%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP110^2 : 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 : n015.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 0.55s 0.41s
% Output : Refutation 0.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP110^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n015.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 19:58:18 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.22/0.27 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.55/0.41 % (4034744)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.55/0.41 % (4034754)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1546124162:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.55/0.41 % (4034755)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.55/0.41 % (4034755)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
% 0.55/0.41 % (4034751)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=355077009:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.55/0.41 % (4034749)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3581413217:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.55/0.41 % (4034753)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2568938077:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.55/0.41 % (4034752)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=3397809680: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)
% 0.55/0.41 % (4034755)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=2795048994:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.55/0.41 % (4034751)Instruction limit reached!
% 0.55/0.41 % (4034751)------------------------------
% 0.55/0.41 % (4034751)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.55/0.41 % (4034751)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.55/0.41 % (4034751)CaDiCaL version: 2.1.3
% 0.55/0.41 % (4034751)Termination reason: Instruction limit
% 0.55/0.41 % (4034751)Termination phase: shuffling
% 0.55/0.41 % (4034751)Time elapsed: 0.003 s
% 0.55/0.41 % (4034751)Peak memory usage: 10 MB
% 0.55/0.41 % (4034751)Instructions burned: 4 (million)
% 0.55/0.41 % (4034750)lrs+10_16_si=on:nwc=1.5:random_seed=2056177045:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.55/0.41 % (4034754)Instruction limit reached!
% 0.55/0.41 % (4034754)------------------------------
% 0.55/0.41 % (4034754)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.55/0.41 % (4034754)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.55/0.41 % (4034754)CaDiCaL version: 2.1.3
% 0.55/0.41 % (4034754)Termination reason: Instruction limit
% 0.55/0.41 % (4034754)Termination phase: Property scanning
% 0.55/0.41 % (4034754)Time elapsed: 0.019 s
% 0.55/0.41 % (4034754)Peak memory usage: 12 MB
% 0.55/0.41 % (4034754)Instructions burned: 77 (million)
% 0.55/0.41 % (4034753)Instruction limit reached!
% 0.55/0.41 % (4034753)------------------------------
% 0.55/0.41 % (4034753)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.55/0.41 % (4034753)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.55/0.41 % (4034753)CaDiCaL version: 2.1.3
% 0.55/0.41 % (4034753)Termination reason: Instruction limit
% 0.55/0.41 % (4034753)Termination phase: shuffling
% 0.55/0.41 % (4034753)Time elapsed: 0.012 s
% 0.55/0.41 % (4034753)Peak memory usage: 10 MB
% 0.55/0.41 % (4034753)Instructions burned: 26 (million)
% 0.55/0.41 % (4034763)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=655825219:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.55/0.41 % (4034764)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=446078451:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.55/0.41 % (4034764)Instruction limit reached!
% 0.55/0.41 % (4034764)------------------------------
% 0.55/0.41 % (4034764)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.55/0.41 % (4034764)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.55/0.41 % (4034764)CaDiCaL version: 2.1.3
% 0.55/0.41 % (4034764)Termination reason: Instruction limit
% 0.55/0.41 % (4034764)Termination phase: shuffling
% 0.55/0.41 % (4034764)Time elapsed: 0.001 s
% 0.55/0.41 % (4034764)Peak memory usage: 10 MB
% 0.55/0.41 % (4034764)Instructions burned: 6 (million)
% 0.55/0.41 % (4034763)Instruction limit reached!
% 0.55/0.41 % (4034763)------------------------------
% 0.55/0.41 % (4034763)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.55/0.41 % (4034763)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.55/0.41 % (4034763)CaDiCaL version: 2.1.3
% 0.55/0.41 % (4034763)Termination reason: Instruction limit
% 0.55/0.41 % (4034763)Termination phase: shuffling
% 0.55/0.41 % (4034763)Time elapsed: 0.002 s
% 0.55/0.41 % (4034763)Peak memory usage: 10 MB
% 0.55/0.41 % (4034763)Instructions burned: 3 (million)
% 0.55/0.41 % (4034750)Instruction limit reached!
% 0.55/0.41 % (4034750)------------------------------
% 0.55/0.41 % (4034750)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.55/0.41 % (4034750)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.55/0.41 % (4034750)CaDiCaL version: 2.1.3
% 0.55/0.41 % (4034750)Termination reason: Instruction limit
% 0.55/0.41 % (4034750)Termination phase: Property scanning
% 0.55/0.41 % (4034750)Time elapsed: 0.021 s
% 0.55/0.41 % (4034750)Peak memory usage: 10 MB
% 0.55/0.41 % (4034750)Instructions burned: 19 (million)
% 0.55/0.41 % (4034765)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.55/0.41 % (4034765)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2031766496:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.55/0.41 % (4034768)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=3133610560:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.55/0.41 % (4034765)Instruction limit reached!
% 0.55/0.41 % (4034765)------------------------------
% 0.55/0.41 % (4034765)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.55/0.41 % (4034765)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.55/0.41 % (4034765)CaDiCaL version: 2.1.3
% 0.55/0.41 % (4034765)Termination reason: Instruction limit
% 0.55/0.41 % (4034765)Termination phase: shuffling
% 0.55/0.41 % (4034765)Time elapsed: 0.004 s
% 0.55/0.41 % (4034765)Peak memory usage: 10 MB
% 0.55/0.41 % (4034765)Instructions burned: 7 (million)
% 0.55/0.41 % (4034768)Instruction limit reached!
% 0.55/0.41 % (4034768)------------------------------
% 0.55/0.41 % (4034768)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.55/0.41 % (4034768)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.55/0.41 % (4034768)CaDiCaL version: 2.1.3
% 0.55/0.41 % (4034768)Termination reason: Instruction limit
% 0.55/0.41 % (4034768)Termination phase: shuffling
% 0.55/0.41 % (4034768)Time elapsed: 0.003 s
% 0.55/0.41 % (4034768)Peak memory usage: 10 MB
% 0.55/0.41 % (4034768)Instructions burned: 12 (million)
% 0.55/0.41 % (4034749)Instruction limit reached!
% 0.55/0.41 % (4034749)------------------------------
% 0.55/0.41 % (4034749)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.55/0.41 % (4034749)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.55/0.41 % (4034749)CaDiCaL version: 2.1.3
% 0.55/0.41 % (4034749)Termination reason: Instruction limit
% 0.55/0.41 % (4034749)Termination phase: Saturation
% 0.55/0.41 % (4034749)Time elapsed: 0.041 s
% 0.55/0.41 % (4034749)Peak memory usage: 13 MB
% 0.55/0.41 % (4034749)Instructions burned: 88 (million)
% 0.55/0.41 % (4034770)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
% 0.55/0.41 % (4034770)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.55/0.41 % (4034770)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3113214582:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.55/0.41 % (4034775)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.55/0.41 % (4034775)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=1706021270:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.55/0.41 % (4034775)Instruction limit reached!
% 0.55/0.41 % (4034775)------------------------------
% 0.55/0.41 % (4034775)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.55/0.41 % (4034775)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.55/0.41 % (4034775)CaDiCaL version: 2.1.3
% 0.55/0.41 % (4034775)Termination reason: Instruction limit
% 0.55/0.41 % (4034775)Termination phase: shuffling
% 0.55/0.41 % (4034775)Time elapsed: 0.002 s
% 0.55/0.41 % (4034775)Peak memory usage: 10 MB
% 0.55/0.41 % (4034775)Instructions burned: 6 (million)
% 0.55/0.41 % (4034774)lrs+10_1_si=on:cs=on:random_seed=1782478973:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.55/0.41 % (4034770)Instruction limit reached!
% 0.55/0.41 % (4034770)------------------------------
% 0.55/0.41 % (4034770)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.55/0.41 % (4034770)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.55/0.41 % (4034770)CaDiCaL version: 2.1.3
% 0.55/0.41 % (4034770)Termination reason: Instruction limit
% 0.55/0.41 % (4034770)Termination phase: Property scanning
% 0.55/0.41 % (4034770)Time elapsed: 0.014 s
% 0.55/0.41 % (4034770)Peak memory usage: 10 MB
% 0.55/0.41 % (4034770)Instructions burned: 30 (million)
% 0.55/0.41 % (4034776)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=406866787:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.55/0.41 % (4034774)Instruction limit reached!
% 0.55/0.41 % (4034774)------------------------------
% 0.55/0.41 % (4034774)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.55/0.41 % (4034774)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.55/0.41 % (4034774)CaDiCaL version: 2.1.3
% 0.55/0.41 % (4034774)Termination reason: Instruction limit
% 0.55/0.41 % (4034774)Termination phase: shuffling
% 0.55/0.41 % (4034774)Time elapsed: 0.005 s
% 0.55/0.41 % (4034774)Peak memory usage: 10 MB
% 0.55/0.41 % (4034774)Instructions burned: 10 (million)
% 0.55/0.41 % (4034779)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=2621211919:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 0.55/0.41 % (4034771)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=1968078592:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.55/0.41 % (4034752) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4034744-4034752"...
% 0.55/0.41 % (4034752)...printing done.
% 0.55/0.41 % (4034779) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4034744-4034779"...
% 0.55/0.41 % (4034752)Refutation found. Thanks to Tanya!
% 0.55/0.41 % SZS status Theorem for theBenchmark
% 0.55/0.41 % SZS output start Proof for theBenchmark
% 0.55/0.41 thf(type_def_5, type, extended_ereal: $tType).
% 0.55/0.41 thf(type_def_6, type, product_prod: ($tType * $tType) > $tType).
% 0.55/0.41 thf(type_def_7, type, real: $tType).
% 0.55/0.41 thf(type_def_8, type, set: $tType > $tType).
% 0.55/0.41 thf(type_def_9, type, a: $tType).
% 0.55/0.41 thf(type_def_10, type, sTfun: ($tType * $tType) > $tType).
% 0.55/0.41 thf(func_def_0, type, ordere890947078_space: !>[X0: $tType]:($o)).
% 0.55/0.41 thf(func_def_1, type, type: !>[X0: $tType]:($o)).
% 0.55/0.41 thf(func_def_2, type, ring: !>[X0: $tType]:($o)).
% 0.55/0.41 thf(func_def_3, type, zero: !>[X0: $tType]:($o)).
% 0.55/0.41 thf(func_def_4, type, field: !>[X0: $tType]:($o)).
% 0.55/0.41 thf(func_def_5, type, uminus: !>[X0: $tType]:($o)).
% 0.55/0.41 thf(func_def_6, type, ord: !>[X0: $tType]:($o)).
% 0.55/0.41 thf(func_def_7, type, top: !>[X0: $tType]:($o)).
% 0.55/0.41 thf(func_def_8, type, order: !>[X0: $tType]:($o)).
% 0.55/0.41 thf(func_def_9, type, mult_zero: !>[X0: $tType]:($o)).
% 0.55/0.41 thf(func_def_10, type, group_add: !>[X0: $tType]:($o)).
% 0.55/0.41 thf(func_def_11, type, no_bot: !>[X0: $tType]:($o)).
% 0.55/0.41 thf(func_def_12, type, linorder: !>[X0: $tType]:($o)).
% 0.55/0.41 thf(func_def_13, type, preorder: !>[X0: $tType]:($o)).
% 0.55/0.41 thf(func_def_14, type, finite_lattice: !>[X0: $tType]:($o)).
% 0.55/0.41 thf(func_def_15, type, order_top: !>[X0: $tType]:($o)).
% 0.55/0.41 thf(func_def_16, type, division_ring: !>[X0: $tType]:($o)).
% 0.55/0.41 thf(func_def_17, type, semiring_bits: !>[X0: $tType]:($o)).
% 0.55/0.41 thf(func_def_18, type, semidom_divide: !>[X0: $tType]:($o)).
% 0.55/0.41 thf(func_def_19, type, linordered_field: !>[X0: $tType]:($o)).
% 0.55/0.41 thf(func_def_20, type, boolean_algebra: !>[X0: $tType]:($o)).
% 0.55/0.41 thf(func_def_21, type, ordered_ab_group_add: !>[X0: $tType]:($o)).
% 0.55/0.41 thf(func_def_22, type, linord219039673up_add: !>[X0: $tType]:($o)).
% 0.55/0.41 thf(func_def_23, type, real_V1076094709vector: !>[X0: $tType]:($o)).
% 0.55/0.41 thf(func_def_24, type, euclid925273238_space: !>[X0: $tType]:($o)).
% 0.55/0.41 thf(func_def_25, type, real_V2090557954_space: !>[X0: $tType]:($o)).
% 0.55/0.41 thf(func_def_26, type, semiri1193490041visors: !>[X0: $tType]:($o)).
% 0.55/0.41 thf(func_def_27, type, linord1659791738miring: !>[X0: $tType]:($o)).
% 0.55/0.41 thf(func_def_28, type, comple187826305attice: !>[X0: $tType]:($o)).
% 0.55/0.41 thf(func_def_29, type, canoni770627133id_add: !>[X0: $tType]:($o)).
% 0.55/0.41 thf(func_def_30, type, semiri1923998003cancel: !>[X0: $tType]:($o)).
% 0.55/0.41 thf(func_def_31, type, euclid24285859cancel: !>[X0: $tType]:($o)).
% 0.55/0.41 thf(func_def_32, type, condit378418413attice: !>[X0: $tType]:($o)).
% 0.55/0.41 thf(func_def_33, type, complete_Sup_Sup: !>[X0: $tType]:((set @ X0 > X0))).
% 0.55/0.41 thf(func_def_34, type, convex: !>[X0: $tType]:((set @ X0 > $o))).
% 0.55/0.41 thf(func_def_35, type, extend1396239628finity: !>[X0: $tType]:(X0)).
% 0.55/0.41 thf(func_def_36, type, extended_MInfty: extended_ereal).
% 0.55/0.41 thf(func_def_37, type, extended_PInfty: extended_ereal).
% 0.55/0.41 thf(func_def_38, type, extended_ereal2: (real > extended_ereal)).
% 0.55/0.41 thf(func_def_39, type, extended_rec_ereal: !>[X0: $tType]:(((real > X0) > X0 > X0 > extended_ereal > X0))).
% 0.55/0.41 thf(func_def_40, type, extend1716541707_ereal: (extended_ereal > real)).
% 0.55/0.41 thf(func_def_41, type, times_times: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.55/0.41 thf(func_def_42, type, uminus_uminus: !>[X0: $tType]:((X0 > X0))).
% 0.55/0.41 thf(func_def_43, type, zero_zero: !>[X0: $tType]:(X0)).
% 0.55/0.41 thf(func_def_44, type, lower_261390618igraph: !>[X0: $tType]:((set @ X0 > (X0 > extended_ereal) > set @ product_prod @ X0 @ real))).
% 0.55/0.41 thf(func_def_45, type, lower_500881736ine_on: !>[X0: $tType]:((set @ X0 > (X0 > extended_ereal) > $o))).
% 0.55/0.41 thf(func_def_46, type, lower_708069572ave_on: !>[X0: $tType]:((set @ X0 > (X0 > extended_ereal) > $o))).
% 0.55/0.41 thf(func_def_47, type, lower_673667120vex_on: !>[X0: $tType]:((set @ X0 > (X0 > extended_ereal) > $o))).
% 0.55/0.41 thf(func_def_48, type, lower_272802190domain: !>[X0: $tType]:(((X0 > extended_ereal) > set @ X0))).
% 0.55/0.41 thf(func_def_49, type, lower_728871928ite_on: !>[X0: $tType]:((set @ X0 > (X0 > extended_ereal) > $o))).
% 0.55/0.41 thf(func_def_50, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.55/0.41 thf(func_def_51, type, order_Greatest: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.55/0.41 thf(func_def_52, type, top_top: !>[X0: $tType]:(X0)).
% 0.55/0.41 thf(func_def_53, type, divide_divide: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.55/0.41 thf(func_def_54, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 0.55/0.41 thf(func_def_55, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.55/0.41 thf(func_def_56, type, f: (a > extended_ereal)).
% 0.55/0.41 thf(func_def_60, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.55/0.41 thf(func_def_61, type, vIMP: ($o > $o > $o)).
% 0.55/0.41 thf(func_def_62, type, db0: !>[X0: $tType]:(X0)).
% 0.55/0.41 thf(func_def_63, type, db2: !>[X0: $tType]:(X0)).
% 0.55/0.41 thf(func_def_64, type, vAND: ($o > $o > $o)).
% 0.55/0.41 thf(func_def_65, type, db1: !>[X0: $tType]:(X0)).
% 0.55/0.41 thf(func_def_66, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.55/0.41 thf(func_def_67, type, vNOT: ($o > $o)).
% 0.55/0.41 thf(func_def_68, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.55/0.41 thf(func_def_69, type, vOR: ($o > $o > $o)).
% 0.55/0.41 thf(func_def_70, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.55/0.41 thf(func_def_71, type, sP0: (extended_ereal > extended_ereal > $o)).
% 0.55/0.41 thf(func_def_72, type, sP1: (extended_ereal > extended_ereal > $o)).
% 0.55/0.41 thf(func_def_73, type, sP2: (extended_ereal > extended_ereal > $o)).
% 0.55/0.41 thf(func_def_74, type, sP3: (extended_ereal > extended_ereal > $o)).
% 0.55/0.41 thf(func_def_75, type, sP4: (extended_ereal > extended_ereal > $o)).
% 0.55/0.41 thf(func_def_76, type, sP5: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.55/0.41 thf(func_def_77, type, sP6: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.55/0.41 thf(func_def_78, type, sP7: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 0.55/0.41 thf(func_def_79, type, sP8: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 0.55/0.41 thf(func_def_80, type, sP9: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 0.55/0.41 thf(func_def_81, type, sP10: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 0.55/0.41 thf(func_def_82, type, sP11: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 0.55/0.41 thf(func_def_83, type, sP12: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 0.55/0.41 thf(func_def_84, type, sP13: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 0.55/0.41 thf(func_def_85, type, sP14: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 0.55/0.41 thf(func_def_86, type, sP15: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 0.55/0.41 thf(func_def_87, type, sP16: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 0.55/0.41 thf(func_def_88, type, sP17: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 0.55/0.41 thf(func_def_89, type, sP18: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 0.55/0.41 thf(func_def_90, type, sP19: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 0.55/0.41 thf(func_def_91, type, sP20: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 0.55/0.41 thf(func_def_92, type, sP21: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 0.55/0.41 thf(func_def_93, type, sP22: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 0.55/0.41 thf(func_def_94, type, sP23: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 0.55/0.41 thf(func_def_95, type, sP24: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 0.55/0.41 thf(func_def_96, type, sP25: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 0.55/0.41 thf(func_def_97, type, sP26: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 0.55/0.41 thf(func_def_98, type, sP27: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 0.55/0.41 thf(func_def_99, type, sP28: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 0.55/0.41 thf(func_def_100, type, sP29: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 0.55/0.41 thf(func_def_101, type, sP30: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 0.55/0.41 thf(func_def_102, type, sP31: (extended_ereal > extended_ereal > extended_ereal > $o)).
% 0.55/0.41 thf(func_def_103, type, sK32: (extended_ereal > real)).
% 0.55/0.41 thf(func_def_104, type, sK33: !>[X0: $tType]:((set @ X0 > set @ set @ X0 > set @ X0))).
% 0.55/0.41 thf(func_def_105, type, sK34: !>[X0: $tType]:((set @ set @ X0 > (X0 > $o) > X0))).
% 0.55/0.41 thf(func_def_106, type, sK35: !>[X0: $tType]:((set @ set @ X0 > (X0 > $o) > set @ X0))).
% 0.55/0.41 thf(func_def_107, type, sK36: !>[X0: $tType]:((set @ set @ X0 > (X0 > $o) > X0))).
% 0.55/0.41 thf(func_def_108, type, sK37: !>[X0: $tType]:(((X0 > extended_ereal) > set @ X0))).
% 0.55/0.41 thf(func_def_109, type, sK38: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.55/0.41 thf(func_def_110, type, sK39: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.55/0.41 thf(func_def_111, type, sK40: (set @ extended_ereal > extended_ereal)).
% 0.55/0.41 thf(func_def_112, type, sK41: (extended_ereal > set @ extended_ereal > extended_ereal)).
% 0.55/0.41 thf(func_def_113, type, sK42: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.55/0.41 thf(func_def_114, type, sK43: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.55/0.41 thf(func_def_115, type, sK44: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.55/0.41 thf(func_def_116, type, sK45: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.55/0.41 thf(func_def_117, type, sK46: (extended_ereal > real)).
% 0.55/0.41 thf(func_def_118, type, sK47: !>[X0: $tType]:((set @ X0 > X0))).
% 0.55/0.41 thf(func_def_119, type, sK48: ((extended_ereal > $o) > real)).
% 0.55/0.41 thf(func_def_120, type, sK49: ((extended_ereal > $o) > real)).
% 0.55/0.41 thf(func_def_121, type, sK50: !>[X0: $tType]:((X0 > (X0 > $o) > X0))).
% 0.55/0.41 thf(func_def_122, type, sK51: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 0.55/0.41 thf(func_def_123, type, sK52: ((extended_ereal > extended_ereal > $o) > real)).
% 0.55/0.41 thf(func_def_124, type, sK53: ((extended_ereal > extended_ereal > $o) > real)).
% 0.55/0.41 thf(func_def_125, type, sK54: ((extended_ereal > extended_ereal > $o) > real)).
% 0.55/0.41 thf(func_def_126, type, sK55: ((extended_ereal > extended_ereal > $o) > real)).
% 0.55/0.41 thf(func_def_127, type, sK56: ((extended_ereal > extended_ereal > $o) > real)).
% 0.55/0.41 thf(func_def_128, type, sK57: ((extended_ereal > extended_ereal > $o) > real)).
% 0.55/0.41 thf(func_def_129, type, sK58: !>[X0: $tType]:((set @ set @ X0 > set @ set @ X0 > set @ X0))).
% 0.55/0.41 thf(func_def_130, type, sK59: (extended_ereal > real)).
% 0.55/0.41 thf(func_def_131, type, sK60: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 0.55/0.41 thf(func_def_132, type, sK61: !>[X0: $tType]:((set @ set @ X0 > X0 > set @ X0))).
% 0.55/0.41 thf(func_def_133, type, sK62: ((extended_ereal > $o) > real)).
% 0.55/0.41 thf(func_def_134, type, sK63: (extended_ereal > real)).
% 0.55/0.41 thf(func_def_135, type, sK64: (extended_ereal > real)).
% 0.55/0.41 thf(func_def_136, type, sK65: (extended_ereal > real)).
% 0.55/0.41 thf(func_def_137, type, sK66: (extended_ereal > real)).
% 0.55/0.41 thf(func_def_138, type, sK67: (extended_ereal > real)).
% 0.55/0.41 thf(func_def_139, type, sK68: (extended_ereal > real)).
% 0.55/0.41 thf(func_def_140, type, sK69: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.55/0.41 thf(func_def_141, type, sK70: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.55/0.41 thf(func_def_142, type, sK71: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.55/0.41 thf(func_def_143, type, sK72: (extended_ereal > extended_ereal > real)).
% 0.55/0.41 thf(func_def_144, type, sK73: !>[X0: $tType]:(((set @ X0 > $o) > set @ X0))).
% 0.55/0.41 thf(func_def_145, type, sK74: !>[X0: $tType]:(((set @ X0 > $o) > set @ X0))).
% 0.55/0.41 thf(func_def_146, type, sK75: !>[X0: $tType]:((X0 > set @ X0 > X0))).
% 0.55/0.41 thf(func_def_147, type, sK76: !>[X0: $tType]:(X0)).
% 0.55/0.41 thf(func_def_148, type, sK77: !>[X0: $tType]:((set @ X0 > X0 > X0))).
% 0.55/0.41 thf(func_def_149, type, sK78: ((extended_ereal > extended_ereal > $o) > real)).
% 0.55/0.41 thf(func_def_150, type, sK79: ((extended_ereal > extended_ereal > $o) > extended_ereal)).
% 0.55/0.41 thf(func_def_151, type, sK80: ((extended_ereal > extended_ereal > $o) > real)).
% 0.55/0.41 thf(func_def_152, type, sK81: ((extended_ereal > extended_ereal > $o) > real)).
% 0.55/0.41 thf(func_def_153, type, sK82: ((extended_ereal > extended_ereal > $o) > extended_ereal)).
% 0.55/0.41 thf(func_def_154, type, sK83: ((extended_ereal > extended_ereal > $o) > real)).
% 0.55/0.41 thf(func_def_155, type, sK84: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > X1) > X0))).
% 0.55/0.41 thf(func_def_156, type, sK85: (extended_ereal > extended_ereal > real)).
% 0.55/0.41 thf(func_def_157, type, sK86: (extended_ereal > real)).
% 0.55/0.41 thf(func_def_158, type, sK87: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.55/0.41 thf(func_def_159, type, sK88: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.55/0.41 thf(func_def_160, type, sK89: !>[X0: $tType]:((X0 > set @ X0 > X0))).
% 0.55/0.41 thf(func_def_161, type, sK90: !>[X0: $tType]:((set @ X0 > X0 > X0))).
% 0.55/0.41 thf(func_def_162, type, sK91: !>[X0: $tType]:((set @ X0 > X0 > X0))).
% 0.55/0.41 thf(func_def_163, type, sK92: !>[X0: $tType]:((X0 > set @ set @ X0 > set @ X0))).
% 0.55/0.41 thf(func_def_164, type, sK93: ((extended_ereal > extended_ereal > $o) > extended_ereal)).
% 0.55/0.41 thf(func_def_165, type, sK94: ((extended_ereal > extended_ereal > $o) > real)).
% 0.55/0.41 thf(func_def_166, type, sK95: ((extended_ereal > extended_ereal > $o) > extended_ereal)).
% 0.55/0.41 thf(func_def_167, type, sK96: ((extended_ereal > extended_ereal > $o) > real)).
% 0.55/0.41 thf(func_def_168, type, sK97: ((extended_ereal > extended_ereal > $o) > real)).
% 0.55/0.41 thf(func_def_169, type, sK98: ((extended_ereal > extended_ereal > $o) > real)).
% 0.55/0.41 thf(func_def_170, type, sK99: !>[X0: $tType]:((X0 > set @ X0 > X0))).
% 0.55/0.41 thf(func_def_171, type, sK100: !>[X0: $tType]:((X0 > set @ X0 > X0))).
% 0.55/0.41 thf(func_def_172, type, sK101: (extended_ereal > real)).
% 0.55/0.41 thf(func_def_173, type, sK102: (extended_ereal > real)).
% 0.55/0.41 thf(func_def_174, type, sK103: !>[X0: $tType]:(((X0 > $o) > set @ set @ X0 > set @ X0))).
% 0.55/0.41 thf(func_def_175, type, sK104: !>[X0: $tType]:(((X0 > $o) > set @ set @ X0 > X0))).
% 0.55/0.41 thf(func_def_176, type, sK105: !>[X0: $tType]:(((X0 > $o) > set @ set @ X0 > X0))).
% 0.55/0.41 thf(func_def_177, type, sK106: (extended_ereal > real)).
% 0.55/0.41 thf(func_def_178, type, sK107: (extended_ereal > real)).
% 0.55/0.41 thf(func_def_179, type, sK108: (set @ extended_ereal > extended_ereal)).
% 0.55/0.41 thf(func_def_180, type, sK109: (extended_ereal > set @ extended_ereal > extended_ereal)).
% 0.55/0.41 thf(func_def_181, type, sK110: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.55/0.41 thf(func_def_182, type, sK111: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.55/0.41 thf(func_def_183, type, sK112: (extended_ereal > real)).
% 0.55/0.41 thf(func_def_184, type, sK113: (extended_ereal > real)).
% 0.55/0.41 thf(func_def_185, type, sK114: (extended_ereal > real)).
% 0.55/0.41 thf(func_def_186, type, sK115: (extended_ereal > real)).
% 0.55/0.41 thf(func_def_187, type, sK116: (extended_ereal > real)).
% 0.55/0.41 thf(func_def_188, type, sK117: (extended_ereal > real)).
% 0.55/0.41 thf(func_def_189, type, sK118: (extended_ereal > real)).
% 0.55/0.41 thf(func_def_190, type, sK119: (extended_ereal > real)).
% 0.55/0.41 thf(func_def_191, type, sK120: (extended_ereal > real)).
% 0.55/0.41 thf(func_def_192, type, sK121: (extended_ereal > real)).
% 0.55/0.41 thf(func_def_193, type, sK122: (extended_ereal > real)).
% 0.55/0.41 thf(func_def_194, type, sK123: (extended_ereal > real)).
% 0.55/0.41 thf(func_def_195, type, sK124: (extended_ereal > real)).
% 0.55/0.41 thf(func_def_196, type, sK125: (extended_ereal > real)).
% 0.55/0.41 thf(func_def_197, type, sK126: (extended_ereal > real)).
% 0.55/0.41 thf(func_def_198, type, sK127: (extended_ereal > real)).
% 0.55/0.41 thf(func_def_199, type, sK128: (extended_ereal > real)).
% 0.55/0.41 thf(func_def_200, type, sK129: (extended_ereal > real)).
% 0.55/0.41 thf(func_def_201, type, sK130: (extended_ereal > real)).
% 0.55/0.41 thf(func_def_202, type, sK131: (extended_ereal > real)).
% 0.55/0.41 thf(func_def_203, type, sK132: (extended_ereal > real)).
% 0.55/0.41 thf(func_def_204, type, sK133: (extended_ereal > real)).
% 0.55/0.41 thf(func_def_205, type, sK134: (extended_ereal > real)).
% 0.55/0.41 thf(func_def_206, type, sK135: (extended_ereal > real)).
% 0.55/0.41 thf(func_def_207, type, sK136: (extended_ereal > real)).
% 0.55/0.41 thf(func_def_208, type, sK137: (extended_ereal > real)).
% 0.55/0.41 thf(func_def_209, type, sK138: (extended_ereal > real)).
% 0.55/0.41 thf(func_def_210, type, sK139: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.55/0.41 thf(func_def_211, type, sK140: !>[X0: $tType]:(((X0 > extended_ereal) > (X0 > extended_ereal) > X0))).
% 0.55/0.41 thf(func_def_212, type, sK141: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.55/0.41 thf(func_def_213, type, sK142: !>[X0: $tType]:((X0 > (X0 > $o) > X0))).
% 0.55/0.41 thf(func_def_214, type, sK143: ((extended_ereal > $o) > real)).
% 0.55/0.41 thf(func_def_215, type, sK144: !>[X0: $tType]:(((X0 > extended_ereal) > set @ X0))).
% 0.55/0.41 thf(func_def_216, type, sK145: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.55/0.41 thf(func_def_217, type, sK146: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.55/0.41 thf(func_def_219, type, inv_uminus_uminus_148: !>[X0: $tType]:((X0 > X0))).
% 0.55/0.41 thf(f1,axiom,(
% 0.55/0.41 (convex @ a @ (lower_272802190domain @ a @ f)) => (lower_673667120vex_on @ a @ top_top @ set @ a @ f)),
% 0.55/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__092_060open_062convex_A_Idomain_Af_J_A_092_060Longrightarrow_062_ALower__Semicontinuous__Mirabelle__quczrylfpw_Oconvex__on_AUNIV_Af_092_060close_062)).
% 0.55/0.41 thf(f2,axiom,(
% 0.55/0.41 ! [X0 : $tType] : (euclid925273238_space @ X0 => ! [X1 : (X0 > extended_ereal)] : ((lower_673667120vex_on @ X0 @ top_top @ set @ X0 @ X1) => (convex @ X0 @ (lower_272802190domain @ X0 @ X1))))),
% 0.55/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_convex__domain)).
% 0.55/0.41 thf(f341,axiom,(
% 0.55/0.41 euclid925273238_space @ a),
% 0.55/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_0)).
% 0.55/0.41 thf(f342,conjecture,(
% 0.55/0.41 (((lower_673667120vex_on @ a @ top_top @ set @ a @ f)) = ((convex @ a @ (lower_272802190domain @ a @ f))))),
% 0.55/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 0.55/0.41 thf(f343,negated_conjecture,(
% 0.55/0.41 ~ (((lower_673667120vex_on @ a @ top_top @ set @ a @ f)) = ((convex @ a @ (lower_272802190domain @ a @ f))))),
% 0.55/0.41 inference(negated_conjecture,[status(cth)],[f342])).
% 0.55/0.41 thf(f358,plain,(
% 0.55/0.41 (convex @ a @ (lower_272802190domain @ a @ f)) => (lower_673667120vex_on @ a @ top_top @ set @ a @ f)),
% 0.55/0.41 inference(rectify,[],[f1])).
% 0.55/0.41 thf(f359,plain,(
% 0.55/0.41 (((convex @ a @ (lower_272802190domain @ a @ f))) = $true) => (((lower_673667120vex_on @ a @ top_top @ set @ a @ f)) = $true)),
% 0.55/0.41 inference(fool_elimination,[],[f358])).
% 0.55/0.41 thf(f585,plain,(
% 0.55/0.41 ! [X0 : $tType] : (euclid925273238_space @ X0 => ! [X1 : (X0 > extended_ereal)] : ((lower_673667120vex_on @ X0 @ top_top @ set @ X0 @ X1) => (convex @ X0 @ (lower_272802190domain @ X0 @ X1))))),
% 0.55/0.41 inference(rectify,[],[f2])).
% 0.55/0.41 thf(f586,plain,(
% 0.55/0.41 ! [X0 : $tType] : ((euclid925273238_space @ X0 = $true) => ! [X1 : (X0 > extended_ereal)] : ((((lower_673667120vex_on @ X0 @ top_top @ set @ X0 @ X1)) = $true) => (((convex @ X0 @ (lower_272802190domain @ X0 @ X1))) = $true)))),
% 0.55/0.41 inference(fool_elimination,[],[f585])).
% 0.55/0.41 thf(f895,plain,(
% 0.55/0.41 euclid925273238_space @ a),
% 0.55/0.41 inference(rectify,[],[f341])).
% 0.55/0.41 thf(f896,plain,(
% 0.55/0.41 (euclid925273238_space @ a = $true)),
% 0.55/0.41 inference(fool_elimination,[],[f895])).
% 0.55/0.41 thf(f913,plain,(
% 0.55/0.41 (((convex @ a @ (lower_272802190domain @ a @ f))) != ((lower_673667120vex_on @ a @ top_top @ set @ a @ f)))),
% 0.55/0.41 inference(flattening,[],[f343])).
% 0.55/0.41 thf(f1162,plain,(
% 0.55/0.41 (((convex @ a @ (lower_272802190domain @ a @ f))) != $true) | (((lower_673667120vex_on @ a @ top_top @ set @ a @ f)) = $true)),
% 0.55/0.41 inference(ennf_transformation,[],[f359])).
% 0.55/0.41 thf(f1169,plain,(
% 0.55/0.41 ! [X0 : $tType] : ((euclid925273238_space @ X0 != $true) | ! [X1 : (X0 > extended_ereal)] : ((((lower_673667120vex_on @ X0 @ top_top @ set @ X0 @ X1)) != $true) | (((convex @ X0 @ (lower_272802190domain @ X0 @ X1))) = $true)))),
% 0.55/0.41 inference(ennf_transformation,[],[f586])).
% 0.55/0.41 thf(f1597,plain,(
% 0.55/0.41 (((convex @ a @ (lower_272802190domain @ a @ f))) != $true) | (((lower_673667120vex_on @ a @ top_top @ set @ a @ f)) = $true)),
% 0.55/0.41 inference(cnf_transformation,[],[f1162])).
% 0.55/0.41 thf(f1620,plain,(
% 0.55/0.41 (euclid925273238_space @ a = $true)),
% 0.55/0.41 inference(cnf_transformation,[],[f896])).
% 0.55/0.41 thf(f1809,plain,(
% 0.55/0.41 (((convex @ a @ (lower_272802190domain @ a @ f))) != ((lower_673667120vex_on @ a @ top_top @ set @ a @ f)))),
% 0.55/0.41 inference(cnf_transformation,[],[f913])).
% 0.55/0.41 thf(f1812,plain,(
% 0.55/0.41 ( ! [X0 : $tType,X1 : (X0 > extended_ereal)] : ((((lower_673667120vex_on @ X0 @ top_top @ set @ X0 @ X1)) != $true) | (euclid925273238_space @ X0 != $true) | (((convex @ X0 @ (lower_272802190domain @ X0 @ X1))) = $true)) )),
% 0.55/0.41 inference(cnf_transformation,[],[f1169])).
% 0.55/0.41 thf(f2224,plain,(
% 0.55/0.41 (((convex @ a @ (lower_272802190domain @ a @ f))) = $true) | (((lower_673667120vex_on @ a @ top_top @ set @ a @ f)) = $true)),
% 0.55/0.41 inference(xor_proxy_clausification,[],[f1809])).
% 0.55/0.41 thf(f2225,plain,(
% 0.55/0.41 (((convex @ a @ (lower_272802190domain @ a @ f))) = $false) | (((lower_673667120vex_on @ a @ top_top @ set @ a @ f)) = $false)),
% 0.55/0.41 inference(xor_proxy_clausification,[],[f1809])).
% 0.55/0.41 thf(f2382,definition,(
% 0.55/0.41 spl147_23 <=> (((convex @ a @ (lower_272802190domain @ a @ f))) = $false)),
% 0.55/0.41 introduced(definition,[new_symbols(definition,[spl147_23])],[avatar_definition])).
% 0.55/0.41 thf(f2384,plain,(
% 0.55/0.41 (((convex @ a @ (lower_272802190domain @ a @ f))) = $false) | ~spl147_23),
% 0.55/0.41 inference(avatar_component_clause,[],[f2382])).
% 0.55/0.41 thf(f2386,definition,(
% 0.55/0.41 spl147_24 <=> (((lower_673667120vex_on @ a @ top_top @ set @ a @ f)) = $false)),
% 0.55/0.41 introduced(definition,[new_symbols(definition,[spl147_24])],[avatar_definition])).
% 0.55/0.41 thf(f2388,plain,(
% 0.55/0.41 (((lower_673667120vex_on @ a @ top_top @ set @ a @ f)) = $false) | ~spl147_24),
% 0.55/0.41 inference(avatar_component_clause,[],[f2386])).
% 0.55/0.41 thf(f2389,plain,(
% 0.55/0.41 spl147_23 | spl147_24),
% 0.55/0.41 inference(avatar_split_clause,[],[f2225,f2386,f2382])).
% 0.55/0.41 thf(f2391,definition,(
% 0.55/0.41 spl147_25 <=> (((lower_673667120vex_on @ a @ top_top @ set @ a @ f)) = $true)),
% 0.55/0.41 introduced(definition,[new_symbols(definition,[spl147_25])],[avatar_definition])).
% 0.55/0.41 thf(f2393,plain,(
% 0.55/0.41 (((lower_673667120vex_on @ a @ top_top @ set @ a @ f)) = $true) | ~spl147_25),
% 0.55/0.41 inference(avatar_component_clause,[],[f2391])).
% 0.55/0.41 thf(f2395,definition,(
% 0.55/0.41 spl147_26 <=> (((convex @ a @ (lower_272802190domain @ a @ f))) = $true)),
% 0.55/0.41 introduced(definition,[new_symbols(definition,[spl147_26])],[avatar_definition])).
% 0.55/0.41 thf(f2398,plain,(
% 0.55/0.41 spl147_25 | spl147_26),
% 0.55/0.41 inference(avatar_split_clause,[],[f2224,f2395,f2391])).
% 0.55/0.41 thf(f2399,plain,(
% 0.55/0.41 spl147_25 | ~spl147_26),
% 0.55/0.41 inference(avatar_split_clause,[],[f1597,f2395,f2391])).
% 0.55/0.41 thf(f2416,definition,(
% 0.55/0.41 spl147_30 <=> (euclid925273238_space @ a = $true)),
% 0.55/0.41 introduced(definition,[new_symbols(definition,[spl147_30])],[avatar_definition])).
% 0.55/0.41 thf(f2418,plain,(
% 0.55/0.41 (euclid925273238_space @ a = $true) | ~spl147_30),
% 0.55/0.41 inference(avatar_component_clause,[],[f2416])).
% 0.55/0.41 thf(f2419,plain,(
% 0.55/0.41 spl147_30),
% 0.55/0.41 inference(avatar_split_clause,[],[f1620,f2416])).
% 0.55/0.41 thf(f2610,plain,(
% 0.55/0.41 ($true = $false) | (~spl147_24 | ~spl147_25)),
% 0.55/0.41 inference(forward_demodulation,[],[f2393,f2388])).
% 0.55/0.41 thf(f2611,plain,(
% 0.55/0.41 $false | (~spl147_24 | ~spl147_25)),
% 0.55/0.41 inference(trivial_inequality_removal,[],[f2610])).
% 0.55/0.41 thf(f2612,plain,(
% 0.55/0.41 ~spl147_24 | ~spl147_25),
% 0.55/0.41 inference(avatar_contradiction_clause,[],[f2611])).
% 0.55/0.41 thf(f2654,plain,(
% 0.55/0.41 ($true != $true) | (((convex @ a @ (lower_272802190domain @ a @ f))) = $true) | (euclid925273238_space @ a != $true) | ~spl147_25),
% 0.55/0.41 inference(superposition,[],[f1812,f2393])).
% 0.55/0.41 thf(f2655,plain,(
% 0.55/0.41 (euclid925273238_space @ a != $true) | (((convex @ a @ (lower_272802190domain @ a @ f))) = $true) | ~spl147_25),
% 0.55/0.41 inference(trivial_inequality_removal,[],[f2654])).
% 0.55/0.41 thf(f2656,plain,(
% 0.55/0.41 (((convex @ a @ (lower_272802190domain @ a @ f))) = $true) | (~spl147_25 | ~spl147_30)),
% 0.55/0.41 inference(forward_subsumption_resolution,[],[f2655,f2418])).
% 0.55/0.41 thf(f2657,plain,(
% 0.55/0.41 ($true = $false) | (~spl147_23 | ~spl147_25 | ~spl147_30)),
% 0.55/0.41 inference(forward_demodulation,[],[f2656,f2384])).
% 0.55/0.41 thf(f2658,plain,(
% 0.55/0.41 $false | (~spl147_23 | ~spl147_25 | ~spl147_30)),
% 0.55/0.41 inference(trivial_inequality_removal,[],[f2657])).
% 0.55/0.41 thf(f2659,plain,(
% 0.55/0.41 ~spl147_23 | ~spl147_25 | ~spl147_30),
% 0.55/0.41 inference(avatar_contradiction_clause,[],[f2658])).
% 0.55/0.41 cnf(s23, plain, spl147_23 | spl147_24, inference(sat_conversion,[],[f2389])).
% 0.55/0.41 cnf(s24, plain, spl147_25 | spl147_26, inference(sat_conversion,[],[f2398])).
% 0.55/0.41 cnf(s25, plain, spl147_25 | ~spl147_26, inference(sat_conversion,[],[f2399])).
% 0.55/0.41 cnf(s29, plain, spl147_30, inference(sat_conversion,[],[f2419])).
% 0.55/0.41 cnf(s71, plain, ~spl147_24 | ~spl147_25, inference(sat_conversion,[],[f2612])).
% 0.55/0.41 cnf(s75, plain, ~spl147_23 | ~spl147_25 | ~spl147_30, inference(sat_conversion,[],[f2659])).
% 0.55/0.41 cnf(s79, plain, spl147_25, inference(rat,[],[s24,s25])).
% 0.55/0.41 cnf(s80, plain, ~spl147_23, inference(rat,[],[s75,s29,s79])).
% 0.55/0.41 cnf(s81, plain, ~spl147_24, inference(rat,[],[s71,s79])).
% 0.55/0.41 cnf(s82, plain, $false, inference(rat,[],[s23,s81,s80])).
% 0.55/0.41 thf(f2660,plain,(
% 0.55/0.41 $false),
% 0.55/0.41 inference(avatar_sat_refutation,[],[s82])).
% 0.55/0.41 % SZS output end Proof for theBenchmark
% 0.55/0.41 % (4034752)------------------------------
% 0.55/0.41 % (4034752)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.55/0.41 % (4034752)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.55/0.41 % (4034752)CaDiCaL version: 2.1.3
% 0.55/0.41 % (4034752)Termination reason: Refutation
% 0.55/0.41 % (4034752)Time elapsed: 0.070 s
% 0.55/0.41 % (4034752)Peak memory usage: 14 MB
% 0.55/0.41 % (4034752)Instructions burned: 139 (million)
% 0.55/0.41 % (4034744)Success in time 0.127 s
% 0.55/0.41 % Vampire exiting
%------------------------------------------------------------------------------