%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP135^2 : 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 : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:08:30 AM UTC 2026
% Result : Theorem 0.48s 0.40s
% Output : Refutation 0.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP135^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n019.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 19:59:03 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running higher-order theorem proving
% 0.22/0.27 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
% 0.48/0.40 % (1274809)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.48/0.40 % (1274826)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2294347197:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.48/0.40 % (1274827)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.48/0.40 % (1274827)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
% 0.48/0.40 % (1274821)lrs+10_16_si=on:nwc=1.5:random_seed=1569166698:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.48/0.40 % (1274820)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3019021759:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.48/0.40 % (1274822)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1271124735:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.48/0.40 % (1274825)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1100594070:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.48/0.40 % (1274824)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=2574365918: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)
% 0.48/0.40 % (1274827)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=2125208002:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.48/0.40 % (1274822)Instruction limit reached!
% 0.48/0.40 % (1274822)------------------------------
% 0.48/0.40 % (1274822)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.40 % (1274822)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.40 % (1274822)CaDiCaL version: 2.1.3
% 0.48/0.40 % (1274822)Termination reason: Instruction limit
% 0.48/0.40 % (1274822)Termination phase: shuffling
% 0.48/0.40 % (1274822)Time elapsed: 0.003 s
% 0.48/0.40 % (1274822)Peak memory usage: 10 MB
% 0.48/0.40 % (1274822)Instructions burned: 5 (million)
% 0.48/0.40 % (1274821)Instruction limit reached!
% 0.48/0.40 % (1274821)------------------------------
% 0.48/0.40 % (1274821)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.40 % (1274821)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.40 % (1274821)CaDiCaL version: 2.1.3
% 0.48/0.40 % (1274821)Termination reason: Instruction limit
% 0.48/0.40 % (1274821)Termination phase: Property scanning
% 0.48/0.40 % (1274821)Time elapsed: 0.010 s
% 0.48/0.40 % (1274821)Peak memory usage: 10 MB
% 0.48/0.40 % (1274821)Instructions burned: 19 (million)
% 0.48/0.40 % (1274825)Instruction limit reached!
% 0.48/0.40 % (1274825)------------------------------
% 0.48/0.40 % (1274825)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.40 % (1274825)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.40 % (1274825)CaDiCaL version: 2.1.3
% 0.48/0.40 % (1274825)Termination reason: Instruction limit
% 0.48/0.40 % (1274825)Termination phase: Property scanning
% 0.48/0.40 % (1274825)Time elapsed: 0.012 s
% 0.48/0.40 % (1274825)Peak memory usage: 10 MB
% 0.48/0.40 % (1274825)Instructions burned: 24 (million)
% 0.48/0.40 % (1274826)Instruction limit reached!
% 0.48/0.40 % (1274826)------------------------------
% 0.48/0.40 % (1274826)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.40 % (1274826)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.40 % (1274826)CaDiCaL version: 2.1.3
% 0.48/0.40 % (1274826)Termination reason: Instruction limit
% 0.48/0.40 % (1274826)Termination phase: Function definition elimination
% 0.48/0.40 % (1274826)Time elapsed: 0.020 s
% 0.48/0.40 % (1274826)Peak memory usage: 12 MB
% 0.48/0.40 % (1274826)Instructions burned: 77 (million)
% 0.48/0.40 % (1274847)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.48/0.40 % (1274841)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3166642747:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.48/0.40 % (1274847)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2685341203:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.48/0.40 % (1274841)Instruction limit reached!
% 0.48/0.40 % (1274841)------------------------------
% 0.48/0.40 % (1274841)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.40 % (1274847)Instruction limit reached!
% 0.48/0.40 % (1274847)------------------------------
% 0.48/0.40 % (1274847)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.40 % (1274841)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.40 % (1274847)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.40 % (1274847)CaDiCaL version: 2.1.3
% 0.48/0.40 % (1274847)Termination reason: Instruction limit
% 0.48/0.40 % (1274847)Termination phase: shuffling
% 0.48/0.40 % (1274841)CaDiCaL version: 2.1.3
% 0.48/0.40 % (1274847)Time elapsed: 0.002 s
% 0.48/0.40 % (1274847)Peak memory usage: 10 MB
% 0.48/0.40 % (1274841)Termination reason: Instruction limit
% 0.48/0.40 % (1274841)Termination phase: shuffling
% 0.48/0.40 % (1274847)Instructions burned: 9 (million)
% 0.48/0.40 % (1274841)Time elapsed: 0.003 s
% 0.48/0.40 % (1274841)Peak memory usage: 10 MB
% 0.48/0.40 % (1274841)Instructions burned: 5 (million)
% 0.48/0.40 % (1274844)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1747627786:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.48/0.40 % (1274848)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2689121244:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.48/0.40 % (1274844)Instruction limit reached!
% 0.48/0.40 % (1274844)------------------------------
% 0.48/0.40 % (1274844)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.40 % (1274844)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.40 % (1274844)CaDiCaL version: 2.1.3
% 0.48/0.40 % (1274844)Termination reason: Instruction limit
% 0.48/0.40 % (1274844)Termination phase: shuffling
% 0.48/0.40 % (1274844)Time elapsed: 0.003 s
% 0.48/0.40 % (1274844)Peak memory usage: 10 MB
% 0.48/0.40 % (1274844)Instructions burned: 5 (million)
% 0.48/0.40 % (1274853)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
% 0.48/0.40 % (1274853)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.48/0.40 % (1274853)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2930211460:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.48/0.40 % (1274848)Instruction limit reached!
% 0.48/0.40 % (1274848)------------------------------
% 0.48/0.40 % (1274848)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.40 % (1274848)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.40 % (1274848)CaDiCaL version: 2.1.3
% 0.48/0.40 % (1274848)Termination reason: Instruction limit
% 0.48/0.40 % (1274848)Termination phase: shuffling
% 0.48/0.40 % (1274848)Time elapsed: 0.006 s
% 0.48/0.40 % (1274848)Peak memory usage: 10 MB
% 0.48/0.40 % (1274848)Instructions burned: 12 (million)
% 0.48/0.40 % (1274820)Instruction limit reached!
% 0.48/0.40 % (1274820)------------------------------
% 0.48/0.40 % (1274820)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.40 % (1274853)Instruction limit reached!
% 0.48/0.40 % (1274853)------------------------------
% 0.48/0.40 % (1274853)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.40 % (1274853)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.40 % (1274820)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.40 % (1274853)CaDiCaL version: 2.1.3
% 0.48/0.40 % (1274820)CaDiCaL version: 2.1.3
% 0.48/0.40 % (1274853)Termination reason: Instruction limit
% 0.48/0.40 % (1274853)Termination phase: shuffling
% 0.48/0.40 % (1274820)Termination reason: Instruction limit
% 0.48/0.40 % (1274820)Termination phase: Property scanning
% 0.48/0.40 % (1274820)Time elapsed: 0.044 s
% 0.48/0.40 % (1274853)Time elapsed: 0.007 s
% 0.48/0.40 % (1274820)Peak memory usage: 12 MB
% 0.48/0.40 % (1274820)Instructions burned: 88 (million)
% 0.48/0.40 % (1274853)Peak memory usage: 11 MB
% 0.48/0.40 % (1274853)Instructions burned: 30 (million)
% 0.48/0.40 % (1274855)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=1040481177:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.48/0.40 % (1274858)lrs+10_1_si=on:cs=on:random_seed=2765935322:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.48/0.40 % (1274862)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.48/0.40 % (1274863)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=3761206181:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.48/0.40 % (1274858)Instruction limit reached!
% 0.48/0.40 % (1274858)------------------------------
% 0.48/0.40 % (1274858)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.40 % (1274858)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.40 % (1274858)CaDiCaL version: 2.1.3
% 0.48/0.40 % (1274858)Termination reason: Instruction limit
% 0.48/0.40 % (1274858)Termination phase: shuffling
% 0.48/0.40 % (1274858)Time elapsed: 0.005 s
% 0.48/0.40 % (1274858)Peak memory usage: 10 MB
% 0.48/0.40 % (1274858)Instructions burned: 10 (million)
% 0.48/0.40 % (1274862)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=3811055359:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.48/0.40 % (1274862)Instruction limit reached!
% 0.48/0.40 % (1274862)------------------------------
% 0.48/0.40 % (1274862)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.40 % (1274862)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.40 % (1274862)CaDiCaL version: 2.1.3
% 0.48/0.40 % (1274862)Termination reason: Instruction limit
% 0.48/0.40 % (1274862)Termination phase: shuffling
% 0.48/0.40 % (1274862)Time elapsed: 0.002 s
% 0.48/0.40 % (1274862)Peak memory usage: 10 MB
% 0.48/0.40 % (1274862)Instructions burned: 3 (million)
% 0.48/0.40 % (1274864)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=3287045492:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.48/0.40 % (1274863)Instruction limit reached!
% 0.48/0.40 % (1274863)------------------------------
% 0.48/0.40 % (1274863)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.40 % (1274863)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.40 % (1274863)CaDiCaL version: 2.1.3
% 0.48/0.40 % (1274863)Termination reason: Instruction limit
% 0.48/0.40 % (1274863)Termination phase: Preprocessing 3
% 0.48/0.40 % (1274863)Time elapsed: 0.011 s
% 0.48/0.40 % (1274863)Peak memory usage: 11 MB
% 0.48/0.40 % (1274863)Instructions burned: 40 (million)
% 0.48/0.40 % (1274824) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1274809-1274824"...
% 0.48/0.40 % (1274824)...printing done.
% 0.48/0.40 % (1274824)Refutation found. Thanks to Tanya!
% 0.48/0.40 % SZS status Theorem for theBenchmark
% 0.48/0.40 % SZS output start Proof for theBenchmark
% 0.48/0.40 thf(type_def_5, type, paraco415392788lle_tv: $tType).
% 0.48/0.40 thf(type_def_6, type, paraco414474393lle_fm: $tType).
% 0.48/0.40 thf(type_def_7, type, product_prod: ($tType * $tType) > $tType).
% 0.48/0.40 thf(type_def_8, type, char: $tType).
% 0.48/0.40 thf(type_def_9, type, list: $tType > $tType).
% 0.48/0.40 thf(type_def_10, type, set: $tType > $tType).
% 0.48/0.40 thf(type_def_11, type, nat: $tType).
% 0.48/0.40 thf(type_def_12, type, sTfun: ($tType * $tType) > $tType).
% 0.48/0.40 thf(func_def_0, type, type: !>[X0: $tType]:($o)).
% 0.48/0.40 thf(func_def_1, type, ord: !>[X0: $tType]:($o)).
% 0.48/0.40 thf(func_def_2, type, top: !>[X0: $tType]:($o)).
% 0.48/0.40 thf(func_def_3, type, order: !>[X0: $tType]:($o)).
% 0.48/0.40 thf(func_def_4, type, linorder: !>[X0: $tType]:($o)).
% 0.48/0.40 thf(func_def_5, type, preorder: !>[X0: $tType]:($o)).
% 0.48/0.40 thf(func_def_6, type, order_top: !>[X0: $tType]:($o)).
% 0.48/0.40 thf(func_def_7, type, inj_on: !>[X0: $tType, X1: $tType]:(((X0 > X1) > set @ X0 > $o))).
% 0.48/0.40 thf(func_def_8, type, the_inv_into: !>[X0: $tType, X1: $tType]:((set @ X0 > (X0 > X1) > X1 > X0))).
% 0.48/0.40 thf(func_def_9, type, if: !>[X0: $tType]:(($o > X0 > X0 > X0))).
% 0.48/0.40 thf(func_def_10, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.48/0.40 thf(func_def_11, type, top_top: !>[X0: $tType]:(X0)).
% 0.48/0.40 thf(func_def_12, type, paraco753463838ge_int: ((nat > nat) > (list @ char > paraco415392788lle_tv) > list @ char > paraco415392788lle_tv)).
% 0.48/0.40 thf(func_def_13, type, paraco1920534163nge_tv: ((nat > nat) > paraco415392788lle_tv > paraco415392788lle_tv)).
% 0.48/0.40 thf(func_def_14, type, paraco2077297190tv_rel: (product_prod @ (nat > nat) @ paraco415392788lle_tv > product_prod @ (nat > nat) @ paraco415392788lle_tv > $o)).
% 0.48/0.40 thf(func_def_15, type, paraco876059933e_eval: ((list @ char > paraco415392788lle_tv) > paraco414474393lle_fm > paraco415392788lle_tv)).
% 0.48/0.40 thf(func_def_16, type, paraco2100061555le_Con: (paraco414474393lle_fm > paraco414474393lle_fm > paraco414474393lle_fm)).
% 0.48/0.40 thf(func_def_17, type, paraco2084319816le_Eql: (paraco414474393lle_fm > paraco414474393lle_fm > paraco414474393lle_fm)).
% 0.48/0.40 thf(func_def_18, type, paraco1628874225le_Eql: (paraco414474393lle_fm > paraco414474393lle_fm > paraco414474393lle_fm)).
% 0.48/0.40 thf(func_def_19, type, paraco329115265le_Neg: (paraco414474393lle_fm > paraco414474393lle_fm)).
% 0.48/0.40 thf(func_def_20, type, paraco27778325le_Pro: (list @ char > paraco414474393lle_fm)).
% 0.48/0.40 thf(func_def_21, type, paraco251304083_Truth: paraco414474393lle_fm).
% 0.48/0.40 thf(func_def_22, type, paraco1246693743ase_fm: !>[X0: $tType]:(((list @ char > X0) > X0 > (paraco414474393lle_fm > X0) > (paraco414474393lle_fm > paraco414474393lle_fm > X0) > (paraco414474393lle_fm > paraco414474393lle_fm > X0) > (paraco414474393lle_fm > paraco414474393lle_fm > X0) > paraco414474393lle_fm > X0))).
% 0.48/0.40 thf(func_def_23, type, paraco2040174112le_Det: ($o > paraco415392788lle_tv)).
% 0.48/0.40 thf(func_def_24, type, paraco676387099_Indet: (nat > paraco415392788lle_tv)).
% 0.48/0.40 thf(func_def_25, type, paraco490622181ase_tv: !>[X0: $tType]:((($o > X0) > (nat > X0) > paraco415392788lle_tv > X0))).
% 0.48/0.40 thf(func_def_26, type, paraco152590079rec_tv: !>[X0: $tType]:((($o > X0) > (nat > X0) > paraco415392788lle_tv > X0))).
% 0.48/0.40 thf(func_def_27, type, paraco769098683_valid: (paraco414474393lle_fm > $o)).
% 0.48/0.40 thf(func_def_28, type, paraco2086025920lid_in: (set @ nat > paraco414474393lle_fm > $o)).
% 0.48/0.40 thf(func_def_29, type, product_Pair: !>[X0: $tType, X1: $tType]:((X0 > X1 > product_prod @ X0 @ X1))).
% 0.48/0.40 thf(func_def_30, type, product_apfst: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1) > product_prod @ X0 @ X2 > product_prod @ X1 @ X2))).
% 0.48/0.40 thf(func_def_31, type, product_apsnd: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1) > product_prod @ X2 @ X0 > product_prod @ X2 @ X1))).
% 0.48/0.40 thf(func_def_32, type, product_case_bool: !>[X0: $tType]:((X0 > X0 > $o > X0))).
% 0.48/0.40 thf(func_def_33, type, product_curry: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X0 @ X1 > X2) > X0 > X1 > X2))).
% 0.48/0.40 thf(func_def_34, type, produc2004651681e_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 0.48/0.40 thf(func_def_35, type, product_map_prod: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((X0 > X1) > (X2 > X3) > product_prod @ X0 @ X2 > product_prod @ X1 @ X3))).
% 0.48/0.40 thf(func_def_36, type, product_rec_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 0.48/0.40 thf(func_def_37, type, product_fst: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 0.48/0.40 thf(func_def_38, type, product_snd: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1))).
% 0.48/0.40 thf(func_def_39, type, product_swap: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > product_prod @ X1 @ X0))).
% 0.48/0.40 thf(func_def_40, type, inv_image: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X0 > (X1 > X0) > set @ product_prod @ X1 @ X1))).
% 0.48/0.40 thf(func_def_41, type, inv_imagep: !>[X0: $tType, X1: $tType]:(((X0 > X0 > $o) > (X1 > X0) > X1 > X1 > $o))).
% 0.48/0.40 thf(func_def_42, type, total_on: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > $o))).
% 0.48/0.40 thf(func_def_43, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 0.48/0.40 thf(func_def_44, type, image: !>[X0: $tType, X1: $tType]:(((X0 > X1) > set @ X0 > set @ X1))).
% 0.48/0.40 thf(func_def_45, type, accp: !>[X0: $tType]:(((X0 > X0 > $o) > X0 > $o))).
% 0.48/0.40 thf(func_def_46, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.48/0.40 thf(func_def_47, type, f: (nat > nat)).
% 0.48/0.40 thf(func_def_48, type, i: (list @ char > paraco415392788lle_tv)).
% 0.48/0.40 thf(func_def_49, type, p1: paraco414474393lle_fm).
% 0.48/0.40 thf(func_def_50, type, p2: paraco414474393lle_fm).
% 0.48/0.40 thf(func_def_54, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.48/0.40 thf(func_def_55, type, db2: !>[X0: $tType]:(X0)).
% 0.48/0.40 thf(func_def_56, type, db1: !>[X0: $tType]:(X0)).
% 0.48/0.40 thf(func_def_57, type, db0: !>[X0: $tType]:(X0)).
% 0.48/0.40 thf(func_def_58, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.48/0.40 thf(func_def_59, type, db3: !>[X0: $tType]:(X0)).
% 0.48/0.40 thf(func_def_60, type, vAND: ($o > $o > $o)).
% 0.48/0.40 thf(func_def_61, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.48/0.40 thf(func_def_62, type, vIMP: ($o > $o > $o)).
% 0.48/0.40 thf(func_def_63, type, vNOT: ($o > $o)).
% 0.48/0.40 thf(func_def_64, type, vOR: ($o > $o > $o)).
% 0.48/0.40 thf(func_def_65, type, sP0: ((paraco414474393lle_fm > $o) > $o)).
% 0.48/0.40 thf(func_def_66, type, sP1: ((paraco414474393lle_fm > $o) > $o)).
% 0.48/0.40 thf(func_def_67, type, sP2: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.48/0.40 thf(func_def_68, type, sP3: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.48/0.40 thf(func_def_69, type, sP4: ((paraco414474393lle_fm > $o) > $o)).
% 0.48/0.40 thf(func_def_70, type, sP5: ((paraco414474393lle_fm > $o) > $o)).
% 0.48/0.40 thf(func_def_71, type, sK6: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 0.48/0.40 thf(func_def_72, type, sK7: !>[X0: $tType, X1: $tType]:((set @ X1 > set @ X0 > (X1 > X0) > X1))).
% 0.48/0.40 thf(func_def_73, type, sK8: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X1))).
% 0.48/0.40 thf(func_def_74, type, sK9: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X0))).
% 0.48/0.40 thf(func_def_75, type, sK10: (paraco415392788lle_tv > nat)).
% 0.48/0.40 thf(func_def_76, type, sK11: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2))).
% 0.48/0.40 thf(func_def_77, type, sK12: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0))).
% 0.48/0.40 thf(func_def_78, type, sK13: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1))).
% 0.48/0.40 thf(func_def_79, type, sK14: (product_prod @ (nat > nat) @ paraco415392788lle_tv > nat)).
% 0.48/0.40 thf(func_def_80, type, sK15: (product_prod @ (nat > nat) @ paraco415392788lle_tv > nat > nat)).
% 0.48/0.40 thf(func_def_81, type, sK16: (product_prod @ (nat > nat) @ paraco415392788lle_tv > $o)).
% 0.48/0.40 thf(func_def_82, type, sK17: (product_prod @ (nat > nat) @ paraco415392788lle_tv > nat > nat)).
% 0.48/0.40 thf(func_def_83, type, sK18: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X1 @ product_prod @ X0 @ product_prod @ X5 @ X2 > $o) > X4))).
% 0.48/0.40 thf(func_def_84, type, sK19: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X1 @ product_prod @ X0 @ product_prod @ X5 @ X2 > $o) > X0))).
% 0.48/0.40 thf(func_def_85, type, sK20: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X1 @ product_prod @ X0 @ product_prod @ X5 @ X2 > $o) > X5))).
% 0.48/0.40 thf(func_def_86, type, sK21: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X1 @ product_prod @ X0 @ product_prod @ X5 @ X2 > $o) > X3))).
% 0.48/0.40 thf(func_def_87, type, sK22: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X1 @ product_prod @ X0 @ product_prod @ X5 @ X2 > $o) > X1))).
% 0.48/0.40 thf(func_def_88, type, sK23: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X1 @ product_prod @ X0 @ product_prod @ X5 @ X2 > $o) > X2))).
% 0.48/0.40 thf(func_def_89, type, sK24: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X5 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X0 @ product_prod @ X3 @ product_prod @ X6 @ X4 > $o) > X5))).
% 0.48/0.40 thf(func_def_90, type, sK25: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X5 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X0 @ product_prod @ X3 @ product_prod @ X6 @ X4 > $o) > X0))).
% 0.48/0.40 thf(func_def_91, type, sK26: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X5 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X0 @ product_prod @ X3 @ product_prod @ X6 @ X4 > $o) > X6))).
% 0.48/0.40 thf(func_def_92, type, sK27: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X5 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X0 @ product_prod @ X3 @ product_prod @ X6 @ X4 > $o) > X4))).
% 0.48/0.40 thf(func_def_93, type, sK28: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X5 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X0 @ product_prod @ X3 @ product_prod @ X6 @ X4 > $o) > X3))).
% 0.48/0.40 thf(func_def_94, type, sK29: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X5 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X0 @ product_prod @ X3 @ product_prod @ X6 @ X4 > $o) > X1))).
% 0.48/0.40 thf(func_def_95, type, sK30: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X5 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X0 @ product_prod @ X3 @ product_prod @ X6 @ X4 > $o) > X2))).
% 0.48/0.40 thf(func_def_96, type, sK31: !>[X0: $tType, X1: $tType]:((set @ X1 > set @ X0 > (X1 > X0) > set @ X1))).
% 0.48/0.40 thf(func_def_97, type, sK32: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.48/0.40 thf(func_def_98, type, sK33: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 0.48/0.40 thf(func_def_99, type, sK34: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1))).
% 0.48/0.40 thf(func_def_100, type, sK35: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.48/0.40 thf(func_def_101, type, sK36: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.48/0.40 thf(func_def_102, type, sK37: !>[X0: $tType, X1: $tType]:((set @ X1 > (X0 > X1) > (X1 > X0) > X1))).
% 0.48/0.40 thf(func_def_103, type, sK38: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.48/0.40 thf(func_def_104, type, sK39: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.48/0.40 thf(func_def_105, type, sK40: ((paraco414474393lle_fm > $o) > paraco414474393lle_fm)).
% 0.48/0.40 thf(func_def_106, type, sK41: ((paraco414474393lle_fm > $o) > paraco414474393lle_fm)).
% 0.48/0.40 thf(func_def_107, type, sK42: ((paraco414474393lle_fm > $o) > paraco414474393lle_fm)).
% 0.48/0.40 thf(func_def_108, type, sK43: ((paraco414474393lle_fm > $o) > paraco414474393lle_fm)).
% 0.48/0.40 thf(func_def_109, type, sK44: ((paraco414474393lle_fm > $o) > list @ char)).
% 0.48/0.40 thf(func_def_110, type, sK45: ((paraco414474393lle_fm > $o) > paraco414474393lle_fm)).
% 0.48/0.40 thf(func_def_111, type, sK46: ((paraco414474393lle_fm > $o) > paraco414474393lle_fm)).
% 0.48/0.40 thf(func_def_112, type, sK47: ((paraco414474393lle_fm > $o) > paraco414474393lle_fm)).
% 0.48/0.40 thf(func_def_113, type, sK48: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X0))).
% 0.48/0.40 thf(func_def_114, type, sK49: !>[X0: $tType, X1: $tType]:((X0 > (X1 > X0) > X1))).
% 0.48/0.40 thf(func_def_115, type, sK50: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X5 @ product_prod @ X0 @ product_prod @ X1 @ X4 > X0))).
% 0.48/0.40 thf(func_def_116, type, sK51: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X5 @ product_prod @ X0 @ product_prod @ X1 @ X4 > X3))).
% 0.48/0.40 thf(func_def_117, type, sK52: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X5 @ product_prod @ X0 @ product_prod @ X1 @ X4 > X2))).
% 0.48/0.40 thf(func_def_118, type, sK53: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X5 @ product_prod @ X0 @ product_prod @ X1 @ X4 > X1))).
% 0.48/0.40 thf(func_def_119, type, sK54: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X5 @ product_prod @ X0 @ product_prod @ X1 @ X4 > X5))).
% 0.48/0.40 thf(func_def_120, type, sK55: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X5 @ product_prod @ X0 @ product_prod @ X1 @ X4 > X4))).
% 0.48/0.40 thf(func_def_121, type, sK56: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X0 > X1) > X0))).
% 0.48/0.40 thf(func_def_122, type, sK57: !>[X0: $tType, X1: $tType]:((set @ X0 > (X0 > X1) > (X1 > $o) > X1))).
% 0.48/0.40 thf(func_def_123, type, sK58: !>[X0: $tType, X1: $tType]:((set @ X0 > (X0 > X1) > (X0 > X0) > X0))).
% 0.48/0.40 thf(func_def_124, type, sK59: !>[X0: $tType, X1: $tType]:((set @ X0 > (X0 > X1) > (X0 > X0) > X0))).
% 0.48/0.40 thf(func_def_125, type, sK60: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.48/0.40 thf(func_def_126, type, sK61: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X1 @ product_prod @ X0 @ product_prod @ X3 @ product_prod @ X2 @ X4 > $o) > X4))).
% 0.48/0.40 thf(func_def_127, type, sK62: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X1 @ product_prod @ X0 @ product_prod @ X3 @ product_prod @ X2 @ X4 > $o) > X2))).
% 0.48/0.40 thf(func_def_128, type, sK63: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X1 @ product_prod @ X0 @ product_prod @ X3 @ product_prod @ X2 @ X4 > $o) > X1))).
% 0.48/0.40 thf(func_def_129, type, sK64: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X1 @ product_prod @ X0 @ product_prod @ X3 @ product_prod @ X2 @ X4 > $o) > X3))).
% 0.48/0.40 thf(func_def_130, type, sK65: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X1 @ product_prod @ X0 @ product_prod @ X3 @ product_prod @ X2 @ X4 > $o) > X0))).
% 0.48/0.40 thf(func_def_131, type, sK66: !>[X0: $tType, X1: $tType]:((X0 > (X1 > X0) > X1))).
% 0.48/0.40 thf(func_def_132, type, sK67: ((paraco415392788lle_tv > $o) > nat)).
% 0.48/0.40 thf(func_def_133, type, sK68: ((paraco415392788lle_tv > $o) > $o)).
% 0.48/0.40 thf(func_def_134, type, sK69: !>[X0: $tType, X1: $tType]:(((X0 > X1) > set @ X0 > X1 > X0))).
% 0.48/0.40 thf(func_def_135, type, sK70: (paraco414474393lle_fm > paraco414474393lle_fm)).
% 0.48/0.40 thf(func_def_136, type, sK71: (paraco414474393lle_fm > paraco414474393lle_fm)).
% 0.48/0.40 thf(func_def_137, type, sK72: (paraco414474393lle_fm > paraco414474393lle_fm)).
% 0.48/0.40 thf(func_def_138, type, sK73: (paraco414474393lle_fm > paraco414474393lle_fm)).
% 0.48/0.40 thf(func_def_139, type, sK74: (paraco414474393lle_fm > paraco414474393lle_fm)).
% 0.48/0.40 thf(func_def_140, type, sK75: (paraco414474393lle_fm > paraco414474393lle_fm)).
% 0.48/0.40 thf(func_def_141, type, sK76: (paraco414474393lle_fm > list @ char)).
% 0.48/0.40 thf(func_def_142, type, sK77: (paraco414474393lle_fm > paraco414474393lle_fm)).
% 0.48/0.40 thf(func_def_143, type, sK78: !>[X0: $tType, X1: $tType]:((set @ X0 > (X0 > X1) > set @ X1 > set @ X0))).
% 0.48/0.40 thf(func_def_144, type, sK79: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X0))).
% 0.48/0.40 thf(func_def_145, type, sK80: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X1))).
% 0.48/0.40 thf(func_def_146, type, sK81: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X2 @ product_prod @ X0 @ product_prod @ X3 @ X1 > X0))).
% 0.48/0.40 thf(func_def_147, type, sK82: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X2 @ product_prod @ X0 @ product_prod @ X3 @ X1 > X2))).
% 0.48/0.40 thf(func_def_148, type, sK83: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X2 @ product_prod @ X0 @ product_prod @ X3 @ X1 > X3))).
% 0.48/0.40 thf(func_def_149, type, sK84: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X2 @ product_prod @ X0 @ product_prod @ X3 @ X1 > X1))).
% 0.48/0.40 thf(func_def_150, type, sK85: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.48/0.40 thf(func_def_151, type, sK86: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X2 @ product_prod @ X0 @ product_prod @ X1 @ X3 > X1))).
% 0.48/0.40 thf(func_def_152, type, sK87: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X2 @ product_prod @ X0 @ product_prod @ X1 @ X3 > X4))).
% 0.48/0.40 thf(func_def_153, type, sK88: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X2 @ product_prod @ X0 @ product_prod @ X1 @ X3 > X3))).
% 0.48/0.40 thf(func_def_154, type, sK89: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X2 @ product_prod @ X0 @ product_prod @ X1 @ X3 > X2))).
% 0.48/0.40 thf(func_def_155, type, sK90: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X2 @ product_prod @ X0 @ product_prod @ X1 @ X3 > X0))).
% 0.48/0.40 thf(func_def_156, type, sK91: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X1 @ X2 > X0))).
% 0.48/0.40 thf(func_def_157, type, sK92: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X1 @ X2 > X2))).
% 0.48/0.40 thf(func_def_158, type, sK93: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X1 @ X2 > X1))).
% 0.48/0.40 thf(func_def_159, type, sK94: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > (X1 > X0) > X1))).
% 0.48/0.40 thf(func_def_160, type, sK95: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.48/0.40 thf(func_def_161, type, sK96: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.48/0.40 thf(func_def_162, type, sK97: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X1))).
% 0.48/0.40 thf(func_def_163, type, sK98: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X1))).
% 0.48/0.40 thf(func_def_164, type, sK99: (paraco415392788lle_tv > $o)).
% 0.48/0.40 thf(func_def_165, type, sK100: (paraco415392788lle_tv > nat)).
% 0.48/0.40 thf(func_def_166, type, sK101: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((set @ product_prod @ X0 @ X1 > product_prod @ X3 @ X2 > (X1 > X2) > (X0 > X3) > X0))).
% 0.48/0.40 thf(func_def_167, type, sK102: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((set @ product_prod @ X0 @ X1 > product_prod @ X3 @ X2 > (X1 > X2) > (X0 > X3) > X1))).
% 0.48/0.40 thf(func_def_168, type, sK103: ((paraco415392788lle_tv > $o) > nat)).
% 0.48/0.40 thf(func_def_169, type, sK104: !>[X0: $tType, X1: $tType]:((set @ X0 > set @ X1 > (X0 > X1) > set @ X0))).
% 0.48/0.40 thf(func_def_170, type, sK105: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > set @ product_prod @ X1 @ X0 > X1))).
% 0.48/0.40 thf(func_def_171, type, sK106: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > set @ product_prod @ X1 @ X0 > X0))).
% 0.48/0.40 thf(func_def_172, type, sK107: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 0.48/0.40 thf(func_def_173, type, sK108: !>[X0: $tType]:((set @ X0 > set @ product_prod @ X0 @ X0 > X0))).
% 0.48/0.40 thf(func_def_174, type, sK109: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X1 > X0))).
% 0.48/0.40 thf(func_def_175, type, sK110: !>[X0: $tType, X1: $tType]:(((X0 > $o) > set @ X1 > (X1 > X0) > X1))).
% 0.48/0.40 thf(func_def_176, type, sK111: !>[X0: $tType, X1: $tType]:(((X1 > X0) > set @ X1 > set @ X0 > X1))).
% 0.48/0.40 thf(func_def_177, type, sK112: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.48/0.40 thf(func_def_178, type, sK113: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.48/0.40 thf(func_def_179, type, sK114: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.48/0.40 thf(func_def_180, type, sK115: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.48/0.40 thf(func_def_181, type, sK116: !>[X0: $tType]:((set @ X0 > X0))).
% 0.48/0.40 thf(func_def_182, type, sK117: (paraco415392788lle_tv > paraco415392788lle_tv > (nat > nat) > nat)).
% 0.48/0.40 thf(func_def_183, type, sK118: (paraco415392788lle_tv > paraco415392788lle_tv > (nat > nat) > $o)).
% 0.48/0.40 thf(func_def_184, type, sK119: (product_prod @ (list @ char > paraco415392788lle_tv) @ paraco414474393lle_fm > paraco414474393lle_fm)).
% 0.48/0.40 thf(func_def_185, type, sK120: (product_prod @ (list @ char > paraco415392788lle_tv) @ paraco414474393lle_fm > paraco414474393lle_fm)).
% 0.48/0.40 thf(func_def_186, type, sK121: (product_prod @ (list @ char > paraco415392788lle_tv) @ paraco414474393lle_fm > list @ char > paraco415392788lle_tv)).
% 0.48/0.40 thf(func_def_187, type, sK122: (product_prod @ (list @ char > paraco415392788lle_tv) @ paraco414474393lle_fm > paraco414474393lle_fm)).
% 0.48/0.40 thf(func_def_188, type, sK123: (product_prod @ (list @ char > paraco415392788lle_tv) @ paraco414474393lle_fm > paraco414474393lle_fm)).
% 0.48/0.40 thf(func_def_189, type, sK124: (product_prod @ (list @ char > paraco415392788lle_tv) @ paraco414474393lle_fm > list @ char > paraco415392788lle_tv)).
% 0.48/0.40 thf(func_def_190, type, sK125: (product_prod @ (list @ char > paraco415392788lle_tv) @ paraco414474393lle_fm > list @ char > paraco415392788lle_tv)).
% 0.48/0.40 thf(func_def_191, type, sK126: (product_prod @ (list @ char > paraco415392788lle_tv) @ paraco414474393lle_fm > list @ char > paraco415392788lle_tv)).
% 0.48/0.40 thf(func_def_192, type, sK127: (product_prod @ (list @ char > paraco415392788lle_tv) @ paraco414474393lle_fm > list @ char)).
% 0.48/0.40 thf(func_def_193, type, sK128: (product_prod @ (list @ char > paraco415392788lle_tv) @ paraco414474393lle_fm > paraco414474393lle_fm)).
% 0.48/0.40 thf(func_def_194, type, sK129: (product_prod @ (list @ char > paraco415392788lle_tv) @ paraco414474393lle_fm > paraco414474393lle_fm)).
% 0.48/0.40 thf(func_def_195, type, sK130: (product_prod @ (list @ char > paraco415392788lle_tv) @ paraco414474393lle_fm > list @ char > paraco415392788lle_tv)).
% 0.48/0.40 thf(func_def_196, type, sK131: (product_prod @ (list @ char > paraco415392788lle_tv) @ paraco414474393lle_fm > paraco414474393lle_fm)).
% 0.48/0.40 thf(func_def_197, type, sK132: (product_prod @ (list @ char > paraco415392788lle_tv) @ paraco414474393lle_fm > list @ char > paraco415392788lle_tv)).
% 0.48/0.40 thf(func_def_198, type, sK133: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 0.48/0.40 thf(func_def_199, type, sK134: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1))).
% 0.48/0.40 thf(func_def_200, type, sK135: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.48/0.40 thf(func_def_201, type, sK136: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.48/0.40 thf(func_def_202, type, sK137: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.48/0.40 thf(func_def_203, type, sK138: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.48/0.40 thf(func_def_204, type, sK139: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X1 @ product_prod @ X3 @ product_prod @ X2 @ X0 > $o) > X3))).
% 0.48/0.40 thf(func_def_205, type, sK140: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X1 @ product_prod @ X3 @ product_prod @ X2 @ X0 > $o) > X0))).
% 0.48/0.40 thf(func_def_206, type, sK141: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X1 @ product_prod @ X3 @ product_prod @ X2 @ X0 > $o) > X2))).
% 0.48/0.41 thf(func_def_207, type, sK142: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X1 @ product_prod @ X3 @ product_prod @ X2 @ X0 > $o) > X1))).
% 0.48/0.41 thf(func_def_208, type, sK143: (((nat > nat) > paraco415392788lle_tv > $o) > nat > nat)).
% 0.48/0.41 thf(func_def_209, type, sK144: (((nat > nat) > paraco415392788lle_tv > $o) > nat)).
% 0.48/0.41 thf(func_def_210, type, sK145: (((nat > nat) > paraco415392788lle_tv > $o) > nat > nat)).
% 0.48/0.41 thf(func_def_211, type, sK146: (((nat > nat) > paraco415392788lle_tv > $o) > $o)).
% 0.48/0.41 thf(func_def_212, type, sK147: (paraco415392788lle_tv > paraco415392788lle_tv > $o)).
% 0.48/0.41 thf(func_def_213, type, sK148: (paraco415392788lle_tv > paraco415392788lle_tv > (nat > nat) > nat)).
% 0.48/0.41 thf(func_def_214, type, sK149: !>[X0: $tType, X1: $tType]:((X0 > (X1 > X0) > X1))).
% 0.48/0.41 thf(func_def_215, type, sK150: !>[X0: $tType, X1: $tType]:((X1 > X0 > (X1 > X0) > X1))).
% 0.48/0.41 thf(func_def_216, type, sK151: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.48/0.41 thf(func_def_217, type, sK152: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.48/0.41 thf(func_def_218, type, sK153: ((paraco414474393lle_fm > $o) > paraco414474393lle_fm)).
% 0.48/0.41 thf(func_def_219, type, sK154: ((paraco414474393lle_fm > $o) > paraco414474393lle_fm)).
% 0.48/0.41 thf(func_def_220, type, sK155: ((paraco414474393lle_fm > $o) > paraco414474393lle_fm)).
% 0.48/0.41 thf(func_def_221, type, sK156: ((paraco414474393lle_fm > $o) > paraco414474393lle_fm)).
% 0.48/0.41 thf(func_def_222, type, sK157: ((paraco414474393lle_fm > $o) > paraco414474393lle_fm)).
% 0.48/0.41 thf(func_def_223, type, sK158: ((paraco414474393lle_fm > $o) > paraco414474393lle_fm)).
% 0.48/0.41 thf(func_def_224, type, sK159: ((paraco414474393lle_fm > $o) > list @ char)).
% 0.48/0.41 thf(func_def_225, type, sK160: ((paraco414474393lle_fm > $o) > paraco414474393lle_fm)).
% 0.48/0.41 thf(func_def_226, type, sK161: !>[X0: $tType]:(X0)).
% 0.48/0.41 thf(func_def_227, type, sK162: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.48/0.41 thf(func_def_228, type, sK163: !>[X0: $tType, X1: $tType]:(((X1 > X0) > set @ X1 > (X1 > X0) > X1))).
% 0.48/0.41 thf(func_def_229, type, sK164: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X0 @ X1 > X6))).
% 0.48/0.41 thf(func_def_230, type, sK165: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X0 @ X1 > X2))).
% 0.48/0.41 thf(func_def_231, type, sK166: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X0 @ X1 > X4))).
% 0.48/0.41 thf(func_def_232, type, sK167: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X0 @ X1 > X0))).
% 0.48/0.41 thf(func_def_233, type, sK168: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X0 @ X1 > X1))).
% 0.48/0.41 thf(func_def_234, type, sK169: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X0 @ X1 > X3))).
% 0.48/0.41 thf(func_def_235, type, sK170: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X0 @ X1 > X5))).
% 0.48/0.41 thf(func_def_236, type, sK171: (paraco414474393lle_fm > paraco414474393lle_fm)).
% 0.48/0.41 thf(func_def_237, type, sK172: (paraco414474393lle_fm > paraco414474393lle_fm)).
% 0.48/0.41 thf(func_def_238, type, sK173: (paraco414474393lle_fm > list @ char)).
% 0.48/0.41 thf(func_def_239, type, sK174: (paraco414474393lle_fm > paraco414474393lle_fm)).
% 0.48/0.41 thf(func_def_240, type, sK175: (paraco414474393lle_fm > paraco414474393lle_fm)).
% 0.48/0.41 thf(func_def_241, type, sK176: (paraco414474393lle_fm > paraco414474393lle_fm)).
% 0.48/0.41 thf(func_def_242, type, sK177: (paraco414474393lle_fm > paraco414474393lle_fm)).
% 0.48/0.41 thf(func_def_243, type, sK178: (paraco414474393lle_fm > paraco414474393lle_fm)).
% 0.48/0.41 thf(func_def_244, type, sK179: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > X1) > X0))).
% 0.48/0.41 thf(f2,axiom,(
% 0.48/0.41 (((paraco2040174112le_Det @ $true)) = ((paraco1920534163nge_tv @ f @ (paraco876059933e_eval @ i @ p2))))),
% 0.48/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__092_060open_062change__tv_Af_A_Ieval_Ai_Ap2_J_A_061_ADet_ATrue_092_060close_062)).
% 0.48/0.41 thf(f3,axiom,(
% 0.48/0.41 (((paraco876059933e_eval @ (paraco753463838ge_int @ f @ i) @ p2)) = ((paraco1920534163nge_tv @ f @ (paraco876059933e_eval @ i @ p2))))),
% 0.48/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_ih2)).
% 0.48/0.41 thf(f280,conjecture,(
% 0.48/0.41 (((paraco2040174112le_Det @ $true)) = ((paraco876059933e_eval @ (paraco753463838ge_int @ f @ i) @ p2)))),
% 0.48/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 0.48/0.41 thf(f281,negated_conjecture,(
% 0.48/0.41 ~ (((paraco2040174112le_Det @ $true)) = ((paraco876059933e_eval @ (paraco753463838ge_int @ f @ i) @ p2)))),
% 0.48/0.41 inference(negated_conjecture,[status(cth)],[f280])).
% 0.48/0.41 thf(f551,plain,(
% 0.48/0.41 ~ (((paraco2040174112le_Det @ $true)) = ((paraco876059933e_eval @ (paraco753463838ge_int @ f @ i) @ p2)))),
% 0.48/0.41 inference(rectify,[],[f281])).
% 0.48/0.41 thf(f552,plain,(
% 0.48/0.41 ~ (((paraco876059933e_eval @ (paraco753463838ge_int @ f @ i) @ p2)) = ((paraco2040174112le_Det @ $true)))),
% 0.48/0.41 inference(fool_elimination,[],[f551])).
% 0.48/0.41 thf(f625,plain,(
% 0.48/0.41 (((paraco2040174112le_Det @ $true)) = ((paraco1920534163nge_tv @ f @ (paraco876059933e_eval @ i @ p2))))),
% 0.48/0.41 inference(rectify,[],[f2])).
% 0.48/0.41 thf(f626,plain,(
% 0.48/0.41 (((paraco1920534163nge_tv @ f @ (paraco876059933e_eval @ i @ p2))) = ((paraco2040174112le_Det @ $true)))),
% 0.48/0.41 inference(fool_elimination,[],[f625])).
% 0.48/0.41 thf(f710,plain,(
% 0.48/0.41 (((paraco876059933e_eval @ (paraco753463838ge_int @ f @ i) @ p2)) != ((paraco2040174112le_Det @ $true)))),
% 0.48/0.41 inference(flattening,[],[f552])).
% 0.48/0.41 thf(f1256,plain,(
% 0.48/0.41 (((paraco876059933e_eval @ (paraco753463838ge_int @ f @ i) @ p2)) != ((paraco2040174112le_Det @ $true)))),
% 0.48/0.41 inference(cnf_transformation,[],[f710])).
% 0.48/0.41 thf(f1461,plain,(
% 0.48/0.41 (((paraco1920534163nge_tv @ f @ (paraco876059933e_eval @ i @ p2))) = ((paraco876059933e_eval @ (paraco753463838ge_int @ f @ i) @ p2)))),
% 0.48/0.41 inference(cnf_transformation,[],[f3])).
% 0.48/0.41 thf(f1479,plain,(
% 0.48/0.41 (((paraco1920534163nge_tv @ f @ (paraco876059933e_eval @ i @ p2))) = ((paraco2040174112le_Det @ $true)))),
% 0.48/0.41 inference(cnf_transformation,[],[f626])).
% 0.48/0.41 thf(f1795,definition,(
% 0.48/0.41 spl180_1 <=> (((paraco876059933e_eval @ (paraco753463838ge_int @ f @ i) @ p2)) = ((paraco2040174112le_Det @ $true)))),
% 0.48/0.41 introduced(definition,[new_symbols(definition,[spl180_1])],[avatar_definition])).
% 0.48/0.41 thf(f1798,plain,(
% 0.48/0.41 ~spl180_1),
% 0.48/0.41 inference(avatar_split_clause,[],[f1256,f1795])).
% 0.48/0.41 thf(f1805,definition,(
% 0.48/0.41 spl180_3 <=> (((paraco1920534163nge_tv @ f @ (paraco876059933e_eval @ i @ p2))) = ((paraco876059933e_eval @ (paraco753463838ge_int @ f @ i) @ p2)))),
% 0.48/0.41 introduced(definition,[new_symbols(definition,[spl180_3])],[avatar_definition])).
% 0.48/0.41 thf(f1808,plain,(
% 0.48/0.41 spl180_3),
% 0.48/0.41 inference(avatar_split_clause,[],[f1461,f1805])).
% 0.48/0.41 thf(f1825,definition,(
% 0.48/0.41 spl180_7 <=> (((paraco1920534163nge_tv @ f @ (paraco876059933e_eval @ i @ p2))) = ((paraco2040174112le_Det @ $true)))),
% 0.48/0.41 introduced(definition,[new_symbols(definition,[spl180_7])],[avatar_definition])).
% 0.48/0.41 thf(f1828,plain,(
% 0.48/0.41 spl180_7),
% 0.48/0.41 inference(avatar_split_clause,[],[f1479,f1825])).
% 0.48/0.41 thf(f1904,definition,(
% 0.48/0.41 (((paraco1920534163nge_tv @ f @ (paraco876059933e_eval @ i @ p2))) != ((paraco2040174112le_Det @ $true))) | (((paraco1920534163nge_tv @ f @ (paraco876059933e_eval @ i @ p2))) != ((paraco876059933e_eval @ (paraco753463838ge_int @ f @ i) @ p2))) | (((paraco876059933e_eval @ (paraco753463838ge_int @ f @ i) @ p2)) = ((paraco2040174112le_Det @ $true)))),
% 0.48/0.41 introduced(theory,[theory_tautology_sat_conflict])).
% 0.48/0.41 cnf(s1, plain, ~spl180_1, inference(sat_conversion,[],[f1798])).
% 0.48/0.41 cnf(s3, plain, spl180_3, inference(sat_conversion,[],[f1808])).
% 0.48/0.41 cnf(s7, plain, spl180_7, inference(sat_conversion,[],[f1828])).
% 0.48/0.41 cnf(s23, plain, spl180_1 | ~spl180_3 | ~spl180_7, inference(sat_conversion,[],[f1904])).
% 0.48/0.41 cnf(s24, plain, spl180_1, inference(rat,[],[s23,s7,s3])).
% 0.48/0.41 cnf(s25, plain, $false, inference(rat,[],[s1,s24])).
% 0.48/0.41 thf(f1905,plain,(
% 0.48/0.41 $false),
% 0.48/0.41 inference(avatar_sat_refutation,[],[s25])).
% 0.48/0.41 % SZS output end Proof for theBenchmark
% 0.48/0.41 % (1274824)------------------------------
% 0.48/0.41 % (1274824)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.48/0.41 % (1274824)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.48/0.41 % (1274824)CaDiCaL version: 2.1.3
% 0.48/0.41 % (1274824)Termination reason: Refutation
% 0.48/0.41 % (1274824)Time elapsed: 0.068 s
% 0.48/0.41 % (1274824)Peak memory usage: 14 MB
% 0.48/0.41 % (1274824)Instructions burned: 132 (million)
% 0.48/0.41 % (1274809)Success in time 0.125 s
% 0.48/0.41 % Vampire exiting
%------------------------------------------------------------------------------