%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COM206^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 07:46:27 AM UTC 2026
% Result : Theorem 0.66s 0.38s
% Output : Refutation 0.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COM206^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 % Computer : n008.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Sep 29 17:52:54 UTC 2026
% 0.07/0.17 % CPUTime :
% 0.07/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 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
% 0.66/0.38 % (3501985)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.66/0.38 % (3501996)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.66/0.38 % (3501996)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
% 0.66/0.38 % (3501990)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3985172756:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.66/0.38 % (3501991)lrs+10_16_si=on:nwc=1.5:random_seed=628517469:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.66/0.38 % (3501992)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=379434485:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.66/0.38 % (3501993)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=1422082128: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)
% 0.66/0.38 % (3501994)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2685449775:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.66/0.38 % (3501995)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=629910877:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.66/0.38 % (3501996)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=1803723982:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.66/0.38 % (3501992)Instruction limit reached!
% 0.66/0.38 % (3501992)------------------------------
% 0.66/0.38 % (3501992)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.38 % (3501992)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.38 % (3501992)CaDiCaL version: 2.1.3
% 0.66/0.38 % (3501992)Termination reason: Instruction limit
% 0.66/0.38 % (3501992)Termination phase: shuffling
% 0.66/0.38 % (3501992)Time elapsed: 0.002 s
% 0.66/0.38 % (3501992)Peak memory usage: 10 MB
% 0.66/0.38 % (3501992)Instructions burned: 3 (million)
% 0.66/0.38 % (3501991)Instruction limit reached!
% 0.66/0.38 % (3501991)------------------------------
% 0.66/0.38 % (3501991)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.38 % (3501991)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.38 % (3501991)CaDiCaL version: 2.1.3
% 0.66/0.38 % (3501991)Termination reason: Instruction limit
% 0.66/0.38 % (3501991)Termination phase: Property scanning
% 0.66/0.38 % (3501991)Time elapsed: 0.009 s
% 0.66/0.38 % (3501991)Peak memory usage: 10 MB
% 0.66/0.38 % (3501991)Instructions burned: 19 (million)
% 0.66/0.38 % (3501994)Instruction limit reached!
% 0.66/0.38 % (3501994)------------------------------
% 0.66/0.38 % (3501994)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.38 % (3501994)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.38 % (3501994)CaDiCaL version: 2.1.3
% 0.66/0.38 % (3501994)Termination reason: Instruction limit
% 0.66/0.38 % (3501994)Termination phase: Property scanning
% 0.66/0.38 % (3501994)Time elapsed: 0.012 s
% 0.66/0.38 % (3501994)Peak memory usage: 10 MB
% 0.66/0.38 % (3501994)Instructions burned: 24 (million)
% 0.66/0.38 % (3502004)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3155691879:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.66/0.38 % (3502004)Instruction limit reached!
% 0.66/0.38 % (3502004)------------------------------
% 0.66/0.38 % (3502004)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.38 % (3502004)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.38 % (3502004)CaDiCaL version: 2.1.3
% 0.66/0.38 % (3502004)Termination reason: Instruction limit
% 0.66/0.38 % (3502004)Termination phase: shuffling
% 0.66/0.38 % (3502004)Time elapsed: 0.002 s
% 0.66/0.38 % (3502004)Peak memory usage: 10 MB
% 0.66/0.38 % (3502004)Instructions burned: 3 (million)
% 0.66/0.38 % (3502005)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2574533179:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.66/0.38 % (3502006)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.66/0.38 % (3502005)Instruction limit reached!
% 0.66/0.38 % (3502005)------------------------------
% 0.66/0.38 % (3502005)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.38 % (3502005)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.38 % (3502005)CaDiCaL version: 2.1.3
% 0.66/0.38 % (3502005)Termination reason: Instruction limit
% 0.66/0.38 % (3502005)Termination phase: shuffling
% 0.66/0.38 % (3502005)Time elapsed: 0.003 s
% 0.66/0.38 % (3502005)Peak memory usage: 10 MB
% 0.66/0.38 % (3502005)Instructions burned: 5 (million)
% 0.66/0.38 % (3502006)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1360028159:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.66/0.38 % (3502008)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2549374899:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.66/0.38 % (3502006)Instruction limit reached!
% 0.66/0.38 % (3502006)------------------------------
% 0.66/0.38 % (3502006)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.38 % (3502006)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.38 % (3502006)CaDiCaL version: 2.1.3
% 0.66/0.38 % (3502006)Termination reason: Instruction limit
% 0.66/0.38 % (3502006)Termination phase: shuffling
% 0.66/0.38 % (3502006)Time elapsed: 0.004 s
% 0.66/0.38 % (3502006)Peak memory usage: 10 MB
% 0.66/0.38 % (3502006)Instructions burned: 8 (million)
% 0.66/0.38 % (3501995)Instruction limit reached!
% 0.66/0.38 % (3501995)------------------------------
% 0.66/0.38 % (3501995)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.38 % (3501995)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.38 % (3501995)CaDiCaL version: 2.1.3
% 0.66/0.38 % (3501995)Termination reason: Instruction limit
% 0.66/0.38 % (3501995)Termination phase: Function definition elimination
% 0.66/0.38 % (3501995)Time elapsed: 0.037 s
% 0.66/0.38 % (3501995)Peak memory usage: 12 MB
% 0.66/0.38 % (3501995)Instructions burned: 75 (million)
% 0.66/0.38 % (3502008)Instruction limit reached!
% 0.66/0.38 % (3502008)------------------------------
% 0.66/0.38 % (3502008)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.38 % (3502008)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.38 % (3502008)CaDiCaL version: 2.1.3
% 0.66/0.38 % (3502008)Termination reason: Instruction limit
% 0.66/0.38 % (3502008)Termination phase: Property scanning
% 0.66/0.38 % (3502008)Time elapsed: 0.004 s
% 0.66/0.38 % (3502008)Peak memory usage: 11 MB
% 0.66/0.38 % (3502008)Instructions burned: 15 (million)
% 0.66/0.38 % (3501990)Instruction limit reached!
% 0.66/0.38 % (3501990)------------------------------
% 0.66/0.38 % (3501990)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.38 % (3501990)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.38 % (3501990)CaDiCaL version: 2.1.3
% 0.66/0.38 % (3501990)Termination reason: Instruction limit
% 0.66/0.38 % (3501990)Termination phase: Property scanning
% 0.66/0.38 % (3501990)Time elapsed: 0.043 s
% 0.66/0.38 % (3501990)Peak memory usage: 12 MB
% 0.66/0.38 % (3501990)Instructions burned: 89 (million)
% 0.66/0.38 % (3502011)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
% 0.66/0.38 % (3502011)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.66/0.38 % (3502015)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.66/0.38 % (3502011)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3061895606:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.66/0.38 % (3502015)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=345131117:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.66/0.38 % (3502015)Instruction limit reached!
% 0.66/0.38 % (3502015)------------------------------
% 0.66/0.38 % (3502015)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.38 % (3502015)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.38 % (3502015)CaDiCaL version: 2.1.3
% 0.66/0.38 % (3502015)Termination reason: Instruction limit
% 0.66/0.38 % (3502015)Termination phase: shuffling
% 0.66/0.38 % (3502015)Time elapsed: 0.001 s
% 0.66/0.38 % (3502015)Peak memory usage: 10 MB
% 0.66/0.38 % (3502015)Instructions burned: 4 (million)
% 0.66/0.38 % (3502013)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=213613865:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.66/0.38 % (3502014)lrs+10_1_si=on:cs=on:random_seed=1226285151:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.66/0.38 % (3502016)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=1191216963:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.66/0.38 % (3501993) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3501985-3501993"...
% 0.66/0.38 % (3502014)Instruction limit reached!
% 0.66/0.38 % (3502014)------------------------------
% 0.66/0.38 % (3502014)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.38 % (3502014)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.38 % (3502014)CaDiCaL version: 2.1.3
% 0.66/0.38 % (3502014)Termination reason: Instruction limit
% 0.66/0.38 % (3502014)Termination phase: shuffling
% 0.66/0.38 % (3502014)Time elapsed: 0.005 s
% 0.66/0.38 % (3502014)Peak memory usage: 10 MB
% 0.66/0.38 % (3502014)Instructions burned: 9 (million)
% 0.66/0.38 % (3502019)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=109475875:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.66/0.38 % (3502011)Instruction limit reached!
% 0.66/0.38 % (3502011)------------------------------
% 0.66/0.38 % (3502011)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.38 % (3502011)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.38 % (3502011)CaDiCaL version: 2.1.3
% 0.66/0.38 % (3502011)Termination reason: Instruction limit
% 0.66/0.38 % (3502011)Termination phase: shuffling
% 0.66/0.38 % (3502011)Time elapsed: 0.013 s
% 0.66/0.38 % (3502011)Peak memory usage: 11 MB
% 0.66/0.38 % (3502011)Instructions burned: 28 (million)
% 0.66/0.38 % (3501993)...printing done.
% 0.66/0.38 % (3501993)Refutation found. Thanks to Tanya!
% 0.66/0.38 % SZS status Theorem for theBenchmark
% 0.66/0.38 % SZS output start Proof for theBenchmark
% 0.66/0.38 thf(type_def_5, type, product_prod: ($tType * $tType) > $tType).
% 0.66/0.38 thf(type_def_6, type, sum_sum: ($tType * $tType) > $tType).
% 0.66/0.38 thf(type_def_7, type, dtree: $tType).
% 0.66/0.38 thf(type_def_8, type, set: $tType > $tType).
% 0.66/0.38 thf(type_def_9, type, t: $tType).
% 0.66/0.38 thf(type_def_10, type, itself: $tType > $tType).
% 0.66/0.38 thf(type_def_11, type, sTfun: ($tType * $tType) > $tType).
% 0.66/0.38 thf(func_def_0, type, bounded_lattice: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.66/0.38 thf(func_def_1, type, type: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.66/0.38 thf(func_def_2, type, lattice: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.66/0.38 thf(func_def_3, type, distrib_lattice: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.66/0.38 thf(func_def_4, type, semilattice_inf: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.66/0.38 thf(func_def_5, type, semilattice_sup: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.66/0.38 thf(func_def_6, type, bounded_lattice_top: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.66/0.38 thf(func_def_7, type, bounde1561333602nf_top: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.66/0.38 thf(func_def_8, type, bNF_Greatest_image2: !>[X0: $tType, X1: $tType, X2: $tType]:((set @ X0 > (X0 > X1) > (X0 > X2) > set @ product_prod @ X1 @ X2))).
% 0.66/0.38 thf(func_def_9, type, cont: (dtree > set @ sum_sum @ t @ dtree)).
% 0.66/0.38 thf(func_def_10, type, comp: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1) > (X2 > X0) > X2 > X1))).
% 0.66/0.38 thf(func_def_11, type, if: !>[X0: $tType]:(($o > X0 > X0 > X0))).
% 0.66/0.38 thf(func_def_12, type, inf_inf: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.66/0.38 thf(func_def_13, type, sup_sup: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.66/0.38 thf(func_def_14, type, top_top: !>[X0: $tType]:(X0)).
% 0.66/0.38 thf(func_def_15, type, parall1899940088le_par: (product_prod @ dtree @ dtree > dtree)).
% 0.66/0.38 thf(func_def_16, type, product_Pair: !>[X0: $tType, X1: $tType]:((X0 > X1 > product_prod @ X0 @ X1))).
% 0.66/0.38 thf(func_def_17, type, product_curry: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X0 @ X1 > X2) > X0 > X1 > X2))).
% 0.66/0.38 thf(func_def_18, type, produc2004651681e_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 0.66/0.38 thf(func_def_19, type, product_map_prod: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((X0 > X1) > (X2 > X3) > product_prod @ X0 @ X2 > product_prod @ X1 @ X3))).
% 0.66/0.38 thf(func_def_20, type, product_rec_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 0.66/0.38 thf(func_def_21, type, product_case_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 0.66/0.38 thf(func_def_22, type, product_swap: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > product_prod @ X1 @ X0))).
% 0.66/0.38 thf(func_def_23, type, product_scomp: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((X0 > product_prod @ X1 @ X2) > (X1 > X2 > X3) > X0 > X3))).
% 0.66/0.38 thf(func_def_24, type, type2: !>[X0: $tType]:(itself @ X0)).
% 0.66/0.38 thf(func_def_25, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 0.66/0.38 thf(func_def_26, type, image: !>[X0: $tType, X1: $tType]:(((X0 > X1) > set @ X0 > set @ X1))).
% 0.66/0.38 thf(func_def_27, type, vimage: !>[X0: $tType, X1: $tType]:(((X0 > X1) > set @ X1 > set @ X0))).
% 0.66/0.38 thf(func_def_28, type, sum_Inl: !>[X0: $tType, X1: $tType]:((X0 > sum_sum @ X0 @ X1))).
% 0.66/0.38 thf(func_def_29, type, sum_Inr: !>[X0: $tType, X1: $tType]:((X0 > sum_sum @ X1 @ X0))).
% 0.66/0.38 thf(func_def_30, type, sum_Plus: !>[X0: $tType, X1: $tType]:((set @ X0 > set @ X1 > set @ sum_sum @ X0 @ X1))).
% 0.66/0.38 thf(func_def_31, type, sum_Suml: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1) > sum_sum @ X0 @ X2 > X1))).
% 0.66/0.38 thf(func_def_32, type, sum_Sumr: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1) > sum_sum @ X2 @ X0 > X1))).
% 0.66/0.38 thf(func_def_33, type, sum_rec_sum: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1) > (X2 > X1) > sum_sum @ X0 @ X2 > X1))).
% 0.66/0.38 thf(func_def_34, type, sum_case_sum: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1) > (X2 > X1) > sum_sum @ X0 @ X2 > X1))).
% 0.66/0.38 thf(func_def_35, type, type_definition: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X1 > X0) > set @ X1 > $o))).
% 0.66/0.38 thf(func_def_36, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.66/0.38 thf(func_def_37, type, tr1: dtree).
% 0.66/0.38 thf(func_def_38, type, tr1a: dtree).
% 0.66/0.38 thf(func_def_39, type, tr2: dtree).
% 0.66/0.38 thf(func_def_40, type, tr2a: dtree).
% 0.66/0.38 thf(func_def_41, type, trA: dtree).
% 0.66/0.38 thf(func_def_42, type, trA2: dtree).
% 0.66/0.38 thf(func_def_43, type, trB: dtree).
% 0.66/0.38 thf(func_def_47, type, db0: !>[X0: $tType]:(X0)).
% 0.66/0.38 thf(func_def_48, type, db1: !>[X0: $tType]:(X0)).
% 0.66/0.38 thf(func_def_49, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.66/0.38 thf(func_def_50, type, db2: !>[X0: $tType]:(X0)).
% 0.66/0.38 thf(func_def_51, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.66/0.38 thf(func_def_52, type, vOR: ($o > $o > $o)).
% 0.66/0.38 thf(func_def_53, type, vAND: ($o > $o > $o)).
% 0.66/0.38 thf(func_def_54, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.66/0.38 thf(func_def_55, type, sK0: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X1 @ product_prod @ X0 @ product_prod @ X4 @ product_prod @ X3 @ X2 > $o) > X3))).
% 0.66/0.38 thf(func_def_56, type, sK1: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X1 @ product_prod @ X0 @ product_prod @ X4 @ product_prod @ X3 @ X2 > $o) > X1))).
% 0.66/0.38 thf(func_def_57, type, sK2: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X1 @ product_prod @ X0 @ product_prod @ X4 @ product_prod @ X3 @ X2 > $o) > X0))).
% 0.66/0.38 thf(func_def_58, type, sK3: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X1 @ product_prod @ X0 @ product_prod @ X4 @ product_prod @ X3 @ X2 > $o) > X4))).
% 0.66/0.38 thf(func_def_59, type, sK4: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X1 @ product_prod @ X0 @ product_prod @ X4 @ product_prod @ X3 @ X2 > $o) > X2))).
% 0.66/0.38 thf(func_def_60, type, sK5: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X1 > $o) > set @ X0 > X1))).
% 0.66/0.38 thf(func_def_61, type, sK6: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X3 @ product_prod @ X5 @ product_prod @ X1 @ product_prod @ X4 @ product_prod @ X0 @ X2 > $o) > X2))).
% 0.66/0.38 thf(func_def_62, type, sK7: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X3 @ product_prod @ X5 @ product_prod @ X1 @ product_prod @ X4 @ product_prod @ X0 @ X2 > $o) > X0))).
% 0.66/0.38 thf(func_def_63, type, sK8: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X3 @ product_prod @ X5 @ product_prod @ X1 @ product_prod @ X4 @ product_prod @ X0 @ X2 > $o) > X1))).
% 0.66/0.38 thf(func_def_64, type, sK9: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X3 @ product_prod @ X5 @ product_prod @ X1 @ product_prod @ X4 @ product_prod @ X0 @ X2 > $o) > X3))).
% 0.66/0.38 thf(func_def_65, type, sK10: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X3 @ product_prod @ X5 @ product_prod @ X1 @ product_prod @ X4 @ product_prod @ X0 @ X2 > $o) > X5))).
% 0.66/0.38 thf(func_def_66, type, sK11: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X3 @ product_prod @ X5 @ product_prod @ X1 @ product_prod @ X4 @ product_prod @ X0 @ X2 > $o) > X4))).
% 0.66/0.38 thf(func_def_67, type, sK12: !>[X0: $tType, X1: $tType]:(((X0 > $o) > (X1 > $o) > (X0 > X1) > X0))).
% 0.66/0.38 thf(func_def_68, type, sK13: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((set @ product_prod @ X0 @ X3 > product_prod @ X1 @ X2 > (X0 > X1) > (X3 > X2) > X3))).
% 0.66/0.38 thf(func_def_69, type, sK14: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((set @ product_prod @ X0 @ X3 > product_prod @ X1 @ X2 > (X0 > X1) > (X3 > X2) > X0))).
% 0.66/0.38 thf(func_def_70, type, sK15: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ X1 > X2 > (X0 > X1 > set @ X2) > X1))).
% 0.66/0.38 thf(func_def_71, type, sK16: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ X1 > X2 > (X0 > X1 > set @ X2) > X0))).
% 0.66/0.38 thf(func_def_72, type, sK17: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X3 @ X2 > X0))).
% 0.66/0.38 thf(func_def_73, type, sK18: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X3 @ X2 > X2))).
% 0.66/0.38 thf(func_def_74, type, sK19: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X3 @ X2 > X3))).
% 0.66/0.38 thf(func_def_75, type, sK20: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X3 @ X2 > X1))).
% 0.66/0.38 thf(func_def_76, type, sK21: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.66/0.38 thf(func_def_77, type, sK22: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X4 @ product_prod @ X5 @ product_prod @ X3 @ product_prod @ X1 @ product_prod @ X0 @ product_prod @ X2 @ X6 > X1))).
% 0.66/0.38 thf(func_def_78, type, sK23: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X4 @ product_prod @ X5 @ product_prod @ X3 @ product_prod @ X1 @ product_prod @ X0 @ product_prod @ X2 @ X6 > X0))).
% 0.66/0.38 thf(func_def_79, type, sK24: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X4 @ product_prod @ X5 @ product_prod @ X3 @ product_prod @ X1 @ product_prod @ X0 @ product_prod @ X2 @ X6 > X3))).
% 0.66/0.38 thf(func_def_80, type, sK25: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X4 @ product_prod @ X5 @ product_prod @ X3 @ product_prod @ X1 @ product_prod @ X0 @ product_prod @ X2 @ X6 > X4))).
% 0.66/0.38 thf(func_def_81, type, sK26: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X4 @ product_prod @ X5 @ product_prod @ X3 @ product_prod @ X1 @ product_prod @ X0 @ product_prod @ X2 @ X6 > X6))).
% 0.66/0.38 thf(func_def_82, type, sK27: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X4 @ product_prod @ X5 @ product_prod @ X3 @ product_prod @ X1 @ product_prod @ X0 @ product_prod @ X2 @ X6 > X2))).
% 0.66/0.38 thf(func_def_83, type, sK28: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X4 @ product_prod @ X5 @ product_prod @ X3 @ product_prod @ X1 @ product_prod @ X0 @ product_prod @ X2 @ X6 > X5))).
% 0.66/0.38 thf(func_def_84, type, sK29: ((product_prod @ dtree @ dtree > $o) > dtree)).
% 0.66/0.38 thf(func_def_85, type, sK30: ((product_prod @ dtree @ dtree > $o) > dtree)).
% 0.66/0.38 thf(func_def_86, type, sK31: !>[X0: $tType, X1: $tType]:(((X0 > X1) > set @ X0 > (X0 > X1) > X0))).
% 0.66/0.38 thf(func_def_87, type, sK32: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X3 @ X2 > $o) > X2))).
% 0.66/0.38 thf(func_def_88, type, sK33: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X3 @ X2 > $o) > X1))).
% 0.66/0.38 thf(func_def_89, type, sK34: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X3 @ X2 > $o) > X3))).
% 0.66/0.38 thf(func_def_90, type, sK35: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X3 @ X2 > $o) > X0))).
% 0.66/0.38 thf(func_def_91, type, sK36: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > (X0 > X1 > X2) > product_prod @ X0 @ X1 > X1))).
% 0.66/0.38 thf(func_def_92, type, sK37: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > (X0 > X1 > X2) > product_prod @ X0 @ X1 > X0))).
% 0.66/0.38 thf(func_def_93, type, sK38: !>[X0: $tType, X1: $tType]:((sum_sum @ X1 @ X0 > X1))).
% 0.66/0.38 thf(func_def_94, type, sK39: !>[X0: $tType, X1: $tType]:((sum_sum @ X1 @ X0 > X0))).
% 0.66/0.38 thf(func_def_95, type, sK40: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1))).
% 0.66/0.38 thf(func_def_96, type, sK41: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 0.66/0.38 thf(func_def_97, type, sK42: dtree).
% 0.66/0.38 thf(func_def_98, type, sK43: dtree).
% 0.66/0.38 thf(func_def_99, type, sK44: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > (X0 > $o) > X1))).
% 0.66/0.38 thf(func_def_100, type, sK45: !>[X0: $tType]:((set @ X0 > set @ X0 > (X0 > $o) > X0))).
% 0.66/0.38 thf(func_def_101, type, sK46: !>[X0: $tType]:((set @ X0 > (X0 > $o) > X0))).
% 0.66/0.38 thf(func_def_102, type, sK47: !>[X0: $tType]:((set @ X0 > (X0 > $o) > X0))).
% 0.66/0.38 thf(func_def_103, type, sK48: !>[X0: $tType, X1: $tType]:((sum_sum @ X1 @ X0 > set @ X0 > X0))).
% 0.66/0.38 thf(func_def_104, type, sK49: !>[X0: $tType, X1: $tType]:((sum_sum @ X1 @ X0 > set @ X1 > X1))).
% 0.66/0.38 thf(func_def_105, type, sK50: !>[X0: $tType, X1: $tType]:((set @ X0 > (X0 > X1) > (X0 > X1) > X0))).
% 0.66/0.38 thf(func_def_106, type, sK51: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X0 > X1))).
% 0.66/0.38 thf(func_def_107, type, sK52: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > X1))).
% 0.66/0.38 thf(func_def_108, type, sK53: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > X0))).
% 0.66/0.38 thf(func_def_109, type, sK54: !>[X0: $tType, X1: $tType]:(((sum_sum @ X0 @ X1 > $o) > X0))).
% 0.66/0.38 thf(func_def_110, type, sK55: !>[X0: $tType, X1: $tType]:(((sum_sum @ X0 @ X1 > $o) > X1))).
% 0.66/0.38 thf(func_def_111, type, sK56: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X0 > X1))).
% 0.66/0.38 thf(func_def_112, type, sK57: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > X1) > (X0 > X2) > (X0 > X2) > (X2 > X1) > X2))).
% 0.66/0.38 thf(func_def_113, type, sK58: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > X1) > (X0 > X2) > (X0 > X2) > (X2 > X1) > X2))).
% 0.66/0.38 thf(func_def_114, type, sK59: !>[X0: $tType, X1: $tType, X2: $tType]:(((X1 > X0) > (X1 > X0) > (X2 > X1) > X1))).
% 0.66/0.38 thf(func_def_115, type, sK60: !>[X0: $tType, X1: $tType]:((sum_sum @ X0 @ X1 > X0))).
% 0.66/0.38 thf(func_def_116, type, sK61: !>[X0: $tType, X1: $tType]:((sum_sum @ X0 @ X1 > X1))).
% 0.66/0.38 thf(func_def_117, type, sK62: !>[X0: $tType]:((set @ X0 > (X0 > $o) > set @ X0 > X0))).
% 0.66/0.38 thf(func_def_118, type, sK63: !>[X0: $tType]:(((X0 > $o) > set @ X0 > X0))).
% 0.66/0.38 thf(func_def_119, type, sK64: !>[X0: $tType]:((set @ X0 > (X0 > $o) > X0))).
% 0.66/0.38 thf(func_def_120, type, sK65: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X1 > X0))).
% 0.66/0.38 thf(func_def_121, type, sK66: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X1 @ product_prod @ X2 @ X0 > $o) > X1))).
% 0.66/0.38 thf(func_def_122, type, sK67: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X1 @ product_prod @ X2 @ X0 > $o) > X0))).
% 0.66/0.38 thf(func_def_123, type, sK68: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X1 @ product_prod @ X2 @ X0 > $o) > X2))).
% 0.66/0.38 thf(func_def_124, type, sK69: !>[X0: $tType]:(X0)).
% 0.66/0.38 thf(func_def_125, type, sK70: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X1 @ X2 > X2))).
% 0.66/0.38 thf(func_def_126, type, sK71: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X1 @ X2 > X1))).
% 0.66/0.38 thf(func_def_127, type, sK72: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X1 @ X2 > X0))).
% 0.66/0.38 thf(func_def_128, type, sK73: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > X1) > (X1 > X0) > (X1 > X0) > X1))).
% 0.66/0.38 thf(func_def_129, type, sK74: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X3 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X4 @ X0 > X2))).
% 0.66/0.38 thf(func_def_130, type, sK75: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X3 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X4 @ X0 > X4))).
% 0.66/0.38 thf(func_def_131, type, sK76: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X3 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X4 @ X0 > X0))).
% 0.66/0.38 thf(func_def_132, type, sK77: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X3 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X4 @ X0 > X3))).
% 0.66/0.38 thf(func_def_133, type, sK78: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X3 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X4 @ X0 > X1))).
% 0.66/0.38 thf(func_def_134, type, sK79: !>[X0: $tType]:((set @ X0 > X0))).
% 0.66/0.38 thf(func_def_135, type, sK80: !>[X0: $tType, X1: $tType]:((sum_sum @ X0 @ X1 > X1))).
% 0.66/0.38 thf(func_def_136, type, sK81: !>[X0: $tType, X1: $tType]:((sum_sum @ X0 @ X1 > X0))).
% 0.66/0.38 thf(func_def_137, type, sK82: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X0 > X1) > X0))).
% 0.66/0.38 thf(func_def_138, type, sK83: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.66/0.38 thf(func_def_139, type, sK84: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X1))).
% 0.66/0.38 thf(func_def_140, type, sK85: !>[X0: $tType, X1: $tType]:((X1 > (X0 > X1) > X0))).
% 0.66/0.38 thf(func_def_141, type, sK86: !>[X0: $tType]:(X0)).
% 0.66/0.38 thf(func_def_142, type, sK87: !>[X0: $tType]:(X0)).
% 0.66/0.38 thf(func_def_143, type, sK88: !>[X0: $tType]:(X0)).
% 0.66/0.38 thf(func_def_144, type, sK89: (product_prod @ dtree @ dtree > dtree)).
% 0.66/0.38 thf(func_def_145, type, sK90: (product_prod @ dtree @ dtree > dtree)).
% 0.66/0.38 thf(func_def_146, type, sK91: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > $o > (sum_sum @ X1 @ X0 > X2) > X0))).
% 0.66/0.38 thf(func_def_147, type, sK92: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > $o > (sum_sum @ X1 @ X0 > X2) > X1))).
% 0.66/0.38 thf(func_def_148, type, sK93: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X4 @ product_prod @ X5 @ product_prod @ X1 @ X0 > $o) > X3))).
% 0.66/0.38 thf(func_def_149, type, sK94: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X4 @ product_prod @ X5 @ product_prod @ X1 @ X0 > $o) > X1))).
% 0.66/0.38 thf(func_def_150, type, sK95: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X4 @ product_prod @ X5 @ product_prod @ X1 @ X0 > $o) > X6))).
% 0.66/0.38 thf(func_def_151, type, sK96: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X4 @ product_prod @ X5 @ product_prod @ X1 @ X0 > $o) > X0))).
% 0.66/0.38 thf(func_def_152, type, sK97: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X4 @ product_prod @ X5 @ product_prod @ X1 @ X0 > $o) > X2))).
% 0.66/0.38 thf(func_def_153, type, sK98: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X4 @ product_prod @ X5 @ product_prod @ X1 @ X0 > $o) > X5))).
% 0.66/0.38 thf(func_def_154, type, sK99: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X4 @ product_prod @ X5 @ product_prod @ X1 @ X0 > $o) > X4))).
% 0.66/0.38 thf(func_def_155, type, sK100: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X0))).
% 0.66/0.38 thf(func_def_156, type, sK101: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X1))).
% 0.66/0.38 thf(func_def_157, type, sK102: !>[X0: $tType, X1: $tType]:(((X1 > X0) > set @ X1 > (X1 > X0) > X1))).
% 0.66/0.38 thf(func_def_158, type, sK103: !>[X0: $tType, X1: $tType]:((set @ X0 > (X0 > X1) > (X0 > X1) > X0))).
% 0.66/0.38 thf(func_def_159, type, sK104: !>[X0: $tType]:(X0)).
% 0.66/0.38 thf(func_def_160, type, sK105: !>[X0: $tType]:(X0)).
% 0.66/0.38 thf(func_def_161, type, sK106: !>[X0: $tType]:(X0)).
% 0.66/0.38 thf(func_def_162, type, sK107: !>[X0: $tType, X1: $tType]:((X0 > set @ X1 > (X1 > X0) > X1))).
% 0.66/0.38 thf(func_def_163, type, sK108: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X1))).
% 0.66/0.38 thf(func_def_164, type, sK109: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X0))).
% 0.66/0.38 thf(func_def_165, type, sK110: dtree).
% 0.66/0.38 thf(func_def_166, type, sK111: dtree).
% 0.66/0.38 thf(func_def_167, type, sK112: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X2) > (X2 > X1) > (X2 > X1) > set @ X0 > X0))).
% 0.66/0.38 thf(func_def_168, type, sK113: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X1 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X2 @ product_prod @ X0 @ X5 > X2))).
% 0.66/0.38 thf(func_def_169, type, sK114: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X1 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X2 @ product_prod @ X0 @ X5 > X5))).
% 0.66/0.38 thf(func_def_170, type, sK115: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X1 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X2 @ product_prod @ X0 @ X5 > X3))).
% 0.66/0.38 thf(func_def_171, type, sK116: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X1 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X2 @ product_prod @ X0 @ X5 > X4))).
% 0.66/0.38 thf(func_def_172, type, sK117: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X1 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X2 @ product_prod @ X0 @ X5 > X0))).
% 0.66/0.38 thf(func_def_173, type, sK118: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X1 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X2 @ product_prod @ X0 @ X5 > X1))).
% 0.66/0.38 thf(func_def_174, type, vNOT: ($o > $o)).
% 0.66/0.38 thf(f4,axiom,(
% 0.66/0.38 (trA = ((parall1899940088le_par @ (product_Pair @ dtree @ dtree @ tr1 @ tr2))))),
% 0.66/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3__092_060open_062trA_H_A_061_Atr1_H_A_092_060parallel_062_Atr2_H_092_060close_062)).
% 0.66/0.38 thf(f6,axiom,(
% 0.66/0.38 ~ ! [X0 : dtree,X1 : dtree] : ((trA = ((parall1899940088le_par @ (product_Pair @ dtree @ dtree @ X0 @ X1)))) => ((member @ sum_sum @ t @ dtree @ (sum_Inr @ dtree @ t @ X0) @ (cont @ tr1a)) => ~(member @ sum_sum @ t @ dtree @ (sum_Inr @ dtree @ t @ X1) @ (cont @ tr2a))))),
% 0.66/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062tr1_H_Atr2_H_O_A_092_060lbrakk_062trA_H_A_061_Atr1_H_A_092_060parallel_062_Atr2_H_059_AInr_Atr1_H_A_092_060in_062_Acont_Atr1_059_AInr_Atr2_H_A_092_060in_062_Acont_Atr2_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062)).
% 0.66/0.38 thf(f284,conjecture,(
% 0.66/0.38 ? [X1 : dtree,X0 : dtree] : ((((parall1899940088le_par @ (product_Pair @ dtree @ dtree @ tr2 @ tr1))) = ((parall1899940088le_par @ (product_Pair @ dtree @ dtree @ X1 @ X0)))) & (trA = ((parall1899940088le_par @ (product_Pair @ dtree @ dtree @ X0 @ X1)))))),
% 0.66/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_3)).
% 0.66/0.38 thf(f285,negated_conjecture,(
% 0.66/0.38 ~ ? [X1 : dtree,X0 : dtree] : ((((parall1899940088le_par @ (product_Pair @ dtree @ dtree @ tr2 @ tr1))) = ((parall1899940088le_par @ (product_Pair @ dtree @ dtree @ X1 @ X0)))) & (trA = ((parall1899940088le_par @ (product_Pair @ dtree @ dtree @ X0 @ X1)))))),
% 0.66/0.38 inference(negated_conjecture,[status(cth)],[f284])).
% 0.66/0.38 thf(f523,plain,(
% 0.66/0.38 ~ ! [X0 : dtree,X1 : dtree] : ((trA = ((parall1899940088le_par @ (product_Pair @ dtree @ dtree @ X0 @ X1)))) => ((member @ sum_sum @ t @ dtree @ (sum_Inr @ dtree @ t @ X0) @ (cont @ tr1a)) => ~(member @ sum_sum @ t @ dtree @ (sum_Inr @ dtree @ t @ X1) @ (cont @ tr2a))))),
% 0.66/0.38 inference(rectify,[],[f6])).
% 0.66/0.38 thf(f524,plain,(
% 0.66/0.38 ~ ! [X0 : dtree,X1 : dtree] : ((trA = ((parall1899940088le_par @ (product_Pair @ dtree @ dtree @ X0 @ X1)))) => ((((member @ sum_sum @ t @ dtree @ (sum_Inr @ dtree @ t @ X0) @ (cont @ tr1a))) = $true) => ~ (((member @ sum_sum @ t @ dtree @ (sum_Inr @ dtree @ t @ X1) @ (cont @ tr2a))) = $true)))),
% 0.66/0.38 inference(fool_elimination,[],[f523])).
% 0.66/0.38 thf(f666,plain,(
% 0.66/0.38 ~ ? [X0 : dtree,X1 : dtree] : ((trA = ((parall1899940088le_par @ (product_Pair @ dtree @ dtree @ X1 @ X0)))) & (((parall1899940088le_par @ (product_Pair @ dtree @ dtree @ X0 @ X1))) = ((parall1899940088le_par @ (product_Pair @ dtree @ dtree @ tr2 @ tr1)))))),
% 0.66/0.38 inference(rectify,[],[f285])).
% 0.66/0.38 thf(f684,plain,(
% 0.66/0.38 ~ ! [X1 : dtree,X0 : dtree] : ((trA = ((parall1899940088le_par @ (product_Pair @ dtree @ dtree @ X0 @ X1)))) => ((((member @ sum_sum @ t @ dtree @ (sum_Inr @ dtree @ t @ X0) @ (cont @ tr1a))) = $true) => (((member @ sum_sum @ t @ dtree @ (sum_Inr @ dtree @ t @ X1) @ (cont @ tr2a))) != $true)))),
% 0.66/0.38 inference(flattening,[],[f524])).
% 0.66/0.38 thf(f818,plain,(
% 0.66/0.38 ? [X1 : dtree,X0 : dtree] : (((((member @ sum_sum @ t @ dtree @ (sum_Inr @ dtree @ t @ X1) @ (cont @ tr2a))) = $true) & (((member @ sum_sum @ t @ dtree @ (sum_Inr @ dtree @ t @ X0) @ (cont @ tr1a))) = $true)) & (trA = ((parall1899940088le_par @ (product_Pair @ dtree @ dtree @ X0 @ X1)))))),
% 0.66/0.38 inference(ennf_transformation,[],[f684])).
% 0.66/0.38 thf(f819,plain,(
% 0.66/0.38 ? [X1 : dtree,X0 : dtree] : ((((member @ sum_sum @ t @ dtree @ (sum_Inr @ dtree @ t @ X0) @ (cont @ tr1a))) = $true) & (trA = ((parall1899940088le_par @ (product_Pair @ dtree @ dtree @ X0 @ X1)))) & (((member @ sum_sum @ t @ dtree @ (sum_Inr @ dtree @ t @ X1) @ (cont @ tr2a))) = $true))),
% 0.66/0.38 inference(flattening,[],[f818])).
% 0.66/0.38 thf(f836,plain,(
% 0.66/0.38 ! [X1 : dtree,X0 : dtree] : ((trA != ((parall1899940088le_par @ (product_Pair @ dtree @ dtree @ X1 @ X0)))) | (((parall1899940088le_par @ (product_Pair @ dtree @ dtree @ X0 @ X1))) != ((parall1899940088le_par @ (product_Pair @ dtree @ dtree @ tr2 @ tr1)))))),
% 0.66/0.38 inference(ennf_transformation,[],[f666])).
% 0.66/0.38 thf(f1118,plain,(
% 0.66/0.38 ! [X0 : dtree,X1 : dtree] : ((trA != ((parall1899940088le_par @ (product_Pair @ dtree @ dtree @ X0 @ X1)))) | (((parall1899940088le_par @ (product_Pair @ dtree @ dtree @ tr2 @ tr1))) != ((parall1899940088le_par @ (product_Pair @ dtree @ dtree @ X1 @ X0)))))),
% 0.66/0.38 inference(rectify,[],[f836])).
% 0.66/0.38 thf(f1153,plain,(
% 0.66/0.38 ? [X0 : dtree,X1 : dtree] : ((((member @ sum_sum @ t @ dtree @ (sum_Inr @ dtree @ t @ X1) @ (cont @ tr1a))) = $true) & (trA = ((parall1899940088le_par @ (product_Pair @ dtree @ dtree @ X1 @ X0)))) & (((member @ sum_sum @ t @ dtree @ (sum_Inr @ dtree @ t @ X0) @ (cont @ tr2a))) = $true))),
% 0.66/0.38 inference(rectify,[],[f819])).
% 0.66/0.38 thf(f1154,plain,(
% 0.66/0.38 (((member @ sum_sum @ t @ dtree @ (sum_Inr @ dtree @ t @ sK111) @ (cont @ tr1a))) = $true) & (trA = ((parall1899940088le_par @ (product_Pair @ dtree @ dtree @ sK111 @ sK110)))) & (((member @ sum_sum @ t @ dtree @ (sum_Inr @ dtree @ t @ sK110) @ (cont @ tr2a))) = $true)),
% 0.66/0.38 inference(skolemize,[status(esa),new_symbols(skolem,[sK110,sK111]),skolemize(X0,sK110),skolemize(X1,sK111)],[f1153])).
% 0.66/0.38 thf(f1341,plain,(
% 0.66/0.38 (trA = ((parall1899940088le_par @ (product_Pair @ dtree @ dtree @ tr1 @ tr2))))),
% 0.66/0.38 inference(cnf_transformation,[],[f4])).
% 0.66/0.38 thf(f1455,plain,(
% 0.66/0.38 ( ! [X0 : dtree,X1 : dtree] : ((((parall1899940088le_par @ (product_Pair @ dtree @ dtree @ tr2 @ tr1))) != ((parall1899940088le_par @ (product_Pair @ dtree @ dtree @ X1 @ X0)))) | (trA != ((parall1899940088le_par @ (product_Pair @ dtree @ dtree @ X0 @ X1))))) )),
% 0.66/0.38 inference(cnf_transformation,[],[f1118])).
% 0.66/0.38 thf(f1501,plain,(
% 0.66/0.38 (trA = ((parall1899940088le_par @ (product_Pair @ dtree @ dtree @ sK111 @ sK110))))),
% 0.66/0.38 inference(cnf_transformation,[],[f1154])).
% 0.66/0.38 thf(f1635,definition,(
% 0.66/0.38 spl119_11 <=> (trA = ((parall1899940088le_par @ (product_Pair @ dtree @ dtree @ sK111 @ sK110))))),
% 0.66/0.38 introduced(definition,[new_symbols(definition,[spl119_11])],[avatar_definition])).
% 0.66/0.38 thf(f1637,plain,(
% 0.66/0.38 (trA = ((parall1899940088le_par @ (product_Pair @ dtree @ dtree @ sK111 @ sK110)))) | ~spl119_11),
% 0.66/0.38 inference(avatar_component_clause,[],[f1635])).
% 0.66/0.38 thf(f1638,plain,(
% 0.66/0.38 spl119_11),
% 0.66/0.38 inference(avatar_split_clause,[],[f1501,f1635])).
% 0.66/0.38 thf(f1655,definition,(
% 0.66/0.38 spl119_15 <=> (trA = ((parall1899940088le_par @ (product_Pair @ dtree @ dtree @ tr1 @ tr2))))),
% 0.66/0.38 introduced(definition,[new_symbols(definition,[spl119_15])],[avatar_definition])).
% 0.66/0.38 thf(f1657,plain,(
% 0.66/0.38 (trA = ((parall1899940088le_par @ (product_Pair @ dtree @ dtree @ tr1 @ tr2)))) | ~spl119_15),
% 0.66/0.38 inference(avatar_component_clause,[],[f1655])).
% 0.66/0.38 thf(f1658,plain,(
% 0.66/0.38 spl119_15),
% 0.66/0.38 inference(avatar_split_clause,[],[f1341,f1655])).
% 0.66/0.38 thf(f1664,plain,(
% 0.66/0.38 (((parall1899940088le_par @ (product_Pair @ dtree @ dtree @ tr1 @ tr2))) = ((parall1899940088le_par @ (product_Pair @ dtree @ dtree @ sK111 @ sK110)))) | (~spl119_11 | ~spl119_15)),
% 0.66/0.38 inference(forward_demodulation,[],[f1657,f1637])).
% 0.66/0.38 thf(f1666,definition,(
% 0.66/0.38 spl119_17 <=> (((parall1899940088le_par @ (product_Pair @ dtree @ dtree @ tr1 @ tr2))) = ((parall1899940088le_par @ (product_Pair @ dtree @ dtree @ sK111 @ sK110))))),
% 0.66/0.38 introduced(definition,[new_symbols(definition,[spl119_17])],[avatar_definition])).
% 0.66/0.38 thf(f1669,plain,(
% 0.66/0.38 spl119_17 | ~spl119_11 | ~spl119_15),
% 0.66/0.38 inference(avatar_split_clause,[],[f1664,f1655,f1635,f1666])).
% 0.66/0.38 thf(f1684,plain,(
% 0.66/0.38 ( ! [X0 : dtree,X1 : dtree] : ((((parall1899940088le_par @ (product_Pair @ dtree @ dtree @ tr2 @ tr1))) != ((parall1899940088le_par @ (product_Pair @ dtree @ dtree @ X1 @ X0)))) | (((parall1899940088le_par @ (product_Pair @ dtree @ dtree @ X0 @ X1))) != ((parall1899940088le_par @ (product_Pair @ dtree @ dtree @ sK111 @ sK110))))) ) | ~spl119_11),
% 0.66/0.38 inference(forward_demodulation,[],[f1455,f1637])).
% 0.66/0.38 thf(f1688,plain,(
% 0.66/0.38 (((parall1899940088le_par @ (product_Pair @ dtree @ dtree @ tr1 @ tr2))) != ((parall1899940088le_par @ (product_Pair @ dtree @ dtree @ sK111 @ sK110)))) | ~spl119_11),
% 0.66/0.38 inference(equality_resolution,[],[f1684])).
% 0.66/0.38 thf(f1689,plain,(
% 0.66/0.38 ~spl119_17 | ~spl119_11),
% 0.66/0.38 inference(avatar_split_clause,[],[f1688,f1635,f1666])).
% 0.66/0.38 cnf(s11, plain, spl119_11, inference(sat_conversion,[],[f1638])).
% 0.66/0.38 cnf(s15, plain, spl119_15, inference(sat_conversion,[],[f1658])).
% 0.66/0.38 cnf(s17, plain, ~spl119_11 | ~spl119_15 | spl119_17, inference(sat_conversion,[],[f1669])).
% 0.66/0.38 cnf(s18, plain, ~spl119_11 | ~spl119_17, inference(sat_conversion,[],[f1689])).
% 0.66/0.38 cnf(s19, plain, ~spl119_17, inference(rat,[],[s18,s11])).
% 0.66/0.38 cnf(s20, plain, $false, inference(rat,[],[s17,s15,s19,s11])).
% 0.66/0.38 thf(f1690,plain,(
% 0.66/0.38 $false),
% 0.66/0.38 inference(avatar_sat_refutation,[],[s20])).
% 0.66/0.38 % SZS output end Proof for theBenchmark
% 0.66/0.38 % (3501993)------------------------------
% 0.66/0.38 % (3501993)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.66/0.38 % (3501993)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.38 % (3501993)CaDiCaL version: 2.1.3
% 0.66/0.38 % (3501993)Termination reason: Refutation
% 0.66/0.38 % (3501993)Time elapsed: 0.064 s
% 0.66/0.38 % (3501993)Peak memory usage: 14 MB
% 0.66/0.38 % (3501993)Instructions burned: 126 (million)
% 0.66/0.38 % (3501985)Success in time 0.105 s
% 0.66/0.38 % Vampire exiting
%------------------------------------------------------------------------------