%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP090^2 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : 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 08:08:18 AM UTC 2026
% Result : Theorem 0.32s 0.46s
% Output : Refutation 0.32s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP090^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.19 % Computer : n020.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Sep 29 19:52:56 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 Running higher-order theorem proving
% 0.23/0.29 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.32/0.45 % (1508478)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.32/0.45 % (1508484)lrs+10_16_si=on:nwc=1.5:random_seed=35096830:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.32/0.45 % (1508484)Instruction limit reached!
% 0.32/0.45 % (1508484)------------------------------
% 0.32/0.45 % (1508484)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.32/0.45 % (1508484)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.32/0.45 % (1508484)CaDiCaL version: 2.1.3
% 0.32/0.45 % (1508484)Termination reason: Instruction limit
% 0.32/0.45 % (1508484)Termination phase: shuffling
% 0.32/0.45 % (1508484)Time elapsed: 0.007 s
% 0.32/0.45 % (1508484)Peak memory usage: 10 MB
% 0.32/0.45 % (1508484)Instructions burned: 20 (million)
% 0.32/0.45 % (1508483)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1272843393:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.32/0.45 % (1508485)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2591864961:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.32/0.45 % (1508487)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2593609358:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.32/0.45 % (1508485)Instruction limit reached!
% 0.32/0.45 % (1508485)------------------------------
% 0.32/0.45 % (1508485)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.32/0.45 % (1508485)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.32/0.45 % (1508485)CaDiCaL version: 2.1.3
% 0.32/0.45 % (1508485)Termination reason: Instruction limit
% 0.32/0.45 % (1508485)Termination phase: shuffling
% 0.32/0.45 % (1508485)Time elapsed: 0.003 s
% 0.32/0.45 % (1508485)Peak memory usage: 10 MB
% 0.32/0.45 % (1508485)Instructions burned: 4 (million)
% 0.32/0.45 % (1508486)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=2120585677: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 % (1508489)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 % (1508489)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 % (1508489)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=3237047902:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.32/0.45 % (1508487)Instruction limit reached!
% 0.32/0.45 % (1508487)------------------------------
% 0.32/0.45 % (1508487)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.32/0.45 % (1508487)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.32/0.45 % (1508487)CaDiCaL version: 2.1.3
% 0.32/0.45 % (1508487)Termination reason: Instruction limit
% 0.32/0.45 % (1508487)Termination phase: shuffling
% 0.32/0.45 % (1508487)Time elapsed: 0.012 s
% 0.32/0.45 % (1508487)Peak memory usage: 10 MB
% 0.32/0.45 % (1508487)Instructions burned: 25 (million)
% 0.32/0.45 % (1508494)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2616722959:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.32/0.45 % (1508494)Instruction limit reached!
% 0.32/0.45 % (1508494)------------------------------
% 0.32/0.45 % (1508494)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.32/0.45 % (1508494)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.32/0.45 % (1508494)CaDiCaL version: 2.1.3
% 0.32/0.45 % (1508494)Termination reason: Instruction limit
% 0.32/0.45 % (1508494)Termination phase: shuffling
% 0.32/0.45 % (1508494)Time elapsed: 0.002 s
% 0.32/0.45 % (1508494)Peak memory usage: 10 MB
% 0.32/0.45 % (1508494)Instructions burned: 4 (million)
% 0.32/0.45 % (1508488)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2990241248:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.32/0.45 % (1508496)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=445818400:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.32/0.46 % (1508499)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.32/0.46 % (1508496)Instruction limit reached!
% 0.32/0.46 % (1508496)------------------------------
% 0.32/0.46 % (1508496)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.32/0.46 % (1508496)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.32/0.46 % (1508496)CaDiCaL version: 2.1.3
% 0.32/0.46 % (1508496)Termination reason: Instruction limit
% 0.32/0.46 % (1508496)Termination phase: shuffling
% 0.32/0.46 % (1508496)Time elapsed: 0.003 s
% 0.32/0.46 % (1508496)Peak memory usage: 10 MB
% 0.32/0.46 % (1508496)Instructions burned: 5 (million)
% 0.32/0.46 % (1508499)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2501852698:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.32/0.46 % (1508500)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=763082968:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.32/0.46 % (1508499)Instruction limit reached!
% 0.32/0.46 % (1508499)------------------------------
% 0.32/0.46 % (1508499)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.32/0.46 % (1508499)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.32/0.46 % (1508499)CaDiCaL version: 2.1.3
% 0.32/0.46 % (1508499)Termination reason: Instruction limit
% 0.32/0.46 % (1508499)Termination phase: shuffling
% 0.32/0.46 % (1508499)Time elapsed: 0.004 s
% 0.32/0.46 % (1508499)Peak memory usage: 10 MB
% 0.32/0.46 % (1508499)Instructions burned: 8 (million)
% 0.32/0.46 % (1508500)Instruction limit reached!
% 0.32/0.46 % (1508500)------------------------------
% 0.32/0.46 % (1508500)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.32/0.46 % (1508500)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.32/0.46 % (1508500)CaDiCaL version: 2.1.3
% 0.32/0.46 % (1508500)Termination reason: Instruction limit
% 0.32/0.46 % (1508500)Termination phase: shuffling
% 0.32/0.46 % (1508500)Time elapsed: 0.006 s
% 0.32/0.46 % (1508500)Peak memory usage: 10 MB
% 0.32/0.46 % (1508500)Instructions burned: 13 (million)
% 0.32/0.46 % (1508483)Instruction limit reached!
% 0.32/0.46 % (1508483)------------------------------
% 0.32/0.46 % (1508483)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.32/0.46 % (1508483)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.32/0.46 % (1508483)CaDiCaL version: 2.1.3
% 0.32/0.46 % (1508483)Termination reason: Instruction limit
% 0.32/0.46 % (1508483)Termination phase: Property scanning
% 0.32/0.46 % (1508483)Time elapsed: 0.040 s
% 0.32/0.46 % (1508483)Peak memory usage: 12 MB
% 0.32/0.46 % (1508483)Instructions burned: 88 (million)
% 0.32/0.46 % (1508503)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
% 0.32/0.46 % (1508503)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.32/0.46 % (1508503)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2539778909:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.32/0.46 % (1508506)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=3082993135:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.32/0.46 % (1508508)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.32/0.46 % (1508507)lrs+10_1_si=on:cs=on:random_seed=3443186509:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.32/0.46 % (1508508)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=1363940763:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.32/0.46 % (1508503)Instruction limit reached!
% 0.32/0.46 % (1508503)------------------------------
% 0.32/0.46 % (1508503)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.32/0.46 % (1508503)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.32/0.46 % (1508503)CaDiCaL version: 2.1.3
% 0.32/0.46 % (1508503)Termination reason: Instruction limit
% 0.32/0.46 % (1508503)Termination phase: shuffling
% 0.32/0.46 % (1508503)Time elapsed: 0.012 s
% 0.32/0.46 % (1508503)Peak memory usage: 10 MB
% 0.32/0.46 % (1508503)Instructions burned: 28 (million)
% 0.32/0.46 % (1508508)Instruction limit reached!
% 0.32/0.46 % (1508508)------------------------------
% 0.32/0.46 % (1508508)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.32/0.46 % (1508508)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.32/0.46 % (1508508)CaDiCaL version: 2.1.3
% 0.32/0.46 % (1508508)Termination reason: Instruction limit
% 0.32/0.46 % (1508508)Termination phase: shuffling
% 0.32/0.46 % (1508508)Time elapsed: 0.002 s
% 0.32/0.46 % (1508508)Peak memory usage: 10 MB
% 0.32/0.46 % (1508508)Instructions burned: 3 (million)
% 0.32/0.46 % (1508507)Instruction limit reached!
% 0.32/0.46 % (1508507)------------------------------
% 0.32/0.46 % (1508507)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.32/0.46 % (1508507)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.32/0.46 % (1508507)CaDiCaL version: 2.1.3
% 0.32/0.46 % (1508507)Termination reason: Instruction limit
% 0.32/0.46 % (1508507)Termination phase: shuffling
% 0.32/0.46 % (1508507)Time elapsed: 0.004 s
% 0.32/0.46 % (1508507)Peak memory usage: 10 MB
% 0.32/0.46 % (1508507)Instructions burned: 8 (million)
% 0.32/0.46 % (1508489)Instruction limit reached!
% 0.32/0.46 % (1508489)------------------------------
% 0.32/0.46 % (1508489)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.32/0.46 % (1508489)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.32/0.46 % (1508489)CaDiCaL version: 2.1.3
% 0.32/0.46 % (1508489)Termination reason: Instruction limit
% 0.32/0.46 % (1508489)Termination phase: Saturation
% 0.32/0.46 % (1508489)Time elapsed: 0.069 s
% 0.32/0.46 % (1508489)Peak memory usage: 13 MB
% 0.32/0.46 % (1508489)Instructions burned: 158 (million)
% 0.32/0.46 % (1508513)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=1836366792:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 0.32/0.46 % (1508514)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=3409739103:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 0.32/0.46 % (1508488)Instruction limit reached!
% 0.32/0.46 % (1508488)------------------------------
% 0.32/0.46 % (1508488)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.32/0.46 % (1508488)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.32/0.46 % (1508488)CaDiCaL version: 2.1.3
% 0.32/0.46 % (1508488)Termination reason: Instruction limit
% 0.32/0.46 % (1508488)Termination phase: Property scanning
% 0.32/0.46 % (1508488)Time elapsed: 0.063 s
% 0.32/0.46 % (1508488)Peak memory usage: 12 MB
% 0.32/0.46 % (1508488)Instructions burned: 76 (million)
% 0.32/0.46 % (1508515)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=756002346:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 0.32/0.46 % (1508506)Instruction limit reached!
% 0.32/0.46 % (1508506)------------------------------
% 0.32/0.46 % (1508506)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.32/0.46 % (1508506)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.32/0.46 % (1508506)CaDiCaL version: 2.1.3
% 0.32/0.46 % (1508506)Termination reason: Instruction limit
% 0.32/0.46 % (1508506)Termination phase: Property scanning
% 0.32/0.46 % (1508506)Time elapsed: 0.037 s
% 0.32/0.46 % (1508506)Peak memory usage: 11 MB
% 0.32/0.46 % (1508506)Instructions burned: 87 (million)
% 0.32/0.46 % (1508513)Instruction limit reached!
% 0.32/0.46 % (1508513)------------------------------
% 0.32/0.46 % (1508513)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.32/0.46 % (1508513)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.32/0.46 % (1508513)CaDiCaL version: 2.1.3
% 0.32/0.46 % (1508513)Termination reason: Instruction limit
% 0.32/0.46 % (1508513)Termination phase: Property scanning
% 0.32/0.46 % (1508513)Time elapsed: 0.017 s
% 0.32/0.46 % (1508513)Peak memory usage: 10 MB
% 0.32/0.46 % (1508513)Instructions burned: 39 (million)
% 0.32/0.46 % (1508486) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1508478-1508486"...
% 0.32/0.46 % (1508486)...printing done.
% 0.32/0.46 % (1508486)Refutation found. Thanks to Tanya!
% 0.32/0.46 % SZS status Theorem for theBenchmark
% 0.32/0.46 % SZS output start Proof for theBenchmark
% 0.32/0.46 thf(type_def_5, type, secrecy_Expression: $tType).
% 0.32/0.46 thf(type_def_6, type, secrecy_Secrets: $tType).
% 0.32/0.46 thf(type_def_7, type, secrecy_specID: $tType).
% 0.32/0.46 thf(type_def_8, type, secrecy_chanID: $tType).
% 0.32/0.46 thf(type_def_9, type, secrecy_Keys: $tType).
% 0.32/0.46 thf(type_def_10, type, secrecy_KS: $tType).
% 0.32/0.46 thf(type_def_11, type, list: $tType > $tType).
% 0.32/0.46 thf(type_def_12, type, set: $tType > $tType).
% 0.32/0.46 thf(type_def_13, type, nat: $tType).
% 0.32/0.46 thf(type_def_14, type, sTfun: ($tType * $tType) > $tType).
% 0.32/0.46 thf(func_def_0, type, bounded_lattice: !>[X0: $tType]:($o)).
% 0.32/0.46 thf(func_def_1, type, type: !>[X0: $tType]:($o)).
% 0.32/0.46 thf(func_def_2, type, bot: !>[X0: $tType]:($o)).
% 0.32/0.46 thf(func_def_3, type, ord: !>[X0: $tType]:($o)).
% 0.32/0.46 thf(func_def_4, type, order: !>[X0: $tType]:($o)).
% 0.32/0.46 thf(func_def_5, type, linorder: !>[X0: $tType]:($o)).
% 0.32/0.46 thf(func_def_6, type, preorder: !>[X0: $tType]:($o)).
% 0.32/0.46 thf(func_def_7, type, bounde1808546759up_bot: !>[X0: $tType]:($o)).
% 0.32/0.46 thf(func_def_8, type, localSecrets: (secrecy_specID > set @ secrecy_KS)).
% 0.32/0.46 thf(func_def_9, type, knowle1667810483orrect: (secrecy_specID > secrecy_KS > $o)).
% 0.32/0.46 thf(func_def_10, type, knowle1437066798e_know: (secrecy_specID > secrecy_KS > $o)).
% 0.32/0.46 thf(func_def_11, type, knowle2055185861_knows: (secrecy_specID > list @ secrecy_Expression > $o)).
% 0.32/0.46 thf(func_def_12, type, sup_sup: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.32/0.46 thf(func_def_13, type, mem: !>[X0: $tType]:((X0 > list @ X0 > $o))).
% 0.32/0.46 thf(func_def_14, type, bot_bot: !>[X0: $tType]:(X0)).
% 0.32/0.46 thf(func_def_15, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.32/0.46 thf(func_def_16, type, decr: (secrecy_Keys > list @ secrecy_Expression > list @ secrecy_Expression)).
% 0.32/0.46 thf(func_def_17, type, enc: (secrecy_Keys > list @ secrecy_Expression > list @ secrecy_Expression)).
% 0.32/0.46 thf(func_def_18, type, encrDecrKeys: (secrecy_Keys > secrecy_Keys > $o)).
% 0.32/0.46 thf(func_def_19, type, ext: (secrecy_Keys > list @ secrecy_Expression > list @ secrecy_Expression)).
% 0.32/0.46 thf(func_def_20, type, sign: (secrecy_Keys > list @ secrecy_Expression > list @ secrecy_Expression)).
% 0.32/0.46 thf(func_def_21, type, correctCompositionKS: (secrecy_specID > $o)).
% 0.32/0.46 thf(func_def_22, type, eout: (secrecy_specID > secrecy_Expression > $o)).
% 0.32/0.46 thf(func_def_23, type, eoutM: (secrecy_specID > set @ secrecy_chanID > secrecy_Expression > $o)).
% 0.32/0.46 thf(func_def_24, type, exprChannel: (secrecy_chanID > secrecy_Expression > $o)).
% 0.32/0.46 thf(func_def_25, type, ine: (secrecy_specID > secrecy_Expression > $o)).
% 0.32/0.46 thf(func_def_26, type, ineM: (secrecy_specID > set @ secrecy_chanID > secrecy_Expression > $o)).
% 0.32/0.46 thf(func_def_27, type, ine_exprChannelSet: (secrecy_specID > set @ secrecy_chanID > secrecy_Expression > $o)).
% 0.32/0.46 thf(func_def_28, type, ine_ex1303305700Single: (secrecy_specID > secrecy_chanID > secrecy_Expression > $o)).
% 0.32/0.46 thf(func_def_29, type, notSpe1586871396tsExpr: (secrecy_specID > list @ secrecy_Expression > $o)).
% 0.32/0.46 thf(func_def_30, type, out_exprChannelSet: (secrecy_specID > set @ secrecy_chanID > secrecy_Expression > $o)).
% 0.32/0.46 thf(func_def_31, type, out_ex985543062Single: (secrecy_specID > secrecy_chanID > secrecy_Expression > $o)).
% 0.32/0.46 thf(func_def_32, type, specKeys: (secrecy_specID > set @ secrecy_Keys)).
% 0.32/0.46 thf(func_def_33, type, specKeysSecrets: (secrecy_specID > set @ secrecy_KS)).
% 0.32/0.46 thf(func_def_34, type, specSecrets: (secrecy_specID > set @ secrecy_Secrets)).
% 0.32/0.46 thf(func_def_35, type, secrecy_kE: (secrecy_Keys > secrecy_Expression)).
% 0.32/0.46 thf(func_def_36, type, secrecy_sE: (secrecy_Secrets > secrecy_Expression)).
% 0.32/0.46 thf(func_def_37, type, secrec1016742679ession: (secrecy_KS > secrecy_Expression)).
% 0.32/0.46 thf(func_def_38, type, secrecy_case_KS: !>[X0: $tType]:(((secrecy_Keys > X0) > (secrecy_Secrets > X0) > secrecy_KS > X0))).
% 0.32/0.46 thf(func_def_39, type, secrecy_kKS: (secrecy_Keys > secrecy_KS)).
% 0.32/0.46 thf(func_def_40, type, secrecy_rec_KS: !>[X0: $tType]:(((secrecy_Keys > X0) > (secrecy_Secrets > X0) > secrecy_KS > X0))).
% 0.32/0.46 thf(func_def_41, type, secrecy_sKS: (secrecy_Secrets > secrecy_KS)).
% 0.32/0.46 thf(func_def_42, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 0.32/0.46 thf(func_def_43, type, insert: !>[X0: $tType]:((X0 > set @ X0 > set @ X0))).
% 0.32/0.46 thf(func_def_44, type, is_empty: !>[X0: $tType]:((set @ X0 > $o))).
% 0.32/0.46 thf(func_def_45, type, is_singleton: !>[X0: $tType]:((set @ X0 > $o))).
% 0.32/0.46 thf(func_def_46, type, the_elem: !>[X0: $tType]:((set @ X0 > X0))).
% 0.32/0.46 thf(func_def_47, type, correctCompositionIn: (secrecy_specID > $o)).
% 0.32/0.46 thf(func_def_48, type, correc965049635ionLoc: (secrecy_specID > $o)).
% 0.32/0.46 thf(func_def_49, type, correc990227761ionOut: (secrecy_specID > $o)).
% 0.32/0.46 thf(func_def_50, type, inStream: (secrecy_specID > set @ secrecy_chanID > $o)).
% 0.32/0.46 thf(func_def_51, type, ins: (secrecy_specID > set @ secrecy_chanID)).
% 0.32/0.46 thf(func_def_52, type, loc: (secrecy_specID > set @ secrecy_chanID)).
% 0.32/0.46 thf(func_def_53, type, locStream: (secrecy_specID > set @ secrecy_chanID > $o)).
% 0.32/0.46 thf(func_def_54, type, out: (secrecy_specID > set @ secrecy_chanID)).
% 0.32/0.46 thf(func_def_55, type, outStream: (secrecy_specID > set @ secrecy_chanID > $o)).
% 0.32/0.46 thf(func_def_56, type, subcomponents: (secrecy_specID > set @ secrecy_specID)).
% 0.32/0.46 thf(func_def_57, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.32/0.46 thf(func_def_58, type, p: secrecy_specID).
% 0.32/0.46 thf(func_def_59, type, pq: secrecy_specID).
% 0.32/0.46 thf(func_def_60, type, q: secrecy_specID).
% 0.32/0.46 thf(func_def_61, type, key: secrecy_Keys).
% 0.32/0.46 thf(func_def_62, type, m: secrecy_KS).
% 0.32/0.46 thf(func_def_66, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.32/0.46 thf(func_def_67, type, db0: !>[X0: $tType]:(X0)).
% 0.32/0.46 thf(func_def_68, type, vAND: ($o > $o > $o)).
% 0.32/0.46 thf(func_def_69, type, db1: !>[X0: $tType]:(X0)).
% 0.32/0.46 thf(func_def_70, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.32/0.46 thf(func_def_71, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.32/0.46 thf(func_def_72, type, db2: !>[X0: $tType]:(X0)).
% 0.32/0.46 thf(func_def_73, type, db3: !>[X0: $tType]:(X0)).
% 0.32/0.46 thf(func_def_74, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.32/0.46 thf(func_def_75, type, vIMP: ($o > $o > $o)).
% 0.32/0.46 thf(func_def_76, type, vNOT: ($o > $o)).
% 0.32/0.46 thf(func_def_77, type, sP0: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.32/0.46 thf(func_def_78, type, sP1: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.32/0.46 thf(func_def_79, type, sK2: (secrecy_Secrets > secrecy_specID > secrecy_specID)).
% 0.32/0.46 thf(func_def_80, type, sK3: !>[X0: $tType]:((set @ X0 > X0 > set @ X0))).
% 0.32/0.46 thf(func_def_81, type, sK4: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 0.32/0.46 thf(func_def_82, type, sK5: !>[X0: $tType]:((set @ X0 > set @ X0 > (X0 > $o) > X0))).
% 0.32/0.46 thf(func_def_83, type, sK6: !>[X0: $tType]:((set @ X0 > (X0 > $o) > X0))).
% 0.32/0.46 thf(func_def_84, type, sK7: !>[X0: $tType]:((set @ X0 > (X0 > $o) > X0))).
% 0.32/0.46 thf(func_def_85, type, sK8: (secrecy_specID > secrecy_Secrets > secrecy_chanID)).
% 0.32/0.46 thf(func_def_86, type, sK9: (set @ secrecy_chanID > secrecy_specID > secrecy_chanID)).
% 0.32/0.46 thf(func_def_87, type, sK10: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.32/0.46 thf(func_def_88, type, sK11: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.32/0.46 thf(func_def_89, type, sK12: !>[X0: $tType]:((X0 > X0 > set @ X0 > set @ X0 > set @ X0))).
% 0.32/0.46 thf(func_def_90, type, sK13: (secrecy_specID > set @ secrecy_chanID > secrecy_chanID)).
% 0.32/0.46 thf(func_def_91, type, sK14: (set @ secrecy_chanID > secrecy_specID > secrecy_chanID)).
% 0.32/0.46 thf(func_def_92, type, sK15: (secrecy_specID > secrecy_KS > secrecy_specID > secrecy_Keys)).
% 0.32/0.46 thf(func_def_93, type, sK16: (secrecy_specID > secrecy_KS > secrecy_specID > secrecy_Secrets)).
% 0.32/0.46 thf(func_def_94, type, sK17: ((secrecy_KS > $o) > secrecy_Keys)).
% 0.32/0.46 thf(func_def_95, type, sK18: ((secrecy_KS > $o) > secrecy_Secrets)).
% 0.32/0.46 thf(func_def_96, type, sK19: (secrecy_specID > set @ secrecy_chanID > secrecy_chanID)).
% 0.32/0.46 thf(func_def_97, type, sK20: (secrecy_Keys > secrecy_specID > secrecy_chanID)).
% 0.32/0.46 thf(func_def_98, type, sK21: !>[X0: $tType]:((set @ X0 > X0))).
% 0.32/0.46 thf(func_def_99, type, sK22: (set @ secrecy_chanID > secrecy_specID > secrecy_chanID)).
% 0.32/0.46 thf(func_def_100, type, sK23: (set @ secrecy_chanID > secrecy_specID > secrecy_chanID)).
% 0.32/0.46 thf(func_def_101, type, sK24: !>[X0: $tType]:((set @ X0 > set @ X0 > set @ X0 > set @ X0))).
% 0.32/0.46 thf(func_def_102, type, sK25: !>[X0: $tType]:((set @ X0 > set @ X0 > set @ X0 > set @ X0))).
% 0.32/0.46 thf(func_def_103, type, sK26: !>[X0: $tType]:((set @ X0 > X0 > set @ X0))).
% 0.32/0.46 thf(func_def_104, type, sK27: (secrecy_specID > set @ secrecy_chanID > secrecy_chanID)).
% 0.32/0.46 thf(func_def_105, type, sK28: (secrecy_specID > set @ secrecy_chanID > secrecy_chanID)).
% 0.32/0.46 thf(func_def_106, type, sK29: !>[X0: $tType]:((set @ X0 > X0))).
% 0.32/0.46 thf(func_def_107, type, sK30: (set @ secrecy_chanID > secrecy_specID > secrecy_chanID)).
% 0.32/0.46 thf(func_def_108, type, sK31: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.32/0.46 thf(func_def_109, type, sK32: (secrecy_specID > secrecy_Expression > secrecy_chanID)).
% 0.32/0.46 thf(func_def_110, type, sK33: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.32/0.46 thf(func_def_111, type, sK34: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.32/0.46 thf(func_def_112, type, sK35: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.32/0.46 thf(func_def_113, type, sK36: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.32/0.46 thf(func_def_114, type, sK37: (secrecy_specID > secrecy_Keys > secrecy_chanID)).
% 0.32/0.46 thf(func_def_115, type, sK38: !>[X0: $tType]:((set @ X0 > X0))).
% 0.32/0.46 thf(func_def_116, type, sK39: (secrecy_KS > secrecy_specID > secrecy_specID > secrecy_Secrets)).
% 0.32/0.46 thf(func_def_117, type, sK40: (secrecy_KS > secrecy_specID > secrecy_specID > secrecy_Keys)).
% 0.32/0.46 thf(func_def_118, type, sK41: (secrecy_Keys > secrecy_specID > secrecy_specID)).
% 0.32/0.46 thf(func_def_119, type, sK42: (secrecy_specID > secrecy_Secrets > secrecy_chanID)).
% 0.32/0.46 thf(func_def_120, type, sK43: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.32/0.46 thf(func_def_121, type, sK44: (secrecy_KS > secrecy_Secrets)).
% 0.32/0.46 thf(func_def_122, type, sK45: (secrecy_KS > secrecy_Keys)).
% 0.32/0.46 thf(func_def_123, type, sK46: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.32/0.46 thf(func_def_124, type, sK47: !>[X0: $tType]:((set @ X0 > X0))).
% 0.32/0.46 thf(func_def_125, type, sK48: !>[X0: $tType]:((set @ X0 > X0))).
% 0.32/0.46 thf(func_def_126, type, sK49: (set @ secrecy_chanID > secrecy_specID > secrecy_chanID)).
% 0.32/0.46 thf(func_def_127, type, sK50: (set @ secrecy_chanID > secrecy_specID > secrecy_chanID)).
% 0.32/0.46 thf(func_def_128, type, sK51: !>[X0: $tType]:((set @ X0 > (X0 > $o) > set @ X0 > X0))).
% 0.32/0.46 thf(func_def_129, type, sK52: !>[X0: $tType]:((set @ X0 > (X0 > $o) > X0))).
% 0.32/0.46 thf(func_def_130, type, sK53: !>[X0: $tType]:(((X0 > $o) > set @ X0 > X0))).
% 0.32/0.46 thf(func_def_131, type, sK54: !>[X0: $tType]:((set @ X0 > X0))).
% 0.32/0.46 thf(func_def_132, type, sK55: (set @ secrecy_chanID > secrecy_specID > secrecy_chanID)).
% 0.32/0.46 thf(func_def_133, type, sK56: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.32/0.46 thf(func_def_135, type, inv_secrecy_kKS_58: (secrecy_KS > secrecy_Keys)).
% 0.32/0.46 thf(f1,axiom,(
% 0.32/0.46 ~(knowle1437066798e_know @ q @ m)),
% 0.32/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_not__knowQm)).
% 0.32/0.46 thf(f2,axiom,(
% 0.32/0.46 (m = ((secrecy_kKS @ key)))),
% 0.32/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_a1)).
% 0.32/0.46 thf(f11,axiom,(
% 0.32/0.46 ! [X1 : secrecy_Keys,X0 : secrecy_specID] : ((ine @ X0 @ (secrecy_kE @ X1)) | (member @ secrecy_KS @ (secrecy_kKS @ X1) @ (localSecrets @ X0)) = ((knowle1437066798e_know @ X0 @ (secrecy_kKS @ X1))))),
% 0.32/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_know_Osimps_I1_J)).
% 0.32/0.46 thf(f281,conjecture,(
% 0.32/0.46 ~(member @ secrecy_KS @ (secrecy_kKS @ key) @ (localSecrets @ q))),
% 0.32/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 0.32/0.46 thf(f282,negated_conjecture,(
% 0.32/0.46 ~ ~(member @ secrecy_KS @ (secrecy_kKS @ key) @ (localSecrets @ q))),
% 0.32/0.46 inference(negated_conjecture,[status(cth)],[f281])).
% 0.32/0.46 thf(f326,plain,(
% 0.32/0.46 ! [X0 : secrecy_Keys,X1 : secrecy_specID] : ((ine @ X1 @ (secrecy_kE @ X0)) | (member @ secrecy_KS @ (secrecy_kKS @ X0) @ (localSecrets @ X1)) = ((knowle1437066798e_know @ X1 @ (secrecy_kKS @ X0))))),
% 0.32/0.46 inference(rectify,[],[f11])).
% 0.32/0.46 thf(f327,plain,(
% 0.32/0.46 ! [X1 : secrecy_specID,X0 : secrecy_Keys] : (((((member @ secrecy_KS @ (secrecy_kKS @ X0) @ (localSecrets @ X1))) = $true) | (((ine @ X1 @ (secrecy_kE @ X0))) = $true)) <=> (((knowle1437066798e_know @ X1 @ (secrecy_kKS @ X0))) = $true))),
% 0.32/0.46 inference(fool_elimination,[],[f326])).
% 0.32/0.46 thf(f390,plain,(
% 0.32/0.46 ~(knowle1437066798e_know @ q @ m)),
% 0.32/0.46 inference(rectify,[],[f1])).
% 0.32/0.46 thf(f391,plain,(
% 0.32/0.46 ~ (((knowle1437066798e_know @ q @ m)) = $true)),
% 0.32/0.46 inference(fool_elimination,[],[f390])).
% 0.32/0.46 thf(f504,plain,(
% 0.32/0.46 ~ ~(member @ secrecy_KS @ (secrecy_kKS @ key) @ (localSecrets @ q))),
% 0.32/0.46 inference(rectify,[],[f282])).
% 0.32/0.46 thf(f505,plain,(
% 0.32/0.46 ~ ~ (((member @ secrecy_KS @ (secrecy_kKS @ key) @ (localSecrets @ q))) = $true)),
% 0.32/0.46 inference(fool_elimination,[],[f504])).
% 0.32/0.46 thf(f794,plain,(
% 0.32/0.46 (((knowle1437066798e_know @ q @ m)) != $true)),
% 0.32/0.46 inference(flattening,[],[f391])).
% 0.32/0.46 thf(f819,plain,(
% 0.32/0.46 (((member @ secrecy_KS @ (secrecy_kKS @ key) @ (localSecrets @ q))) = $true)),
% 0.32/0.46 inference(flattening,[],[f505])).
% 0.32/0.46 thf(f1384,plain,(
% 0.32/0.46 ! [X1 : secrecy_specID,X0 : secrecy_Keys] : ((((((member @ secrecy_KS @ (secrecy_kKS @ X0) @ (localSecrets @ X1))) = $true) | (((ine @ X1 @ (secrecy_kE @ X0))) = $true)) | (((knowle1437066798e_know @ X1 @ (secrecy_kKS @ X0))) != $true)) & ((((knowle1437066798e_know @ X1 @ (secrecy_kKS @ X0))) = $true) | ((((member @ secrecy_KS @ (secrecy_kKS @ X0) @ (localSecrets @ X1))) != $true) & (((ine @ X1 @ (secrecy_kE @ X0))) != $true))))),
% 0.32/0.46 inference(nnf_transformation,[],[f327])).
% 0.32/0.46 thf(f1385,plain,(
% 0.32/0.46 ! [X1 : secrecy_specID,X0 : secrecy_Keys] : (((((member @ secrecy_KS @ (secrecy_kKS @ X0) @ (localSecrets @ X1))) = $true) | (((ine @ X1 @ (secrecy_kE @ X0))) = $true) | (((knowle1437066798e_know @ X1 @ (secrecy_kKS @ X0))) != $true)) & ((((knowle1437066798e_know @ X1 @ (secrecy_kKS @ X0))) = $true) | ((((member @ secrecy_KS @ (secrecy_kKS @ X0) @ (localSecrets @ X1))) != $true) & (((ine @ X1 @ (secrecy_kE @ X0))) != $true))))),
% 0.32/0.46 inference(flattening,[],[f1384])).
% 0.32/0.46 thf(f1386,plain,(
% 0.32/0.46 ! [X0 : secrecy_specID,X1 : secrecy_Keys] : (((((member @ secrecy_KS @ (secrecy_kKS @ X1) @ (localSecrets @ X0))) = $true) | (((ine @ X0 @ (secrecy_kE @ X1))) = $true) | (((knowle1437066798e_know @ X0 @ (secrecy_kKS @ X1))) != $true)) & ((((knowle1437066798e_know @ X0 @ (secrecy_kKS @ X1))) = $true) | ((((member @ secrecy_KS @ (secrecy_kKS @ X1) @ (localSecrets @ X0))) != $true) & (((ine @ X0 @ (secrecy_kE @ X1))) != $true))))),
% 0.32/0.46 inference(rectify,[],[f1385])).
% 0.32/0.46 thf(f1624,plain,(
% 0.32/0.46 (((knowle1437066798e_know @ q @ m)) != $true)),
% 0.32/0.46 inference(cnf_transformation,[],[f794])).
% 0.32/0.46 thf(f1741,plain,(
% 0.32/0.46 (((member @ secrecy_KS @ (secrecy_kKS @ key) @ (localSecrets @ q))) = $true)),
% 0.32/0.46 inference(cnf_transformation,[],[f819])).
% 0.32/0.46 thf(f1807,plain,(
% 0.32/0.46 ( ! [X0 : secrecy_specID,X1 : secrecy_Keys] : ((((member @ secrecy_KS @ (secrecy_kKS @ X1) @ (localSecrets @ X0))) != $true) | (((knowle1437066798e_know @ X0 @ (secrecy_kKS @ X1))) = $true)) )),
% 0.32/0.46 inference(cnf_transformation,[],[f1386])).
% 0.32/0.46 thf(f1835,plain,(
% 0.32/0.46 (m = ((secrecy_kKS @ key)))),
% 0.32/0.46 inference(cnf_transformation,[],[f2])).
% 0.32/0.46 thf(f1983,definition,(
% 0.32/0.46 spl57_2 <=> (((knowle1437066798e_know @ q @ m)) = $true)),
% 0.32/0.46 introduced(definition,[new_symbols(definition,[spl57_2])],[avatar_definition])).
% 0.32/0.46 thf(f1985,plain,(
% 0.32/0.46 (((knowle1437066798e_know @ q @ m)) != $true) | spl57_2),
% 0.32/0.46 inference(avatar_component_clause,[],[f1983])).
% 0.32/0.46 thf(f1986,plain,(
% 0.32/0.46 ~spl57_2),
% 0.32/0.46 inference(avatar_split_clause,[],[f1624,f1983])).
% 0.32/0.46 thf(f2058,definition,(
% 0.32/0.46 spl57_17 <=> (m = ((secrecy_kKS @ key)))),
% 0.32/0.46 introduced(definition,[new_symbols(definition,[spl57_17])],[avatar_definition])).
% 0.32/0.46 thf(f2060,plain,(
% 0.32/0.46 (m = ((secrecy_kKS @ key))) | ~spl57_17),
% 0.32/0.46 inference(avatar_component_clause,[],[f2058])).
% 0.32/0.46 thf(f2061,plain,(
% 0.32/0.46 spl57_17),
% 0.32/0.46 inference(avatar_split_clause,[],[f1835,f2058])).
% 0.32/0.46 thf(f2133,definition,(
% 0.32/0.46 spl57_32 <=> (((member @ secrecy_KS @ (secrecy_kKS @ key) @ (localSecrets @ q))) = $true)),
% 0.32/0.46 introduced(definition,[new_symbols(definition,[spl57_32])],[avatar_definition])).
% 0.32/0.46 thf(f2135,plain,(
% 0.32/0.46 (((member @ secrecy_KS @ (secrecy_kKS @ key) @ (localSecrets @ q))) = $true) | ~spl57_32),
% 0.32/0.46 inference(avatar_component_clause,[],[f2133])).
% 0.32/0.46 thf(f2136,plain,(
% 0.32/0.46 spl57_32),
% 0.32/0.46 inference(avatar_split_clause,[],[f1741,f2133])).
% 0.32/0.46 thf(f2149,plain,(
% 0.32/0.46 (((knowle1437066798e_know @ q @ (secrecy_kKS @ key))) != $true) | (spl57_2 | ~spl57_17)),
% 0.32/0.46 inference(forward_demodulation,[],[f1985,f2060])).
% 0.32/0.46 thf(f2151,definition,(
% 0.32/0.46 spl57_35 <=> (((knowle1437066798e_know @ q @ (secrecy_kKS @ key))) = $true)),
% 0.32/0.46 introduced(definition,[new_symbols(definition,[spl57_35])],[avatar_definition])).
% 0.32/0.46 thf(f2154,plain,(
% 0.32/0.46 ~spl57_35 | spl57_2 | ~spl57_17),
% 0.32/0.46 inference(avatar_split_clause,[],[f2149,f2058,f1983,f2151])).
% 0.32/0.46 thf(f2155,plain,(
% 0.32/0.46 (((knowle1437066798e_know @ q @ (secrecy_kKS @ key))) = $true) | ($true != $true) | ~spl57_32),
% 0.32/0.46 inference(superposition,[],[f1807,f2135])).
% 0.32/0.46 thf(f2158,plain,(
% 0.32/0.46 (((knowle1437066798e_know @ q @ (secrecy_kKS @ key))) = $true) | ~spl57_32),
% 0.32/0.46 inference(trivial_inequality_removal,[],[f2155])).
% 0.32/0.46 thf(f2164,plain,(
% 0.32/0.46 spl57_35 | ~spl57_32),
% 0.32/0.46 inference(avatar_split_clause,[],[f2158,f2133,f2151])).
% 0.32/0.46 cnf(s2, plain, ~spl57_2, inference(sat_conversion,[],[f1986])).
% 0.32/0.46 cnf(s17, plain, spl57_17, inference(sat_conversion,[],[f2061])).
% 0.32/0.46 cnf(s32, plain, spl57_32, inference(sat_conversion,[],[f2136])).
% 0.32/0.46 cnf(s35, plain, spl57_2 | ~spl57_17 | ~spl57_35, inference(sat_conversion,[],[f2154])).
% 0.32/0.46 cnf(s37, plain, ~spl57_32 | spl57_35, inference(sat_conversion,[],[f2164])).
% 0.32/0.46 cnf(s38, plain, spl57_35, inference(rat,[],[s37,s32])).
% 0.32/0.46 cnf(s39, plain, spl57_2, inference(rat,[],[s35,s38,s17])).
% 0.32/0.46 cnf(s41, plain, $false, inference(rat,[],[s2,s39])).
% 0.32/0.46 thf(f2165,plain,(
% 0.32/0.46 $false),
% 0.32/0.46 inference(avatar_sat_refutation,[],[s41])).
% 0.32/0.46 % SZS output end Proof for theBenchmark
% 0.32/0.46 % (1508486)------------------------------
% 0.32/0.46 % (1508486)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.32/0.46 % (1508486)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.32/0.46 % (1508486)CaDiCaL version: 2.1.3
% 0.32/0.46 % (1508486)Termination reason: Refutation
% 0.32/0.46 % (1508486)Time elapsed: 0.097 s
% 0.32/0.46 % (1508486)Peak memory usage: 15 MB
% 0.32/0.46 % (1508486)Instructions burned: 176 (million)
% 0.32/0.46 % (1508478)Success in time 0.159 s
% 0.32/0.46 % Vampire exiting
%------------------------------------------------------------------------------