%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP117^2 : 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 : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:08:25 AM UTC 2026
% Result : Theorem 0.32s 0.45s
% Output : Refutation 0.32s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP117^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 % Computer : n005.cluster.edu
% 0.09/0.21 % Model : x86_64 x86_64
% 0.09/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.21 % Memory : 8046.5625MB
% 0.09/0.21 % OS : Linux 6.8.0-71-generic
% 0.09/0.21 % CPULimit : 300
% 0.09/0.21 % WCLimit : 300
% 0.09/0.21 % DateTime : Tue Sep 29 19:56:01 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.25 Running higher-order theorem proving
% 0.22/0.31 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
% 0.32/0.45 % (2130281)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.32/0.45 % (2130291)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3353990684:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.32/0.45 % (2130292)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.32/0.45 % (2130292)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
% 0.32/0.45 % (2130286)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=885792799:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.32/0.45 % (2130287)lrs+10_16_si=on:nwc=1.5:random_seed=211122150:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.32/0.45 % (2130288)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=887911902:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.32/0.45 % (2130290)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2346051248:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.32/0.45 % (2130289)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=1498686200: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)
% 0.32/0.45 % (2130292)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=2484846247:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.32/0.45 % (2130288)Instruction limit reached!
% 0.32/0.45 % (2130288)------------------------------
% 0.32/0.45 % (2130288)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.32/0.45 % (2130288)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.32/0.45 % (2130288)CaDiCaL version: 2.1.3
% 0.32/0.45 % (2130288)Termination reason: Instruction limit
% 0.32/0.45 % (2130288)Termination phase: shuffling
% 0.32/0.45 % (2130288)Time elapsed: 0.002 s
% 0.32/0.45 % (2130288)Peak memory usage: 10 MB
% 0.32/0.45 % (2130288)Instructions burned: 4 (million)
% 0.32/0.45 % (2130287)Instruction limit reached!
% 0.32/0.45 % (2130287)------------------------------
% 0.32/0.45 % (2130287)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.32/0.45 % (2130287)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.32/0.45 % (2130287)CaDiCaL version: 2.1.3
% 0.32/0.45 % (2130287)Termination reason: Instruction limit
% 0.32/0.45 % (2130287)Termination phase: shuffling
% 0.32/0.45 % (2130287)Time elapsed: 0.009 s
% 0.32/0.45 % (2130287)Peak memory usage: 10 MB
% 0.32/0.45 % (2130287)Instructions burned: 18 (million)
% 0.32/0.45 % (2130290)Instruction limit reached!
% 0.32/0.45 % (2130290)------------------------------
% 0.32/0.45 % (2130290)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.32/0.45 % (2130290)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.32/0.45 % (2130290)CaDiCaL version: 2.1.3
% 0.32/0.45 % (2130290)Termination reason: Instruction limit
% 0.32/0.45 % (2130290)Termination phase: Property scanning
% 0.32/0.45 % (2130290)Time elapsed: 0.012 s
% 0.32/0.45 % (2130290)Peak memory usage: 10 MB
% 0.32/0.45 % (2130290)Instructions burned: 24 (million)
% 0.32/0.45 % (2130291)Instruction limit reached!
% 0.32/0.45 % (2130291)------------------------------
% 0.32/0.45 % (2130291)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.32/0.45 % (2130291)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.32/0.45 % (2130291)CaDiCaL version: 2.1.3
% 0.32/0.45 % (2130291)Termination reason: Instruction limit
% 0.32/0.45 % (2130291)Termination phase: Property scanning
% 0.32/0.45 % (2130291)Time elapsed: 0.019 s
% 0.32/0.45 % (2130291)Peak memory usage: 12 MB
% 0.32/0.45 % (2130291)Instructions burned: 75 (million)
% 0.32/0.45 % (2130300)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=341064617:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.32/0.45 % (2130303)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2657925238:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.32/0.45 % (2130300)Instruction limit reached!
% 0.32/0.45 % (2130300)------------------------------
% 0.32/0.45 % (2130300)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.32/0.45 % (2130300)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.32/0.45 % (2130300)CaDiCaL version: 2.1.3
% 0.32/0.45 % (2130300)Termination reason: Instruction limit
% 0.32/0.45 % (2130300)Termination phase: shuffling
% 0.32/0.45 % (2130300)Time elapsed: 0.002 s
% 0.32/0.45 % (2130300)Peak memory usage: 10 MB
% 0.32/0.45 % (2130300)Instructions burned: 3 (million)
% 0.32/0.45 % (2130303)Instruction limit reached!
% 0.32/0.45 % (2130303)------------------------------
% 0.32/0.45 % (2130303)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.32/0.45 % (2130303)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.32/0.45 % (2130303)CaDiCaL version: 2.1.3
% 0.32/0.45 % (2130303)Termination reason: Instruction limit
% 0.32/0.45 % (2130303)Termination phase: shuffling
% 0.32/0.45 % (2130303)Time elapsed: 0.003 s
% 0.32/0.45 % (2130303)Peak memory usage: 10 MB
% 0.32/0.45 % (2130303)Instructions burned: 13 (million)
% 0.32/0.45 % (2130302)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.32/0.45 % (2130301)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3172904800:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.32/0.45 % (2130302)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=679721426:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.32/0.45 % (2130301)Instruction limit reached!
% 0.32/0.45 % (2130301)------------------------------
% 0.32/0.45 % (2130301)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.32/0.45 % (2130301)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.32/0.45 % (2130301)CaDiCaL version: 2.1.3
% 0.32/0.45 % (2130301)Termination reason: Instruction limit
% 0.32/0.45 % (2130301)Termination phase: shuffling
% 0.32/0.45 % (2130301)Time elapsed: 0.003 s
% 0.32/0.45 % (2130301)Peak memory usage: 10 MB
% 0.32/0.45 % (2130301)Instructions burned: 5 (million)
% 0.32/0.45 % (2130302)Instruction limit reached!
% 0.32/0.45 % (2130302)------------------------------
% 0.32/0.45 % (2130302)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.32/0.45 % (2130302)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.32/0.45 % (2130302)CaDiCaL version: 2.1.3
% 0.32/0.45 % (2130302)Termination reason: Instruction limit
% 0.32/0.45 % (2130302)Termination phase: shuffling
% 0.32/0.45 % (2130302)Time elapsed: 0.004 s
% 0.32/0.45 % (2130302)Peak memory usage: 10 MB
% 0.32/0.45 % (2130302)Instructions burned: 8 (million)
% 0.32/0.45 % (2130312)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=1391201889:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.32/0.45 % (2130310)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
% 0.32/0.45 % (2130310)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.32/0.45 % (2130286)Instruction limit reached!
% 0.32/0.45 % (2130286)------------------------------
% 0.32/0.45 % (2130286)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.32/0.45 % (2130286)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.32/0.45 % (2130286)CaDiCaL version: 2.1.3
% 0.32/0.45 % (2130286)Termination reason: Instruction limit
% 0.32/0.45 % (2130286)Termination phase: Property scanning
% 0.32/0.45 % (2130286)Time elapsed: 0.042 s
% 0.32/0.45 % (2130286)Peak memory usage: 12 MB
% 0.32/0.45 % (2130286)Instructions burned: 87 (million)
% 0.32/0.45 % (2130310)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=4050204817:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.32/0.45 % (2130317)lrs+10_1_si=on:cs=on:random_seed=1008522099:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.32/0.45 % (2130319)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.32/0.45 % (2130317)Instruction limit reached!
% 0.32/0.45 % (2130317)------------------------------
% 0.32/0.45 % (2130317)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.32/0.45 % (2130317)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.32/0.45 % (2130317)CaDiCaL version: 2.1.3
% 0.32/0.45 % (2130317)Termination reason: Instruction limit
% 0.32/0.45 % (2130317)Termination phase: shuffling
% 0.32/0.45 % (2130317)Time elapsed: 0.004 s
% 0.32/0.45 % (2130317)Peak memory usage: 10 MB
% 0.32/0.45 % (2130317)Instructions burned: 8 (million)
% 0.32/0.45 % (2130319)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=682945378:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.32/0.45 % (2130319)Instruction limit reached!
% 0.32/0.45 % (2130319)------------------------------
% 0.32/0.45 % (2130319)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.32/0.45 % (2130319)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.32/0.45 % (2130319)CaDiCaL version: 2.1.3
% 0.32/0.45 % (2130319)Termination reason: Instruction limit
% 0.32/0.45 % (2130319)Termination phase: shuffling
% 0.32/0.45 % (2130319)Time elapsed: 0.002 s
% 0.32/0.45 % (2130319)Peak memory usage: 10 MB
% 0.32/0.45 % (2130319)Instructions burned: 3 (million)
% 0.32/0.45 % (2130310)Instruction limit reached!
% 0.32/0.45 % (2130310)------------------------------
% 0.32/0.45 % (2130310)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.32/0.45 % (2130310)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.32/0.45 % (2130310)CaDiCaL version: 2.1.3
% 0.32/0.45 % (2130310)Termination reason: Instruction limit
% 0.32/0.45 % (2130310)Termination phase: shuffling
% 0.32/0.45 % (2130310)Time elapsed: 0.014 s
% 0.32/0.45 % (2130310)Peak memory usage: 10 MB
% 0.32/0.45 % (2130310)Instructions burned: 30 (million)
% 0.32/0.45 % (2130312)Instruction limit reached!
% 0.32/0.45 % (2130312)------------------------------
% 0.32/0.45 % (2130312)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.32/0.45 % (2130312)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.32/0.45 % (2130312)CaDiCaL version: 2.1.3
% 0.32/0.45 % (2130312)Termination reason: Instruction limit
% 0.32/0.45 % (2130312)Termination phase: Preprocessing 3
% 0.32/0.45 % (2130312)Time elapsed: 0.020 s
% 0.32/0.45 % (2130312)Peak memory usage: 11 MB
% 0.32/0.45 % (2130312)Instructions burned: 89 (million)
% 0.32/0.45 % (2130323)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=2273996796:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.32/0.45 % (2130289) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2130281-2130289"...
% 0.32/0.45 % (2130338)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=2175294341:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 0.32/0.45 % (2130289)...printing done.
% 0.32/0.45 % (2130289)Refutation found. Thanks to Tanya!
% 0.32/0.45 % SZS status Theorem for theBenchmark
% 0.32/0.45 % SZS output start Proof for theBenchmark
% 0.32/0.45 thf(type_def_5, type, extend1814228343nnreal: $tType).
% 0.32/0.45 thf(type_def_6, type, finite_Cartesian_vec: ($tType * $tType) > $tType).
% 0.32/0.45 thf(type_def_7, type, sigma_measure: $tType > $tType).
% 0.32/0.45 thf(type_def_8, type, real: $tType).
% 0.32/0.45 thf(type_def_9, type, set: $tType > $tType).
% 0.32/0.45 thf(type_def_10, type, nat: $tType).
% 0.32/0.45 thf(type_def_11, type, int: $tType).
% 0.32/0.45 thf(type_def_12, type, n: $tType).
% 0.32/0.45 thf(type_def_13, type, sTfun: ($tType * $tType) > $tType).
% 0.32/0.45 thf(func_def_0, type, ring_1: !>[X0: $tType]:($o)).
% 0.32/0.45 thf(func_def_1, type, ordere890947078_space: !>[X0: $tType]:($o)).
% 0.32/0.45 thf(func_def_2, type, type: !>[X0: $tType]:($o)).
% 0.32/0.45 thf(func_def_3, type, one: !>[X0: $tType]:($o)).
% 0.32/0.45 thf(func_def_4, type, zero: !>[X0: $tType]:($o)).
% 0.32/0.45 thf(func_def_5, type, ring_char_0: !>[X0: $tType]:($o)).
% 0.32/0.45 thf(func_def_6, type, neg_numeral: !>[X0: $tType]:($o)).
% 0.32/0.45 thf(func_def_7, type, group_add: !>[X0: $tType]:($o)).
% 0.32/0.45 thf(func_def_8, type, finite_finite: !>[X0: $tType]:($o)).
% 0.32/0.45 thf(func_def_9, type, monoid_add: !>[X0: $tType]:($o)).
% 0.32/0.45 thf(func_def_10, type, countable: !>[X0: $tType]:($o)).
% 0.32/0.45 thf(func_def_11, type, ab_group_add: !>[X0: $tType]:($o)).
% 0.32/0.45 thf(func_def_12, type, semigroup_add: !>[X0: $tType]:($o)).
% 0.32/0.45 thf(func_def_13, type, complete_Sup: !>[X0: $tType]:($o)).
% 0.32/0.45 thf(func_def_14, type, comm_monoid_add: !>[X0: $tType]:($o)).
% 0.32/0.45 thf(func_def_15, type, ab_semigroup_add: !>[X0: $tType]:($o)).
% 0.32/0.45 thf(func_def_16, type, comm_monoid_diff: !>[X0: $tType]:($o)).
% 0.32/0.45 thf(func_def_17, type, cancel_semigroup_add: !>[X0: $tType]:($o)).
% 0.32/0.45 thf(func_def_18, type, ordered_ab_group_add: !>[X0: $tType]:($o)).
% 0.32/0.45 thf(func_def_19, type, cancel1352612707id_add: !>[X0: $tType]:($o)).
% 0.32/0.45 thf(func_def_20, type, cancel146912293up_add: !>[X0: $tType]:($o)).
% 0.32/0.45 thf(func_def_21, type, linord219039673up_add: !>[X0: $tType]:($o)).
% 0.32/0.45 thf(func_def_22, type, ordere779506340up_add: !>[X0: $tType]:($o)).
% 0.32/0.45 thf(func_def_23, type, linord1659791738miring: !>[X0: $tType]:($o)).
% 0.32/0.45 thf(func_def_24, type, comple187826305attice: !>[X0: $tType]:($o)).
% 0.32/0.45 thf(func_def_25, type, comple1035589618norder: !>[X0: $tType]:($o)).
% 0.32/0.45 thf(func_def_26, type, canoni770627133id_add: !>[X0: $tType]:($o)).
% 0.32/0.45 thf(func_def_27, type, ordere236663937imp_le: !>[X0: $tType]:($o)).
% 0.32/0.45 thf(func_def_28, type, ordere223160158up_add: !>[X0: $tType]:($o)).
% 0.32/0.45 thf(func_def_29, type, strict2144017051up_add: !>[X0: $tType]:($o)).
% 0.32/0.45 thf(func_def_30, type, ordere516151231imp_le: !>[X0: $tType]:($o)).
% 0.32/0.45 thf(func_def_31, type, complete_Sup_Sup: !>[X0: $tType]:((set @ X0 > X0))).
% 0.32/0.45 thf(func_def_32, type, complete_completion: !>[X0: $tType]:((sigma_measure @ X0 > sigma_measure @ X0))).
% 0.32/0.45 thf(func_def_33, type, counta609264050t_into: !>[X0: $tType]:((set @ X0 > nat > X0))).
% 0.32/0.45 thf(func_def_34, type, minus_minus: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.32/0.45 thf(func_def_35, type, one_one: !>[X0: $tType]:(X0)).
% 0.32/0.45 thf(func_def_36, type, plus_plus: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.32/0.45 thf(func_def_37, type, zero_zero: !>[X0: $tType]:(X0)).
% 0.32/0.45 thf(func_def_38, type, inf_inf: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.32/0.45 thf(func_def_39, type, lebesgue_lborel: !>[X0: $tType]:(sigma_measure @ X0)).
% 0.32/0.45 thf(func_def_40, type, measure_null_sets: !>[X0: $tType]:((sigma_measure @ X0 > set @ set @ X0))).
% 0.32/0.45 thf(func_def_41, type, minkow1937162798nt_vec: !>[X0: $tType, X1: $tType]:((finite_Cartesian_vec @ int @ X0 > finite_Cartesian_vec @ X1 @ X0))).
% 0.32/0.45 thf(func_def_42, type, ord_less: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.32/0.45 thf(func_def_43, type, top_top: !>[X0: $tType]:(X0)).
% 0.32/0.45 thf(func_def_44, type, sums: !>[X0: $tType]:(((nat > X0) > X0 > $o))).
% 0.32/0.45 thf(func_def_45, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 0.32/0.45 thf(func_def_46, type, image: !>[X0: $tType, X1: $tType]:(((X0 > X1) > set @ X0 > set @ X1))).
% 0.32/0.45 thf(func_def_47, type, vimage: !>[X0: $tType, X1: $tType]:(((X0 > X1) > set @ X1 > set @ X0))).
% 0.32/0.45 thf(func_def_48, type, sigma_emeasure: !>[X0: $tType]:((sigma_measure @ X0 > set @ X0 > extend1814228343nnreal))).
% 0.32/0.45 thf(func_def_49, type, sigma_sets: !>[X0: $tType]:((sigma_measure @ X0 > set @ set @ X0))).
% 0.32/0.45 thf(func_def_50, type, sigma_space: !>[X0: $tType]:((sigma_measure @ X0 > set @ X0))).
% 0.32/0.45 thf(func_def_51, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.32/0.45 thf(func_def_52, type, r: (finite_Cartesian_vec @ int @ n > set @ finite_Cartesian_vec @ real @ n)).
% 0.32/0.45 thf(func_def_53, type, s: set @ finite_Cartesian_vec @ real @ n).
% 0.32/0.45 thf(func_def_54, type, t: (finite_Cartesian_vec @ int @ n > set @ finite_Cartesian_vec @ real @ n)).
% 0.32/0.45 thf(func_def_55, type, t2: (finite_Cartesian_vec @ int @ n > set @ finite_Cartesian_vec @ real @ n)).
% 0.32/0.45 thf(func_def_56, type, f: (nat > finite_Cartesian_vec @ int @ n)).
% 0.32/0.45 thf(func_def_60, type, db0: !>[X0: $tType]:(X0)).
% 0.32/0.45 thf(func_def_61, type, db1: !>[X0: $tType]:(X0)).
% 0.32/0.45 thf(func_def_62, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.32/0.45 thf(func_def_63, type, db2: !>[X0: $tType]:(X0)).
% 0.32/0.45 thf(func_def_64, type, vAND: ($o > $o > $o)).
% 0.32/0.45 thf(func_def_65, type, vOR: ($o > $o > $o)).
% 0.32/0.45 thf(func_def_66, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.32/0.45 thf(func_def_67, type, vNOT: ($o > $o)).
% 0.32/0.45 thf(func_def_68, type, sK0: !>[X0: $tType, X1: $tType]:(((X0 > set @ X1) > (X1 > $o) > set @ X0 > X0))).
% 0.32/0.45 thf(func_def_69, type, sK1: !>[X0: $tType, X1: $tType]:(((X0 > set @ X1) > (X1 > $o) > set @ X0 > X1))).
% 0.32/0.45 thf(func_def_70, type, sK2: !>[X0: $tType, X1: $tType]:(((X0 > set @ X1) > (X1 > $o) > set @ X0 > X1))).
% 0.32/0.45 thf(func_def_71, type, sK3: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X0 > X1))).
% 0.32/0.45 thf(func_def_72, type, sK4: !>[X0: $tType, X1: $tType]:(((X0 > $o) > (X1 > $o) > (X1 > X0) > X1))).
% 0.32/0.45 thf(func_def_73, type, sK5: !>[X0: $tType, X1: $tType]:((X1 > (X0 > X1) > X0))).
% 0.32/0.45 thf(func_def_74, type, sK6: !>[X0: $tType]:((X0 > set @ X0 > X0))).
% 0.32/0.45 thf(func_def_75, type, sK7: !>[X0: $tType]:((set @ X0 > X0))).
% 0.32/0.45 thf(func_def_76, type, sK8: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > X1) > X0))).
% 0.32/0.45 thf(func_def_77, type, sK9: !>[X0: $tType]:((set @ X0 > X0 > X0))).
% 0.32/0.45 thf(func_def_78, type, sK10: !>[X0: $tType]:(((X0 > $o) > set @ set @ X0 > set @ X0))).
% 0.32/0.45 thf(func_def_79, type, sK11: !>[X0: $tType]:(((X0 > $o) > set @ set @ X0 > X0))).
% 0.32/0.45 thf(func_def_80, type, sK12: !>[X0: $tType]:(((X0 > $o) > set @ set @ X0 > X0))).
% 0.32/0.45 thf(func_def_81, type, sK13: !>[X0: $tType, X1: $tType]:((X1 > set @ X0 > (X0 > X1) > X0))).
% 0.32/0.45 thf(func_def_82, type, sK14: !>[X0: $tType, X1: $tType]:((set @ X0 > (X0 > X1) > (X1 > $o) > X0))).
% 0.32/0.45 thf(func_def_83, type, sK15: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > (X1 > X0) > X1))).
% 0.32/0.45 thf(func_def_84, type, sK16: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.32/0.45 thf(func_def_85, type, sK17: !>[X0: $tType, X1: $tType]:((X0 > set @ X1 > (X1 > set @ X0) > X1))).
% 0.32/0.45 thf(func_def_86, type, sK18: !>[X0: $tType]:((set @ X0 > X0))).
% 0.32/0.45 thf(func_def_87, type, sK19: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > X1) > set @ X0 > X0))).
% 0.32/0.45 thf(func_def_88, type, sK20: !>[X0: $tType, X1: $tType]:(((X1 > X0) > set @ X1 > (X0 > $o) > X0))).
% 0.32/0.45 thf(func_def_89, type, sK21: !>[X0: $tType, X1: $tType]:(((X0 > set @ X1) > set @ X0 > (X1 > $o) > X1))).
% 0.32/0.45 thf(func_def_90, type, sK22: !>[X0: $tType, X1: $tType]:(((X0 > set @ X1) > set @ X0 > (X1 > $o) > X0))).
% 0.32/0.45 thf(func_def_91, type, sK23: !>[X0: $tType, X1: $tType]:(((X0 > set @ X1) > set @ X0 > (X1 > $o) > X1))).
% 0.32/0.45 thf(func_def_92, type, sK24: !>[X0: $tType]:(X0)).
% 0.32/0.45 thf(func_def_93, type, sK25: !>[X0: $tType, X1: $tType]:(((X1 > X0) > set @ X1 > X0 > X1))).
% 0.32/0.45 thf(func_def_94, type, sK26: !>[X0: $tType, X1: $tType]:((X0 > (X1 > X0) > X1))).
% 0.32/0.45 thf(func_def_95, type, sK27: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X0))).
% 0.32/0.45 thf(func_def_96, type, sK28: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X0 > set @ X1 > X1))).
% 0.32/0.45 thf(func_def_97, type, sK29: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > sigma_measure @ X0) > set @ X0 > X1))).
% 0.32/0.45 thf(func_def_98, type, sK30: !>[X0: $tType, X1: $tType]:((set @ X0 > (X1 > $o) > (X0 > set @ X1) > X0))).
% 0.32/0.45 thf(func_def_99, type, sK31: !>[X0: $tType, X1: $tType]:((set @ X0 > (X1 > $o) > (X0 > set @ X1) > X1))).
% 0.32/0.45 thf(func_def_100, type, sK32: !>[X0: $tType, X1: $tType]:((set @ X0 > (X1 > $o) > (X0 > set @ X1) > X1))).
% 0.32/0.45 thf(func_def_101, type, sK33: !>[X0: $tType, X1: $tType]:((set @ X0 > (X0 > X1) > (X0 > X1) > X0))).
% 0.32/0.45 thf(func_def_102, type, sK34: !>[X0: $tType, X1: $tType]:((sigma_measure @ X1 > (X0 > set @ X1) > X0))).
% 0.32/0.45 thf(func_def_103, type, sK35: !>[X0: $tType, X1: $tType]:(((X0 > sigma_measure @ X1) > set @ X0 > (X0 > sigma_measure @ X1) > X0))).
% 0.32/0.45 thf(func_def_104, type, sK36: !>[X0: $tType]:((set @ set @ X0 > X0 > set @ X0))).
% 0.32/0.45 thf(func_def_105, type, sK37: !>[X0: $tType]:((sigma_measure @ X0 > (nat > set @ X0) > nat))).
% 0.32/0.45 thf(func_def_106, type, sK38: !>[X0: $tType]:((sigma_measure @ X0 > (nat > set @ X0) > nat))).
% 0.32/0.45 thf(func_def_107, type, sK39: !>[X0: $tType]:((sigma_measure @ X0 > (nat > set @ X0) > nat))).
% 0.32/0.45 thf(func_def_108, type, sK40: !>[X0: $tType]:((set @ X0 > set @ sigma_measure @ X0 > sigma_measure @ X0))).
% 0.32/0.45 thf(func_def_109, type, sK41: !>[X0: $tType, X1: $tType]:(((X0 > set @ X1) > X1 > set @ X0 > X0))).
% 0.32/0.45 thf(func_def_110, type, sK42: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 0.32/0.45 thf(func_def_111, type, sK43: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > X1) > set @ X0 > X0))).
% 0.32/0.45 thf(func_def_112, type, sK44: !>[X0: $tType]:((X0 > set @ set @ X0 > set @ X0))).
% 0.32/0.45 thf(func_def_113, type, sK45: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X0 > X1) > X1))).
% 0.32/0.45 thf(func_def_114, type, sK46: !>[X0: $tType, X1: $tType]:(((X0 > set @ X1) > set @ X0 > (X1 > $o) > X1))).
% 0.32/0.45 thf(func_def_115, type, sK47: !>[X0: $tType, X1: $tType]:(((X0 > set @ X1) > set @ X0 > (X1 > $o) > X0))).
% 0.32/0.45 thf(func_def_116, type, sK48: !>[X0: $tType, X1: $tType]:(((X0 > set @ X1) > set @ X0 > (X1 > $o) > X1))).
% 0.32/0.45 thf(func_def_117, type, sK49: !>[X0: $tType, X1: $tType]:((X1 > set @ X0 > (X0 > X1) > X0))).
% 0.32/0.45 thf(func_def_118, type, sK50: !>[X0: $tType, X1: $tType]:((set @ X0 > (X0 > X1) > X1))).
% 0.32/0.45 thf(func_def_119, type, sK51: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X1 > X0))).
% 0.32/0.45 thf(func_def_120, type, sK52: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > set @ X1 > X1))).
% 0.32/0.45 thf(func_def_121, type, sK53: !>[X0: $tType]:((set @ set @ X0 > (X0 > $o) > X0))).
% 0.32/0.45 thf(func_def_122, type, sK54: !>[X0: $tType]:((set @ set @ X0 > (X0 > $o) > set @ X0))).
% 0.32/0.45 thf(func_def_123, type, sK55: !>[X0: $tType]:((set @ set @ X0 > (X0 > $o) > X0))).
% 0.32/0.45 thf(func_def_125, type, sK57: nat).
% 0.32/0.45 thf(f1,axiom,(
% 0.32/0.45 ! [X2 : finite_Cartesian_vec @ int @ n] : (((sigma_emeasure @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n) @ (t @ X2))) = ((sigma_emeasure @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n) @ (t2 @ X2))))),
% 0.32/0.45 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_emeasure__T_H)).
% 0.32/0.45 thf(f382,conjecture,(
% 0.32/0.45 ((^[X0 : nat] : ((sigma_emeasure @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n) @ (t2 @ (f @ X0))))) = (^[X0 : nat] : ((sigma_emeasure @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n) @ (t @ (f @ X0))))))),
% 0.32/0.45 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 0.32/0.45 thf(f383,negated_conjecture,(
% 0.32/0.45 ~ ((^[X0 : nat] : ((sigma_emeasure @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n) @ (t2 @ (f @ X0))))) = (^[X0 : nat] : ((sigma_emeasure @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n) @ (t @ (f @ X0))))))),
% 0.32/0.45 inference(negated_conjecture,[status(cth)],[f382])).
% 0.32/0.45 thf(f820,plain,(
% 0.32/0.45 ~ ((^[X0 : nat] : ((sigma_emeasure @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n) @ (t2 @ (f @ X0))))) = (^[X1 : nat] : ((sigma_emeasure @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n) @ (t @ (f @ X1))))))),
% 0.32/0.45 inference(rectify,[],[f383])).
% 0.32/0.45 thf(f821,plain,(
% 0.32/0.45 ~ ((^[Y0 : nat]: (sigma_emeasure @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n) @ (t2 @ (f @ Y0)))) = (^[Y0 : nat]: (sigma_emeasure @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n) @ (t @ (f @ Y0)))))),
% 0.32/0.45 inference(fool_elimination,[],[f820])).
% 0.32/0.45 thf(f1092,plain,(
% 0.32/0.45 ((^[Y0 : nat]: (sigma_emeasure @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n) @ (t2 @ (f @ Y0)))) != (^[Y0 : nat]: (sigma_emeasure @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n) @ (t @ (f @ Y0)))))),
% 0.32/0.45 inference(flattening,[],[f821])).
% 0.32/0.45 thf(f1102,plain,(
% 0.32/0.45 ! [X0 : finite_Cartesian_vec @ int @ n] : (((sigma_emeasure @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n) @ (t2 @ X0))) = ((sigma_emeasure @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n) @ (t @ X0))))),
% 0.32/0.45 inference(rectify,[],[f1])).
% 0.32/0.45 thf(f1758,plain,(
% 0.32/0.45 ((^[Y0 : nat]: (sigma_emeasure @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n) @ (t2 @ (f @ Y0)))) != (^[Y0 : nat]: (sigma_emeasure @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n) @ (t @ (f @ Y0)))))),
% 0.32/0.45 inference(cnf_transformation,[],[f1092])).
% 0.32/0.45 thf(f1893,plain,(
% 0.32/0.45 ( ! [X0 : finite_Cartesian_vec @ int @ n] : ((((sigma_emeasure @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n) @ (t2 @ X0))) = ((sigma_emeasure @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n) @ (t @ X0))))) )),
% 0.32/0.45 inference(cnf_transformation,[],[f1102])).
% 0.32/0.45 thf(f2647,definition,(
% 0.32/0.45 spl56_96 <=> ((^[Y0 : nat]: (sigma_emeasure @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n) @ (t2 @ (f @ Y0)))) = (^[Y0 : nat]: (sigma_emeasure @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n) @ (t @ (f @ Y0)))))),
% 0.32/0.45 introduced(definition,[new_symbols(definition,[spl56_96])],[avatar_definition])).
% 0.32/0.45 thf(f2649,plain,(
% 0.32/0.45 ((^[Y0 : nat]: (sigma_emeasure @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n) @ (t2 @ (f @ Y0)))) != (^[Y0 : nat]: (sigma_emeasure @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n) @ (t @ (f @ Y0))))) | spl56_96),
% 0.32/0.45 inference(avatar_component_clause,[],[f2647])).
% 0.32/0.45 thf(f2650,plain,(
% 0.32/0.45 ~spl56_96),
% 0.32/0.45 inference(avatar_split_clause,[],[f1758,f2647])).
% 0.32/0.45 thf(f2659,plain,(
% 0.32/0.45 ((((^[Y0 : nat]: (sigma_emeasure @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n) @ (t @ (f @ Y0)))) @ sK57)) != (((^[Y0 : nat]: (sigma_emeasure @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n) @ (t2 @ (f @ Y0)))) @ sK57))) | spl56_96),
% 0.32/0.45 inference(negative_extensionality,[],[f2649])).
% 0.32/0.45 thf(f2660,plain,(
% 0.32/0.45 (((sigma_emeasure @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n) @ (t2 @ (f @ sK57)))) != ((sigma_emeasure @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n) @ (t @ (f @ sK57))))) | spl56_96),
% 0.32/0.45 inference(beta-eta_normalization,[],[f2659])).
% 0.32/0.45 thf(f2662,definition,(
% 0.32/0.45 spl56_97 <=> (((sigma_emeasure @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n) @ (t2 @ (f @ sK57)))) = ((sigma_emeasure @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n) @ (t @ (f @ sK57)))))),
% 0.32/0.45 introduced(definition,[new_symbols(definition,[spl56_97])],[avatar_definition])).
% 0.32/0.45 thf(f2664,plain,(
% 0.32/0.45 (((sigma_emeasure @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n) @ (t2 @ (f @ sK57)))) != ((sigma_emeasure @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n) @ (t @ (f @ sK57))))) | spl56_97),
% 0.32/0.45 inference(avatar_component_clause,[],[f2662])).
% 0.32/0.45 thf(f2665,plain,(
% 0.32/0.45 ~spl56_97 | spl56_96),
% 0.32/0.45 inference(avatar_split_clause,[],[f2660,f2647,f2662])).
% 0.32/0.45 thf(f2705,plain,(
% 0.32/0.45 (((sigma_emeasure @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n) @ (t2 @ (f @ sK57)))) != ((sigma_emeasure @ finite_Cartesian_vec @ real @ n @ (complete_completion @ finite_Cartesian_vec @ real @ n @ lebesgue_lborel @ finite_Cartesian_vec @ real @ n) @ (t2 @ (f @ sK57))))) | spl56_97),
% 0.32/0.45 inference(superposition,[],[f2664,f1893])).
% 0.32/0.45 thf(f2706,plain,(
% 0.32/0.45 $false | spl56_97),
% 0.32/0.45 inference(trivial_inequality_removal,[],[f2705])).
% 0.32/0.45 thf(f2707,plain,(
% 0.32/0.45 spl56_97),
% 0.32/0.45 inference(avatar_contradiction_clause,[],[f2706])).
% 0.32/0.45 cnf(s96, plain, ~spl56_96, inference(sat_conversion,[],[f2650])).
% 0.32/0.45 cnf(s97, plain, spl56_96 | ~spl56_97, inference(sat_conversion,[],[f2665])).
% 0.32/0.45 cnf(s100, plain, spl56_97, inference(sat_conversion,[],[f2707])).
% 0.32/0.45 cnf(s101, plain, spl56_96, inference(rat,[],[s97,s100])).
% 0.32/0.45 cnf(s102, plain, $false, inference(rat,[],[s96,s101])).
% 0.32/0.45 thf(f2708,plain,(
% 0.32/0.45 $false),
% 0.32/0.45 inference(avatar_sat_refutation,[],[s102])).
% 0.32/0.45 % SZS output end Proof for theBenchmark
% 0.32/0.45 % (2130289)------------------------------
% 0.32/0.45 % (2130289)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.32/0.45 % (2130289)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.32/0.45 % (2130289)CaDiCaL version: 2.1.3
% 0.32/0.45 % (2130289)Termination reason: Refutation
% 0.32/0.45 % (2130289)Time elapsed: 0.070 s
% 0.32/0.45 % (2130289)Peak memory usage: 15 MB
% 0.32/0.45 % (2130289)Instructions burned: 139 (million)
% 0.32/0.45 % (2130281)Success in time 0.126 s
% 0.32/0.45 % Vampire exiting
%------------------------------------------------------------------------------