%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP041^2 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:08:05 AM UTC 2026
% Result : Theorem 0.31s 0.45s
% Output : Refutation 0.31s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP041^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.19 % Computer : n010.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Sep 29 19:40:48 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 Running higher-order theorem proving
% 0.24/0.30 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
% 0.31/0.44 % (3310904)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.31/0.44 % (3310909)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1152703806:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.31/0.44 % (3310915)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.31/0.44 % (3310915)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
% 0.31/0.44 % (3310910)lrs+10_16_si=on:nwc=1.5:random_seed=3862457985:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.31/0.44 % (3310911)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=4096299954:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.31/0.44 % (3310913)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2852486666:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.31/0.44 % (3310912)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=2443066666: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)
% 0.31/0.44 % (3310914)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3636834364:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.31/0.44 % (3310915)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=3887607877:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.31/0.44 % (3310911)Instruction limit reached!
% 0.31/0.44 % (3310911)------------------------------
% 0.31/0.44 % (3310911)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.31/0.44 % (3310911)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.31/0.44 % (3310911)CaDiCaL version: 2.1.3
% 0.31/0.44 % (3310911)Termination reason: Instruction limit
% 0.31/0.44 % (3310911)Termination phase: shuffling
% 0.31/0.44 % (3310911)Time elapsed: 0.003 s
% 0.31/0.44 % (3310911)Peak memory usage: 10 MB
% 0.31/0.44 % (3310911)Instructions burned: 5 (million)
% 0.31/0.44 % (3310910)Instruction limit reached!
% 0.31/0.44 % (3310910)------------------------------
% 0.31/0.44 % (3310910)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.31/0.44 % (3310910)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.31/0.44 % (3310910)CaDiCaL version: 2.1.3
% 0.31/0.44 % (3310910)Termination reason: Instruction limit
% 0.31/0.44 % (3310910)Termination phase: shuffling
% 0.31/0.44 % (3310910)Time elapsed: 0.009 s
% 0.31/0.44 % (3310910)Peak memory usage: 10 MB
% 0.31/0.44 % (3310910)Instructions burned: 19 (million)
% 0.31/0.44 % (3310913)Instruction limit reached!
% 0.31/0.44 % (3310913)------------------------------
% 0.31/0.44 % (3310913)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.31/0.44 % (3310913)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.31/0.44 % (3310913)CaDiCaL version: 2.1.3
% 0.31/0.44 % (3310913)Termination reason: Instruction limit
% 0.31/0.44 % (3310913)Termination phase: shuffling
% 0.31/0.44 % (3310913)Time elapsed: 0.013 s
% 0.31/0.44 % (3310913)Peak memory usage: 10 MB
% 0.31/0.44 % (3310913)Instructions burned: 26 (million)
% 0.31/0.44 % (3310909)Instruction limit reached!
% 0.31/0.44 % (3310909)------------------------------
% 0.31/0.44 % (3310909)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.31/0.44 % (3310909)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.31/0.44 % (3310909)CaDiCaL version: 2.1.3
% 0.31/0.44 % (3310909)Termination reason: Instruction limit
% 0.31/0.44 % (3310909)Termination phase: Property scanning
% 0.31/0.44 % (3310909)Time elapsed: 0.023 s
% 0.31/0.44 % (3310909)Peak memory usage: 12 MB
% 0.31/0.44 % (3310909)Instructions burned: 89 (million)
% 0.31/0.44 % (3310923)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1272396527:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.31/0.44 % (3310923)Instruction limit reached!
% 0.31/0.44 % (3310923)------------------------------
% 0.31/0.44 % (3310923)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.31/0.45 % (3310923)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.31/0.45 % (3310923)CaDiCaL version: 2.1.3
% 0.31/0.45 % (3310923)Termination reason: Instruction limit
% 0.31/0.45 % (3310923)Termination phase: shuffling
% 0.31/0.45 % (3310923)Time elapsed: 0.002 s
% 0.31/0.45 % (3310923)Peak memory usage: 10 MB
% 0.31/0.45 % (3310923)Instructions burned: 3 (million)
% 0.31/0.45 % (3310926)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1925639815:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.31/0.45 % (3310925)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.31/0.45 % (3310924)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3008608834:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.31/0.45 % (3310926)Instruction limit reached!
% 0.31/0.45 % (3310926)------------------------------
% 0.31/0.45 % (3310926)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.31/0.45 % (3310926)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.31/0.45 % (3310926)CaDiCaL version: 2.1.3
% 0.31/0.45 % (3310926)Termination reason: Instruction limit
% 0.31/0.45 % (3310926)Termination phase: shuffling
% 0.31/0.45 % (3310926)Time elapsed: 0.004 s
% 0.31/0.45 % (3310926)Peak memory usage: 10 MB
% 0.31/0.45 % (3310926)Instructions burned: 16 (million)
% 0.31/0.45 % (3310924)Instruction limit reached!
% 0.31/0.45 % (3310924)------------------------------
% 0.31/0.45 % (3310924)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.31/0.45 % (3310924)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.31/0.45 % (3310924)CaDiCaL version: 2.1.3
% 0.31/0.45 % (3310924)Termination reason: Instruction limit
% 0.31/0.45 % (3310924)Termination phase: shuffling
% 0.31/0.45 % (3310924)Time elapsed: 0.003 s
% 0.31/0.45 % (3310924)Peak memory usage: 10 MB
% 0.31/0.45 % (3310924)Instructions burned: 5 (million)
% 0.31/0.45 % (3310925)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=4209497388:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.31/0.45 % (3310925)Instruction limit reached!
% 0.31/0.45 % (3310925)------------------------------
% 0.31/0.45 % (3310925)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.31/0.45 % (3310925)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.31/0.45 % (3310925)CaDiCaL version: 2.1.3
% 0.31/0.45 % (3310925)Termination reason: Instruction limit
% 0.31/0.45 % (3310925)Termination phase: shuffling
% 0.31/0.45 % (3310925)Time elapsed: 0.004 s
% 0.31/0.45 % (3310925)Peak memory usage: 10 MB
% 0.31/0.45 % (3310925)Instructions burned: 8 (million)
% 0.31/0.45 % (3310914)Instruction limit reached!
% 0.31/0.45 % (3310914)------------------------------
% 0.31/0.45 % (3310914)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.31/0.45 % (3310914)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.31/0.45 % (3310914)CaDiCaL version: 2.1.3
% 0.31/0.45 % (3310914)Termination reason: Instruction limit
% 0.31/0.45 % (3310914)Termination phase: Preprocessing 3
% 0.31/0.45 % (3310914)Time elapsed: 0.038 s
% 0.31/0.45 % (3310914)Peak memory usage: 12 MB
% 0.31/0.45 % (3310914)Instructions burned: 77 (million)
% 0.31/0.45 % (3310928)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
% 0.31/0.45 % (3310928)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.31/0.45 % (3310931)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=1091526417:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.31/0.45 % (3310928)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=1546618766:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.31/0.45 % (3310933)lrs+10_1_si=on:cs=on:random_seed=1064620536:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.31/0.45 % (3310934)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.31/0.45 % (3310934)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=434226001:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.31/0.45 % (3310933)Instruction limit reached!
% 0.31/0.45 % (3310933)------------------------------
% 0.31/0.45 % (3310933)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.31/0.45 % (3310933)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.31/0.45 % (3310933)CaDiCaL version: 2.1.3
% 0.31/0.45 % (3310933)Termination reason: Instruction limit
% 0.31/0.45 % (3310933)Termination phase: shuffling
% 0.31/0.45 % (3310933)Time elapsed: 0.005 s
% 0.31/0.45 % (3310933)Peak memory usage: 10 MB
% 0.31/0.45 % (3310933)Instructions burned: 9 (million)
% 0.31/0.45 % (3310934)Instruction limit reached!
% 0.31/0.45 % (3310934)------------------------------
% 0.31/0.45 % (3310934)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.31/0.45 % (3310934)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.31/0.45 % (3310934)CaDiCaL version: 2.1.3
% 0.31/0.45 % (3310934)Termination reason: Instruction limit
% 0.31/0.45 % (3310934)Termination phase: shuffling
% 0.31/0.45 % (3310934)Time elapsed: 0.002 s
% 0.31/0.45 % (3310934)Peak memory usage: 10 MB
% 0.31/0.45 % (3310934)Instructions burned: 3 (million)
% 0.31/0.45 % (3310928)Instruction limit reached!
% 0.31/0.45 % (3310928)------------------------------
% 0.31/0.45 % (3310928)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.31/0.45 % (3310928)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.31/0.45 % (3310928)CaDiCaL version: 2.1.3
% 0.31/0.45 % (3310928)Termination reason: Instruction limit
% 0.31/0.45 % (3310928)Termination phase: shuffling
% 0.31/0.45 % (3310928)Time elapsed: 0.014 s
% 0.31/0.45 % (3310928)Peak memory usage: 11 MB
% 0.31/0.45 % (3310928)Instructions burned: 29 (million)
% 0.31/0.45 % (3310935)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=1267560171:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.31/0.45 % (3310931)Instruction limit reached!
% 0.31/0.45 % (3310931)------------------------------
% 0.31/0.45 % (3310931)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.31/0.45 % (3310931)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.31/0.45 % (3310931)CaDiCaL version: 2.1.3
% 0.31/0.45 % (3310931)Termination reason: Instruction limit
% 0.31/0.45 % (3310931)Termination phase: Preprocessing 1
% 0.31/0.45 % (3310931)Time elapsed: 0.021 s
% 0.31/0.45 % (3310931)Peak memory usage: 11 MB
% 0.31/0.45 % (3310931)Instructions burned: 90 (million)
% 0.31/0.45 % (3310944)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=2863388267:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 0.31/0.45 % (3310940)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=2131794782:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 0.31/0.45 % (3310935)Instruction limit reached!
% 0.31/0.45 % (3310935)------------------------------
% 0.31/0.45 % (3310935)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.31/0.45 % (3310935)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.31/0.45 % (3310935)CaDiCaL version: 2.1.3
% 0.31/0.45 % (3310935)Termination reason: Instruction limit
% 0.31/0.45 % (3310935)Termination phase: Property scanning
% 0.31/0.45 % (3310935)Time elapsed: 0.018 s
% 0.31/0.45 % (3310935)Peak memory usage: 11 MB
% 0.31/0.45 % (3310935)Instructions burned: 39 (million)
% 0.31/0.45 % (3310942)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2677579054:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 0.31/0.45 % (3310943)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=150272570:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.31/0.45 % (3310915)Instruction limit reached!
% 0.31/0.45 % (3310915)------------------------------
% 0.31/0.45 % (3310915)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.31/0.45 % (3310915)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.31/0.45 % (3310915)CaDiCaL version: 2.1.3
% 0.31/0.45 % (3310915)Termination reason: Instruction limit
% 0.31/0.45 % (3310915)Termination phase: Saturation
% 0.31/0.45 % (3310915)Time elapsed: 0.081 s
% 0.31/0.45 % (3310915)Peak memory usage: 14 MB
% 0.31/0.45 % (3310915)Instructions burned: 163 (million)
% 0.31/0.45 % (3310912) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3310904-3310912"...
% 0.31/0.45 % (3310912)...printing done.
% 0.31/0.45 % (3310912)Refutation found. Thanks to Tanya!
% 0.31/0.45 % SZS status Theorem for theBenchmark
% 0.31/0.45 % SZS output start Proof for theBenchmark
% 0.31/0.45 thf(type_def_5, type, denota1663640101rp_ext: ($tType * $tType * $tType * $tType) > $tType).
% 0.31/0.45 thf(type_def_6, type, finite_Cartesian_vec: ($tType * $tType) > $tType).
% 0.31/0.45 thf(type_def_7, type, product_unit: $tType).
% 0.31/0.45 thf(type_def_8, type, product_prod: ($tType * $tType) > $tType).
% 0.31/0.45 thf(type_def_9, type, formula: ($tType * $tType * $tType) > $tType).
% 0.31/0.45 thf(type_def_10, type, sum_sum: ($tType * $tType) > $tType).
% 0.31/0.45 thf(type_def_11, type, filter: $tType > $tType).
% 0.31/0.45 thf(type_def_12, type, trm: ($tType * $tType) > $tType).
% 0.31/0.45 thf(type_def_13, type, ode: ($tType * $tType) > $tType).
% 0.31/0.45 thf(type_def_14, type, hp: ($tType * $tType * $tType) > $tType).
% 0.31/0.45 thf(type_def_15, type, real: $tType).
% 0.31/0.45 thf(type_def_16, type, list: $tType > $tType).
% 0.31/0.45 thf(type_def_17, type, set: $tType > $tType).
% 0.31/0.45 thf(type_def_18, type, d: $tType).
% 0.31/0.45 thf(type_def_19, type, c: $tType).
% 0.31/0.45 thf(type_def_20, type, b: $tType).
% 0.31/0.45 thf(type_def_21, type, a: $tType).
% 0.31/0.45 thf(type_def_22, type, sTfun: ($tType * $tType) > $tType).
% 0.31/0.45 thf(func_def_0, type, cARD_1: !>[X0: $tType]:($o)).
% 0.31/0.45 thf(func_def_1, type, ordere890947078_space: !>[X0: $tType]:($o)).
% 0.31/0.45 thf(func_def_2, type, type: !>[X0: $tType]:($o)).
% 0.31/0.45 thf(func_def_3, type, zero: !>[X0: $tType]:($o)).
% 0.31/0.45 thf(func_def_4, type, uminus: !>[X0: $tType]:($o)).
% 0.31/0.45 thf(func_def_5, type, ord: !>[X0: $tType]:($o)).
% 0.31/0.45 thf(func_def_6, type, order: !>[X0: $tType]:($o)).
% 0.31/0.45 thf(func_def_7, type, group_add: !>[X0: $tType]:($o)).
% 0.31/0.45 thf(func_def_8, type, no_bot: !>[X0: $tType]:($o)).
% 0.31/0.45 thf(func_def_9, type, no_top: !>[X0: $tType]:($o)).
% 0.31/0.45 thf(func_def_10, type, finite_finite: !>[X0: $tType]:($o)).
% 0.31/0.45 thf(func_def_11, type, linorder: !>[X0: $tType]:($o)).
% 0.31/0.45 thf(func_def_12, type, preorder: !>[X0: $tType]:($o)).
% 0.31/0.45 thf(func_def_13, type, boolean_algebra: !>[X0: $tType]:($o)).
% 0.31/0.45 thf(func_def_14, type, semilattice_sup: !>[X0: $tType]:($o)).
% 0.31/0.45 thf(func_def_15, type, ordered_ab_group_add: !>[X0: $tType]:($o)).
% 0.31/0.45 thf(func_def_16, type, linord219039673up_add: !>[X0: $tType]:($o)).
% 0.31/0.45 thf(func_def_17, type, linord1659791738miring: !>[X0: $tType]:($o)).
% 0.31/0.45 thf(func_def_18, type, topolo503727757_space: !>[X0: $tType]:($o)).
% 0.31/0.45 thf(func_def_19, type, canoni770627133id_add: !>[X0: $tType]:($o)).
% 0.31/0.45 thf(func_def_20, type, lattic1601792062up_add: !>[X0: $tType]:($o)).
% 0.31/0.45 thf(func_def_21, type, real_V55928688vector: !>[X0: $tType]:($o)).
% 0.31/0.45 thf(func_def_22, type, euclid1678468529ng_gcd: !>[X0: $tType]:($o)).
% 0.31/0.45 thf(func_def_23, type, unique1598680935umeral: !>[X0: $tType]:($o)).
% 0.31/0.45 thf(func_def_24, type, euclid1155270486miring: !>[X0: $tType]:($o)).
% 0.31/0.45 thf(func_def_25, type, bNF_Ca1785829860lChain: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X0 > (X0 > X1) > $o))).
% 0.31/0.45 thf(func_def_26, type, coinci1993344360de_fml: !>[X0: $tType, X1: $tType, X2: $tType]:((formula @ X0 @ X1 @ X2 > $o))).
% 0.31/0.45 thf(func_def_27, type, coinci32832645ide_hp: !>[X0: $tType, X1: $tType, X2: $tType]:((hp @ X0 @ X1 @ X2 > denota1663640101rp_ext @ X0 @ X1 @ X2 @ product_unit > denota1663640101rp_ext @ X0 @ X1 @ X2 @ product_unit > $o))).
% 0.31/0.45 thf(func_def_28, type, coinci554967470ide_hp: !>[X0: $tType, X1: $tType, X2: $tType]:((hp @ X0 @ X1 @ X2 > $o))).
% 0.31/0.45 thf(func_def_29, type, coinci1495174342_equiv: !>[X0: $tType, X1: $tType, X2: $tType]:((hp @ X0 @ X1 @ X2 > denota1663640101rp_ext @ X0 @ X1 @ X2 @ product_unit > $o))).
% 0.31/0.45 thf(func_def_30, type, denotational_Iagree: !>[X0: $tType, X1: $tType, X2: $tType]:((denota1663640101rp_ext @ X0 @ X1 @ X2 @ product_unit > denota1663640101rp_ext @ X0 @ X1 @ X2 @ product_unit > set @ sum_sum @ X0 @ sum_sum @ X1 @ X2 > $o))).
% 0.31/0.45 thf(func_def_31, type, denotational_ODE_sem: !>[X0: $tType, X1: $tType, X2: $tType]:((denota1663640101rp_ext @ X0 @ X1 @ X2 @ product_unit > ode @ X0 @ X2 > finite_Cartesian_vec @ real @ X2 > finite_Cartesian_vec @ real @ X2))).
% 0.31/0.45 thf(func_def_32, type, denota811733865E_vars: !>[X0: $tType, X1: $tType, X2: $tType]:((denota1663640101rp_ext @ X0 @ X1 @ X2 @ product_unit > ode @ X0 @ X2 > set @ X2))).
% 0.31/0.45 thf(func_def_33, type, denotational_VSagree: !>[X0: $tType]:((finite_Cartesian_vec @ real @ X0 > finite_Cartesian_vec @ real @ X0 > set @ X0 > $o))).
% 0.31/0.45 thf(func_def_34, type, denotational_Vagree: !>[X0: $tType]:((product_prod @ finite_Cartesian_vec @ real @ X0 @ finite_Cartesian_vec @ real @ X0 > product_prod @ finite_Cartesian_vec @ real @ X0 @ finite_Cartesian_vec @ real @ X0 > set @ sum_sum @ X0 @ X0 > $o))).
% 0.31/0.45 thf(func_def_35, type, denotational_fml_sem: !>[X0: $tType, X1: $tType, X2: $tType]:((denota1663640101rp_ext @ X0 @ X1 @ X2 @ product_unit > formula @ X0 @ X1 @ X2 > set @ product_prod @ finite_Cartesian_vec @ real @ X2 @ finite_Cartesian_vec @ real @ X2))).
% 0.31/0.45 thf(func_def_36, type, denotational_mk_v: !>[X0: $tType, X1: $tType, X2: $tType]:((denota1663640101rp_ext @ X0 @ X1 @ X2 @ product_unit > ode @ X0 @ X2 > product_prod @ finite_Cartesian_vec @ real @ X2 @ finite_Cartesian_vec @ real @ X2 > finite_Cartesian_vec @ real @ X2 > product_prod @ finite_Cartesian_vec @ real @ X2 @ finite_Cartesian_vec @ real @ X2))).
% 0.31/0.45 thf(func_def_37, type, denotational_mk_xode: !>[X0: $tType, X1: $tType, X2: $tType]:((denota1663640101rp_ext @ X0 @ X1 @ X2 @ product_unit > ode @ X0 @ X2 > finite_Cartesian_vec @ real @ X2 > product_prod @ finite_Cartesian_vec @ real @ X2 @ finite_Cartesian_vec @ real @ X2))).
% 0.31/0.45 thf(func_def_38, type, denotational_semBV: !>[X0: $tType, X1: $tType, X2: $tType]:((denota1663640101rp_ext @ X0 @ X1 @ X2 @ product_unit > ode @ X0 @ X2 > set @ sum_sum @ X2 @ X2))).
% 0.31/0.45 thf(func_def_39, type, has_ve2132708402vative: !>[X0: $tType]:(((real > X0) > X0 > filter @ real > $o))).
% 0.31/0.45 thf(func_def_40, type, unique455577585es_aux: !>[X0: $tType]:((product_prod @ X0 @ X0 > $o))).
% 0.31/0.45 thf(func_def_41, type, uminus_uminus: !>[X0: $tType]:((X0 > X0))).
% 0.31/0.45 thf(func_def_42, type, zero_zero: !>[X0: $tType]:(X0)).
% 0.31/0.45 thf(func_def_43, type, the: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.31/0.45 thf(func_def_44, type, ids: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X0 > X0 > X1 > X1 > X1 > X2 > X2 > X2 > X2 > $o))).
% 0.31/0.45 thf(func_def_45, type, initia1685620758es_ode: !>[X0: $tType]:(((real > X0) > (real > X0 > X0) > set @ real > set @ X0 > $o))).
% 0.31/0.45 thf(func_def_46, type, sup_sup: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.31/0.45 thf(func_def_47, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.31/0.45 thf(func_def_48, type, product_Pair: !>[X0: $tType, X1: $tType]:((X0 > X1 > product_prod @ X0 @ X1))).
% 0.31/0.45 thf(func_def_49, type, produc2004651681e_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 0.31/0.45 thf(func_def_50, type, product_rec_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 0.31/0.45 thf(func_def_51, type, product_rec_set_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2 > $o))).
% 0.31/0.45 thf(func_def_52, type, product_rec_set_unit: !>[X0: $tType]:((X0 > product_unit > X0 > $o))).
% 0.31/0.45 thf(func_def_53, type, product_rec_unit: !>[X0: $tType]:((X0 > product_unit > X0))).
% 0.31/0.45 thf(func_def_54, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 0.31/0.45 thf(func_def_55, type, image: !>[X0: $tType, X1: $tType]:(((X0 > X1) > set @ X0 > set @ X1))).
% 0.31/0.45 thf(func_def_56, type, set_ord_atLeast: !>[X0: $tType]:((X0 > set @ X0))).
% 0.31/0.45 thf(func_def_57, type, set_or331188842AtMost: !>[X0: $tType]:((X0 > X0 > set @ X0))).
% 0.31/0.45 thf(func_def_58, type, set_ord_atMost: !>[X0: $tType]:((X0 > set @ X0))).
% 0.31/0.45 thf(func_def_59, type, static_BVO: !>[X0: $tType, X1: $tType]:((ode @ X0 @ X1 > set @ sum_sum @ X1 @ X1))).
% 0.31/0.45 thf(func_def_60, type, static_FVF: !>[X0: $tType, X1: $tType, X2: $tType]:((formula @ X0 @ X1 @ X2 > set @ sum_sum @ X2 @ X2))).
% 0.31/0.45 thf(func_def_61, type, static_FVO: !>[X0: $tType, X1: $tType]:((ode @ X0 @ X1 > set @ X1))).
% 0.31/0.45 thf(func_def_62, type, static_SIGF: !>[X0: $tType, X1: $tType, X2: $tType]:((formula @ X0 @ X1 @ X2 > set @ sum_sum @ X0 @ sum_sum @ X1 @ X2))).
% 0.31/0.45 thf(func_def_63, type, sum_Inl: !>[X0: $tType, X1: $tType]:((X0 > sum_sum @ X0 @ X1))).
% 0.31/0.45 thf(func_def_64, type, sum_Inr: !>[X0: $tType, X1: $tType]:((X0 > sum_sum @ X1 @ X0))).
% 0.31/0.45 thf(func_def_65, type, equiv: !>[X0: $tType, X1: $tType, X2: $tType]:((formula @ X0 @ X1 @ X2 > formula @ X0 @ X1 @ X2 > formula @ X0 @ X1 @ X2))).
% 0.31/0.45 thf(func_def_66, type, implies: !>[X0: $tType, X1: $tType, X2: $tType]:((formula @ X0 @ X1 @ X2 > formula @ X0 @ X1 @ X2 > formula @ X0 @ X1 @ X2))).
% 0.31/0.45 thf(func_def_67, type, oDE_dom: !>[X0: $tType, X1: $tType]:((ode @ X0 @ X1 > set @ X1))).
% 0.31/0.45 thf(func_def_68, type, fsafe: !>[X0: $tType, X1: $tType, X2: $tType]:((formula @ X0 @ X1 @ X2 > $o))).
% 0.31/0.45 thf(func_def_69, type, evolveODE: !>[X0: $tType, X1: $tType, X2: $tType]:((ode @ X0 @ X1 > formula @ X0 @ X2 @ X1 > hp @ X0 @ X2 @ X1))).
% 0.31/0.45 thf(func_def_70, type, hpsafe: !>[X0: $tType, X1: $tType, X2: $tType]:((hp @ X0 @ X1 @ X2 > $o))).
% 0.31/0.45 thf(func_def_71, type, osafe: !>[X0: $tType, X1: $tType]:((ode @ X0 @ X1 > $o))).
% 0.31/0.45 thf(func_def_72, type, topolo507301023within: !>[X0: $tType]:((X0 > set @ X0 > filter @ X0))).
% 0.31/0.45 thf(func_def_73, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.31/0.45 thf(func_def_74, type, i: denota1663640101rp_ext @ a @ b @ c @ product_unit).
% 0.31/0.45 thf(func_def_75, type, j: denota1663640101rp_ext @ a @ b @ c @ product_unit).
% 0.31/0.45 thf(func_def_76, type, ode2: ode @ a @ c).
% 0.31/0.45 thf(func_def_77, type, p: formula @ a @ b @ c).
% 0.31/0.45 thf(func_def_78, type, v: set @ sum_sum @ c @ c).
% 0.31/0.45 thf(func_def_79, type, a2: finite_Cartesian_vec @ real @ c).
% 0.31/0.45 thf(func_def_80, type, aa: finite_Cartesian_vec @ real @ c).
% 0.31/0.45 thf(func_def_81, type, ab: finite_Cartesian_vec @ real @ c).
% 0.31/0.45 thf(func_def_82, type, b2: finite_Cartesian_vec @ real @ c).
% 0.31/0.45 thf(func_def_83, type, ba: finite_Cartesian_vec @ real @ c).
% 0.31/0.45 thf(func_def_84, type, bb: finite_Cartesian_vec @ real @ c).
% 0.31/0.45 thf(func_def_85, type, s: real).
% 0.31/0.45 thf(func_def_86, type, sol: (real > finite_Cartesian_vec @ real @ c)).
% 0.31/0.45 thf(func_def_87, type, t: real).
% 0.31/0.45 thf(func_def_91, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.31/0.45 thf(func_def_92, type, db2: !>[X0: $tType]:(X0)).
% 0.31/0.45 thf(func_def_93, type, db0: !>[X0: $tType]:(X0)).
% 0.31/0.45 thf(func_def_94, type, db1: !>[X0: $tType]:(X0)).
% 0.31/0.45 thf(func_def_95, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.31/0.45 thf(func_def_96, type, vAND: ($o > $o > $o)).
% 0.31/0.45 thf(func_def_97, type, vIMP: ($o > $o > $o)).
% 0.31/0.45 thf(func_def_98, type, db3: !>[X0: $tType]:(X0)).
% 0.31/0.45 thf(func_def_99, type, db4: !>[X0: $tType]:(X0)).
% 0.31/0.45 thf(func_def_100, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.31/0.45 thf(func_def_101, type, vNOT: ($o > $o)).
% 0.31/0.45 thf(func_def_102, type, vOR: ($o > $o > $o)).
% 0.31/0.45 thf(func_def_103, type, sP0: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.31/0.45 thf(func_def_104, type, sP1: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.31/0.45 thf(func_def_105, type, sK2: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.31/0.45 thf(func_def_106, type, sK3: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.31/0.45 thf(func_def_107, type, sK4: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.31/0.45 thf(func_def_108, type, sK5: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X3 @ product_prod @ X4 @ product_prod @ X0 @ product_prod @ X2 @ X1 > $o) > X3))).
% 0.31/0.45 thf(func_def_109, type, sK6: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X3 @ product_prod @ X4 @ product_prod @ X0 @ product_prod @ X2 @ X1 > $o) > X1))).
% 0.31/0.45 thf(func_def_110, type, sK7: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X3 @ product_prod @ X4 @ product_prod @ X0 @ product_prod @ X2 @ X1 > $o) > X2))).
% 0.31/0.45 thf(func_def_111, type, sK8: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X3 @ product_prod @ X4 @ product_prod @ X0 @ product_prod @ X2 @ X1 > $o) > X0))).
% 0.31/0.45 thf(func_def_112, type, sK9: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X3 @ product_prod @ X4 @ product_prod @ X0 @ product_prod @ X2 @ X1 > $o) > X4))).
% 0.31/0.45 thf(func_def_113, type, sK10: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X2 @ product_prod @ X4 @ product_prod @ X5 @ product_prod @ X1 @ product_prod @ X0 @ X3 > $o) > X2))).
% 0.31/0.45 thf(func_def_114, type, sK11: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X2 @ product_prod @ X4 @ product_prod @ X5 @ product_prod @ X1 @ product_prod @ X0 @ X3 > $o) > X4))).
% 0.31/0.45 thf(func_def_115, type, sK12: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X2 @ product_prod @ X4 @ product_prod @ X5 @ product_prod @ X1 @ product_prod @ X0 @ X3 > $o) > X3))).
% 0.31/0.45 thf(func_def_116, type, sK13: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X2 @ product_prod @ X4 @ product_prod @ X5 @ product_prod @ X1 @ product_prod @ X0 @ X3 > $o) > X0))).
% 0.31/0.45 thf(func_def_117, type, sK14: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X2 @ product_prod @ X4 @ product_prod @ X5 @ product_prod @ X1 @ product_prod @ X0 @ X3 > $o) > X1))).
% 0.31/0.45 thf(func_def_118, type, sK15: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X2 @ product_prod @ X4 @ product_prod @ X5 @ product_prod @ X1 @ product_prod @ X0 @ X3 > $o) > X5))).
% 0.31/0.45 thf(func_def_119, type, sK16: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X2 @ product_prod @ X5 @ product_prod @ X6 @ product_prod @ X0 @ product_prod @ X1 @ product_prod @ X3 @ X4 > X2))).
% 0.31/0.45 thf(func_def_120, type, sK17: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X2 @ product_prod @ X5 @ product_prod @ X6 @ product_prod @ X0 @ product_prod @ X1 @ product_prod @ X3 @ X4 > X4))).
% 0.31/0.45 thf(func_def_121, type, sK18: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X2 @ product_prod @ X5 @ product_prod @ X6 @ product_prod @ X0 @ product_prod @ X1 @ product_prod @ X3 @ X4 > X6))).
% 0.31/0.45 thf(func_def_122, type, sK19: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X2 @ product_prod @ X5 @ product_prod @ X6 @ product_prod @ X0 @ product_prod @ X1 @ product_prod @ X3 @ X4 > X0))).
% 0.31/0.45 thf(func_def_123, type, sK20: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X2 @ product_prod @ X5 @ product_prod @ X6 @ product_prod @ X0 @ product_prod @ X1 @ product_prod @ X3 @ X4 > X5))).
% 0.31/0.45 thf(func_def_124, type, sK21: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X2 @ product_prod @ X5 @ product_prod @ X6 @ product_prod @ X0 @ product_prod @ X1 @ product_prod @ X3 @ X4 > X3))).
% 0.31/0.45 thf(func_def_125, type, sK22: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X2 @ product_prod @ X5 @ product_prod @ X6 @ product_prod @ X0 @ product_prod @ X1 @ product_prod @ X3 @ X4 > X1))).
% 0.31/0.45 thf(func_def_126, type, sK23: !>[X0: $tType, X1: $tType]:((set @ X1 > set @ X0 > (X1 > X0) > X1))).
% 0.31/0.45 thf(func_def_127, type, sK24: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.31/0.45 thf(func_def_128, type, sK25: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.31/0.45 thf(func_def_129, type, sK26: !>[X0: $tType]:((product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ X0 > X0))).
% 0.31/0.45 thf(func_def_130, type, sK27: !>[X0: $tType]:((product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ X0 > X0))).
% 0.31/0.45 thf(func_def_131, type, sK28: !>[X0: $tType]:((product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ X0 > X0))).
% 0.31/0.45 thf(func_def_132, type, sK29: !>[X0: $tType]:((product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ X0 > X0))).
% 0.31/0.45 thf(func_def_133, type, sK30: !>[X0: $tType]:((product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ X0 > X0))).
% 0.31/0.45 thf(func_def_134, type, sK31: !>[X0: $tType]:((product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ product_prod @ X0 @ X0 > X0))).
% 0.31/0.45 thf(func_def_135, type, sK32: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > set @ X0 > X0))).
% 0.31/0.45 thf(func_def_136, type, sK33: !>[X0: $tType, X1: $tType]:((set @ X0 > (X0 > X1) > (X0 > X1) > X0))).
% 0.31/0.45 thf(func_def_137, type, sK34: !>[X0: $tType, X1: $tType]:(((product_prod @ X0 @ X1 > $o) > X0))).
% 0.31/0.45 thf(func_def_138, type, sK35: !>[X0: $tType, X1: $tType]:(((product_prod @ X0 @ X1 > $o) > X1))).
% 0.31/0.45 thf(func_def_139, type, sK36: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.31/0.45 thf(func_def_140, type, sK37: !>[X0: $tType, X1: $tType]:((product_prod @ trm @ X1 @ X0 @ X0 > trm @ X1 @ X0))).
% 0.31/0.45 thf(func_def_141, type, sK38: !>[X0: $tType, X1: $tType]:((product_prod @ trm @ X1 @ X0 @ X0 > X0))).
% 0.31/0.45 thf(func_def_142, type, sK39: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > (X0 > X1 > $o) > X0))).
% 0.31/0.45 thf(func_def_143, type, sK40: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > (X0 > X1 > $o) > X1))).
% 0.31/0.45 thf(func_def_144, type, sK41: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.31/0.45 thf(func_def_145, type, sK42: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X3 @ product_prod @ X0 @ product_prod @ X1 @ product_prod @ X4 @ X2 > X0))).
% 0.31/0.45 thf(func_def_146, type, sK43: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X3 @ product_prod @ X0 @ product_prod @ X1 @ product_prod @ X4 @ X2 > X3))).
% 0.31/0.45 thf(func_def_147, type, sK44: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X3 @ product_prod @ X0 @ product_prod @ X1 @ product_prod @ X4 @ X2 > X2))).
% 0.31/0.45 thf(func_def_148, type, sK45: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X3 @ product_prod @ X0 @ product_prod @ X1 @ product_prod @ X4 @ X2 > X4))).
% 0.31/0.45 thf(func_def_149, type, sK46: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X3 @ product_prod @ X0 @ product_prod @ X1 @ product_prod @ X4 @ X2 > X1))).
% 0.31/0.45 thf(func_def_150, type, sK47: !>[X0: $tType]:(((X0 > $o) > set @ X0 > X0))).
% 0.31/0.45 thf(func_def_151, type, sK48: !>[X0: $tType, X1: $tType]:(((X0 > $o) > (X0 > X1) > set @ X1 > X0))).
% 0.31/0.45 thf(func_def_152, type, sK49: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.31/0.45 thf(func_def_153, type, sK50: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.31/0.45 thf(func_def_154, type, sK51: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X1 > set @ product_prod @ X0 @ X1 > X1))).
% 0.31/0.45 thf(func_def_155, type, sK52: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X1 > set @ product_prod @ X0 @ X1 > X0))).
% 0.31/0.45 thf(func_def_156, type, sK53: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.31/0.45 thf(func_def_157, type, sK54: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.31/0.45 thf(func_def_158, type, sK55: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.31/0.45 thf(func_def_159, type, sK56: !>[X0: $tType, X1: $tType]:(((trm @ X0 @ X1 > X1 > $o) > X1))).
% 0.31/0.45 thf(func_def_160, type, sK57: !>[X0: $tType, X1: $tType]:(((trm @ X0 @ X1 > X1 > $o) > trm @ X0 @ X1))).
% 0.31/0.45 thf(func_def_161, type, sK58: !>[X0: $tType, X1: $tType]:(((X1 > X0) > set @ X1 > X0 > X1))).
% 0.31/0.45 thf(func_def_162, type, sK59: !>[X0: $tType, X1: $tType]:((set @ X0 > (X0 > X1) > X1 > X0))).
% 0.31/0.45 thf(func_def_163, type, sK60: !>[X0: $tType, X1: $tType]:((set @ X1 > set @ X0 > (X0 > X1) > set @ X0))).
% 0.31/0.45 thf(func_def_164, type, sK61: !>[X0: $tType, X1: $tType, X2: $tType]:((finite_Cartesian_vec @ real @ X1 > denota1663640101rp_ext @ X0 @ X2 @ X1 @ product_unit > product_prod @ finite_Cartesian_vec @ real @ X1 @ finite_Cartesian_vec @ real @ X1 > ode @ X0 @ X1 > product_prod @ finite_Cartesian_vec @ real @ X1 @ finite_Cartesian_vec @ real @ X1))).
% 0.31/0.45 thf(func_def_165, type, sK62: !>[X0: $tType, X1: $tType, X2: $tType]:(((denota1663640101rp_ext @ X2 @ X0 @ X1 @ product_unit > product_prod @ list @ formula @ X2 @ X0 @ X1 @ list @ formula @ X2 @ X0 @ X1 > $o) > denota1663640101rp_ext @ X2 @ X0 @ X1 @ product_unit))).
% 0.31/0.45 thf(func_def_166, type, sK63: !>[X0: $tType, X1: $tType, X2: $tType]:(((denota1663640101rp_ext @ X2 @ X0 @ X1 @ product_unit > product_prod @ list @ formula @ X2 @ X0 @ X1 @ list @ formula @ X2 @ X0 @ X1 > $o) > product_prod @ list @ formula @ X2 @ X0 @ X1 @ list @ formula @ X2 @ X0 @ X1))).
% 0.31/0.45 thf(func_def_167, type, sK64: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X1 @ X2 > X1))).
% 0.31/0.45 thf(func_def_168, type, sK65: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X1 @ X2 > X0))).
% 0.31/0.45 thf(func_def_169, type, sK66: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X1 @ X2 > X2))).
% 0.31/0.45 thf(func_def_170, type, sK67: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ denota1663640101rp_ext @ X2 @ X1 @ X0 @ product_unit @ product_prod @ list @ formula @ X2 @ X1 @ X0 @ list @ formula @ X2 @ X1 @ X0 > denota1663640101rp_ext @ X2 @ X1 @ X0 @ product_unit))).
% 0.31/0.45 thf(func_def_171, type, sK68: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ denota1663640101rp_ext @ X2 @ X1 @ X0 @ product_unit @ product_prod @ list @ formula @ X2 @ X1 @ X0 @ list @ formula @ X2 @ X1 @ X0 > product_prod @ list @ formula @ X2 @ X1 @ X0 @ list @ formula @ X2 @ X1 @ X0))).
% 0.31/0.45 thf(func_def_172, type, sK69: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X1))).
% 0.31/0.45 thf(func_def_173, type, sK70: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X0))).
% 0.31/0.45 thf(func_def_174, type, sK71: !>[X0: $tType, X1: $tType, X2: $tType]:((hp @ X0 @ X1 @ X2 > denota1663640101rp_ext @ X0 @ X1 @ X2 @ product_unit))).
% 0.31/0.45 thf(func_def_175, type, sK72: !>[X0: $tType, X1: $tType, X2: $tType]:((hp @ X0 @ X1 @ X2 > denota1663640101rp_ext @ X0 @ X1 @ X2 @ product_unit))).
% 0.31/0.45 thf(func_def_176, type, sK73: !>[X0: $tType, X1: $tType]:((set @ X0 > set @ X1 > (X0 > X1) > X0))).
% 0.31/0.45 thf(func_def_177, type, sK74: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X3 @ product_prod @ X2 @ X1 > X3))).
% 0.31/0.45 thf(func_def_178, type, sK75: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X3 @ product_prod @ X2 @ X1 > X2))).
% 0.31/0.45 thf(func_def_179, type, sK76: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X3 @ product_prod @ X2 @ X1 > X1))).
% 0.31/0.45 thf(func_def_180, type, sK77: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X3 @ product_prod @ X2 @ X1 > X0))).
% 0.31/0.45 thf(func_def_181, type, sK78: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.31/0.45 thf(func_def_182, type, sK79: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.31/0.45 thf(func_def_183, type, sK80: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 0.31/0.45 thf(func_def_184, type, sK81: !>[X0: $tType, X1: $tType]:(((X0 > $o) > set @ X1 > (X1 > X0) > X0))).
% 0.31/0.45 thf(func_def_185, type, sK82: !>[X0: $tType, X1: $tType]:((set @ X1 > (X0 > X1) > set @ X0 > set @ X0))).
% 0.31/0.45 thf(func_def_186, type, sK83: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > X1))).
% 0.31/0.45 thf(func_def_187, type, sK84: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > X0))).
% 0.31/0.45 thf(func_def_188, type, sK85: !>[X0: $tType, X1: $tType, X2: $tType]:((formula @ X0 @ X2 @ X1 > denota1663640101rp_ext @ X0 @ X2 @ X1 @ product_unit))).
% 0.31/0.45 thf(func_def_189, type, sK86: !>[X0: $tType, X1: $tType, X2: $tType]:((formula @ X0 @ X2 @ X1 > denota1663640101rp_ext @ X0 @ X2 @ X1 @ product_unit))).
% 0.31/0.45 thf(func_def_190, type, sK87: !>[X0: $tType, X1: $tType, X2: $tType]:((formula @ X0 @ X2 @ X1 > product_prod @ finite_Cartesian_vec @ real @ X1 @ finite_Cartesian_vec @ real @ X1))).
% 0.31/0.45 thf(func_def_191, type, sK88: !>[X0: $tType, X1: $tType, X2: $tType]:((formula @ X0 @ X2 @ X1 > product_prod @ finite_Cartesian_vec @ real @ X1 @ finite_Cartesian_vec @ real @ X1))).
% 0.31/0.45 thf(func_def_192, type, sK89: !>[X0: $tType, X1: $tType]:((set @ X0 > (X0 > X1) > (X1 > $o) > X0))).
% 0.31/0.45 thf(func_def_193, type, sK90: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > $o) > X1))).
% 0.31/0.45 thf(func_def_194, type, sK91: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > $o) > X0))).
% 0.31/0.45 thf(func_def_195, type, sK92: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > $o) > X2))).
% 0.31/0.45 thf(func_def_196, type, sK93: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > $o) > X3))).
% 0.31/0.45 thf(func_def_197, type, sK94: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.31/0.45 thf(func_def_198, type, sK95: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (set @ X0 > $o) > set @ X1 > set @ X1))).
% 0.31/0.45 thf(func_def_199, type, sK96: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (set @ X0 > $o) > set @ X1 > set @ X0))).
% 0.31/0.45 thf(func_def_200, type, sK97: !>[X0: $tType]:((product_prod @ X0 @ X0 > X0))).
% 0.31/0.45 thf(func_def_201, type, sK98: !>[X0: $tType]:((product_prod @ X0 @ X0 > X0))).
% 0.31/0.45 thf(func_def_202, type, sK99: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.31/0.45 thf(func_def_203, type, sK100: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.31/0.45 thf(func_def_204, type, sK101: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.31/0.45 thf(func_def_205, type, sK102: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.31/0.45 thf(func_def_206, type, sK103: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X3 @ product_prod @ X0 @ product_prod @ X2 @ product_prod @ X5 @ product_prod @ X1 @ X4 > X3))).
% 0.31/0.45 thf(func_def_207, type, sK104: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X3 @ product_prod @ X0 @ product_prod @ X2 @ product_prod @ X5 @ product_prod @ X1 @ X4 > X0))).
% 0.31/0.45 thf(func_def_208, type, sK105: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X3 @ product_prod @ X0 @ product_prod @ X2 @ product_prod @ X5 @ product_prod @ X1 @ X4 > X2))).
% 0.31/0.45 thf(func_def_209, type, sK106: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X3 @ product_prod @ X0 @ product_prod @ X2 @ product_prod @ X5 @ product_prod @ X1 @ X4 > X4))).
% 0.31/0.45 thf(func_def_210, type, sK107: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X3 @ product_prod @ X0 @ product_prod @ X2 @ product_prod @ X5 @ product_prod @ X1 @ X4 > X5))).
% 0.31/0.45 thf(func_def_211, type, sK108: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X3 @ product_prod @ X0 @ product_prod @ X2 @ product_prod @ X5 @ product_prod @ X1 @ X4 > X1))).
% 0.31/0.45 thf(func_def_212, type, sK109: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > X0))).
% 0.31/0.45 thf(func_def_213, type, sK110: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > X1))).
% 0.31/0.45 thf(func_def_214, type, sK111: !>[X0: $tType]:((set @ real > (real > X0) > (real > X0) > real))).
% 0.31/0.45 thf(func_def_215, type, sK112: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ product_prod @ X0 @ X1 > $o) > X0))).
% 0.31/0.45 thf(func_def_216, type, sK113: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ product_prod @ X0 @ X1 > $o) > X1))).
% 0.31/0.45 thf(func_def_217, type, sK114: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ product_prod @ X0 @ X1 > $o) > X2))).
% 0.31/0.45 thf(func_def_218, type, sK115: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X1 @ product_prod @ X3 @ product_prod @ X6 @ product_prod @ X2 @ product_prod @ X0 @ product_prod @ X4 @ X5 > $o) > X5))).
% 0.31/0.45 thf(func_def_219, type, sK116: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X1 @ product_prod @ X3 @ product_prod @ X6 @ product_prod @ X2 @ product_prod @ X0 @ product_prod @ X4 @ X5 > $o) > X3))).
% 0.31/0.45 thf(func_def_220, type, sK117: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X1 @ product_prod @ X3 @ product_prod @ X6 @ product_prod @ X2 @ product_prod @ X0 @ product_prod @ X4 @ X5 > $o) > X4))).
% 0.31/0.45 thf(func_def_221, type, sK118: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X1 @ product_prod @ X3 @ product_prod @ X6 @ product_prod @ X2 @ product_prod @ X0 @ product_prod @ X4 @ X5 > $o) > X6))).
% 0.31/0.45 thf(func_def_222, type, sK119: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X1 @ product_prod @ X3 @ product_prod @ X6 @ product_prod @ X2 @ product_prod @ X0 @ product_prod @ X4 @ X5 > $o) > X2))).
% 0.31/0.45 thf(func_def_223, type, sK120: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X1 @ product_prod @ X3 @ product_prod @ X6 @ product_prod @ X2 @ product_prod @ X0 @ product_prod @ X4 @ X5 > $o) > X0))).
% 0.31/0.45 thf(func_def_224, type, sK121: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X1 @ product_prod @ X3 @ product_prod @ X6 @ product_prod @ X2 @ product_prod @ X0 @ product_prod @ X4 @ X5 > $o) > X1))).
% 0.31/0.45 thf(f2,axiom,(
% 0.31/0.45 (denotational_Vagree @ c @ (denotational_mk_v @ a @ b @ c @ j @ ode2 @ (product_Pair @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ aa @ ba) @ (sol @ s)) @ (denotational_mk_xode @ a @ b @ c @ j @ ode2 @ (sol @ s)) @ (denotational_semBV @ a @ b @ c @ j @ ode2)) & (denotational_Vagree @ c @ (denotational_mk_v @ a @ b @ c @ j @ ode2 @ (product_Pair @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ aa @ ba) @ (sol @ s)) @ (product_Pair @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ aa @ ba) @ (uminus_uminus @ set @ sum_sum @ c @ c @ (denotational_semBV @ a @ b @ c @ j @ ode2)))),
% 0.31/0.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1__092_060open_062Vagree_A_Imk__v_AJ_AODE_A_Iaa_M_Aba_J_A_Isol_As_J_J_A_Iaa_M_Aba_J_A_I_N_AsemBV_AJ_AODE_J_A_092_060and_062_AVagree_A_Imk__v_AJ_AODE_A_Iaa_M_Aba_J_A_Isol_As_J_J_A_Imk__xode_AJ_AODE_A_Isol_As_J_J_A_IsemBV_AJ_AODE_J_092_060close_062)).
% 0.31/0.45 thf(f341,conjecture,(
% 0.31/0.45 (denotational_Vagree @ c @ (denotational_mk_v @ a @ b @ c @ j @ ode2 @ (product_Pair @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ aa @ ba) @ (sol @ s)) @ (denotational_mk_xode @ a @ b @ c @ j @ ode2 @ (sol @ s)) @ (denotational_semBV @ a @ b @ c @ j @ ode2))),
% 0.31/0.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 0.31/0.45 thf(f342,negated_conjecture,(
% 0.31/0.45 ~(denotational_Vagree @ c @ (denotational_mk_v @ a @ b @ c @ j @ ode2 @ (product_Pair @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ aa @ ba) @ (sol @ s)) @ (denotational_mk_xode @ a @ b @ c @ j @ ode2 @ (sol @ s)) @ (denotational_semBV @ a @ b @ c @ j @ ode2))),
% 0.31/0.45 inference(negated_conjecture,[status(cth)],[f341])).
% 0.31/0.45 thf(f527,plain,(
% 0.31/0.45 (denotational_Vagree @ c @ (denotational_mk_v @ a @ b @ c @ j @ ode2 @ (product_Pair @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ aa @ ba) @ (sol @ s)) @ (denotational_mk_xode @ a @ b @ c @ j @ ode2 @ (sol @ s)) @ (denotational_semBV @ a @ b @ c @ j @ ode2)) & (denotational_Vagree @ c @ (denotational_mk_v @ a @ b @ c @ j @ ode2 @ (product_Pair @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ aa @ ba) @ (sol @ s)) @ (product_Pair @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ aa @ ba) @ (uminus_uminus @ set @ sum_sum @ c @ c @ (denotational_semBV @ a @ b @ c @ j @ ode2)))),
% 0.31/0.45 inference(rectify,[],[f2])).
% 0.31/0.45 thf(f528,plain,(
% 0.31/0.45 (((denotational_Vagree @ c @ (denotational_mk_v @ a @ b @ c @ j @ ode2 @ (product_Pair @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ aa @ ba) @ (sol @ s)) @ (denotational_mk_xode @ a @ b @ c @ j @ ode2 @ (sol @ s)) @ (denotational_semBV @ a @ b @ c @ j @ ode2))) = $true) & (((denotational_Vagree @ c @ (denotational_mk_v @ a @ b @ c @ j @ ode2 @ (product_Pair @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ aa @ ba) @ (sol @ s)) @ (product_Pair @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ aa @ ba) @ (uminus_uminus @ set @ sum_sum @ c @ c @ (denotational_semBV @ a @ b @ c @ j @ ode2)))) = $true)),
% 0.31/0.45 inference(fool_elimination,[],[f527])).
% 0.31/0.45 thf(f629,plain,(
% 0.31/0.45 ~(denotational_Vagree @ c @ (denotational_mk_v @ a @ b @ c @ j @ ode2 @ (product_Pair @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ aa @ ba) @ (sol @ s)) @ (denotational_mk_xode @ a @ b @ c @ j @ ode2 @ (sol @ s)) @ (denotational_semBV @ a @ b @ c @ j @ ode2))),
% 0.31/0.45 inference(rectify,[],[f342])).
% 0.31/0.45 thf(f630,plain,(
% 0.31/0.45 ~ (((denotational_Vagree @ c @ (denotational_mk_v @ a @ b @ c @ j @ ode2 @ (product_Pair @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ aa @ ba) @ (sol @ s)) @ (denotational_mk_xode @ a @ b @ c @ j @ ode2 @ (sol @ s)) @ (denotational_semBV @ a @ b @ c @ j @ ode2))) = $true)),
% 0.31/0.45 inference(fool_elimination,[],[f629])).
% 0.31/0.45 thf(f1004,plain,(
% 0.31/0.45 (((denotational_Vagree @ c @ (denotational_mk_v @ a @ b @ c @ j @ ode2 @ (product_Pair @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ aa @ ba) @ (sol @ s)) @ (denotational_mk_xode @ a @ b @ c @ j @ ode2 @ (sol @ s)) @ (denotational_semBV @ a @ b @ c @ j @ ode2))) != $true)),
% 0.31/0.45 inference(flattening,[],[f630])).
% 0.31/0.45 thf(f1996,plain,(
% 0.31/0.45 (((denotational_Vagree @ c @ (denotational_mk_v @ a @ b @ c @ j @ ode2 @ (product_Pair @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ aa @ ba) @ (sol @ s)) @ (denotational_mk_xode @ a @ b @ c @ j @ ode2 @ (sol @ s)) @ (denotational_semBV @ a @ b @ c @ j @ ode2))) != $true)),
% 0.31/0.45 inference(cnf_transformation,[],[f1004])).
% 0.31/0.45 thf(f2007,plain,(
% 0.31/0.45 (((denotational_Vagree @ c @ (denotational_mk_v @ a @ b @ c @ j @ ode2 @ (product_Pair @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ aa @ ba) @ (sol @ s)) @ (denotational_mk_xode @ a @ b @ c @ j @ ode2 @ (sol @ s)) @ (denotational_semBV @ a @ b @ c @ j @ ode2))) = $true)),
% 0.31/0.45 inference(cnf_transformation,[],[f528])).
% 0.31/0.45 thf(f2280,definition,(
% 0.31/0.45 spl122_13 <=> (((denotational_Vagree @ c @ (denotational_mk_v @ a @ b @ c @ j @ ode2 @ (product_Pair @ finite_Cartesian_vec @ real @ c @ finite_Cartesian_vec @ real @ c @ aa @ ba) @ (sol @ s)) @ (denotational_mk_xode @ a @ b @ c @ j @ ode2 @ (sol @ s)) @ (denotational_semBV @ a @ b @ c @ j @ ode2))) = $true)),
% 0.31/0.45 introduced(definition,[new_symbols(definition,[spl122_13])],[avatar_definition])).
% 0.31/0.45 thf(f2283,plain,(
% 0.31/0.45 ~spl122_13),
% 0.31/0.45 inference(avatar_split_clause,[],[f1996,f2280])).
% 0.31/0.45 thf(f2299,plain,(
% 0.31/0.45 spl122_13),
% 0.31/0.45 inference(avatar_split_clause,[],[f2007,f2280])).
% 0.31/0.45 cnf(s11, plain, ~spl122_13, inference(sat_conversion,[],[f2283])).
% 0.31/0.45 cnf(s15, plain, spl122_13, inference(sat_conversion,[],[f2299])).
% 0.31/0.45 cnf(s76, plain, $false, inference(rat,[],[s11,s15])).
% 0.31/0.45 thf(f2578,plain,(
% 0.31/0.45 $false),
% 0.31/0.45 inference(avatar_sat_refutation,[],[s76])).
% 0.31/0.45 % SZS output end Proof for theBenchmark
% 0.31/0.45 % (3310912)------------------------------
% 0.31/0.45 % (3310912)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.31/0.45 % (3310912)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.31/0.45 % (3310912)CaDiCaL version: 2.1.3
% 0.31/0.45 % (3310912)Termination reason: Refutation
% 0.31/0.45 % (3310912)Time elapsed: 0.084 s
% 0.31/0.45 % (3310912)Peak memory usage: 15 MB
% 0.31/0.45 % (3310912)Instructions burned: 170 (million)
% 0.31/0.45 % (3310904)Success in time 0.143 s
% 0.31/0.45 % Vampire exiting
%------------------------------------------------------------------------------