%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP110^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:08:23 AM UTC 2026
% Result : Theorem 1.29s 0.73s
% Output : Refutation 1.29s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ITP110^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.30 % Computer : n008.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8046.5625MB
% 0.11/0.30 % OS : Linux 6.8.0-71-generic
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % WCLimit : 300
% 0.11/0.30 % DateTime : Tue Sep 29 19:55:55 UTC 2026
% 0.11/0.30 % CPUTime :
% 0.11/0.30 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.31/0.36 Running higher-order theorem proving
% 0.35/0.45 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.29/0.73 % (3653444)Detected a higher-order problem, will run a greedy HOL sequence.
% 1.29/0.73 % (3653450)lrs+10_16_si=on:nwc=1.5:random_seed=4242311948:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 1.29/0.73 % (3653453)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1534985529:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 1.29/0.73 % (3653450)Instruction limit reached!
% 1.29/0.73 % (3653450)------------------------------
% 1.29/0.73 % (3653450)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.29/0.73 % (3653450)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.29/0.73 % (3653450)CaDiCaL version: 2.1.3
% 1.29/0.73 % (3653450)Termination reason: Instruction limit
% 1.29/0.73 % (3653450)Termination phase: Property scanning
% 1.29/0.73 % (3653450)Time elapsed: 0.016 s
% 1.29/0.73 % (3653450)Peak memory usage: 11 MB
% 1.29/0.73 % (3653450)Instructions burned: 18 (million)
% 1.29/0.73 % (3653453)Instruction limit reached!
% 1.29/0.73 % (3653453)------------------------------
% 1.29/0.73 % (3653453)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.29/0.73 % (3653453)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.29/0.73 % (3653453)CaDiCaL version: 2.1.3
% 1.29/0.73 % (3653453)Termination reason: Instruction limit
% 1.29/0.73 % (3653453)Termination phase: Property scanning
% 1.29/0.73 % (3653453)Time elapsed: 0.010 s
% 1.29/0.73 % (3653453)Peak memory usage: 10 MB
% 1.29/0.73 % (3653453)Instructions burned: 24 (million)
% 1.29/0.73 % (3653449)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=375495551:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 1.29/0.73 % (3653451)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=262655527:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 1.29/0.73 % (3653455)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 1.29/0.73 % (3653455)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
% 1.29/0.73 % (3653451)Instruction limit reached!
% 1.29/0.73 % (3653451)------------------------------
% 1.29/0.73 % (3653451)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.29/0.73 % (3653451)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.29/0.73 % (3653451)CaDiCaL version: 2.1.3
% 1.29/0.73 % (3653451)Termination reason: Instruction limit
% 1.29/0.73 % (3653451)Termination phase: shuffling
% 1.29/0.73 % (3653451)Time elapsed: 0.004 s
% 1.29/0.73 % (3653451)Peak memory usage: 10 MB
% 1.29/0.73 % (3653451)Instructions burned: 4 (million)
% 1.29/0.73 % (3653455)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=3608462371:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 1.29/0.73 % (3653452)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=2278147856: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)
% 1.29/0.73 % (3653454)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=4017792144:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 1.29/0.73 % (3653462)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.29/0.73 % (3653462)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1528923571:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2998 on theBenchmark for (2998ds/7Mi)
% 1.29/0.73 % (3653458)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=987993058:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 1.29/0.73 % (3653462)Instruction limit reached!
% 1.29/0.73 % (3653462)------------------------------
% 1.29/0.73 % (3653462)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.29/0.73 % (3653462)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.29/0.73 % (3653462)CaDiCaL version: 2.1.3
% 1.29/0.73 % (3653462)Termination reason: Instruction limit
% 1.29/0.73 % (3653462)Termination phase: shuffling
% 1.29/0.73 % (3653462)Time elapsed: 0.003 s
% 1.29/0.73 % (3653462)Peak memory usage: 10 MB
% 1.29/0.73 % (3653462)Instructions burned: 7 (million)
% 1.29/0.73 % (3653458)Instruction limit reached!
% 1.29/0.73 % (3653458)------------------------------
% 1.29/0.73 % (3653458)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.29/0.73 % (3653458)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.29/0.73 % (3653458)CaDiCaL version: 2.1.3
% 1.29/0.73 % (3653458)Termination reason: Instruction limit
% 1.29/0.73 % (3653458)Termination phase: shuffling
% 1.29/0.73 % (3653458)Time elapsed: 0.003 s
% 1.29/0.73 % (3653458)Peak memory usage: 10 MB
% 1.29/0.73 % (3653458)Instructions burned: 2 (million)
% 1.29/0.73 % (3653459)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1310759607:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2998 on theBenchmark for (2998ds/5Mi)
% 1.29/0.73 % (3653459)Instruction limit reached!
% 1.29/0.73 % (3653459)------------------------------
% 1.29/0.73 % (3653459)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.29/0.73 % (3653459)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.29/0.73 % (3653459)CaDiCaL version: 2.1.3
% 1.29/0.73 % (3653459)Termination reason: Instruction limit
% 1.29/0.73 % (3653459)Termination phase: shuffling
% 1.29/0.73 % (3653459)Time elapsed: 0.005 s
% 1.29/0.73 % (3653459)Peak memory usage: 10 MB
% 1.29/0.73 % (3653459)Instructions burned: 5 (million)
% 1.29/0.73 % (3653468)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1618444227:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2998 on theBenchmark for (2998ds/12Mi)
% 1.29/0.73 % (3653468)Instruction limit reached!
% 1.29/0.73 % (3653468)------------------------------
% 1.29/0.73 % (3653468)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.29/0.73 % (3653468)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.29/0.73 % (3653468)CaDiCaL version: 2.1.3
% 1.29/0.73 % (3653468)Termination reason: Instruction limit
% 1.29/0.73 % (3653468)Termination phase: shuffling
% 1.29/0.73 % (3653468)Time elapsed: 0.006 s
% 1.29/0.73 % (3653468)Peak memory usage: 10 MB
% 1.29/0.73 % (3653468)Instructions burned: 13 (million)
% 1.29/0.73 % (3653469)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
% 1.29/0.73 % (3653469)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.29/0.73 % (3653469)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=1204483462:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2998 on theBenchmark for (2998ds/28Mi)
% 1.29/0.73 % (3653449)Instruction limit reached!
% 1.29/0.73 % (3653449)------------------------------
% 1.29/0.73 % (3653449)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.29/0.73 % (3653449)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.29/0.73 % (3653449)CaDiCaL version: 2.1.3
% 1.29/0.73 % (3653449)Termination reason: Instruction limit
% 1.29/0.73 % (3653449)Termination phase: Property scanning
% 1.29/0.73 % (3653449)Time elapsed: 0.073 s
% 1.29/0.73 % (3653449)Peak memory usage: 12 MB
% 1.29/0.73 % (3653449)Instructions burned: 87 (million)
% 1.29/0.73 % (3653471)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=1732707932:i=86:piset=equals:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/86Mi)
% 1.29/0.73 % (3653473)lrs+10_1_si=on:cs=on:random_seed=3389157263:i=8:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.29/0.73 % (3653454)Instruction limit reached!
% 1.29/0.73 % (3653454)------------------------------
% 1.29/0.73 % (3653454)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.29/0.73 % (3653454)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.29/0.73 % (3653454)CaDiCaL version: 2.1.3
% 1.29/0.73 % (3653454)Termination reason: Instruction limit
% 1.29/0.73 % (3653454)Termination phase: Property scanning
% 1.29/0.73 % (3653454)Time elapsed: 0.067 s
% 1.29/0.73 % (3653454)Peak memory usage: 12 MB
% 1.29/0.73 % (3653454)Instructions burned: 75 (million)
% 1.29/0.73 % (3653469)Instruction limit reached!
% 1.29/0.73 % (3653469)------------------------------
% 1.29/0.73 % (3653469)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.29/0.73 % (3653469)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.29/0.73 % (3653469)CaDiCaL version: 2.1.3
% 1.29/0.73 % (3653469)Termination reason: Instruction limit
% 1.29/0.73 % (3653469)Termination phase: shuffling
% 1.29/0.73 % (3653469)Time elapsed: 0.025 s
% 1.29/0.73 % (3653469)Peak memory usage: 10 MB
% 1.29/0.73 % (3653469)Instructions burned: 29 (million)
% 1.29/0.73 % (3653475)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 1.29/0.73 % (3653473)Instruction limit reached!
% 1.29/0.73 % (3653473)------------------------------
% 1.29/0.73 % (3653473)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.29/0.73 % (3653473)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.29/0.73 % (3653473)CaDiCaL version: 2.1.3
% 1.29/0.73 % (3653473)Termination reason: Instruction limit
% 1.29/0.73 % (3653473)Termination phase: shuffling
% 1.29/0.73 % (3653473)Time elapsed: 0.007 s
% 1.29/0.73 % (3653473)Peak memory usage: 10 MB
% 1.29/0.73 % (3653473)Instructions burned: 8 (million)
% 1.29/0.73 % (3653475)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=2286957405:i=2:add=on:rtra=on_2998 on theBenchmark for (2998ds/2Mi)
% 1.29/0.73 % (3653475)Instruction limit reached!
% 1.29/0.73 % (3653475)------------------------------
% 1.29/0.73 % (3653475)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.29/0.73 % (3653475)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.29/0.73 % (3653475)CaDiCaL version: 2.1.3
% 1.29/0.73 % (3653475)Termination reason: Instruction limit
% 1.29/0.73 % (3653475)Termination phase: shuffling
% 1.29/0.73 % (3653475)Time elapsed: 0.003 s
% 1.29/0.73 % (3653475)Peak memory usage: 10 MB
% 1.29/0.73 % (3653475)Instructions burned: 3 (million)
% 1.29/0.73 % (3653478)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=1236545938:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2997 on theBenchmark for (2997ds/38Mi)
% 1.29/0.73 % (3653479)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=201720379:st=2:i=249:sd=1:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/249Mi)
% 1.29/0.73 % (3653480)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=1288800143:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2997 on theBenchmark for (2997ds/25Mi)
% 1.29/0.73 % (3653482)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=1858483912:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2997 on theBenchmark for (2997ds/14Mi)
% 1.29/0.73 % (3653452) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3653444-3653452"...
% 1.29/0.73 % (3653455)Instruction limit reached!
% 1.29/0.73 % (3653455)------------------------------
% 1.29/0.73 % (3653455)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.29/0.73 % (3653455)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.29/0.73 % (3653455)CaDiCaL version: 2.1.3
% 1.29/0.73 % (3653455)Termination reason: Instruction limit
% 1.29/0.73 % (3653455)Termination phase: Saturation
% 1.29/0.73 % (3653455)Time elapsed: 0.132 s
% 1.29/0.73 % (3653455)Peak memory usage: 14 MB
% 1.29/0.73 % (3653455)Instructions burned: 157 (million)
% 1.29/0.73 % (3653471)Instruction limit reached!
% 1.29/0.73 % (3653471)------------------------------
% 1.29/0.73 % (3653471)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.29/0.73 % (3653471)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.29/0.73 % (3653471)CaDiCaL version: 2.1.3
% 1.29/0.73 % (3653471)Termination reason: Instruction limit
% 1.29/0.73 % (3653471)Termination phase: Property scanning
% 1.29/0.73 % (3653471)Time elapsed: 0.069 s
% 1.29/0.73 % (3653471)Peak memory usage: 11 MB
% 1.29/0.73 % (3653471)Instructions burned: 86 (million)
% 1.29/0.73 % (3653452)...printing done.
% 1.29/0.73 % (3653452)Refutation found. Thanks to Tanya!
% 1.29/0.73 % SZS status Theorem for theBenchmark
% 1.29/0.73 % SZS output start Proof for theBenchmark
% 1.29/0.73 thf(type_def_5, type, set_Pr1158285382l_real: $tType).
% 1.29/0.73 thf(type_def_6, type, set_Pr597221087l_real: $tType).
% 1.29/0.73 thf(type_def_7, type, set_se1849684334_ereal: $tType).
% 1.29/0.73 thf(type_def_8, type, set_Pr1928503567a_real: $tType).
% 1.29/0.73 thf(type_def_9, type, set_se767749006_ereal: $tType).
% 1.29/0.73 thf(type_def_10, type, set_Extended_ereal_o: $tType).
% 1.29/0.73 thf(type_def_11, type, set_set_set_a: $tType).
% 1.29/0.73 thf(type_def_12, type, product_prod_a_real: $tType).
% 1.29/0.73 thf(type_def_13, type, set_Extended_ereal: $tType).
% 1.29/0.73 thf(type_def_14, type, set_set_a: $tType).
% 1.29/0.73 thf(type_def_15, type, set_a_o: $tType).
% 1.29/0.73 thf(type_def_16, type, set_real: $tType).
% 1.29/0.73 thf(type_def_17, type, extended_ereal: $tType).
% 1.29/0.73 thf(type_def_18, type, set_a: $tType).
% 1.29/0.73 thf(type_def_19, type, real: $tType).
% 1.29/0.73 thf(type_def_20, type, a: $tType).
% 1.29/0.73 thf(type_def_21, type, sTfun: ($tType * $tType) > $tType).
% 1.29/0.73 thf(func_def_0, type, comple179807490real_o: (set_Extended_ereal_o > extended_ereal > $o)).
% 1.29/0.73 thf(func_def_1, type, complete_Sup_Sup_a_o: (set_a_o > a > $o)).
% 1.29/0.73 thf(func_def_2, type, comple1161760187_ereal: (set_Extended_ereal > extended_ereal)).
% 1.29/0.73 thf(func_def_3, type, comple2129349247p_real: (set_real > real)).
% 1.29/0.73 thf(func_def_4, type, comple767846299_ereal: (set_se767749006_ereal > set_Extended_ereal)).
% 1.29/0.73 thf(func_def_5, type, comple1517911419_ereal: (set_se1849684334_ereal > set_se767749006_ereal)).
% 1.29/0.73 thf(func_def_6, type, comple968993579_set_a: (set_set_set_a > set_set_a)).
% 1.29/0.73 thf(func_def_7, type, comple1766734283_set_a: (set_set_a > set_a)).
% 1.29/0.73 thf(func_def_8, type, convex291263275l_real: (set_Pr1158285382l_real > $o)).
% 1.29/0.73 thf(func_def_9, type, convex78185044a_real: (set_Pr1928503567a_real > $o)).
% 1.29/0.73 thf(func_def_10, type, convex_a: (set_a > $o)).
% 1.29/0.73 thf(func_def_11, type, extend1289208545_ereal: extended_ereal).
% 1.29/0.73 thf(func_def_12, type, extended_MInfty: extended_ereal).
% 1.29/0.73 thf(func_def_13, type, extended_PInfty: extended_ereal).
% 1.29/0.73 thf(func_def_14, type, extended_ereal2: (real > extended_ereal)).
% 1.29/0.73 thf(func_def_15, type, extend1716541707_ereal: (extended_ereal > real)).
% 1.29/0.73 thf(func_def_16, type, times_1966848393_ereal: (extended_ereal > extended_ereal > extended_ereal)).
% 1.29/0.73 thf(func_def_17, type, times_times_real: (real > real > real)).
% 1.29/0.73 thf(func_def_18, type, uminus1208298309_ereal: (extended_ereal > extended_ereal)).
% 1.29/0.73 thf(func_def_19, type, uminus_uminus_real: (real > real)).
% 1.29/0.73 thf(func_def_20, type, uminus360668453_ereal: (set_Extended_ereal > set_Extended_ereal)).
% 1.29/0.73 thf(func_def_21, type, uminus_uminus_set_a: (set_a > set_a)).
% 1.29/0.73 thf(func_def_22, type, zero_z163181189_ereal: extended_ereal).
% 1.29/0.73 thf(func_def_23, type, zero_zero_real: real).
% 1.29/0.73 thf(func_def_24, type, lower_331963542_ereal: (set_Extended_ereal > (extended_ereal > extended_ereal) > set_Pr597221087l_real)).
% 1.29/0.73 thf(func_def_25, type, lower_870348689a_real: (set_Pr1928503567a_real > (product_prod_a_real > extended_ereal) > set_Pr1158285382l_real)).
% 1.29/0.73 thf(func_def_26, type, lower_930854854raph_a: (set_a > (a > extended_ereal) > set_Pr1928503567a_real)).
% 1.29/0.73 thf(func_def_27, type, lower_128423320e_on_a: (set_a > (a > extended_ereal) > $o)).
% 1.29/0.73 thf(func_def_28, type, lower_1023700310e_on_a: (set_a > (a > extended_ereal) > $o)).
% 1.29/0.73 thf(func_def_29, type, lower_591730471a_real: (set_Pr1928503567a_real > (product_prod_a_real > extended_ereal) > $o)).
% 1.29/0.73 thf(func_def_30, type, lower_311861424x_on_a: (set_a > (a > extended_ereal) > $o)).
% 1.29/0.73 thf(func_def_31, type, lower_1359521925a_real: ((product_prod_a_real > extended_ereal) > set_Pr1928503567a_real)).
% 1.29/0.73 thf(func_def_32, type, lower_1391529426main_a: ((a > extended_ereal) > set_a)).
% 1.29/0.73 thf(func_def_33, type, lower_1486931688e_on_a: (set_a > (a > extended_ereal) > $o)).
% 1.29/0.73 thf(func_def_34, type, ord_le824540014_ereal: (extended_ereal > extended_ereal > $o)).
% 1.29/0.73 thf(func_def_35, type, ord_less_eq_real: (real > real > $o)).
% 1.29/0.73 thf(func_def_36, type, ord_le88246606_ereal: (set_Extended_ereal > set_Extended_ereal > $o)).
% 1.29/0.73 thf(func_def_37, type, ord_le1586073967a_real: (set_Pr1928503567a_real > set_Pr1928503567a_real > $o)).
% 1.29/0.73 thf(func_def_38, type, ord_less_eq_set_real: (set_real > set_real > $o)).
% 1.29/0.73 thf(func_def_39, type, ord_le1153389358_ereal: (set_se767749006_ereal > set_se767749006_ereal > $o)).
% 1.29/0.73 thf(func_def_40, type, ord_le318720350_set_a: (set_set_a > set_set_a > $o)).
% 1.29/0.73 thf(func_def_41, type, ord_less_eq_set_a: (set_a > set_a > $o)).
% 1.29/0.73 thf(func_def_42, type, order_1158471719_ereal: ((extended_ereal > $o) > extended_ereal)).
% 1.29/0.73 thf(func_def_43, type, order_Greatest_real: ((real > $o) > real)).
% 1.29/0.73 thf(func_def_44, type, top_to398855007real_o: (extended_ereal > $o)).
% 1.29/0.73 thf(func_def_45, type, top_top_a_o: (a > $o)).
% 1.29/0.73 thf(func_def_46, type, top_top_o: $o).
% 1.29/0.73 thf(func_def_47, type, top_to802031902_ereal: extended_ereal).
% 1.29/0.73 thf(func_def_48, type, top_to772344469real_o: set_Extended_ereal_o).
% 1.29/0.73 thf(func_def_49, type, top_top_set_a_o: set_a_o).
% 1.29/0.73 thf(func_def_50, type, top_to1767659262_ereal: set_Extended_ereal).
% 1.29/0.73 thf(func_def_51, type, top_to2138011583a_real: set_Pr1928503567a_real).
% 1.29/0.73 thf(func_def_52, type, top_top_set_real: set_real).
% 1.29/0.73 thf(func_def_53, type, top_to692740318_ereal: set_se767749006_ereal).
% 1.29/0.73 thf(func_def_54, type, top_to1791633086_ereal: set_se1849684334_ereal).
% 1.29/0.73 thf(func_def_55, type, top_to1486684270_set_a: set_set_set_a).
% 1.29/0.73 thf(func_def_56, type, top_top_set_set_a: set_set_a).
% 1.29/0.73 thf(func_def_57, type, top_top_set_a: set_a).
% 1.29/0.73 thf(func_def_58, type, divide595620860_ereal: (extended_ereal > extended_ereal > extended_ereal)).
% 1.29/0.73 thf(func_def_59, type, divide_divide_real: (real > real > real)).
% 1.29/0.73 thf(func_def_60, type, collec247695033_ereal: ((extended_ereal > $o) > set_Extended_ereal)).
% 1.29/0.73 thf(func_def_61, type, collec1714955950a_real: ((product_prod_a_real > $o) > set_Pr1928503567a_real)).
% 1.29/0.73 thf(func_def_62, type, collect_a: ((a > $o) > set_a)).
% 1.29/0.73 thf(func_def_63, type, member1900190071_ereal: (extended_ereal > set_Extended_ereal > $o)).
% 1.29/0.73 thf(func_def_64, type, member1103263856a_real: (product_prod_a_real > set_Pr1928503567a_real > $o)).
% 1.29/0.73 thf(func_def_65, type, member_real: (real > set_real > $o)).
% 1.29/0.73 thf(func_def_66, type, member450560855_ereal: (set_Extended_ereal > set_se767749006_ereal > $o)).
% 1.29/0.73 thf(func_def_67, type, member_set_a: (set_a > set_set_a > $o)).
% 1.29/0.73 thf(func_def_68, type, member_a: (a > set_a > $o)).
% 1.29/0.73 thf(func_def_69, type, f: (a > extended_ereal)).
% 1.29/0.73 thf(func_def_73, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 1.29/0.73 thf(func_def_74, type, vIMP: ($o > $o > $o)).
% 1.29/0.73 thf(func_def_75, type, db0: !>[X0: $tType]:(X0)).
% 1.29/0.73 thf(func_def_76, type, db2: !>[X0: $tType]:(X0)).
% 1.29/0.73 thf(func_def_77, type, db1: !>[X0: $tType]:(X0)).
% 1.29/0.73 thf(func_def_78, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 1.29/0.73 thf(func_def_79, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 1.29/0.73 thf(func_def_80, type, vAND: ($o > $o > $o)).
% 1.29/0.73 thf(func_def_81, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 1.29/0.73 thf(func_def_82, type, vOR: ($o > $o > $o)).
% 1.29/0.73 thf(func_def_83, type, sP0: (real > real > real > $o)).
% 1.29/0.73 thf(func_def_84, type, sP1: (real > real > real > $o)).
% 1.29/0.73 thf(func_def_85, type, sP2: (extended_ereal > extended_ereal > $o)).
% 1.29/0.73 thf(func_def_86, type, sP3: (extended_ereal > extended_ereal > $o)).
% 1.29/0.73 thf(func_def_87, type, sP4: (extended_ereal > extended_ereal > $o)).
% 1.29/0.73 thf(func_def_88, type, sP5: (extended_ereal > extended_ereal > $o)).
% 1.29/0.73 thf(func_def_89, type, sP6: (extended_ereal > extended_ereal > $o)).
% 1.29/0.73 thf(func_def_90, type, sP7: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 1.29/0.73 thf(func_def_91, type, sP8: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 1.29/0.73 thf(func_def_92, type, sP9: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 1.29/0.73 thf(func_def_93, type, sP10: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 1.29/0.73 thf(func_def_94, type, sP11: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 1.29/0.73 thf(func_def_95, type, sP12: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 1.29/0.73 thf(func_def_96, type, sP13: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 1.29/0.73 thf(func_def_97, type, sP14: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 1.29/0.73 thf(func_def_98, type, sP15: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 1.29/0.73 thf(func_def_99, type, sP16: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 1.29/0.73 thf(func_def_100, type, sP17: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 1.29/0.73 thf(func_def_101, type, sP18: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 1.29/0.73 thf(func_def_102, type, sP19: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 1.29/0.73 thf(func_def_103, type, sP20: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 1.29/0.73 thf(func_def_104, type, sP21: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 1.29/0.73 thf(func_def_105, type, sP22: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 1.29/0.73 thf(func_def_106, type, sP23: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 1.29/0.73 thf(func_def_107, type, sP24: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 1.29/0.73 thf(func_def_108, type, sP25: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 1.29/0.73 thf(func_def_109, type, sP26: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 1.29/0.73 thf(func_def_110, type, sP27: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 1.29/0.73 thf(func_def_111, type, sP28: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 1.29/0.73 thf(func_def_112, type, sP29: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 1.29/0.73 thf(func_def_113, type, sP30: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 1.29/0.73 thf(func_def_114, type, sP31: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 1.29/0.73 thf(func_def_115, type, sP32: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 1.29/0.73 thf(func_def_116, type, sP33: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 1.29/0.73 thf(func_def_117, type, sK34: set_a).
% 1.29/0.73 thf(func_def_118, type, sK35: ((real > real) > real)).
% 1.29/0.73 thf(func_def_119, type, sK36: ((real > real) > real)).
% 1.29/0.73 thf(func_def_120, type, sK37: ((real > extended_ereal) > real)).
% 1.29/0.73 thf(func_def_121, type, sK38: ((real > extended_ereal) > real)).
% 1.29/0.73 thf(func_def_122, type, sK39: (set_Extended_ereal > extended_ereal)).
% 1.29/0.73 thf(func_def_123, type, sK40: ((extended_ereal > extended_ereal > $o) > extended_ereal)).
% 1.29/0.73 thf(func_def_124, type, sK41: ((extended_ereal > extended_ereal > $o) > extended_ereal)).
% 1.29/0.73 thf(func_def_125, type, sK42: ((extended_ereal > extended_ereal > $o) > extended_ereal)).
% 1.29/0.73 thf(func_def_126, type, sK43: ((extended_ereal > extended_ereal > $o) > extended_ereal)).
% 1.29/0.73 thf(func_def_127, type, sK44: (extended_ereal > real)).
% 1.29/0.73 thf(func_def_128, type, sK45: ((set_a > real) > set_a)).
% 1.29/0.73 thf(func_def_129, type, sK46: ((set_a > real) > set_a)).
% 1.29/0.73 thf(func_def_130, type, sK47: (set_Extended_ereal > extended_ereal > extended_ereal)).
% 1.29/0.73 thf(func_def_131, type, sK48: (set_Extended_ereal > extended_ereal > extended_ereal)).
% 1.29/0.73 thf(func_def_132, type, sK49: (set_Extended_ereal > extended_ereal)).
% 1.29/0.73 thf(func_def_133, type, sK50: (extended_ereal > set_Extended_ereal > extended_ereal)).
% 1.29/0.73 thf(func_def_134, type, sK51: set_Extended_ereal).
% 1.29/0.73 thf(func_def_135, type, sK52: ((real > extended_ereal) > real)).
% 1.29/0.73 thf(func_def_136, type, sK53: ((real > extended_ereal) > real)).
% 1.29/0.73 thf(func_def_137, type, sK54: (set_Extended_ereal > extended_ereal)).
% 1.29/0.73 thf(func_def_138, type, sK55: (extended_ereal > set_Extended_ereal > extended_ereal)).
% 1.29/0.73 thf(func_def_139, type, sK56: (set_a > a)).
% 1.29/0.73 thf(func_def_140, type, sK57: ((real > $o) > real > real)).
% 1.29/0.73 thf(func_def_141, type, sK58: ((real > $o) > (real > $o) > real)).
% 1.29/0.73 thf(func_def_142, type, sK59: ((extended_ereal > real) > extended_ereal)).
% 1.29/0.73 thf(func_def_143, type, sK60: ((extended_ereal > real) > extended_ereal)).
% 1.29/0.73 thf(func_def_144, type, sK61: ((extended_ereal > real) > extended_ereal)).
% 1.29/0.73 thf(func_def_145, type, sK62: ((extended_ereal > real) > extended_ereal)).
% 1.29/0.73 thf(func_def_146, type, sK63: (set_real > real > real)).
% 1.29/0.73 thf(func_def_147, type, sK64: (set_real > real > real)).
% 1.29/0.73 thf(func_def_148, type, sK65: ((product_prod_a_real > $o) > (product_prod_a_real > $o) > product_prod_a_real)).
% 1.29/0.73 thf(func_def_149, type, sK66: ((set_Pr1928503567a_real > set_a) > set_Pr1928503567a_real)).
% 1.29/0.73 thf(func_def_150, type, sK67: ((set_Pr1928503567a_real > set_a) > set_Pr1928503567a_real)).
% 1.29/0.73 thf(func_def_151, type, sK68: ((real > extended_ereal) > real)).
% 1.29/0.73 thf(func_def_152, type, sK69: ((real > extended_ereal) > real)).
% 1.29/0.73 thf(func_def_153, type, sK70: (extended_ereal > real)).
% 1.29/0.73 thf(func_def_154, type, sK71: (extended_ereal > real)).
% 1.29/0.73 thf(func_def_155, type, sK72: (extended_ereal > real)).
% 1.29/0.73 thf(func_def_156, type, sK73: (extended_ereal > real)).
% 1.29/0.73 thf(func_def_157, type, sK74: (extended_ereal > real)).
% 1.29/0.73 thf(func_def_158, type, sK75: (extended_ereal > real)).
% 1.29/0.73 thf(func_def_159, type, sK76: (a > set_set_a > set_a)).
% 1.29/0.73 thf(func_def_160, type, sK77: ((extended_ereal > $o) > real)).
% 1.29/0.73 thf(func_def_161, type, sK78: ((real > real) > real)).
% 1.29/0.73 thf(func_def_162, type, sK79: ((real > real) > real)).
% 1.29/0.73 thf(func_def_163, type, sK80: (extended_ereal > real)).
% 1.29/0.73 thf(func_def_164, type, sK81: (extended_ereal > real)).
% 1.29/0.73 thf(func_def_165, type, sK82: (extended_ereal > real)).
% 1.29/0.73 thf(func_def_166, type, sK83: (extended_ereal > real)).
% 1.29/0.73 thf(func_def_167, type, sK84: (extended_ereal > real)).
% 1.29/0.73 thf(func_def_168, type, sK85: (extended_ereal > real)).
% 1.29/0.73 thf(func_def_169, type, sK86: (extended_ereal > real)).
% 1.29/0.73 thf(func_def_170, type, sK87: (extended_ereal > real)).
% 1.29/0.73 thf(func_def_171, type, sK88: (extended_ereal > real)).
% 1.29/0.73 thf(func_def_172, type, sK89: (extended_ereal > real)).
% 1.29/0.73 thf(func_def_173, type, sK90: (extended_ereal > real)).
% 1.29/0.73 thf(func_def_174, type, sK91: (extended_ereal > real)).
% 1.29/0.73 thf(func_def_175, type, sK92: (extended_ereal > real)).
% 1.29/0.73 thf(func_def_176, type, sK93: (extended_ereal > real)).
% 1.29/0.74 thf(func_def_177, type, sK94: (extended_ereal > real)).
% 1.29/0.74 thf(func_def_178, type, sK95: (extended_ereal > real)).
% 1.29/0.74 thf(func_def_179, type, sK96: (extended_ereal > real)).
% 1.29/0.74 thf(func_def_180, type, sK97: (extended_ereal > real)).
% 1.29/0.74 thf(func_def_181, type, sK98: (extended_ereal > real)).
% 1.29/0.74 thf(func_def_182, type, sK99: (extended_ereal > real)).
% 1.29/0.74 thf(func_def_183, type, sK100: (extended_ereal > real)).
% 1.29/0.74 thf(func_def_184, type, sK101: (extended_ereal > real)).
% 1.29/0.74 thf(func_def_185, type, sK102: (extended_ereal > real)).
% 1.29/0.74 thf(func_def_186, type, sK103: (extended_ereal > real)).
% 1.29/0.74 thf(func_def_187, type, sK104: (extended_ereal > real)).
% 1.29/0.74 thf(func_def_188, type, sK105: (extended_ereal > real)).
% 1.29/0.74 thf(func_def_189, type, sK106: (extended_ereal > real)).
% 1.29/0.74 thf(func_def_190, type, sK107: ((a > extended_ereal) > set_a)).
% 1.29/0.74 thf(func_def_191, type, sK108: ((extended_ereal > real) > extended_ereal)).
% 1.29/0.74 thf(func_def_192, type, sK109: ((extended_ereal > real) > extended_ereal)).
% 1.29/0.74 thf(func_def_193, type, sK110: ((extended_ereal > extended_ereal) > extended_ereal)).
% 1.29/0.74 thf(func_def_194, type, sK111: ((extended_ereal > extended_ereal) > extended_ereal)).
% 1.29/0.74 thf(func_def_195, type, sK112: ((a > $o) > (a > $o) > a)).
% 1.29/0.74 thf(func_def_196, type, sK113: ((extended_ereal > extended_ereal > $o) > real)).
% 1.29/0.74 thf(func_def_197, type, sK114: ((extended_ereal > extended_ereal > $o) > real)).
% 1.29/0.74 thf(func_def_198, type, sK115: ((extended_ereal > extended_ereal > $o) > extended_ereal)).
% 1.29/0.74 thf(func_def_199, type, sK116: ((extended_ereal > extended_ereal > $o) > extended_ereal)).
% 1.29/0.74 thf(func_def_200, type, sK117: ((extended_ereal > extended_ereal > $o) > real)).
% 1.29/0.74 thf(func_def_201, type, sK118: ((extended_ereal > extended_ereal > $o) > real)).
% 1.29/0.74 thf(func_def_202, type, sK119: (extended_ereal > (extended_ereal > $o) > extended_ereal)).
% 1.29/0.74 thf(func_def_203, type, sK120: ((real > real) > real)).
% 1.29/0.74 thf(func_def_204, type, sK121: ((real > real) > real)).
% 1.29/0.74 thf(func_def_205, type, sK122: (extended_ereal > real)).
% 1.29/0.74 thf(func_def_206, type, sK123: ((set_Pr1928503567a_real > set_Pr1928503567a_real) > set_Pr1928503567a_real)).
% 1.29/0.74 thf(func_def_207, type, sK124: ((set_Pr1928503567a_real > set_Pr1928503567a_real) > set_Pr1928503567a_real)).
% 1.29/0.74 thf(func_def_208, type, sK125: ((extended_ereal > extended_ereal > $o) > real)).
% 1.29/0.74 thf(func_def_209, type, sK126: ((extended_ereal > extended_ereal > $o) > real)).
% 1.29/0.74 thf(func_def_210, type, sK127: ((extended_ereal > extended_ereal > $o) > real)).
% 1.29/0.74 thf(func_def_211, type, sK128: ((extended_ereal > extended_ereal > $o) > real)).
% 1.29/0.74 thf(func_def_212, type, sK129: ((extended_ereal > extended_ereal > $o) > real)).
% 1.29/0.74 thf(func_def_213, type, sK130: ((extended_ereal > extended_ereal > $o) > real)).
% 1.29/0.74 thf(func_def_214, type, sK131: ((real > real > $o) > real)).
% 1.29/0.74 thf(func_def_215, type, sK132: ((real > real > $o) > real)).
% 1.29/0.74 thf(func_def_216, type, sK133: ((real > real > $o) > real)).
% 1.29/0.74 thf(func_def_217, type, sK134: ((real > real > $o) > real)).
% 1.29/0.74 thf(func_def_218, type, sK135: ((real > real) > real)).
% 1.29/0.74 thf(func_def_219, type, sK136: ((real > real) > real)).
% 1.29/0.74 thf(func_def_220, type, sK137: ((a > extended_ereal) > set_a)).
% 1.29/0.74 thf(func_def_221, type, sK138: (extended_ereal > real)).
% 1.29/0.74 thf(func_def_222, type, sK139: ((real > set_a) > real)).
% 1.29/0.74 thf(func_def_223, type, sK140: ((real > set_a) > real)).
% 1.29/0.74 thf(func_def_224, type, sK141: (set_se767749006_ereal > set_se767749006_ereal > set_Extended_ereal)).
% 1.29/0.74 thf(func_def_225, type, sK142: ((a > extended_ereal) > (a > extended_ereal) > a)).
% 1.29/0.74 thf(func_def_226, type, sK143: (set_set_a > set_a)).
% 1.29/0.74 thf(func_def_227, type, sK144: (set_Extended_ereal > extended_ereal > extended_ereal)).
% 1.29/0.74 thf(func_def_228, type, sK145: (set_se767749006_ereal > set_Extended_ereal)).
% 1.29/0.74 thf(func_def_229, type, sK146: (set_real > set_real > real)).
% 1.29/0.74 thf(func_def_230, type, sK147: extended_ereal).
% 1.29/0.74 thf(func_def_231, type, sK148: ((real > extended_ereal) > real)).
% 1.29/0.74 thf(func_def_232, type, sK149: ((real > extended_ereal) > real)).
% 1.29/0.74 thf(func_def_233, type, sK150: ((extended_ereal > extended_ereal) > extended_ereal)).
% 1.29/0.74 thf(func_def_234, type, sK151: ((extended_ereal > extended_ereal) > extended_ereal)).
% 1.29/0.74 thf(func_def_235, type, sK152: (set_Extended_ereal > set_Extended_ereal > extended_ereal)).
% 1.29/0.74 thf(func_def_236, type, sK153: ((extended_ereal > $o) > (extended_ereal > $o) > extended_ereal)).
% 1.29/0.74 thf(func_def_237, type, sK154: ((extended_ereal > extended_ereal) > extended_ereal)).
% 1.29/0.74 thf(func_def_238, type, sK155: ((extended_ereal > extended_ereal) > extended_ereal)).
% 1.29/0.74 thf(func_def_239, type, sK156: (extended_ereal > set_se767749006_ereal > set_Extended_ereal)).
% 1.29/0.74 thf(func_def_240, type, sK157: ((extended_ereal > real) > extended_ereal)).
% 1.29/0.74 thf(func_def_241, type, sK158: ((extended_ereal > real) > extended_ereal)).
% 1.29/0.74 thf(func_def_242, type, sK159: (extended_ereal > real)).
% 1.29/0.74 thf(func_def_243, type, sK160: ((set_Pr1928503567a_real > set_Extended_ereal) > set_Pr1928503567a_real)).
% 1.29/0.74 thf(func_def_244, type, sK161: ((set_Pr1928503567a_real > set_Extended_ereal) > set_Pr1928503567a_real)).
% 1.29/0.74 thf(func_def_245, type, sK162: ((a > $o) > (a > $o) > a)).
% 1.29/0.74 thf(func_def_246, type, sK163: (set_Extended_ereal > extended_ereal > extended_ereal)).
% 1.29/0.74 thf(func_def_247, type, sK164: ((real > $o) > real > real)).
% 1.29/0.74 thf(func_def_248, type, sK165: (set_Extended_ereal > set_Extended_ereal > extended_ereal)).
% 1.29/0.74 thf(func_def_249, type, sK166: (extended_ereal > real)).
% 1.29/0.74 thf(func_def_250, type, sK167: (extended_ereal > (extended_ereal > $o) > extended_ereal)).
% 1.29/0.74 thf(func_def_251, type, sK168: ((extended_ereal > $o) > (extended_ereal > $o) > extended_ereal)).
% 1.29/0.74 thf(func_def_252, type, sK169: ((set_Extended_ereal > extended_ereal) > set_Extended_ereal)).
% 1.29/0.74 thf(func_def_253, type, sK170: ((set_Extended_ereal > extended_ereal) > set_Extended_ereal)).
% 1.29/0.74 thf(func_def_254, type, sK171: (set_real > real > real)).
% 1.29/0.74 thf(func_def_255, type, sK172: (set_real > real)).
% 1.29/0.74 thf(func_def_256, type, sK173: ((extended_ereal > $o) > (extended_ereal > $o) > extended_ereal)).
% 1.29/0.74 thf(func_def_257, type, sK174: ((set_Extended_ereal > real) > set_Extended_ereal)).
% 1.29/0.74 thf(func_def_258, type, sK175: ((set_Extended_ereal > real) > set_Extended_ereal)).
% 1.29/0.74 thf(func_def_259, type, sK176: (set_se767749006_ereal > extended_ereal > set_Extended_ereal)).
% 1.29/0.74 thf(func_def_260, type, sK177: ((product_prod_a_real > $o) > (product_prod_a_real > $o) > product_prod_a_real)).
% 1.29/0.74 thf(func_def_261, type, sK178: ((extended_ereal > $o) > real)).
% 1.29/0.74 thf(func_def_262, type, sK179: ((extended_ereal > extended_ereal) > extended_ereal)).
% 1.29/0.74 thf(func_def_263, type, sK180: ((extended_ereal > extended_ereal) > extended_ereal)).
% 1.29/0.74 thf(func_def_264, type, sK181: ((set_a > extended_ereal) > set_a)).
% 1.29/0.74 thf(func_def_265, type, sK182: ((set_a > extended_ereal) > set_a)).
% 1.29/0.74 thf(func_def_266, type, sK183: real).
% 1.29/0.74 thf(func_def_267, type, sK184: a).
% 1.29/0.74 thf(func_def_268, type, sK185: ((extended_ereal > $o) > real)).
% 1.29/0.74 thf(func_def_269, type, sK186: (set_Pr1928503567a_real > set_Pr1928503567a_real > product_prod_a_real)).
% 1.29/0.74 thf(func_def_270, type, sK187: (extended_ereal > real)).
% 1.29/0.74 thf(func_def_271, type, sK188: (extended_ereal > extended_ereal > real)).
% 1.29/0.74 thf(func_def_272, type, sK189: (extended_ereal > real)).
% 1.29/0.74 thf(func_def_273, type, sK190: ((extended_ereal > set_a) > extended_ereal)).
% 1.29/0.74 thf(func_def_274, type, sK191: ((extended_ereal > set_a) > extended_ereal)).
% 1.29/0.74 thf(func_def_275, type, sK192: (set_set_a > a > set_a)).
% 1.29/0.74 thf(func_def_276, type, sK193: ((extended_ereal > $o) > real)).
% 1.29/0.74 thf(func_def_277, type, sK194: (set_a > set_a > a)).
% 1.29/0.74 thf(func_def_278, type, sK195: (extended_ereal > extended_ereal > real)).
% 1.29/0.74 thf(func_def_279, type, sK196: (set_set_a > set_set_a > set_a)).
% 1.29/0.74 thf(func_def_280, type, sK197: (extended_ereal > set_Extended_ereal > extended_ereal)).
% 1.29/0.74 thf(func_def_281, type, sK198: ((extended_ereal > extended_ereal > $o) > real)).
% 1.29/0.74 thf(func_def_282, type, sK199: ((extended_ereal > extended_ereal > $o) > real)).
% 1.29/0.74 thf(func_def_283, type, sK200: ((extended_ereal > extended_ereal > $o) > extended_ereal)).
% 1.29/0.74 thf(func_def_284, type, sK201: ((extended_ereal > extended_ereal > $o) > real)).
% 1.29/0.74 thf(func_def_285, type, sK202: ((extended_ereal > extended_ereal > $o) > real)).
% 1.29/0.74 thf(func_def_286, type, sK203: ((extended_ereal > extended_ereal > $o) > extended_ereal)).
% 1.29/0.74 thf(func_def_287, type, sK204: (extended_ereal > real)).
% 1.29/0.74 thf(func_def_288, type, vNOT: ($o > $o)).
% 1.29/0.74 thf(f1,axiom,(
% 1.29/0.74 (convex_a @ (lower_1391529426main_a @ f)) => (lower_311861424x_on_a @ top_top_set_a @ f)),
% 1.29/0.74 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__092_060open_062convex_A_Idomain_Af_J_A_092_060Longrightarrow_062_ALower__Semicontinuous__Mirabelle__mxyexokbxt_Oconvex__on_AUNIV_Af_092_060close_062)).
% 1.29/0.74 thf(f3,axiom,(
% 1.29/0.74 ! [X0 : (a > extended_ereal)] : ((lower_311861424x_on_a @ top_top_set_a @ X0) => (convex_a @ (lower_1391529426main_a @ X0)))),
% 1.29/0.74 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_convex__domain)).
% 1.29/0.74 thf(f355,conjecture,(
% 1.29/0.74 (((lower_311861424x_on_a @ top_top_set_a @ f)) = ((convex_a @ (lower_1391529426main_a @ f))))),
% 1.29/0.74 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 1.29/0.74 thf(f356,negated_conjecture,(
% 1.29/0.74 ~ (((lower_311861424x_on_a @ top_top_set_a @ f)) = ((convex_a @ (lower_1391529426main_a @ f))))),
% 1.29/0.74 inference(negated_conjecture,[status(cth)],[f355])).
% 1.29/0.74 thf(f724,plain,(
% 1.29/0.74 ! [X0 : (a > extended_ereal)] : ((lower_311861424x_on_a @ top_top_set_a @ X0) => (convex_a @ (lower_1391529426main_a @ X0)))),
% 1.29/0.74 inference(rectify,[],[f3])).
% 1.29/0.74 thf(f725,plain,(
% 1.29/0.74 ! [X0 : (a > extended_ereal)] : ((((lower_311861424x_on_a @ top_top_set_a @ X0)) = $true) => (((convex_a @ (lower_1391529426main_a @ X0))) = $true))),
% 1.29/0.74 inference(fool_elimination,[],[f724])).
% 1.29/0.74 thf(f848,plain,(
% 1.29/0.74 (convex_a @ (lower_1391529426main_a @ f)) => (lower_311861424x_on_a @ top_top_set_a @ f)),
% 1.29/0.74 inference(rectify,[],[f1])).
% 1.29/0.74 thf(f849,plain,(
% 1.29/0.74 (((convex_a @ (lower_1391529426main_a @ f))) = $true) => (((lower_311861424x_on_a @ top_top_set_a @ f)) = $true)),
% 1.29/0.74 inference(fool_elimination,[],[f848])).
% 1.29/0.74 thf(f893,plain,(
% 1.29/0.74 (((convex_a @ (lower_1391529426main_a @ f))) != ((lower_311861424x_on_a @ top_top_set_a @ f)))),
% 1.29/0.74 inference(flattening,[],[f356])).
% 1.29/0.74 thf(f923,plain,(
% 1.29/0.74 ! [X0 : (a > extended_ereal)] : ((((lower_311861424x_on_a @ top_top_set_a @ X0)) != $true) | (((convex_a @ (lower_1391529426main_a @ X0))) = $true))),
% 1.29/0.74 inference(ennf_transformation,[],[f725])).
% 1.29/0.74 thf(f1096,plain,(
% 1.29/0.74 (((lower_311861424x_on_a @ top_top_set_a @ f)) = $true) | (((convex_a @ (lower_1391529426main_a @ f))) != $true)),
% 1.29/0.74 inference(ennf_transformation,[],[f849])).
% 1.29/0.74 thf(f1772,plain,(
% 1.29/0.74 ( ! [X0 : (a > extended_ereal)] : ((((lower_311861424x_on_a @ top_top_set_a @ X0)) != $true) | (((convex_a @ (lower_1391529426main_a @ X0))) = $true)) )),
% 1.29/0.74 inference(cnf_transformation,[],[f923])).
% 1.29/0.74 thf(f1881,plain,(
% 1.29/0.74 (((convex_a @ (lower_1391529426main_a @ f))) != ((lower_311861424x_on_a @ top_top_set_a @ f)))),
% 1.29/0.74 inference(cnf_transformation,[],[f893])).
% 1.29/0.74 thf(f1973,plain,(
% 1.29/0.74 (((convex_a @ (lower_1391529426main_a @ f))) != $true) | (((lower_311861424x_on_a @ top_top_set_a @ f)) = $true)),
% 1.29/0.74 inference(cnf_transformation,[],[f1096])).
% 1.29/0.74 thf(f2355,plain,(
% 1.29/0.74 (((lower_311861424x_on_a @ top_top_set_a @ f)) = $true) | (((convex_a @ (lower_1391529426main_a @ f))) = $true)),
% 1.29/0.74 inference(xor_proxy_clausification,[],[f1881])).
% 1.29/0.74 thf(f2356,plain,(
% 1.29/0.74 (((convex_a @ (lower_1391529426main_a @ f))) = $false) | (((lower_311861424x_on_a @ top_top_set_a @ f)) = $false)),
% 1.29/0.74 inference(xor_proxy_clausification,[],[f1881])).
% 1.29/0.74 thf(f2491,definition,(
% 1.29/0.74 spl205_18 <=> (((lower_311861424x_on_a @ top_top_set_a @ f)) = $false)),
% 1.29/0.74 introduced(definition,[new_symbols(definition,[spl205_18])],[avatar_definition])).
% 1.29/0.74 thf(f2495,definition,(
% 1.29/0.74 spl205_19 <=> (((convex_a @ (lower_1391529426main_a @ f))) = $false)),
% 1.29/0.74 introduced(definition,[new_symbols(definition,[spl205_19])],[avatar_definition])).
% 1.29/0.74 thf(f2497,plain,(
% 1.29/0.74 (((convex_a @ (lower_1391529426main_a @ f))) = $false) | ~spl205_19),
% 1.29/0.74 inference(avatar_component_clause,[],[f2495])).
% 1.29/0.74 thf(f2498,plain,(
% 1.29/0.74 spl205_18 | spl205_19),
% 1.29/0.74 inference(avatar_split_clause,[],[f2356,f2495,f2491])).
% 1.29/0.74 thf(f2500,definition,(
% 1.29/0.74 spl205_20 <=> (((convex_a @ (lower_1391529426main_a @ f))) = $true)),
% 1.29/0.74 introduced(definition,[new_symbols(definition,[spl205_20])],[avatar_definition])).
% 1.29/0.74 thf(f2504,definition,(
% 1.29/0.74 spl205_21 <=> (((lower_311861424x_on_a @ top_top_set_a @ f)) = $true)),
% 1.29/0.74 introduced(definition,[new_symbols(definition,[spl205_21])],[avatar_definition])).
% 1.29/0.74 thf(f2506,plain,(
% 1.29/0.74 (((lower_311861424x_on_a @ top_top_set_a @ f)) = $true) | ~spl205_21),
% 1.29/0.74 inference(avatar_component_clause,[],[f2504])).
% 1.29/0.74 thf(f2507,plain,(
% 1.29/0.74 spl205_20 | spl205_21),
% 1.29/0.74 inference(avatar_split_clause,[],[f2355,f2504,f2500])).
% 1.29/0.74 thf(f2533,plain,(
% 1.29/0.74 ~spl205_20 | spl205_21),
% 1.29/0.74 inference(avatar_split_clause,[],[f1973,f2504,f2500])).
% 1.29/0.74 thf(f2717,plain,(
% 1.29/0.74 ($true != $true) | (((convex_a @ (lower_1391529426main_a @ f))) = $true) | ~spl205_21),
% 1.29/0.74 inference(superposition,[],[f1772,f2506])).
% 1.29/0.74 thf(f2718,plain,(
% 1.29/0.74 (((convex_a @ (lower_1391529426main_a @ f))) = $true) | ~spl205_21),
% 1.29/0.74 inference(trivial_inequality_removal,[],[f2717])).
% 1.29/0.74 thf(f2719,plain,(
% 1.29/0.74 ($false = $true) | (~spl205_19 | ~spl205_21)),
% 1.29/0.74 inference(forward_demodulation,[],[f2718,f2497])).
% 1.29/0.74 thf(f2720,plain,(
% 1.29/0.74 $false | (~spl205_19 | ~spl205_21)),
% 1.29/0.74 inference(trivial_inequality_removal,[],[f2719])).
% 1.29/0.74 thf(f2721,plain,(
% 1.29/0.74 ~spl205_19 | ~spl205_21),
% 1.29/0.74 inference(avatar_contradiction_clause,[],[f2720])).
% 1.29/0.74 thf(f2722,plain,(
% 1.29/0.74 spl205_20 | ~spl205_21),
% 1.29/0.74 inference(avatar_split_clause,[],[f2718,f2504,f2500])).
% 1.29/0.74 thf(f2723,definition,(
% 1.29/0.74 (((lower_311861424x_on_a @ top_top_set_a @ f)) != $false) | (((lower_311861424x_on_a @ top_top_set_a @ f)) != $true) | (((convex_a @ (lower_1391529426main_a @ f))) != $true) | (((convex_a @ (lower_1391529426main_a @ f))) = $false)),
% 1.29/0.74 introduced(theory,[theory_tautology_sat_conflict])).
% 1.29/0.74 cnf(s18, plain, spl205_18 | spl205_19, inference(sat_conversion,[],[f2498])).
% 1.29/0.74 cnf(s19, plain, spl205_20 | spl205_21, inference(sat_conversion,[],[f2507])).
% 1.29/0.74 cnf(s27, plain, ~spl205_20 | spl205_21, inference(sat_conversion,[],[f2533])).
% 1.29/0.74 cnf(s80, plain, ~spl205_19 | ~spl205_21, inference(sat_conversion,[],[f2721])).
% 1.29/0.74 cnf(s81, plain, spl205_20 | ~spl205_21, inference(sat_conversion,[],[f2722])).
% 1.29/0.74 cnf(s82, plain, ~spl205_18 | spl205_19 | ~spl205_20 | ~spl205_21, inference(sat_conversion,[],[f2723])).
% 1.29/0.74 cnf(s84, plain, spl205_21, inference(rat,[],[s19,s27])).
% 1.29/0.74 cnf(s85, plain, spl205_20, inference(rat,[],[s81,s84])).
% 1.29/0.74 cnf(s86, plain, ~spl205_19, inference(rat,[],[s80,s84])).
% 1.29/0.74 cnf(s87, plain, ~spl205_18, inference(rat,[],[s82,s84,s85,s86])).
% 1.29/0.74 cnf(s88, plain, $false, inference(rat,[],[s18,s86,s87])).
% 1.29/0.74 thf(f2724,plain,(
% 1.29/0.74 $false),
% 1.29/0.74 inference(avatar_sat_refutation,[],[s88])).
% 1.29/0.74 % SZS output end Proof for theBenchmark
% 1.29/0.74 % (3653452)------------------------------
% 1.29/0.74 % (3653452)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.29/0.74 % (3653452)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.29/0.74 % (3653452)CaDiCaL version: 2.1.3
% 1.29/0.74 % (3653452)Termination reason: Refutation
% 1.29/0.74 % (3653452)Time elapsed: 0.134 s
% 1.29/0.74 % (3653452)Peak memory usage: 15 MB
% 1.29/0.74 % (3653452)Instructions burned: 155 (million)
% 1.29/0.74 % (3653444)Success in time 0.264 s
% 1.29/0.74 % Vampire exiting
%------------------------------------------------------------------------------