%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : DAT253^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 07:48:38 AM UTC 2026
% Result : Theorem 0.63s 0.40s
% Output : Refutation 0.63s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT253^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n020.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 18:16:19 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 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
% 0.63/0.40 % (1414808)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.63/0.40 % (1414814)lrs+10_16_si=on:nwc=1.5:random_seed=439866846:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.63/0.40 % (1414819)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.63/0.40 % (1414814)Instruction limit reached!
% 0.63/0.40 % (1414814)------------------------------
% 0.63/0.40 % (1414814)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.40 % (1414819)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
% 0.63/0.40 % (1414814)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.40 % (1414814)CaDiCaL version: 2.1.3
% 0.63/0.40 % (1414814)Termination reason: Instruction limit
% 0.63/0.40 % (1414814)Termination phase: Property scanning
% 0.63/0.40 % (1414814)Time elapsed: 0.005 s
% 0.63/0.40 % (1414814)Peak memory usage: 10 MB
% 0.63/0.40 % (1414814)Instructions burned: 19 (million)
% 0.63/0.40 % (1414813)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1828916423:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.63/0.40 % (1414815)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3006813340:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.63/0.40 % (1414818)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=710114105:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.63/0.40 % (1414817)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=384140774:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.63/0.40 % (1414816)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=2250102615: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)
% 0.63/0.40 % (1414819)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=3079306278:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.63/0.40 % (1414815)Instruction limit reached!
% 0.63/0.40 % (1414815)------------------------------
% 0.63/0.40 % (1414815)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.40 % (1414815)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.40 % (1414815)CaDiCaL version: 2.1.3
% 0.63/0.40 % (1414815)Termination reason: Instruction limit
% 0.63/0.40 % (1414815)Termination phase: shuffling
% 0.63/0.40 % (1414815)Time elapsed: 0.004 s
% 0.63/0.40 % (1414815)Peak memory usage: 10 MB
% 0.63/0.40 % (1414815)Instructions burned: 7 (million)
% 0.63/0.40 % (1414821)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1113362295:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.63/0.40 % (1414821)Instruction limit reached!
% 0.63/0.40 % (1414821)------------------------------
% 0.63/0.40 % (1414821)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.40 % (1414821)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.40 % (1414821)CaDiCaL version: 2.1.3
% 0.63/0.40 % (1414821)Termination reason: Instruction limit
% 0.63/0.40 % (1414821)Termination phase: shuffling
% 0.63/0.40 % (1414821)Time elapsed: 0.002 s
% 0.63/0.40 % (1414821)Peak memory usage: 10 MB
% 0.63/0.40 % (1414821)Instructions burned: 7 (million)
% 0.63/0.40 % (1414817)Instruction limit reached!
% 0.63/0.40 % (1414817)------------------------------
% 0.63/0.40 % (1414817)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.40 % (1414817)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.40 % (1414817)CaDiCaL version: 2.1.3
% 0.63/0.40 % (1414817)Termination reason: Instruction limit
% 0.63/0.40 % (1414817)Termination phase: Preprocessing 1
% 0.63/0.40 % (1414817)Time elapsed: 0.011 s
% 0.63/0.40 % (1414817)Peak memory usage: 10 MB
% 0.63/0.40 % (1414817)Instructions burned: 24 (million)
% 0.63/0.40 % (1414830)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.63/0.40 % (1414830)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3201956174:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.63/0.40 % (1414828)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3429694791:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.63/0.40 % (1414830)Instruction limit reached!
% 0.63/0.40 % (1414830)------------------------------
% 0.63/0.40 % (1414830)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.40 % (1414830)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.40 % (1414830)CaDiCaL version: 2.1.3
% 0.63/0.40 % (1414830)Termination reason: Instruction limit
% 0.63/0.40 % (1414830)Termination phase: shuffling
% 0.63/0.40 % (1414830)Time elapsed: 0.002 s
% 0.63/0.40 % (1414830)Peak memory usage: 10 MB
% 0.63/0.40 % (1414830)Instructions burned: 9 (million)
% 0.63/0.40 % (1414828)Instruction limit reached!
% 0.63/0.40 % (1414828)------------------------------
% 0.63/0.40 % (1414828)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.40 % (1414828)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.40 % (1414828)CaDiCaL version: 2.1.3
% 0.63/0.40 % (1414828)Termination reason: Instruction limit
% 0.63/0.40 % (1414828)Termination phase: shuffling
% 0.63/0.40 % (1414828)Time elapsed: 0.003 s
% 0.63/0.40 % (1414828)Peak memory usage: 10 MB
% 0.63/0.40 % (1414828)Instructions burned: 6 (million)
% 0.63/0.40 % (1414831)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=826308606:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.63/0.40 % (1414834)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
% 0.63/0.40 % (1414834)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.63/0.40 % (1414834)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3114633709:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.63/0.40 % (1414818)Instruction limit reached!
% 0.63/0.40 % (1414818)------------------------------
% 0.63/0.40 % (1414818)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.40 % (1414818)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.40 % (1414818)CaDiCaL version: 2.1.3
% 0.63/0.40 % (1414818)Termination reason: Instruction limit
% 0.63/0.40 % (1414818)Termination phase: Saturation
% 0.63/0.40 % (1414818)Time elapsed: 0.036 s
% 0.63/0.40 % (1414818)Peak memory usage: 13 MB
% 0.63/0.40 % (1414818)Instructions burned: 77 (million)
% 0.63/0.40 % (1414831)Instruction limit reached!
% 0.63/0.40 % (1414831)------------------------------
% 0.63/0.40 % (1414831)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.40 % (1414831)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.40 % (1414831)CaDiCaL version: 2.1.3
% 0.63/0.40 % (1414831)Termination reason: Instruction limit
% 0.63/0.40 % (1414831)Termination phase: shuffling
% 0.63/0.40 % (1414831)Time elapsed: 0.006 s
% 0.63/0.40 % (1414831)Peak memory usage: 10 MB
% 0.63/0.40 % (1414831)Instructions burned: 13 (million)
% 0.63/0.40 % (1414834)Instruction limit reached!
% 0.63/0.40 % (1414834)------------------------------
% 0.63/0.40 % (1414834)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.40 % (1414834)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.40 % (1414834)CaDiCaL version: 2.1.3
% 0.63/0.40 % (1414834)Termination reason: Instruction limit
% 0.63/0.40 % (1414834)Termination phase: Property scanning
% 0.63/0.40 % (1414834)Time elapsed: 0.007 s
% 0.63/0.40 % (1414834)Peak memory usage: 10 MB
% 0.63/0.40 % (1414834)Instructions burned: 30 (million)
% 0.63/0.40 % (1414840)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=3268721793:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.63/0.40 % (1414839)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.63/0.40 % (1414837)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=3441225811:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.63/0.40 % (1414838)lrs+10_1_si=on:cs=on:random_seed=777912522:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.63/0.40 % (1414839)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=3604604140:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.63/0.40 % (1414839)Instruction limit reached!
% 0.63/0.40 % (1414839)------------------------------
% 0.63/0.40 % (1414839)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.40 % (1414839)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.40 % (1414839)CaDiCaL version: 2.1.3
% 0.63/0.40 % (1414839)Termination reason: Instruction limit
% 0.63/0.40 % (1414839)Termination phase: shuffling
% 0.63/0.40 % (1414839)Time elapsed: 0.002 s
% 0.63/0.40 % (1414839)Peak memory usage: 10 MB
% 0.63/0.40 % (1414839)Instructions burned: 3 (million)
% 0.63/0.40 % (1414838)Instruction limit reached!
% 0.63/0.40 % (1414838)------------------------------
% 0.63/0.40 % (1414838)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.40 % (1414838)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.40 % (1414838)CaDiCaL version: 2.1.3
% 0.63/0.40 % (1414838)Termination reason: Instruction limit
% 0.63/0.40 % (1414838)Termination phase: shuffling
% 0.63/0.40 % (1414838)Time elapsed: 0.004 s
% 0.63/0.40 % (1414838)Peak memory usage: 10 MB
% 0.63/0.40 % (1414838)Instructions burned: 8 (million)
% 0.63/0.40 % (1414840)Instruction limit reached!
% 0.63/0.40 % (1414840)------------------------------
% 0.63/0.40 % (1414840)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.40 % (1414840)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.40 % (1414840)CaDiCaL version: 2.1.3
% 0.63/0.40 % (1414840)Termination reason: Instruction limit
% 0.63/0.40 % (1414840)Termination phase: Saturation
% 0.63/0.40 % (1414840)Time elapsed: 0.009 s
% 0.63/0.40 % (1414840)Peak memory usage: 12 MB
% 0.63/0.40 % (1414840)Instructions burned: 38 (million)
% 0.63/0.40 % (1414813)Instruction limit reached!
% 0.63/0.40 % (1414813)------------------------------
% 0.63/0.40 % (1414813)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.40 % (1414813)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.40 % (1414813)CaDiCaL version: 2.1.3
% 0.63/0.40 % (1414813)Termination reason: Instruction limit
% 0.63/0.40 % (1414813)Termination phase: Saturation
% 0.63/0.40 % (1414813)Time elapsed: 0.069 s
% 0.63/0.40 % (1414813)Peak memory usage: 13 MB
% 0.63/0.40 % (1414813)Instructions burned: 88 (million)
% 0.63/0.40 % (1414845)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=440236386:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 0.63/0.40 % (1414816) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1414808-1414816"...
% 0.63/0.40 % (1414846)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=3808302032:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 0.63/0.40 % (1414819)Instruction limit reached!
% 0.63/0.40 % (1414819)------------------------------
% 0.63/0.40 % (1414819)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.40 % (1414819)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.40 % (1414819)CaDiCaL version: 2.1.3
% 0.63/0.40 % (1414819)Termination reason: Instruction limit
% 0.63/0.40 % (1414819)Termination phase: Saturation
% 0.63/0.40 % (1414819)Time elapsed: 0.078 s
% 0.63/0.40 % (1414819)Peak memory usage: 13 MB
% 0.63/0.40 % (1414819)Instructions burned: 158 (million)
% 0.63/0.40 % (1414847)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=2551148771:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.63/0.40 % (1414848)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=2804268113:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 0.63/0.40 % (1414816)...printing done.
% 0.63/0.40 % (1414816)Refutation found. Thanks to Tanya!
% 0.63/0.40 % SZS status Theorem for theBenchmark
% 0.63/0.40 % SZS output start Proof for theBenchmark
% 0.63/0.40 thf(type_def_5, type, stream170649215stream: $tType > $tType).
% 0.63/0.40 thf(type_def_6, type, set: $tType > $tType).
% 0.63/0.40 thf(type_def_7, type, num: $tType).
% 0.63/0.40 thf(type_def_8, type, nat: $tType).
% 0.63/0.40 thf(type_def_9, type, itself: $tType > $tType).
% 0.63/0.40 thf(type_def_10, type, a: $tType).
% 0.63/0.40 thf(type_def_11, type, sTfun: ($tType * $tType) > $tType).
% 0.63/0.40 thf(func_def_0, type, bounded_lattice: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.63/0.40 thf(func_def_1, type, type: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.63/0.40 thf(func_def_2, type, one: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.63/0.40 thf(func_def_3, type, idom: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.63/0.40 thf(func_def_4, type, ring: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.63/0.40 thf(func_def_5, type, numeral: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.63/0.40 thf(func_def_6, type, ring_1: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.63/0.40 thf(func_def_7, type, uminus: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.63/0.40 thf(func_def_8, type, top: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.63/0.40 thf(func_def_9, type, semiring: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.63/0.40 thf(func_def_10, type, ring_char_0: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.63/0.40 thf(func_def_11, type, neg_numeral: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.63/0.40 thf(func_def_12, type, group_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.63/0.40 thf(func_def_13, type, lattice: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.63/0.40 thf(func_def_14, type, comm_ring_1: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.63/0.40 thf(func_def_15, type, monoid_mult: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.63/0.40 thf(func_def_16, type, ab_group_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.63/0.40 thf(func_def_17, type, semiring_char_0: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.63/0.40 thf(func_def_18, type, comm_semiring: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.63/0.40 thf(func_def_19, type, semigroup_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.63/0.40 thf(func_def_20, type, semiring_numeral: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.63/0.40 thf(func_def_21, type, semigroup_mult: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.63/0.40 thf(func_def_22, type, comm_semiring_1: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.63/0.40 thf(func_def_23, type, linordered_field: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.63/0.40 thf(func_def_24, type, ab_semigroup_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.63/0.40 thf(func_def_25, type, comm_monoid_mult: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.63/0.40 thf(func_def_26, type, ab_semigroup_mult: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.63/0.40 thf(func_def_27, type, boolean_algebra: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.63/0.40 thf(func_def_28, type, semilattice_sup: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.63/0.40 thf(func_def_29, type, cancel_semigroup_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.63/0.40 thf(func_def_30, type, bounded_lattice_top: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.63/0.40 thf(func_def_31, type, ring_11004092258visors: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.63/0.40 thf(func_def_32, type, ordere779506340up_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.63/0.40 thf(func_def_33, type, semiri456707255roduct: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.63/0.40 thf(func_def_34, type, one_one: !>[X0: $tType]:(X0)).
% 0.63/0.40 thf(func_def_35, type, plus_plus: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.63/0.40 thf(func_def_36, type, times_times: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.63/0.40 thf(func_def_37, type, uminus_uminus: !>[X0: $tType]:((X0 > X0))).
% 0.63/0.40 thf(func_def_38, type, sup_sup: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.63/0.40 thf(func_def_39, type, suc: (nat > nat)).
% 0.63/0.40 thf(func_def_40, type, inc: (num > num)).
% 0.63/0.40 thf(func_def_41, type, neg_numeral_dbl: !>[X0: $tType]:((X0 > X0))).
% 0.63/0.40 thf(func_def_42, type, bit0: (num > num)).
% 0.63/0.40 thf(func_def_43, type, one2: num).
% 0.63/0.40 thf(func_def_44, type, numeral_numeral: !>[X0: $tType]:((num > X0))).
% 0.63/0.40 thf(func_def_45, type, top_top: !>[X0: $tType]:(X0)).
% 0.63/0.40 thf(func_def_46, type, type2: !>[X0: $tType]:(itself @ X0)).
% 0.63/0.40 thf(func_def_47, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 0.63/0.40 thf(func_def_48, type, image: !>[X0: $tType, X1: $tType]:(((X0 > X1) > set @ X0 > set @ X1))).
% 0.63/0.40 thf(func_def_49, type, stream865922174rleave: !>[X0: $tType]:((stream170649215stream @ X0 > stream170649215stream @ X0 > stream170649215stream @ X0))).
% 0.63/0.40 thf(func_def_50, type, stream1586597341member: !>[X0: $tType]:((X0 > stream170649215stream @ X0 > $o))).
% 0.63/0.40 thf(func_def_51, type, stream857257621smerge: !>[X0: $tType]:((stream170649215stream @ stream170649215stream @ X0 > stream170649215stream @ X0))).
% 0.63/0.40 thf(func_def_52, type, stream370371455e_snth: !>[X0: $tType]:((stream170649215stream @ X0 > nat > X0))).
% 0.63/0.40 thf(func_def_53, type, stream30925839e_sset: !>[X0: $tType]:((stream170649215stream @ X0 > set @ X0))).
% 0.63/0.40 thf(func_def_54, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.63/0.40 thf(func_def_55, type, n: nat).
% 0.63/0.40 thf(func_def_56, type, s1: stream170649215stream @ a).
% 0.63/0.40 thf(func_def_57, type, s2: stream170649215stream @ a).
% 0.63/0.40 thf(func_def_58, type, x: a).
% 0.63/0.40 thf(func_def_62, type, db0: !>[X0: $tType]:(X0)).
% 0.63/0.40 thf(func_def_63, type, db1: !>[X0: $tType]:(X0)).
% 0.63/0.40 thf(func_def_64, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.63/0.40 thf(func_def_65, type, db2: !>[X0: $tType]:(X0)).
% 0.63/0.40 thf(func_def_66, type, sK0: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.63/0.40 thf(func_def_67, type, sK1: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > X1) > X0))).
% 0.63/0.40 thf(func_def_68, type, sK2: !>[X0: $tType, X1: $tType]:(((X1 > $o) > set @ X0 > (X0 > X1) > X0))).
% 0.63/0.40 thf(func_def_69, type, sK3: !>[X0: $tType, X1: $tType]:((X0 > (X1 > X0) > X1))).
% 0.63/0.40 thf(func_def_70, type, sK4: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X1 > X0) > X0))).
% 0.63/0.40 thf(func_def_71, type, sK5: !>[X0: $tType, X1: $tType]:((X1 > (X0 > X1) > X0))).
% 0.63/0.40 thf(func_def_72, type, sK6: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X1))).
% 0.63/0.40 thf(func_def_73, type, sK7: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X1 > X0))).
% 0.63/0.40 thf(func_def_74, type, sK8: !>[X0: $tType, X1: $tType]:((set @ X1 > (X0 > $o) > (X1 > X0) > X0))).
% 0.63/0.40 thf(func_def_75, type, sK9: !>[X0: $tType]:(X0)).
% 0.63/0.40 thf(func_def_76, type, sK10: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > (X1 > X0) > X1))).
% 0.63/0.40 thf(func_def_77, type, sK11: nat).
% 0.63/0.40 thf(func_def_78, type, sK12: !>[X0: $tType, X1: $tType]:((X1 > (X0 > X1) > set @ X0 > X0))).
% 0.63/0.40 thf(func_def_79, type, sK13: !>[X0: $tType]:((set @ X0 > (X0 > $o) > set @ X0 > X0))).
% 0.63/0.40 thf(func_def_80, type, sK14: !>[X0: $tType]:(((X0 > $o) > set @ X0 > X0))).
% 0.63/0.40 thf(func_def_81, type, sK15: !>[X0: $tType]:((set @ X0 > (X0 > $o) > X0))).
% 0.63/0.40 thf(func_def_82, type, sK16: !>[X0: $tType]:((set @ X0 > (X0 > $o) > X0))).
% 0.63/0.40 thf(func_def_83, type, sK17: !>[X0: $tType]:((set @ X0 > (X0 > $o) > X0))).
% 0.63/0.40 thf(func_def_84, type, sK18: !>[X0: $tType]:((set @ X0 > set @ X0 > (X0 > $o) > X0))).
% 0.63/0.40 thf(func_def_85, type, sK19: !>[X0: $tType]:((set @ X0 > X0))).
% 0.63/0.40 thf(func_def_86, type, vNOT: ($o > $o)).
% 0.63/0.40 thf(func_def_88, type, inv_uminus_uminus_21: !>[X0: $tType]:((X0 > X0))).
% 0.63/0.40 thf(func_def_89, type, inv_plus_plus_22: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.63/0.40 thf(func_def_90, type, inv_plus_plus_23: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.63/0.40 thf(f2,axiom,(
% 0.63/0.40 ~ ! [X0 : nat] : (x != ((stream370371455e_snth @ a @ s1 @ X0)))),
% 0.63/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062n_O_Ax_A_061_As1_A_B_B_An_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062)).
% 0.63/0.40 thf(f3,axiom,(
% 0.63/0.40 (((stream370371455e_snth @ a @ (stream865922174rleave @ a @ s1 @ s2) @ (times_times @ nat @ (numeral_numeral @ nat @ (bit0 @ one2)) @ n))) = x)),
% 0.63/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2__092_060open_062sinterleave_As1_As2_A_B_B_A_I2_A_K_An_J_A_061_Ax_092_060close_062)).
% 0.63/0.40 thf(f13,axiom,(
% 0.63/0.40 ! [X0 : $tType,X1 : $tType,X3 : X1,X2 : (X1 > X0)] : (member @ X0 @ (X2 @ X3) @ (image @ X1 @ X0 @ X2 @ top_top @ set @ X1))),
% 0.63/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_rangeI)).
% 0.63/0.40 thf(f291,conjecture,(
% 0.63/0.40 (member @ a @ x @ (image @ nat @ a @ (stream370371455e_snth @ a @ (stream865922174rleave @ a @ s1 @ s2)) @ top_top @ set @ nat))),
% 0.63/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 0.63/0.40 thf(f292,negated_conjecture,(
% 0.63/0.40 ~(member @ a @ x @ (image @ nat @ a @ (stream370371455e_snth @ a @ (stream865922174rleave @ a @ s1 @ s2)) @ top_top @ set @ nat))),
% 0.63/0.40 inference(negated_conjecture,[status(cth)],[f291])).
% 0.63/0.40 thf(f450,plain,(
% 0.63/0.40 ~(member @ a @ x @ (image @ nat @ a @ (stream370371455e_snth @ a @ (stream865922174rleave @ a @ s1 @ s2)) @ top_top @ set @ nat))),
% 0.63/0.40 inference(rectify,[],[f292])).
% 0.63/0.40 thf(f451,plain,(
% 0.63/0.40 ~ (((member @ a @ x @ (image @ nat @ a @ (stream370371455e_snth @ a @ (stream865922174rleave @ a @ s1 @ s2)) @ top_top @ set @ nat))) = $true)),
% 0.63/0.40 inference(fool_elimination,[],[f450])).
% 0.63/0.40 thf(f569,plain,(
% 0.63/0.40 ! [X0 : $tType,X1 : $tType,X2 : X1,X3 : (X1 > X0)] : (member @ X0 @ (X3 @ X2) @ (image @ X1 @ X0 @ X3 @ top_top @ set @ X1))),
% 0.63/0.40 inference(rectify,[],[f13])).
% 0.63/0.40 thf(f570,plain,(
% 0.63/0.40 ! [X1 : $tType,X0 : $tType,X2 : X1,X3 : (X1 > X0)] : (((member @ X0 @ (X3 @ X2) @ (image @ X1 @ X0 @ X3 @ top_top @ set @ X1))) = $true)),
% 0.63/0.40 inference(fool_elimination,[],[f569])).
% 0.63/0.40 thf(f769,plain,(
% 0.63/0.40 (((member @ a @ x @ (image @ nat @ a @ (stream370371455e_snth @ a @ (stream865922174rleave @ a @ s1 @ s2)) @ top_top @ set @ nat))) != $true)),
% 0.63/0.40 inference(flattening,[],[f451])).
% 0.63/0.40 thf(f845,plain,(
% 0.63/0.40 ? [X0 : nat] : (x = ((stream370371455e_snth @ a @ s1 @ X0)))),
% 0.63/0.40 inference(ennf_transformation,[],[f2])).
% 0.63/0.40 thf(f1016,plain,(
% 0.63/0.40 ! [X0 : $tType,X1 : $tType,X2 : X0,X3 : (X0 > X1)] : (((member @ X1 @ (X3 @ X2) @ (image @ X0 @ X1 @ X3 @ top_top @ set @ X0))) = $true)),
% 0.63/0.40 inference(rectify,[],[f570])).
% 0.63/0.40 thf(f1086,plain,(
% 0.63/0.40 (x = ((stream370371455e_snth @ a @ s1 @ sK11)))),
% 0.63/0.40 inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X0,sK11)],[f845])).
% 0.63/0.40 thf(f1223,plain,(
% 0.63/0.40 (x = ((stream370371455e_snth @ a @ (stream865922174rleave @ a @ s1 @ s2) @ (times_times @ nat @ (numeral_numeral @ nat @ (bit0 @ one2)) @ n))))),
% 0.63/0.40 inference(cnf_transformation,[],[f3])).
% 0.63/0.40 thf(f1231,plain,(
% 0.63/0.40 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : (X0 > X1)] : ((((member @ X1 @ (X3 @ X2) @ (image @ X0 @ X1 @ X3 @ top_top @ set @ X0))) = $true)) )),
% 0.63/0.40 inference(cnf_transformation,[],[f1016])).
% 0.63/0.40 thf(f1375,plain,(
% 0.63/0.40 (x = ((stream370371455e_snth @ a @ s1 @ sK11)))),
% 0.63/0.40 inference(cnf_transformation,[],[f1086])).
% 0.63/0.40 thf(f1376,plain,(
% 0.63/0.40 (((member @ a @ x @ (image @ nat @ a @ (stream370371455e_snth @ a @ (stream865922174rleave @ a @ s1 @ s2)) @ top_top @ set @ nat))) != $true)),
% 0.63/0.40 inference(cnf_transformation,[],[f769])).
% 0.63/0.40 thf(f1616,definition,(
% 0.63/0.40 spl20_12 <=> (x = ((stream370371455e_snth @ a @ (stream865922174rleave @ a @ s1 @ s2) @ (times_times @ nat @ (numeral_numeral @ nat @ (bit0 @ one2)) @ n))))),
% 0.63/0.40 introduced(definition,[new_symbols(definition,[spl20_12])],[avatar_definition])).
% 0.63/0.40 thf(f1618,plain,(
% 0.63/0.40 (x = ((stream370371455e_snth @ a @ (stream865922174rleave @ a @ s1 @ s2) @ (times_times @ nat @ (numeral_numeral @ nat @ (bit0 @ one2)) @ n)))) | ~spl20_12),
% 0.63/0.40 inference(avatar_component_clause,[],[f1616])).
% 0.63/0.40 thf(f1619,plain,(
% 0.63/0.40 spl20_12),
% 0.63/0.40 inference(avatar_split_clause,[],[f1223,f1616])).
% 0.63/0.40 thf(f1651,definition,(
% 0.63/0.40 spl20_19 <=> (x = ((stream370371455e_snth @ a @ s1 @ sK11)))),
% 0.63/0.40 introduced(definition,[new_symbols(definition,[spl20_19])],[avatar_definition])).
% 0.63/0.40 thf(f1653,plain,(
% 0.63/0.40 (x = ((stream370371455e_snth @ a @ s1 @ sK11))) | ~spl20_19),
% 0.63/0.40 inference(avatar_component_clause,[],[f1651])).
% 0.63/0.40 thf(f1654,plain,(
% 0.63/0.40 spl20_19),
% 0.63/0.40 inference(avatar_split_clause,[],[f1375,f1651])).
% 0.63/0.40 thf(f1716,definition,(
% 0.63/0.40 spl20_32 <=> (((member @ a @ x @ (image @ nat @ a @ (stream370371455e_snth @ a @ (stream865922174rleave @ a @ s1 @ s2)) @ top_top @ set @ nat))) = $true)),
% 0.63/0.40 introduced(definition,[new_symbols(definition,[spl20_32])],[avatar_definition])).
% 0.63/0.40 thf(f1718,plain,(
% 0.63/0.40 (((member @ a @ x @ (image @ nat @ a @ (stream370371455e_snth @ a @ (stream865922174rleave @ a @ s1 @ s2)) @ top_top @ set @ nat))) != $true) | spl20_32),
% 0.63/0.40 inference(avatar_component_clause,[],[f1716])).
% 0.63/0.40 thf(f1719,plain,(
% 0.63/0.40 ~spl20_32),
% 0.63/0.40 inference(avatar_split_clause,[],[f1376,f1716])).
% 0.63/0.40 thf(f1750,plain,(
% 0.63/0.40 (((member @ a @ (stream370371455e_snth @ a @ s1 @ sK11) @ (image @ nat @ a @ (stream370371455e_snth @ a @ (stream865922174rleave @ a @ s1 @ s2)) @ top_top @ set @ nat))) != $true) | (~spl20_19 | spl20_32)),
% 0.63/0.40 inference(superposition,[],[f1718,f1653])).
% 0.63/0.40 thf(f1752,definition,(
% 0.63/0.40 spl20_39 <=> (((member @ a @ (stream370371455e_snth @ a @ s1 @ sK11) @ (image @ nat @ a @ (stream370371455e_snth @ a @ (stream865922174rleave @ a @ s1 @ s2)) @ top_top @ set @ nat))) = $true)),
% 0.63/0.40 introduced(definition,[new_symbols(definition,[spl20_39])],[avatar_definition])).
% 0.63/0.40 thf(f1754,plain,(
% 0.63/0.40 (((member @ a @ (stream370371455e_snth @ a @ s1 @ sK11) @ (image @ nat @ a @ (stream370371455e_snth @ a @ (stream865922174rleave @ a @ s1 @ s2)) @ top_top @ set @ nat))) != $true) | spl20_39),
% 0.63/0.40 inference(avatar_component_clause,[],[f1752])).
% 0.63/0.40 thf(f1755,plain,(
% 0.63/0.40 ~spl20_39 | ~spl20_19 | spl20_32),
% 0.63/0.40 inference(avatar_split_clause,[],[f1750,f1716,f1651,f1752])).
% 0.63/0.40 thf(f2125,plain,(
% 0.63/0.40 (((stream370371455e_snth @ a @ (stream865922174rleave @ a @ s1 @ s2) @ (times_times @ nat @ (numeral_numeral @ nat @ (bit0 @ one2)) @ n))) = ((stream370371455e_snth @ a @ s1 @ sK11))) | (~spl20_12 | ~spl20_19)),
% 0.63/0.40 inference(forward_demodulation,[],[f1618,f1653])).
% 0.63/0.40 thf(f2127,definition,(
% 0.63/0.40 spl20_45 <=> (((stream370371455e_snth @ a @ (stream865922174rleave @ a @ s1 @ s2) @ (times_times @ nat @ (numeral_numeral @ nat @ (bit0 @ one2)) @ n))) = ((stream370371455e_snth @ a @ s1 @ sK11)))),
% 0.63/0.40 introduced(definition,[new_symbols(definition,[spl20_45])],[avatar_definition])).
% 0.63/0.40 thf(f2129,plain,(
% 0.63/0.40 (((stream370371455e_snth @ a @ (stream865922174rleave @ a @ s1 @ s2) @ (times_times @ nat @ (numeral_numeral @ nat @ (bit0 @ one2)) @ n))) = ((stream370371455e_snth @ a @ s1 @ sK11))) | ~spl20_45),
% 0.63/0.40 inference(avatar_component_clause,[],[f2127])).
% 0.63/0.40 thf(f2130,plain,(
% 0.63/0.40 spl20_45 | ~spl20_12 | ~spl20_19),
% 0.63/0.40 inference(avatar_split_clause,[],[f2125,f1651,f1616,f2127])).
% 0.63/0.40 thf(f2220,plain,(
% 0.63/0.40 (((member @ a @ (stream370371455e_snth @ a @ s1 @ sK11) @ (image @ nat @ a @ (stream370371455e_snth @ a @ (stream865922174rleave @ a @ s1 @ s2)) @ top_top @ set @ nat))) = $true) | ~spl20_45),
% 0.63/0.40 inference(superposition,[],[f1231,f2129])).
% 0.63/0.40 thf(f2221,plain,(
% 0.63/0.40 $false | (spl20_39 | ~spl20_45)),
% 0.63/0.40 inference(forward_subsumption_resolution,[],[f2220,f1754])).
% 0.63/0.40 thf(f2222,plain,(
% 0.63/0.40 spl20_39 | ~spl20_45),
% 0.63/0.40 inference(avatar_contradiction_clause,[],[f2221])).
% 0.63/0.40 cnf(s12, plain, spl20_12, inference(sat_conversion,[],[f1619])).
% 0.63/0.40 cnf(s19, plain, spl20_19, inference(sat_conversion,[],[f1654])).
% 0.63/0.40 cnf(s33, plain, ~spl20_32, inference(sat_conversion,[],[f1719])).
% 0.63/0.40 cnf(s40, plain, ~spl20_19 | spl20_32 | ~spl20_39, inference(sat_conversion,[],[f1755])).
% 0.63/0.40 cnf(s52, plain, ~spl20_12 | ~spl20_19 | spl20_45, inference(sat_conversion,[],[f2130])).
% 0.63/0.40 cnf(s58, plain, spl20_39 | ~spl20_45, inference(sat_conversion,[],[f2222])).
% 0.63/0.40 cnf(s65, plain, ~spl20_39, inference(rat,[],[s40,s33,s19])).
% 0.63/0.40 cnf(s67, plain, ~spl20_45, inference(rat,[],[s58,s65])).
% 0.63/0.40 cnf(s68, plain, ~spl20_12, inference(rat,[],[s52,s19,s67])).
% 0.63/0.40 cnf(s69, plain, $false, inference(rat,[],[s12,s68])).
% 0.63/0.40 thf(f2228,plain,(
% 0.63/0.40 $false),
% 0.63/0.40 inference(avatar_sat_refutation,[],[s69])).
% 0.63/0.40 % SZS output end Proof for theBenchmark
% 0.63/0.40 % (1414816)------------------------------
% 0.63/0.40 % (1414816)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.40 % (1414816)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.40 % (1414816)CaDiCaL version: 2.1.3
% 0.63/0.40 % (1414816)Termination reason: Refutation
% 0.63/0.40 % (1414816)Time elapsed: 0.079 s
% 0.63/0.40 % (1414816)Peak memory usage: 14 MB
% 0.63/0.40 % (1414816)Instructions burned: 150 (million)
% 0.63/0.40 % (1414808)Success in time 0.126 s
% 0.63/0.40 % Vampire exiting
%------------------------------------------------------------------------------