.40 thf(type_def_16, type, sTfun: ($tType * $tType) > $tType).
% 0.71/0.40 thf(func_def_0, type, type: !>[X0: $tType]:($o)).
% 0.71/0.40 thf(func_def_1, type, size: !>[X0: $tType]:($o)).
% 0.71/0.40 thf(func_def_2, type, one: !>[X0: $tType]:($o)).
% 0.71/0.40 thf(func_def_3, type, zero: !>[X0: $tType]:($o)).
% 0.71/0.40 thf(func_def_4, type, ring_1: !>[X0: $tType]:($o)).
% 0.71/0.40 thf(func_def_5, type, ord: !>[X0: $tType]:($o)).
% 0.71/0.40 thf(func_def_6, type, ring_char_0: !>[X0: $tType]:($o)).
% 0.71/0.40 thf(func_def_7, type, order: !>[X0: $tType]:($o)).
% 0.71/0.40 thf(func_def_8, type, group_add: !>[X0: $tType]:($o)).
% 0.71/0.40 thf(func_def_9, type, semiring_1: !>[X0: $tType]:($o)).
% 0.71/0.40 thf(func_def_10, type, linorder: !>[X0: $tType]:($o)).
% 0.71/0.40 thf(func_def_11, type, semiring_char_0: !>[X0: $tType]:($o)).
% 0.71/0.40 thf(func_def_12, type, wellorder: !>[X0: $tType]:($o)).
% 0.71/0.40 thf(func_def_13, type, linordered_idom: !>[X0: $tType]:($o)).
% 0.71/0.40 thf(func_def_14, type, boolean_algebra: !>[X0: $tType]:($o)).
% 0.71/0.40 thf(func_def_15, type, ordered_ab_group_add: !>[X0: $tType]:($o)).
% 0.71/0.40 thf(func_def_16, type, linord219039673up_add: !>[X0: $tType]:($o)).
% 0.71/0.40 thf(func_def_17, type, linord1659791738miring: !>[X0: $tType]:($o)).
% 0.71/0.40 thf(func_def_18, type, canoni770627133id_add: !>[X0: $tType]:($o)).
% 0.71/0.40 thf(func_def_19, type, bNF_Greatest_shift: !>[X0: $tType, X1: $tType]:(((list @ X0 > X1) > X0 > list @ X0 > X1))).
% 0.71/0.40 thf(func_def_20, type, fLPThe1922692578sensus: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > messageValue @ X2 > X1) > (X0 > X1 > messageValue @ X2 > message @ X0 @ X2 > nat) > (X0 > X1) > $o))).
% 0.71/0.40 thf(func_def_21, type, fLPThe137922386ionCfg: !>[X0: $tType, X1: $tType, X2: $tType]:((configuration_ext @ X0 @ X1 @ X2 @ product_unit > (list @ configuration_ext @ X0 @ X1 @ X2 @ product_unit > list @ message @ X0 @ X1 > list @ configuration_ext @ X0 @ X1 @ X2 @ product_unit) > (list @ configuration_ext @ X0 @ X1 @ X2 @ product_unit > list @ message @ X0 @ X1 > list @ message @ X0 @ X1) > nat > list @ configuration_ext @ X0 @ X1 @ X2 @ product_unit))).
% 0.71/0.40 thf(func_def_22, type, fLPThe221390223ionMsg: !>[X0: $tType, X1: $tType, X2: $tType]:((configuration_ext @ X0 @ X1 @ X2 @ product_unit > (list @ configuration_ext @ X0 @ X1 @ X2 @ product_unit > list @ message @ X0 @ X1 > list @ configuration_ext @ X0 @ X1 @ X2 @ product_unit) > (list @ configuration_ext @ X0 @ X1 @ X2 @ product_unit > list @ message @ X0 @ X1 > list @ message @ X0 @ X1) > nat > list @ message @ X0 @ X1))).
% 0.71/0.40 thf(func_def_23, type, fLPThe2031355932ionFLP: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > messageValue @ X2 > X1) > (X0 > X1 > messageValue @ X2 > message @ X0 @ X2 > nat) > (X0 > X1) > (nat > list @ configuration_ext @ X0 @ X2 @ X1 @ product_unit) > (nat > list @ message @ X0 @ X2) > $o))).
% 0.71/0.40 thf(func_def_24, type, one_one: !>[X0: $tType]:(X0)).
% 0.71/0.40 thf(func_def_25, type, uminus_uminus: !>[X0: $tType]:((X0 > X0))).
% 0.71/0.40 thf(func_def_26, type, zero_zero: !>[X0: $tType]:(X0)).
% 0.71/0.40 thf(func_def_27, type, nat2: (int > nat)).
% 0.71/0.40 thf(func_def_28, type, ring_1_of_int: !>[X0: $tType]:((int > X0))).
% 0.71/0.40 thf(func_def_29, type, prefixList: !>[X0: $tType]:((list @ X0 > list @ X0 > $o))).
% 0.71/0.40 thf(func_def_30, type, gen_length: !>[X0: $tType]:((nat > list @ X0 > nat))).
% 0.71/0.40 thf(func_def_31, type, insert: !>[X0: $tType]:((X0 > list @ X0 > list @ X0))).
% 0.71/0.40 thf(func_def_32, type, cons: !>[X0: $tType]:((X0 > list @ X0 > list @ X0))).
% 0.71/0.40 thf(func_def_33, type, nil: !>[X0: $tType]:(list @ X0)).
% 0.71/0.40 thf(func_def_34, type, list_ex1: !>[X0: $tType]:(((X0 > $o) > list @ X0 > $o))).
% 0.71/0.40 thf(func_def_35, type, n_lists: !>[X0: $tType]:((nat > list @ X0 > list @ list @ X0))).
% 0.71/0.40 thf(func_def_36, type, nths: !>[X0: $tType]:((list @ X0 > set @ nat > list @ X0))).
% 0.71/0.40 thf(func_def_37, type, product_lists: !>[X0: $tType]:((list @ list @ X0 > list @ list @ X0))).
% 0.71/0.40 thf(func_def_38, type, subseqs: !>[X0: $tType]:((list @ X0 > list @ list @ X0))).
% 0.71/0.40 thf(func_def_39, type, suc: (nat > nat)).
% 0.71/0.40 thf(func_def_40, type, semiring_1_of_nat: !>[X0: $tType]:((nat > X0))).
% 0.71/0.40 thf(func_def_41, type, size_size: !>[X0: $tType]:((X0 > nat))).
% 0.71/0.40 thf(func_def_42, type, ord_less: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.71/0.40 thf(func_def_43, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.71/0.40 thf(func_def_44, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 0.71/0.40 thf(func_def_45, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.71/0.40 thf(func_def_46, type, cfg: configuration_ext @ p @ v @ s @ product_unit).
% 0.71/0.40 thf(func_def_47, type, fe: (nat > list @ configuration_ext @ p @ v @ s @ product_unit)).
% 0.71/0.40 thf(func_def_48, type, m: nat).
% 0.71/0.40 thf(func_def_49, type, n: nat).
% 0.71/0.40 thf(func_def_50, type, na: nat).
% 0.71/0.40 thf(func_def_54, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.71/0.40 thf(func_def_55, type, vOR: ($o > $o > $o)).
% 0.71/0.40 thf(func_def_56, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.71/0.40 thf(func_def_57, type, vAND: ($o > $o > $o)).
% 0.71/0.40 thf(func_def_58, type, db3: !>[X0: $tType]:(X0)).
% 0.71/0.40 thf(func_def_59, type, db1: !>[X0: $tType]:(X0)).
% 0.71/0.40 thf(func_def_60, type, db0: !>[X0: $tType]:(X0)).
% 0.71/0.40 thf(func_def_61, type, db2: !>[X0: $tType]:(X0)).
% 0.71/0.40 thf(func_def_62, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.71/0.40 thf(func_def_63, type, db4: !>[X0: $tType]:(X0)).
% 0.71/0.40 thf(func_def_64, type, vNOT: ($o > $o)).
% 0.71/0.40 thf(func_def_65, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.71/0.40 thf(func_def_66, type, vIMP: ($o > $o > $o)).
% 0.71/0.40 thf(func_def_67, type, sP0: ((configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > (configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > $o)).
% 0.71/0.40 thf(func_def_68, type, sP1: ((configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > (configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > $o)).
% 0.71/0.40 thf(func_def_69, type, sK2: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > list @ X0))).
% 0.71/0.40 thf(func_def_70, type, sK3: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > X0))).
% 0.71/0.40 thf(func_def_71, type, sK4: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > X0))).
% 0.71/0.40 thf(func_def_72, type, sK5: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > list @ X0))).
% 0.71/0.40 thf(func_def_73, type, sK6: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > list @ X0))).
% 0.71/0.40 thf(func_def_74, type, sK7: ((nat > $o) > nat)).
% 0.71/0.40 thf(func_def_75, type, sK8: !>[X0: $tType]:(((X0 > nat) > (X0 > $o) > X0))).
% 0.71/0.40 thf(func_def_76, type, sK9: !>[X0: $tType, X1: $tType]:(((list @ X1 > list @ X0 > $o) > list @ X1))).
% 0.71/0.40 thf(func_def_77, type, sK10: !>[X0: $tType, X1: $tType]:(((list @ X1 > list @ X0 > $o) > list @ X0))).
% 0.71/0.40 thf(func_def_78, type, sK11: !>[X0: $tType, X1: $tType]:(((list @ X1 > list @ X0 > $o) > X0))).
% 0.71/0.40 thf(func_def_79, type, sK12: !>[X0: $tType, X1: $tType]:(((list @ X1 > list @ X0 > $o) > X1))).
% 0.71/0.40 thf(func_def_80, type, sK13: !>[X0: $tType, X1: $tType]:(((list @ X1 > list @ X0 > $o) > X1))).
% 0.71/0.40 thf(func_def_81, type, sK14: !>[X0: $tType, X1: $tType]:(((list @ X1 > list @ X0 > $o) > list @ X1))).
% 0.71/0.40 thf(func_def_82, type, sK15: !>[X0: $tType, X1: $tType]:(((list @ X1 > list @ X0 > $o) > X0))).
% 0.71/0.40 thf(func_def_83, type, sK16: !>[X0: $tType, X1: $tType]:(((list @ X1 > list @ X0 > $o) > list @ X0))).
% 0.71/0.40 thf(func_def_84, type, sK17: !>[X0: $tType]:(((X0 > nat) > (X0 > $o) > X0))).
% 0.71/0.40 thf(func_def_85, type, sK18: !>[X0: $tType]:(((X0 > nat) > (X0 > $o) > X0))).
% 0.71/0.40 thf(func_def_86, type, sK19: !>[X0: $tType]:((((X0 > X0 > $o) > list @ X0 > $o) > X0))).
% 0.71/0.40 thf(func_def_87, type, sK20: !>[X0: $tType]:((((X0 > X0 > $o) > list @ X0 > $o) > X0))).
% 0.71/0.40 thf(func_def_88, type, sK21: !>[X0: $tType]:((((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o))).
% 0.71/0.40 thf(func_def_89, type, sK22: !>[X0: $tType]:((((X0 > X0 > $o) > list @ X0 > $o) > list @ X0))).
% 0.71/0.40 thf(func_def_90, type, sK23: !>[X0: $tType]:((((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o))).
% 0.71/0.40 thf(func_def_91, type, sK24: !>[X0: $tType]:((((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o))).
% 0.71/0.40 thf(func_def_92, type, sK25: !>[X0: $tType]:((((X0 > X0 > $o) > list @ X0 > $o) > X0))).
% 0.71/0.40 thf(func_def_93, type, sK26: ((configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > (configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > nat)).
% 0.71/0.40 thf(func_def_94, type, sK27: ((configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > (configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v)).
% 0.71/0.40 thf(func_def_95, type, sK28: ((configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > (configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit)).
% 0.71/0.40 thf(func_def_96, type, sK29: ((configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > (configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > configuration_ext @ p @ v @ s @ product_unit)).
% 0.71/0.40 thf(func_def_97, type, sK30: ((configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v)).
% 0.71/0.40 thf(func_def_98, type, sK31: ((configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit)).
% 0.71/0.40 thf(func_def_99, type, sK32: ((configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > configuration_ext @ p @ v @ s @ product_unit)).
% 0.71/0.40 thf(func_def_100, type, sK33: ((configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > (configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > nat)).
% 0.71/0.40 thf(func_def_101, type, sK34: ((configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > (configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > configuration_ext @ p @ v @ s @ product_unit)).
% 0.71/0.40 thf(func_def_102, type, sK35: ((configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > (configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit)).
% 0.71/0.40 thf(func_def_103, type, sK36: ((configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > (configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v)).
% 0.71/0.40 thf(func_def_104, type, sK37: ((configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v)).
% 0.71/0.40 thf(func_def_105, type, sK38: ((configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > configuration_ext @ p @ v @ s @ product_unit)).
% 0.71/0.40 thf(func_def_106, type, sK39: ((configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit)).
% 0.71/0.40 thf(func_def_107, type, sK40: !>[X0: $tType]:(((list @ X0 > $o) > list @ X0))).
% 0.71/0.40 thf(func_def_108, type, sK41: !>[X0: $tType]:(((list @ X0 > $o) > X0))).
% 0.71/0.40 thf(func_def_109, type, sK42: !>[X0: $tType]:(((list @ X0 > $o) > X0))).
% 0.71/0.40 thf(func_def_110, type, sK43: !>[X0: $tType]:((list @ list @ X0 > X0))).
% 0.71/0.40 thf(func_def_111, type, sK44: !>[X0: $tType]:((list @ list @ X0 > list @ list @ X0))).
% 0.71/0.40 thf(func_def_112, type, sK45: !>[X0: $tType]:((list @ list @ X0 > list @ X0))).
% 0.71/0.40 thf(func_def_113, type, sK46: !>[X0: $tType]:((list @ list @ X0 > list @ list @ X0))).
% 0.71/0.40 thf(func_def_114, type, sK47: (nat > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > configuration_ext @ p @ v @ s @ product_unit > list @ configuration_ext @ p @ v @ s @ product_unit > nat)).
% 0.71/0.40 thf(func_def_115, type, sK48: ((nat > $o) > nat)).
% 0.71/0.40 thf(func_def_116, type, sK49: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > list @ X0))).
% 0.71/0.40 thf(func_def_117, type, sK50: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > list @ X0))).
% 0.71/0.40 thf(func_def_118, type, sK51: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > X0))).
% 0.71/0.40 thf(func_def_119, type, sK52: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > list @ X0))).
% 0.71/0.40 thf(func_def_120, type, sK53: !>[X0: $tType]:((list @ X0 > X0))).
% 0.71/0.40 thf(func_def_121, type, sK54: !>[X0: $tType]:((list @ X0 > list @ X0))).
% 0.71/0.40 thf(func_def_122, type, sK55: !>[X0: $tType]:((list @ X0 > X0))).
% 0.71/0.40 thf(func_def_123, type, sK56: !>[X0: $tType]:((list @ X0 > X0))).
% 0.71/0.40 thf(func_def_124, type, sK57: !>[X0: $tType]:(((list @ X0 > $o) > X0))).
% 0.71/0.40 thf(func_def_125, type, sK58: !>[X0: $tType]:(((list @ X0 > $o) > X0))).
% 0.71/0.40 thf(func_def_126, type, sK59: !>[X0: $tType]:(((list @ X0 > $o) > X0))).
% 0.71/0.40 thf(func_def_127, type, sK60: !>[X0: $tType]:(((list @ X0 > $o) > list @ X0))).
% 0.71/0.40 thf(func_def_128, type, sK61: (nat > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > nat)).
% 0.71/0.40 thf(func_def_129, type, sK62: ((nat > $o) > nat)).
% 0.71/0.40 thf(func_def_130, type, sK63: !>[X0: $tType]:(((list @ X0 > $o) > X0))).
% 0.71/0.40 thf(func_def_131, type, sK64: !>[X0: $tType]:(((list @ X0 > $o) > list @ X0))).
% 0.71/0.40 thf(func_def_132, type, sK65: !>[X0: $tType]:(((list @ X0 > $o) > X0))).
% 0.71/0.40 thf(func_def_133, type, sK66: !>[X0: $tType]:(((list @ X0 > $o) > X0))).
% 0.71/0.40 thf(func_def_134, type, sK67: !>[X0: $tType, X1: $tType]:((((X1 > X0) > list @ X1 > list @ X0 > $o) > list @ X0))).
% 0.71/0.40 thf(func_def_135, type, sK68: !>[X0: $tType, X1: $tType]:((((X1 > X0) > list @ X1 > list @ X0 > $o) > X1 > X0))).
% 0.71/0.40 thf(func_def_136, type, sK69: !>[X0: $tType, X1: $tType]:((((X1 > X0) > list @ X1 > list @ X0 > $o) > list @ X0))).
% 0.71/0.40 thf(func_def_137, type, sK70: !>[X0: $tType, X1: $tType]:((((X1 > X0) > list @ X1 > list @ X0 > $o) > list @ X1))).
% 0.71/0.40 thf(func_def_138, type, sK71: !>[X0: $tType, X1: $tType]:((((X1 > X0) > list @ X1 > list @ X0 > $o) > X1))).
% 0.71/0.40 thf(func_def_139, type, sK72: !>[X0: $tType, X1: $tType]:((((X1 > X0) > list @ X1 > list @ X0 > $o) > X1 > X0))).
% 0.71/0.40 thf(func_def_140, type, sK73: ((configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > (configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > nat)).
% 0.71/0.40 thf(func_def_141, type, sK74: ((configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > (configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit)).
% 0.71/0.40 thf(func_def_142, type, sK75: ((configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > (configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v)).
% 0.71/0.40 thf(func_def_143, type, sK76: ((configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > (configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > configuration_ext @ p @ v @ s @ product_unit)).
% 0.71/0.40 thf(func_def_144, type, sK77: ((configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit)).
% 0.71/0.40 thf(func_def_145, type, sK78: ((configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > configuration_ext @ p @ v @ s @ product_unit)).
% 0.71/0.40 thf(func_def_146, type, sK79: ((configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v)).
% 0.71/0.40 thf(func_def_147, type, sK80: ((configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit)).
% 0.71/0.40 thf(func_def_148, type, sK81: ((configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > configuration_ext @ p @ v @ s @ product_unit)).
% 0.71/0.40 thf(func_def_149, type, sK82: ((configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v)).
% 0.71/0.40 thf(func_def_150, type, sK83: ((configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > (configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > nat)).
% 0.71/0.40 thf(func_def_151, type, sK84: ((configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > (configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > configuration_ext @ p @ v @ s @ product_unit)).
% 0.71/0.40 thf(func_def_152, type, sK85: ((configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > (configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit)).
% 0.71/0.40 thf(func_def_153, type, sK86: ((configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > (configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v)).
% 0.71/0.40 thf(func_def_154, type, sK87: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > X0))).
% 0.71/0.40 thf(func_def_155, type, sK88: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > list @ X0))).
% 0.71/0.40 thf(func_def_156, type, sK89: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > list @ X0))).
% 0.71/0.40 thf(func_def_157, type, sK90: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > X0))).
% 0.71/0.40 thf(func_def_158, type, sK91: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > list @ X0))).
% 0.71/0.40 thf(func_def_159, type, sK92: !>[X0: $tType]:(((list @ X0 > list @ X0 > $o) > list @ X0))).
% 0.71/0.40 thf(func_def_160, type, sK93: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > X1) > X0))).
% 0.71/0.40 thf(func_def_161, type, sK94: !>[X0: $tType]:((list @ X0 > list @ X0))).
% 0.71/0.40 thf(func_def_162, type, sK95: !>[X0: $tType]:((list @ X0 > X0))).
% 0.71/0.40 thf(func_def_163, type, sK96: !>[X0: $tType]:((list @ X0 > list @ X0))).
% 0.71/0.40 thf(func_def_164, type, sK97: !>[X0: $tType]:((list @ X0 > X0))).
% 0.71/0.40 thf(func_def_165, type, sK98: !>[X0: $tType]:((list @ X0 > list @ X0 > X0))).
% 0.71/0.40 thf(func_def_166, type, sK99: !>[X0: $tType]:((list @ X0 > list @ X0 > list @ X0))).
% 0.71/0.40 thf(func_def_167, type, sK100: !>[X0: $tType]:((list @ X0 > list @ X0 > list @ X0))).
% 0.71/0.40 thf(func_def_168, type, sK101: !>[X0: $tType]:(((list @ X0 > $o) > list @ X0))).
% 0.71/0.40 thf(func_def_169, type, sK102: !>[X0: $tType]:(((list @ X0 > $o) > X0))).
% 0.71/0.40 thf(func_def_170, type, sK103: !>[X0: $tType]:((((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o))).
% 0.71/0.40 thf(func_def_171, type, sK104: !>[X0: $tType]:((((X0 > X0 > $o) > list @ X0 > $o) > X0))).
% 0.71/0.40 thf(func_def_172, type, sK105: !>[X0: $tType]:((((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o))).
% 0.71/0.40 thf(func_def_173, type, sK106: !>[X0: $tType]:((((X0 > X0 > $o) > list @ X0 > $o) > list @ X0))).
% 0.71/0.40 thf(f1,axiom,(
% 0.71/0.40 (ord_less @ nat @ m @ na)),
% 0.71/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__092_060open_062m_A_060_An_092_060close_062)).
% 0.71/0.40 thf(f3,axiom,(
% 0.71/0.40 (ord_less @ nat @ m @ na) => (prefixList @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ m) @ (fe @ na))),
% 0.71/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_IA_I1_J)).
% 0.71/0.40 thf(f294,conjecture,(
% 0.71/0.40 (prefixList @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ m) @ (fe @ na))),
% 0.71/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 0.71/0.40 thf(f295,negated_conjecture,(
% 0.71/0.40 ~(prefixList @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ m) @ (fe @ na))),
% 0.71/0.40 inference(negated_conjecture,[status(cth)],[f294])).
% 0.71/0.40 thf(f387,plain,(
% 0.71/0.40 (ord_less @ nat @ m @ na)),
% 0.71/0.40 inference(rectify,[],[f1])).
% 0.71/0.40 thf(f388,plain,(
% 0.71/0.40 (((ord_less @ nat @ m @ na)) = $true)),
% 0.71/0.40 inference(fool_elimination,[],[f387])).
% 0.71/0.40 thf(f522,plain,(
% 0.71/0.40 ~(prefixList @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ m) @ (fe @ na))),
% 0.71/0.40 inference(rectify,[],[f295])).
% 0.71/0.40 thf(f523,plain,(
% 0.71/0.40 ~ (((prefixList @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ m) @ (fe @ na))) = $true)),
% 0.71/0.40 inference(fool_elimination,[],[f522])).
% 0.71/0.40 thf(f624,plain,(
% 0.71/0.40 (ord_less @ nat @ m @ na) => (prefixList @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ m) @ (fe @ na))),
% 0.71/0.40 inference(rectify,[],[f3])).
% 0.71/0.40 thf(f625,plain,(
% 0.71/0.40 (((ord_less @ nat @ m @ na)) = $true) => (((prefixList @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ m) @ (fe @ na))) = $true)),
% 0.71/0.40 inference(fool_elimination,[],[f624])).
% 0.71/0.40 thf(f774,plain,(
% 0.71/0.40 (((prefixList @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ m) @ (fe @ na))) != $true)),
% 0.71/0.40 inference(flattening,[],[f523])).
% 0.71/0.40 thf(f821,plain,(
% 0.71/0.40 (((ord_less @ nat @ m @ na)) != $true) | (((prefixList @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ m) @ (fe @ na))) = $true)),
% 0.71/0.40 inference(ennf_transformation,[],[f625])).
% 0.71/0.40 thf(f961,plain,(
% 0.71/0.40 (((prefixList @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ m) @ (fe @ na))) != $true)),
% 0.71/0.40 inference(cnf_transformation,[],[f774])).
% 0.71/0.40 thf(f965,plain,(
% 0.71/0.40 (((ord_less @ nat @ m @ na)) = $true)),
% 0.71/0.40 inference(cnf_transformation,[],[f388])).
% 0.71/0.40 thf(f1004,plain,(
% 0.71/0.40 (((prefixList @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ m) @ (fe @ na))) = $true) | (((ord_less @ nat @ m @ na)) != $true)),
% 0.71/0.40 inference(cnf_transformation,[],[f821])).
% 0.71/0.40 thf(f1033,plain,(
% 0.71/0.40 (((ord_less @ nat @ m @ na)) != $true) | ($true != $true)),
% 0.71/0.40 inference(superposition,[],[f961,f1004])).
% 0.71/0.40 thf(f1038,plain,(
% 0.71/0.40 (((ord_less @ nat @ m @ na)) != $true)),
% 0.71/0.40 inference(trivial_inequality_removal,[],[f1033])).
% 0.71/0.40 thf(f1039,plain,(
% 0.71/0.40 $false),
% 0.71/0.40 inference(forward_subsumption_resolution,[],[f1038,f965])).
% 0.71/0.40 % SZS output end Proof for theBenchmark
% 0.71/0.40 % (819766)------------------------------
% 0.71/0.40 % (819766)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.71/0.40 % (819766)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.71/0.40 % (819766)CaDiCaL version: 2.1.3
% 0.71/0.40 % (819766)Termination reason: Refutation
% 0.71/0.40 % (819766)Time elapsed: 0.030 s
% 0.71/0.40 % (819766)Peak memory usage: 13 MB
% 0.71/0.40 % (819766)Instructions burned: 87 (million)
% 0.71/0.40 % (819733)Success in time 0.137 s
% 0.71/0.40 % Vampire exiting
%------------------------------------------------------------------------------