%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COM205^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 0.54s 0.41s
% Output : Refutation 0.54s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM205^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n005.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 17:52:01 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.22/0.28 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.54/0.41 % (1994345)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.54/0.41 % (1994354)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3837689848:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.54/0.41 % (1994356)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.54/0.41 % (1994356)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
% 0.54/0.41 % (1994354)Instruction limit reached!
% 0.54/0.41 % (1994354)------------------------------
% 0.54/0.41 % (1994354)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.41 % (1994350)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1109049041:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.54/0.41 % (1994354)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.41 % (1994354)CaDiCaL version: 2.1.3
% 0.54/0.41 % (1994354)Termination reason: Instruction limit
% 0.54/0.41 % (1994354)Termination phase: Property scanning
% 0.54/0.41 % (1994354)Time elapsed: 0.007 s
% 0.54/0.41 % (1994354)Peak memory usage: 10 MB
% 0.54/0.41 % (1994354)Instructions burned: 26 (million)
% 0.54/0.41 % (1994352)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2299313241:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.54/0.41 % (1994356)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=2747592726:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.54/0.41 % (1994353)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=2152273525: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)
% 0.54/0.41 % (1994355)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1621327602:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.54/0.41 % (1994352)Instruction limit reached!
% 0.54/0.41 % (1994352)------------------------------
% 0.54/0.41 % (1994352)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.41 % (1994352)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.41 % (1994352)CaDiCaL version: 2.1.3
% 0.54/0.41 % (1994352)Termination reason: Instruction limit
% 0.54/0.41 % (1994352)Termination phase: shuffling
% 0.54/0.41 % (1994352)Time elapsed: 0.002 s
% 0.54/0.41 % (1994352)Peak memory usage: 10 MB
% 0.54/0.41 % (1994352)Instructions burned: 3 (million)
% 0.54/0.41 % (1994351)lrs+10_16_si=on:nwc=1.5:random_seed=1736299799:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.54/0.41 % (1994362)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1144341154:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.54/0.41 % (1994362)Instruction limit reached!
% 0.54/0.41 % (1994362)------------------------------
% 0.54/0.41 % (1994362)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.41 % (1994362)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.41 % (1994362)CaDiCaL version: 2.1.3
% 0.54/0.41 % (1994362)Termination reason: Instruction limit
% 0.54/0.41 % (1994362)Termination phase: shuffling
% 0.54/0.41 % (1994362)Time elapsed: 0.002 s
% 0.54/0.41 % (1994362)Peak memory usage: 10 MB
% 0.54/0.41 % (1994362)Instructions burned: 6 (million)
% 0.54/0.41 % (1994351)Instruction limit reached!
% 0.54/0.41 % (1994351)------------------------------
% 0.54/0.41 % (1994351)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.41 % (1994351)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.41 % (1994351)CaDiCaL version: 2.1.3
% 0.54/0.41 % (1994351)Termination reason: Instruction limit
% 0.54/0.41 % (1994351)Termination phase: Property scanning
% 0.54/0.41 % (1994351)Time elapsed: 0.013 s
% 0.54/0.41 % (1994351)Peak memory usage: 10 MB
% 0.54/0.41 % (1994351)Instructions burned: 18 (million)
% 0.54/0.41 % (1994364)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1433896554:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.54/0.41 % (1994364)Instruction limit reached!
% 0.54/0.41 % (1994364)------------------------------
% 0.54/0.41 % (1994364)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.41 % (1994364)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.41 % (1994364)CaDiCaL version: 2.1.3
% 0.54/0.41 % (1994364)Termination reason: Instruction limit
% 0.54/0.41 % (1994364)Termination phase: shuffling
% 0.54/0.41 % (1994364)Time elapsed: 0.004 s
% 0.54/0.41 % (1994364)Peak memory usage: 10 MB
% 0.54/0.41 % (1994364)Instructions burned: 6 (million)
% 0.54/0.41 % (1994368)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=662436818:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.54/0.41 % (1994368)Instruction limit reached!
% 0.54/0.41 % (1994368)------------------------------
% 0.54/0.41 % (1994368)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.41 % (1994368)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.41 % (1994368)CaDiCaL version: 2.1.3
% 0.54/0.41 % (1994368)Termination reason: Instruction limit
% 0.54/0.41 % (1994368)Termination phase: shuffling
% 0.54/0.41 % (1994368)Time elapsed: 0.004 s
% 0.54/0.41 % (1994368)Peak memory usage: 10 MB
% 0.54/0.41 % (1994368)Instructions burned: 15 (million)
% 0.54/0.41 % (1994355)Instruction limit reached!
% 0.54/0.41 % (1994355)------------------------------
% 0.54/0.41 % (1994355)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.41 % (1994355)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.41 % (1994355)CaDiCaL version: 2.1.3
% 0.54/0.41 % (1994355)Termination reason: Instruction limit
% 0.54/0.41 % (1994355)Termination phase: Property scanning
% 0.54/0.41 % (1994355)Time elapsed: 0.039 s
% 0.54/0.41 % (1994355)Peak memory usage: 12 MB
% 0.54/0.41 % (1994355)Instructions burned: 77 (million)
% 0.54/0.41 % (1994367)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.54/0.41 % (1994370)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
% 0.54/0.41 % (1994370)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.54/0.41 % (1994350)Instruction limit reached!
% 0.54/0.41 % (1994350)------------------------------
% 0.54/0.41 % (1994350)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.41 % (1994350)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.41 % (1994350)CaDiCaL version: 2.1.3
% 0.54/0.41 % (1994350)Termination reason: Instruction limit
% 0.54/0.41 % (1994350)Termination phase: Saturation
% 0.54/0.41 % (1994350)Time elapsed: 0.043 s
% 0.54/0.41 % (1994350)Peak memory usage: 13 MB
% 0.54/0.41 % (1994350)Instructions burned: 87 (million)
% 0.54/0.41 % (1994372)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=2283879551:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.54/0.41 % (1994367)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3775069368:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.54/0.41 % (1994370)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3200028440:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.54/0.41 % (1994367)Instruction limit reached!
% 0.54/0.41 % (1994367)------------------------------
% 0.54/0.41 % (1994367)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.41 % (1994367)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.41 % (1994367)CaDiCaL version: 2.1.3
% 0.54/0.41 % (1994367)Termination reason: Instruction limit
% 0.54/0.41 % (1994367)Termination phase: shuffling
% 0.54/0.41 % (1994367)Time elapsed: 0.007 s
% 0.54/0.41 % (1994367)Peak memory usage: 10 MB
% 0.54/0.41 % (1994367)Instructions burned: 8 (million)
% 0.54/0.41 % (1994374)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.54/0.41 % (1994373)lrs+10_1_si=on:cs=on:random_seed=544849540:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.54/0.41 % (1994370)Instruction limit reached!
% 0.54/0.41 % (1994370)------------------------------
% 0.54/0.41 % (1994370)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.41 % (1994370)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.41 % (1994370)CaDiCaL version: 2.1.3
% 0.54/0.41 % (1994370)Termination reason: Instruction limit
% 0.54/0.41 % (1994370)Termination phase: shuffling
% 0.54/0.41 % (1994370)Time elapsed: 0.014 s
% 0.54/0.41 % (1994370)Peak memory usage: 11 MB
% 0.54/0.41 % (1994370)Instructions burned: 28 (million)
% 0.54/0.41 % (1994374)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=2660080731:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.54/0.41 % (1994373)Instruction limit reached!
% 0.54/0.41 % (1994373)------------------------------
% 0.54/0.41 % (1994373)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.41 % (1994373)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.41 % (1994373)CaDiCaL version: 2.1.3
% 0.54/0.41 % (1994373)Termination reason: Instruction limit
% 0.54/0.41 % (1994373)Termination phase: shuffling
% 0.54/0.41 % (1994373)Time elapsed: 0.004 s
% 0.54/0.41 % (1994373)Peak memory usage: 10 MB
% 0.54/0.41 % (1994373)Instructions burned: 8 (million)
% 0.54/0.41 % (1994374)Instruction limit reached!
% 0.54/0.41 % (1994374)------------------------------
% 0.54/0.41 % (1994374)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.41 % (1994374)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.41 % (1994374)CaDiCaL version: 2.1.3
% 0.54/0.41 % (1994374)Termination reason: Instruction limit
% 0.54/0.41 % (1994374)Termination phase: shuffling
% 0.54/0.41 % (1994374)Time elapsed: 0.002 s
% 0.54/0.41 % (1994374)Peak memory usage: 10 MB
% 0.54/0.41 % (1994374)Instructions burned: 4 (million)
% 0.54/0.41 % (1994372)Instruction limit reached!
% 0.54/0.41 % (1994372)------------------------------
% 0.54/0.41 % (1994372)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.41 % (1994372)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.41 % (1994372)CaDiCaL version: 2.1.3
% 0.54/0.41 % (1994372)Termination reason: Instruction limit
% 0.54/0.41 % (1994372)Termination phase: Preprocessing 3
% 0.54/0.41 % (1994372)Time elapsed: 0.021 s
% 0.54/0.41 % (1994372)Peak memory usage: 11 MB
% 0.54/0.41 % (1994372)Instructions burned: 87 (million)
% 0.54/0.41 % (1994356) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1994345-1994356"...
% 0.54/0.41 % (1994378)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=4249748893:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 0.54/0.41 % (1994356)...printing done.
% 0.54/0.41 % (1994356)Refutation found. Thanks to Tanya!
% 0.54/0.41 % SZS status Theorem for theBenchmark
% 0.54/0.41 % SZS output start Proof for theBenchmark
% 0.54/0.41 thf(type_def_5, type, product_prod: ($tType * $tType) > $tType).
% 0.54/0.41 thf(type_def_6, type, sum_sum: ($tType * $tType) > $tType).
% 0.54/0.41 thf(type_def_7, type, option: $tType > $tType).
% 0.54/0.41 thf(type_def_8, type, dtree: $tType).
% 0.54/0.41 thf(type_def_9, type, fset: $tType > $tType).
% 0.54/0.41 thf(type_def_10, type, set: $tType > $tType).
% 0.54/0.41 thf(type_def_11, type, t: $tType).
% 0.54/0.41 thf(type_def_12, type, n: $tType).
% 0.54/0.41 thf(type_def_13, type, itself: $tType > $tType).
% 0.54/0.41 thf(type_def_14, type, sTfun: ($tType * $tType) > $tType).
% 0.54/0.41 thf(func_def_0, type, bounded_lattice: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.54/0.41 thf(func_def_1, type, type: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.54/0.41 thf(func_def_2, type, lattice: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.54/0.41 thf(func_def_3, type, finite_finite: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.54/0.41 thf(func_def_4, type, semiring_char_0: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.54/0.41 thf(func_def_5, type, distrib_lattice: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.54/0.41 thf(func_def_6, type, semilattice_sup: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.54/0.41 thf(func_def_7, type, bounded_lattice_bot: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.54/0.41 thf(func_def_8, type, bounded_lattice_top: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.54/0.41 thf(func_def_9, type, bounde1808546759up_bot: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.54/0.41 thf(func_def_10, type, bNF_Greatest_image2: !>[X0: $tType, X1: $tType, X2: $tType]:((set @ X0 > (X0 > X1) > (X0 > X2) > set @ product_prod @ X1 @ X2))).
% 0.54/0.41 thf(func_def_11, type, node: (n > set @ sum_sum @ t @ dtree > dtree)).
% 0.54/0.41 thf(func_def_12, type, cont: (dtree > set @ sum_sum @ t @ dtree)).
% 0.54/0.41 thf(func_def_13, type, corec: !>[X0: $tType]:(((X0 > n) > (X0 > set @ sum_sum @ t @ sum_sum @ dtree @ X0) > X0 > dtree))).
% 0.54/0.41 thf(func_def_14, type, nNode: (n > fset @ sum_sum @ t @ dtree > dtree)).
% 0.54/0.41 thf(func_def_15, type, case_dtree: !>[X0: $tType]:(((n > fset @ sum_sum @ t @ dtree > X0) > dtree > X0))).
% 0.54/0.41 thf(func_def_16, type, ccont: (dtree > fset @ sum_sum @ t @ dtree)).
% 0.54/0.41 thf(func_def_17, type, corec_dtree: !>[X0: $tType]:(((X0 > n) > (X0 > fset @ sum_sum @ t @ sum_sum @ dtree @ X0) > X0 > dtree))).
% 0.54/0.41 thf(func_def_18, type, root: (dtree > n)).
% 0.54/0.41 thf(func_def_19, type, unfold: !>[X0: $tType]:(((X0 > n) > (X0 > set @ sum_sum @ t @ X0) > X0 > dtree))).
% 0.54/0.41 thf(func_def_20, type, finite_finite2: !>[X0: $tType]:((set @ X0 > $o))).
% 0.54/0.41 thf(func_def_21, type, inf_inf: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.54/0.41 thf(func_def_22, type, sup_sup: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.54/0.41 thf(func_def_23, type, bot_bot: !>[X0: $tType]:(X0)).
% 0.54/0.41 thf(func_def_24, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.54/0.41 thf(func_def_25, type, top_top: !>[X0: $tType]:(X0)).
% 0.54/0.41 thf(func_def_26, type, parall1518086719_Nplus: (n > n > n)).
% 0.54/0.41 thf(func_def_27, type, parall1899940088le_par: (product_prod @ dtree @ dtree > dtree)).
% 0.54/0.41 thf(func_def_28, type, parall1914194347_par_c: (product_prod @ dtree @ dtree > set @ sum_sum @ t @ product_prod @ dtree @ dtree)).
% 0.54/0.41 thf(func_def_29, type, parall1914194362_par_r: (product_prod @ dtree @ dtree > n)).
% 0.54/0.41 thf(func_def_30, type, parall556292031_r_rel: (product_prod @ dtree @ dtree > product_prod @ dtree @ dtree > $o)).
% 0.54/0.41 thf(func_def_31, type, product_Pair: !>[X0: $tType, X1: $tType]:((X0 > X1 > product_prod @ X0 @ X1))).
% 0.54/0.41 thf(func_def_32, type, product_curry: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X0 @ X1 > X2) > X0 > X1 > X2))).
% 0.54/0.41 thf(func_def_33, type, produc2004651681e_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 0.54/0.41 thf(func_def_34, type, product_map_prod: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((X0 > X1) > (X2 > X3) > product_prod @ X0 @ X2 > product_prod @ X1 @ X3))).
% 0.54/0.41 thf(func_def_35, type, product_rec_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 0.54/0.41 thf(func_def_36, type, product_case_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 0.54/0.41 thf(func_def_37, type, product_swap: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > product_prod @ X1 @ X0))).
% 0.54/0.41 thf(func_def_38, type, type2: !>[X0: $tType]:(itself @ X0)).
% 0.54/0.41 thf(func_def_39, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 0.54/0.41 thf(func_def_40, type, image: !>[X0: $tType, X1: $tType]:(((X0 > X1) > set @ X0 > set @ X1))).
% 0.54/0.41 thf(func_def_41, type, vimage: !>[X0: $tType, X1: $tType]:(((X0 > X1) > set @ X1 > set @ X0))).
% 0.54/0.41 thf(func_def_42, type, sum_Inl: !>[X0: $tType, X1: $tType]:((X0 > sum_sum @ X0 @ X1))).
% 0.54/0.41 thf(func_def_43, type, sum_Inr: !>[X0: $tType, X1: $tType]:((X0 > sum_sum @ X1 @ X0))).
% 0.54/0.41 thf(func_def_44, type, sum_Plus: !>[X0: $tType, X1: $tType]:((set @ X0 > set @ X1 > set @ sum_sum @ X0 @ X1))).
% 0.54/0.41 thf(func_def_45, type, sum_Suml: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1) > sum_sum @ X0 @ X2 > X1))).
% 0.54/0.41 thf(func_def_46, type, sum_Sumr: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1) > sum_sum @ X2 @ X0 > X1))).
% 0.54/0.41 thf(func_def_47, type, sum_rec_sum: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1) > (X2 > X1) > sum_sum @ X0 @ X2 > X1))).
% 0.54/0.41 thf(func_def_48, type, accp: !>[X0: $tType]:(((X0 > X0 > $o) > X0 > $o))).
% 0.54/0.41 thf(func_def_49, type, lex_prod: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X0 > set @ product_prod @ X1 @ X1 > set @ product_prod @ product_prod @ X0 @ X1 @ product_prod @ X0 @ X1))).
% 0.54/0.41 thf(func_def_50, type, adm_wf: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X0 > ((X0 > X1) > X0 > X1) > $o))).
% 0.54/0.41 thf(func_def_51, type, cut: !>[X0: $tType, X1: $tType]:(((X0 > X1) > set @ product_prod @ X0 @ X0 > X0 > X0 > X1))).
% 0.54/0.41 thf(func_def_52, type, same_fst: !>[X0: $tType, X1: $tType]:(((X0 > $o) > (X0 > set @ product_prod @ X1 @ X1) > set @ product_prod @ product_prod @ X0 @ X1 @ product_prod @ X0 @ X1))).
% 0.54/0.41 thf(func_def_53, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.54/0.41 thf(func_def_54, type, tr1a: dtree).
% 0.54/0.41 thf(func_def_55, type, tr2a: dtree).
% 0.54/0.41 thf(func_def_56, type, trA: dtree).
% 0.54/0.41 thf(func_def_57, type, trB: dtree).
% 0.54/0.41 thf(func_def_61, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.54/0.41 thf(func_def_62, type, vAND: ($o > $o > $o)).
% 0.54/0.41 thf(func_def_63, type, vOR: ($o > $o > $o)).
% 0.54/0.41 thf(func_def_64, type, db1: !>[X0: $tType]:(X0)).
% 0.54/0.41 thf(func_def_65, type, db0: !>[X0: $tType]:(X0)).
% 0.54/0.41 thf(func_def_66, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.54/0.41 thf(func_def_67, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.54/0.41 thf(func_def_68, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.54/0.41 thf(func_def_69, type, vIMP: ($o > $o > $o)).
% 0.54/0.41 thf(func_def_70, type, db3: !>[X0: $tType]:(X0)).
% 0.54/0.41 thf(func_def_71, type, vNOT: ($o > $o)).
% 0.54/0.41 thf(func_def_72, type, db2: !>[X0: $tType]:(X0)).
% 0.54/0.41 thf(func_def_73, type, db5: !>[X0: $tType]:(X0)).
% 0.54/0.41 thf(func_def_74, type, sP0: !>[X0: $tType, X1: $tType, X2: $tType]:(($o > (sum_sum @ X0 @ X1 > X2) > X2 > $o))).
% 0.54/0.41 thf(func_def_75, type, sP1: !>[X0: $tType, X1: $tType]:((sum_sum @ X0 @ X1 > set @ X0 > $o))).
% 0.54/0.41 thf(func_def_76, type, sP2: !>[X0: $tType]:(((X0 > X0 > X0) > $o))).
% 0.54/0.41 thf(func_def_77, type, sP3: !>[X0: $tType]:(((X0 > $o) > (X0 > X0 > $o) > $o))).
% 0.54/0.41 thf(func_def_78, type, sP4: (n > product_prod @ dtree @ dtree > $o)).
% 0.54/0.41 thf(func_def_79, type, sP5: !>[X0: $tType]:(((X0 > X0 > $o) > (X0 > $o) > $o))).
% 0.54/0.41 thf(func_def_80, type, sP6: !>[X0: $tType]:(((X0 > $o) > (X0 > X0 > $o) > $o))).
% 0.54/0.41 thf(func_def_81, type, sP7: !>[X0: $tType, X1: $tType]:(((X0 > X1) > set @ X1 > set @ X0 > $o))).
% 0.54/0.41 thf(func_def_82, type, sK8: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > X0 > set @ X1) > X1 > product_prod @ X2 @ X0 > X0))).
% 0.54/0.41 thf(func_def_83, type, sK9: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > X0 > set @ X1) > X1 > product_prod @ X2 @ X0 > X2))).
% 0.54/0.41 thf(func_def_84, type, sK10: !>[X0: $tType, X1: $tType]:(((product_prod @ X0 @ X1 > $o) > X1))).
% 0.54/0.41 thf(func_def_85, type, sK11: !>[X0: $tType, X1: $tType]:(((product_prod @ X0 @ X1 > $o) > X0))).
% 0.54/0.41 thf(func_def_86, type, sK12: !>[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))).
% 0.54/0.41 thf(func_def_87, type, sK13: !>[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))).
% 0.54/0.41 thf(func_def_88, type, sK14: !>[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))).
% 0.54/0.41 thf(func_def_89, type, sK15: !>[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))).
% 0.54/0.41 thf(func_def_90, type, sK16: !>[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))).
% 0.54/0.41 thf(func_def_91, type, sK17: !>[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))).
% 0.54/0.41 thf(func_def_92, type, sK18: !>[X0: $tType, X1: $tType, X2: $tType]:(($o > (sum_sum @ X0 @ X1 > X2) > X2 > X1))).
% 0.54/0.41 thf(func_def_93, type, sK19: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > (sum_sum @ X1 @ X2 > X0) > $o > X1))).
% 0.54/0.41 thf(func_def_94, type, sK20: !>[X0: $tType]:((set @ X0 > X0))).
% 0.54/0.41 thf(func_def_95, type, sK21: !>[X0: $tType, X1: $tType]:((sum_sum @ X0 @ X1 > set @ X0 > X0))).
% 0.54/0.41 thf(func_def_96, type, sK22: !>[X0: $tType, X1: $tType]:((sum_sum @ X0 @ X1 > set @ X1 > X1))).
% 0.54/0.41 thf(func_def_97, type, sK23: !>[X0: $tType, X1: $tType]:((set @ X0 > (X0 > X1 > $o) > X0 > X1))).
% 0.54/0.41 thf(func_def_98, type, sK24: !>[X0: $tType, X1: $tType]:((set @ X0 > (X0 > X1 > $o) > X0))).
% 0.54/0.41 thf(func_def_99, type, sK25: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X0 @ product_prod @ X2 @ X1 > $o) > X0))).
% 0.54/0.41 thf(func_def_100, type, sK26: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X0 @ product_prod @ X2 @ X1 > $o) > X2))).
% 0.54/0.41 thf(func_def_101, type, sK27: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X0 @ product_prod @ X2 @ X1 > $o) > X1))).
% 0.54/0.41 thf(func_def_102, type, sK28: dtree).
% 0.54/0.41 thf(func_def_103, type, sK29: dtree).
% 0.54/0.41 thf(func_def_104, type, sK30: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 0.54/0.41 thf(func_def_105, type, sK31: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1))).
% 0.54/0.41 thf(func_def_106, type, sK32: !>[X0: $tType, X1: $tType]:((sum_sum @ X0 @ X1 > X1))).
% 0.54/0.41 thf(func_def_107, type, sK33: !>[X0: $tType, X1: $tType]:((sum_sum @ X0 @ X1 > X0))).
% 0.54/0.41 thf(func_def_108, type, sK34: (product_prod @ dtree @ dtree > dtree)).
% 0.54/0.41 thf(func_def_109, type, sK35: (product_prod @ dtree @ dtree > dtree)).
% 0.54/0.41 thf(func_def_110, type, sK36: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 0.54/0.41 thf(func_def_111, type, sK37: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 0.54/0.41 thf(func_def_112, type, sK38: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 0.54/0.41 thf(func_def_113, type, sK39: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 0.54/0.41 thf(func_def_114, type, sK40: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 0.54/0.41 thf(func_def_115, type, sK41: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 0.54/0.41 thf(func_def_116, type, sK42: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 0.54/0.41 thf(func_def_117, type, sK43: !>[X0: $tType]:(((X0 > $o) > (X0 > X0 > $o) > X0))).
% 0.54/0.41 thf(func_def_118, type, sK44: !>[X0: $tType, X1: $tType]:((sum_sum @ X1 @ X0 > X1))).
% 0.54/0.41 thf(func_def_119, type, sK45: !>[X0: $tType, X1: $tType]:((sum_sum @ X1 @ X0 > X0))).
% 0.54/0.41 thf(func_def_120, type, sK46: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X1 @ product_prod @ X3 @ product_prod @ X0 @ product_prod @ X4 @ X2 > X0))).
% 0.54/0.41 thf(func_def_121, type, sK47: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X1 @ product_prod @ X3 @ product_prod @ X0 @ product_prod @ X4 @ X2 > X1))).
% 0.54/0.41 thf(func_def_122, type, sK48: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X1 @ product_prod @ X3 @ product_prod @ X0 @ product_prod @ X4 @ X2 > X2))).
% 0.54/0.41 thf(func_def_123, type, sK49: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X1 @ product_prod @ X3 @ product_prod @ X0 @ product_prod @ X4 @ X2 > X4))).
% 0.54/0.41 thf(func_def_124, type, sK50: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X1 @ product_prod @ X3 @ product_prod @ X0 @ product_prod @ X4 @ X2 > X3))).
% 0.54/0.41 thf(func_def_125, type, sK51: (n > product_prod @ dtree @ dtree > dtree)).
% 0.54/0.41 thf(func_def_126, type, sK52: (n > product_prod @ dtree @ dtree > dtree)).
% 0.54/0.41 thf(func_def_127, type, sK53: !>[X0: $tType, X1: $tType]:((sum_sum @ X0 @ X1 > X0))).
% 0.54/0.41 thf(func_def_128, type, sK54: !>[X0: $tType, X1: $tType]:((sum_sum @ X0 @ X1 > X1))).
% 0.54/0.41 thf(func_def_129, type, sK55: (product_prod @ dtree @ dtree > n > dtree)).
% 0.54/0.41 thf(func_def_130, type, sK56: (product_prod @ dtree @ dtree > n > dtree)).
% 0.54/0.41 thf(func_def_131, type, sK57: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X1 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X4 @ X0 > $o) > X0))).
% 0.54/0.41 thf(func_def_132, type, sK58: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X1 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X4 @ X0 > $o) > X1))).
% 0.54/0.41 thf(func_def_133, type, sK59: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X1 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X4 @ X0 > $o) > X4))).
% 0.54/0.41 thf(func_def_134, type, sK60: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X1 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X4 @ X0 > $o) > X3))).
% 0.54/0.41 thf(func_def_135, type, sK61: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X1 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X4 @ X0 > $o) > X2))).
% 0.54/0.41 thf(func_def_136, type, sK62: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.54/0.41 thf(func_def_137, type, sK63: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X0 @ product_prod @ X1 @ X2 > $o) > X2))).
% 0.54/0.41 thf(func_def_138, type, sK64: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X0 @ product_prod @ X1 @ X2 > $o) > X3))).
% 0.54/0.41 thf(func_def_139, type, sK65: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X0 @ product_prod @ X1 @ X2 > $o) > X0))).
% 0.54/0.41 thf(func_def_140, type, sK66: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X0 @ product_prod @ X1 @ X2 > $o) > X1))).
% 0.54/0.41 thf(func_def_141, type, sK67: !>[X0: $tType]:(((X0 > X0 > $o) > X0 > X0))).
% 0.54/0.41 thf(func_def_142, type, sK68: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X1))).
% 0.54/0.41 thf(func_def_143, type, sK69: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X0))).
% 0.54/0.41 thf(func_def_144, type, sK70: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X0 @ X1 > X0))).
% 0.54/0.41 thf(func_def_145, type, sK71: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X0 @ X1 > X5))).
% 0.54/0.41 thf(func_def_146, type, sK72: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X0 @ X1 > X1))).
% 0.54/0.41 thf(func_def_147, type, sK73: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X0 @ X1 > X4))).
% 0.54/0.41 thf(func_def_148, type, sK74: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X0 @ X1 > X6))).
% 0.54/0.41 thf(func_def_149, type, sK75: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X0 @ X1 > X2))).
% 0.54/0.41 thf(func_def_150, type, sK76: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X0 @ X1 > X3))).
% 0.54/0.41 thf(func_def_151, type, sK77: !>[X0: $tType]:(X0)).
% 0.54/0.41 thf(func_def_152, type, sK78: !>[X0: $tType]:(X0)).
% 0.54/0.41 thf(func_def_153, type, sK79: !>[X0: $tType]:(X0)).
% 0.54/0.41 thf(func_def_154, type, sK80: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X1 @ X2 > (X3 > X1) > (X0 > X2) > set @ product_prod @ X3 @ X0 > X3))).
% 0.54/0.41 thf(func_def_155, type, sK81: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X1 @ X2 > (X3 > X1) > (X0 > X2) > set @ product_prod @ X3 @ X0 > X0))).
% 0.54/0.41 thf(func_def_156, type, sK82: (dtree > n)).
% 0.54/0.41 thf(func_def_157, type, sK83: (dtree > fset @ sum_sum @ t @ dtree)).
% 0.54/0.41 thf(func_def_158, type, sK84: ((product_prod @ dtree @ dtree > $o) > dtree)).
% 0.54/0.41 thf(func_def_159, type, sK85: ((product_prod @ dtree @ dtree > $o) > dtree)).
% 0.54/0.41 thf(func_def_160, type, sK86: !>[X0: $tType]:(((X0 > X0 > $o) > (X0 > $o) > X0))).
% 0.54/0.41 thf(func_def_161, type, sK87: !>[X0: $tType]:(((X0 > $o) > (X0 > X0 > $o) > X0))).
% 0.54/0.41 thf(func_def_162, type, sK88: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > X0))).
% 0.54/0.41 thf(func_def_163, type, sK89: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > X1))).
% 0.54/0.41 thf(func_def_164, type, sK90: !>[X0: $tType]:(((X0 > X0 > $o) > X0 > X0))).
% 0.54/0.41 thf(func_def_165, type, sK91: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X0 @ X1 > X3))).
% 0.54/0.41 thf(func_def_166, type, sK92: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X0 @ X1 > X2))).
% 0.54/0.41 thf(func_def_167, type, sK93: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X0 @ X1 > X1))).
% 0.54/0.41 thf(func_def_168, type, sK94: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X0 @ X1 > X0))).
% 0.54/0.41 thf(func_def_169, type, sK95: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ X2 > (X0 > X2 > X1) > (X0 > X2 > X1) > X2))).
% 0.54/0.41 thf(func_def_170, type, sK96: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ X2 > (X0 > X2 > X1) > (X0 > X2 > X1) > X0))).
% 0.54/0.41 thf(func_def_171, type, sK97: (dtree > set @ sum_sum @ t @ dtree)).
% 0.54/0.41 thf(func_def_172, type, sK98: (dtree > n)).
% 0.54/0.41 thf(func_def_173, type, sK99: !>[X0: $tType, X1: $tType]:(((sum_sum @ X0 @ X1 > $o) > X0))).
% 0.54/0.41 thf(func_def_174, type, sK100: !>[X0: $tType, X1: $tType]:(((sum_sum @ X0 @ X1 > $o) > X1))).
% 0.54/0.41 thf(func_def_175, type, sK101: !>[X0: $tType, X1: $tType]:(((X0 > X1) > set @ X1 > set @ X0 > set @ X0))).
% 0.54/0.41 thf(func_def_176, type, sK102: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.54/0.41 thf(func_def_177, type, sK103: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X5 @ product_prod @ X6 @ product_prod @ X1 @ product_prod @ X4 @ product_prod @ X0 @ product_prod @ X2 @ X3 > $o) > X4))).
% 0.54/0.41 thf(func_def_178, type, sK104: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X5 @ product_prod @ X6 @ product_prod @ X1 @ product_prod @ X4 @ product_prod @ X0 @ product_prod @ X2 @ X3 > $o) > X1))).
% 0.54/0.41 thf(func_def_179, type, sK105: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X5 @ product_prod @ X6 @ product_prod @ X1 @ product_prod @ X4 @ product_prod @ X0 @ product_prod @ X2 @ X3 > $o) > X3))).
% 0.54/0.41 thf(func_def_180, type, sK106: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X5 @ product_prod @ X6 @ product_prod @ X1 @ product_prod @ X4 @ product_prod @ X0 @ product_prod @ X2 @ X3 > $o) > X6))).
% 0.54/0.41 thf(func_def_181, type, sK107: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X5 @ product_prod @ X6 @ product_prod @ X1 @ product_prod @ X4 @ product_prod @ X0 @ product_prod @ X2 @ X3 > $o) > X0))).
% 0.54/0.41 thf(func_def_182, type, sK108: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X5 @ product_prod @ X6 @ product_prod @ X1 @ product_prod @ X4 @ product_prod @ X0 @ product_prod @ X2 @ X3 > $o) > X2))).
% 0.54/0.41 thf(func_def_183, type, sK109: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X5 @ product_prod @ X6 @ product_prod @ X1 @ product_prod @ X4 @ product_prod @ X0 @ product_prod @ X2 @ X3 > $o) > X5))).
% 0.54/0.41 thf(func_def_184, type, sK110: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X0 @ product_prod @ X2 @ X1 > X0))).
% 0.54/0.41 thf(func_def_185, type, sK111: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X0 @ product_prod @ X2 @ X1 > X1))).
% 0.54/0.41 thf(func_def_186, type, sK112: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X0 @ product_prod @ X2 @ X1 > X4))).
% 0.54/0.41 thf(func_def_187, type, sK113: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X0 @ product_prod @ X2 @ X1 > X5))).
% 0.54/0.41 thf(func_def_188, type, sK114: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X0 @ product_prod @ X2 @ X1 > X3))).
% 0.54/0.41 thf(func_def_189, type, sK115: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X0 @ product_prod @ X2 @ X1 > X2))).
% 0.54/0.41 thf(func_def_190, type, sK116: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X1 > $o) > (X0 > $o) > X0))).
% 0.54/0.41 thf(func_def_191, type, sK117: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ product_prod @ X0 @ X1 > X0))).
% 0.54/0.41 thf(func_def_192, type, sK118: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ product_prod @ X0 @ X1 > X2))).
% 0.54/0.41 thf(func_def_193, type, sK119: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ product_prod @ X0 @ X1 > X1))).
% 0.54/0.41 thf(func_def_194, type, sK120: !>[X0: $tType]:(X0)).
% 0.54/0.41 thf(func_def_195, type, sK121: !>[X0: $tType]:(X0)).
% 0.54/0.41 thf(func_def_196, type, sK122: !>[X0: $tType]:(X0)).
% 0.54/0.41 thf(func_def_197, type, sF123: n).
% 0.54/0.41 thf(func_def_198, type, sF124: n).
% 0.54/0.41 thf(func_def_199, type, sF125: n).
% 0.54/0.41 thf(func_def_200, type, sF126: n).
% 0.54/0.41 thf(func_def_201, type, sK127: !>[X0: $tType]:(((X0 > $o) > set @ X0 > set @ X0 > X0))).
% 0.54/0.41 thf(func_def_202, type, sK128: !>[X0: $tType]:(((X0 > $o) > set @ X0 > set @ X0 > X0))).
% 0.54/0.41 thf(func_def_203, type, sK129: !>[X0: $tType]:(((X0 > $o) > set @ X0 > X0))).
% 0.54/0.41 thf(func_def_204, type, sK130: !>[X0: $tType]:(((X0 > $o) > set @ X0 > X0))).
% 0.54/0.41 thf(func_def_205, type, sK131: !>[X0: $tType, X1: $tType]:((X0 > set @ product_prod @ X0 @ X0 > (X0 > X1) > (X0 > X1) > X0))).
% 0.54/0.41 thf(func_def_206, type, sK132: !>[X0: $tType]:((set @ X0 > (X0 > $o) > X0))).
% 0.54/0.41 thf(func_def_207, type, sK133: !>[X0: $tType]:((set @ X0 > (X0 > $o) > X0))).
% 0.54/0.41 thf(func_def_208, type, sK134: !>[X0: $tType]:((set @ X0 > (X0 > $o) > set @ X0 > X0))).
% 0.54/0.41 thf(func_def_209, type, sK135: !>[X0: $tType]:((set @ X0 > (X0 > $o) > set @ X0 > X0))).
% 0.54/0.41 thf(f1,axiom,(
% 0.54/0.41 ((^[X5 : n, X6 : n] : ((parall1518086719_Nplus @ X6 @ X5))) = parall1518086719_Nplus)),
% 0.54/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_Nplus__comm)).
% 0.54/0.41 thf(f292,conjecture,(
% 0.54/0.41 (((parall1518086719_Nplus @ (root @ tr1a) @ (root @ tr2a))) = ((parall1518086719_Nplus @ (root @ tr2a) @ (root @ tr1a))))),
% 0.54/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 0.54/0.41 thf(f293,negated_conjecture,(
% 0.54/0.41 ~ (((parall1518086719_Nplus @ (root @ tr1a) @ (root @ tr2a))) = ((parall1518086719_Nplus @ (root @ tr2a) @ (root @ tr1a))))),
% 0.54/0.41 inference(negated_conjecture,[status(cth)],[f292])).
% 0.54/0.41 thf(f367,plain,(
% 0.54/0.41 ((^[X0 : n, X1 : n] : ((parall1518086719_Nplus @ X1 @ X0))) = parall1518086719_Nplus)),
% 0.54/0.41 inference(rectify,[],[f1])).
% 0.54/0.41 thf(f368,plain,(
% 0.54/0.41 (parall1518086719_Nplus = (^[Y0 : n]: ((^[Y1 : n]: (parall1518086719_Nplus @ Y1 @ Y0)))))),
% 0.54/0.41 inference(fool_elimination,[],[f367])).
% 0.54/0.41 thf(f717,plain,(
% 0.54/0.41 (((parall1518086719_Nplus @ (root @ tr1a) @ (root @ tr2a))) != ((parall1518086719_Nplus @ (root @ tr2a) @ (root @ tr1a))))),
% 0.54/0.41 inference(flattening,[],[f293])).
% 0.54/0.41 thf(f1352,plain,(
% 0.54/0.41 (((parall1518086719_Nplus @ (root @ tr1a) @ (root @ tr2a))) != ((parall1518086719_Nplus @ (root @ tr2a) @ (root @ tr1a))))),
% 0.54/0.41 inference(cnf_transformation,[],[f717])).
% 0.54/0.41 thf(f1390,plain,(
% 0.54/0.41 (parall1518086719_Nplus = (^[Y0 : n]: ((^[Y1 : n]: (parall1518086719_Nplus @ Y1 @ Y0)))))),
% 0.54/0.41 inference(cnf_transformation,[],[f368])).
% 0.54/0.41 thf(f1599,definition,(
% 0.54/0.41 (sF123 = ((root @ tr1a)))),
% 0.54/0.41 introduced(definition,[new_symbols(definition,[sF123])],[function_definition])).
% 0.54/0.41 thf(f1600,plain,(
% 0.54/0.41 (((root @ tr1a)) = sF123)),
% 0.54/0.41 inference(reorient_equations,[],[f1599])).
% 0.54/0.41 thf(f1601,definition,(
% 0.54/0.41 (sF124 = ((root @ tr2a)))),
% 0.54/0.41 introduced(definition,[new_symbols(definition,[sF124])],[function_definition])).
% 0.54/0.41 thf(f1602,plain,(
% 0.54/0.41 (((root @ tr2a)) = sF124)),
% 0.54/0.41 inference(reorient_equations,[],[f1601])).
% 0.54/0.41 thf(f1603,definition,(
% 0.54/0.41 (sF125 = ((parall1518086719_Nplus @ sF123 @ sF124)))),
% 0.54/0.41 introduced(definition,[new_symbols(definition,[sF125])],[function_definition])).
% 0.54/0.41 thf(f1604,definition,(
% 0.54/0.41 (sF126 = ((parall1518086719_Nplus @ sF124 @ sF123)))),
% 0.54/0.41 introduced(definition,[new_symbols(definition,[sF126])],[function_definition])).
% 0.54/0.41 thf(f1605,plain,(
% 0.54/0.41 (((parall1518086719_Nplus @ sF124 @ sF123)) = sF126)),
% 0.54/0.41 inference(reorient_equations,[],[f1604])).
% 0.54/0.41 thf(f1606,plain,(
% 0.54/0.41 (sF125 != sF126)),
% 0.54/0.41 inference(definition_folding,[],[f1352,f1605,f1600,f1602,f1603,f1602,f1600])).
% 0.54/0.41 thf(f2382,plain,(
% 0.54/0.41 ( ! [X1 : n] : ((((parall1518086719_Nplus @ X1)) = (((^[Y0 : n]: ((^[Y1 : n]: (parall1518086719_Nplus @ Y1 @ Y0)))) @ X1)))) )),
% 0.54/0.41 inference(argument_congruence,[],[f1390])).
% 0.54/0.41 thf(f2383,plain,(
% 0.54/0.41 ( ! [X1 : n] : ((((parall1518086719_Nplus @ X1)) = (^[Y0 : n]: (parall1518086719_Nplus @ Y0 @ X1)))) )),
% 0.54/0.41 inference(beta-eta_normalization,[],[f2382])).
% 0.54/0.41 thf(f2384,plain,(
% 0.54/0.41 ( ! [X2 : n,X1 : n] : ((((parall1518086719_Nplus @ X1 @ X2)) = (((^[Y0 : n]: (parall1518086719_Nplus @ Y0 @ X1)) @ X2)))) )),
% 0.54/0.41 inference(argument_congruence,[],[f2383])).
% 0.54/0.41 thf(f2385,plain,(
% 0.54/0.41 ( ! [X2 : n,X1 : n] : ((((parall1518086719_Nplus @ X1 @ X2)) = ((parall1518086719_Nplus @ X2 @ X1)))) )),
% 0.54/0.41 inference(beta-eta_normalization,[],[f2384])).
% 0.54/0.41 thf(f2387,plain,(
% 0.54/0.41 (sF126 = ((parall1518086719_Nplus @ sF123 @ sF124)))),
% 0.54/0.41 inference(constrained_superposition,[],[f2385,f1605])).
% 0.54/0.41 thf(f2390,plain,(
% 0.54/0.41 (sF125 = sF126)),
% 0.54/0.41 inference(forward_demodulation,[],[f2387,f1603])).
% 0.54/0.41 thf(f2394,plain,(
% 0.54/0.41 $false),
% 0.54/0.41 inference(forward_subsumption_resolution,[],[f2390,f1606])).
% 0.54/0.41 % SZS output end Proof for theBenchmark
% 0.54/0.41 % (1994356)------------------------------
% 0.54/0.41 % (1994356)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.41 % (1994356)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.41 % (1994356)CaDiCaL version: 2.1.3
% 0.54/0.41 % (1994356)Termination reason: Refutation
% 0.54/0.41 % (1994356)Time elapsed: 0.074 s
% 0.54/0.41 % (1994356)Peak memory usage: 14 MB
% 0.54/0.41 % (1994356)Instructions burned: 139 (million)
% 0.54/0.41 % (1994345)Success in time 0.126 s
% 0.54/0.41 % Vampire exiting
%------------------------------------------------------------------------------