%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP149^2 : 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 : n007.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 08:08:34 AM UTC 2026
% Result : Theorem 0.54s 0.44s
% Output : Refutation 0.54s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP149^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n007.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 20:00:08 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running higher-order theorem proving
% 0.23/0.27 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
% 0.54/0.44 % (3855643)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.54/0.44 % (3855653)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1197524897:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.54/0.44 % (3855654)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.54/0.44 % (3855654)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
% 0.54/0.44 % (3855650)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3341603085:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.54/0.44 % (3855648)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2617323448:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.54/0.44 % (3855654)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=2949537447:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.54/0.44 % (3855652)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=685665251:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.54/0.44 % (3855651)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=2386793126: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)
% 0.54/0.44 % (3855650)Instruction limit reached!
% 0.54/0.44 % (3855650)------------------------------
% 0.54/0.44 % (3855650)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.44 % (3855650)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.44 % (3855650)CaDiCaL version: 2.1.3
% 0.54/0.44 % (3855650)Termination reason: Instruction limit
% 0.54/0.44 % (3855650)Termination phase: shuffling
% 0.54/0.44 % (3855650)Time elapsed: 0.002 s
% 0.54/0.44 % (3855650)Peak memory usage: 10 MB
% 0.54/0.44 % (3855650)Instructions burned: 4 (million)
% 0.54/0.44 % (3855649)lrs+10_16_si=on:nwc=1.5:random_seed=312682330:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.54/0.44 % (3855652)Instruction limit reached!
% 0.54/0.44 % (3855652)------------------------------
% 0.54/0.44 % (3855652)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.44 % (3855652)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.44 % (3855652)CaDiCaL version: 2.1.3
% 0.54/0.44 % (3855652)Termination reason: Instruction limit
% 0.54/0.44 % (3855652)Termination phase: Property scanning
% 0.54/0.44 % (3855652)Time elapsed: 0.011 s
% 0.54/0.44 % (3855652)Peak memory usage: 10 MB
% 0.54/0.44 % (3855652)Instructions burned: 24 (million)
% 0.54/0.44 % (3855653)Instruction limit reached!
% 0.54/0.44 % (3855653)------------------------------
% 0.54/0.44 % (3855653)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.44 % (3855653)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.44 % (3855653)CaDiCaL version: 2.1.3
% 0.54/0.44 % (3855653)Termination reason: Instruction limit
% 0.54/0.44 % (3855653)Termination phase: Property scanning
% 0.54/0.44 % (3855653)Time elapsed: 0.020 s
% 0.54/0.44 % (3855653)Peak memory usage: 12 MB
% 0.54/0.44 % (3855653)Instructions burned: 78 (million)
% 0.54/0.44 % (3855649)Instruction limit reached!
% 0.54/0.44 % (3855649)------------------------------
% 0.54/0.44 % (3855649)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.44 % (3855649)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.44 % (3855649)CaDiCaL version: 2.1.3
% 0.54/0.44 % (3855649)Termination reason: Instruction limit
% 0.54/0.44 % (3855649)Termination phase: Property scanning
% 0.54/0.44 % (3855649)Time elapsed: 0.018 s
% 0.54/0.44 % (3855649)Peak memory usage: 10 MB
% 0.54/0.44 % (3855649)Instructions burned: 24 (million)
% 0.54/0.44 % (3855664)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.54/0.44 % (3855664)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1992358668:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.54/0.44 % (3855664)Instruction limit reached!
% 0.54/0.44 % (3855664)------------------------------
% 0.54/0.44 % (3855664)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.44 % (3855664)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.44 % (3855664)CaDiCaL version: 2.1.3
% 0.54/0.44 % (3855664)Termination reason: Instruction limit
% 0.54/0.44 % (3855664)Termination phase: shuffling
% 0.54/0.44 % (3855664)Time elapsed: 0.002 s
% 0.54/0.44 % (3855664)Peak memory usage: 10 MB
% 0.54/0.44 % (3855664)Instructions burned: 9 (million)
% 0.54/0.44 % (3855662)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2913070098:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.54/0.44 % (3855662)Instruction limit reached!
% 0.54/0.44 % (3855662)------------------------------
% 0.54/0.44 % (3855662)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.44 % (3855662)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.44 % (3855662)CaDiCaL version: 2.1.3
% 0.54/0.44 % (3855662)Termination reason: Instruction limit
% 0.54/0.44 % (3855662)Termination phase: shuffling
% 0.54/0.44 % (3855662)Time elapsed: 0.003 s
% 0.54/0.44 % (3855662)Peak memory usage: 10 MB
% 0.54/0.44 % (3855662)Instructions burned: 2 (million)
% 0.54/0.44 % (3855663)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2330331157:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.54/0.44 % (3855663)Instruction limit reached!
% 0.54/0.44 % (3855663)------------------------------
% 0.54/0.44 % (3855663)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.44 % (3855663)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.44 % (3855663)CaDiCaL version: 2.1.3
% 0.54/0.44 % (3855663)Termination reason: Instruction limit
% 0.54/0.44 % (3855663)Termination phase: shuffling
% 0.54/0.44 % (3855663)Time elapsed: 0.003 s
% 0.54/0.44 % (3855663)Peak memory usage: 10 MB
% 0.54/0.44 % (3855663)Instructions burned: 5 (million)
% 0.54/0.44 % (3855668)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
% 0.54/0.44 % (3855668)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.54/0.44 % (3855668)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2617397582:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.54/0.44 % (3855648)Instruction limit reached!
% 0.54/0.44 % (3855648)------------------------------
% 0.54/0.44 % (3855648)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.44 % (3855648)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.44 % (3855648)CaDiCaL version: 2.1.3
% 0.54/0.44 % (3855648)Termination reason: Instruction limit
% 0.54/0.44 % (3855648)Termination phase: Saturation
% 0.54/0.44 % (3855648)Time elapsed: 0.041 s
% 0.54/0.44 % (3855648)Peak memory usage: 12 MB
% 0.54/0.44 % (3855648)Instructions burned: 89 (million)
% 0.54/0.44 % (3855665)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2055344974:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.54/0.44 % (3855668)Instruction limit reached!
% 0.54/0.44 % (3855668)------------------------------
% 0.54/0.44 % (3855668)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.44 % (3855668)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.44 % (3855668)CaDiCaL version: 2.1.3
% 0.54/0.44 % (3855668)Termination reason: Instruction limit
% 0.54/0.44 % (3855668)Termination phase: Property scanning
% 0.54/0.44 % (3855668)Time elapsed: 0.007 s
% 0.54/0.44 % (3855668)Peak memory usage: 10 MB
% 0.54/0.44 % (3855668)Instructions burned: 30 (million)
% 0.54/0.44 % (3855665)Instruction limit reached!
% 0.54/0.44 % (3855665)------------------------------
% 0.54/0.44 % (3855665)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.44 % (3855665)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.44 % (3855665)CaDiCaL version: 2.1.3
% 0.54/0.44 % (3855665)Termination reason: Instruction limit
% 0.54/0.44 % (3855665)Termination phase: shuffling
% 0.54/0.44 % (3855665)Time elapsed: 0.007 s
% 0.54/0.44 % (3855665)Peak memory usage: 10 MB
% 0.54/0.44 % (3855665)Instructions burned: 14 (million)
% 0.54/0.44 % (3855673)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.54/0.44 % (3855669)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=433350930:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.54/0.44 % (3855671)lrs+10_1_si=on:cs=on:random_seed=2428472436:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.54/0.44 % (3855675)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=2678577807:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 0.54/0.44 % (3855673)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=823751593:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.54/0.44 % (3855671)Instruction limit reached!
% 0.54/0.44 % (3855671)------------------------------
% 0.54/0.44 % (3855671)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.44 % (3855671)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.44 % (3855671)CaDiCaL version: 2.1.3
% 0.54/0.44 % (3855671)Termination reason: Instruction limit
% 0.54/0.44 % (3855671)Termination phase: shuffling
% 0.54/0.44 % (3855671)Time elapsed: 0.005 s
% 0.54/0.44 % (3855671)Peak memory usage: 10 MB
% 0.54/0.44 % (3855671)Instructions burned: 8 (million)
% 0.54/0.44 % (3855673)Instruction limit reached!
% 0.54/0.44 % (3855673)------------------------------
% 0.54/0.44 % (3855673)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.44 % (3855673)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.44 % (3855673)CaDiCaL version: 2.1.3
% 0.54/0.44 % (3855673)Termination reason: Instruction limit
% 0.54/0.44 % (3855673)Termination phase: shuffling
% 0.54/0.44 % (3855673)Time elapsed: 0.004 s
% 0.54/0.44 % (3855673)Peak memory usage: 10 MB
% 0.54/0.44 % (3855673)Instructions burned: 7 (million)
% 0.54/0.44 % (3855654)Instruction limit reached!
% 0.54/0.44 % (3855654)------------------------------
% 0.54/0.44 % (3855654)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.44 % (3855654)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.44 % (3855654)CaDiCaL version: 2.1.3
% 0.54/0.44 % (3855654)Termination reason: Instruction limit
% 0.54/0.44 % (3855654)Termination phase: Saturation
% 0.54/0.44 % (3855654)Time elapsed: 0.078 s
% 0.54/0.44 % (3855654)Peak memory usage: 13 MB
% 0.54/0.44 % (3855654)Instructions burned: 158 (million)
% 0.54/0.44 % (3855676)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=355007417:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 0.54/0.44 % (3855675)Instruction limit reached!
% 0.54/0.44 % (3855675)------------------------------
% 0.54/0.44 % (3855675)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.44 % (3855675)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.44 % (3855675)CaDiCaL version: 2.1.3
% 0.54/0.44 % (3855675)Termination reason: Instruction limit
% 0.54/0.44 % (3855675)Termination phase: shuffling
% 0.54/0.44 % (3855675)Time elapsed: 0.027 s
% 0.54/0.44 % (3855675)Peak memory usage: 11 MB
% 0.54/0.44 % (3855675)Instructions burned: 40 (million)
% 0.54/0.44 % (3855685)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=2507301660:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 0.54/0.44 % (3855651) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3855643-3855651"...
% 0.54/0.44 % (3855682)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=23196429:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.54/0.44 % (3855685)Instruction limit reached!
% 0.54/0.44 % (3855685)------------------------------
% 0.54/0.44 % (3855685)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.44 % (3855685)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.44 % (3855685)CaDiCaL version: 2.1.3
% 0.54/0.44 % (3855685)Termination reason: Instruction limit
% 0.54/0.44 % (3855685)Termination phase: shuffling
% 0.54/0.44 % (3855685)Time elapsed: 0.004 s
% 0.54/0.44 % (3855685)Peak memory usage: 10 MB
% 0.54/0.44 % (3855651)...printing done.
% 0.54/0.44 % (3855685)Instructions burned: 16 (million)
% 0.54/0.44 % (3855683)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=1953990384:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 0.54/0.44 % (3855651)Refutation found. Thanks to Tanya!
% 0.54/0.44 % SZS status Theorem for theBenchmark
% 0.54/0.44 % SZS output start Proof for theBenchmark
% 0.54/0.44 thf(type_def_5, type, bounde2145540817linfun: ($tType * $tType) > $tType).
% 0.54/0.44 thf(type_def_6, type, real: $tType).
% 0.54/0.44 thf(type_def_7, type, set: $tType > $tType).
% 0.54/0.44 thf(type_def_8, type, a: $tType).
% 0.54/0.44 thf(type_def_9, type, sTfun: ($tType * $tType) > $tType).
% 0.54/0.44 thf(func_def_0, type, finite_finite: !>[X0: $tType]:($o)).
% 0.54/0.44 thf(func_def_1, type, type: !>[X0: $tType]:($o)).
% 0.54/0.44 thf(func_def_2, type, countable: !>[X0: $tType]:($o)).
% 0.54/0.44 thf(func_def_3, type, zero: !>[X0: $tType]:($o)).
% 0.54/0.44 thf(func_def_4, type, minus: !>[X0: $tType]:($o)).
% 0.54/0.44 thf(func_def_5, type, uminus: !>[X0: $tType]:($o)).
% 0.54/0.44 thf(func_def_6, type, ord: !>[X0: $tType]:($o)).
% 0.54/0.44 thf(func_def_7, type, order: !>[X0: $tType]:($o)).
% 0.54/0.44 thf(func_def_8, type, group_add: !>[X0: $tType]:($o)).
% 0.54/0.44 thf(func_def_9, type, linorder: !>[X0: $tType]:($o)).
% 0.54/0.44 thf(func_def_10, type, preorder: !>[X0: $tType]:($o)).
% 0.54/0.44 thf(func_def_11, type, ab_group_add: !>[X0: $tType]:($o)).
% 0.54/0.44 thf(func_def_12, type, comm_monoid_diff: !>[X0: $tType]:($o)).
% 0.54/0.44 thf(func_def_13, type, inner_real_inner: !>[X0: $tType]:($o)).
% 0.54/0.44 thf(func_def_14, type, boolean_algebra: !>[X0: $tType]:($o)).
% 0.54/0.44 thf(func_def_15, type, ordered_ab_group_add: !>[X0: $tType]:($o)).
% 0.54/0.44 thf(func_def_16, type, cancel1352612707id_add: !>[X0: $tType]:($o)).
% 0.54/0.44 thf(func_def_17, type, cancel146912293up_add: !>[X0: $tType]:($o)).
% 0.54/0.44 thf(func_def_18, type, linord219039673up_add: !>[X0: $tType]:($o)).
% 0.54/0.44 thf(func_def_19, type, euclid925273238_space: !>[X0: $tType]:($o)).
% 0.54/0.44 thf(func_def_20, type, real_V2090557954_space: !>[X0: $tType]:($o)).
% 0.54/0.44 thf(func_def_21, type, topolo890362671_space: !>[X0: $tType]:($o)).
% 0.54/0.44 thf(func_def_22, type, canoni770627133id_add: !>[X0: $tType]:($o)).
% 0.54/0.44 thf(func_def_23, type, ordere890947078_space: !>[X0: $tType]:($o)).
% 0.54/0.44 thf(func_def_24, type, execut510477386_space: !>[X0: $tType]:($o)).
% 0.54/0.44 thf(func_def_25, type, elemen321786957_cball: !>[X0: $tType]:((X0 > real > set @ X0))).
% 0.54/0.44 thf(func_def_26, type, auto_l1112008849e_ivl0: !>[X0: $tType]:(((X0 > X0) > set @ X0 > X0 > set @ real))).
% 0.54/0.44 thf(func_def_27, type, minus_minus: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.54/0.44 thf(func_def_28, type, uminus_uminus: !>[X0: $tType]:((X0 > X0))).
% 0.54/0.44 thf(func_def_29, type, zero_zero: !>[X0: $tType]:(X0)).
% 0.54/0.44 thf(func_def_30, type, initia826609931terval: (set @ real > $o)).
% 0.54/0.44 thf(func_def_31, type, inner_780170721_inner: !>[X0: $tType]:((X0 > X0 > real))).
% 0.54/0.44 thf(func_def_32, type, auto_ll_on_invariant: !>[X0: $tType]:(((X0 > X0) > set @ X0 > set @ X0 > $o))).
% 0.54/0.44 thf(func_def_33, type, line_closed_segment: !>[X0: $tType]:((X0 > X0 > set @ X0))).
% 0.54/0.44 thf(func_def_34, type, line_open_segment: !>[X0: $tType]:((X0 > X0 > set @ X0))).
% 0.54/0.44 thf(func_def_35, type, oDE_au1039603466rapped: !>[X0: $tType]:(((X0 > X0) > set @ X0 > X0 > set @ X0 > $o))).
% 0.54/0.44 thf(func_def_36, type, ord_less: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.54/0.44 thf(func_def_37, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.54/0.44 thf(func_def_38, type, top_top: !>[X0: $tType]:(X0)).
% 0.54/0.44 thf(func_def_39, type, period385816147_orbit: !>[X0: $tType]:(((X0 > X0) > set @ X0 > X0 > $o))).
% 0.54/0.44 thf(func_def_40, type, period1153813292period: !>[X0: $tType]:(((X0 > X0) > set @ X0 > X0 > real))).
% 0.54/0.44 thf(func_def_41, type, period862636932_orbit: !>[X0: $tType]:(((X0 > X0) > set @ X0 > X0 > $o))).
% 0.54/0.44 thf(func_def_42, type, poinca1750768982en_rot: !>[X0: $tType]:((X0 > X0))).
% 0.54/0.44 thf(func_def_43, type, poinca272511729egment: !>[X0: $tType]:(((X0 > X0) > set @ X0 > X0 > X0 > $o))).
% 0.54/0.44 thf(func_def_44, type, reacha1084862253ection: !>[X0: $tType]:(((X0 > X0) > set @ X0 > (X0 > real) > (X0 > bounde2145540817linfun @ X0 @ real) > set @ X0 > $o))).
% 0.54/0.44 thf(func_def_45, type, real_V2000881966t_dist: !>[X0: $tType]:((X0 > X0 > real))).
% 0.54/0.44 thf(func_def_46, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 0.54/0.44 thf(func_def_47, type, set_or331188842AtMost: !>[X0: $tType]:((X0 > X0 > set @ X0))).
% 0.54/0.44 thf(func_def_48, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.54/0.44 thf(func_def_49, type, x: set @ a).
% 0.54/0.44 thf(func_def_50, type, a2: a).
% 0.54/0.44 thf(func_def_51, type, b: a).
% 0.54/0.44 thf(func_def_52, type, d: real).
% 0.54/0.44 thf(func_def_53, type, f: (a > a)).
% 0.54/0.44 thf(func_def_54, type, s: a).
% 0.54/0.44 thf(func_def_55, type, thesis: $o).
% 0.54/0.44 thf(func_def_56, type, x2: a).
% 0.54/0.44 thf(func_def_57, type, z: a).
% 0.54/0.44 thf(func_def_61, type, db1: !>[X0: $tType]:(X0)).
% 0.54/0.44 thf(func_def_62, type, db0: !>[X0: $tType]:(X0)).
% 0.54/0.44 thf(func_def_63, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.54/0.44 thf(func_def_64, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.54/0.44 thf(func_def_65, type, db2: !>[X0: $tType]:(X0)).
% 0.54/0.44 thf(func_def_66, type, vAND: ($o > $o > $o)).
% 0.54/0.44 thf(func_def_67, type, vOR: ($o > $o > $o)).
% 0.54/0.44 thf(func_def_68, type, vNOT: ($o > $o)).
% 0.54/0.44 thf(func_def_69, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.54/0.44 thf(func_def_70, type, vIMP: ($o > $o > $o)).
% 0.54/0.44 thf(func_def_71, type, sP0: ((real > real > $o) > real > real > $o)).
% 0.54/0.44 thf(func_def_72, type, sK1: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.54/0.44 thf(func_def_73, type, sK2: (set @ a > (a > a) > a)).
% 0.54/0.44 thf(func_def_74, type, sK3: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.54/0.44 thf(func_def_75, type, sK4: (set @ a > a)).
% 0.54/0.44 thf(func_def_76, type, sK5: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 0.54/0.44 thf(func_def_77, type, sK6: (a > a)).
% 0.54/0.44 thf(func_def_78, type, sK7: (a > a)).
% 0.54/0.44 thf(func_def_79, type, sK8: (real > real > a)).
% 0.54/0.44 thf(func_def_80, type, sK9: (real > real > a)).
% 0.54/0.44 thf(func_def_81, type, sK10: real).
% 0.54/0.44 thf(func_def_82, type, sK11: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.54/0.44 thf(func_def_83, type, sK12: (real > real > a)).
% 0.54/0.44 thf(func_def_84, type, sK13: (a > real)).
% 0.54/0.44 thf(func_def_85, type, sK14: !>[X0: $tType]:((real > X0 > X0))).
% 0.54/0.44 thf(func_def_86, type, sK15: ((real > real > $o) > real > real > real)).
% 0.54/0.44 thf(func_def_87, type, sK16: (real > (real > real > $o) > real > real > real)).
% 0.54/0.44 thf(func_def_88, type, sK17: (real > (real > real > $o) > real > real > real)).
% 0.54/0.44 thf(func_def_89, type, sK18: ((real > real > $o) > real)).
% 0.54/0.44 thf(func_def_90, type, sK19: ((real > real > $o) > real)).
% 0.54/0.44 thf(func_def_91, type, sK20: ((real > real > $o) > real)).
% 0.54/0.44 thf(func_def_92, type, sK21: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.54/0.44 thf(func_def_93, type, sK22: (a > a > a)).
% 0.54/0.44 thf(func_def_94, type, sK23: !>[X0: $tType]:((X0 > X0))).
% 0.54/0.44 thf(func_def_95, type, sK24: (a > real)).
% 0.54/0.44 thf(func_def_96, type, sK25: (a > real)).
% 0.54/0.44 thf(func_def_97, type, sK26: (a > real)).
% 0.54/0.44 thf(func_def_98, type, sK27: (a > real)).
% 0.54/0.44 thf(func_def_99, type, sK28: a).
% 0.54/0.44 thf(func_def_100, type, sK29: (set @ a > a)).
% 0.54/0.44 thf(func_def_101, type, sK30: (a > real)).
% 0.54/0.44 thf(func_def_102, type, sK31: (set @ a > (a > a) > a)).
% 0.54/0.44 thf(func_def_103, type, sK32: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 0.54/0.44 thf(func_def_104, type, sK33: a).
% 0.54/0.44 thf(f1,axiom,(
% 0.54/0.44 (ord_less @ real @ zero_zero @ real @ d)),
% 0.54/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_d_I1_J)).
% 0.54/0.44 thf(f2,axiom,(
% 0.54/0.44 (member @ a @ s @ (elemen321786957_cball @ a @ x2 @ d))),
% 0.54/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1__092_060open_062s_A_092_060in_062_Acball_Ax_Ad_092_060close_062)).
% 0.54/0.44 thf(f6,axiom,(
% 0.54/0.44 ! [X0 : a] : ((member @ a @ X0 @ (elemen321786957_cball @ a @ x2 @ d)) => (ord_less_eq @ real @ (inner_780170721_inner @ a @ (f @ s) @ (poinca1750768982en_rot @ a @ (minus_minus @ a @ a2 @ b))) @ (inner_780170721_inner @ a @ (f @ X0) @ (poinca1750768982en_rot @ a @ (minus_minus @ a @ a2 @ b)))))),
% 0.54/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5__092_060open_062_092_060forall_062x_092_060in_062cball_Ax_Ad_O_Af_As_A_092_060bullet_062_Arot_A_Ia_A_N_Ab_J_A_092_060le_062_Af_Ax_A_092_060bullet_062_Arot_A_Ia_A_N_Ab_J_092_060close_062)).
% 0.54/0.44 thf(f9,axiom,(
% 0.54/0.44 ! [X0 : a] : ((member @ a @ X0 @ (elemen321786957_cball @ a @ x2 @ d)) => ((ord_less @ real @ zero_zero @ real @ (inner_780170721_inner @ a @ (f @ X0) @ (poinca1750768982en_rot @ a @ (minus_minus @ a @ a2 @ b)))) & (member @ a @ X0 @ x) & (((f @ X0)) != zero_zero @ a)))),
% 0.54/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_d_I2_J)).
% 0.54/0.44 thf(f320,conjecture,(
% 0.54/0.44 ? [X0 : real] : ((ord_less @ real @ zero_zero @ real @ X0) & ? [X1 : real] : (! [X2 : a] : ((member @ a @ X2 @ (elemen321786957_cball @ a @ x2 @ X0)) => (ord_less_eq @ real @ X1 @ (inner_780170721_inner @ a @ (f @ X2) @ (poinca1750768982en_rot @ a @ (minus_minus @ a @ a2 @ b))))) & (ord_less @ real @ zero_zero @ real @ X1)))),
% 0.54/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 0.54/0.44 thf(f321,negated_conjecture,(
% 0.54/0.44 ~ ? [X0 : real] : ((ord_less @ real @ zero_zero @ real @ X0) & ? [X1 : real] : (! [X2 : a] : ((member @ a @ X2 @ (elemen321786957_cball @ a @ x2 @ X0)) => (ord_less_eq @ real @ X1 @ (inner_780170721_inner @ a @ (f @ X2) @ (poinca1750768982en_rot @ a @ (minus_minus @ a @ a2 @ b))))) & (ord_less @ real @ zero_zero @ real @ X1)))),
% 0.54/0.44 inference(negated_conjecture,[status(cth)],[f320])).
% 0.54/0.44 thf(f380,plain,(
% 0.54/0.44 ! [X0 : a] : ((member @ a @ X0 @ (elemen321786957_cball @ a @ x2 @ d)) => ((ord_less @ real @ zero_zero @ real @ (inner_780170721_inner @ a @ (f @ X0) @ (poinca1750768982en_rot @ a @ (minus_minus @ a @ a2 @ b)))) & (member @ a @ X0 @ x) & (((f @ X0)) != zero_zero @ a)))),
% 0.54/0.44 inference(rectify,[],[f9])).
% 0.54/0.44 thf(f381,plain,(
% 0.54/0.44 ! [X0 : a] : ((((member @ a @ X0 @ (elemen321786957_cball @ a @ x2 @ d))) = $true) => ((((member @ a @ X0 @ x)) = $true) & (((f @ X0)) != zero_zero @ a) & (((ord_less @ real @ zero_zero @ real @ (inner_780170721_inner @ a @ (f @ X0) @ (poinca1750768982en_rot @ a @ (minus_minus @ a @ a2 @ b))))) = $true)))),
% 0.54/0.44 inference(fool_elimination,[],[f380])).
% 0.54/0.44 thf(f562,plain,(
% 0.54/0.44 ! [X0 : a] : ((member @ a @ X0 @ (elemen321786957_cball @ a @ x2 @ d)) => (ord_less_eq @ real @ (inner_780170721_inner @ a @ (f @ s) @ (poinca1750768982en_rot @ a @ (minus_minus @ a @ a2 @ b))) @ (inner_780170721_inner @ a @ (f @ X0) @ (poinca1750768982en_rot @ a @ (minus_minus @ a @ a2 @ b)))))),
% 0.54/0.44 inference(rectify,[],[f6])).
% 0.54/0.44 thf(f563,plain,(
% 0.54/0.44 ! [X0 : a] : ((((member @ a @ X0 @ (elemen321786957_cball @ a @ x2 @ d))) = $true) => (((ord_less_eq @ real @ (inner_780170721_inner @ a @ (f @ s) @ (poinca1750768982en_rot @ a @ (minus_minus @ a @ a2 @ b))) @ (inner_780170721_inner @ a @ (f @ X0) @ (poinca1750768982en_rot @ a @ (minus_minus @ a @ a2 @ b))))) = $true))),
% 0.54/0.44 inference(fool_elimination,[],[f562])).
% 0.54/0.44 thf(f568,plain,(
% 0.54/0.44 (ord_less @ real @ zero_zero @ real @ d)),
% 0.54/0.44 inference(rectify,[],[f1])).
% 0.54/0.44 thf(f569,plain,(
% 0.54/0.44 (((ord_less @ real @ zero_zero @ real @ d)) = $true)),
% 0.54/0.44 inference(fool_elimination,[],[f568])).
% 0.54/0.44 thf(f866,plain,(
% 0.54/0.44 ~ ? [X0 : real] : ((ord_less @ real @ zero_zero @ real @ X0) & ? [X1 : real] : (! [X2 : a] : ((member @ a @ X2 @ (elemen321786957_cball @ a @ x2 @ X0)) => (ord_less_eq @ real @ X1 @ (inner_780170721_inner @ a @ (f @ X2) @ (poinca1750768982en_rot @ a @ (minus_minus @ a @ a2 @ b))))) & (ord_less @ real @ zero_zero @ real @ X1)))),
% 0.54/0.44 inference(rectify,[],[f321])).
% 0.54/0.44 thf(f867,plain,(
% 0.54/0.44 ~ ? [X0 : real] : (? [X1 : real] : (! [X2 : a] : ((((member @ a @ X2 @ (elemen321786957_cball @ a @ x2 @ X0))) = $true) => (((ord_less_eq @ real @ X1 @ (inner_780170721_inner @ a @ (f @ X2) @ (poinca1750768982en_rot @ a @ (minus_minus @ a @ a2 @ b))))) = $true)) & (((ord_less @ real @ zero_zero @ real @ X1)) = $true)) & (((ord_less @ real @ zero_zero @ real @ X0)) = $true))),
% 0.54/0.44 inference(fool_elimination,[],[f866])).
% 0.54/0.44 thf(f916,plain,(
% 0.54/0.44 (member @ a @ s @ (elemen321786957_cball @ a @ x2 @ d))),
% 0.54/0.44 inference(rectify,[],[f2])).
% 0.54/0.44 thf(f917,plain,(
% 0.54/0.44 (((member @ a @ s @ (elemen321786957_cball @ a @ x2 @ d))) = $true)),
% 0.54/0.44 inference(fool_elimination,[],[f916])).
% 0.54/0.44 thf(f1053,plain,(
% 0.54/0.44 ! [X0 : real] : ((((ord_less @ real @ zero_zero @ real @ X0)) != $true) | ! [X1 : real] : (? [X2 : a] : ((((ord_less_eq @ real @ X1 @ (inner_780170721_inner @ a @ (f @ X2) @ (poinca1750768982en_rot @ a @ (minus_minus @ a @ a2 @ b))))) != $true) & (((member @ a @ X2 @ (elemen321786957_cball @ a @ x2 @ X0))) = $true)) | (((ord_less @ real @ zero_zero @ real @ X1)) != $true)))),
% 0.54/0.44 inference(ennf_transformation,[],[f867])).
% 0.54/0.44 thf(f1054,plain,(
% 0.54/0.44 ! [X0 : a] : ((((member @ a @ X0 @ (elemen321786957_cball @ a @ x2 @ d))) != $true) | ((((member @ a @ X0 @ x)) = $true) & (((f @ X0)) != zero_zero @ a) & (((ord_less @ real @ zero_zero @ real @ (inner_780170721_inner @ a @ (f @ X0) @ (poinca1750768982en_rot @ a @ (minus_minus @ a @ a2 @ b))))) = $true)))),
% 0.54/0.44 inference(ennf_transformation,[],[f381])).
% 0.54/0.44 thf(f1119,plain,(
% 0.54/0.44 ! [X0 : a] : ((((member @ a @ X0 @ (elemen321786957_cball @ a @ x2 @ d))) != $true) | (((ord_less_eq @ real @ (inner_780170721_inner @ a @ (f @ s) @ (poinca1750768982en_rot @ a @ (minus_minus @ a @ a2 @ b))) @ (inner_780170721_inner @ a @ (f @ X0) @ (poinca1750768982en_rot @ a @ (minus_minus @ a @ a2 @ b))))) = $true))),
% 0.54/0.44 inference(ennf_transformation,[],[f563])).
% 0.54/0.44 thf(f1306,plain,(
% 0.54/0.44 ! [X0 : real] : ((((ord_less @ real @ zero_zero @ real @ X0)) != $true) | ! [X1 : real] : (((((ord_less_eq @ real @ X1 @ (inner_780170721_inner @ a @ (f @ (sK12 @ X1 @ X0)) @ (poinca1750768982en_rot @ a @ (minus_minus @ a @ a2 @ b))))) != $true) & (((member @ a @ (sK12 @ X1 @ X0) @ (elemen321786957_cball @ a @ x2 @ X0))) = $true)) | (((ord_less @ real @ zero_zero @ real @ X1)) != $true)))),
% 0.54/0.44 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X4,sK1 @ X0 @ X1 @ X3 @ X2)],[f1053])).
% 0.54/0.44 thf(f1525,plain,(
% 0.54/0.44 ( ! [X0 : a] : ((((ord_less_eq @ real @ (inner_780170721_inner @ a @ (f @ s) @ (poinca1750768982en_rot @ a @ (minus_minus @ a @ a2 @ b))) @ (inner_780170721_inner @ a @ (f @ X0) @ (poinca1750768982en_rot @ a @ (minus_minus @ a @ a2 @ b))))) = $true) | (((member @ a @ X0 @ (elemen321786957_cball @ a @ x2 @ d))) != $true)) )),
% 0.54/0.44 inference(cnf_transformation,[],[f1119])).
% 0.54/0.44 thf(f1577,plain,(
% 0.54/0.44 ( ! [X0 : real,X1 : real] : ((((member @ a @ (sK12 @ X1 @ X0) @ (elemen321786957_cball @ a @ x2 @ X0))) = $true) | (((ord_less @ real @ zero_zero @ real @ X0)) != $true) | (((ord_less @ real @ zero_zero @ real @ X1)) != $true)) )),
% 0.54/0.44 inference(cnf_transformation,[],[f1306])).
% 0.54/0.44 thf(f1578,plain,(
% 0.54/0.44 ( ! [X0 : real,X1 : real] : ((((ord_less_eq @ real @ X1 @ (inner_780170721_inner @ a @ (f @ (sK12 @ X1 @ X0)) @ (poinca1750768982en_rot @ a @ (minus_minus @ a @ a2 @ b))))) != $true) | (((ord_less @ real @ zero_zero @ real @ X1)) != $true) | (((ord_less @ real @ zero_zero @ real @ X0)) != $true)) )),
% 0.54/0.44 inference(cnf_transformation,[],[f1306])).
% 0.54/0.44 thf(f1628,plain,(
% 0.54/0.44 ( ! [X0 : a] : ((((ord_less @ real @ zero_zero @ real @ (inner_780170721_inner @ a @ (f @ X0) @ (poinca1750768982en_rot @ a @ (minus_minus @ a @ a2 @ b))))) = $true) | (((member @ a @ X0 @ (elemen321786957_cball @ a @ x2 @ d))) != $true)) )),
% 0.54/0.44 inference(cnf_transformation,[],[f1054])).
% 0.54/0.44 thf(f1830,plain,(
% 0.54/0.44 (((ord_less @ real @ zero_zero @ real @ d)) = $true)),
% 0.54/0.44 inference(cnf_transformation,[],[f569])).
% 0.54/0.44 thf(f1834,plain,(
% 0.54/0.44 (((member @ a @ s @ (elemen321786957_cball @ a @ x2 @ d))) = $true)),
% 0.54/0.44 inference(cnf_transformation,[],[f917])).
% 0.54/0.44 thf(f2016,definition,(
% 0.54/0.44 spl34_14 <=> (((member @ a @ s @ (elemen321786957_cball @ a @ x2 @ d))) = $true)),
% 0.54/0.44 introduced(definition,[new_symbols(definition,[spl34_14])],[avatar_definition])).
% 0.54/0.44 thf(f2018,plain,(
% 0.54/0.44 (((member @ a @ s @ (elemen321786957_cball @ a @ x2 @ d))) = $true) | ~spl34_14),
% 0.54/0.44 inference(avatar_component_clause,[],[f2016])).
% 0.54/0.44 thf(f2019,plain,(
% 0.54/0.44 spl34_14),
% 0.54/0.44 inference(avatar_split_clause,[],[f1834,f2016])).
% 0.54/0.44 thf(f2036,definition,(
% 0.54/0.44 spl34_18 <=> (((ord_less @ real @ zero_zero @ real @ d)) = $true)),
% 0.54/0.44 introduced(definition,[new_symbols(definition,[spl34_18])],[avatar_definition])).
% 0.54/0.44 thf(f2039,plain,(
% 0.54/0.44 spl34_18),
% 0.54/0.44 inference(avatar_split_clause,[],[f1830,f2036])).
% 0.54/0.44 thf(f2618,plain,(
% 0.54/0.44 ( ! [X0 : real] : ((((member @ a @ (sK12 @ (inner_780170721_inner @ a @ (f @ s) @ (poinca1750768982en_rot @ a @ (minus_minus @ a @ a2 @ b))) @ X0) @ (elemen321786957_cball @ a @ x2 @ d))) != $true) | (((ord_less @ real @ zero_zero @ real @ X0)) != $true) | ($true != $true) | (((ord_less @ real @ zero_zero @ real @ (inner_780170721_inner @ a @ (f @ s) @ (poinca1750768982en_rot @ a @ (minus_minus @ a @ a2 @ b))))) != $true)) )),
% 0.54/0.44 inference(superposition,[],[f1578,f1525])).
% 0.54/0.44 thf(f2619,plain,(
% 0.54/0.44 ( ! [X0 : real] : ((((member @ a @ (sK12 @ (inner_780170721_inner @ a @ (f @ s) @ (poinca1750768982en_rot @ a @ (minus_minus @ a @ a2 @ b))) @ X0) @ (elemen321786957_cball @ a @ x2 @ d))) != $true) | (((ord_less @ real @ zero_zero @ real @ (inner_780170721_inner @ a @ (f @ s) @ (poinca1750768982en_rot @ a @ (minus_minus @ a @ a2 @ b))))) != $true) | (((ord_less @ real @ zero_zero @ real @ X0)) != $true)) )),
% 0.54/0.44 inference(trivial_inequality_removal,[],[f2618])).
% 0.54/0.44 thf(f2621,definition,(
% 0.54/0.44 spl34_86 <=> ! [X0 : real] : ((((member @ a @ (sK12 @ (inner_780170721_inner @ a @ (f @ s) @ (poinca1750768982en_rot @ a @ (minus_minus @ a @ a2 @ b))) @ X0) @ (elemen321786957_cball @ a @ x2 @ d))) != $true) | (((ord_less @ real @ zero_zero @ real @ X0)) != $true))),
% 0.54/0.44 introduced(definition,[new_symbols(definition,[spl34_86])],[avatar_definition])).
% 0.54/0.44 thf(f2622,plain,(
% 0.54/0.44 ( ! [X0 : real] : ((((member @ a @ (sK12 @ (inner_780170721_inner @ a @ (f @ s) @ (poinca1750768982en_rot @ a @ (minus_minus @ a @ a2 @ b))) @ X0) @ (elemen321786957_cball @ a @ x2 @ d))) != $true) | (((ord_less @ real @ zero_zero @ real @ X0)) != $true)) ) | ~spl34_86),
% 0.54/0.44 inference(avatar_component_clause,[],[f2621])).
% 0.54/0.44 thf(f2624,definition,(
% 0.54/0.44 spl34_87 <=> (((ord_less @ real @ zero_zero @ real @ (inner_780170721_inner @ a @ (f @ s) @ (poinca1750768982en_rot @ a @ (minus_minus @ a @ a2 @ b))))) = $true)),
% 0.54/0.44 introduced(definition,[new_symbols(definition,[spl34_87])],[avatar_definition])).
% 0.54/0.44 thf(f2625,plain,(
% 0.54/0.44 (((ord_less @ real @ zero_zero @ real @ (inner_780170721_inner @ a @ (f @ s) @ (poinca1750768982en_rot @ a @ (minus_minus @ a @ a2 @ b))))) = $true) | ~spl34_87),
% 0.54/0.44 inference(avatar_component_clause,[],[f2624])).
% 0.54/0.44 thf(f2626,plain,(
% 0.54/0.44 (((ord_less @ real @ zero_zero @ real @ (inner_780170721_inner @ a @ (f @ s) @ (poinca1750768982en_rot @ a @ (minus_minus @ a @ a2 @ b))))) != $true) | spl34_87),
% 0.54/0.44 inference(avatar_component_clause,[],[f2624])).
% 0.54/0.44 thf(f2627,plain,(
% 0.54/0.44 spl34_86 | ~spl34_87),
% 0.54/0.44 inference(avatar_split_clause,[],[f2619,f2624,f2621])).
% 0.54/0.44 thf(f2642,plain,(
% 0.54/0.44 (((member @ a @ s @ (elemen321786957_cball @ a @ x2 @ d))) != $true) | ($true != $true) | spl34_87),
% 0.54/0.44 inference(superposition,[],[f2626,f1628])).
% 0.54/0.44 thf(f2646,plain,(
% 0.54/0.44 (((member @ a @ s @ (elemen321786957_cball @ a @ x2 @ d))) != $true) | spl34_87),
% 0.54/0.44 inference(trivial_inequality_removal,[],[f2642])).
% 0.54/0.44 thf(f2657,plain,(
% 0.54/0.44 $false | (~spl34_14 | spl34_87)),
% 0.54/0.44 inference(forward_subsumption_resolution,[],[f2646,f2018])).
% 0.54/0.44 thf(f2658,plain,(
% 0.54/0.44 ~spl34_14 | spl34_87),
% 0.54/0.44 inference(avatar_contradiction_clause,[],[f2657])).
% 0.54/0.44 thf(f2692,plain,(
% 0.54/0.44 (((ord_less @ real @ zero_zero @ real @ d)) != $true) | ($true != $true) | (((ord_less @ real @ zero_zero @ real @ d)) != $true) | (((ord_less @ real @ zero_zero @ real @ (inner_780170721_inner @ a @ (f @ s) @ (poinca1750768982en_rot @ a @ (minus_minus @ a @ a2 @ b))))) != $true) | ~spl34_86),
% 0.54/0.44 inference(superposition,[],[f2622,f1577])).
% 0.54/0.44 thf(f2698,plain,(
% 0.54/0.44 ($true != $true) | (((ord_less @ real @ zero_zero @ real @ (inner_780170721_inner @ a @ (f @ s) @ (poinca1750768982en_rot @ a @ (minus_minus @ a @ a2 @ b))))) != $true) | (((ord_less @ real @ zero_zero @ real @ d)) != $true) | ~spl34_86),
% 0.54/0.44 inference(duplicate_literal_removal,[],[f2692])).
% 0.54/0.44 thf(f2699,plain,(
% 0.54/0.44 (((ord_less @ real @ zero_zero @ real @ (inner_780170721_inner @ a @ (f @ s) @ (poinca1750768982en_rot @ a @ (minus_minus @ a @ a2 @ b))))) != $true) | (((ord_less @ real @ zero_zero @ real @ d)) != $true) | ~spl34_86),
% 0.54/0.44 inference(trivial_inequality_removal,[],[f2698])).
% 0.54/0.44 thf(f2701,plain,(
% 0.54/0.44 (((ord_less @ real @ zero_zero @ real @ d)) != $true) | (~spl34_86 | ~spl34_87)),
% 0.54/0.44 inference(forward_subsumption_resolution,[],[f2699,f2625])).
% 0.54/0.44 thf(f2702,plain,(
% 0.54/0.44 ~spl34_18 | ~spl34_86 | ~spl34_87),
% 0.54/0.44 inference(avatar_split_clause,[],[f2701,f2624,f2621,f2036])).
% 0.54/0.44 cnf(s12, plain, spl34_14, inference(sat_conversion,[],[f2019])).
% 0.54/0.44 cnf(s16, plain, spl34_18, inference(sat_conversion,[],[f2039])).
% 0.54/0.44 cnf(s91, plain, spl34_86 | ~spl34_87, inference(sat_conversion,[],[f2627])).
% 0.54/0.44 cnf(s95, plain, ~spl34_14 | spl34_87, inference(sat_conversion,[],[f2658])).
% 0.54/0.44 cnf(s99, plain, ~spl34_18 | ~spl34_86 | ~spl34_87, inference(sat_conversion,[],[f2702])).
% 0.54/0.44 cnf(s107, plain, spl34_87, inference(rat,[],[s95,s12])).
% 0.54/0.44 cnf(s110, plain, spl34_86, inference(rat,[],[s91,s107])).
% 0.54/0.44 cnf(s111, plain, $false, inference(rat,[],[s99,s16,s107,s110])).
% 0.54/0.44 thf(f2703,plain,(
% 0.54/0.44 $false),
% 0.54/0.44 inference(avatar_sat_refutation,[],[s111])).
% 0.54/0.44 % SZS output end Proof for theBenchmark
% 0.54/0.44 % (3855651)------------------------------
% 0.54/0.44 % (3855651)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.54/0.44 % (3855651)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.54/0.44 % (3855651)CaDiCaL version: 2.1.3
% 0.54/0.44 % (3855651)Termination reason: Refutation
% 0.54/0.44 % (3855651)Time elapsed: 0.100 s
% 0.54/0.44 % (3855651)Peak memory usage: 15 MB
% 0.54/0.44 % (3855651)Instructions burned: 187 (million)
% 0.54/0.44 % (3855643)Success in time 0.161 s
% 0.54/0.44 % Vampire exiting
%------------------------------------------------------------------------------